diff --git a/storage/6LLZ5HCC/.zotero-ft-cache b/storage/6LLZ5HCC/.zotero-ft-cache new file mode 100644 index 0000000..eb2b053 --- /dev/null +++ b/storage/6LLZ5HCC/.zotero-ft-cache @@ -0,0 +1,343 @@ +iii +Highest Velocities +Lowest Velocities +The Dynamic Ether +of Cosmic Space +Correcting a Major Error in Modern Science +James DeMeo, PhD + + + v +The Dynamic Ether +of Cosmic Space +Correcting a Major Error in Modern Science +by +James DeMeo +2019 Natural Energy Works Ashland, Oregon, USA +www.naturalenergyworks.net + + + viii +The Dynamic Ether of Cosmic Space +CONTENTS +Page Table of Figures ......................................................... x Table of Tables .......................................................... xii Acknowledgments ..................................................... xiii +Author’s Introduction ................................................ 1 +Part I: Cosmic Ether as Theory and Experimentally Confirmed Fact 23 +The Matter of Space, Light Waves and Motion ........ 25 Positive Results of Michelson-Morley ...................... 45 FitzGerald, Lorentz and Morley-Miller ..................... 57 Millers Positive Ether Experiments, 1921-1926 ....... 79 Which Way Drifting? Miller’s Mis-Step ................... 115 Sagnac and Michelson-Gale ...................................... 131 Michelson Returns to the Ether ................................. 141 Recent Confirmations of Ether ................................. 167 + + + ix +Page Part II: The Empire Strikes Back: Erasure, Mystification and Falsification of History 191 +Einstein Rising ......................................................... 193 The Shankland, et al. Hatchet Job on Miller ........... 213 +Part III: Into New Territory: Additional Evidence for a Material, Motional and Dynamic Ether 227 +Ether and Cosmic Life-Energy ................................ 229 Direct Evidence for the Dynamic Ether ................... 265 Implications and Consequences of Ether ................. 297 Conclusions .............................................................. 337 +Appendix 1. Model to View Earth-Ether Motions ... 347 Appendix 2. Newton’s Letter to Boyle 1687 ........... 349 References ................................................................ 361 Web References ...................................................... 375 Newspaper Clippings ............................................... 376 Glossary ................................................................... 378 Index ........................................................................ 381 About the Author ...................................................... 389 + + + x +The Dynamic Ether of Cosmic Space +Table of Figures Page 1. Newtonian Static Ether “Absolute Space” 11 2. A Static but Dragged Ether 12 3. Competing Theories of a Material Cosmic Ether 14 4. A Motional-Material Dynamic Ether 16 5. Earth’s Net Motion Through the Galaxy? 17 6. The Earth’s Spiral Path Through the Cosmos 18 7. Young’s Double-Slit Experiment 38 8. Fizeau & Foucault’s Experiments 43 9. The Michelson 1881 Interferometer 47 10. Michelson’s Two-Swimmer Analogy 48 11. Light Paths of the M-M 1887 Interferometer 51 12. The Michelson-Morley 1887 Interferometer 52 13. Miller’s Review of the Michelson-Morley Data 55 14. Morley-Miller Magnetic Experiment 62 15. The Morley-Miller Wood Interferometer 65 16. The Morley-Miller 64-meter Steel Interferometer 67 17. Morley-Miller 1905 Error in Computations 70 18. Miller’s 1933 Graph of Ether Drift Measures 75 19. Light Paths of Morley-Miller Steel Interferometer 83 20. Light-Interference Fringes 83 21. The Mt. Wilson Observatory 84 22. Miller's Ether Rocks Interferometer House, Mt. Wilson 85 23. Miller's Rebuilt Interferometer, 1921 Ether Rocks 86 24. Miller’s Concrete Interferometer, 1921 Ether Rocks 87 25. Miller’s Interferometer, 1922 Case School Physics Lab 90 26. Rockefeller Physics Building 91 27 Miller's Interferometer, Grass Knoll, 1924 Mt. Wilson 93 28. Miller's Interferometer House, 1924, Grass Knoll 94 29. Miller’s Calculations of Azimuth vs Velocity 95 30. Miller’s Preliminary Computation 97 31. A Typical Interferometer Data Sheet 102 32: Velocities and Azimuths of Ether-Drift 105 33: Shifting Global Ether-Drift Azimuths 106 34: Average Velocity and Azimuth of Ether Drift 107 35. Miller’s Determination for a Northerly Axis 111 36. Miller’s Interferometer Orientations 112 37. A Conventional View of Solar System Motions 126 38. Northern Orbital Plane Poles of the Planets and Sun 128 39. Sagnac’s Rotating Interferometer 132 + + + xi +40. Sagnac Interferometer & Optical Gyroscope 134 41. The Michelson-Gale Experiment 137 42. Variability in the Michelson-Gale Results 138 43. Dayton Miller and Albert Michelson 141 44. The Michelson-Pease-Pearson Invar Interferometer 143 45. Michelson-Pease-Pearson Mount Wilson Experiment 147 46. Concrete Base of the Mt. Wilson Observatory 148 47. Michelson-Pease-Pearson Experiment at Irvine Ranch 156 48. The Irvine Ranch Experiment 157 49. The Joos-Zeiss Interferometer 160 50. The Kennedy-Thorndike Experiment 163 51. Galaev’s Radiowave Antenna 169 52. Galaev’s Radiowave Experimental Diagram 169 53. Galaev’s Radiolink Interference Variations 170 54. Diagram of Galaev’s Optical Interferometer 172 55. Galaev’s Optical Interferometer 173 56. The Galaev Interferometer on a Rooftop 175 57. Galaev’s Ether-Wind Velocity Determinations 177 58. Galaev’s Sidereal Azimuth Determinations 178 59. Ether-Wind Velocity Versus Altitude 179 60. The Múnera Team’s Stationary Interferometer 181 61. The Múnera Interferometer, in Bogotá 182 62. Ether-Wind Velocity versus Altitude 186 63. Mercury’s Orbital Perihelion Advance 202 64. Eddington’s Eclipse Observations, Principe 204 65. The 1919 Eclipse Expeditions 205 66. Exaggerated Starlight Bending 206 67. The Solar Corona at Larger Distances 207 68. The Orgone Energy Accumulator 233 69. Orgone Accumulator Thermal Anomaly (To-T) 234 70. Biological Effects of the Orgone Accumulator 235 71. Kreiselwelle and Cosmic Superimposition 241 72. The Orgone Anti-Nuclear Radiation Effect 242 73. Planetary Motions and Gravitational Superimposition 245 74. The Kreiselwelle or Spinning Wave 246 75. Kepler Incongruent with Spiral Ether-Wind Velocities 248 76. Miller’s Ether-Drift and Reich’s Spiral Motions 250 77. The Earth’s Spiral Path Through the Cosmos 253 78. Polar Map of Cosmic Vectors, Update 1 254 79. Piccardi’s Helicoidal Earth-Orbit Diagram 259 + + + xii +The Dynamic Ether of Cosmic Space +Table of Tables Page 1. Summary of the Morley-Miller Experiments 72 2. Miller’s 1921 Results at Mount Wilson 88 3. Miller’s 4-Epoch Ether Drift Determinations 102 4. The Epoch-Average Daily Swing of Ether Wind 105 5. Miller’s 1928 versus 1933 Determinations 109 6. Miller’s 1931 Table on the Absolute Motion of the Earth 121 7. Miller’s Ether Velocity “k-Factor” 123 8. Velocities of Post-Miller Ether Drift Experiments 164 9. Summary of Successful Ether-Drift Experiments 187 10. Orbital Properties of the Planets and Solar Surface 203 11. Miller’s 4-Epoch Averages of Ether Wind Velocity 248 +80. Piccardi’s Animated Model of Helicoidal Motion 260 81. Sidereal-Hour Variations in Biological Clock 261 82. Seasonal Cosmic Variations in Biological Clocks 262 83. Kuiper Belt Planetoids & “Planet 9” 271 84. Direction of “Planet 9” Gravitational Anomaly 271 85. Andromeda Galaxy: Tilting of the Core Mass 273 86. Satellite Images of Earth’s Plasmasphere 275 87. UV-Glowing Charged Clouds of Interstellar Medium 278 88. The Super-Kamiokande Neutrino Detector 282 89. Galactic Rotation Anomaly for M33 284 90. Seasonal Variations in Dark Matter Wind 286 91. 17 Independent Vectors of Cosmic Motion 289 92. Spectroscopic Changes in ORAC-Charged Water 291 93. The Two LIGO Experiments 299 94. Massive Mirror Ends of the LIGO Light-Paths 301 95. One LIGO Event, 18 August 2017 303 96. Variation in Raw GPS Signal Data 308 97. Unit-Elements of Film Emulsions and CCDs 311 98. Low-Intensity Lightwaves through a Double Slit 311 99. Galaxies in Hubble Extreme Deep Field Image 316 100. Structure of Galaxy Distribution in the Universe 317 101. Close-up Center of the Milky Way Galaxy 325 102. The M87 “Black Hole” Image 328 103. Is This the Unprocessed M87 “Black Hole” Image? 328 104. Superluminal Motion in the M87 Jet 332 105. Vortex-Spiral Motion Yields Apparent Straight Lines 336 106. Apparent Straight Line Motion is Curved in Space 336 + + + xiv +The Dynamic Ether of Cosmic Space +“I believe that I have really found the relationship between gravitation and electricity, assuming that the Miller experiments are based on a fundamental error. Otherwise, the whole relativity theory collapses like a house of cards.” — Albert Einstein, letter to Robert Millikan June 1921 +“My opinion about Miller’s experiments is the following. ... Should the positive result be confirmed, then the special theory of relativity and with it the general theory of relativity, in its current form, would be invalid. Experimentum summus judex. Only the equivalence of inertia and gravitation would remain, however, they would have to lead to a significantly different theory.” — Albert Einstein, letter to Edwin Slosson, 8 July 1925, Hebrew Univ. Archive Jerusalem. +“The effect [of ether-drift] has persisted throughout. After considering all the possible sources of error, there always remained a positive effect.” — Dayton Miller, 1928, p.399 +“You imagine that I look back on my life’s work with calm satisfaction. But from nearby it looks quite different. There is not a single concept of which I am convinced that it will stand firm, and I feel uncertain whether I am in general on the right track.” — Albert Einstein, on his 70th birthday, letter to Maurice Solovine, 28 March 1949 + + + 1 +Author’s Introduction +Author’s Introduction +Intergalactic Medium! Interstellar Medium! Interstellar Wind! Neutrino Sea! Neutrino Wind! Dark Matter! Dark Matter Wind! Gravitational Waves! Higgs “God” Field! Cosmic Strings! Cosmic Ray Anisotropy! CMBR Anisotropy! Zero-Point Vacuum Fluctuation! Torsion Fields! Solitons! +Modern astrophysics and astronomy describe the cosmic space between the planets, stars and galaxies as an empty void, a hard vacuum lacking in inherent properties or substance. And yet, scientists working in these disciplines continue to discover “empty space” to be saturated with energy and particles, with turbulence and motion, as with the above concepts. Each is considered, by convention, to be a completely separate phenomenon from all the others, in spite of numerous points of similarities and agreement. Each term stands for its own presumed “soup” of discrete mystery particles. No matter how fantastically abundant, the space between them remains an empty void, save for scatterings of light and other electromagnetic waves. The scientists have identified all these specific “trees”, but deny the existence of any “forest”, whereby their basic nature could be more logically understood. As with the example of 10 blind men in a room with an elephant, each describes in exceedingly precise detail what they have individually grasped – the trunk, tusk, body, tail, legs – but the word “elephant” has become taboo. Like the proverbial naked emperor, nobody dares speak about a possible single ocean of cosmic energy, which offers a more unified and simpler understanding of all the diverse particles and “winds”. In a related manner, a casual look at images of deep space shows us billowing clouds of nebulae, of objects pushing through an unknown fluid and leaving behind a trail within a resisting transparent medium, all frozen in time. They appear more like something seen in the depths of the oceans or lakes. In some areas, a surrounding cosmic substance glows brilliantly with luminating stars, while elsewhere, everything appears darkened and dirty, as if smoke blanketed a patch of space. + + + 23 +Part I: +Cosmic Ether as Theory +and Experimentally +Confirmed Fact + + + 25 +The Matter of Space, Waves and Motion +The Matter of Space, +Light Waves and Motion +“...when primordia are being carried downwards straight through the void by their own weight, at times quite undetermined and at undetermined spots they push a little from their path, but only just so much as you could call a change of trend. But if they were not used to swerve, all things would fall downwards through the deep void like drops of rain, nor could collision come to be, nor a blow brought to pass for the primordia. So nature would never have brought anything into existence.” – Lucretius, Roman Poet, c.75 BC De Rerum Natura, Book II +Lucretius’ primordial “swerve”, quoted above, was a reference to curved or circular motion in the Great Void of the Cosmic Heavens, an early concept of creation in motion, resting upon ideas that ranged back to Greek philosophers such as Aristotle, and the Roman Epicureans. For those ancient philosophers, creation was a role played out by the gods, but they also put reasoned explanations to the physical world they could touch and see. The nature of cosmic motions, the passage of the Sun, Moon, stars and “wandering” planets, was always a central human interest, but only dimly understood, and set apart from the confined material existence of humankind on the Earth’s surface. Aristotle divided the material world into four elements, of fire, air, water and earth, but the heavens were composed of a fifth element, a +Lucretius (c.75 BC) + + + 45 +The Positive Results of Michelson-Morley +The Positive Results of the +Michelson-Morley Experiment +The history of science records the July 8-12, 1887 ether-drift experiment of Albert Michelson and Edward Morley as a pivotal turning point, after which the energetic ether, filling all of cosmic space, was discarded by mainstream physics and astronomy. Thereafter, the postulate of “empty space” devoid of ether was embraced, along with related concepts which demanded constancy of light speed in all directions, in harmony with Albert Einstein's relativity theory. The now famous Michelson-Morley experiment continues to be widely cited today, in nearly every physics textbook, for its claimed “null”, “zero”, or “negative” results. These claims, however, are not true, something easily determined by a careful reading of the original MichelsonMorley paper, which appeared in the American Journal of Science in November 1887. In fact, their experiment reported a slight positive result, later to be independently replicated by others, including by both Michelson and Morley, working separately from each other, with different research associates. Twentieth Century science nevertheless ignored all such positive evidence for the cosmic ether, as if psychologically compelled to make a wrong turn. +Albert Michelson (1852-1931) +Edward Morley (1838-1923) + + + 57 +FitzGerald-Lorentz and Morley-Miller +The FitzGerald-Lorentz Theory +and Morley-Miller Experiments +“Strictly speaking, the condensation [of ether] must be still more considerable than the value we have found to be necessary. If the ether be attracted by the earth, it is natural to suppose that it is acted on likewise by the sun; thus the earth will describe its orbit in a space in which the ether is already condensed. In this dense ether, the earth must produce a new condensation.” — Heinrik Lorentz 1899, p.446. +The years before the Michelson-Morley experiment of 1887 were characterized by a scientific discourse on the nature and properties of the ether, and its role in the properties of light and space. Nearly all had accepted the ether theory for most of their professional lives, and also accepted the wave theory of light, which demanded such a medium for light-wave transmission. Disagreements persisted on just what kind of ether might actually exist. Into that discussion came the 1887 result, variously described as “null” or “zero”, but which as pointed out in the last chapter was a substantial quantity. A significant ether-wind velocity was recorded, of up to 5 to 7.5 km/sec by Michelson-Morley’s own statements, or an average of ~8.4 km/sec as their data was later recalculated by Miller in 1933, using a new theory and understanding about Earth’s net motion in space. The Michelson-Morley result was too small to accommodate the static ether of Newton, but it was significant and sufficient enough to warrant further investigation along the lines of a partially entrained ether-drag effect. Such an ether drag would by definition reduce the conventionally (at that time) “expected” velocity close to the surface of the Earth. A trend was also set into motion following a new theory of “matter contraction”, to dismiss the Michelson-Morley result as purely “null”, and to explain away the cosmic ether itself, as if it were a nuisance. And + + + 79 +Dayton Miller’s Experiments +Dayton Miller’s Positive +Ether Drift Experiments, 1921-1926 +“I believe that I have really found the relationship between gravitation and electricity, assuming that the Miller experiments are based on a fundamental error. Otherwise, the whole relativity theory collapses like a house of cards.” — Albert Einstein, letter to Robert Millikan June 1921 (in Clark 1971, p.328) +In the decades following the MichelsonMorley experiment of 1887, the worlds of physics and astronomy were thrown into confusion, given how the cosmic ether had been a foundational theory for understanding the wave-theory of light, as well as a variety of astronomical and physical phenomena. While the Michelson-Morley experiment obtained a slight positive result, as already discussed, the phrase “null result” and similar misrepresentations came into widespread use when referencing their experiment. Conference lectures and published papers of that period, as by FitzGerald and Lorentz, also previously described, carried forward with an increasingly mystified matter-contraction postulate, as a means to “explain” why the cosmic ether was not, or could never be detected – even though it had already been detected, repeatedly. Astrophysics thereby retreated away from real, tangible results on a critical experiment, in what psychologists might call emotional denial, substituting in its place a new metaphysics, which had its historical foundation in Newton’s metaphysically-demanded static ether concepts. +Dayton Miller (1866-1941) + + + 115 +Which Way Ether Drifting? +Which Way Ether Drifting? +Miller’s Mis-Step, and Last Years +Ether Confirmed, Ether Velocity Confirmed, Axis of Ether Drift Determined, but... +In Which Direction Does Earth Move Along That Axis? +The preceding chapter reviewed Dayton Miller’s exceptional work on the ether-drift question, his confirmation of both ether and ether drift or ether wind, with a set of velocities and azimuths determined at four different seasonal epochs atop Mount Wilson. He also plotted the axis of ether drift, finding it close to the axis of the solar system’s ecliptic plane. However, by the time of his comprehensive 1933 paper on the subject, he had reversed his long-standing view on the northerly direction of Earth’s motion along that axis, and instead argued for a southerly direction. I object to his change in direction of motion along the ether-drift axis, but not to the axis itself. My claim requires a clear discussion of the evidence, both pro and contra. As noted by Miller in the preceding chapter, the interferometer could determine the axis of ether drift using the Michelson interferometer, but not the direction of ether motion along that axis. For that determination, one needs to logically compare the axis of ether-drift findings against other astronomical observations related to the Earth’s velocity and movements relative to nearby stars, and other cosmic coordinates and determinations. +After Mount Wilson +By 1926, after Miller concluded his four major seasonal epochs of ether experiments, he began to reveal his thinking as to the larger issues of the Earth’s net velocity through the universe, as well as about an Earth pushing through a dragged ether. His writings on these matters reveal a level of comprehension and skill certainly equal to that of + + + 131 +Sagnac and Michelson-Gale +Sagnac and Michelson-Gale: +Ether Detection by Rotation +Another variant of the ether-drift experiments employed a rotating platform which sent two light beams around an irregular “racetrack” path by use of mirrors, one moving clockwise and the other counterclockwise. After completing the circuit, the two beams were recombined back into one beam, whereupon interference fringes would appear for observation. The experiment could evaluate for both the existence of an ether, and for changes in light speed dependent upon direction of rotation. The success of these experiments, reported below but nearly forgotten or obfuscated by the Einstein followers today, provided even more direct proof that light has variable velocities, dependent upon the speed of the emitter and observer, but irrespective of whether the cosmic ether is static, is in motion along one or another preferred direction, or is even fully stagnant as per the Stokes concepts. +1913-1914: George Sagnac Proves Variable Light Speed and Ether +Enter Georges Sagnac, who undertook the original rotating interferometer experiment in 1913, only 8 years after Einstein’s 1905 published papers on the subject of his new relativity theory. In this experiment, Sagnac created a rotating tabletop interferometer, turning at a speed of 2 revolutions per second. On the surface of the rotating table, two light beams were sent to bounce along different mirrors, so as to move either with the direction of the rotating disk, or in opposition to the rotation. The two light beams originated from the same light source, being split into two beams, much as in the Michelson interferometer. After moving around the rotat +Georges Sagnac 1869-1928 + + + 141 +Michelson and Others Return to the Ether +Figure 43. Dayton Miller (left) and Albert Michelson (right) at a Conference on the Michelson-Morley Experiment held at Mount Wilson Observatory, February 1927. +Michelson and Others Return +to the Ether-Drift Question +1926-1928: Michelson, Pease and Pearson Confirm, but Nevertheless Deny an Ether-Drift +In apparent efforts to replicate Miller’s results as obtained at Mount Wilson in 1925 and 1926, Albert Michelson, with assistance from F.G. Pease and F. Pearson (hereafter “MPP”), undertook a new set of ether experiments. Their results, with the title “Repetition of the MichelsonMorley Experiment”, were published in the January 1929 issue of Nature magazine, followed by a nearly identical article a few months later in the Journal of the Optical Society of America. Unfortunately in both cases only a frustratingly vague and short report was given, exposing shortcomings well below the standards an optical expert such + + + 167 +Recent Confirmations of Ether +Recent Confirmations +of an Ether Wind +Yuri Galaev, Kharkiv Ukraine Experiments, 1998-2003 +Yuri Galaev is a radio engineer at the Institute for Radiophysics & Electronics, a part of the National Academy of Sciences of Ukraine, in Kharkiv4. His work, using both optical light and radiofrequencies to investigate the cosmic ether produced a confirmation of Dayton Miller’s work, “down to the details”. His methods were unique, employing new designs, including both a radio wave analysis and a simplified Michelson-type apparatus. Like Miller, Galaev was one of the very few who embraced rather than ignored the material nature of the ether and the importance of removing shielding materials in the surroundings of the interferometer. This appears as a major reason for his success, and for the failure of so many others. He summarized the matter succinctly: +“In 1933, Miller has marked the shielding property of metal covers in his work. However the scientific community did not react properly to such peculiarity, shown by him in this work... there was a lot of experiments with zero results obtained with the interferometers screened by metallic chambers by that time. ...proper significance [had not been given] to Miller’s conclusions 1933 about the inapplicability of metal boxes in the experiments with an ethereal wind. Thus, proper checks of Miller’s experiments weren’t conducted yet until nowadays, in spite of numerous physicists’ attempts to repeat his experiments! All his followers carefully screened the devices from an ethereal wind by metal chambers, and, according to A.A. +Yuri Galaev +4. Kharkiv is the Ukranian city once called “Kharkov” during the Soviet era. + + + 191 +Part II: +The Empire Strikes Back: +Erasure, Mystification, +and Falsification +of History + + + 193 +Einstein Rising +Einstein Rising +“My opinion about Miller’s experiments is the following... Should the positive result be confirmed, then the special theory of relativity and with it the general theory of relativity, in its current form, would be invalid. Experimentum summus judex. Only the equivalence of inertia and gravitation would remain, however, they would have to lead to a significantly different theory.” — Albert Einstein, letter to Edwin Slosson, 8 July 1925 (Hebrew U. Archive) +The Rise of Einstein’s Theory of Relativity +In 1905, Albert Einstein published several research papers that are considered to be cornerstones of modern physics and astronomy. Upon first reading his works decades ago, I found his relativity theory to be deeply mystical, referencing unseen forces such as “curved spacetime”. He ignored measured real-world cosmic motions that affected the velocity of light, and conjured up cosmic motions in a space-time unreality, which still remains as sheer speculation, heavy with maths but never convincingly affirmed by empirical reality. Today I accept him as a humanitarian, and his ideas on energy-mass equivalency (E=mc2) as approximations. However, the proofs of variable light-speed, as from the successful ether-drift experiments, completely destroy a central assumption of Einstein’s relativity theory, that of light-speed constancy. Above that concern, when the evidence claiming to prove the accuracy of his relativity theory is critically examined from the viewpoint of the +Albert Einstein (1879-1955) + + + 213 +The Shankland, et al. Hatchet Job +The Shankland, et al. +Hatchet Job on Miller * +Over the years after Miller’s death in 1941, his Mount Wilson etherdrift results continued to trouble Einstein and his followers. A postmortem of Miller’s work was finally undertaken in the early 1950s by a team from Case School, led by Robert Shankland, and with “extensive consultations” with Einstein. As one might anticipate, the new evaluation of Miller’s findings made all the wrong assumptions about the cosmic ether as previously exposed in prior chapters, with a clear bias to “disprove Miller”. Given how Einstein’s supporters continue to place a high value on the Shankland, et al. study, I will go into some detail to expose its serious flaws and biases. Shankland in fact was Miller’s graduate student for many years, and only emerged to become a professional advocate of Einstein’s relativity after the death of Miller in 1941. His early career as a scientist got off to a rocky start, in his first published paper (1936) “An Apparent Failure of the Photon Theory of Scattering”. In that paper, Shankland +Robert S. Shankland, former student of Dayton Miller and later Chairman of the Physics Department at Case Western Reserve University in Cleveland Ohio. Shankland’s academic career soared following publication of several widely read interviews with Einstein, and after he organized a post-mortem on Miller's work in cooperation with Einstein, pronouncing Miller’s work as worthless. Shankland subsequently became a bureaucrat within the Atomic Energy Commission. +* This chapter was originally presented to a meeting of the Natural Philosophy Alliance, in Berkeley, California, May 2000, titled “Critical Review of the Shankland, et al. Analysis of Dayton Miller’s Ether-Drift Experiments”. + + + 227 +Part III: +Into New Territory: +Additional Evidence +for a +Material, Motional +and Dynamic Ether + + + 229 +Ether as Cosmic Life Energy +Ether as Cosmic Life-Energy +“There is no such thing as ‘empty space’. There exists no ‘vacuum’. Space reveals definite physical qualities [which] can be observed and demonstrated. Some can be reproduced experimentally...” – Wilhelm Reich, +Ether, God and Devil, 1948, p.111 +In the years after the historic ether-drift experiments were concluded, and figuratively “driven into exile”, multiple converging lines of evidence from other scientific disciplines indicated the discovery of an interconnecting self-organizing cosmic medium, a cosmic life-energy with ether-like dynamic and plasmatic properties. The discovered lifeenergy functioned within living systems, influencing chemistry and biology, and could change the physical structure of water. It also existed as a background medium filling the atmosphere and vacuum of space. Experimenters such as Jacques Benveniste (memory of water), Frank Brown (external biological clock mechanisms), Harold Burr (electrodynamic fields), Björn Nordenström (bioelectrical circuits), Giorgio Piccardi (physical-chemical fields), Wilhelm Reich (orgone energy) and Viktor Schauberger (living water) independently documented different aspects of this phenomenon. Entire bodies of scientific work and literature have been developed over the years by these and similar scientists, far too large to review here. For some, I can only give a general citation to their work in the References. For those in the 20th Century up to c.1995, an annotated bibliography was developed by John Burns (1997), Cosmic Influences on Humans, Animals and Plants. Science journals such as Cycles and the Interdisciplinary Journal of Cycle Research published numerous papers on these subjects. Today their journals have nearly vanished, their leading scientific luminaries passed away. When alive, most were subjected to public “skeptic” attacks, academic misrepresentations, and unethical erasure. + + + The Dynamic Ether of Cosmic Space +230 +Regrettably, nothing of the most insightful and productive of the above list of life-energy scientists, Wilhelm Reich, is found in Burns annotations, and little of fact about him is found elsewhere in mainstream science, pop-media or internet. This was the result of a deadly 20th Century’s slander and book-burning campaign directed against him in the 1940s and thereafter, as discussed in the Introduction. (WebRef.1) He published his findings in his own institute’s journals and books, which were eventually reprinted in the 1970s, after the book-burning epoch. In this chapter I will survey the facts on Reich’s experimental findings, speak to my own positive replications of his experiments over the last decades, and end with a short discussion on Piccardi and Brown. These latter two scientists identified specific cosmic components in their investigations which, I will show, are agreeable in the details with Reich and Miller. Taken together and merged with the prior findings on cosmic ether under discussion, these studies collectively document a major scientific breakthrough, the discovery of a unitary cosmicatmospheric-biological energy, ignored, suppressed and dismissed prematurely during the 20th Century. +Wilhelm Reich’s Dynamic Ether-Like Orgone Energy +From 1934 to 1957, Wilhelm Reich produced a series of experimental reports documenting the existence of a unique form of energy, called the orgone, or orgone energy. Reich’s line of research began with the clinical and experimental investigation of Freudian libido theory, including a milestone study on the bioelectric nature of emotions, somatic impulses, sexual excitation and sensory perception. Reich’s research proceeded also into microbiology, with a study of motility and impulse-creation within simple microbes such as the ameba, which has no brain, nerves or muscle tissue by which to move its protoplasm towards food or away from irritating influences. His studies (Reich 1934, 1938) identified bioelectric commonalities in the motions of raw protoplasm in ameba, to nervous and muscular impulses in humans. The work by Seifriz (1936) and others on motile slime molds suggests related findings. Slime molds are a large single cell of +Wilhelm Reich 1897-1957 + + + 265 +Evidence for a Dynamic Ether +Direct Evidence +For a Dynamic Ether +Motional, Dynamic, Spiralling, Luminiferous, Variable Density, Matter-Forming, Substantive +A Review of What We Know +Let’s start this chapter by reviewing the specific nature and properties of the cosmic ether as learned from the different experiments already recounted in this work. From Michelson-Morley 1887, we learned a cosmic ether wind with an upper value of ~5 to 7.5 km/sec was detected, able to partially penetrate through the stone basement building in which the light-beam interferometer experiment was conducted. Their results were a much lower velocity than the ~200-300 km/sec anticipated from Newtonian static ether “absolute space” assumptions. While the 36 turns of their interferometer were minimal, over only a few days, their results were never “null” or “zero”. They stated the experiment would have to be repeated again at a higher altitude over intervals of three months. This repetition was never conducted by them. From Morley-Miller 1898 to 1906, we learned that light speed is not affected by a strong magnetic field. They later constructed a larger and more sensitive light-beam interferometer, used for experiments over several years, with nearly a thousand individual turns of the instrument over different months. They experimentally tested their interferometer for the postulated “matter contraction” of FitzGerald-Lorentz, which was never confirmed. This was accomplished by mounting the interferometer optical components on a base of different density materials, such as wood, concrete or steel, and comparing that to the sandstone base used in the Michelson-Morley experiment. However, in the process, Morley-Miller repeatedly confirmed a real ether drift of ~7.5 to ~9 km/sec. The highest ether velocity was obtained when the + + + 297 +Implications of Cosmic Ether +Implications and Consequences of a Material-Motional Cosmic Ether for Modern Astrophysics +The Cosmic Ether Changes Everything! +For more than 100 years, empirical experimental evidence identifying a real material and motional ether has been consistently ignored, overlooked and suppressed, while at the same time, ambiguous and speculative, mystical theories have been promulgated and hungrily devoured. And whenever evidence was asserted to support such mysticisms, it was never so unequivocal that opposing ether theory could not equally or better explain it. Factually, proof for a motional and material cosmic ether changes everything!It upsets the modern applecart, and forces us back to unfinished discussions of the early 1900s. To this we must add the considerable work of Reich, who independently and experimentally confirmed an ether-like life energy, and described how it moved in living tissues, in the atmosphere and in the cosmos, thereby adding additional detail to what is known about cosmic ether. The two objective discoveries, and their respective bodies of evidence – of cosmic ether and cosmic orgone – are at root, functionally identical. And not accidentally, some of the same players, notably Einstein and his followers, worked towards the erasure of both Reich and Miller. In this closing chapter I will review modern cosmological concepts and experiments currently underway, and will challenge their basic foundational assumptions from the viewpoint of a dynamic cosmic energy in space. As a prelude, I would remind the scientific reader of a major fallacy in contemporary physics, where modern theories as from Einstein, the big bang and quantum entanglement, are stretched so thin in efforts to basically “explain everything”, that in the process must resort to increasingly fantastic and unbelievable claims. By contrast, the cosmic ether of space already has considerable independent evidence and equally valid explanatory and predictive power, resting firstly upon the historical proofs of its own existence. + + + 337 +Conclusions +Conclusion +Figure 105 on the facing page was first presented in the Introduction. The lower part is Figure 106, also reproduced for emphasis from the chapter on Ether and Cosmic Life Energy. Together with all the other figures in Part III, they present a concluding, though generalized and non-mathematical, ether/life-energetic understanding of cosmic forces ruling celestial motions, gravitation and other aspects of matter and life. Figure 106 depicts Mass 1 moving towards Mass 2 in a straight line, but only if one is standing upon the rotating Earth. It is only an apparent straight-line motion. Standing as an observer out in space, what we call “gravitation” is seen as a curve of motion, with both objects captured in a sweep of merging, negatively entropic and self-attracting cosmic energy, carrying matter with it. Ether/life-energy, orgone energy as Reich described it, superimposes in a curve of energetic attraction which brings the two objects together. This is standard old-fashioned Galilean relativity, which often gets lost in the modern discussions about Einstein’s relativity and imaginary “space-time gravity wells”. The old master Galileo had, in the 1600s, already proven basic properties of gravitation in his famous experiments at the Tower of Pisa, where balls of unequal weight were dropped from a height of around 55 meters, arriving at the ground at the same time. This refuted the older view of Aristotle that different weight objects fell at different velocities. Galileo also wrote several logical premises, today called “thought experiments”. He imagined (and possibly confirmed by experiment) a man on horseback riding in a straight line, who holds a ball off to the side of his direction of motion, and then drops the ball which falls downwards. From the perspective of the horseback rider, the ball moves downwards in a straight line, with a forward motion the same as the horse, until landing directly next to where the horse is galloping. From the perspective of someone standing on the ground, watching the horseman ride by and drop the ball, however, the ball falls downwards in a long curve, not a straight line. This observation led Galileo to go beyond his initial weight-drop experiments at Pisa, to + + + 349 +Appendix 2: Newton Letter to Boyle +Isaac Newton's 1679 Letter to Robert Boyle, on the Cosmic Ether of Space +Appendix 2 +Newton the Younger (1689) Newton the Elder (1712) +Prefacing Comments +Below is a letter on the question of the cosmic ether of space, written by Isaac Newton in 1679 to Robert Boyle, a fellow scientist about 15 years older than Newton at the time, and who is remembered with a fame nearly equal to that of Newton. This letter first came to my attention when it was reprinted in a relatively-unknown journal edited by the heretic-scientist Wilhelm Reich, his International Journal of Sex-Economy and Orgone Research (vol.3 1944, p.191-194). The original reference from Reich's journal is found in the 1938 volume Isaac Newton: 1642-1727, by J.W.N. Sullivan (Macmillan, NY, p.118124). However, a longer and more complete version of the letter was thereafter found in an 1846 publication of lengthy title by William Vernon Harcourt, cited (as Newton 1679) in the Reference section of this book, containing pertinent information not previously available. The letter below is significant firstly because it is not well-known outside of a few historians. Where it is quoted, significant parts as I have now restored, are often left out. + + + 361 +References +References +A chronologically-ordered list of the historical ether-drift citations, with download links, is found at: www.orgonelab.org/energyinspace.htm +Abbot BP (2018) GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs. arXiv:1811.12907v2 Alfven H (1981) Cosmic Plasma, Springer. +Allais M (1997) L’Anisotropie de L’Espace:La nécessaire révision de certains postulats des théories contemporaines, Clément Juglar, Paris. +Allais M (2002) Experiments of Dayton C. Miller (1925-1926) and the Theory of Relativity. Pulse of the Planet #5, p.132-137. +Arp H (1987) Quasars, Redshifts and Controversy, Interstellar Media. Arp H (1997) Seeing Red: Redshifts, Cosmology and Academic Science, Aperion. Canada. +Arp H (2003) Catalogue of Discordant Redshift Associations. Aperion, Montreal. Asimov I (1966) The Neutrino, Ghost particle, Doubleday, NY. Baker CF (pseud. Rosenblum CF) (1972) An Analysis of the United States Food and Drug Administration's Scientific Evidence Against Wilhelm Reich, Part II, the Physical Concepts. J. Orgonomy, 6(2) 222-231. Baker CF (pseud. Rosenblum CF) (1973) An Analysis of the Food and Drug Administration's Scientific Evidence Against Wilhelm Reich, Part III, Physical Evidence. J. Orgonomy, 7(2) 234-245. Baker CF (1980) The Orgone Energy Continuum. J. Orgonomy, 14(1) 37-60. Baker, CF (1982) The Orgone Energy Continuum: the Ether and Relativity. J. Orgonomy, 16(1) 41-67. +Becker RO (1998) The Body Electric: Electromagnetism and the Foundation of Life, Wm. Morrow, NY. Bauer I (1987) Erethrocyte Sedimentation: A New parameter for the measurement of Energetic Vitality. Annals, Inst. Orgonomic Sci.4:49-65. Baumer H (1987) Sferics: Die Entdeckung der Wetterstrahlung. Rowohlt Verlag, Hamburg. Becker RO, Selden G (1985) The Body Electric. Wm. Morrow, NY. Bernabei R (2007) DAMA sheds light on dark-matter particles. Nature 449, 24, 6 September. Bernabei R (2010). Particle Dark Matter in the Galactic Halo: Recent Results from DAMA//LIBRA. CRIS 2010 lecture, September, Catania Italy; see WebRef.10 Beloussov L, Popp FA, Voeikov V, Wijk RV, eds. (2000) Biophotons and Coherent Systems: Proc. 2nd Alexander Gurwitsch Conference. Moscow U. Press; republished by Springer Press 2007. + + + 381 +Index +A +aberration, stellar 12, 37-39, 59-60, 74, 82, 116, 119, 208-209, 340 absolute space 10-11, 139, 181,185, 187, 198, 208, 265, 269, 319, 350 Aether 2, 4, 26 Allais, Maurice 9 Andromeda Galaxy 32, 124, 272273 blue halo 287, 292-293 Aristotle 25-26, 337 Arp, Halton 4, 6, 211, 321-322, 334 astrologers 2, 318 atomic clocks 304-307 +B +Bell, Alexander Graham 46 Benveniste, J. 229 Bernabei, R. 251, 286-287 Biblical creationism 320 big-bang creationism 2, 4-6, 13, 22, 212, 236, 280-281, 283, 297, 300, 303, 314-324, 335, 341-344 biophotons 293 Biretta, John 331-332 black holes 2, 22, 212, 285, 301303, 324-331, 333-335, 341, 345 as ring of stars 328-330 as ether vortex Sagittarius-A 325 M87 image, problems 326-330 Bode’s Law 341 book-burning 19-21, 230, 319, 343344 Boyle, Robert 32-24, 60, 349-360 Brace, D.B. 63 Bradley, James 37 Brown, Frank 4, 6, 15, 229-230, 252, 254, 261-263, 268, 286, 288-289, 242 +Index +Bruno, Giordano 27 Burr, Harold S. 8, 15, 229, 263 +C +Cahill, Reginald 184-187, 190, 252, 254, 268, 288-289 Campbell 119, 209 Carnegie 119 Case Western Reserve University 8, 52, 54, 80, 130, 213, 225 Case School of Applied Science, Pierce Hall 50-52, 54, 62, 66-67, 69, 73, 80, 86, 90-91, 101, 118, 122, 130, 161, 213-216, 221, 266 Western Reserve University 50, 73, 80, 130 Catholic Church 5, 26, 33, 314-315, 318-319, 333, 350 Cedarholm 188 Champeney, D.C. 188 Chappell, John xi, 8 cloudbuster 5-6, 236 Copernicus, Nicolaus 3, 13, 27, 335 Cosmic Microwave Background Radiation, CMBR, 1, 5, 118, 323 cosmic strings 1, 335 cosmic superimposition, see Reich, Wilhelm cosmic rays 1, 119, 238, 276, 279280, 283, 285, 288-289, 293-294 winds, anisotropy 279 Courviosier 118 +D +dark matter 1, 236, 242, 251, 272, 276, 280, 292-293, 295, 334 MACHOS 285, 294, 334 WIMPS 285-286, 294, 334 wind, anisotropy 283-289 + + + The Dyamic Ether of Cosmic Space +382 +DAMA Project, see Bernabei DeMeo findings, theory, graphics Atomic clock variable inertia 307 blue glows 292-295 comet velocities 354 correlations of cosmic motions 111, 128, 254, 288-290 dubious black holes 326-330 ether lens effect 210 ether velocity/altitude 186-187 ether-vortex tornado 325, 330 galactic and solar tilting 272-273 GPS experiment 308 LIGO 302-304 Miller’s ether velocities 248-250 Miller’s data sheets 8, 225 planet nine 270 Reich and Kepler, 248-250 orgone accumulator 233-235, 242 rotation of plasmasphere 274-275 spectroscopical analysis 290-292 spiral-form vortex motions 16, 18, 250, 253, 325, 328 Descartes 15, 19, 29-33, 36, 39, 42, 257 Dewitte, Roland 189-190 dowsing 7 +E +Edison, Thomas 344 Einstein, Albert xiv, 5, 8, 15, 22, 61, 193-212, computational error 77 E=mc2 15, 193 Einstein rings 210-211 equivocal nature 200 ether concept 198-199 gravity wells 198, 211, 334, 337, 341, 345, 339, 345 last years 200, 223 mysticism 199, 342 perihelion of Mercury, problems 200-203 +relativity theory 5, 8-9, 15, 45, 74, 76-77, 79, 84, 87-88, 98-100, 110, 131, 136, 138, 140, 143, 162-164, 185-187, 190-213, 224, 236, 240, 256, 266-267, 298, 305, 313, 318, 324, 331-334, 337-344 Shankland affair 200, 223-224 space-time distortion 15, 22, 76, 187, 193, 195, 210-211, 236, 304, 326, 330 , 334-335, 342 starlight bending near Sun, problems 203-210 Epicureans 25 epicycles 2, 27, 333, 335 Esclangon 119 Essen, Louis 188, 305 ether, cosmic blocking by materials 54, 63 dielectric 39, 63, 231-232, 293, 295, 305, 346, 197-198, 265, 267 entrained, dragged, static, as cosmic braking force 13-14 ether turbulence in LIGO 303 experimental summary 186-187 luminiferous 2-3, 19, 26, 32, 36, 53, 58, 60-61, 133, 237, 240, 292 magnetism 11, 33, 39, 62-63, 8788, 231, 265, 304 prime mover 13-14, 26, 28, 3233, 35, 42, 113, 236, 257, 268269, 319, 339, 341, 350 properties 178-179, 339-341 static-dragged versus dynamicmotional 10-15, 32-37, 265-295 tornado vortex 325, 330 velocity and altitude 186-187 velocity zero in December 251 water drag experiments 42-43 winds, substitute names for 276 Event Horizon Telescope EHT 326329 + + + 383 +Index +F +Faraday, Michael 304, 345 Faraday cage 231, 233, 236 Fibonacci 340 Fickinger, William xiii, 8, 225 first order/second order 172 FitzGerald, George 58-76 FitzGerald-Lorentz matter contraction 57, 60-65, 67-68, 70, 73, 76, 79, 117, 129-130, 198, 265, 352 Fizeau, Hippolyte 40-43, 171 Food and Drug Administration, see book burnng Foucault, Léon 41-43, 54, 155, 171 fractals 340 freedom of speech, loss in universities 9-10, 335 Fresnel, August-Jean 38-40, 60-61, 74, 133, 135, 139 +G +galactic core and solar rotational tilting 272-273 galactic redshifts 320-322 Galaev, Yuri 9, 49, 167-179, 183189, 252, 254, 260, 267, 269, 288-289, 306, 351 galaxy distribution in universe 317 Galilei, Galileo 3, 5, 13, 21, 27-28, 33, 36, 40, 301, 333, 335, 337338, 350 Galilean relativity 194, 337-338 Gell-Mann, Murray 314 Gerson, Max 344 golden section 340 GPS 307-309 gravitational redshifts 210-211 gravitational waves 1, 298-304 Grusenick, Martin 189-190 Grimaldi, Francesco 29-30 Gurwitsch, Alexander 263 +H +Hafele and Keating 306 H-bombs 345 Heisenberg uncertainty 313-314 Helmholtz, Hermann von 46 Hicks, W.M. 70 Higgs “God” particle field 1, 276, 287 Holy Ghost, ether as 28, 33, 37 Hoxsey, Harry 344 Hubble, Edwin 32, 314 Hubble constant 334 Hubble telescope 277, 315-316, 326, 331 deep-field image 316 Huygens, Christiaan 37, 359 +I +IMAGE satellite, see plasmasphere intergalactic medium or wind, see interstellar medium International Society for Biometeorology, Piccardi Group 7 interstellar medium or wind 1, 236, 276-278, 280, 283, 288-289, 292293 +J +Jaesja 188 Joos, Georg 158-162, 216, 206 +K +Kelvin, Lord 64, 77, 224 Kennedy, Roy 149-151, 266 Kennedy-Thorndike 162-163, 266 Kepler, Johannes 28, 33, 37, 39 theory and equations 20, 96, 127, 202, 245, 247-252, 268, 287, 339 Kervran, Louis 263 Kreiselwelle, spinning wave, see Reich, Wilhelm Kuiper Belt planetoids 271 + + + The Dyamic Ether of Cosmic Space +384 +L +Lemaitre, George 315 life-energy, see Reich, Wilhelm +light phenomena double-slit experiment 38, 309313 refraction 29-30, 37, 39, 74, 206, 210, 304, 353 corpuscular photons or particles 10, 36-38, 194-195, 199, 208, 210, 213, 238, 309-314 Light Interferometric Gravitational Observatory LIGO/ALIGO 298304 ether turbulence 303 results not unequivocal 301-303 light flashes, visible, background radiation 294 visible orgone energy phenomena, see Reich, Wilhelm Lodge, Oliver 59, 209, 319 Lorentz, Heinrik 57-74, 76, 79, 116-117, 129, 186, 198, 220, 305, 340, 342 Lorentz-FitzGerald matter contraction, see FitzGerald-Lorentz Lucretius, primordial swerve 25 luminiferous ether, see ether, luminiferous Lysenkoism 10 +M +mainstream media “fake news” and slander 6, 19-21, 230, 233, 243-244, 343 hysteria, hype, bias 56, 74, 98100, 198, 200, 205, 208-209, 212, 224-225, 230, 233, 318, 326, 335, 343 Marett, David 279 Marinov, Stefan 188 +Massive Compact Halo Objects MACHOS, see dark matter Maxwell, James Clerk 39 Mersenne, Martin 29 Messier, Charles, spiral nebulae 32 Michelson, Albert 45-56, 134-140, 141-149, 154-158, 265-267 1881 experiment 46-47 early studies 46 invention of the interferometer 46-50 last years 149, 165 two swimmer example 48 Michelson-Morley experiment 4556, 60-61 absence of null-zero result 53-58 re-calculation by Miller 53-56 Conference on, at Mt. Wilson 103, 108, 117, 141, 220 Michelson-Gale experiment 134140, 196, 266 Michelson-Pease-Pearson experiments 141-149, 154-158, 266 Milian, Viktor 240 Millikan, Robert xiv, 79, 88, 197198 Miller, Dayton 61-77, 79-113 1921 Mt. Wilson experiments 8489 1922-1924 Cleveland control experiments 90-92 1924 Mt. Wilson experiments 9396 1925-1926 Mt. Wilson experiments 96-110 axis of drift closer to Vega 251 early studies 80 error of southerly apex 115-130 Joos, response to 161-162 last years 130 phonodiek 77, 122, 224 rebuilt interferometer 81-83 + + + 385 +Index +work with Morley 61-77, 265266 Morgan, J.P. 344 Morley, Edward 45-56, 61-77, 80, 265-266 Morley-Miller experiments 4, 80. 61-77, 265-266 absence of null result 68-69, 73 compute error 69-70, 73-74, 76 Euclid Heights 69-76 magnetic experiment 62 new computation by Miller 7072, 75-76 new interferometer 64-67 Morse, P.M. 122, 124-125 Mount Wilson Observatory 84-85, 148 1927 Conference on Ether Drift 103, 108, 117, 141, 220 also see Miller and MichelsonPease-Pearson experiments Müller 189 multiple universes 22, 313, 335 Múnera, Héctor 180-187, 190, 252, 254, 267-268, 288-289 +N +Nassau, J.J. 122, 124-125 Nazis 19, 255 neutrinos 1, 236, 242, 276, 285, 288-289, 293-294 wind, anisotropy 280-283 Super-Kamiokande detector 282 Newtonian static ether, see ether, static Newton, Isaac 10-13, 19, 32-38, 42, 57-60, 79, 124, 135, 139, 181, 183, 187, 198-201, 204, 208-211, 245, 265-267, 301, 304, 313, 319, 335, 339 on precession of Mercury 201, 204 on bending of starlight 208-210 +letter to Robert Boyle 32-33, 349360 Queries 34-35 Noble, H.R. 63 Nordenström, Björn 229 +O +Occam’s Razor 13, 196, 294 Oracles of Delphi 330 Orgone Biophysical Research Laboratory 7 orgone energy, see Reich, Wilhelm orgone energy accumulator, see Reich, Wilhelm +P +Pauli, Wolfgang 280 pendants, pyramids, gizmos 21 Penzias, Arno 5, 318 perihelion of Mercury, problems, see Einstein ether explanation for 200-203 photomultiplier tube detectors PMTs in water or ice, for neutrinos 281283, 285, 293 with NaI(Tl) for dark-matter WIMPs 285, 293 for cosmic ray and gamma ray detection 293 for biophoton detection 293-294 Piccardi, Giorgio 4, 7, 15, 229-230, 251-254, 257-261, 263, 268-269, 288-289, 306, 342, 351 Piccard-Stahl 151-154, 266 Planck, Max 239, 322, 346 Planet 9 gravitational anomaly 270271 plasmasphere 208, 274-275 Pollack, Gerald 263 Pope John Paul II 319 + + + The Dyamic Ether of Cosmic Space +386 +prime mover 13-14, 26, 28, 32-35, 42, 113, 236, 240, 252, 257, 268269, 319, 339, 341, 350 Ptolemy, Claudius 29 +Q +quantum magic 22, 310, 313-314, 342 quantum vitamin pills 22 quantum flapdoodle 314 quasars 292-293 ejected from Seyfert galaxies 321-322, 292 high redshifts 322, 334 superluminal jets 333-334 water-drenched 294-295 +R +Rankine, A.O. 63 Rayleigh, Lord 59-60, 63, 292 redshifts, see galactic, gravitational or quasar redshifts Reich and Miller 20, 258-259 Reich, Wilhelm 4, 19-22, 229-264, 268-269 bions 236, 320 cosmic superimposition 15, 20, 32, 236, 239-247, 255, 257, 336 discovery of orgone energy and accumulator 230-231 effects of orgone energy accumulator 231-235 Einstein, meeting with 256-258 kreiselwelle, spinning wave 236, 239-241, 245-249. observations of orgone energy 235-242 orgone energy, summaries 236, 339-341 orgone lumination 32, 237, 281, 321, 339 orgone pulsation 19, 232, 236, 238, 244, 319, 340 +Reichian relativity 336, 338 slander and destruction of 19-22 spiral motions agreeable with Miller 247-250, 258-259 vacor tubes 237, 240, 242 visible fog-like form 238 visible orgone units 238-239, 281, 294 Royal Society (British) 64 Russell, Walter 18 +S +Sagnac, Georges 78, 131-134, 139140, 161, 196, 266, 298, 307-308 Sagittarius-A 324-325, 330 Schauberger 229 Seaver, Jay 187 self-organizing principle 19, 33, 36, 229, 268-269, 318-320, 341 Shankland, Robert 8, 92, 186, 200, 213-225 biased study of Miller 213-225 betrayal of Miller 223-224 Shapley, Harlow 343 skeptic clubs 6, 21-22, 225, 229, 294 Silvertooth, E.W. 188 Slosson, Edwin xiv, 99, 193, 197 Shnoll, Simon 263 solitons 1 Solovine, Maurice xiv, 200 solar flares 17, 239 solar extended corona 206-208 solar pulsation 17 spinthariscope, see light flashes spiral vortex motions 13, 15-20, 3132, 39, 42, 61, 70, 96, 107, 112, 127, 133, 171, 201-202, 211, 232, 236-239, 241, 244-260, 268-269, 272-273, 277, 283-287, 324, 326, 328, 330, 339-340 starlight bending near Sun ether explanation for 203-210 + + + 387 +Index +Stokes, George 39-40, 54, 59-60, 74, 129, 131, 135-138 stratospheric and planetary winds 276 Sun’s Way 113, 116, 120, 125-129, 171, 251, 254, 269, 273, 288-289 superluminal objects 330-334 Swenson, Lloyd 4, 87, 96, 122, 142-143, 149-150, 224 +T +Tchijevski, A.I. 263 Tesla, Nikola 344 torsion fields 1 Tromp, Solco 7 Trouton, Fredrick 63 +U +University of Kansas 4 +V +vacor high-vacuum tubes, see Reich, Wilhelm Velikovsky, Immanuel 343 +W +Weakly Interacting Massive Particles WIMPS, see dark matter Wedler, Eric 7 Westinghouse 344 Wheeler, Raymond 263 Wikipedia, disreputable 21 +Y +Young, Thomas 37-38 +Z +zero-point vacuum fluctuation 1, 4 + + + The Dynamic Ether of Cosmic Space +388 +Other Books by James DeMeo +Saharasia: The 4000 BCE Origins of Child Abuse, Sex-Repression, Warfare and Social Violence In the Deserts of the Old World, Revised Second Edition. +The Orgone Accumulator Handbook: Wilhelm Reich’s Life-Energy Discoveries and Healing Tools for the 21st Century, with Construction Plans, Third Revised Edition. +In Defense of Wilhelm Reich: Opposing the 80-Years’ War of Mainstream Defamatory Slander Against One of the 20th Century’s Most Brilliant Physicians and Natural Scientists. +Marx Engels Lenin Trotsky: Genocide Quotes. The Hidden History of Communism’s Founding Tyrants, in their Own Words. +Preliminary Analysis of Changes in Kansas Weather Coincidental to Experimental Operations with a Reich Cloudbuster: From a 1979 Research Project, reprinted 2010. +(as Editor) Heretic’s Notebook: Emotions, Protocells, EtherDrift and Cosmic Life-Energy, with New Research Supporting Wilhelm Reich. +(as Co-Editor) Nach Reich: Neue Forschungen zur Orgonomie: Sexualökonomie, Die Entdeckung der Orgonenergie. +(as Editor) On Wilhelm Reich and Orgonomy. \ No newline at end of file diff --git a/storage/6LLZ5HCC/DeMeo - The Dynamic Ether of Cosmic Space.pdf b/storage/6LLZ5HCC/DeMeo - The Dynamic Ether of Cosmic Space.pdf new file mode 100644 index 0000000..8aa0869 Binary files /dev/null and b/storage/6LLZ5HCC/DeMeo - The Dynamic Ether of Cosmic Space.pdf differ diff --git a/storage/AX6PSDNR/Miles-Board - The Radio War waged by the Royal Air Force against Germany, 1940 - 1945.pdf b/storage/AX6PSDNR/Miles-Board - The Radio War waged by the Royal Air Force against Germany, 1940 - 1945.pdf index 23a3887..07441ad 100644 Binary files a/storage/AX6PSDNR/Miles-Board - The Radio War waged by the Royal Air Force against Germany, 1940 - 1945.pdf and b/storage/AX6PSDNR/Miles-Board - The Radio War waged by the Royal Air Force against Germany, 1940 - 1945.pdf differ diff --git a/storage/BS4RDHXA/.zotero-ft-cache b/storage/BS4RDHXA/.zotero-ft-cache new file mode 100644 index 0000000..8b8f52a --- /dev/null +++ b/storage/BS4RDHXA/.zotero-ft-cache @@ -0,0 +1,687 @@ +General covariance and general relativity 791 +General covariance and the foundations of general relativity: eight decades of dispute +John D Norton +Department of History and Philosophy, University of Pittsburgh, Pittsburgh, PA 15260, USA +Abstract +Einstein o ered the principle of general covariance as the fundamental physical principle of his general theory of relativity, and as responsible for extending the principle of relativity to accelerated motion. This view was disputed almost immediately with the counter-claim that the principle was no relativity principle and was physically vacuous. The disagreement persists today. This article reviews the development of Einstein's thought on general covariance, its relation to the foundations of general relativity and the evolution of the continuing debate over his viewpoint. +This review was received in march 1993. + + + 792 J D Norton +Contents +1. Introduction 794 +2. The background of special relativity 796 2.1. Lorentz covariance and the relativity of inertial motion 796 2.2. Minkowski's introduction of geometrical methods 796 2.3. Covariance versus invariance in special relativity 797 +3. Einstein's development of general relativity 797 3.1. The early years 1907-1912: principle of equivalence and the relativity of inertia 798 3.2. The `Entwurf' theory 1912-1915: general covariance gained and lost 799 3.3. The hole argument: general covariance condemned 801 3.4. Einstein's 1916 account of the foundations of general relativity: general covariance regained 802 3.5. The point-coincidence argument 804 3.6. The Gottingen defense of general covariance 805 3.7. Einstein's three principles of 1918 806 3.8. Mach's principle forsaken 808 3.9. Einstein's objection to absolutes 809 +4. The favourable text-book assimilation of Einstein's view: fragmentation and mutation 811 4.1. Einstein's principle of equivalence as a covariance principle and its later misrepresentation 812 4.2. The early years: 1916-1930 814 4.3. The lean years: 1930-1960 815 4.4. Rebirth: 1960-1980 815 4.5. Recent years since 1980 816 +5. Is general covariance physically vacuous? 817 5.1. Kretschmann's objection: the point-coincidence argument turned against Einstein 817 5.2. Einstein's reply 819 5.3. Generally covariant formulations of Newtonian mechanics 820 5.4. Automatic general covariance: coordinate free formulation 821 5.5. Later responses to Kretschmann's objection 825 +6. Is the requirement of general covariance a relativity principle? 829 6.1. Disanalogies with the principle of relativity of special relativity 829 6.2. Relativity principles as symmetry principles 831 6.3. Coordinate systems versus frames of reference 835 6.4. Relativity principles and the equivalence of frames 837 +7. General relativity without principles 841 7.1. General relativity without general relativity 841 7.2. The principle of equivalence as the fundamental principle 842 7.3. Challenges to the principle of equivalence 842 + + + General covariance and general relativity 793 +8. Eliminating the absolute 843 8.1. Anderson's absolute and dynamical objects 843 8.2. Responses to Anderson's viewpoint 846 8.3. No gravitational eld-no spacetime points 847 8.4. What are absolute objects and why should we despise them? 847 +9. Boundaries and puzzles 849 9.1. Is general covariance too general? Or not general enough? 849 9.2. The Einstein puzzle 850 +10. Conclusion 852 + + + 794 J D Norton +1. Introduction +In November 1915, Einstein completed his general theory of relativity. Almost eight decades later, we universally acclaim his discovery as one of the most sublime acts of human speculative thought. However, the question of precisely what Einstein discovered remains unanswered, for we have no consensus over the exact nature of the theory's foundations. Is this the theory that extends the relativity of motion from inertial motion to accelerated motion, as Einstein contended? Or is it just a theory that treats gravitation geometrically in the spacetime setting? When Einstein completed his theory, his own account of the foundations of the theory was adopted nearly universally. However, among the voices welcoming the new theory were small murmurs of dissent. Over the brief moments of history that followed, these murmurs grew until they are now some of the loudest voices of the continuing debate. In any logical system, we have great freedom to exchange theorem and axiom without altering the system's content. Thus we need no longer formulate Euclidean geometry with exactly the de nitions and postulates of Euclid or use precisely Newton's three laws of motion as the foundations of classical mechanics. However, some two millennia after Euclid and three centuries after Newton, we still nd their postulates and laws within our systems, now possibly as theorems and sometimes even in a wording remarkably close to the original. The continuing disagreement over the foundations of Einstein's theory extends well beyond such an orderly expansion of our understanding of a theory's foundations. It is far more than a squabble over the most perspicacious way to reorganize postulate and theorem or to clarify brief moments of vagueness. The voices of dissent proclaim that Einstein was mistaken over the fundamental ideas of his own theory and that the basic principles Einstein proposed are simply incompatible with his theory. Many newer texts make no mention of the principles Einstein listed as fundamental to his theory; they appear as neither axiom nor theorem. At best, they are recalled as ideas of purely historical importance in the theory's formation. The very name `general relativity' is now routinely condemned as a misnomer and its use often zealously avoided in favour of, say, \Einstein's theory of gravitation". What has complicated an easy resolution of the debate are the alterations of Einstein's own position on the foundations of his theory. At di erent times of his life, he sought these foundations in three principles and with varying emphasis. They were the principle of equivalence, Mach's principle and the principle of relativity. By his own admission (Einstein 1918), he did not always distinguish clearly between the last two. Again, he lost completely his enthusiasm for Mach's principle, abandoning it unequivocally in his later life. The reception an development of Einstein's account in the literature has been anything but a graceful evolution. It has been more a process of uncontrolled mutation, fragmentation and even disintegration. The principle of equivalence took root in so many variant forms that Anderson and Gautreau (1969, p1656) eventually lamented that there are `almost as many formulations of the principle as there are authors writing about it.' This dissipation is at least partially fuelled by skeptical attacks on the principle such as Synge's (1960, p ix) famous complaint that he has never been able to nd a version of the principle that is not false or trivial. The locus of greatest controversy has been at the core of Einstein's interpretation, the principle of relativity. Does the general theory extend the principle of relativity to accelerated motion and is this extension captured by the general covariance of its laws? It is routinely allowed that the special theory of relativity satis es the principle of relativity of inertial motion simply because it is Lorentz covariant: its laws remain unchanged in form + + + General covariance and general relativity 795 +under a Lorentz transformation of the space and time coordinates. Now Einstein's general theory is generally covariant: its laws remain unchanged under an arbitrary transformation of the spacetime coordinates. Does this formal property allow the theory to extend the relativity of motion to accelerated motion? Until recent decades, the majority of expositions of general relativity answered yes and some still do. As early as 1917, Kretschmann (1917) argued that general covariance has no real physical content and no connection to an extension of the principle of relativity. Rather, the nding a generally covariant formulation of a theory amounts essentially to a challenge to the mathematical ingenuity of the theorist. Skeptical sentiments such as these drove a dissident tradition that has grown from a minority in Kretschmann's time to one of the dominant traditions at present. It had derived further support from the development of more sophisticated mathematical techniques that are now routinely used to give generally covariant formulations of essentially all commonly discussed spacetime theories, including special relativity and Newtonian spacetime theory. Finally, to many, Einstein's statements of his views seemed too simple or abbreviated to stand without further elaboration or repair; whereas their at rejection by the skeptics seemed too easy. Thus much energy has been devoted to nding ways in which the general covariance of Einstein's theory can be seen to be distinctive even in comparison with the generally covariant formulatons of special relativity and Newtonian spacetime theory. The best developed of these attempts is due to Anderson (1967) and is based on the distinction of absolute from dynamical objects. General relativity satis es Anderson's `principle of general invariance' which entails that the theory can employ no non-trivial absolute objects. This principle is o ered as a clearer statement of Einstein's real intentions and as giving a precise interpretation of Einstein's repeated disavowal of the absolutes of Newton's space and time. The purpose of this article is to review the development of Einstein's views on general covariance, their relation to the foundations of general relativity and the evolution of the continuing debate that sprang up around these views. Section 2 and 3 will review the development of Einstein's views. Section 4 will outline the ways in which attempts were made to receive and assimilate Einstein's views in a favourable manner. Section 5 will review Kretschmann's famous objection, Einstein's response and the diverse ways in which both were received in the literature. It includes discussion of modern geometrical methods that ensure automatic general covariance. Section 6 reviews the development of the characterization of a relativity principle as a symmetry principle rather than a covariance principle. Section 7 explores the tradition of exposition of general relativity that simply ignores the entire debate and makes no mention of principles of general relativity and of general covariance. Section 8 develops Anderson's theory of absolute and dynamical objects as it relates to Einstein's views. Section 9 examines Fock's and Arzelies proposals for alterations to the covariance of general relativity and gives an historical explanation of why so many of Einstein's pronouncements on coordinates and covariance are puzzling to modern readers. In the time period covered in this review article, the mathematical methods used in relativity theory evolved from a coordinate based calculus of tensors to a coordinate free, geometric approach. The mathematical language and sensibilities used in various stages of the article will match those of the particular subject under review. The alternative of translating everything into a single language would harmfully distort the subject (see section 9.2). + + + 796 J D Norton +2. The background of special relativity +2.1. Lorentz covariance and the relativity of inertial motion +Einstein's (1905) celebrated paper on special relativity brought the notion of the covariance of a theory to prominence in physics and introduced a theme that would come to dominate Einstein's work in relativity theory. The project of the paper was to restore the principle of relativity of inertial motion to electrodynamics. In its then current state, the theory distinguished a preferred frame of rest, although that frame had eluded all experiment and even failed to appear in the observational consequences of electrodynamics itself. Einstein's renowned solution was not to modify electrodynamics, but the background space and time itself. He devised a theory in which inertial frames of reference were related by the Lorentz transformation. If an inertial frame has Cartesian spatial coordinates (x; y; z) and time t and a second frame moving at velocity v in the x direction has spatial coordinates (; ; ) and time coordinate  , then, under the Lorentz transformation, + = (x t)  = (t vx=c2)  = y  = z (1) +where = (1 v2=c2) 1=2 and c is the speed of light. Hitherto classical theory had in e ect employed what was shortly called (by, for example, Laue (1911, p3)) the Galileitransformation. + = x t)  = t  = y  = z +Selecting suitable transformation laws for the eld and other quantities, Einstein was able to show that the laws of electrodynamics remained unchanged under the Lorentz transformation. That is, they were Lorentz covariant. Therefore, within the space and time of special relativity, electrodynamics could no longer pick out any inertial frame of reference as preferred. Each inertial frame was fully equivalent within the laws of the theory. Anything said about one by the laws of electrodynamics must also be said of all the rest. Electrodynamics was now compatible with the relativity of inertial motion. With the example of electrodynamics as its paradigm, the task of constructing a special relativistic version of a physical theory reduced essentially to formulating its laws in such a way that they remained unchanged under Lorentz transformation. Thus Einstein's (1905, section 10) original paper proceeded to formulate a modi ed mechanics for slowly accelerated electrons with this property. Thermodynamics soon also received some of its earliest relativistic reformulations in the same manner (see Einstein 1907, part IV, for example). The lesson of Einstein's 1905 paper was simple and clear. To construct a physical theory that satis ed the principle of relativity of inertial motion, it was sucient to ensure that it had a particular formal property: its laws must be Lorentz covariant. Lorentz covariance became synonymous with satisfaction of the principle of relativity of inertial motion and the whole theory itself, as Einstein (1940,p329) later declared: The content of the restricted relativity theory can accordingly be summarized in one sentence: all natural laws must be so conditioned that they are covariant with respect to Lorentz transformations. +2.2. Minkowski's introduction of geometrical methods +In Einstein's hands, Lorentz covariance was a purely algebraic property. Space and time coordinates were, in e ect, variables that transformed according to certain formulae. Hermann Minkowski (1908, 1909) was responsible for introducing geometric methods and thinking into relativity theory. He explained the background to his approach in his more + + + General covariance and general relativity 797 +popular (1909) lecture. It amounted to an inspired but essentially straightforward application of then current ideas in geometry. Minkowski's colleague at Gottingen, Felix Klein, had brought a fertile order to the world of 19th century geometry. That world was beginning to fragment after the discovery that geometry did not have to be Euclidean. In his famous Erlangen program, Klein (1872) proposed categorizing the new geometries by their characteristic groups of transformations. Euclidean geometry, for example, was characterized by the group of rotations, translations and re ections. The entities of the geometry were the invariants of these transformations. Minkowski pointed out that geometers had concentrated on the characteristic transformations of space. But they had ignored the groups of transformations associated with mechanics, those that connected various inertial states of motion. Minkowski proceeded to treat these groups in exactly the same way as the geometric groups. In particular he constructed the geometry associated with the Lorentz transformation. To begin, it was not the geometry of a space, but of a spacetime, and the notion of spacetime was introduced into physics almost as a perfunctory by-product of the Erlangen program. Moreover he found the spacetime had the hyperbolic structure now associated with a Minkowski spacetime. From this geometric perspective, the formulation of a theory that satis ed the principle of relativity became trivial. One merely needed to formulate the theory in terms of the geometric entities of the spacetime|in e ect the various types of spacetime vectors Minkowski had de ned|and the theory would be automatically Lorentz covariant. Thus Minkowski (1908, appendix;1908, section V) could write down the principle of relativity, for the theory was constructed purely geometrically. Thus, in his exposition of four-dimensional vector algebra and analysis, Sommerfeld (1910,749) could state: According to Minkowski, as is well known, one can formulate the content of the principle of relativity as: only spacetime vectors may appear in physical equations. . . +2.3. Covariance versus invariance in special relativity +The di erence between Einstein and Minkowski's approach to the same theory and even the same formalism is a polarity that will persist in various manifestations throughout the whole development of relativity theory, both special and general. Einstein's emphasis is on the algebraic properties of the theory, the equations that express its laws and their behaviour under transformation, its covariance. Thus the satisfaction of the principle of relativity is established by often arduous algebraic manipulation. The equations of the theory are transformed under the Lorentz transformation and the resulting equations are shown to have preserved their form. Minkowski's emphasis is on the geometric properties of the theory, on those geometric entities which remain unchanged behind the transformations, its invariance. Thus Minkowski ensures satisfaction of the principle of relativity by quite di erent means. The only structures allowed in constructing a theory are spacetime invariants. This restriction ensures compatibility with the principle of relativity and that its satisfaction can be settled by inspection. +3. Einstein's development of general relativity +While it may have been some years in preparation, the special theory of relativity coalesced into its nal form quite suddenly so that Einstein's rst paper on the theory remains one of its classic expositions. The development of general relativity was far slower and more tangled. Eight years elapsed between the inception and completion of the theory, during which time Einstein published repeated reports on the intermediate phases, false turns and unproven expectations. Even after the completion of the theory Einstein's account of its + + + 798 J D Norton +foundations continued to evolve. The modern image of Einstein's view of the foundations of general relativity is drawn fairly haphazardly from pronouncements that were made at di ering times in this evolution. As a result they are not always compatible. Indeed the pronouncements were sometimes as much expressions of results anticipated as demonstrated. For this reason, it would be misleading to construct any single edi ce and proclaim it Einstein's account of the foundations of general relativity. Rather we shall have to trace the evolution of Einstein's views as they were elaborated and modi ed in pace with the development of the theory. In developing general relativity, Einstein sought to satisfy many requirements. However we shall see that his e orts were dominated by a single theme, covariance, and they reduced essentially to an enduring task, expanding the covariance of relativity theory beyond Lorentz covariance. +3.1. The early years 1907{1912: principle of equivalence and the relativity of inertia +Two years after his completion of the special theory, Einstein began developing ideas that would ultimately lead him to the general theory of relativity. In a nal speculative section of a 1907 review article on relativity theory, he raised the question of whether the principle of relativity could be extended to accelerated motion (Einstein 1907, part V). The question was immediately understood as asking whether he could expand the covariance group of relativity theory. Feeling unable to tackle the general question, Einstein considered the simple case of a transformation from an inertial reference frame of special relativity to a reference frame in uniform rectilinear acceleration. In the accelerated frame of reference a homogeneous inertial eld arises. Because of the key empirical fact the the equality of inertial and gravitational mass, Einstein was able to identify this eld as a gravitational eld. He then made the postulate that would dominate the early years of his work on gravitation. In the wording of Einstein (1911, section 1) . . . we assume that the systems K [inertial system in a homogeneous gravitational eld] and K0 [uniformly accelerated system in gravitation free space] are exactly equivalent, that is, . . . we assume that we may just as well regard the system K as being in space free from gravitational elds, if we then regard K as uniformly accelerated. This assumption soon acquired the name `hypothesis of equivalence' (Einstein 1912a, p355) and then `principle of equivalence' (Einstein 1912b, p443). Through it, Einstein generated a novel theory of static gravitational elds (Einstein 1907, part V, 1911,1912a,b). In it, the now variable speed of light played the role of the gravitational potential; light from a heavy body such as the sun would be red shifted; and light grazing a heavy body such as the sun would be de ected. For our purposes, the important point is that Einstein saw in the principle an extension of the principle of relativity. Continuing the above passage he observed: This assumption of exact physical equivalence makes it impossible for us to speak of the absolute acceleration of the system of reference, just as the usual theory of relativity forbids us to talk of the absolute velocity of a system. . . The principle of equivalence formed just one part of Einstein's assault on the problem of extending the principle of relativity. He had also to answer the more general worry that acceleration seemed distinguishable from inertial motion by observable consequences, whereas no such consequences enable us to distinguish inertial motion from rest. Newton had driven home the point in the Scholium to the De nitions of Book 1 of his Principia (1687). He noted that the absolute of rotation of water in a bucket was revealed by the observable curvature of the water's surface. The inertia of the water was responsible for this e ect, leading it to recede from the axis of rotation. + + + General covariance and general relativity 799 +Einstein found his answer to Newton in his reading of Ernst Mach. Mach (1893,p284) pointed out that all that was revealed in Newton's bucket thought experiment was correlation between the curvature of the water and its rotation with respect to the Earth and other celestial bodies. Thus Einstein (1912c) was delighted to report his 1912 theory entailed certain weak eld e ects that promised to convert this correlation into a physical interaction, with the rotation of the stars with respect to the water directly causing the curvature of its surface. He found that the inertia of a test mass is increased if it is surrounded by a shell of inertial masses and that, if these same masses are accelerated, they tend to drag the test mass with it. These results raised the possibility of an idea which he attributed (p39) directly to Mach: . . . the entire inertia of a point mass is an interaction with the presence of all the remaining masses and based on a kind of interaction with them. Einstein (1913,p1261) soon called this idea the `hypothesis of the relativity of inertia.' Clearly if a theory could be found that implemented this hypothesis, Einstein would have succeeded in generalizing the principle of relativity to acceleration. For, in such a theory, the preferred set of inertial frames would cease to be an absolute feature of the background space and time; the disposition of inertial frames of reference would merely be an accident of the overall distribution of matter in the universe. However, by the middle of 1912, Einstein was still far from such a theory. In concluding his response to a polemical assault by Max Abraham, Einstein (1912d, pp1063{4) described his project in terms of the expansion of the covariance of the current theory of relativity and his hope that `the equations of theory of relativity that also embraced gravitation would be invariant with respect to acceleration (and rotation) transformations.' however he confessed that `it still cannot be foreseen what form the general spacetime transformation equations could have.' The Einstein who wrote these words in July 1912 had not yet foreseen that his name would be irrevocably associated with a generally covariant theory. +3.2. The `Entwurf' theory 1912{1915: general covariance gained and lost +All this changed with Einstein's move to Zurich in August 1912. There he began collaborating with the mathematician Marcel Grossmann, a good friend from his student days. Grossman discovered for Einstein the existence of the `absolute di erential calculus' 1 of Ricci and Levi-Civita (1901) and pointed out that this calculus would enable Einstein to construct a generally covariant theory. The focus of this calculus was the fundamental quadratic di erential form +'= +Xn +r;s=1 +arsdxrdxs (2) +which was assumed to remain invariant under arbitrary transformations of the variables x1; : : : ; xn. Of course the modern reader immediately associates this form with the invariant line element of a non-Euclidean surface of variable curvature, such as was introduced by Gauss and developed by Riemann. However, Ricci and Levi-Civita's x1; : : : ; xn were variables and not necessarily geometric coordinates. They were at pains to emphasize that what was then called in nitesimal geometry was just one of many possible applications of their calculus. +1The Ricci-Levi-Civita calculus only later acquired its modern name of `tensor calculus' after Einstein and Grossman (1913) renamed all of Ricci and Levi-Civita's `contravariant and covariant systems' as `tensors' thereby extending the formerly rather restricted compass of the term `tensor.' See Norton (1992, appendix). + + + 800 J D Norton +As late as 1912, Einstein had not adopted the four-dimensional methods of Minkowski, even though these methods had already found their rst text book exposition (Laue 1911). Einstein's 1912 static gravitational theory had been developed using essentially the same mathematical techniques as his 1905 special relativity paper. Thus it is an odd quirk of history that, when Einstein did nally immerse himself in the four-dimensional spacetime approach, he turned to exploit a calculus whose creators sought to skirt its geometric interpretation in favour of a broader interpretation. Einstein and Grossmann published the results of their joint research early the following year with Einstein writing the `Physical Part' and Grossmann the `Mathematical part.' The theory of the resulting paper (Einstein and Grossmann 1913) is commonly known as the `Entwurf ' theory for the title of the paper. `Entwurf einer verallgemeinerten Relativitatstheorie und einer Theorie der Gravitation' (`outline of a generalized theory of relativity and a theory of gravitation'). Its central idea involved the introduction of Ricci and Levi-Civita's fundamental form (2). They started with the invariant interval of Minkowski in di erential form +ds2 = c2dt2 dx2 dy2 dz2 (3) +where (x; y; z; t) are the space and time coordinates of an inertial frame of reference in a Minkowski spacetime. Transforming to arbitrary coordinates x for  = 1; : : : ; 4 (3) +becomes 2 +ds2 = g dxdx : (4) +Einstein employed his principle of equivalence to interpret the matrix of quantities guv that had arisen with the introduction of arbitrary coordinates. In the special case of the principle, the transformation from (3) to (4) is from an inertial coordinate system to a uniformly accelerated coordinate system. In that case, the matrix of coecients g +reduces to that of (3), except that c now is a function of the coordinates (x0; y0; z0). That is, (4) becomes +ds2 = c2(x0; y0; z0)dt2 dx02 dy02 dz02: (30) +According to the principle of equivalence, the presence of a gravitational eld was the only di erence between the spacetime of (3') and that of special relativity (3). Therefore Einstein interpreted the coordinate dependent c of (3') as representing a gravitational eld and, more generally, the g of (4) as representing a gravitational eld. Einstein and Grossmann proceeded to develop essentially all the major components of the nal general theory of relativity. Just one eluded them. The spacetimes represented by (3), (3') and (4) are all at. To treat the general case of the gravitational eld, non- at metrics must also be admitted and, in the nal theory, the decision of which are admitted is made by the gravitational eld equations. Einstein expected these equations to take the now familiar form +G = T (5) +where T is the stress-energy tensor and G a gravitation tensor constructed solely from the metric tensor g and its derivatives. Einstein and Grossmann considered the Ricci tensor as the gravitation tensor|just a hair's breath away from Einstein's nal choice of the Einstein tensor. However they reported that the resulting eld equations failed to give +2Henceforth summation over repeated indices is implied. Einstein himself did not introduce this summation convention until 1916. + + + General covariance and general relativity 801 +the Newtonian limit in the case of weak, static gravitational elds. In their place, to the astonishment of modern readers, they o ered a set of gravitational eld equations that was not generally covariant. Einstein then descended into a long struggle with his imperfect theory that lasted almost three intense years before he emerged victoriously with the nal generally covariant theory in hand.3 +3.3. The hole argument: general covariance condemned +During these three years, Einstein formulated an argument that would decisively redirect his understanding of general covariance. He and Grossmann had been unable to nd acceptable generally covariant eld equations. The so-called `hole argument' purported to show that this circumstance need not worry them since all generally covariant eld equations would be physically uninteresting. Einstein published the argument four times in 1914, appearing, for example, as a later appendix to the journal printing of Einstein and Grossmann (1913). Its clearest exposition was in a review article (Einstein 1914, pp1066{7).4 The argument was beguilingly simple. Einstein asked us to imagine a region of spacetime devoid of matter|the `hole'|in which the stress energy tensor T vanished. He now assumed that we had generally covariant gravitational eld equations and that g was a solution for this spacetime in a coordinate system x . Einstein transformed to a new coor +dinate system x0 , which agreed with x outside the hole but came smoothly to di er from +it within the hole. In the new coordinate system the metric would be g0 and constructed according to the usual tensor transformation law. That is, the same gravitational eld would be represented by g in coordinate system x , and by g0 in coordinate system x0 . At this point Einstein e ected a subtle manipulation that is the key to the hole argument. One could consider the symmetric matrix g(x ) as a set of ten functions of the +variable x and g0(x0 ) as a set of ten functions of the variable x0 . One can now construct +a new set of ten functions g0(x ). That is, take the ten functions of the new matrix g0 and consider them as functions of the old coordinates x . The original g(x ) and the +construction g0(x ) cannot represent the same gravitational eld in di erent coordinate systems. They are both de ned on the same coordinate system x , yet they have di er +ent components, since g and g0 are di erent functions. That is, g(x ) and g0(x ) represent di erent gravitational elds in the same coordinate system. Now, by their construction, the functions g(x ) and g0(x ) will be the same outside the hole, but they will come smoothly to di er within the hole. Thus the two sets of functions represent distinct gravitational elds. Let us call them g and g0. The elds g and g0 are the same outside the hole but come smoothly to di er within the hole. +3This fascinating episode has been dissected in some detail with some help from his private calculation (see Stachel 1980 and Norton 1984). 4For further discussion see Norton (1987). + + + 802 J D Norton +Einstein has presumed the eld equations general covariant. Therefore, if they are solved by the g(x ), then they must be solved by g0(x0 ) and therefore also by the +construction g0(x ). That is, generally covariant gravitational eld equations allow as +solutions the two distinct gravitational elds g and g0. Einstein found this outcome unacceptable. For the one matter distribution outside the hole now clearly fails to determine what the gravitational eld would be within the hole. That is, we could specify the matter distribution and gravitational eld everywhere in spacetime excepting some matter-free hole that could be arbitrarily small in both spatial and temporal extent. Nonetheless generally covariant eld equations would be unable to determine what the gravitational eld would be within this hole. This was a dramatic failure of what he called the law of causality and we might now call determinism. Einstein deemed the failure suciently troublesome to warrant rejection of generally covariant gravitational eld equations as physically interesting.5 +3.4. Einstein's 1916 account of the foundations of general relativity: general covariance regained +In November 1915, Einstein's long struggle with his `Entwurf' theory came to a close. His resistance to general covariance nally broke under the accumulating weight of serious problems in his `Entwurf' theory. His return to general covariance and the nal general theory of relativity were reported to the Prussian Academy in a series of hasty communications that chronicle the tense confusions of these last desperate days.6 Early the following year, Einstein (1916) sent Annalen der Physik a review article on the nal theory. The article's account of the theory's foundations was written with a freedom unavailable to Einstein in the dark years of the `Entwurf' theory. Thoughout those years, Einstein had maintained his allegiance to the relativity of inertia. That allegiance had to rest principally on a sincere hope of what might be demonstrable. He had not demonstrated the unconditional relativity of inertia in his `Entwurf' theory; he was still sure only of weak eld e ects compatible with the relativity of inertia (Einstein 1913, section 9) and similar to those he had found in his 1912 theory. More vexing, however, was the very public failure of general covariance, which compromised the claim that he was extending the principle of relativity. Einstein did not report on equally serious problems that had befallen the principle of equivalence. The simple 1907/1911 version of the principle required only equivalence of uniform acceleration and a homogeneous gravitational eld. Yet in the nal version of the 1912 theory, the principle had to be restricted to in nitesimally small regions of space. Einstein found the need for this restriction extremely puzzling since the restriction was not invoked to homogenize an inhomogeneous eld. Worse, in the `Entwurf' theory, even this restriction failed to save this form of the principle, which had to be reported as a result of his earlier 1912 theory (see Norton (1985, section 4.3) for a discussion). By 1916, Einstein's problem with general covariance had evaporated and with them the problems with the principle of equivalence. Thus the 1916 review article could commence with a more con dent account of the theory's foundations which remains today one of +5It was pointed out much later by Stachel (1980), using mathematical notions not available to Einstein in 1913, that the new gravitational eld g0 was generated from g as the carry along g0 = hg under the di eomorphism h induced by the coordinate transformation x , to x0 . The indeterminism that worried Einstein so profoundly is now routinely obliterated as a gauge freedom associated with arbitrary di eomorphism so that, while g and g0 may be mathematically distinct, they are not judged to represent physically distinct gravitational elds (see Wald 1984, p438). 6Einstein 1915. For disscussion of this episode, see Norton (1984, sections 7,8). + + + General covariance and general relativity 803 +the most widely known of Einstein's accounts. The exposition began with a series of now familiar considerations all of which drove towards general covariance. Both special relativity and classical mechanics, Einstein reported, su ered an epistemological defect. It was illustrated with Einstein's variant of Newton's bucket. Two uid bodies hover in space. They are in an observable state of constant relative rotation about a line that connects them. In spite of the obvious symmetry of this setup, Einstein supposed that one sphere S1 proves to be spherical when surveyed and the other S2 proves to be an ellipsoid of revolution. Classical mechanics and special relativity could explain the di erence by supposing that the rst sphere is at rest in an inertial frame of reference, introduced by Einstein into the argument as a `privileged Galilean space,' and that the second is not. This explanation, Einstein objected, violates the `demand of causality', for these privileged frames are `merely factitious causes' and not an observable thing. The true cause of the di erence must lie outside the system, Einstein continued, immediately identifying the true cause in the disposition of distant masses. In e ect Einstein used his example to conclude that the only theory that could satisfactorily account for this example was one that satis ed the requirement of the relativity of inertia. Any such theory, Einstein continued, cannot single out any inertial frame as preferred. Therefore: The laws of physics must be of such a nature that they apply to systems of reference in any kind of motion. along this road we arrive at an extension of the postulate of relativity. (Einstein's emphasis) Einstein then introduced the principle of equivalence in the form given above in section 3.1 in which it asserts the equivalence of uniform acceleration and a homogeneous gravitational eld. The principle is used to suggest that a theory which implements a generalized principle of relativity will also be a theory of gravitation. Einstein then turns to deal with a complication that arises from using accelerated frames of reference in special relativity. In accelerated frames, in particular in rotating frames, geometry ceases to be Euclidean and clocks are slowed in a position-dependent manner. As a result it turns out that one can no longer easily de ne space and time coordinate systems by the familiar operations of laying out rods and using standard clocks. This apparent complication|and not the need for a generalization of the principle of relativity|leads Einstein to propose general +covariance:7 +The method hitherto employed for laying coordinates into the space-time continuum in a de nite manner thus breaks down, and there seems to be no other way which would allow us to adapt systems of coordinates to the four-dimensional universe so that we might expect from their application a particularly simple formulation of the laws of nature. So there is nothing for it but to regard all imaginable systems of coordinates, on principle, as equally suitable for the description of nature. This comes to requiring that: The general laws of nature are to be expressed by equations which hold good for all systems of coordinates, that is, are co-variant with respect to any substitutions whatever (generally covariant). It is clear that a physics theory which satis es this postulate will also be suitable for the general postulate of relativity. For the sum of all substitutions in any case includes the those which correspond to all relative motions of three-dimensional systems of coordinates (Einstein's emphasis) +7A footnote at the word `imaginable' was omitted from the standard Perrett and Je ery English translation. It says: `Here we do not want to discuss certain restrictions which correspond to the requirement of unique coordination and of continuity.' This now essentially unknown footnote shows that Einstein did at least once apologize for his failure to specify precisely which group of transformations was intended by `any substitutions whatever.' + + + 804 J D Norton +Why did Einstein not simply insist that the generalization of the principle of relativity to accelerated motion forces general covariance? Following the analogy with Lorentz covariance, the generalized principle of relativity would require an extension of the covariance of the theory to include transformations between frames in arbitrary states of motion. But general covariance extends it even further. It includes transformations that have nothing to do with changes of states of motion, such as the transformation between Cartesian and polar spatial coordinates. But, as Einstein indicates, he feels compelled to go to this larger group since he can see no natural way of restricting the spacetime coordinate system. +3.5. The point-coincidence argument +Immediately following the above statement of the requirement of general covariance, Einstein gave another argument for general covariance which John Stachel has conveniently labelled the `point-coincidence argument'. That this requirement of general co-variance, which takes away from space and time the last remnant of physical objectivity, is a natural one, will be seen from the following re exion. All our space-time veri cations invariably amount to a determination of space-time coincidences. If, for example, events consisted merely in the motion of material points, then ultimately nothing would be observable but the meetings of two or more of these points. Moreover, the results of our measurings are nothing but veri cations of such meetings of the material points of our measuring instruments with other material points, coincidences between the hands of a clock and points on the clock dial, and observed point-events happening at the same place and the same time. The introduction of a system of reference serves no other purpose than to facilitate the description of the totality of such coincidences. We allot to the universe four space-time variables, x1, x2, x3, x4 in such a way that for every point there is a corresponding system of values of the variables x1 . . . x4. To two coincident point events there corresponds one system of values of the variables x1 . . . x4 i.e. coincidence is characterized by the identity of the co-ordinates. If, in the place of the variables x1 +. . . x4, we introduce functions of them, x01, x02, x03, x04, as a new system of co-ordinates, so that the system of values are made to correspond to one another without ambiguity, the equality of all four co-ordinates in the new system will also serve as an expression for the space-time coincidence of the two point-events. As all our physical experience can be ultimately reduced to such coincidences, there is no immediate reason for preferring certain systems of co-ordinates to others, that is to say, we arrive at the requirement of general co-variance. +This point-coincidence argument is cited very frequently in the literature since 1916. However its real purpose was essentially completely forgotten until it was rediscovered and revealed by John Stachel (1980). Einstein's 1916 exposition of general relativity contained a very puzzling omission. In the years immediately preceding, by means of the hole argument, Einstein had apparently proved that any generally covariant theory would be physically uninteresting. Yet there was Einstein extolling exactly such a theory without explaining where the hole argument went astray. +That melancholy task of correcting his past error was the real function of the pointcoincidence argument. This was precisely the use to which the argument was put in Einstein's correspondence of December 1915 and January 1916 (see Norton 1987, section 4). According to Einstein's assumption, the physical content of a theory is fully exhausted by a catalogue of the spacetime coincidences it sanctions. Therefore any transformation that preserves these coincidences preserves its physical content. Now the transformation used in the hole argument from the eld g to the mathematically distinct eld g0 is more than a + + + General covariance and general relativity 805 +mere transformation of coordinates. For g and g0 are mathematically distinct elds in the same coordinate system. However the transformation from g to g0 is one that preserves all coincidences. Therefore g and g0 represent the same physical eld. Whatever indeterminism is revealed in the hole argument is a purely mathematical freedom akin to a gauge freedom and o ers no obstacle to the physical interest of a generally covariant theory. Einstein scarcely ever mentioned the debacle of the hole argument again in print. However it continued to inform his ideas about covariance, spacetime, eld and coordinate systems. For example, in executing the hole argument, in order to e ect the transition from g(x ) to g0(x ), one has to assume, in e ect, that the coordinate system x , has +some real existence, independent of the g or g0. For, guratively speaking, one has to remove the eld g, leaving the bare coordinate system x , and then insert the new +eld g0. In a letter of December 26, 1915, to Paul Ehrenfest, Einstein explained that one defeats the hole argument by assuming among other things that `the reference system signi es nothing real'.8 We hear these echoes of the hole argument when Einstein (1922,p21) proclaims in a May 1920 address in Leiden: There can be no space nor any part of space without gravitational potentials; for these confer upon space its metrical qualities, without which it cannot be imagined at all. These same echoes still reverberate in the 1952 appendix to Einstein's popular text Relativity: the Special and the General Theory, when Einstein (1952,p155) insists . . . a pure gravitational eld might have been described in terms of the gik (as functions of the co-ordinates), by solution of the gravitational equations. If we imagine the gravitational eld, i.e. the functions gik, to be removed, there does not remain a space of the type (1) [Minkowski spacetime], but absolutely nothing, and also no `topological space' (Einstein's emphasis). Most recently, the hole argument has enjoyed a revival in the philosophy of space and time literature where, in variant form, it provides a strong argument against the doctrine of spacetime substantivalism (Earman and Norton 1987). For further discussion of the background an rami cations of the hole and point-coincidence arguments see Howard (1992) and Ryckman (1992). +3.6. The Gottingen defense of general covariance +The most prominent legacy of the hole argument in the literature on general relativity does not arise from Einstein's analysis, however. In 1915 and 1917 David Hilbert (1915, 1917) published a two-part paper on general relativity which proved to be enormously in uential. Citing the hole argument, Hilbert (1917,pp59{63) turned to the question of the `principle of causality'. He observed that his formulation of general relativity employed fourteen independent variables, that is, ten metrical components for the gravitational eld and four potentials for the electromagnetic eld. However in the joint theory of gravitational and electromagnetic elds, four identities reduced the fourteen eld equations to only ten independent equations. These four conditions could, however, be absorbed in four stipulations used to specify a coordinate system. Hilbert insisted that his underdetermination of the eld was not physical. Echoing the geometric themes of his Gottingen colleagues Klein and the late Minkowski, he recalled (p61) `. . . an assertion that does not remain invariant under any arbitrary transformation of the coordinate system is marked as physically meaningless' (Hilbert's emphasis). He then argued that the four degrees of freedom did not leave the invariant content of the theory underdetermined. His example was an electron at rest in some coordinate system. A coordinate transformation leaves the electron unchanged in the past of some instant +8As quoted in Norton (1987,p 169). + + + 806 J D Norton +speci ed by time coordinate x4 = 0, but sets it in motion in the future. The two coordinate descriptions are the same in the past, the electron is at rest, but in the future only one describes the electron as moving. The one past can extend to di erent futures. The di erences, however, have no physical signi cance, since the relevant assertions about the electron's motion are not invariant. One could make the invariant by introducing an invariant coordinate system adapted to the spacetime geometry, such as the Gaussian system Hilbert considered. Coordinate based assertions of the electron's motion would now be invariant, but they would no longer be underdetermined since the introduction of the Gaussian system used up the four remaining degrees of freedom. Hilbert's depiction of the indeterminism of a generally covariant theory was in terms of a count of independent eld variables and independent eld equations. It is the version that rapidly came to appear most often in the literature (e.g. Pauli 1921, section 56). The four identities among the eld equations that allowed the underdeterminism were only later connected with the contracted Bianchi identities (see Mehra 1974, section 7.3). Again Hilbert's discussion and his example of the electron was the rst treatment of the Cauchy problem in general relativity, so that the literature on the Cauchy problem can trace its descent back to Einstein's hole argument (see Stachel 1992).9 +3.7. Einstein's three principles of 1918 +In March 1918, Einstein (1918) returned to the question of the fundamental principles of general relativity. As he made clear in his introductory remarks, the paper was provoked by Kretschmann's (1917) criticism (see section 5.2 below). However its purpose was to lay out his understanding of the foundations of his theory. This exposition di ered from the 1916 account in at least one major area. In 1916, Einstein assumed that his generally covariant theory would satisfy the relativity of inertia, although no proof had been given. At best Einstein would have been able to point to weak eld e ects compatible with the relativity of inertia. (These weak eld e ects are of the same type as those he reported in the `Entwurf' theory of Einstein (1913, section 9) and are described in his text (Einstein 1922a, p100)). By 1917, Einstein had found that a simple reading of the relativity of inertia was incompatible with his theory. He reported his failure in an introductory section (section 2) to his famous paper on relativistic cosmology (Einstein 1917). On the basis of the relativity of inertia, he expected that the inertia of a body would approach zero if it was moved suciently far from other masses in the universe. This expectation would be realized in the theory if the spacetime metric adopted certain degenerate values at a mass-free spatial in nity. However Einstein found that such degenerate behaviour was inadmissible in his theory. Instead he seemed compelled to postulate some non-degenerate boundary conditions for the metric at a mass-free spatial in nity, such as Minkowskian values. This Minkowskian boundary condition became the embodiment for Einstein of the failure of the relativity of inertia. For this boundary condition made a de nite contribution to the inertia of a test body that could not be traced to other masses. That is, with these boundary condition, the inertia of a body was in uenced by the presence of other masses, in so far as they a ected the metric eld. However its inertia was not fully determined by the other masses. Therefore, if the relativity of inertia was to be satis ed, it was necessary to abolish these arbitrarily postulated boundary conditions. (The question of whether this was also sucient remained unaddressed.) Einstein succeeded in abolishing these boundary +9Howard and Norton (forthcoming) conjecture that there was an encounter in 1915 between the Gottingen resolution of the hole argument and an unreceptive Einstein, still convinced of the correctness of the hole argument. + + + General covariance and general relativity 807 +conditions at spatial in nity by a most ingenious ploy: he abolished spatial in nity itself. He introduced the rst of the modern relativistic cosmologies, the one we now call the `Einstein universe', which is spatially closed and nite. The price Einstein had to pay turned out to be high. In order for his eld equations to admit the Einstein universe as a solution, he needed to introduce the extra `cosmological' term in his eld equations. In his notation and formulation of 1917, with G representing the Ricci tensor and  a constant, this meant that the old eld equations +G =  (T 1 +2 g T ) +were replaced by +G g =  (T 1 +2 g T ) +The cosmological term is g and  is the cosmological constant. This development was essential background to understanding the three principles Einstein listed in (Einstein 1918,pp241{2) as those on which his theory rested. (a) Principle of relativity. The laws of nature are only assertions of timespace coincidences; therefore they nd their unique, natural expression in generally covariant equations. (b) Principle of equivalence. Inertia and weight are identical in essence. From this and from the results of the special theory of relativity, it follows necessarily that the symmetric `fundamental tensor' (g) determines the metric properties of space, the inertial relations of bodies in it, as well as gravitational e ects. We will call the condition of space, described by the fundamental tensor, the `G- eld.' (c) Mach's principle. the G- eld is determined without residue by the masses of bodies. Since mass and energy are equivalent according to the results of the special theory of relativity and since energy is described formally by the symmetric energy tensor (T), this means that the G- eld is conditioned and determined by the energy tensor. The separation of the principle of relativity and Mach's principle into two distinct principles was clearly the product of Einstein's experience with the cosmological problem. If the Einstein of 1916 had assumed that the relativity of inertia would be satis ed automatically within a generally covariant theory, then the Einstein of 1918 no longer harboured such delusions. The 1918 version of the principle of relativity seems to assert something less than a fully generalized relativity of the motion of bodies. In e ect it merely asserts the key thesis of the point-coincidence argument: the physical content of a theory is exhausted by its catalogue of allowed spacetime coincidences. General covariance follows from this thesis as a consequence. The principle of relativity (a) is now supplemented by the new Mach's principle (c) and it is only their conjunction that begins to resemble Einstein's original goal of a fully generalized relativity of motion. In e ect Mach's principle (c) was intended to capture in a eld theoretic setting the old, Mach-inspired conditions for the metric eld at spatial in nity, which, Einstein reported in 1917, compromised the relativity of inertia. All this was alluded to by Einstein in a footnote to the title `Mach's principle', which also announced that he was introducing the name for the rst time: + + + 808 J D Norton +Up to now I have not distinguished principles (a) and (c) and that caused confusion. I have chosen the name `Mach's principle' since this principle is a generalization of Mach's requirement that inertia be reducible to an interaction of bodies. Einstein's wording of the principle of equivalence (b) was an interesting departure in so far as it now emphasized that the principle depended on the empirical equality of two quantities, inertial and gravitational mass, and that the e ect of the principle had been to unify them completely. However there was little real change from Einstein's earlier use of the principle, as was shown by the remainder of the paragraph that described the principle. In e ect it gave a synopsis of the transition form the line element (3) to (3') and (4) and the resulting interpretation of the non-constant coecients of (3') and (4) as representing the gravitational eld, as well as the inertial and geometric properties of spacetime. +3.8. Mach's principle forsaken +For all his e orts, Einstein's portrayal of the foundations of general relativity had still not reached its nal form with the 1918 list. Over the years following, the principle of relativity and of equivalence retained their 1918 forms. However Einstein came to abandon Mach's principle. The seeds of Einstein's disenchantment with Mach's principle were becoming apparent as early as 1919. Einstein (1919, section 1) described its o spring, the cosmological term added to his 1915 eld equations, as `gravely detrimental to the formal beauty of the theory'. With the discovery of the expansion of the universe, Einstein formally disowed the cosmological term (Einstein and de Sitter 1932). In any case, the augmentation of his eld equations with the cosmological term had forced neither the relativity of inertia nor Mach's principle into his theory, for it had not eliminated the possibility of essentially matter-free solutions of the eld equations. In such solutions, the inertia of a test body could not be attributed to other masses. These solutions were the subject of an extended exchange in publication an in private between Einstein and de Sitter towards the end of the 1910s (See Kerzberg 1989). Einstein also began to distance himself from the relativity of inertia. Whereas the idea was urged without reservation up to 1916, he soon came to describe it as a very signi cant idea, but one of essentially historical interest only. For example, Einstein (1924, p87) attributed to Mach the idea that inertia arose as an unmediated interaction between masses. But he dismissed it casually as `logically possible, but cannot be considered seriously any more today by us since it is an action-at-a-distance theory'.10 Einstein (1924, p90) did still maintain that the metric is fully determined by ponderable masses in a spatially nite cosmology according to his theory, although the term `Mach's principle' was not used. As time passed, Einstein had fewer and fewer kind words for this Machian approach to inertia. He explained in 1946 for example in his Autobiographical notes (1949, p27) Mach conjectures that, in a truly reasonable theory, inertia would have to depend upon the interaction of the masses, precisely as was true for Newton's other forces, a conception that for a long time I considered in principle the correct one. It presupposes implicitly, however, that the basic theory should be of the general type of Newton's mechanics: masses and their interaction as the original concepts. Such an attempt at a resolution does not t into a consistent eld theory, as will be immediately recognized. His 1918 Mach's Principle had been an attempt to translate this requirement on masses and their interactions into eld theoretic terms, but he soon seemed to lose enthusiasm even for this enterprise. The diculty was that the 1918 principle required that the metric eld g be determined by the masses of bodies as represented by the stress-energy tensor +10The same point is made less forcefully in Einstein (1922, pp17{18) and Einstein (1922a, p56) + + + General covariance and general relativity 809 +T. However this gave a primary determining function to a quantity, T, which Einstein (1949, p71) reported he had always felt was `a formal condensation of all things whose comprehension in the sense of a eld theory is still problematic' and one that was `merely a makeshift'. Einstein gave a nal synopsis of Mach's principle in a letter of February 2, 1954 to Felix Pirani in the year prior to his death. Citing the above diculty with the stress-energy tensor and the fact that this tensor presumes the metric, he labeled his 1918 version of Mach's principle `a ticklish a air' and concluded `In my opinion we ought not to speak about Mach's principle any more.'11 +3.9. Einstein's causal objection to absolutes +When Einstein disowed the relativity of inertia and Mach's principle, he actually disowed somewhat less than it rst seemed. Both these principles were introduced to solve a problem in earlier theories of space and time: these theories were defective in the way they used inertial systems as causes. Einstein still clearly maintained that the problem was serious and that his general theory of relativity had solved it. However he had originally thought the solution was best expressed in terms inspired by his reading of Mach; that is, as a generalized relativity of the motion of bodies. As he put it in Einstein (1913, p1260) To talk of the motion and therefore also acceleration of a body A in itself has no meaning. One can only speak of the motion or acceleration of a body relative to other bodies B, C etc. What holds in kinematic relation of acceleration ought also to hold for the inertial resistance, with which bodies oppose acceleration . . . He was led away from this Machian characterization of the solution by his work on Mach's principle and the cosmological problem, as well as his preference for eld rather than body as a primitive notion. We shall see that his mature characterization of the solution was that general relativity allowed space and time to be mutable. They no longer just acted causally, they could also be acted upon and, in this sense, had lost their absolute character. In Einstein's mature view, it is this special causal property that distinguishes general relativity from earlier theories and possibly even justi es the name `general relativity', in so far as it is the eld theoretic translation of Einstein's original notion of the generalized relativity of the motion of bodies. In the early years of Einstein's theory, the causal defect was located most prominently in the mere fact of the older theories' use of an inertial reference system as a cause. Thus in Einstein's 1916 review article, he sought to account for the centrifugal bulges in a rotating uid body (see section 3.4 above). To say that the body bulges because it rotated with respect to an inertial frame of reference is to introduce a `merely factitious cause, and not a thing that can be observed' (1916, p113). This same example is treated similarly in Einstein (1914a,pp344{6), Einstein (1917a) makes clear the sort of cause that he would nd acceptable in his popular exposition of relativity. In ch XXI he asks for the reason for the preferred status of inertial systems. He draws an analogy with two pans of water on a gas range. One is boiling, one is not. The di erence, Einstein insists, only becomes satisfactorily explained when we notice the bluish ame under the boiling pan and none under the other. Einstein soon came to stress a di erent aspect of these earlier theories as causally defective. He identi ed this aspect with their absolute character. In his Meaning of relativity (1922a, p55) he wrote in parody of Newton's Latin +11Translation from Torretti (1983, p202) with `dem Mach'schen Prinzip' rendered as `Mach's principle'. + + + 810 J D Norton +. . . from the standpoint of the special theory of relativity we must say, continuum spatii et temporis est absolutum. In this latter statement absolutum means not only `physically real', but also `independent in its physical properties, having a physical e ect, but not itself in uenced by physical conditions'. And he continued to explain that such absolutes are objectionable since (pp55{6) . . . it is contrary to the mode of thinking in science to conceive of a thing (the spacetime continuum) which acts itself, but which is not acted upon. The text immediately turned to Mach's ideas and, later (pp99{108) to the weak eld e ects compatible with the relativity of inertia and his 1917 eld formulation of this idea in a spatially closed cosmology. Around the same time, Einstein's briefer summaries advertised general relativity as eliminating the absoluteness of space and time (Einstein 1972, p260):12 Space and time were thereby divested not of their reality but of their causal absoluteness|i.e.a ecting but not a ected. In these briefer summaries, Einstein was no longer insisting that the spacetime metric was to be fully determined by the distribution of masses. Space and time had lost their absoluteness simply because they were no longer immutable. By the 1950s, as Einstein explained to Pirani, he no longer endorsed his 1918 Mach's principle. However he did retain the idea that the earlier theories were causally defective in admitting such absolutes (e.g. Einstein 1950, p348) and, as he explained in the `completely revised' (p0) 1954 appendix to his Meaning of relativity (1922, p139{40), general relativity had resolved the problem as its essential achievement: It is the essential achievement of the general theory of relativity that it has freed physics from the necessity of introducing, the `inertial system' (or inertial systems). . . . Thereby [in earlier theories], space as such is assigned a role in the system of physics that distinguishes it from all other elements of physical description. It plays a determining role in all processes, without in its turn being in uenced by them. This view of the de ciency of earlier theories and general relativity's achievement is not one that grew in the wake of Einstein's disenchantment with Mach's principle. Rather, it was present even in his earliest writings beneath the concerns for the relative motion of bodies and the observability of causes. Einstein (1913, pp1260{1) makes the essential point: . . . in [theories current today], the inertial system is introduced; its state of motion, on the one hand, is not conditioned by the status of observable objects (and therefore caused by nothing accessible to perception) but, on the other hand, it is supposed to determine the relations of material points. A footnote earlier in the paragraph also tried to identify what was so unsatisfactory about inertial systems. What is unsatisfactory about this is that it remains unexplained how the inertial system can be singled from other systems. Thus we have here the enduring core of the cluster of ideas that led Einstein to the relativity of inertia and Mach's principle: his concern that, through their introduction of inertial systems, earlier theories allowed absolutes that acted but could not be acted upon. Finally, we may ask whether the `essential achievement' of general relativity, the elimination of the absolute inertial systems, follows automatically from general covariance in Einstein's view, so that general covariance would then truly amount to a generalized principle of relativity in a form adapted to a eld theory. It is hard to nd a clear answer in Einstein's writings. His 1918 catalogue of three principles suggested that the requirement of general covariance (`(a) principle of relativity') needed to be supplemented by something additional (`(c) Mach's principle') to realize fully the general relativity of motion. +12See also Einstein (1922, p18, 1924, p88). + + + General covariance and general relativity 811 +Einstein's text suggests this without clearly stating it, for Einstein (1918, p241) introduces the three principles with the remark that they are `in any case in no way independent from each other'. This it is not clear whether these particular two of the three principles really are independent or, if they are not, whether general covariance somehow leads to Mach's principle. Perhaps the best answer we will nd is Einstein's repeated insistence that general covariance, in conjunction with the requirement of simplicity, leads us directly to general relativity (see, for example, Einstein (1952, pp 152{3, 1949, pp71{3, 1933, p274)). And it is this theory that eliminates the absoluteness of the inertial system. +4. The favourable text-book assimilation of Einstein's view: fragmentation and mutation +Although Einstein had to struggle to gain acceptance of this theory in its earliest years (especially prior to 1916), by 1920 Einstein's new theory was widely celebrated. The extravagant publicity surrounding the success of Eddington's 1919 eclipse expedition had even launched Einstein into the popular press and public eye. During this period, the vast majority of accounts of Einstein's theory merely sought to recapitulate Einstein's own account. Thus began the tradition of writing in what I call the favourable assimilation of Einstein's view and which is to be reviewed in this section. I shall consider an account of the foundations of general relativity favourable to Einstein's view if it names some or all of Einstein's three principles of 1918 as foundations of the theory: principle of relativity/covariance, principle of equivalence and Mach's principle; it must include at least the rst principle. Two things will become clear about the favourable reception of Einstein's account of the foundations of general relativity. First, it is very widespread and still a major tradition today. Second, what is often o ered as a recapitulation of Einstein's account|even if only tacitly|can di er in very signi cant ways from what Einstein really said. Most prominently, the relativity of inertia and Mach's principle is only infrequently reported as part of the foundations of general relativity in more technical expositions. This disfavour is not a response to Einstein's own later disillusionment with Mach's principle. From the earliest moments, the principle failed to nd a place in the majority of accounts within more technical expositions. Rather the favourable accounts rapidly stabilized, most commonly, into locating the foundations of general relativity in the principle of equivalence and the principle of relativity. Even here, these accounts have failed to remain faithful to Einstein's viewpoint. They almost exclusively employ an in nitesimal principle of equivalence, a variant form that Einstein never endorsed and was quite di erent in outlook from Einstein's own form. In order to gauge the magnitude and character of the favourable reception, this section will review the favourable accounts of the foundations of general relativity as they have appeared in the textbooks on general relativity. The review is also limited principally to expositions that either proved a self-contained exposition of tensor calculus or sucient di erential geometry for general relativity or presume such knowledge in the reader and that proceed at least as far as a formulation of the gravitational eld equations. We should note also that the favorable reception extends beyond the realm of relativity theory. Aguirre and Krause (1991, p508) are prepared to label a mechanics as `general relativistic' merely because it is generally covariant. Jean Eisenstaedt (1986, 1989) has described the rising and falling fortunes of general relativity. After an initial period of great interest and activity in the late 1910s and early 1920s, the theory fell into decades of neglect because of many factors: a sense that the theory had only slender con rmation, that its practical utility to physicists was small and + + + 812 J D Norton +that the theory had been eclipsed by the developments in quantum theory. The 1960s saw a new vigour in work on the theory, in part due to a renewed interest in empirical tests of the theory and to the exploitation of new, more sophisticated mathematical tools. In the following, the favourable receptions is divided into periods re ecting these shifts in intensity of work. First, however, I will review the special problem of the principle of equivalence. +4.1 Einstein's principle of equivalence as a covariance principle and its later misrepresentation +There are many instances of later accounts misrepresenting Einstein's ideas. None is as universal and complete as the later treatments of Einstein's principle of equivalence. In his Meaning of Relativity, Einstein gives a statement of the principle typical of all his writing. K is an inertial system in special relativity and K0 a system of coordinates uniformly accelerating with respect to K. Having noted that free masses in K0 are accelerated `just as if a gravitational eld were present and K0 unaccelerated', Einstein (1922a, p57{8) then +writes: +. . . there is nothing to prevent our conceiving this gravitational eld as real, that is, the conception that K0 is `at rest' and a gravitational eld is present we can consider as equivalent to the conception that only K is an `allowable' system of co-ordinates and no gravitational eld is present. The assumption of the complete physical equivalence of the systems of coordinates, K and K0, we call the `principle of equivalence'; . . . [it] signi es an extension of the principle of relativity to co-ordinate systems which are in non-uniform motion relative to each other. In fact, through this conception we arrive at the unity of nature of inertia and gravitation. Einstein however, is nearly universally understood as urging a rather di erent principle, which I shall call the `in nitesimal principle of equivalence'. A canonical formulation is given in Pauli (1921, p145): For every in nitely small world region (i.e. a world region which is so small that the space- and time-variation of gravity can be neglected in it) there always exists a coordinate system K0(X1; X2; X3; X4) in which gravitation has no in uence either on the motion of particles or any other physical process. The key idea here is that in adopting a suciently small region of spacetime, an arbitrary gravitational eld becomes homogenous and can be transformed away by a suitable choice of coordinate system. This principle exists in many variant forms. Sometimes it is strengthened to require that when the gravitational eld is transformed away we recover special relativity locally (for example, Misner et al. 1973, p386) With somewhat di erent quali cations, Pauli's in nitesimal principle corresponds to Dicke's `strong equivalence principle' (Roll et al., 1964, p444). Dicke's `weak equivalence principle', however, requires only the uniqueness of gravitational acceleration, which amounts to requiring that the trajectories of free fall of suitably idealized bodies are independent of their constitutions. Unlike most other writes, Pauli (1921, p145) acknowledged that his in nitesimal version of the principle of equivalence di ered from Einstein's, suggesting that, where Einstein's principle applied only to homogeneous gravitational elds, Pauli's version was for the `general case'. However the di erences ran far deeper than Pauli allowed and pertain to quite fundamental questions of the role of the principle of equivalence in general relativity. These di erences can be summarized in three essential aspects of the principle which remained xed throughout Einstein's writings on general relativity, from the earliest moments in 1907, to his nal years in the 1950s:13 +13The case for these di erences betwee Einstein's version and the common in nitesimal version + + + General covariance and general relativity 813 + Einstein's principle of equivalence was a covariance principle. Special relativity required the complete physical equivalence of all inertial coordinate systems; for Einstein, general relativity required the complete equivalence of all coordinate systems. Einstein's principle of equivalence required the complete equivalence of a set of coordinate systems of intermediate size: inertial systems plus uniformly accelerated coordinate systems. That is, the principle sanctioned the extension of the covariance of special relativity beyond Lorentz covariance but not as far as general covariance. Thus, for Einstein, the principle of equivalence was a relativity principle intermediate in range between the principle of relativity of special relativity and of general relativity. The point is so important for our concerns here that it is helpful to have it in Einstein's own words (1950, p374): This is the gist of the principle of equivalence: In order to account for the equality of inert and gravitational mass within the theory it is necessary to admit non-linear transformations of the four coordinates. That is, the group of Lorentz transformations and hence the set of `permissible' coordinate systems has to be extended. Or, more succinctly, in an article devoted to explicating precisely what he intended with his principle of equivalence, Einstein (1916a, p641) wrote in emphasized text: The requirement of general covariance of equations embraces that of the principle of equivalence as a quite special case. The function of the alternative, in nitesimal principle of equivalence is to stipulate that a spacetime of general relativity with an arbitrary gravitational eld is in some sense locally|that is, in in nitesimal regions|like the spacetime of special relativity. (Einstein objected in correspondence with Schlick to the latter's use of this idea, pointing out to Schlick that the sense in which special relativity holds locally must be so weak that accelerated and unaccelerated particles cannot be distinguished. For details, see Norton (1985, section 9).) As a covariance principle, Einstein's version of the principle served no such function. Therefore it was invariably restricted in the following related ways:  Einstein's principle of equivalence was applied only in special relativity to what we now would call Minkowski space-times. That is, the inertial coordinate system K of Einstein's formulation of the principle is not some kind of free fall coordinate system of general relativity. It is simply an inertial coordinate system of special relativity. Thus the coordinate systems K and K0 are both coordinate systems of a Minkowski spacetime. Because of this, we would now be inclined to picture the entire principle as operating within special relativity. This seems not to have been Einstein's view. He seems to have regarded special relativity supplemented with the principle of equivalence as having more physical content than special relativity alone. The supplemented theory had a wider covariance and it dealt with a new phenomenon, homogeneous gravitational elds.  Einstein's principle of equivalence was not a prescription for transforming away arbitrary gravitational elds; it was just a recipe for creating a special type of gravitational eld. Einstein's principle of equivalence gave a recipe for creating a homogeneous gravitational eld by transforming to a uniformly accelerated coordinate system. The in nitesimal principle gives a recipe for transforming away an arbitrary gravitational eld: one rst homogenizes it by considering an in nitesimal region of spacetime and then transforms it away by the reverse transformation of Einstein's principle. Einstein repeatedly insisted that his principle of equivalence did not allow one to transform away an arbitrary gravitational eld, but only gravitational els of a quite special type, those produced by acceleration +of the principle is laid out is some detail in Norton (1985) + + + 814 J D Norton +of the coordinate system. (Einstein devotes a paragraph of near page length to this point (1916a, pp640{1). See Norton (1985, section 2).)14 +4.2. The early years: 1916{1930 +Einstein had named Mach's principle as one of the three fundamental principles of general relativity. However, the principle or its precursor, the relativity of inertia, has played the least role in accounts of the foundations of general relativity. Typically the principle does not appear in the discussion of the foundations of the theory. If it appears in an exposition, it arises most commonly later in the context of the cosmological problem and not always in a favourable light, even in expositions otherwise well disposed to Einstein's viewpoint. This pattern was set an the earliest moments. In 1916 and 1917 the Dutch astronomer de Sitter took up the task of allowing the Germans and British to exchange more than artillary shells. He presented a three part report to the Britisch royal Astronomical Society on Einstein's new theory of gravitation ( de Sitter 1916). Whilst otherwise favourable to Einstein, its second part concluded with criticism of Einstein's notion of the relativity of inertia. Development of this criticism continued in the third part. Einstein's 1917 work on the cosmological problem and his 1918 formulation of Mach's principle did not improve the reception of his ideas on the origin of inertia. Laue's (1921,pp179{80) early general relativity text mentions them only in passing as incompatible with Minkowskian boundary conditions at spatial in nity. He nds the whole question physically too unclari ed to warrant further discussion. Pauli (1921) does give the question more coverage, but only in a later, closing section (section 62) Einstein's ideas on the relativity of inertia gured more prominently in more popular expositions of general relativity. For example Freundlich (1919, section 4), Thirring (1922, section XV), Born (1924, ch VII, section 1) and Kop (1923, pp 2{5, 191{5) treat the relativity of inertia. Indeed, the more popular the text, the more likely we are to nd these ideas used to explain the foundations of general relativity. The literature on Mach's principle has become enormous and is ourishing today. However its concerns have come to diverge from the concerns of this article, general covariance and the foundations of general relativity. The interested reader is referred to Reinhart (1973) and Torretti (1983, pp194{202) for further discussion. What is most important for our concerns is that the majority of expositions of relativity theory from this period emphasize the general covariance of general relativity as especially important. Of course this emphasis was justi ed if only for the novelty of general covariance. However the achievement of general covariance was also routinely assumed to ensure automatic satisfaction of a generalized principle of relativity. In some expositions this assumption was discussed in detail, in others it was merely suggested by labelling the requirement of general covariance, a principle of relativity. Accounts that emphasize general covariance and presume an automatic connection to a generalized principle of relativity include: de Sitter (1916, pp700{02), Freundlich (1919, p28), Carmicheal (1920, ch VII), Page (1920, p387), Schlick (1920, pp52{3), Cunningham (1921, ch VII), De Donder (1921, pp10{14), Laue (1921, p21), Pauli (1921, section 52), Weyl (1921, section 27), Becquerel (1922), Kottler (1922, pp188{9), Thirring (1922, p151), Kop (1923), Born (1924, ch VII), Reichenbach (1924, p141), Levi-Civita (1926, p294), Levinson and Zeisler (1929, p70). Some of these accounts explicitly invoke Einstein's point-coincidence argument to +14Einstein himself never employed the trick of homogenizing an arbitrary gravitational eld by considering in nitesimal regions of spacetime. In 1912, when his principle still dealt only with homogenous gravitational elds, he was forced to restrict it to in nitesimal regions of space to overcome certain technical diculties with this theory of static gravitational elds. When they were overcome, the restriction disappeared. See Norton (1985, section 4.3). + + + General covariance and general relativity 815 +establish general covariance. They include de Sitter (1916, pp700{02), Carmicheal (1920, ch VII), Schlick (1920, pp52{3). Many of the expositions also place great emphasis on the principle of equivalence. A few from the very earliest years state the principle in exactly Einstein's fashion: Thirring (1922, p109), Kop (1923, p110) (also Carmichael (1920, p80), although critically). Others employ the now familiar in nitesimal principle of equivalence, other variant formulations of the principles or give vague characterizations of the principle that defy clear classi cation. The following at least name a principle of equivalence in the foundations of general relativity: Freundlich (1922, section 55), Kottler (1922, p 192), Born (1924 ch VII), Reichenbach (1924, pp 141{2). +4.3. The lean years: 1930{1960 +During these three lean decades for general relativity, the volume of publication fell to the merest trickle. Within that trickle, Einstein's view of general covariance remained a dominant theme. Accounts of general relativity which emphasized the general covariance of the theory and either explicitly or tacitly took this general covariance to extend the principle of relativity include: Bergmann (1942, ch X), Schrodinger (1950, p2), Moller (1952, ch VII), Jordan (1955, section 14), Kratzer (1956, section 15), Bargmann (1957, p162), Tonnelat (1957, ch XI) All but Schrodinger and Jordan introduce a principle of equivalence by name. Moller (1952, pp219{20) introduces general relativity with a discussion of the relativity of inertia. Tolman (1934, p3 and ch VI) is exceptional in o ering Einstein's three principles of 1918|the principle of covariance, the principle of equivalence and Mach's principle|as the foundations of general relativity. However his version of the principle of equivalence is the in nitesimal version never endorsed by Einstein and he accepts Kretschmann's view of the physical vacuity of the principle of covariance, while insisting with Einstein on its heuristic value. +4.4. Rebirth 1960{1980 +The renaissance of general relativity in the 1960s brought clearer divisions in the literature on the foundations of general relativity. As we shall see below, one increasingly important strand either simply ignored Einstein's view of the foundations of the theory or became quite strident in its denunciation of Einstein's view. Another sought to repair Einstein's account in the face of such assaults. A major part of the literature, however, continued in simple assent with Einstein's view, only making smaller adjustment according to taste. Most commonly, accounts in this last category found both an in nitesimal principle of equivalence and the principle of general covariance in the foundations of general relativity. Such accounts include: Weber (1961, sections 1.3, 2.4), Bergmann (1961, 1962), Lawden (1962, ch 6), Rosser (1964, sections 12.1, 12.2), McVittie (1965, ch 4), Yilmaz (1965, ch 15, 16), Skinner (1969, ch 3), Davis (1970, 5.I.2), Prasanna (1971, preface, ch 1), Mavrides (1973, sections III.4, II.5), Papapetrou (1974, Introduction, section 18), Pathria (1974, ch 6,7), Bowler (1976, ch 9), Adler, Bazin and Schi er (1977, p60 and section 5.1), Stephani (1977, section 8.1), Treder et al. (1980, Introduction). Most of these accounts explicitly connected general covariance with a generalized principle of relativity, either in name or by explicit discussion. These include: Bergman (1961, 1962), Lawden (1962, ch 6), Rosser (1964, sections 12.1, 12.2), Yilmaz (1965, ch 15, 16), Prasanna (1971), Mavrides (1973, sections III.4,), Papapetrou (1974, Introduction), Pathria (1974, ch 6,), Bowler (1976, ch 9), Adler, Bazin and Schi er (1977, p60 and section 5.1), Stephani (1977, section 8.1), + + + 816 J D Norton +Treder et al. (1980, Introduction). Skinner (1969, section 3.3.1) reported that the principle of general relativity required something beyond the principle of covariance: `the laws of physics must determine the geometry of spacetime appropriate for a particular physical circumstance'. Two accounts portrayed general covariance as a generalized principle of relativity but did not place the principle of equivalence by name in the foundations of general relativity: Charon (1963, lecon 8), Atwater (1974). Mach's principle is mentioned by Lawden (1962, p133). Work on general relativity in this period also gave rise to a variant form of the principle of general covariance. Weinberg (1977, pp91{2) de ned his principle of general covariance as: It states that a physical equation holds in a general gravitational eld, if two conditions are met: 1. The equation holds in the absence of gravitation: that is, it agrees with the laws of special relativity when the metric eld g equals the Minkowski tensor  and when the ane connection vanishes. 2. The equation is generally covariant; that is, it preserves its form under a general coordinate transformation x ! x0. The novelty, of course, is that the second condition alone is usually taken as the principle of general covariance, whereas the rst looks like a form of the in nitesimal principle of equivalence. Indeed Weinberg presents the principle as an alternate form of the in nitesimal principle of equivalence and shows how it follows from the principle of equivalence. He insists that it is not a relativity principle like the Lorents invariance of special relativity. Bose (1980, ch 1) locates the foundations of general relativity in a local principle of equivalence and its re-expression in a two condition principle of general covariance equivalent to Weinberg's. Similarly Foster and Nightingale (1979, ppxi-xiii) locate the foundations of general relativity in an in nitesimal principle of equivalence and a version of the principle of general covariance essentially the same as Weinberg's. They strengthen Weinberg's condition 2. to read [2'.] the equation is a tensor equation (i.e. it preserves its form under general coordinate transformation). The strengthening lies in the fact that not only tensor equations are covariant under arbitrary coordinate transformations. See also Treder et al. (1980) +4.5. Recent years since 1980 +The years since 1980 have seen no resolution of the disagreements over the foundations of general relativity. As we shall see later, the literatures that reject Einstein's account or seek major repairs continue to ourish. At the same time, a signi cant literature retains a viewpoint almost as close to Einstein's as the favourable reception in the 1920s. Broadly, in this latter literature, the foundations of general relativity are still located within an in nitesimal principle of equivalence and a principle of general covariance. Two accounts o er essentially Weinberg's view. Both Straumann (1984, ch 2) and Kenyon (1990, ch 1) base general relativity on an in nitesimal principle of equivalence. (Kenyon discusses both Dicke's weak and strong version, with the latter amounting to an in nitesimal principle.) Kenyon (1990, section 6.4) gives a formulation of the principle of general covariance which is essentially Weinberg's as strengthened by Foster and Nightingale (see above). Without explicitly introducing the name, principle of general covariance, Straumann (1984, section 1.3) provides two requirements which are `a mathematical formulation of the principle of equivalence'. The rst is actually the principle of minimal coupling, a version of the principle of equivalence (Trautman 1965, Anderson 1967, p337, + + + General covariance and general relativity 817 +Anderson and Gauteau 1969). The second requirement is essentially Weinberg's version of the principle of general covariance. +De Felice and Clarke (1990, p7{13) locate the foundations of general relativity in the familiar in nitesimal principle of equivalence and principle of general covariance. Cameli (1982, section 1.4, 1.5) locates the foundation of the theory in these same two principles. He does, however, delineate three versions of the principle of general covariance which, he notes, are `not quite equivalent'. 1. All coordinate systems are equally good for stating the laws of physics. Hence all coordinate systems should be treated on the same footing, too. 2. The equations that describe the laws of physics should have tensorial forms and be expressed in a four-dimensional Riemannian spacetime. 3. The equations describing the laws of physics should have the same form in all coordinate systems. +Ellis and Williams (1988, section 5.2) locate the foundations of the theory in an in nitesimal principle of equivalence and what they call an extension of the principle of relativity: `the laws of physics are the same for all observers, no matter what their state of motion'. The term principle of general covariance is not mentioned. Sexl and Urbantke (1983) treat all three of Einstein's principles of 1918. The principle of equivalence (section 1.2) is given most emphasis, although in it in nitesimal form. Mach's principle and the principle of general covariance are mentioned only apparently for historical interest (section 4.5), with the latter o ered as Einstein's attempt to satisfy the former. +Finally, d'Ivorno (1992, ch 9) in a chapter entitled `The Principles of General Relativity', acknowledges that these principles have been a source of much controversy. However, as principles fundamental to general relativity or at least serious candidates for them, he presents Einstein's three principles of 1918, the Anderson and Gautreau principle of minimal coupling and a principle of correspondence (with Newtonian gravitation theory and special relativity in the limiting cases). The in nitesimal principle of eqivalence is presented as the `key principle'. Mach's principle is given three formulations, all closely connected with Einstein's cosmological ideas of 1917 and 1918. d'Ivorno nds the `full import' of the principle of general relativity ('all observers are equivalent') contained in the principle of general covariance (`the equations of physics should have tensorial form'). And, the hole argument, which gured so prominently in Einstein's early thinking about general covariance, is discussed in section 13.6. To my knowledge, this is the rst time the hole argument has been discussed in a general relativity text in over half a century. The hole argument has also recently reappeared in the physics journal literature. See, for example, Rovelli (1991). +5. Is general covariance physically vacuous? +5.1 Kretschmann's objection: the point-coincidence argument turned against Einstein +In the tradition that is skeptical of Einstein's account of the foundations of general relativity, the best known of all objections is due to Kretschmann (1917, pp575{6). He began his paper with the remarks.15 +15I have suppressed Kretschmann's footnotes in this passage to other literature. For further discussion see Norton (1982, section 8). See also Howard and Norton (forthcoming) for speculation that these footnotes direct readers to Einstein's unacknowledged source for his point-coincidence argument, Kretschmann (1915)! + + + 818 J D Norton +The forms in which di erent authors have expressed the postulate of the LorentzEinstein theory of relativity|and especially the forms in which Einstein has recently expressed his postulate of general relativity|admit the following interpretation (in the case of Einstein, it is required explicitly): A system of physical laws satis es a relativity postulate if the equations by means of which it is represented are covariant with respect to the group of spatio-temporal coordinate transformations associated with that postulate. If one accepts this interpretation and recalls that, in the nal analysis, all physical observations consist in the determination of purely topological relations (`coincidences') between objects of spatio-temporal perception, from which it follows that no coordinate system is privileged by these observations, then one is forced to the following conclusion: By means of a purely mathematical reformulation of the equations representing the theory, and with, at most, mathematical complications connected with that reformulation, any physical theory can be brought into agreement with any, arbitrary relativity postulate, even the most general one, and this without modifying any of its content that can be tested by observation. Kretschmann's point is that there must be something more to a relativity principle than covariance. For he argues that we can take any theory and reformulate it so that it is covariant under any group of transformations we pick; the problem is not physical, it is merely a challenge to our mathematical ingenuity. In brief, general covariance is physically vacuous. This at least, is how Kretschmann's point has been understood almost universally and it is almost what he actually argued. His real objection was a little more subtle. It depended on a non-trivial assumption that virtually all later commentators fail to report16 All physical observations consist in the determination of purely topological relations (`coincidences') between objects and spatio-temporal perception. This assumption is clearly recognizable to us as the basic premise of Einstein's own pointcoincidence argument (see section 3.5 above). There can be no question of the importance of this assumption to Kretschmann's point even though it is buried in the grammar of his statement. A little later, he repeats it (p579). . . . according to the investigations of Ricci and Levi-Civita (1901) it may scarcely be doubted that one can bring any physical system of equations into a generally covariant form without alteration of its observationally testable content. This is obvious from the beginning, if one once again recalls that strictly only purely topological facts of natural phenomena or, according to Einstein, coincidences are observable. Thus, allowing that Kretschmann's mention of `topological facts' alludes to his own version of the point-coincidence argument (see Howard and Norton, forthcoming), we nd that Kretschmann's real objection is this: if we accept the point-coincidence argument, then any theory can be given a formulation of arbitrary covariance. This is a most striking reversal of fortunes. The point-coincidence argument had been Einstein's salvation from the hole argument and permitted his return to general covariance. However, in advocating the point-coincidence argument, Einstein had in e ect already agreed to virtually everything in Kretschmann's objection. To establish the admissibility of general covariance for his own theory, Einstein had allowed that the physical content of a theory resides solely in the observable coincidences it sanctions. Since these coincidences are preserved under arbitrary coordinate transformation, the physical content of a theory is una ected by the adoption of a generally covariant formulation. What Kretschmann noticed was that this argument depended on nothing peculiar to general relativity, so it +16I cannot resist speculating that this misreading is at least in part due to the bewildering complexity of his German prose, which has been disentangled considerably in the above translation. This translation also slightly corrects the translation of Norton (1992, section 8.1). + + + General covariance and general relativity 819 +could equally be used to establish the admissibility of a generally covariant formulation of any theory. Again it did not depend on the fact that the covariance group was the general group, so the same argument established the admissibility of formulations of any theory of arbitrary covariance. +5.2. Einstein's reply +Einstein (1918) responded to Kretschmann's objection. Having laid out the three principles upon which he believed general relativity to be based, he turned to Kretschmann's objection, which he restated correctly with its now lost premise (p 242): Concerning (a) [principle of relativity], Herr Kretschmann observes that a principle of relativity, formulated in this way, makes no assertions over physical reality, i.e. over the content of the laws of nature; rather, it is only a requirement on their mathematical formulation. That is, since all physical experience relates only to coincidences, it must always be possible to represent experiences of the lawful connection of these coincidences by generally covariant equations. Therefore he believes it necessary to connect another requirement with the requirement of relativity. Einstein had little choice but to accept Kretschmann's point. The alternative was to renounce the point-coincidence argument that he had advertised so widely. However he tried to salvage something of the special connection between general covariance and general relativity in the heuristics of theory choice. He continued: I believe Herr Kretschmann's argument to be correct, but the innovation proposed by him not to be commendable. That is, if it is correct that one can bring any empirical law into generally covariant form, the principle (a) still possesses a signi cant heuristic force, which has already proved itself brilliantly in the problem of gravitation and rests on the following. Of two theoretical systems compatible with experience, the one is to be preferred that is the simpler and more transparent from the standpoint of the absolute di erential calculus. Let one bring Newtonian gravitational mechanics into the form of absolutely covariant equations (four dimensional) and one will certainly be convinced that principle (a) excludes this theory, not theoretically, but practically! Thus Einstein seems to accept Kretschmann's objection, begrudgingly, with a quali cation on the role of general covariance in theory choice and with the reservation that general covariance in all theories would be impractical. Indeed it is ironic that the version of the principle of relativity given in this same paper by Einstein (quoted in section 3.7 above) essentially just restates Kretschmann's point.17 Whatever concession Einstein made to Kretschmann seems to have had a lesser e ect on Einstein's later writings. He does occasionally allow that general covariance is `more characteristic of the mathematical form of this theory [of general relativity] than its physical content' (1924, p90{1). Or that the `requirement [of general covariance] (combined with that of the greatest possible logical simplicity of the laws) limits the natural laws concerned incomparably more strongly than the special principle of relativity' (1952, p 153). The heuristic role of simplicity in connection with general covariance was emphasized in his Autobiographical Notes (1949, p65). But this emphasis seemed to be forgotten by p73, where he recalled: `We have already given physical reasons for the fact that in physics invariance under the wider [general] group has to be required'. (Einstein's emphasis) More +17The only di erence is that Kretschmann allows the point-coincidence argument to justify a formulation of any covariance, whereas Einstein sees it forcing a generally covariant formulation as the `unique, natural expression' of the theory. Presumably this is because a generally covariant formulation adds the least to the catalog of coincidences. See Einstein to Besso, January 3, 1916, as quoted in Norton (1992, p298) + + + 820 J D Norton +commonly, however, the quali cation over simplicity is simply not mentioned. It does not appear at the relevant point in his text, Einstein (1922a, p61). Again, Einstein (1950, p352) insists, without explicit mention of simplicity considerations that . . . the principle of general relativity imposes exceedingly strong restrictions on the theoretical possibilities. Without this restrictive principle it would be practically impossible for anybody to hit on the gravitational equations . . . How can we reconcile Einstein's concession to Kretschmann and his continuing emphasis on the importance of general covariance? The answer may well lie in Einstein's famous proclamation of his 1933 Herbert Spencer lecture, which revealed a metaphysics not present explicitly in Einstein's writings of 1918: Our experience hitherto justi es us in believing that nature is the realization of the simplest conceivable mathematical ideas. I am convinced that we can discover by means of purely mathematical constructions the concepts and laws connecting them with each other, which furnish the key to understanding the of natural phenomena . . . the creative principle resides in mathematics. When Einstein replied to Kretschmann that one ought to pick of two empirically viable systems the simpler and more transparent within the absolute di erential calculus, he may have been urging something more than merely a matter of practical convenience. It is not just that the simpler is more convenient, so that generally covariant formulations of Newtonian gravitational are (he believed) practical impossibilities. We can recognize the truth of a theory in its mathematical simplicity, And instead of being physically vacuous, general covariance is the right language in which to seek this simplicity. Later writers who endorsed Einstein's 1918 reply to Kretschmann may well have armed a more extreme metaphysics than they realized! +5.3. Generally covariant formulations of Newtonian mechanics +In 1918 Einstein sought to protect the special connection between general covariance and his general theory of relativity by issuing a challenge: nd a generally covariant formulation of Newtonian gravitational mechanics. He had con dently predicted that should anyone try the result would be unworkable practically. Einstein was shortly proved wrong. Cartan (1923) and Friedrichs (1927) found serviceable, generally covariant formulations of Newtonian gravitation theory. Einstein was right in so far as these generally covariant formulations were more complex than general relativity. However Einstein was quite wrong in predicting that such formulations would not be usable practically. Although they are not as attractive a host for routine calculation as the far simpler Galilean covariant formulation, they are of the same order of complexity as other theories routinely examined in physics. However there are certain circumstances in which their use is preferable if not mandatory. In an article comparing Newtonian and relativistic theories of gravitation, Trautman (1966, p413) pointed out such comparison can really only be e ected reliably if the two theories under comparison are formulated in the same mathematical language. Otherwise it is hard to ascertain which di erences are physical and which are accidents of the di erences in formulation. Since general relativity is known only in a generally covariant formulation, this means we ought to compare it only with the generally covariant formulation of Newtonian theory. (For similar sentiments, see also Havas (1964, p939) and Malament (1986, p 181).) For this reason, a few expositions of relativity include a treatment of Newtonian spacetie theory in a generally covariant formulation, although the practice is not common. See for example Trautman (1964, ch 5), and Misner et al (1973, ch 12). In the philosophy of space and time literature, however, the use of the general covariant formulation of Newtonian + + + General covariance and general relativity 821 +theory is becoming standard, even at the introductory level, see Earman and Friedman (1973), Earman (1974, pp276{7), Friedman (1983, ch III), Malament (1986) and Norton (1992a). Although both Cartan and Friedrichs were very much concerned with the relationship between their work and Einstein's general theory of relativity, it is striking that neither made the obvious point that their work had seriously weakened Einstein's 1918 reply to Kretschmann and raised very serious doubts over Einstein's claim to have generalized the principle of relativity to acceleration.18 It is only later that this obvious point about generally covariant formulations of Newtonian theory is made: they provide an instantation of Kretschmann's claim that any theory can be made generally covariant. See Havas (1964, p 939) and Misner et al (1973, p302). +5.4. Automatic general covariance: coordinate free geometric formulation +It did not need the labours of Cartan and Friedrichs to show that theories other than general relativity admitted generally covariant formulations. In a sense this possibility had been known for a long time. As Painleve pointed out as early as 1921 in his discussion of general relativity (1921, p877), Lagrangian mechanics has always been invariant under arbitrary spatial transformation. Again, the moment Einstein applied the absolute di erential calculus of Ricci and Levi-Civita to relativity theory in 1913, it was obvious that special relativity could be given generally covariant formulation. In this form, special relativity is simply the theory of spacetime with line element (4), where g is symmetric with Lorentz signature and whose Riemann-Christo el curvature tensor vanishes. That Einstein never embraced this obvious possibility suggests that his understanding of general covariance was a little more complex than the simple one supposed in Kretschmann's objection.19 Perhaps for this reason or perhaps just for its simplicity, the Lorentz covariant formulation of special relativity remains popular today. The possibility of formulating special relativity in arbitrary coordinates, however, was explicitly recognized in the literature quite early (see for example Kretschmann (1917, p579), De Donder (1925, ch 1), Fock (1959, ch IV, p350). A number of commentators have observed that Ricci and Levi-Civita's calculus vindicates Kretschmann's objection in the sense that it provides the necessary mathematical apparatus for nding generally covariance formulation of `practically any assumed law' (Whittaker 1951, Vol II, p 159) or `almost any law' (North 1965, p58). This possibility has not really been exploited widely in the relativity literature until the 1960s and 1970s with the introduction of what Misner, Thorne and Wheeler (1973) label as the `geometric' or ` coordinate free' approach. This approach is based on Ricci and Levi-Civita's calculus. However, as was pointed out in section 3.2 above, the calculus was created explicitly as an abstract calculus, as independent as possible from geometric notions. The calculus was signi cantly altered to arrive at its modern geometric incarnation. It is now augmented with geometric ideas from topology. The most signi cant augmentations are the modern ideas of a di erential manifold and of a geometric object of Veblen and Whitehead (1932), as well as an abstract, algebraic approach to vectors, tensors and the like, attributed to +18Thus Ho man (1932, p177) makes no mention of Cartan's and Friedrich's work when he remarks that the general principle of relativity `holds in exactly the same words for the Newtonian theory [as for general relativity]. Rather the remark is supported merely by observing that the principle requires only that the mathematical expression of a theory be independent of the coordinates system and does not restrict the theory's content. 19Indeed, as he made clear through his principle of equivalence, he held that an extension of the covariance of special relativity beyond Lorentz covariance was a physical extension of the theory; his principle of equivalence tells us that extending the covariance to uniformly accelerated coordinates now allows the theory to embrace the phenomenon of gravitation in a special case. + + + 822 J D Norton +Cartan (Misner et al 1973, ch 8 and 9). These methods became standard in the 1960s and 1970s through such expositions of relativity theory as Trautman (1965), Hawking and Ellis (1973), Misner, Thorne and Wheeler (1973), Sachs and Wu (1977). Following their methods, we would characterize special relativity as a theory of Minkowski spacetimes. That is, the theory has models +hM; gabi +Where M is a connected, four-dimensional, di erentiable manifold and gab is a symmetric second rank tensor of Lorentz signature which is at, so that it satis es the equation +Rabcd = 0 +Where Rabcd is the Riemann-Christo el curvature tensor. There are obvious extensions if one wishes to include further elds, such as a Maxwell eld and charge ux. Similarly, general relativity, is the theory with models +hM; gab; Tabi +where now gab need not be at. Tab is the second rank, symmetric stress-energy tensor, which may be required to satisfy further `energy conditions' (Hawking and Ellis, 1973, section 4.3). The metric tensor gab and Tab are related by the gravitational eld equation +Gab = Tab +where Gab is the Einstein tensor and  a constant A typical geometric formulation of Newtonian spacetime theory without absolute rest (after Malament 1986) has models +D +M; ta; hab; ra +E +The theory's temporal metric is ta, is a smooth, non-vanishing co-vector eld. The spatial +metric is second rank, symmetric, smooth non-vanishing contravariant tensor, hab, which is degenerate through its signature (0,1,1,1), ra is a smooth derivative operator, conferring ane structure on the spacetime. These structures satisfy orthogonality and compatibility conditions +habta = 0 ratb = rahbc = 0 +Many alternative, further conditions can be imposed upon this basic spacetime structure, for example, according to whether we wish to add gravitation as distinct scalar eld and leave the background spacetime at or whether we wish to incorporate gravitation into the spacetime as curvature after the model of general relativity (see Friedman 1983, ch III). These are all instances of a general, geometric formulation of spacetime theories. All such theories have models + + + General covariance and general relativity 823 +hM; O1; O2; : : : ; Oni (6) +where O1; O2; : : : ; On are now just n geometric object elds subject to certain constraining equations. Virtually all theories of space and time now given serious consideration can be formulated in this way. 20 Such theories are automatically generally covariant in a sense that actually follows from the de nitions of the mathematical structures used in the formulation. Following Standard de nitions (e.g. Bishop and Goldberg 1968, ch 1, Hawking and Ellis 1973, ch 2, Torretti 1983, appendix), an n-dimensional di erentiable manifold is a connected, topological space with a set of coordinate charts, such that every point of the topological space lies in the domain of a coordinate chart, which is a homeomorphism of an open set of the space with Rn. The set of coordinate charts form a maximal or complete atlas in so far as the atlas contains every coordinate chart that can be constructed in the usual way from its coordinate charts by Ck-transformations on Rn. k is some positive integer or, most commonly, in nity. The next step is complicated by the vagueness of the de nition of `geometric object'. It is given by Veblen and Whitehead (1932, p46) as `an invariant which is related to the space [under consideration]' where an invariant is `anything which is unaltered by transformations of coordinates'.21 Thus for our purposes, it is prudent to assume that our geometric object elds, are like Anderson's (1967, p15) `local geometrical objects'. They are represented by a nite set of numbers for each point in the manifold in each coordinate charts and which transform under coodinate transformation in a way that respect transitivity, identity and inversion. These numbers are the geometric object's components in the coordinate charts. Let us say that a geometric object eld O has components Oik::: where the integer valued i; k; : : : represents a suitable set of index labels. Combining, we now arrive at the sense in which any theory with models (6) is generally covariant. If N is any `local coordinate neighbourhood' of M , an open set of N that is the domain of some coordinate chart xi, then the restriction of the model (6) to N will be represented by +hA; (O1)ik:::; : : : ; (On)ik:::i (7) +Where A is the range of xi and the remaining structures are the components of the objects O1; : : : On in the coordinate chart xi. The theory is generally covariant in the sense that if (7) is a coordinate representation of the model (6), then so is any representation derivable from (7) by arbitrary Ck transformation. This is sometimes known as `passive general covariance ' Put more brie y, once we have formulated a theory as having models of the form (6), then, built into the de nitions of the structures used is the possibility of representing the models in coordinate systems that are related by the arbitrary transformations of Einstein's general covariance. (More precisely, they are related by Ck transformations if the manifold has a Ck maximal atlas of coordinate charts.) These coordinate representations behave +20That is not to say that all intelligible theories of space and time must admit such a formulation. With a precise de nition of geometric object in hand, it is just a matter of mathematical patience to construct a spacetime theory without such a formulation. Oe could begin, for example, by considering spacetimes whose event sets are very large but nite and do not admit smooth coordinate charts. 21The still vague `related to space' clause is an attempt to avoid the problem that `. . . strictly speaking, anything, such as a plant or an animal, which is unrelated to the space which we are talking about, is an invariant'. + + + 824 J D Norton +exactly like the components of the generally covariance formulation of theories used by Einstein and others in the early years of general relativity. It is to this automatic general covariance that Thirring (1979, p 166) referred when he +wrote At the time of the birth of gravitation theory, the requirement of general covariance provided some relief from the labor pains, but later on it was more often a source of confusion. The concept of a manifold incorporates it automatically when the de nition used equivalence classes of atlases, and hence only chart independent statements are regarded as meaningful. This program is by no means unique to gravitation theory| we have also followed in in classical mechanics and electrodynamics. The big di erence [in general relativity] is that the metric g on M is now not determined a priori. While the use of these geometric methods has become standard in modern work on general relativity, it should be noted that their dominance is not viewed universally with unmixed joy. Weinberg (1972, preface) notes that an emphasis on these methods tends to obscure the importance of the principle of equivalence within the theory and the natural connections to quantum theory. Finally, there is a notion that is loosely dual to the notion of passive general covariance described above. It is the notion of `active general covariance'. The main mathematical di erence is that the active version employs maps on the manifold M of the models (6) rather than transformations between coordinate charts. It can be de ned as follows. Let h be an arbitrary di eomorphism 22 from M to M . Then a theory with models of the form (6) is generally covariant in the active sense if every structure +hhM; hO1; hO2; : : : ; hOni (60) +is a model whenever +hM; O1; O2; : : : ; Oni (6) +is a model. In addition, it is routinely assumed that the structure (6) and (6') represent the same physical circumstance (e.g., in the case of general relativity, see Hawking and Ellis 1973, p56). This assumption has been called `Leibniz equivalence' (Earman and Norton 1987). Many theories are generally covariant in the active sense. A sucient condition for active general covariance is that the object elds O1; O2; : : : ; On that can be included in the models (6) are determined solely by tensor equations. Thus general relativity is covariant in this sense as are versions of special relativity and Newtonian spacetime theory. Passive general covariance involves no physically contingent principles. Once models of the form of (6) are selected, passive general covariance follows as a matter of mathematical de nition, no matter what the physical content of the theory. Passive general covariance involves no physically contingent principles, Once models of the form of (6) are selected, passive general covariance follow as a matter of mathematical de nition, no matter what the physical content of the theory. This is not the case with active general covariance/Leibniz equivalence. Structures (6) and (6') are mathematically independent structures, that they represent the same physical circumstance is an assumption dependent on the properties of the physical circumstance and our methods of coordinating the structures to it. The di erences between such pairs of structures as (6) and (6') are generally of a nature that make it uninteresting to suppose anything other than +22For example, if M is a Ch manifold, then h might be any Ch di eomorphism in the sense of Hawking and Ellis (1973, p 23). + + + General covariance and general relativity 825 +Leibniz equivalence. However, it has been argued (Earman and Norton 1987, Norton 1988) that at least one doctrine, spacetime substantivalism, must deny Leibniz equivalence.23 Since the assumption of active general covariance/Leibniz equivalence is a physical assumption albeit weak, it does require physical arguments to support it. It turns out that Einstein's two celebrated arguments|the point-coincidence argument and the hole argument|can be put in to modern forms that support active general covariance/Leibniz equivalence. According to the modernized point-coincidence argument, the two di eomorphic models (6) and (6') would agree on all observables, for all that is observable are coincidences that are preserved by the di eomorphism. Therefore, if we deny Leibniz equivalence, we would have to insist that the two di eomorphic models represent distinct physical circumstances, even though no possible observation could pick between them. To construct the modernized hole argument, we consider some neighbourhood H of the manifold M in models (6) and (6') and pick a di eomorphism h that is the identity outside H but comes smoothly to di er from it within H. The the two di eomorphic models will be the same outside H but will come smoothly do di er within H. We now have a mathematical indeterminism, in the sense that the fullest speci cation of the model outside H will fail to determine how it is to be extended into H according to the theory. This indeterminism is usually dismissed as a purely mathematical gauge freedom associated with active general covariance. If we deny Leibniz equivalence and insist that the two models represent distinct physical circumstances, then we convert this gauge freedom into a physical indeterminism. The di erences between the models within H must now represent a di erence of physical circumstances. Which will obtain within H cannot be determined by the fullest speci cation of the physical circumstances outside H, no matter how small H is in spatial and temporal extension. For further discussion of the di erences between active and passive general covariance, see Norton (1989, section 2.3). +5.5. Later responses to Kretschmann's objection +Kretschmann's objection is probably the single most frequently mentioned of all objections to Einstein's views on the foundations of general relativity. As I have already indicated above, however, the objection which appears universally under Kretschmann's name in the literature is actually a considerably reduced version of what Kretschmann really said. It is commonly reported as the assertion that general covariance is physically vacuous, since it is merely a challenge to our mathematical ingenuity to bring any theory into generally covariant form. For the purposes of this section, which reviews later responses to the objection, I will take `Kretschmann's objection' to be this reduced version, for that is the one that was responded to. Essentially no one other than Einstein seemed to realize that Kretschmann had based his objection on a contingent assumption, the premise of the pointcoincidence argument. That assumption|that `the laws of nature are only assertions of timespace coincidences'|is so non-trivial that Einstein actually made it the statement of his 1918 version of the principle of relativity. In later literature, Kretschmann's objection is commonly accepted. Instances in which Kretschmann is cited by name include Havas (1964, p939), Rindler (1969, p196), Earman +23At present, however, there is no consensus in the philosophy of space and time literature over the connection between spacetime substantivalism, Leibniz equivalence and the hole argument, with virtually every conceivable position being defended. See Bartels (1993), Butter eld (1987, 1988, 1989), Earman (1989, ch 9), Norton (1992a, section 5.12), Cartwright and Hoefer (forthcoming), Maudlin (1988, 1990), Rynasiewicz (forthcoming (a), (b)), Stachel (forthcoming), Teller (forthcoming), Mundy (1992). + + + 826 J D Norton +(1974, p271), Friedman (1973, p55), Ray (1987, p70). Again Kretschmann's assertion of the physical vacuity of general covariance may be made without naming Kretschmann. Instances include Silberstein (1992, pp22{3), Szekeres (1955, p212), Fock (1959, p370, but see p xvi), Thirring (1979, p166). Einstein's 1918 response to Kretschmann also commands considerable assent. Einstein's response is encapsulated in the simple remark that general covariance is physically vacuous alone; however it achieves physical content and signi cant heuristic force when it is supplemented by the requirement that the laws of nature take simple forms. This viewpoint is advocated by: Painleve (1921, p877), Tolman (1934, pp33, 166{67)24, Bridgman (1949, pp339{40, 345), Whittaker (1951, vol II, p159), Weber (1961, p15{16), Skinner (1969, p 324), Adler, Bazin and Schi er (1977, p145). Ohanian (1976, pp253{4) states Kretschmann's objection and quotes Einstein's 1918 reply at length, but he proceeds to elucidate Einstein's response in terms of the requirement of general invariance of the absolute object tradition (see section 8 below). In his 1918 reply to Kretschmann, Einstein urged the heuristic power of general covariance and the basis of his brilliant success with general relativity. d'Ivorno (1992, p131) comes closest to this viewpoint when he suggests that we cannot ignore general covariance, even if it is vacuous, precisely because it was of such importance to Einstein, rather than because of some as yet unrealized heuristic power. But perhaps Misner et al (1973, section 12.5) capture Einstein's metaphysics most clearly when they recapitulate Kretschmann's objection and retort But another viewpoint is cogent. It constructs a powerful sieve in the form of a slightly altered and slightly more nebulous principle: `Nature likes theories that are simple when stated in coordinate free, geometric language' . . . According to this principle, Nature must love general relativity, and it must hate Newtonian theory. Of all theories ever conceived by physicists, general relativity has the simplest, most elegant geometric foundations. . . By contrast, what diabolically clever physicist would ever foist on man a theory with such a complicated geometric foundation as Newtonian theory? There are obvious problems with this view. To begin, it would seem that the view is plainly false. The very simplest laws, which nature ought to love the most, are just incompatible with experience. For example, it would be very simple of all of space, time and the distribution of matter were homogeneous; but they are not homogeneous. So Nature's preferences can only be exercised among the more complicated dregs that remain after experience has drained of the truly simple|Nature's preference here is a rather contrived one. Next, it is not clear by what rules we are to judge which of two theories is the simpler. It cannot just be a matter of intuitive impressions, since then we have no way of adjudicating disagreements. But even a basic count of the number of mathematical structures in a theory is hard to do unambiguously.25 Bondi (1959, p108), however, endorses the view that general covariance is physically vacuous and points out that conservation laws explicitly involving gravitational energy-momentum in general relativity are not tensorial, but pseudo-tensorial. Finally, it is not obvious why nature should be so kind as to prefer laws that we humans deem simple. Thus North (1965, p58) muses that the virtue of simplicity for covariant laws might merely be that they are more likely to be accepted by others. My own view is that one should not look on simplicity as resulting from the emotional attachments of Nature. Rather it arises from the labours of theorists who have constructed languages in which Nature's choices appear simple. Whether Nature's further choices will continue to appear simple in some language seems to me an entirely contingent matter +24Tolman gives Kretschmann's objections in its full form insofar as the possibility of generally covariant formulation is taken to follow necessarily from the point-coincidence argument. 25Is the stress-energy tensor of pressureless dust, T ab = U aU b, counted as one structure T ab or as two, the matter density  and the four-velocity eld U a? + + + General covariance and general relativity 827 +and one takes a great risk elevating any language to the status of Nature's own. As we explore new domains of physical law, the one thing that is most clear is Nature's surprising versatility in frustrating our natural expectations. However this does not mean that there is no value in simplicity. Apart from its pragmatic value, it has an epistemic value. The more complicated a theory, the more likely we are to have introduced structures with no correlations in reality; and the more complicated a theory, the harder it will be to test for these physically irrelevant structures. We should prefer the simpler theory and seek languages that make our theories simple, but not because Nature is simple. Rather, if we restrict ourselves to simpler theories, we are more likely to know the truth when we nd it. There is a variation of Einstein's response to Kretschmann that avoids the dicult questions over simplicity. Its overall e ect is to direct us towards simpler theories by restricting the structures we can employ in our formulations. It focuses on the process of nding generally covariant formulations of arbitrary laws. If we restrict the number of additional mathematical structures that can be introduced in this process, it may no longer be possible to construct a generally covariant formulation for some laws, so that we once again have an interesting division between generally covariant and other theories. Fock (1959, p xvi) describes the idea in its most general form . . . the requirement of covariance of equations has great heuristic value because it limits the variety of possible forms of equations and thereby makes it easier to choose the correct ones. However, one should stress that the equations can so be limited only under the necessary condition that the number of functions introduced is also limited; if one permits the introduction of an arbitrary number of new auxiliary functions, practically any equation can be given covariant form. Trautman (1964, pp122{3) illustrates how unrestricted admission of new structures allows construction of a generally covariant formulation of equations that clearly are coordinate dependent. He considers the equation +A1 = 0 +the vanishing of the rst component of a covector Aa in some coordinate system. If ua is +the coordinate basis vector eld associated with the x1 coordinate, then this law admits generally covariant formulation as +uaAa = 0 +The villain is the vector eld ua, since (p123) one should not introduce such additional structures in addition to those already present in the axioms of the theory (e.g. the metric tensor, ane connection) and to those that are necessary to describe the physical system. If we now apply this thinking to general relativity, we arrive at a popular means of injecting content into the general covariance of general relativity. In a Lorentz covariant version of special relativity, the metrical properties of spacetime are not represented explicitly. In the transition to the generally covariant, general theory of relativity, these properties become explicit as a new structure, the metric tensor gab. It is required that this new structure represent some de nite physical element of reality and nut just be a mathematical contrivance introduced to force through general covariance. The metric tensor satis es this requirement in so far as it represents the gravitational eld as well as the metrical properties of spacetime. Pauli (1921, p150) describes this outcome + + + 828 J D Norton +. . . Kretschmann . . . took the view that the postulate of general covariance does not make any assertions about the physical content of the physical laws, but only about their mathematical formulation, and Einstein : : : entirely concurred with this view. The generally covariant formulation of the physical laws acquires a physical content only through the principle of equivalence, in consequence of which gravitation is described solely by the gik and these latter are not given independently from matter, but are themselves determined by eld equations. We nd a similar view in Borel (1926, p172{3), Weyl (1921, pp226{7) Reichenbach (1924, p141), Anderson (1967, 1971|see section 8.1 below), Graves (1971, p138) and even as recently as Wald (1984, p57) who formulates the principle of general covariance as The principle of general covariance in this context [pre-relativistic and relativistic physics] states that the metric of space is the only quantity pertaining to space that can appear in the laws of physics. Speci cally there are no preferred vector elds or preferred bases of vector elds pertaining only to the structure of space which appear in any law of physics. (He cautions that the `the phrase \pertaining to space" does not have a precise meaning'.) Both Pauli and Weyl stress a special aspect of the physical character of the metric in their discussions: the metric is not given a priori but it is in uenced or determined by the matter distribution via invariant eld equations. This would, of course, rule out generally covariant formulations of special relativity. Weyl, in particular, sees this as the decisive property of general relativity. `Only this fact justi es us in assigning the name \general theory of relativity" to our reasoning . . . ' he wrote (p226). Further, he emphasized the result that `gravitation is a mode of expression of the metrical eld' and that `this assumption, rather than the postulate of general invariance, seems to the author to be the real pivot of the general theory of relativity' (pp226{7). We shall see that this theme will be incorporated into the absolute object approach (see section 8 below). A practical diculty still remains. At the most fundamental level, the general principle is clearly correct: we should deny admission to theories or structures that do not represent elements of reality. The hope is that this restriction will preserve a unique association between general covariance and the general theory of relativity. However the principle may well not be suciently precisely formulated to have any force in realistic examples. Consider the structures dta, hab and ra, introduced in constructing a generally covariant formulation of Newtonian theory. Are they admissible or not? Notice that Pauli and Weyl's emphasis on the dynamic character of the metric may not help us here. In versions of Newtonian gravitation theory, the gravitational eld is incorporated into the ane structure ra which then has similar dynamical properties to the metric of general relativity. The strategy so far has been to augment the requirement of general covariance with additional requirements that make it non-trivial. It turns out that there is an extremely simple way of augmenting the principle of general covariance so that we cannot render generally covariant such theories as special relativity and versions of Newtonian theory that do not incorporate the gravitational eld into ane structure. In both these cases, the associated generally covariant formulations have the property that they can be simpli ed by reintroducing restricted coordinate systems. This is not so in the case of general relativity, so we can pick between these cases by insisting that the generally covariant formulation not admit simpli cation. Bergmann (1942, p159) explicitly incorporates this requirement into the statement of the principle of general covariance: The hypothesis that the geometry of physical space is represented best by a formalism which is covariant with respect to general coordinate transformations, and that a restriction to a less general group of transformations would not simplify that formalism is called the principle of general covariance + + + General covariance and general relativity 829 +At rst this seems like a purely ad hoc contrivance. However Bergmann's proposal connects directly with the view that relativity principles are geometric symmetry principles, as we shall see in section 6.2 below. Alternatively, Bondi (1959, p108) calls the proposal into question by recalling Fock's use of harmonic coordinates to reduce the covariance of general relativity (see section 9 below). There have been other studies of the relationship between a theory and its generally covariant reformulation and these studies arrive at conclusions uncomfortable for Kretschmann's objection. Scheibe (1991, 1981) has considered the relationship within a more precise formal setting. He concludes that it is simply not obvious that any geometry of restricted covariance can always be recast in a generally covariant formulation. Post (1967) concludes that the process of rendering theories generally covariant is far from automatic triviality and must be treated with some care. In the case of electromagnetic theory, he shows how di erent ways of rendering the theory generally covariant actually lead to distinct theories. Mashoon (1986) similarly emphasizes that, while any theory can be rendered generally covariant, the manner in which it is done can have physical consequences, in particular, in the measurements of accelerated observers. Many authors are prepared to accept Kretschmann's objection but feel that it has to be quali ed in signi cant ways if the true signi cance of general covariance is to be appreciated. While accepting Kretschmann's objections and that a requirement of general covariance is not a relativity principle like that of special relativity, Weinberg (1972, pp92, 111{3) characterizes general covariance as akin to the gauge invariance of electromagnetic elds. Accepting Kretschmann's objection, Bunge (1967, section 3.1.3) observes that if general covariance is understood as simply requiring form invariance of laws, then it does become a purely mathematical requirement. Therefore he concludes that general covariance is to be understood as a regulative rather than constitutive principle. Mavrides (1973, p66) also accepts Kretschmann's objection but sees the signi cance of the principle in absorption of acceleration into the non-Euclidean structure of spacetime. Zahar (1989, section 8.1) approaches the problem with a distinction introduced by logicians between an object language and its metalanguage. In this context, the object language contains the assertions about physics systems and the metalanguage contains assertions about the object language. Whether a body of object language assertions, such as Newtonian theory, is generally covariant is not itself an object language assertion. It belongs to the metalanguage. We may be able to nd a generally covariant formulation of Newtonian theory which is logically equivalent to the original Galilean covariant version. However the meta-level property of general covariance is not inherited by the original formulation, for meta-level properties are not transmitted by logical equivalence. Therefore we cannot say that Newtonian theory is itself generally covariant. Several other authors have approached general covariance as a principle of operating a meta-level of language. See Graves (1971, pp143{7). In particular, Tornebohm (1952, section 41) characterizes the principle of general covariance as a closure rule operating on a meta-level in which one quanti es over coordinate systems employed in statements of physical laws. Finally, see Kuchar (1988) for a reincarnations of the issues raised by the debate of Kretschmann's objection in Hamiltonian dynamics and canonical quantization of generally covariant systems. +6. Is the requirement of general covariance a relativity principle? +6.1. Disanalogies with the principle of relativity of special relativity +In addition to accusations that his principle of general covariance is physically vacuous, Einstein's treatment of general covariance has been besieged by continuing complaints + + + 830 J D Norton +that the achievement of general covariance does not amount to a generalization of the principle of relativity to acceleration. These complaints have come in many di erent forms. Some of the earliest make the obvious point that such an extension of the principle of relativity to accelerated motion seems to be atly contradicted by the simplest observations. The principle of relativity of inertial motion ts the experiences of a traveller in a train moving uniformly on smooth tracks; nothing within the carriage reveals the train's motion. However, the same is not so if the train accelerates, as was pointed out acerbically by Lenard (1921, p15), whose involvement in the persecution of Einstein in Germany in the 1920s is +well known: Let the train in consideration undertake a distinct, non-uniform motion . . . If, as a result, everything in the train is wrecked through the e ects of inertia, while outside everything remains undamaged, then, I believe, no sound mind would want to draw any other conclusion than that the train had altered its motion with a jolt and not the surroundings. For Einstein's reply to this exact passage, see Einstein (1918a). It was only in the 1950s and 1960s that such long-standing worries took a prominent though still disputed place in the mainstream literature. This dissident view drew strength from such eminent relativists as Fock and Synge, who dared to proclaim what few would admit: they just could not see how Einstein's theory generalizes the principle of relativity| and they even suspected that Einstein could not see it either. So Synge (1966, p7) wrote: . . . the general theory of relativity. The name is repellent. Relativity? I have never been able to understand what that word means in this connection. I used to think that this was my fault, some aw in my intelligence, but it is now apparent that nobody ever understood it, probably not even Einstein himself. So let it go. What is before us is Einstein's theory of gravitation. See also Synge (1964, p3) and (1960, p ix) where he wrote . . . the geometric way of looking at space-time comes directly from Minkowski. He protested against the use of the word `relativity' to describe a theory based on an `absolute' (spacetime), and, had he lived to see the general theory of relativity, I believe he would have repeated his protest in even stronger terms. In similar vein, Fock (1959, pp xvi{xviii, 367{8, 375{6) treated a relativity principle as stating a uniformity of spacetime. Thus special relativity admits a relativity principle because of the uniformity of a Minkowski spacetime. The spacetimes of general relativity, however, manifest this uniformity only in the in nitesimal, so that the naming of the theory `general relativity' or `general theory of relativity' is simply incorrect, betraying Einstein's failure to understand his own theory. Fock continued (p368) The fact that the theory of gravitation, a theory of such amazing depth, beauty and cogency, was not correctly understood by its author, should not surprise us. We should also not be surprised at the gaps in logic, and even errors, which the author permitted himself when he derived the basic equations of the theory. In the history of physics we have many examples in which the underlying signi cance of a fundamentally new physical theory was realized not by its author but by somebody else an in which he derivation of the basic equations proposed by the author proved to be logically inconsistent. It is sucient, to point to Maxwell's theory of the electromagnetic eld ... Allowing in addition that the only admissible sense of `general relativity' is as purely formal property of general covariance, Fock (1974, p5) concluded Thus we can sum up: general relativity cannot be physical, and physical relativity cannot be general. These confessions were engagingly candid and their iconoclastic sentiments found receptive + + + General covariance and general relativity 831 +audiences. The heresy of disbelief in Einstein became respectable. Fock and Synge are, of course, not alone in divorcing general covariance from a generalization of the principle of relativity and announcing the failure of Einstein's e ort in this regard. See for example Landau and Lifshitz (1951, p229), Davis (1970, p219) , Raine and Heller (1981, p135) and Bondi (1979, p129). +6.2 Relativity principles as symmetry principles +If covariance principles are not relativity principles, then what are relativity principles? New answers to this question have come repeatedly within the tradition that proposes the divorce of general covariance from a generalization of principle of relativity. We shall see that they eventually stabilize on the view that a relativity principle expresses a symmetry of the spacetime structure. One of the earliest proposals comes from Kretschmann. His famous objection to general covariance actually occupies a small part of his lengthy paper (1917). The bulk of it is devoted to developing an alternate interpretation of relativity principles. His proposals are embedded within extended calculations and circuitous verbiage. They appear to reduce to the following. The key idea in identifying the relativity principle of some given theory lies not in extending its covariance, but in reducing it to the minimum group possible. This reduction must be done in a way that identi es a group associated with the theory's physical content rather than some particular formulation of it. In the case of special relativity, his general proposal leads to the expected result: the Lorentz group expresses the theory's relativity principle. Consider the bundle of all lightlike worldlines in the theory. In the Lorentz covariant formulation, this bundle is described by the equation +(x1 x01)2 + : : : + (x4 x04)2 = 0 (8) +Where x = x1; : : : ; x4 = ict are the usual spacetime coordinates and x01; : : : ; x04 some arbitrary origin event. This bundle is mapped back into itself by any Lorentz transformation that preserves the origin. Kretschmann allowed that we could extend the usual Lorentz covariant formulation of the theory even as far as generally covariant formulation, using the methods of Ricci and Levi-Civita. However, in a formulation of extended covariance, an allowed transformation will, in general, not map this bundle back into itself. Rather, such a transformation will alter the coordinate image of the bundle. Again, one could consider a formulation whose covariance is restricted to a group smaller than the Lorentz group. However this formulation could only be constructed at the expense of altering the physical content of the theory26. The Lorentz transformation is the formulation of minimal covariance faithful to the theory's physical content. Therefore the Lorentz transformation is the group associated with the theory's relativity principle. A similar analysis in the case of general relativity leads to a quite di erent result. In e ect Kretschmann nds that the single membered identity group plays the same role in general relativity as does the Lorentz group in special relativity. As a result he can arrive at a conclusion that directly contradicts einstein's (p610) +26How Kretschmann arrived at this crucial conclusion is a little unclear to me. Such a formulation would need to replace (8) by another formula or formulae of more restricted covariance and presumably Kretschmann held that any such formulae would have to alter the physical content of (8). For example, to violate Lorentz covariance, the new formula might pick out one or other spatial direction as preferred, whereas equation (8) describing the bundle admits no such preferred directions. + + + 832 J D Norton +Therefore Einstein's theory satis es no relativity principle at all in the sense developed [earlier in the paper]; on the basis of its content, it is a completely absolute theory. To arrive at this result, Kretschmann considered the bundle of light-like worldlines and of free material particles within the theory. He found the former xed the components of the metric tensor g up to a multiplicative factor  and the latter forced  to be a constant. (Notice that these are now familiar results. In modern language: conformal structure xes the metric up to a conformal factor and specifying ane structure forces the factor to be constant.) Finally consideration of spacetime curvature rules out any value of  other than unity. Thus the physical content of the theory xes the metrical components. But once these components are xed, the coordinate system is xed and no covariance transformation remains; in e ect the covariance group has become the identity group and one has no relativity principle. Kretschmann also showed that the same result could be arrived at in another way. As long as the spacetime metric is suciently non-uniform, it is possible to de ne a unique spacetime coordinate system for each metric by setting the four coordinates equal to unique curvature invariants. This once again reduces the covariance group to the identity. Finally Kretschmann could extract one nal blow from his calculations. In e ect he could conclude that the Lorentz group was the largest group possible for any relativity principle in a spacetime theory of the type of special and general relativity (p610): A physical theory, which accords an observationally accessible meaning to the external principle +  +Z +ds = 0 where ds2 = gdxdx + +of a space-time manifold of Minkowski normal form of the line element or posits that the invariant metrical character of the manifold is in some other way in principle observable to the same extent, can satisfy no broader relativity postulate in the sense [developed earlier in the paper] than that of the original Einsteinian theory of relativity. Kretschmann's proposal has been criticized at length by Anderson (1966). He argues that the proposal fails since one can too readily reduce the covariance of a theory to the identity. His examples include electrodynamics and special relativity, provided that we add some other structure, such as a scalar eld, to the Minkowski spacetime. Cartan (1927) gave a less bellicose and mathematically more perspicacious characterization of the di erence between the general covariance of general relativity and the Lorentz covariance of special relativity. General relativity threw into physics and philosophy the antagonism that existed between the two principle directors of geometry, Riemann and Klein. The space-times of classical mechanics and or special relativity are of the type of Klein, those of general relativity are of the type of Riemann. Under Klein's Erlangen program a wide range of geometries were all characterized by their associated groups and the geometric entities they studied were the invariants of those groups. The key aspect of these Erlangen program geometries|the Euclidean, the projective, the ane, the conformal and others|was that all the spaces were homogeneous. In the Riemann tradition, one considered a space and a group of transformations. But the geometric entities investigated are no longer the invariants of the transformations, for in this case there are essentially none. Instead one is interested in the invariants of a quadratic di erential form, the fundamental or metrical form, that is adjoined to the space. As result, the groups associated with geometries in the two traditions have very di erent signi cance. The spacetime geometry of special relativity, as introduced by Minkowski, is in the tradition of Klein. As a result its characteristic group, the Lorentz group, is + + + General covariance and general relativity 833 +associated with the homogeneity of the spacetime. General relativity lies in the Riemann tradition and, as a result, its general group of transformation is associated with no such homogeneity. Sesmat (1937, pp382{3) gave a more algebraic characterization of why the felt the general covariance of general relativity had failed to implement a generalization of the principle of relativity. What was needed was a theory whose laws would remain unchanged in form under transformations between all frames of reference including accelerated ones, in the same way that the laws of special relativity remained invariant under Lorentz transformation. The general covariance of general relativity just did not do this. Under the transformations of general covariance, such as transformation between Cartesian and polar coordinates, the expression for basic tensors do change. What general covariance does allow, however, is that a tensor, such as the Einstein tensor, can retain its zero value in empty space under these transformations, even though its expression changes. Sesmat's point seems to be precisely the point that Weinberg (1972, p92) is making when he explains the di erence between the Lorentz invariance of special relativity and general covariance. One could, he notes, expand the covariance of Newton's second law by transforming it under Lorentz transformation. However, a new quantity, the velocity of the coordinate frame would appear in the transformed equation. The requirement that this velocity does not appear in the transformed equation is what we call the Principle of Special Relativity, or `Lorentz invariance' for short, and this requirement places very powerful restrictions on the original equation. Similarly, when we make an equation generally covariant, new ingredients will enter, that is, the metric tensor g and the ane connection . The di erence is that we do not require that these quantities drop out at the end, and hence we do not obtain any restriction on the equations to start with; rather we exploit the presence of g and  to represent gravitational elds Fock (1957) (see also Fock 1959, p xiii{xiv, 166) gave a synthesis of all these ideas: the homogeneity of spaces in the Klein tradition, the mapping back into themselves of Kretschmann's bundle of light-like and inertial worldlines and he gave it in an algebraic form indicated by Sesmat and Weinberg. In considering the uniform or homogeneous spacetime of special relativity, he explained (p325): The property of spacetime being homogeneous means that (a) there are no privileged points in space and in time; (b) there are no privileged directions, and (c) there are no privileged inertial frames (that all frames are moving uniformly and in a straight line with respect to one another are on the same footing). The uniformity of space and time manifests itself in the existence of the Lorentz group. In particular, the equality of points in space and time corresponds to the possibility of a displacement, the equality of directions corresponds to that of spatial rotations, and the equality of inertial frames corresponds to a special Lorentz transformation. Fock then gave this condition mathematical expression. The Lorentz transformation leaves unchanged the Minkowski line element +ds2 = dx20 dx21 dx22 dx23 = g dxdx (9) +where the x0; : : : ; x3 are the usual spacetime coordinates of the Lorentz covariant formulation. This same condition can be stated in arbitrary coordinates in which the line element (9) becomes + + + 834 J D Norton +ds2 = g dxdx +The mathematical expression of the homogeneity of the Minkowski spacetime is now stated as the preservation of the functional form of the components of the metric in some class of coordinate systems. That is, if the metric has components g in some arbitrary coordinate +system x, then it will be possible to transform to a new coordinate system x0 in which +the new components of the metric g0 are the same functions of x0 as the g are the x. That is, +g0 (x0) = g (x) (10) +where the equality must be read as holding for equal numerical values of the quadruples x and x0. This condition is considerably more restrictive than merely requiring that the +components g transform into g0 under the usual tensor transformation rule. And it +expresses a homogeneity of the spacetime since both coordinate systems x and x0 relate in indistinguishable fashion to the metric tensor. The set of coordinate systems with this property are related by a ten parameter group which corresponds to the Lorentz group. Notice that the algebraic expression for the transformations from x to x0 in the Lorentz group can no longer be the familiar formulae (1) of Einstein's original 1905 paper. For example, in generalizing the coordinates, the coordinate system of (9) may remain inertial but with the Cartesian spatial coordinates replaced by polar coordinates, in which case the expression for the Lorentz transformation would have to be altered correspondingly. However, whatever may be their altered form, the transformation equations must leave unchanged the fundamental form of the components of the metric tensor. Otherwise the spacetime would distinguish between two inertial coordinate systems, in violation of this uniformity. That is the condition expressed in (10). The distinction between simple covariance and transformation of form (1) seems to be distinction between Buchdahl's (1981, p29) `improper' and `proper form invariance'. In his example, the equation gijSiSj = 0 (where S is a scalar eld and commas denote di erentiation) is improperly form invariant if the transformed equation just retains this +form as, say, gi0j0Si0Sj0 = 0. It is properly form invariant if the gi0j0 of the transformed +equation also remain the same functions of the new coordinates as the untransformed gij were of the old. Fock's proposal now relates directly to Bergmann's (1942, p159) statement of the principle of general covariance as given in section 5.5. above. According to (10), a generally covariant formulation of special relativity will admit a ten parameter subgroup of transformation|the Lorentz transformation|that preserves the functional form of the components of the metric tensor g. It can do so in many di erent ways. One merely selects some arbitrary coordinate system in which the Minkowski metric has components g and allows condition (10) to generate the subgroup. If one begins with the usual diagonal form of the metric, , one arrives at the usual form of the Lorentz transformation (1). Each of these subgroups is associated with a formulation of special relativity of reduced covariance of the particular functional form of the metrical components that remain unaltered according to (10) will be built into its laws. Therefore Bergmann's statement of the principle of general covariance will judge the generally covariant formulation of special relativity to be inadmissible and thus preserves a distinction between the covariance of general relativity and of special relativity. Notice also that the formulations of special relativity of reduced covariance are now of a form compatible with Klein's Erlangen program, since the Riemannian quadratic di erential form are no longer transformed merely covariantly within the theory. Thus, in + + + General covariance and general relativity 835 +accord with Cartan's observations, the transformation groups of the formulations are now associated with the homogeneity of the spacetime. Fock's condition (10) has an immediate expression in the geometric approach to spacetime theories. Let h be the dual manifold di eomorphism of the coordinate transformation de ned on a Minkowski hM; gabi. Then Fock's condition (10) becomes +h  gab = gab (11) +and the group of transformations satisfying this condition is the Lorentz group.27 That is, the Lorentz group is the group of di eomorphisms that are the symmetry transformations or isometries of the Minkowski metric. (Wald, 1984, pp 48, 60, 438). The existence of this group expresses the uniformity of the Minkowski spacetime. With this terminology, we can summarize why Fock and others believe that the transition from special to general relativity has failed to generalize the principle of relativity. Two groups are associated with the formulations of a theory: its covariance group characterizes purely formal aspects of its formulation; its symmetry group characterizes a physical fact, the degree of uniformity of the spacetime and this uniformity group allows the theory to satisfy a relativity principle. In the transition from a Lorentz covariant formulation of special relativity to a generally covariant formulation of general relativity, the covariance group is expanded. This is, however, merely an accident of formulation. The symmetry group is actually reduced from the Lorentz group to the identity group, for the general case. The identity group is associated with no relativity principle at all. Therefore the transition from special to general relativity does not generalize the relativity principle. It eradicates it. +6.3. Coordinate systems versus frames of reference +Fock took it as immediate that his condition (10) automatically realized the equivalence of inertial frames of reference whereas general relativity embodies no such equivalence. That this is correct may not be immediately clear given that such formulations of the principle of general covariance such as Bergmann's do preserve a sense in which the natural covariance. To give a precise statement of this result we require a clearer statement of what is a frame of reference. In traditional developments of special and general relativity it has been customary not to distinguish between two quite distinct ideas. The rst is the notion of a coordinate system, understood simply as the smooth, invertible assignment of four numbers to events +27To see the transition, let the metric gab have components g in some coordinate system and +let the transformation from coordinate systems x to x0 satisfy condition (10). To generate the +dual di eomorphism h, we now just consider the functional relation between x and x0 as a map +from quadruples of reals x to quadruples of reals x0(x). In one of the coordinate systems allowed under (10),the di eomorphism h maps an event p with the four coordinates x to an event hp with +coordinates x0(x) in the same coordinates system. Consider the metric h  gab carried along to hp from p under h. If the metric at p has components g, then the carried along metric at hp will have the same components g in the carried along coordinate system and the carried along coordinate system will assign coordinates x to hp. We now see that this carried along metric is the same as the original metric at hp, as (11) demands, by comparing their components in the original coordinate system. We transform the carried along metric back from the carried along coordinate system to the original by means of the coordinate transformation of (10) and nd that the carried along metric has components g0 at hp, which has coordinates x. Therefore the carried along +metric agrees with the original metric since the functional forms of g and g0 are the same. For further discussion of the duality of coordinate transformation and manifold di eomorphism, see Norton (1989, section 2.3) + + + 836 J D Norton +in spacetime neighbourhoods. The second, the frame of reference, refers to an idealized physical system used to assign such numbers. More precisely, since the physical systems tend to be space- lling, one is concerned with how such hypothetical system would behave were they to be constructed. Many such systems are possible. For example one can imagine space full of similarly constructed clocks and all of them attached to a rigid frame of small rods. The clock readings give us the time coordinates and the counting of rods gives us spatial coordinates. To avoid unnecessary restrictions, we can divorce this arrangement from metrical notions. Following Kopczynski and Trautman (1992, pp24{5), we could require only that the space- lling family of clocks bear three smoothly assigned indices (which could function as spatial coordinates), that the clocks tick smoothly, although not necessarily in proper time, and that time readings vary smoothly from clock to clock. Of special importance for our purposes is that each frame of reference has a de nite state of motion at each event of spacetime. Within the context of special relativity and as long as we restrict ourselves to frames of reference in inertial motion, then little of importance depends on the di erence between an inertial frame of reference and the inertial coordinate system it induces. This comfortable circumstance ceases immediately once we begin to consider frames of reference in nonuniform motion even within special relativity. This became a major problem for Einstein to negotiate as early as 1907, when he began to consider uniformly accelerated frames of reference in his new gravitation theory. He found (1907, section 18) the need to introduce coordinate times which could not be read directly from clock measurements. Similarly, due to the Lorentz contraction of rods oriented in the direction of motion, the geometry associated with a uniformly rotating frame of reference ceased to be Euclidean. As a result, spatial coordinates can no longer be assigned by the usual methods with measuring rods. The point of Einstein's rotating disk thought experiment ( rst published in Einstein (1912, section 1) and best known from Einstein (1916, section 3)) is that spacetime coordinates will lose this direct metrical signi cance once we stray from the familiar inertial coordinate systems of special relativity.28 With the advent of general relativity, Einstein wished to consider frames of reference with arbitrary states of motion. However he deemed it impractical to retain even a vestige of the idealized physical system of the frame of reference. In their place he simply used arbitrary coordinate systems. The association of an arbitrary coordinate system with an arbitrary frame of reference became standard in the literature for many decades. Thus, for example Bergmann (1962, p207) explains In all that follows we shall use the terms `curvilinear four-dimensional coordinate system' and `frame of reference' interchangeably. Thus, in Einstein's writings, whatever equivalence is established by general covariance of arbitrary coordinate systems is also conferred upon arbitrary frames of reference and, if we recall the connection between a frame of reference and a state of motion, the powerful suggestion is that this is all that is needed to extend the principle of relativity to arbitrary motions. The connection is complicated slightly by the fact that some coordinate +28The problem is even more complicated than Einstein indicated. An inertial frame of reference in a Minkowski spacetime is naturally associated with Euclidean spaces, with are the spatial hypersurfaces everywhere orthogonal to the worldlines of the frame's elements. The worldlines of the elements of a rotating disk admit no such orthogonal hypersurfaces. Since the spacetime of special relativity remains at, we may well ask in what space does the geometry become non-Euclidean. The most direct answer is that this geometry is induced onto the `relative space' formed by the worldlines of the elements of the disk. This space can be de ned precisely as in Norton (1985, section 3). For further discussion of the role of the rotating disk thought experiment in Einstein's thought, see Stachel (1980a). + + + General covariance and general relativity 837 +transformations clearly do not relate di erent states of motion, such as the transformation between spatial cartesian and polar coordinates. However some subgroup of the general group of coordinate transformations is the appropriate one, as Einstein (1916, section 3) makes clear when he writes: It is clear that a physical theory which satis es this postulate [of general covariance] will also be suitable of the general postulate of relativity. For the sum of all substitutions in any case includes those which correspond to all relative motions of three-dimensional systems of co-ordinates. More recently, to negotiate the obvious ambiguities of Einstein's treatment, the notion of frame of reference has reappeared as a structure distinct from a coordinate system. If one conceives of a frame of reference as a space lling system of hypothetical instruments moving with arbitrary velocities, then the minimum information needed to pick out the frame is the speci cation of an arbitrary frame of reference|and the one I shall use here| is that it is a congruence of curves, that is, a set of curves such that every event in the spacetime manifold lies on exactly one of its curves. (Torretti 1983, p28, Norton, 1985, section 3, Vladimirov et al 1987, p95). If the notion of timelike is de ned, we would also require the curves be timelike to ensure that they are the worldlines of physical elements. In the case of the semi-Riemannian spacetimes of relativity theory, whatever further information one might need is supplied by the theory's metrical structure. From it we can read the time elapsed as read by proper clocks moving with the frame, or changes in the directions and spatial distances of neighbouring elements of the frame. Various alternative de nitions of frame of reference are possible. Since a smooth congruence of curves can be speci ed as the unique set of integral curves of a smooth, nonvanishing time-like vector eld, one could take a frame of reference to be such a timelike vector eld (Earman 1974, p270, Jones, 1981, p163). Again, one can employ richer structures. The timelike vector eld could be supplemented by a triad of spacelike vectors pointing to the worldlines of neighbouring elements of vectors over the spacetime manifold. (Synge 1960, ch III.5, Vladimirov et al 1987, p95). Finally a coordinate system is adapted to a frame of reference if the curves of the frame coincide with the curves of constant spatial coordinates. Therefore we could take a frame to be the equivalence class of all coordinate systems adapted to some congruence (Earman 1974, 2270). This de nition has the advantage of bringing us closest to the traditional correspondence between frames of reference and coordinate systems. In special relativity, an inertial frame of reference is a congruence of timelike geodesics. An inertial coordinate system is a coordinate system adapted to an inertial frame of reference. +6.4. Relativity principles and the equivalence of frames +With the notion of frame of reference clari ed, it proves possible to give a more precise treatment of the principle of relativity in so far as it asserts an equivalence of various states of motion, that is, of various frames of reference. Einstein's original treatment of the principle of relativity in special relativity amounted to requiring that the laws of physics adopt the same form when expressed in any inertial coordinate system. This type of formulation of the principle was quite serviceable in the context of a Lorentz covariant special theory of relativity. As we have seen, however, there have been signi cant challenges to the idea that form invariance of laws can capture any physical principle when we are prepared to employ mathematical techniques powerful enough to render virtually any theory generally covariant. A precise formulation of the relevant notion of equivalence of frame has been developed + + + 838 J D Norton +within work that includes Earman (1974), Friedman (1983, especially ch IV.5) and Jones (1981). Their proposals explore many variant de nitions and do so within the context of a wide range of theories, including variants of Newtonian spacetime theory. The essential ideas they share can be illustrated by the following treatment of special and general relativity. The essence of the principle of relativity in the special theory is the indistinguishability of all the inertial states of motion. Thus Einstein's 1905 special relativity paper had been motivated by the realization that no experiment in mechanics, optics or electrodynamics could reveal the uniform motion of the earth through the aether. That is, space and time `look the same' experimentally to observers in any state of inertial motion. Einstein's task was to devise a theory in which they looked the same theoretically as well. This condition can be broken up into a kind of pseudo-experiment. We begin with an inertial observer, who performs a range of experiments in kinematics and other branches of physics. The observer is then boosted into uniform motion with respect to his original state of motion and carries along with him a complete record of all the experiments and their outcomes. These experiments are now repeated and the outcomes compared with those of the original set. The principle of relativity requires that both sets of outcomes must be the same and a theory satisfying the principle of relativity must predict that this will be so. (For a comparison of this sense of the principle and the one that requires form invariance of laws, see Anderson (1964, pp176{82).) This pseudo-experimental condition can be translated into a theoretical condition that amounts to the principle of relativity in special relativity. The theoretical dialog of the inertial observer is the inertial frame of reference. The analog of the setting of the observer into uniform motion is a Lorentz transformation of the frame of reference. The setting up and outcome of all experiments performed by the observer will be determined fully by the spacetime structures of the theory. Therefore the carrying along of the complete description of the observer's experiments and outcomes translates into the carrying along under Lorentz transformation of the spacetime structures of the theory.29 The principle of relativity now simply amounts to the requirement that the Lorentz transformation map spacetime structures allowed by the theory into spacetime structures allowed by the theory. Without further assumption it follows that special relativity satis es the principle of relativity as far as all kinematical experiments are concerned. These are idealized experiments in which the frame directly `sees' the metrical structure of the spacetime without assistance from further material systems. Their outcome is determined solely by that metrical structure. The satisfaction of the principle of relativity follows immediately from the fact that an arbitrary Lorentz transformation h is a symmetry of the Minkowski metric gab that is, it satis es Fock's condition (11). Therefore, if h transforms an inertial frame F1 into an inertial frame F2, then the metric seen by F1 and carried along to F2, h  gab, is the same as the metric gab seen by F2. In the more realistic case, the experiments will involve further spacetime structures, such as electromagnetic elds and charges. The principle of relativity will be satis ed only if these further spacetime structures satisfy the following condition, which is the geometric statement of the Lorentz covariance of the theories of these furthers structures. Let the theory have models +hM gab; (O1)ab:::; (O2)ab:::; : : :i (12) +29This treatments assumes that there are no spacetime structures that elude experimental test, such as the absolute spacetime rigging of a Newtonian spacetime, which introduces a state of rest that cannot be revealed in any experiment (see Friedman 1983, ch III). + + + General covariance and general relativity 839 +where M is an R4 di erentiable manifold, gab a Minkowski metric, and (O1)ab:::; (O2)ab:::; : : : the extra spacetime structures. If h is any Lorentz transformation and (12) is a model of the theory, then +hM gab; h  (O1)ab:::; h  (O2)ab:::; : : :i +must also be a model of the theory. The satisfaction of the principle of relativity now follows. Let F1 be an inertial frame of reference in which are conducted experiments associated with structures (O1)ab:::; (O2)ab:::; : : :. If we transform via Lorentz transformation h to any other inertial frame F2, we require that the theory admit precisely the same experiments and outcomes. That is we require that the theory allow structures h(O1)ab:::; h(O2)ab:::; : : : This is precisely what the geometric version of Lorentz covariance allows. This analysis gives us a precise sense in which the equivalence of inertial frames of reference is realized within the special theory of relativity. The basic moral of the work of Earman, Friedman and Jones is that there is no natural sense in which this equivalence obtains in the spacetimes of general relativity and that there is certainly no extension of it to accelerated frames of reference. In this sense, there is no principle of relativity in the general theory of relativity. This moral follows immediately from the fact that special relativity admits a non-trivial symmetry group, the Lorentz group, which maps inertial frames of reference into one another. The spacetimes of general relativity in general admit no symmetries. In general relativity, the closest analog of an inertial frame of reference is a frame in free fall. It is represented by a congruence of timelike geodesics. In general, a transformation of that maps one freely falling frame of reference into another will not be a symmetry of the metrical structure. Therefore spacetime observers of the rst frame will see di erent metrical properties in spacetime than will those of the second. The indistinguishability required for the equivalence of frames does not obtain. Considering arbitrary frames of reference rather than those in free fall clearly does not change this result. That this sense of equivalence of frames fails to obtain in general relativity is not so surprising and it is dicult to imagine that Einstein ever expected that it would. The real puzzle, then, is to determine the sense in which Einstein believed the equivalence to be extended by general relativity. There is one reading in this geometric language that does allow a general equivalence of frames (Norton 1985, section 5). So far it has been assumed that the background spacetime is represented by the combination of manifold and metric. If instead one takes the manifold alone as the background spacetime, then one immediately has an equivalence of all frames of reference. For, considering just R4 manifolds for simplicity, an arbitrary automorphism is a symmetry of the manifold. Since any frame of reference can be mapped into any other by an automorphism, it follows that each frame `sees' the same spacetime background so that they are equivalent in at least that sense. If this equivalence is to be extended to the sort of equivalence of the principle of relativity of special relativity, then the metric tensor eld of general relativity must be treated in a similar fashion to the structures (O1)ab:::; (O2)ab::: of the above discussion of special relativity. Then a similar sense of equivalence of arbitrary frames follows directly from the active general covariance of general relativity. Let F1 be any frame of reference which sees a metrical eld gab and other elds (O1)ab:::; (O2)ab:::; : : :. That is, the theory has a model +hM gab; (O1)ab:::; (O2)ab:::; : : :i (12) +Then, if F2 is any other frame of reference, the theory must allow a model in which F2 sees an identically con gured set of elds. That is, if h is an automorphism that maps F1 into + + + 840 J D Norton +F2, then F2 must see the elds h  (O1)ab:::; h  (O2)ab::: so that the theory must also have a model +hM gab; h  (O1)ab:::; h  (O2)ab:::; : : :i +That it does follows directly from its active general covariance (section 5.4 above). The diculty with this proposal is that it allows an equivalence of arbitrary frames of reference in all theories that are generally covariant. Such theories include versions of special relativity and Newtonian spacetime theory. Thus, if this generalized equivalence of frames is to be distinctive to general relativity, there must be some principled way of relegating the metric tensor to the contents of spacetime in general relativity, whereas in other spacetime theories, such as special relativity, this metrical structure is to be part of the background spacetime. What makes such a division plausible is the fact that the metric tensor of general relativity incorporates the gravitational eld. Thus its state is a ected by the disposition of masses in the same way as a Maxwell eld is a ected by the disposition of charges. The analogy can be pressed further. In special relativity one can conduct an electrical experiment with some con guration of charges in an inertial frame of reference. The principle of relativity requires that, if we were to recreate that same con guration of charges in another inertial frame, then we would produce the identical elds and experimental outcomes. This is the sense in which all inertial frames of reference are equivalent. Similarly, one could consider some con guration of masses and the metric eld they produce in relation to an arbitrary frame of reference in general relativity as a kind of gravitational experiment in that frame. The active general covariance of general relativity then tells us that we could have laid out the same con guration of masses and elds in any other frame of reference, so that the gravitational experiment would have proceeded identically in any frame of reference. This gives us a sense in which arbitrary frames of reference are equivalent in general relativity. The success of this generalized equivalence depends fully on our being able to conceive of the metric eld as apart of the contents of spacetime in general relativity but not in other theories like special relativity. Einstein's 1918 version of Mach's principle allowed this conception since it required that the metric eld be fully determined by the matter distribution, so that this eld would have the same sort of status as the matter distribution. Since Mach's Principle in this form fails in many of the spacetimes of general relativity, it cannot be used to justify a generalized equivalence of frames in that theory. The only other well developed analysis that allows this conception of the metric eld concerns the distinction between absolute and dynamic objects, to be discussed in the section 8 below. As a dynamical object, the metric of general relativity is naturally classi ed as part of the content of spacetime. As an absolute object, the Minkowski metric of special relativity is naturally classi ed as part of the background spacetime. + + + General covariance and general relativity 841 +7. General relativity without principles +7.1. General relativity without general relativity +Einstein's own developments and discussion of the general theory of relativity place so much importance on general covariance and the extension of the principle of relativity that most accounts of the theory seem compelled to take a position on their importance. Many essentially agree with Einstein as we have seen in section 4. Many others, as we have seen in sections 5 and 6, disagree with Einstein's views; they develop general relativity without claiming general covariance as a fundamental physical postulate and they explain why they do so. There is a third category of exposition of general relativity. These are the expositions that take no special notice of general covariance at all. Of course the develop general relativity in a generally covariant formalism, as is the standard practice. However the expositions are conspicuous for the absence of any statement of fundamental principle concerning covariance or relativity. There is no `principle of general covariance', no `general principle of relativity' and no pronouncement that the theory has extended the equivalence of frames of reference to accelerated frames. And there is no explanation of why these principles are not discussed. It is dicult to know what signi cance to read into such formulations of general relativity without general relativity. Many of these expositions are mathematically oriented. So we might suppose that their authors simply decided not to contend with the question of the physical foundations in favor of other more mathematical aspects of the theory. It is hard to imagine, however, that an author of writing on general relativity can be completely unaware of Einstein's views, if not also the disputes over them. Therefore when that author writes textbook length exposition of general relativity which fails to include such phrases as `general principle of relativity' or `principle of general covariance', one must suppose that the author is making a statement by omission. (The omissions are typically so complete that, if the text has an index, these terms will not be listed in it.) We have already seen that Synge and Fock object to `general relativity' as a misnomer. Thus it seems obvious that similar sentiments drive such authors as that of Time and space, Weight and Inertia: A Chronogeometrical Introduction to Einstein's Theory (Fokker 1965) who display remarkable ingenuity in avoiding the term `general relativity'. Finally, even if no statement is being made by omission, the very possibility and frequency of such accounts of general relativity do indicate that the place of these principles in the theory might not be so straightforward. If the principles are fundamental physical axioms, they would be hard to avoid, even as consequences in an alternate axiomatization. One is hard pressed to imagine a formulation of thermodynamics without the law of conservation of energy as a fundamental axiom or one of the earliest and most important theorems! The subtlety of the situation is captured by Trautman, who observed well into his exposition (1964, p122) of general relativity . . . we have managed to obtain general relativity by a (we hope) fairly convincing chain of reasoning without ever mentioning such a principle [of general covariance]. He did proceed, however, to list several senses of the principle and their non-trivial relationships to the theory. Thus one can nd general covariance relevant without mentioning it in development of the theory. With these interpretative cautions, we can proceed to note that the tradition of exposition of general relativity without general relativity extends back to the earliest of the theory. There are many exposition of relativity theory with this character from the 1920s. They include Bauer (1922), Birkho (1927), Darmois (1927), Chazy (1928) and De Donder + + + 842 J D Norton +(1925) (but De Donder (1921, pp10{15) had emphasized the arbitrariness of coordinates in general relativity and the invariance of its fundamental equations). Eddington (1924, ch I, section l ) labours in detail the notion that one can use arbitrary `space-time frames' for describing phenomena, but without ever mentioning a principle of covariance or a generalized principle of relativity. His earlier Eddington (1920, p20) had allowed that a generalization of the principle of relativity in the theory in so far as he conceded `it will be seen that this principle of equivalence is a natural generalization of the principle of relativity'. This remark was not repeated in Eddington (1924). The lean years after the 1920s saw several exposition of general relativity without general relativity: Rainich (1950) and the synopsis of general relativity by Zatskis (1955). The revival of interest in general relativity in the 1960s brought more such expositions and they have included some of the most important expositions of the theory: Fokker (1965), Schild (1967) (although he mentions (p20) that general relativity `shows there are no inertial frames at all'), Robertson and Noonan (1968), Ehlers (1971), Hawking and Ellis (1973), Dirac (1975), Falk and Ruppel (1975) (although the notion of a generalized principle of relativity is alluded to brie y, e.g., p323), Sachs and Wu (1977), Clarke (1979) (although section 3.1.3 does emphasize the loss of global inertial systems and the novelty of arbitrary coordinate systems in general relativity), Frankel (1979), Schutz (1985) (Although it is allowed (p 3) that general relativity is more general in allowing both inertial and accelerated observers), Martin (1988), Hughston and Tod (1990), Stewart (1990). +7.2. The principle of equivalence as the fundamental principle +While many of these accounts of general relativity, avoid mention of principles of general covariance an generalized relativity, many of them do nd a special place for just one of the three fundamental principles listed by Einstein in 1918, the principle of equivalence. Of course, the version used is typically not Einstein's but one or other variant of an in nitesimal principle of equivalence. The principle is not used in Einstein's manner as a stepping stone to a generalized principle of relativity. Rather it is used to establish a notion claimed as a fundamental principle of general relativity, that special relativity holds in nitesimally in the theory; or, less commonly, it is just taken to be as much of the generalized principle of relativity as general relativity will admit. Such treatments, which employ only the principle of equivalence as a fundamental principle, include: Silberstein (1922, p 12), Eddington (1924, section 17) (although emphasizing (p41) that the principle is to be derived rather than postulated in the exposition), Birkho (1927, pp 140{4), Landau and Lifshitz (1951, ch 10) Fokker (1965, section 6.9) (with the principle in Einstein's original form), Robertson and Noonan (1968, section 6.9), Schild (1967), Falk and Ruppel (1975, section 32), Clarke (1979, ch 3), Frankel (1979, ch 2), Raine and Heller (1981, ch 6.8) Schutz (1985, p 184), Martin (1988, section 1.6, 5.11), Stewart (1990, section 1.13). We have the exposition of Tonnelat (1959), who takes the principle of equivalence to be a `principle of generalized relativity' (p 327) and Wasserman (1992), who also remarks brie y (p342) that the principle of equivalence extends the principle of relativity to include accelerated frames of reference. +7.3 Challenges to the principle of equivalence +One might well wonder if we have not at last found the uncontroversial core of Einstein's accounts of the foundational principles of general relativity in these expositions. That core would now just be the principle of equivalence, even if it is in an altered form Einstein never endorsed. However not even the popular versions of the principle of equivalence have escaped telling attack. The best known challenge has been stated most clearly by Synge. His concern is that + + + General covariance and general relativity 843 +the presence or absence of a gravitational eld must be characterized geometrically, that is, in invariant terms. He asserts that the presence of a gravitational eld corresponds just with non-vanishing curvature of spacetime. Such an invariant criterion is una ected by coordinate transformation, by change of frame of reference or by a change of the state of motion of the observer. Therefore none of these changes will be able to transform away a gravitational eld or bring one into existence, contrary to many versions of the principle of equivalence. He is unimpressed with the requirement that the spacetime metric become diag(1,1,1,-1) at some nominated event, thereby mimicking special relativity at least in some in nitesimal sense. Synge deems this trivial since it merely amounts to the requirement that the metric have Lorentz signature. Thus he wrote his famous lament (1960, p ix) about relativists who . . . speak of the Principle of Equivalence. If so, it is my turn to have a blank mind, for I have never been able to understand this principle. Does it mean that the signature of the spacetime metric is +2 (or -2 if you prefer the other convention)? If so, it is important, but hardly a principle. Does it mean that the e ects of a gravitational eld are indistinguishable from the e ects of an observer's acceleration? If so it is false. In Einstein's theory, either there is a gravitational eld or there is none, according as the Riemann tensor does not or does vanish. This is an absolute property, it has nothing to do with any observer's worldline. Spacetime is either at or curved, and in several places in the book I have been at considerable pains to separate truly gravitational e ects due to curvature of spacetime from those due to curvature of the observer's world-line (in most cases the latter predominate). The Principle of Equivalence performed the essential oce of midwife at the birth of general relativity. But, as Einstein remarked, the infant would never get beyond its long-clothes had it not been for Minkowski's concept. I suggest that the midwife be now buried with appropriate honors and the facts of absolute space-time faced. The idea that the presence of a gravitational eld is associated with the invariant property of curvature can be translated in to observational terms. The non-vanishing of the Riemann curvature tensor entails the existence of tidal forces acting on bodies in free fall. The goal of restricting versions of the principle of relativity to in nitesimal regions of spacetime is to eliminate these tidal forces. However they cannot be so eliminated; for example, the tidal bulges on a freely falling droplet remain as the droplet becomes arbitrarily small, ignoring such e ects as surface tension; see Ohanian (1976, ch 1, 1977) and Bondi (1979). See also Norton (1985, section 10) for an attempt to characterize the imprecise restriction to in nitesimal regions as a restriction on access to certain orders of quantities de ned at a point. Following a suggestion from Einstein, it turns out that an in nitesimal principle of equivalence can hold only at the expense of a restriction so severe that it trivializes the principle. See also Norton (1985, section 11) for Einstein's response to the idea that vanishing spacetime curvature is to be associated with the absence of a gravitational eld. +8. Eliminating the absolute +8.1. Anderson's absolute and dynamical objects +However else he may have changed his viewpoints, we have seen (section 3.9) that Einstein maintained throughout the lifetime of his writings on general relativity that it was distinguished from earlier theories by a single achievement, it had eliminated a causal absolute, the inertial system. If we are to have an account that truly captures Einstein's understanding of general covariance, then we should expect this rather imprecisely notion to play a prominent role. This notion surely lies behind Pauli and Weyl's emphasizing that the metric tensor is determined by the matter distribution through eld equations and that + + + 844 J D Norton +this justi es (Weyl) the name `general theory of relativity' (see section 5.5 above). Einstein's notion surfaces more clearly in Bergmann's (1957, pp11{12) conception of weak and strong covariance. Weak covariance is the type we see in when we use many di erent coordinate systems to describe the one phenomenon in Lagrangian mechanics. The fundamentally trivial nature of this `weak covariance' derives from the rigidity of the classical metric. This is quite distinct from the strong covariance of general relativity where30 it is one's task to calculate the metric . . . as a dynamic variable. We can take one coordinate system or another for this job, but all that we can know is the relation of one frame to the other: we do not know the relation of either to the world. `Strong covariance', therefore, contains not only a reference to the structural similarity of an equation and its transformation, it implies as well that one frame is as good a starting point as another|that we do not need prior knowledge of its physical meaning . . . which is generated at the end. Many important themes are touched on here, as has been indicated by Stachel (forthcoming, footnote 3). This distinction between weak and strong covariance amount to that between passive and active covariance. What concerns us here, however, is that contrasting of the `rigidity of the classical metric' with the metric of general relativity `as a dynamic variable'. The most precise context so far for the statement of Einstein's causal concerns has been provided by Anderson (1964, 1967, ch 4, 1971) (but see also Anderson (1962) for a de nition of absolute change within general relativity). In laying out his system, Anderson uses a somewhat idiosyncratic nomenclature. He labels the set of all possible values of the geometric objects of a theory the `kinematically possible trajectories'. Those sanctioned by the `dynamic laws' or `equations of motion' of the theory, he calls the `dynamically possible trajectories'. The principle novelty of Anderson's development is the distinction between `absolute' and `dynamical' objects. That distinction will be used to strengthen the principle of general covariance into a more restrictive `principle of general invariance'. Although allowing for a time that both special and general covariance principles are devoid of physical content (1964, p184), Anderson (1967, section 4.2, 1971, pp162{65) then came to urge that the requirement of general covariance is not physically vacuous. He allowed that one can take a physical theory and generate successive formulations of wider and wide covariance. However there is a point in the hierarchy at which we are forced to introduces elements which are unobservable or transcend measurement. Since we are prohibited from proceeding to this point in the hierarchy, covariance requirements have physical force. (This strategy for injecting physical content into covariance principles is essentially the one used by Pauli and others in section 5.5 above.) The absolute objects of a spacetime theory are distinguished by precisely the causal criterion that allowed Einstein to designate the inertial systems of special relativity as absolute. Anderson and Gautreau (1969, p1657) summarize: Roughly speaking, an absolute object a ects the behaviour of other objects but is not a ected by these objects in turn. +30The two ellipses `. . . ' and emphasis are Bergmann's. + + + General covariance and general relativity 845 +The remaining objects are dynamical. Thus the Minkowski metric of special relativity is an absolute object. In special relativistic electrodynamics, the Minkowski metric a ects the Maxwell eld and charge ux in determining, for example, which are the inertial trajectories of charges. However neither Maxwell eld nor charge ux, the dynamical objects of the theory, a ect the Minkowski metric. Whatever their form, the Minkowski metric stays the same. This is the sense in which it a ects without being a ected. Since the Minkowski metric induces the inertial frames on spacetime, Anderson's identi cation of the Minkowski metric as an absolute object ts exactly with Einstein's identi cation of inertial frames as absolutes. This loose de nition must be made more precise and Anderson (1967, p83{4) (see also Anderson (1971, p166) gives a more precise de nition. Having eliminated irrelevant objects from the set of geometric objects yA allowed in the theory We now proceed to divide the components of yA into two sets,  and za where the  have the following two properties: (1) the  constitute the basis of a faithful realization of the covariance group of the theory. (2) Any  that satis es the equations of motion of the theory appears, together will all its transforms under the covariance group, in every equivalence class of dpt (dynamically possible trajectories) The  if they exist, are the components of the absolute objects of the theory. The remaining part of yA, the za are then the components of the dynamical objects of the theory. Condition (1) is an important but essentially technical condition that the transformation behaviour of the  respect the group structure of the theory's covariance group ( e. g. the  ought to transform back into themselves under an identity transformation of the covariance group.) Condition (2) essentially just says that the absolute objects  are the same in every dynamically possible trajectory (i.e. model) of the theory. The condition, however, must allow that an absolute object, such as a Minkowski metric, g can be manifested on many di erent forms as it transforms under the members of the covariance group. Therefore the second condition collects the dynamically possible trajectories into equivalence classes of intertransformable members. Since each class is closed under transformations of the covariance group, the one set of absolute objects and all their transforms will appear in each class. Thus condition (2) requires, in e ect, that the absolute objects that appear in all models are the same up to a transformation of the theory's covariance group. With this distinction in place, Anderson now de nes the symmetry group or `invariance group of a physical theory' (Anderson 1971, p166) as that subgroup of the covariance group of the theory which leaves invariant the absolute objects of the theory. In particular, if there are no absolute objects, the invariance group and the covariance groups are the same group. The `leaves invariant' is to be understood in the sense of a symmetry transformation such as given in (10) and (11) above. There is an analogous de nition for the `symmetry group of a physical system' (Anderson 1967, p87) Anderson's central claim (e.g. Anderson 1967, p338) is that this symmetry group is what Einstein really had in mind when he associated the Lorentz group with special relativity and the general group with general relativity. For a requirement on a symmetry group, not a covariance group, is the correct way to express a relativity principle. Even if we formulate our theories in generally covariance fashion, they continue to be characterized by the groups expected if we look to their symmetry groups. The symmetry group of a generally covariance special relativity is the Lorentz group. Again, consider a generally co + + + 846 J D Norton +variant formulation of Newtonian spacetime theory with spacetime structures ta; habandra where the gravitational eld is not incorporated into ra. Then these three objects are the absolute objects of the theory and their symmetry group is the Galilean group. Finally, general relativity has no absolute objects. Its symmetry group is the general group. One can grasp the picture urged if one imagines that the background spacetime of a theory is the spacetime manifold together with the theory's absolute objects|although `background spacetime' is not a notion discussed by Anderson. In the cases of special relativity and the above version of Newtonian spacetime theory, both admit a family of preferred inertial frames of reference which remain unchanged under the Lorentz group or Galilean group respectively. In the case of general relativity, the background spacetime is just the manifold whose symmetry group is the group of arbitrary transformations. According to Anderson, what Einstein really intended with his principle of general covariance is what Anderson calls the `principle of general invariance'. This principle requires that the symmetry group of a theory be the general group of transformations or, as Anderson calls them, the `manifold mappings group'. This principle rules out the possibility of any non-trivial absolute objects in the theory, that is, those which have more than merely topological properties. In this sense, the principle of general invariance amounts to a no-absolute-object requirement and o ers a precise reading for Einstein's claim that general covariance has eliminated an absolute from spacetime. +8.2. Responses to Anderson's viewpoint +Anderson's ideas on absolute and dynamical objects have found a limited but favorable response in the literature. Misner et al (1973, section 17.6) present a requirement of no absolute objects in terms of the requirement of `no prior geometry' where: By `prior geometry' one means any aspect of the geometry of spacetime that is xed immutably, i.e. that cannot be changed by changing the distribution of gravitating sources. They describe Einstein as seeking both this requirement as well as a `geometric, coordinate independent formulation of physics' when he required general covariance|and that this has been responsible for half a century of confusion. Anderson's principle of general invariance appears in Trautman (1973), as does the distinction between absolute and dynamical objects in Kopczynski and Trautman (1992, ch 13). Ohanian (1976, pp252{4) uses Anderson's principle of general invariance to respond to Kretschmann's objection that general covariance is physically vacuous. He does insist, however, that the principle is not a relativity principle and that the general theory of relativity is no more relativistic than the special theory (p257). Anderson's ideas seem also to inform Buchdahl's (1981, lecture 6) notion of `absolute form invariance'. The distinction between absolute and dynamical objects has been received and developed most warmly by philosophers of space and time, so that in place of (6), the general model of spacetime theory is given as +hM; A1; A2; : : : ; D1; D2; : : :i +where A1; A2; : : : are the absolute objects and D1; D2; : : : the dynamical. However they do not generally allow that Anderson's reasoning has vindicated Einstein's claim that the general theory of relativity extends the principle of relativity of special relativity. See Earman (1974, 1989, ch 3), Friedman (1973, 1983), and Hiskes (1984). Earman (1989, section 3.4) investigates the possibilities of the symmetry group of the absolute objects of a theory di ering from the symmetry group of the dynamical objects. +8.3. No gravitational eld|no spacetime points + + + General covariance and general relativity 847 +Stachel (1986, sections 5, 6) has provided an interesting extension of the viewpoint advanced by Anderson. Stachel's concern is that our formulations of general relativity are still not in a position to explicate Einstein's idea that spacetime cannot exist without the gravitational eld (see section 3.5 above). Stachel faults our representing of physical spacetime events by the mathematical points of the spacetime manifold. Read naively, this de nition tells us that a manifold without metrical eld represents a physical spacetime of events with topological properties but with no metrical relations. Stachel's proposal applies to spacetime theories without absolute objects, which he calls `generally covariant', and can be reviewed only informally here. To form the models of such theories one assigns various geometric objects|tensor elds, for example|to each point of the manifold in the usual way. In principle, many di erent such elds could be assigned. In the case of general relativity, we have a host of possible metrical elds of all sorts of di erent curvature. The loose notion of the space of all such possible elds is given precise formulation by Stachel as a bre bundle E over the manifold M . The particular elds that are chosen for inclusion in the theory's models are picked out though cross-sections of the bre bundle E. Loosely speaking, a cross section  amounts to an association of a point of the manifold M with the geometric objects assigned to it in some model of the theory. (More precisely, a cross-section  is a map that goes from a point p of the manifold M to a member (p) of the bre bundle E, where (p) must be associated with p by the bundle's projection map , so that (p) = p.) The core of Stachel's proposal is that the physical events of spacetime are represented by the inverse of this map . That is|loosely speaking|the physical events are not represented directly by the points of the spacetime manifold; rather, in their place, we use the association of the points of the manifold with the geometric structures de ned on them. We now automatically have the property of spacetime that Einstein announced. If we take away the gravitational eld, that is the metric eld, from a spacetime in general relativity, then we have taken away the bre bundle and with it the map that represents the physical spacetime events. In a theory with absolute objects, however, physical events are represented directly by points of the base manifold. Therefore their behaviour is quite di erent. See Stachel (1986) for further details of how theories with absolute objects are treated and of the machinery needed to allow that one physical situation is represented by an equivalence class of di eomorphic models. +8.4. What are absolute objects and why should we despise them? +There are two areas of diculty associated with the general theory of absolute and dynamical objects. The rst is that question of how we de ne absolute objects. Anderson's de nition was that an object was absolute if the same object (up to coordinate transformation) appeared in all the theory's models. In the coordinate free, geometric language how are we to understand the `same' ? The obvious candidate is that two objects are the same if they are isomorphic. Global isomorphism is the criterion used in Earman's (1974, p282) de nition of absolute objects to pick out when one has the same object in all models. Friedman (1973, p308{9, 1983, p58{60) uses only the requirement that the objects be locally di eomorphic.31 The rst diculty with this criterion of di eomorphic equivalence as sameness was pointed out by Geroch (Friedman 1983, p59). The criterion deems as the same all timelike +31More precisely, in the 1983 version of the de nition, what Friedman calls `d-equivalence' is this: If a theory has models hM; 1; : : : ; ni and hM; 1; : : : ; ni, then i and i are d-equivalent of, for every p 2 M there are neighbourhoods A and B of p and a di eomorphism h : A ! B such that i = h  i. + + + 848 J D Norton +non-vanishing vector elds, so that however such a eld arises in a theory, it will be one of its absolute objects. Thus, in standard `dust' cosmologies, the velocity eld U a of the dust becomes an absolute object. To avoid the problem, Friedman suggests a rather contrived escape: formulate the theory of dust with the dust ux U a where  is the mass density, instead of  and U a separately. (Friedman is relying her on the possibility that  vanishes somewhere. A better choice would have been the stress-energy tensor for pressureless dust U aU b.) More seriously, modifying slightly an example of Torretti (1984, p285), we could imagine the following hybrid classical cosmology. The spacetime structure is given exactly by any of the Robertson-Walker spacetime metrics. The metrics are posited a priori and not governed by the presumed inhomogeneous matter distribution through gravitational eld equations, Therefore the curvature of the metric is unaltered in the vicinity of massive bodies. In this case, we would judge the metrical spacetime structure to act on the matter distribution without the matter distribution acting back on it. However, since models of the theory would allow metrics of di erent curvature, we cannot use existing de nitions to identify the spacetime metric as an absolute object. Torretti's counterexample shows us that the basic notion of `sameness' does not fully capture the notion of things that act but are not acted upon. The second area of diculty associated with the general theory of absolute and dynamical objects is a presumption of Anderson and Einstein (assuming that he is correctly interpreted by the theory). They presume that there is some compulsion to eliminate absolute objects. Of course they are right in the sense that our best theory of space and time happens not to employ absolute objects. Thus several of Anderson's arguments of the principle of general invariance can form a premise of arguments that lead to empirically con rmed results (Anderson 1967, section 10.3, 1971, p169). However absolutes are supposed to be defective in a deeper sense. It is not just that we happen not to see absolutes in nature; Nature is somehow supposed to abhor things that act but are not acted upon. The diculty is to clarify and justify this deeper sense. Anderson (1967, p339, 1971, p169) sees in nature a `generalized law [principle in 197] of action and reaction'. But the principle is so vague that it is unclear what the principle really says and where it can be applied. Does Planck's constant h or the gravitation constant G `act' on matter without su ering `reaction' ? With this vagueness how can we tell if the law is true or even whether we should hope for it to be true? Is it, perhaps, a dubious guilt by association with Aristotle's Unmoved Mover? Einstein comes closer to an explanation with his analogy (section 3.9 above) to pots of water, one boiling, one not. There has to be a sucient reason for the di erence. Analogously, the diculty with absolute objects is that there is no sucient reason for them to be one way rather than another. Now we might allow that such a principle of sucient reason applies to temporarily successive states of systems, although quantum theory calls even that into doubt. But why should we require this sort of principle to hold for aspects of the universe as a whole? In answer, we might take Born expansion of Einstein's (1916, section 2) denunciation of an absolute, inertial space as an ad hoc cause. Born (1924, p311) explains If, however, we ask what absolute space is and in what other way it expresses itself, no one can furnish an answer other than that absolute space is the cause of centrifugal forces but has no other properties. This consideration shows that space as the cause of physical occurrences must be eliminated from the world picture. It is hard to sympathize with Born's complaint. The absolute Minkowski metric of a special relativistic world has an extremely rich collection of properties all of which can be con rmed by possible experiences. It is dicult not to see the very objection of Born and Einstein as ad hoc. They seek to use vague and speculative metaphysics to convert + + + General covariance and general relativity 849 +something that happens to be false into something that has to be false. These seem to be Schlick's 1920, p40) sentiments when he observes . . . we can . . . consider the expression `absolute space' to be a paraphrase of the mere fact that these [centrifugal] forces exist. They would then simply be immediate data; and the question why they arise in certain bodies and are wanting in others would be on the same level with the question why a body is present at one place in the world and not at another. . . . I believe Newton's dynamics is quite in order as regards the principle of causality. Special relativity has su ered too long form the crank myth that it not just happens to be true but it has to be true and that proper meditation on clocks and light signalling reveals it. Let us not create a similar myth for general relativity. +9. Boundaries and puzzles +9.1. Is general covariance too general? Or not general enough? +While most have been satis ed with general relativity as a general covariant theory, Fock (1957, 1959, pp xv{xvi, section 93) has proposed that the four coordinate degrees of freedom of the generally covariant theory be reduced by application of a coordinate condition. Fock's `harmonic coordinates' are picked out by the condition + x +(p g g) = 0 +Fock applies this condition to the case of spacetimes which are Minkowskian at spatial innity and nds that the resulting equations are the natural generalization of the standard Galilean coordinates of spatial relativity and are xed up to a Lorentzian transformation. Fock sees the physical importance of harmonic coordinates in such problems as the justifying of Copernican of the Ptolemaic cosmology. In harmonic coordinates, the earth orbits the sun and not vice versa. Fock's proposal proved controversial. Criticism of Fock's proposal was aired at a conference in Berne in July 1955 for the jubilee of relativity theory (Fock 1956). Infeld argued that a restriction to harmonic coordinates is acceptable as a convenience. `But to add it always (or almost always) to the gravitational equation and to claim that its virtue lies in the fact that the system is only Lorentz invariant, means to contradict the principle idea of relativity theory.' Trautman (1964, p123) and Kopczynski and Trautman (1992, p124) have also objected that Fock's proposal amount to the postulation of new spacetime structures for which no physical interpretation can be given. + + + 850 J D Norton +In so far as Fock intended to reduce permanently the covariance of general relativity and introduce further structure, then these critical attacks are warranted. The harmonic coordinate condition is unacceptable as a new physical principle. But Fock (1959) seems to hold a milder position. He emphasized (pp350{1) that the introduction of harmonic coordinates is intended in a spirit no di erent from that which introduces preferred Galilean coordinates into a generally covariant formulation of special relativity. Thus `the existence of a preferred set of coordinates . . . is by no means trivial, but re ects intrinsic properties of space-time'. In the case of a spacetime Minkowskian at spatial in nity, harmonic coordinates simply reveal a structure already assumed as part of the boundary condition. Their use does not amount to an unwarranted postulation of new structure|unless one deems the boundary conditions themselves unwarranted. For further discussion see Gorelik (forthcoming) The issue surrounding Fock's proposal was whether a restriction of the covariance of general relativity could be justi ed. Arzelies (1961) has proposed a modi cation of general relativity which amounts to a kind of expansion of its covariance. He urges that Einstein's theory has still not satis ed the requirements of the generalized principle of relativity and that the transformations it allows should be extended in the following sense. If we start with a coordinate system Xi then, under coordinate transformation, the coordinate di erential dXi transform into new coordinate di erentials dxi. It is customarily assumed that the coordinate di erentials dxi are exact, so that they can be integrated into the new coordinate systems xi. Arzelies proposed that this restriction be dropped. This would certainly generalize the group of transformations since the functions ik of the equations dxi = +ikdXk need no longer be restricted by the requirement of exactness. The modi cation of extremely far reaching, however, in so far as it leads to the loss of many familiar theorems. For example, it will now be possible to transform the line elements of non- at metrics to the form +ds2 = (dx1)2 + (dx2)2 + (dx3)2 + (dx4)2 +over a neighbourhood (not just a point), where this was formerly only possible if the metric was at. +9.2 The Einstein puzzle +There is a presumption in much modern interpretation of Einstein's pronouncements on the foundations of the general theory of relativity. It is that much of what he says cannot be taken at face value. (Why does Einstein make such a fuss about introducing arbitrary spacetime coordinates? We have always been able to label spacetime events any way we please!) Thus we are either to translate what he really meant into some more precise context, as does Anderson, or to dismiss it as confused. The proposal of Norton (1989, 1992) is that our modern diculty in reading Einstein literally actually stems from a change of context. (For related concerns see Norton (1993).) The relevant change lies in the mathematical tools used to represent physically possible spacetimes. In recent work in spacetime theories, we begin with a very re ned mathematical entity, an abstract di erentiable manifold, which usually contains the minimum structure to be attributed to the physical spacetimes. We then judiciously add further geometric objects only as the physical content of the theory warrants. Moreover, we have two levels of representation. We rst represent the physically possible spacetimes by the geometric models of form (6) and then these geometric models are represented by the coordinate based structures (7). General covariance is usually understood as passive general covariance and therefore arises as a mathematical de nition, as we have seen. + + + General covariance and general relativity 851 +In the 1910s, mathematical practices in physics were quite di erent. The two levels of representation were not used. When one represented a general space or spacetime, one used number manifolds|Rn or Cn for example. Thus Minkowski's `world' was not a di erentiable manifold that was merely topologically R4. It was literally R4, that is it was the set of all quadruples of real numbers. Now anyone seeking to build a spacetime theory with these mathematical tools of the 1910s faces a very di erent problems from the ones we see now. Modern di erentiable manifolds have too little structure and we must add to them. Number manifolds have far too much structure. They are fully inhomogeneous and anisotropic. The origin h0; 0; 0; 0i is quite di erent from every other point, for examples. And all this structure had canonical physical interpretation. If one took the x4 axis as the time axis, then x4 coordinate di erences were physically interpreted as di erences of clock readings. Timelike straights would be the inertial trajectories of force free particles. The problem was not how to add structure to the manifolds, but how to deny physical signi cance to existing parts of the number manifolds. How do we rule out the idea that h0; 0; 0; 0i represents the preferred center of the universe and that the x4 coordinate axis a preferred state of rest? Felix Klein's Erlangen program provided precisely the tool that was needed. One assigns a characteristic group to the theory. In Minkowski's case, it is the Lorentz group. Only those aspects of the number manifold that remain invariant under this group are allowed physical signi cance. Thus there is no physical signi cance in the preferred origin h0; 0; 0; 0i of the number manifold since it is not invariant under the transformation. But the collection of timelike straights of the manifold are invariant; they represent the physically real collection of all inertial states of motion. As one increases the size of the group, one strips more and more physical signi cance out of the number manifold. We can put this in another way. A spacetime theory coordinates a physically possible spacetime with the number manifold. The characteristic group of the theory tells us that many di erent such coordinations are allowed and equally good. What is physically signi cant is read o as that part of each coordination common to all of them. This coordination of physical events with quadruples of numbers in is what was meant by `coordinate system' and the equivalence of two such systems was far from a mathematical triviality. It was the essence of the physical content of the theory. It is in this tradition that Einstein worked in the 1910s. His project was to expand the group of his theory as far as possible. But he had to proceed carefully since such expansions came with a stripping of physical signi cance from the number manifold. Thus Einstein (1916, section 3) needed to proceed very cautiously in explaining how the general covariance of his new theory had stripped the coordinates of their direct relationship to the results of measurements by rod and clock. The project is clearly also a project of relativization of motion. The imposition of the Lorentz groups stripped the x4 axis of the physical signi cance as a state of rest, implementing a principle of relativity for inertial motion. The transition to the general groups stripped the set of timelike straights of physical signi cance as inertial motion, extending the principle to accelerated motion. If this was all that Einstein had done, then his whole project would have remained within the Erlangen program tradition and there would be no debates today over whether Einstein succeeded in extending the principle of relativity. But, in the transition from the Lorentz tot the general group, Einstein added an element that carried him out of the tradition of the Erlangen program. He associated a Riemannian quadratic di erential form with the spacetime. (Thus Cartan (section 6.2 above) captures precisely the crucial point.) While Einstein could correctly say that he had generalized the principle of relativity insofar as he had stripped physical signi cance from the timelike straights of the number manifold, what remained to be seen was whether he had reintroduced essentially this same structure + + + 852 J D Norton +by means of the quadratic di erential form. In e ect this question has become the focus of the debate over the generalized principle of relativity. Finally, it is helpful to bear in mind that what Einstein meant by `coordinate system' is not the same as the modern `coordinate charts' of a di erentiable manifold. The latter relate structures of (6) and (7) and the equivalence of each representation is a matter of mathematical de nition. Einstein's coordinate systems are actually akin the representation relation between physically possible spacetimes and the models of form (6). That two models represent the one physically possible spacetime is a physical assumption that amounts to assuming that their mathematical di erences have no physical signi cance. Correspondingly, within the context of Einstein's formulation of spacetime theories, that two coordinate system represent a physically possible spacetime is once again a physical assumption and for the same reason. That is, Einstein's covariance principles are most akin to modern active covariance principles. In sum, there is no real puzzle in much that of what Einstein said. Rather it now only seems puzzling since he is solving problems we longer have because of the greater sophistication of our mathematical tools. Indeed, in good measure we owe to Einstein's inspiration the development and widespread use of mathematical tools that automatically solve problems over which he laboured so hard. +10. Conclusion +The debate over the signi cance of general covariance in Einstein's general theory of relativity is far from settled. There are essentially three viewpoints now current. First is the viewpoint routinely attributed to Einstein. It holds that the achievement of general covariance automatically implements a generalized principle of relativity. In view of the considerable weight of criticism, this view is no longer tenable. Relativity principles are symmetry principles, the requirement of general covariance is not a symmetry principle. The requirement of general covariance, taken by itself, is even devoid of physical content. It can be salvaged as a physical principle by supplementing it with further requirements. The most popular are a restriction to simple law forms and a restriction on the additional structures that may be used to achieve general covariance. However neither supplementary condition has been developed systematically beyond the stage of fairly casual remarks. The second viewpoint has been developed by Anderson and is based on his distinction between absolute and dynamical objects. His `principle of general invariance' entails that a spacetime theory can have no non-trivial absolute objects. Anderson argues that the principle is a relativity principle, since it is a symmetry principle, and that it is what Einstein really intended with his principle of general covariance. In this approach, general relativity is able to extend the symmetry group of special relativity form the Lorentz group to the general group. This extension depends on the metric being a dynamical object, which is no longer required to be preserved by the symmetry transformations of the theory's relativity principle. The third viewpoint holds that the dynamical character of the metric is irrelevant in this context an that the metric must be preserved under the theory's symmetry group, if that group is to be associated with a relativity principle. Since the metrics of general relativistic spacetimes have, in general, no non-trivial symmetries, there is no non-trivial relativity principle in general relativity. Whatever may have been its role and place historically, general covariance is now automatically achieved by routine methods in the formulation of all seriously considered spacetime theories. The foundations of general relativity do not lie in one or other principle advanced by Einstein. Rather, they lie in the simple assertion + + + General covariance and general relativity 853 +that spacetime is semi-Riemannian, with gravity represented by its curvature and its metric tensor governed by the Einstein eld equations. +Acknowledgements +The researching and writing of this review was supported by the National Science Foundation under Grant No. SBE-9121326. I thank the foundation for its support and also Jean Eisenstaedt, Don Howard, Al Janis, and Carlo Rovelli for helpful discussions. I am also very grateful to Don Howard for assistance with German translations. +References +Adler R. 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Leibfried and W Biem (New York:Dover) +Bose S K 1980 An Introduction to General Relativity (New York: Wiley) +Bowler M G 1976 Gravitation and Relativity (Oxford: Pergamon) +Bridgman P 1949 Albert Einstein: Philosopher Scientist 2nd edn, ed P A Schilpp (New York: Tudor) pp 315{54 +Buchdahl HA 1981 Seventeen Simple Lectures on General Relativity (New York: Wiley) +Bunge M 1967 Foundations of physics (New York: Springer) +Butter eld J 1987 International Srudies in the Philosophy of Science 2 10{32 +| 1988 Proceedings of the 1988 Biennial Meeting of the Philosophy of Science Association vol. 2 ed A Fine and J Leplin (East Lansing, MI: Philosophy of Science Association) pp 65{81 +| 1989 British J. Phil. Sci. 40 1{28 +Carmeli M 1982 Classical Fields: General Relativity and Gauge Theory (New York: Wiley) +Carmichael R 1920 The Theory of Relativity 2nd edn (New York: Wiley) +Cartan E 1923 Ann. Sci. ENS 40 325{412; 1924 Ann. Sci. ENS 41 1{25; transl 1982 A Magnon and A Ashtekhar in On Manifolds with an Ane Connection and the Theory of General Relativity (Naples: Bibliopolis) +| 1927 L'Ensignment Mathematique 26 200{225: 1952 Oevres Completes Part 1, voI II (Paris: Cauthier-Villars) pp 841{66 +Cartwright N and Hoefer C (forthcoming) Philosophical Problems of the Internal and External Worlds: Essays on the Philosophy of Adolf Grunbaum ed J Earman, A Janis, G Massey, N Rescher (Pittsburgh PA: University of Pittsburgh University of Konstanz) +Charon J E 1963 15 Lecons sur la Relativite Generale avec une Introduction au Calcul +Tensoriel (Geneva: Editions Rene Kister) +Chazy J 1928 La Theorie de la Relativite et la Mecanique Celeste (Paris: Gauthier-Villars) +Clarke C 1979 Elementary General Relativity (London: Edward Arnold) +Cunningham E 1921 Relativity: The Electron Theory and Gravitation (London: Longmans Green & Co.) +d'Iverno R 1992 Introducing Einstein's Relativity (Oxford: Clarendon) +Darmois G 1927 Les Equations de la Gravitation Einsteinienne: Memorial des Sciences Mathematique, L'Academie des Sciences de Paris. Facs. XXV (Paris: Gauthier.Villars) +Davis W R 1970 Classical Fields, Particles and the Theory of Relativity (New York: Gordon and Breach) +De Donder T 1921 La Gravi que Einsteinienne (Paris Gaurhier-Villars) +| 1925 Introduction a la Gravi que Einsteinienne: Memorial des Sciences Mathematique, L'Academie des Sciences de Paris Facs. VIII (Paris: Gauthier-Villars) +De Felice F and Clarke C J S 1990 Relativity on Curved Manifolds (Cambridge: Cambridge University Press) +De Sitter (1916) Mon. Not. R. Astron. Soc. 76 699{728, 1916 77 155{184; 1917 78 3{28 +Dirac P A M 1975 General Theory of Relativity (New York: Wiley) +Earman J 1974 Found. Phys. 4 267{89 +| 1989 World Enough and Spacetime: Absolute versus Relational Theories of Space and Time (Cambridge, MA: Bradford/MIT Press) +Earman J and Friedman M 1973 Phil. Sci. 40 329{59 + + + General covariance and general relativity 855 +Earman J and Norton J D 1987 British J. Phil. Sci. 38 515{25 +Eddington A S 1920 Report on the Relativity Theory of Gravitation 2nd ed (London: Fleetway) +| 1924 The Mathematical Theory of Relativity 2nd edn (1952) (Cambridge: Cambridge University Press) +Ehlers J 1971 Proc. Int. School of Physics 'Enrico Fermi' Course XLVII ed B K Sachs (New York: Academic) pp 1{70 +Einstein A 1905 Ann. Phys. 17 891{921 (transl Lorentz 1923 pp 37{65) +| 1907 Jahrbuch der Radioaktivitat und Elektronik 4 411{462; 1908 5 98{99 +| 1911 Ann. Phys. 35 898{908 (transl Lorentz 1923, pp 99{108) +| 1912a Ann. Phys. 38 355{69 +| 1912b Ann. Phys. 38 443{58 +| 1912c Vierteljahrsschrift fur gerichtliche Medizin und o enrliches Sanitatswesen 44 37{40 +| 1912d Ann. Phys. 38 1059{64 +| 1913 Physikalische Zeitschrift 14 1249{62 +| 1914 Preussische Akademie der Wissenschaften (Berlin), Sitzungsberichte 1030{1085 +| 1914a Scientia 15 337{48. +| 1915 Preussische Akademe der Wissenschaften (Berlin), Sitzungsberichte 778{86, 799{ 86, 831{9, 844{7 +| 1916 Ann. Phys. 49 769{822 (translated 1923 Lorentz et al, pp 111{164 (without p 769)) +| 1916 Ann. Phys. 51 639{642 +| 1917 Preussische Akademie der Wissenschaften (Berlin), Sitzungsberichte 142{152 (transl 1923, Lorentz et al pp 175{88) +| 1917a Relativity: the Special and the General Theory (transl 1977 R W Lawson (London: Methuen)) +| 1918 Ann. Phys. 55 240{44 +| 1918a Naturwissenschaften 6 697{702 +| 1919 Preussische Akademie der Wissenschaften, Sitzungsberichte 349{56 (transl 1923 Lorentz et al pp 191{8) +| 1922 Sidelights on Relativity transl G B Je rey and W Perrett (New York: Dutton) (Reprinted 1983 New York: Dover) +| 1922a The Meaning of Relativity 5th edn (Princeton NJ Princeton University Press) +| 1924 Schweizerische Naturforschende Gesellschaft, Verhandlungen 105 85{93 +| 1927 `The Mechanics of Newton and Their In uence on he Development of Theoretical Physics' Ideas and Opinions (New York: Bonanza) pp 253{61 +| 1933 `On the Methods af Theoretical Physics' Ideas and Opinions (New York: Bonanza) pp 270{7 +| 1940 The Fundaments of Theoretical Physics Ideas and Opinions (New York: Bonanza) pp 33{35 +| 1949 Autobiographical Notes (La Salle, IL: Open Court) +| 1950 `On the Generalized Theory of Gravitation' Ideas and Opinions (New York: Bonanza) pp 341{356 + + + 856 J D Norton +| 1952 Relalivity: the Special and the General Theory transl R W Lawson. (London: Methuen) Appendix V Einstein A and de Sitter W 1932 Proc. Nat. Acad. Sci. (Washington) 18 213{14 +Einstein A and Grossmann M 1913 Entwurf einer verallgemeinerten Relativitatstheorie und einer Theorie der Gravitation (Leipzig: Teubner. separatum); addendum 1913 Einstein Zeitschrift fur Mathematik und Physik 63 225{61 Eisenstaedt J 1986 Archive for History of Exact Sciences 35 115{185 +| 1989 Einstein and the Hislory of General Relativity: Einstein Studies, vol I eds D Howard and J Stachel (Boston: Birkhauser) pp 277v{92 Ellis G F R and Williams R M 1988 Flat and Curved Space-Times (Oxford: Clarendon) +Falk G and Ruppel W 1975 Mechanik RelaIivitat Gravitation: Ein Lehrbuch 2nd edn (Berlin: Springer) Fock V 1956 HeIv. Phys. Acta. Supplementum IV, pp 239{243 | 1957 Reviews of Modern Physics 29 325{333 +| 1959 The Theory of Space Time and Gravitation transl N Kemmer (New York: Pergamon) +| 1974 Die Stellung des Copernicanischen Systems im Ideenkreis der Einsteinschen Gravitationstheorie (Leipzig: Karl Marx Universitat) +Fokker A D 1965 Time and Space, Weight and Inertia: A Chronogeometrical Introduction to Einstein's Theory transl D Bijl; transl and ed D Field (Oxford: Pergamon) +Foster J and Nightingale J D 1979 A Short Course in General Relativity (London: Longman) +Frankel T 1979 Gravitational Curvature: An Introduction to Einstein's Theory (San Francisco: Freeman) +Freundlich E 1919 The Foundations of Einstein's Theory of Gravitation transl H L Brose (London: Methuen) Friedman M 1973 Space, Time and Geometry ed P Suppes (Dordrecht: Reidel) pp 296{320 +| 1983 Foundations of Space-Time Theories: Relativistic Physics and the Philosophy of Science (Princeton, NJ: Princeton University Press) Friedrichs K 1927 Mathhematische Annalen 98 566{75 +Gorelik G (forthcoming) The Attraction of Gravitation: New Studies in History of General Relativity ed J Earman, M Janssen and JD Norton (Boston: Birkauser) +Graves J C 1971 The Conceptual Foundations of Contemporary Relativity Theory (Cambridge, MA: MIT Press) Havas P 1964 Rev. Mod. Phys. 36 938{65 +Hawking S and Ellis G F R 1973 The Large Scale Structure of Space-time (Cambridge: Cambridge University Press) +Hilbert D 1915 Akademie der Wissenschaften, Gottingen, Nachrichten pp 395{407; 1917 Akademie der Wissenschaften, Gottingen, Nachrichten pp 53{76 Hiskes A L D 1984 Found. Phys. 14 307{32 Ho mann B 1932 Rev. Mod. Phys. 4 173{204 +Howard D 1992 Studies in the Hislory of General Relativity ed J Eisenstaedt and A Kox (Boston: Birkhauser) pp 154{243 +Howard D and Norton J D (forthcoming) The Attraction of Gravitation: New Studies in History of General Relativity ed J Earman, M Janssen and J D Norton (Boston: Birkhauser) + + + General covariance and general relativity 857 +Hughston L P and Tod K P 1990 An Introduction to General Relativity (Cambridge: Cambridge University Press) +Jones R 1981 After Einstein ed P Barker and C G Shugart (Memphis, TN: Memphis State University Press) +Jordan P 1955 Schwerkraft und Weltall (Braunschweig: Vieweg) +Kenyon I R 1990 General Relativity (Oxford: Oxford University Press) +Kenzberg P 1989 Einstein and the History of General Relativity ed D Howard and J Stachel (Boston: Birkhauser) pp 325{56 +Klein F 1872 Gesammelte Mathematische Abhnadlungen. vol 1, ed R Fricke and A Ostrowski (Berlin: Springer) pp 460{497 +Kopczynski W und Trautman A 1992 Spacetime and Gravitation (Chichester: Wiley) +Kop A 1923 Grundzuge der Einsteinschen Relativitatstheorie (Leipzig: Hirzel) +Kottler F 1922 Encyklopadie der mathematischen wissenschaften mit Einschluss an ihrer Anwendung vol VI, part2, 22a Astronomie ed K Schwertzschild, S Oppenheim and W v Dyke (Leipzig: Teubner) pp 159{237 +Kratzer A 1956 Relativitatstheorie (Munster: Aschendorfsche) +Kretschmann E 1915 Ann. Phys. 48 907{982 +| 1917 Ann. Phys. 53 575{614 +Kuchar K V 1988 Highlights in Gravitation and Cosmology (Cambridge: Cambridge University Press) +Landau L D and Lifshitz E M 1951 The Classical Theory of Fields transl M Hamermesh (Oxford:Pergamon) +Laue M 1911 Das Relativitatsprinzip (Braunschweig: Vieweg) +| 1921 Die Relativitatstheorie. Vol 2: Die Allgemeine Relativitatstheorie und Einsteins Lehre von der Schwerkraft (Braunschweig: Vieweg) +Lawden D F 1962 An Introduction to Tensor Calculus and Relativity (London: Methuen) +Lenard P 1921 Uber Relativitatsprinzip, Ather, Gravitation 3rd edn (Leipzig: Hirzel) +Levi-Civita T 1926 The Absolute Di erential Calculus transl M Long (New York: Dover) +Levinson H C and Zeisler E B 1929 The Law of Gravitation in Relativity (Chicago: University of Chicago Press) 2nd edn +Lorentz H A et al 1923 Principle of Relativity (London: Methuen); (1952 New York: Dover) +Mach E 1893 Science of Mechanics transl 1960 T J McCormack (La Salle, IL: Open Court) +Malament D 1986 From Quark to Quasars: Philosophical Problems of Modern Physics ed R G Colodny (Pinsburgh, PA: University of Pittsburgh Press) pp 181{201 +Manin J L 1988 General Relativity: A Guide to its Consequences for Gravity and Cosmology (Chichester: Ellis Horwood) +Mashoon B 1986 Found. Phys. 16 619{35. +Maudlin T 1988 Proc. 1988 Biennial Meeting of the Philosophy of Science Association vol. 2, ed A Fine and J Leplin (East Lansing. MI: Philosophy of Science Association) pp 82{91 +| 1990 Stud. Hist. Philos. Sci. 21 531{61 +Mavrides S 1913 L'Univers Relativiste (Paris: Masson) +McVittie G C 1965 General Relativity and Cosmology (Urbana IL: University of Illinois Press) +Mehra J 1974 Einstein. Hilbert and The Theory of Gravitation (Dordrecht: Reidel) + + + 858 J D Norton +Minkowski H 1908 Koniglichen Gesellschaft der Wissenschaften zu Gottingen, MathematischePhysikalische Klasse. Nachrichten, 53{111 | 1909 Physikalische Zeitschrift 10 104{111 (transl Lorentz 1923, pp 75{91) Misner C W, Thorne K S and Wheeler J A 1913 Gravitation (San Francisco: Freeman) Moller C 1952 The Theory of Relativity (Oxford: Clarendon) +Mundy B 1992 Proc. 1992 Biennial Meeting of the Philosophy of Science Association vol. 1 ed D Hull, M Forbes and K Okruhluk (East Lansing, MI: Philosophy of Science Association) pp 515{527 +Newton I 1687 Mathematical Principle of Natural Philosophy transl 1934 F Cajori (Berkeley, CA: University of Los Angeles Press) +North J D 1965 The Measure of the Universe: A History of Modern Cosmology (Oxford:Clarendon) +Norton J D 1984 Historical Studies in the Physical Sciences 14 253{316: reprinted in Einstein and the History of General Relativity: Einstein Studies, Vol 1 eds D Howard and J Stachel (Boston: Birkhauser, 1989) pp 101{159 +| 1985 Studies in History and Philosophy of Science 16 203{246: reprinted in Einstein and the History of General Relativity: Einstein Studies, Vol 1 eds DHoward and J Stachel (Boston: Birkhauser, 1989) pp 3{47. | 1987 Measurement, Realism and Objectivity ed I Forge (Dordrecht: Reidel) pp 153{188 +| 1988 Proceedings of the 1988 Biennial Meeting of the Philosophy of Science Association Vol. 2 eds A Fine and J Leplin (East Lansing, MI: Philosophy of Science Assoc., 1989) pp 56{64 | 1989 Found Phys 19 1215{1263 +| 1992 Studies in the History of General Relativity: Einstein Studies, Vol. 3 J Eisenstaedt and A Kox eds (Boston:Birkhauser) pp 281{315 +| 1992a Introduction to the Philosophy of Science M H Salmon et al (Englewood Cli s, NJ: Prentice-Hall) pp 179{231 +| 1993 Semantical aspects of Spacetime Theories ed U Majer and H I Schmidt (Mannheim: BI) Ohanian H C 1976 Gravitation and Spacetime (New York: Norton) +Page L 1920 The Principle of General Relativity and Einstein's Theory of Gravitation (New Haven. CT: Connecticut Academy of Arts and Sciences) Painleve P 1921 C. R. Acad. Sci. Paris 173 873{887 Papapetrou A 1974 Lectures on General Relativity (Dordrecht: Reidel) Pathria R K 1974 The Theory of Relativity 2nd edn (Oxford.Pergamon) +Pauli W 1921 Encyklopadie der mathematischen Wissenschaften, mit Einschluss an ihrer Anwendung. vol 5 Physik, Part 2 ed A Sommerfeld (Leipzig: Teubner) pp 539{775; 1958 Theory of Relativity transl G Field (London: Pergamon) +Post E J 1967 Delaware Seminar in the Foundations of Physics ed M Bunge (New York: Springer) pp 103{123 +Prasanna A R 1971 Lectures on General Relativity and Cosmology, Matscience Report No 71 (Madras: Institute of Mathematical Sciences) +Raine D J and Heller M 1981 The Science of Space-Time (Tucson, AZ: Pachart Publishing House) Rainich G Y 1950 Mathematics of Relativity (New York: Wiley) Ray C 1987 The Evolution Of Relativity (Bristol and Philadelphia: Adam Hilger) + + + General covariance and general relativity 859 +Reichenbach H 1924 Axiomatization of the Theory of Relativity transl 1969 M Reichenbach (Berkeley, CA: University of California Press, 1969) +Reinhardt M Z Naturf 28a 529{37 +Ricci G and Levi-Civita T 1901 Math. Ann. 54 125{201: reprinted in Levi-Civita 1954 Opere Matematiche, vol. 1 (Bologna) pp 479{559 +Rindler W 1969 Essential Relativity: Special, General, and Cosmological (New York: Van Nostrand-Reinhold) +Robertson H P and Noonan T W 1968 Relativity and Cosmology (Philadelphia, PA: Saunders) +Roll P G, Krotkov R and Dicke R H 1964 Ann. Phys. 26 442{517 +Rosser W G V 1964 An Introduction to the Theory of Relativity (London: Butterworths) +Rovelli C 1991 Class. Quantum Grav. 8 297{316 +Rynasiewicz R (forthcoming (a)) 'Rings, Holes and Substantivalism: On the Program of Leibniz Algebra' Phil. Sci. +Rynasiewicz R (forthcoming (b)) The Lessons of the Hole Argument +Ryckman T A 1992 Stud. History Phil. 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Vol. I The Classical Theories, Vol 2 the Modern Theories 1900-1926 (New York: Dover) Yilmaz H 1965 Introduction to the Theory of Relativity and Principles of Modern Physics (New York: Blaidsdell) Zahar E I989 Einstein's revolution: A study in Heuristic (La Salle, IL: Open Court) Zatzkis H 1955 in Fundamental Formulas of Physics ed D H Menzel (New York: Dover, 1960) Vol 2, ch 7 \ No newline at end of file diff --git a/storage/BS4RDHXA/Norton - 1993 - General covariance and the foundations of general relativity eight decades of dispute.pdf b/storage/BS4RDHXA/Norton - 1993 - General covariance and the foundations of general relativity eight decades of dispute.pdf new file mode 100644 index 0000000..c20e12a Binary files /dev/null and b/storage/BS4RDHXA/Norton - 1993 - General covariance and the foundations of general relativity eight decades of dispute.pdf differ diff --git a/storage/DCHWZ3QS/Clemmow - 1959 - On the theory of the diffraction of a plane wave by a large perfectly conducting cylinder.pdf b/storage/DCHWZ3QS/Clemmow - 1959 - On the theory of the diffraction of a plane wave by a large perfectly conducting cylinder.pdf new file mode 100644 index 0000000..ef18e13 Binary files /dev/null and b/storage/DCHWZ3QS/Clemmow - 1959 - On the theory of the diffraction of a plane wave by a large perfectly conducting cylinder.pdf differ diff --git a/storage/DWL3G6YD/.zotero-ft-cache b/storage/DWL3G6YD/.zotero-ft-cache new file mode 100644 index 0000000..996f6c1 --- /dev/null +++ b/storage/DWL3G6YD/.zotero-ft-cache @@ -0,0 +1,1053 @@ +Diffraction, +Refraction +and +Reflection +of +Radio Waves +V.A. Fock +Published for the +National Aeronautics and Space Administration +1975 +Translation of "Osvoyenlye Kosmicheskogo +Prostranstva v SSSR, 1957-1967," Moscow, +"Nauka" Press, 1971, +TRANSLATED FROM RUSSIAN +Thirteen Papers + + + AFCRC-TN-SM02 A4TIA DOCUMENT NO. AOIWJ74 +DIFFRACTION, REFRACTION, AND REFLECTION OF RADIO WAVES +THIRTEEN PAPERS BY V. A. FOCK +INTRODUCTION BY V. L SMIRNOV APPENDIX BY M. A. 1EONTOVICH +EOHOB, N. A. IMAM ASSOCIATE EDITOR, P. MACKSMITH. JR. +ANTENNA IABORATORY HICTRONICS RESEARCH DIRECTORATE + + + + + Requests (or additional copies by A^r.-.cies of ibe Dtpertrr.est of Defense, tbeir connectors, end other +AHMf'DSERVICES TECHNICAL INFORMATION AGENCY DOCUMENT SERVICE CENTER, DAYTON 2, OHIO +Deportaeol ot DefeoM contractor* oast be eetablished lot ASTIA services, or bare tbeir 'aeed-to-laow* certi fied bp the cogaissst nllitarp egesep of theii project +All other persoos sod argeaizniinaa shotId epplr to the: +U. S. DEPARTMENT OF COMMERCE OFFICE OF TECHNICAL SERVICES, WASHINGTON 2$, D. C. + + + EDITORS' NOR +The S osiet p h y sic ist V.A. Took 1* w ell known ty p h y sicist* fo r hi* work l a quanton nechaniee, p a rtic u la rly In eonnwtloB w ith the B artreoPoek thaory o f ealf-co o e lo ta n t f ie ld s . The purpoie o f th ia eo lleo tlo n i t to »equaint th e reader w ith Peak'* nore recent work on the p ro p o r tio n , r e fra c tio n , and d iffr* o tlo o of radlowavaa. Pock's e a r l/ papare on tM i subject (th e f l r e t f i r e papers in th is c o llec tio n ) appeared la B igllah alnoat a doeado ago. Boweror, a l l of h ie aore recant work haa been pabllehed in Russian and le r e la tiv e ly unknown ontelde the S o riet +The tren e la tio n a In th ia co llec tio n bare been baacl upon tra n s la tio n s obtained fro n e e reral aoureea. H r. Barman V. Cottony o f the Rational Bureau o f Standards and K iss A. P in ta il of th e Raral Reeseroh Laboratory, ree p eo tire ly , aada the o rig in a l tren e la tio n a o f Chapters VX and XX o f th ia e o llo etio n . The tr a n s la to r o f Chapter P IU ia unkn o n to tha e d lto re . The r m e l n il lT ig ahaptsrs ware tra n s la te d ty K orria D, Prlednan. Chapters T ill , XX, and X ware nade ty Itor r l e D. Prlednan, Xno., Kew tonrllla, Kassaohuaette. Chaptars XXX and XXIX wars aada in oooparation w ith Llnooln Laboratory. +According to tha L ibrary o f Congress aohonc f o r the tr a n s lite ra tio n o f the Buseian alphabet, Pook'e nans appears aa Pok. Howerer, because o f the aore general use In s c ie n tific lit e r a t u r e o f tho fo ra Pock th e ed ito rs have reta in e d th is fo n t In th is c o lle c tio n . + + + :3.IESiS +JHTKOXTICN: V.*. FOQC'S CCMEB'.'TTCKS TO DIFFRACTICS TKE3SI ( 7 Ia iiji.tr AIsitsa n d w ic h Fok. 17-32, P rin tin g Rouee o f the Acedesr Science, Katcow, 1956). 1 +I . m METHODS IN DIFFRACTION THECST (Philosophical Haraslne 2 ° , 2AM.35, 1946). 1 +n . THE DUTHIE7E OK CF CHWfllTS EIDUCBB BI A FLANZ WATE CB THE SURFACE CF A CONDUCTOR (Journal s i Thesis». USSR. 1,0, 130-136, 1946). 13 +r u . m p m cT ioK of radio wire? around the earth' s surface (Jou rn al o f Physics. USSR, o , 2 5 W 6 6 , 1945). 31 +1 . Stateaeu t of the Problas and i t s Solution lr. th e Fora of S e ries 32 2 . The S-jnoatlon Foraula 35 3 . The E rol'jaU ca of th e H erts Function f o r th e lliircia aied Region 41 4 . Asymptotic- E x p ressio n fo r the Henkel Function 46 5. The Expression? o f th e Herts Function Valid In th e Pemmbra Region 51 6 . Discussion or th e Expression f e r the Hertc Function 55 +17. SOL'jTIW OF THE ROEi iM OF ISf-FACAT.'W OF ELECTROMAGNETIC WAVES AlOW.- THE KARTj"S S’JRrACE ffi THE METHOD OF PARABCUC EQUATION (sJc'^M k =£ 13-36, 1946).65 +1 . Tr.« Csse of a Flar* E arth 2. The Cate of s Spaerioal Earth Table 1 +7 . THE FIELD CF A PLANE WAVE HPtR THE SURFACE CP A CONDUCTING BODf (Jou rn al £ Physics. USSR. 39*-409, 1946). +1 . The Geometrical Aspect o f the Problem 2 . Sim plified Maxwell's Equations 3 . Sim plified Bcur.-jary Conditions 4 . D sterttinetloc of th e F ield Ccopanent +V OTIC +5S§s 3 sa s + + + C o n o rs (cant'd) +5, D etiralnation of tha Ccxsponool H. aad the Othor Mold Cooponents 116 6, The Plaid In the IU u a ln a tad Region 120 7, Conelualea 124 +n PROPAGATION CP TUB DIRECT NAYS AROUND THE BARTH WITH DOB a c c o m fo r d iffra ctio n akd r e fra c tic h Ciffi. ( s jr . Q | . ) , & 81- 97, - 1948) . 127 +1. D if fe re n tla l Equations and th a Boundary Conditions of tha P ro b lm 129 2. Tranafar to Dlaanslonleae Q uantities 135 3. Solution of Equations 139 4. Inv estig atio n of tha So lu tio n fo r tha Region of O lraot V is ib ility 146 5. Inv estig atio n of tha Solution fo r tha Raglan of th a Psntasbra (F ln lta X and I ) 1£L +m , THEOfll OP RADI0WA7E PROPAGATION I I AH UWCMOGBiBOCS ATMOSPHERE POB A RAISH) SOURCE (UK (Se£. & * .) , JA, 70-94, 1930) . 159 +1. Pundasental Equations aad M a ttin g Conditions 160 2. Approximate Porn of th a Equations 164 3. Analogy with tha Unsteady P roblm of Q u an ta Xeehanlea 167 4. Trenefomatlon to N ondlmnslanal Q uantltloa 175 5. Properties of Partloular Solutions of ths D lffsra n tla l Equations 178 +6. Construction of th s S olution as a Contour In te g ra l or S e ria l 184 7. A pplication of tha Saneral Theory to the Superrafraotlon Case (Schematic Kxanple) 191 8. Appradmata Fomulaa f o r la m s with low A ttenuation 198 +7I U . THE FIELD FRCH A VSiTICAL AHD A HORIZONTAL DIPOLE, RAIS3 ) ABOVE THS EARTH'S SURFACE C z m . 916-929, 1949) . 30? +1. V ertic al H&lsed Olpola. Solution In S e ria l Pom 207 2. Appradaate Series Sum st ld o fo r tha Harts Function 209 3. The Attenuation Paotor 212 4. R aflaction Pomnla 215 5. H o rlw a ta l E la o trlo al D ipole. PrimaryP laid 221 6. S e ries f o r tha Total P la id 224 7. A ppradaate Expressions fo r th a P laid 228 + + + Corral13 (oo n t'd ) H . FRESNO. DIFFRACTION FROt CONVEX BODIES +3 . Computation o f the I n te g r a l $ 4 . Evaluation of the Integral 5 . The A ttenuation Factor In th e Region of the Shadow-Cone +Z. FRESNEL REFLECTION LAWS AND DIFFRACTION LANS (SEES* & 30S-319, 194«). +1 . F resn el R eflection Lave 2. Cross-Section o f a Bean of Refleoted Bars 3 . Klectroiaagnstlo F ield o f the Refleoted Wave 4 . D lffreo tio n Laws In the Penuabra Region 5. Investigation of the Expressions for the F ield s In the Dobra and D ire c t-V isib ility Regions 6 . Comparison o f th e D lffreo tio n F o w l* w ith th e F resn el F o w l s f o r the Lino-of-S ig h t Region +U . QENERALIZATIGN OF THE REFLECTION FORMULAS TO THE CASE OP REFLECTION OF AN ARBIIRAKI NAVE FROM A SURFACE OF ARBITRARI FORK (ZSTF. 2£, 961-978, 1950). +1 . Fresn el Formula* 2 . D iffe re n tia l Oecnetiy of th e Reflecting Surfaeo 3 . Croes-Seotlon of th e Bundle of Reflected Rays 4 . C alcu latio n of th e Determinant 5 . D iffe re n tia l Geometry of th e Nave Surface 6. Reflection F o w l* 7 . R e flec tio n o f th e Spherical Hava from the Surface of a Sphere +H I . APPROXIMATE FORMULA FOR DISTANCE OF THE HORIZON IN THE PRESENCE OF SUPERREFRACTICB (BadloteRh. 1 Elafctr. i , 560-574, 1956). +1. Introduotlon 2. In itia l Fow l** 3 . H o w l Refraction Case 4 . Asymptotic In teg ra tio n o f a D if fe re n tia l Equation with a C o efficien t Having a Mini 5. Investigation of the Attenuation Footer 6 . F o w l* fo r the Distance +(UFR. *1, 587-599, 1951). +1, Fonmlaa for the Attenuation Factor 2 . Reformulation of the A ttoiuatlIoonn FFaacctor +233 +d +S S b S S 8 2 g * 8 2 ? 4$ g 5 S £ m + + + CONTEXTS (c o a t'd ) +n n . OR RAITOWAVB propagation near the horizcx with SUFQQUTRACTIOH (R adlofkh. 1 B * t £ . i , 575-592, 1956). +1. Introduction 2 . On tb* Horlooa Conoa£t l a tb« Prosene* of a Tropospheric Wsreguid* Hoar th« Earth 3 . Fundamental Fom alaa 4 . R eflection Formula 5. Nuaarloal Result* l a Nondlaanalonal Coordinate! 6 . Attenuation Factor l a Deep Shad*. Raaldua Sariaa 7. A a a rlo a l Reault* f o r a Concrete Caaa +APPEDDIZl APPR0X1XATE BOUNDAKT CCNDITICHS FOR S I KUCTRCKAGNSTIC FIELD CM THE SURFACE CP A GOOD CCNDOCTGR +(InvMjl|a&}0g | {ft BadlowaT* Proaa«atlon. P a rt I I . 5-1 2 ^P riatin g b a a * o t tha Aoadsqf o /S cia n ca a, +Abbreviations f o r Soviet Journal* +IAS (Ser. F i t. ) . Isra a tu a Akadcall Rank S3SR 3 * rrla Plilc h ask a la (B o lla tla o f th e Aeada +S a rrlaT falch o ak al* (B o lla tla o f th e Acadsay of Solaneaa of OSSR - Physics Sa riaa ). +Zfauraal E kiparlm entalcol 1 Theoreticheskol Ltlki (Journal o f Experimental and Theoretioal Physios). +Radiotekh. £ K lsk tr. . ( R a d lo an g ln e ar la g +Radlotalchnlka 1 Elolctronlk* and E lectronics) +**m \ + + + 7 . A, FOCI'S COHTRIBOTICSS TO DIFFBACTiai THBORT +1 . DITBODOCTICa +7.A. Foek became in te re ste d In d iffra c tio n problem* cim peratively rec en tly . Within a abort tin e he succeeded in obtaining nueeroue re su lts whioh e re very la p o rten t both In th e o re tic a l end In p ra c tic a l aspects. By fo re ca stin g the paths of fu rth e r In v estig atio n s In th is f ie ld , they undoubtedly a re epochal In d iffra o tlo n theory. The solutio n of the problems of aleotronagnetlc w*ve d if f ra c tio n c onsists of fin d in g so lu tio n s of th e Xaxwell equations su b ject to specific i n i t i a l and boundary conditions on th e d iffra c tin g surface and rad ia tio n c onditions a t I n f i n ity . The I n i t i a l conditions a re often re placed by the requlrenent th a t the solution be sinusoidal in tin s . Foek devoted h la e e lf to an an aly sis of problems of the la s t k ind. P rio r to the Foek In v estig atio n s In th s theory o f electromagnetic wave d if fra c tio n , only so lu tio n s f o r a small masher o f prob i n s f o r o b stacles of a sp e cific shape were know , such se t th e In fin ite wedge, cylinders c irc u la r, e ll i p t l e and parabolic - and a lso fo r the sphere. In addi tio n , the problem of d iffra o tlo n from a paraboloid of rev o lu tio n , solved by Foek b ia se lf in 1944, should bo added to th s above l i s t . + + + The previous so lutions o f th s problems mentioned aboys, which wars represented by s e rie s o r by I n te g ra ls, ware not eery u sefu l In th s Important p ra c tic a l cass tdian the wavelength Is small In comparison to the dimensions o f th e o b sta cle, and thay should be considered as only the f i r s t step In solving the problTM , The next step must bo ths de riva tion o f form ulas fr> 1 and +In th is eaae, the f ie l d w ithin the conductor appears to be van ish in g ly small everywhere except In a surface la y er o f thickness of order where th e lnfluenoe o f th is la y e r can bo taken in to account by using boundary conditions f o r th s ex tern al f ia ld +"V7 - »A> ’ V1*‘ n.*V >ett +in +(i) + + + idler* Jg, Jy, *re the components of th e ourra n t d en sity ; n^, n^, a re tbe u n it v ector components normal to the body aurfaoe. le ad . N.A, Lsontovioh f i r s t suggested tbe aforementioned conditions In a ra th e r different fora. Consequently, tbe approxim ate f em u latio n o f the d iffra c tio n problem I s thereby reduced to a problem Involving the f ie ld s e x terio r to th e body. A fu rth e r e s s e n tia l sim p lifica tio n in problene of rad io wave d lf f ra e tlo n fro * bodies of a rb itra ry shape r e s u lts fro * the p rin c ip le of tb e f ie ld being lo c a l in tbe half-shadow region. I f tbe eleotrcnagnetlo f ie l d n ear th e surface o f a conducting body were to be determined su c cessfu lly , and, th e re fo re , th e current d istrib u tio n in the surface lay er, than the solution of the diffraction problocs would be a tta in e d bjr simple well-known formulae f o r the vector p o te n tia l. Tbe f ie l d in th e illum inated region near th e body i s subject, with a high degree of accuracy, to the Fresnel lava of r e f le c tio n , and, th e re fo re , can be determined e a s ily ; the f ie l d decreases rap id ly to sero In the shadow region. Consequently, th e u n attain ab le lin k In th e approximate so lu tio n of th e d if f ra c tio n problems I s the tr a n s itio n region (half-shadow) located near th e geometric shadow boundary and with the shape of a band o f width +la the rad iu s o f curvature of a normal eaotloc o f the body In the Inoldent plans. Pock succeeded in showing th a t th e electromagnetic f ie l d in the half-shadow region i s , to the accuracy of qu an tities of the order of It + + + of lo c al c h arac ter, 1 ,* ,, i t depemfeonly on the values +of the incident w n f ie l d In tho neighborhood o f the g i f t s p o in t, on tho geometric thtpo of th # body near th is p o in t, and on the a la c trlo properties of tilt conductor. After tho p rin cip le o f tho lo c a l f ie l d had bean estab lish ed , there* remained only to find th e so lu tio n o f th e d if f ra c tio n problem fo r a convex body o f su ffic ie n tly general shape, and to d e rlfe the approxi mate formulae f o r the f ie l d on I ts su rfa ce . I t la convenient to take the paraboloid of rev o lu tio n aa euoh a body, l a solving the problem of plane wave d lffre o tlo n from a paraboloid, V.A, Pock usod separation of varlablaa In parabolic coo rd ln atae, Ha constructed th e exact so lu tio n In the font o f in te g rals and performed th a approximate calc u latio n of theae In tegrale under tho assumption th a t ka » 1 , where k la the wave number and a la a parameter o f th e paraboloid of rev olution: x2 ♦ y2 - 2a» - a2 - 0 . Tha c h arac terla tlc d ire o tlo u o f tho woric on d iffra etlo i. explained above le su ffic ie n t to In d ica te the Important p rln eip lao of th a methods developed. B asically, th e se methods reduce to th e follow ingi Pock Indicated an a ffe c tiv e method o f approxim ately evaluating in ’ln lt e aerlea and In teg ra ls (containing a la rg e parameter) which rep re sent the exact solutions o f c ertain problems o f electromagnetic wave d iffra c tio n . This method perm itted him to develop, f o r example, e rigorous theory on radlowavo d lffre o tlo n around th e e a r th 's surface surrounded by e homogeneous atmosphere '('D iffra c tio n of Badlowavee + + + Around the Earth*» Surface", 1946)1. Ha w i a lso th a f l r a t to a atab llah tha vary Important p rln cip la of tha lo c a l charactar of tha electro®*gn atlo f ie l d l a tha h a lfshadow reg io n ,, u tir^ widely th a Laontovich condition*2 la th a approximate form ulatlon o f radlo-«av* d iffra c tio n problem*. This work afforded him tha opportunity to conatruet an approxim ate, but y e t a u ff lc la n tly accurate fo r p ra c tic a l needs, theory o f radlowave d if f ra c tio n from conductor* of a rb itra ry abape aa m i l aa * theory of radlowave propagation around the e arth taking lahcmogeneltiee of tha atmosphere In to account. Tha explanation of th la theory la given In "Theory of Radlowave Propagation In an Xnhcnogeneous Atmosphere f o r a Raised Source", (1950)3 . These works on d if f ra c tio n have played a very im portant p a rt in the h is to iy of th la question and, a t tha present tin e e ra among th a c le a re st attainm ent* In d iffre o tlo n theory and i t a a p plication*. Let ua tu rn to a mere d e ta ile d explanation of some of those works. The problem o f radlowave d if f ra c tio n In a vacuum r e la tiv e to a oor>dueting sphere la solved in "D iffreo tlo n of Radiowaves Around th e E a rth 's Surface"^, Let the sphere be of rad iu s a and be c haracterized by th e d i e le c tr ic constant C , th a conductivity a . Tha e leotronagnetie f ie ld ax o lted by suoh a d ip o le oan be ex pressed by mean* of the Hart* funotlon 0 ( r ,9 ,f ) which s a tis f ie s the equation vl + + + A u♦ A - o +Bane*, 1® o ri« r to determine the value of the f ie l d on th o sp h e re 'i surface, I t la w ffle lo n t to W w tho quantitiaa: +(3) 0 . - U (» ,e ,f) and o ; - J M L I . vr I +In 190ft, Mia obtalnod an a n a ly tic a l roproaontatlon f o r th e function 0 as an I n fin ite a eries o f apherloal fu n ctio n s, The a x tr n e ly poor convergence of the a a rlss prevented q u a lita tiv e physical consequences from being obtained and prevented p ra c tic a l use o f the aforaaentloned exact solution o f th e problmt. A major step toward a p ra c tic a l use of these s e rie s was made by Watson In 191S. But th e transfom ed fo ra of th e solution was s t i l l u n sa tisfac to ry , both because of i t s complexity and because i t was only applicable in th e geometric shadow region ( l . e . , f a r from the h o rizo n ). Only In 1945 d id Foek suoeeed in obtain ing an expression fo r th e Herts funotlon su itab le fo r a l l cases. Foek transforms th e se rie s f o r Ua and O' in to ocoplex I n te g ra ls, But, In c ontrast to the preceding authors who tended to reduce the In teg ra ls to a sum of resid u es, Foek Iso la ted from the In te g ra ls a p rin cip al term which y ie ld s s u f fic ie n tly exact v alues fo r th e functions Investigated. I t was shown in th is work th a t I f waves passing through the th ic k ness of the earth and waves olroumsorlblng the e a rth because of d if fra c tio n a re negleoted beoause of th e ir n a lln a s s , then th e value of Da be r e p r e s s e d by the follow ing In te g ra l v ii +(2) + + + wke<“o +ft) UA +(5) 9TM +C ^ a y - i Xr . ^ ) f r J K d .) ' +(*) X n ^ = J ^ i2 L ; * « I t O - i * th* w tv.lnjgth) *,

' * +(9) . T)*e*£*-■£.} +a) 1* th* hrp*rgean*trlo function; tb« oontour C 1* * lin * ln ta r* a cting th* p o sltlr* p *rt o f th* r**l axlo going downward (to th* l o f t of th* pol*a o f {f(r))» A a ln ila r In teg ra l i s obtained fo r 0^. Tb* * * s* n tlal fo ata ro of th l* aothod of approach 1* th a t th* Integral* obtain*d oan bo oalomlatod • t a l l y and w ith gro at aoouraoy f o r a iy rain * o f 9 . Till + + + lb s o h a iae tn rletlo pnraantnr o f th« aforaom tlonad in te g ra ls 1* tii* qua ntity p oos y where y 1* tbo angl* between th a v e rtica l a t tbo observation point tad tbo Mors* dlreotlon, I f p>> 1 wA tbo oboorror la In tbo lin o of sight region (nor* aoeoratelyi I f kb cosT> > 1 , i t e r s h la th # h eig h t o f tbo I sure a above tbo e arth ), than tbo a - 'o a tlo n of tbo in te g r a l a loads to tb o wall-known "roflootlo n forn u la", This evaluation o f tbo In teg ra ls loads to tbo Wofl-^ran dor Pol fonnila v a lid f o r p o in ts a t la rg o dlotanoos fro * tbo oouro* but s t i l l w ell w ith in Um lin * - o f -e ig h t. th e half-shadow r*glsn ( i t e r s p « l ) , fo r whloh appraxlnato values of tb o f l* ld worn not know ) i s o f g rootost ln to r o r t. A nstbod Is lndioatod In t h is aork of evaluating tbo Intogrolo fo r th is oaoo and th s following fo ro n li la obtained +In which w^(t) I s tbo complex Alrey funotlon re la te d to the Hanke l function of one th ir d order ty tbo r e la tio n +The contour J 1 goes fro n l o to 0 and fro a 0 to | +(10) +lx + + + The formula f o r tho half-shadow region I s tho main r e s u lt of th is work. I t 1* applicable In a l l cases of p r a c tic a l in ta re a t. I t tran s forms Into tbe Weyl-ran dor Pol formula f a r from geometric shadow In th e lln e -o f-» ig h t roglon. T his fo n aila can b# reduced to a rap id ly converging s e rie s whan the tr a n s itio n I s nade In to th e shadow region idlers ( - p)> > 1 . I n the work "Solution of th e Problwa o f Propagation o f K le ctrcwagnatle Wave* Along the E a rth 's Surface h r th e Method of Parabolic Equations" (w ritten jo in tly w ith M.A. L eontorlch)*, a prohlma i s analysad which le alad la r to th o problma In th e paper mentioned abore but the method la e sse n tia lly d if f e r e n t. The Influence o f tho o a rth 'a surface le taken In to account by the Leontorlch approximate boundary conditions and ta rn s In th e f ie l d equa tio n s a re neglected which a re m a ll and a re o f th e order o f o ^ and . As a r e s u lt, the "approxlnate" form ulation of tho problem f o r +th e sp h e rica l a arth ease la sim p lified s u b sta n tia lly and la reduced to th e problem o f solving the parabolic equation +In the region e x terio r to tho earth and subject to the additional eondltlona + + + J t la d iffic u lt to estimate th« error Introduced ty discarding the • j ^ l l " terms vhsa using th le method. To do th la the vell-knom Pte«M l " re fle c tio n 0 formula n u t a lso be considered. The e sse n tia l advantage of the parabollo equation nethod i s l t a g rea t sim plicity as s e l l as the p o s s ib ility of solving oor* cocgilsx problems (fo r example, save d iffra c tio n from bodies of a rb itra ry shape). In th la work th e f i r s t oase considered I s th a t in which the earth la assumed to bo p la n ar. Than th e apherloal earth case Is con sidered and the sane formulas are obtained ty using th e parabolic equation nethod as bad been previously obtained ty approximately n m ln g the se rie s idiloh y ie ld the exact so lutio n of th e proMsm. The agreement between r e s u lts obtained ty these two methods provides a Ju s tific a tio n f o r th e use o f the parabolic equation method In problsns of radiowave d if f ra c tio n from good conductors. Pock used th is msthod widely In l a t e r works on d if f ra c tio n . In the work "Propagation of the D irec t Wave Around the Earth with Due Account fo r D iffractio n and R ofraotion",^ the problom Is solved undsr the assumption th a t the surface o f th e e arth i s homogeneous as wall aa th at the d ie lec tric oonstant of the a ir la a function £ ^(h) only of the height b ■ r - a of p otato above th e h o tiaan . A v e rtic a l dipole performing harmonic o o c illa tlo iis defined ty the fa c to r e”i4>* la placad on the surface of th e e arth a t th a p oint r - a , 0 ■ 0 . A rap id ly varying f a c to r la Iso la te d from the H erts function 0 ■ad a nsw "slowly* varying fu nction U2 I s Introduced ty moans o f th e + + + fo rm ula +■*% +^0 (h )r f a i n 6 +tdiors a • a9 la the l tf g th o f are on th e te r r e s t r i a l sphere from the p o in t idler* th a dipole la to the p o in t above tha earth a t iddeh tha +obaeirar le eitoated, +/ 2V +the author neglecte quantities o f order r r ^ j In the equation obtained f o r Bj. A fter In troduetlon o f th e noodlnenalonal v aria b le s x and f ty naans o f the formula* +( +16) +vhor* “ ^ j ' ( o ) 1* th e equivalent radlue of th e T * IH o J +e a r th ’s su rface, and a fte r Introducing the new function ty means of tho formula +a +H' ~ W ' +th e p re h lw i s reduoed to determining th e fu netion w^Cz*r) from th a aquation , +(W ) ♦ 1 ♦ 7 (1 ♦ «)wx - 0 (y > 0) 3r +tinder th* condition* + + + end the n a tu ra l ra d ia tio n eoodltlon f o r h >> 1 . Tha q u a n tltla a q • a t g, e ntering l a tha fonsulae raduead abore, hare tha following T*lU8» +( » ) q - g - _ ^ « qW - . 4 < 2 ) . ^ {o) ] . +Zmrastlgatlon of th e aquation fo r *j_ above th a t I f g - 0 and I f tha radlna a la replaced ty tha equivalent radlue of tha earth a*, than tha n a th ao a tlc al prdhlan la reduced to exactly th a aana fo ra aa whan tha atmosphere la absent. In th a general case, g can be eoneldered aa a fu n ctio n o f tha product f i y , Wiere /3 ■ — la +a small parameter. Tha so lu tio n of tha probloa I s su c cessfu lly repre sented fay the contour In teg ra l: +*d»ere f ( y , t ) la aa e n tire transcendental function w ith a d e fin ite be havior a t in f in ity and sa tisfy in g th a aquations +(22) [ r - t ♦ y g ( £ y )J f - 0 | +s ill +A + + + The contour r 1* in f in it e and encloses th s f i r s t quadrant of the t plans. Investig atio n o f the so lu tio n of th e p ro b lai constructed shows th a t the lavs o f geometric o p tic s are co rrec t In th e lln e -o f-e ig h t region f a r from th e h o rlio n . Ths following in e q u ality i s th e condition +for this y2 kh2 (23) ----- ---------» 1 . 2s +The solution transform s In to th s K eyl-ran d sr Pol forsrula f o r a s l l values of x and y end f o r la rg e values of p ■ cos J - , +Ths Investigatio n o f th s so lu tio n In the half-shadow region permits th e conclusion th a t the wave reaches th e horizon w ith an amplitude uid phase corresponding to th s laws o f geometric o p tlo s f o r an unbounded Bsdlun and undergoes d if f ra c tio n according to th e law of the fo ca l H eld in th s half-shadow region a t th e horizon. This r e s u lt agrees completely with the id eas o f L .I . H andel'shtan th at the properties of the s o il are essen tial not along the W ide ray tra je c to ry In ndiowave propagation along the e a r th 's surface but only In th a t region where the tran s m itte r o r rec eiv e rs are lo cated . Let us tu rn to the work In which th e problem d if f ra c tio n from an a rb itra ry convex surface i s analyzsd. An electromagnetic wave In cid en t on a conductor e x cite s surface currents Wilch, in tu rn , a re sources o f sc a ttered waves. Consequently, +xiv + + + ib e sse n tia l step in th e solution of the plane wave d lf f re e tlc a probfrom a eonductor o f a rb itra ry shape Is to fin d th e ourrents excited OO i t s surface. In th e work, "The D istrib u tio n o f Currents Induced by a Plans Ware M the Surface of a Conductor", the cu rren t d istrib u tio n ex cited by a plane wave on the surface o f a convex, p e rfec tly conducting, s u f f i c iw itly smooth body o f a rb itra ry shape i s analyzed under th e c o ndition th a t the length o f th e aleotrcnegnetlc wavs i s very n a i l in comparison with the body dIran alone and the r a d ii of curvature of i t s surface. A fundamental r e s u lt o f th e work i s the proof th a t the f ie ld has lo e a l character near th e g ecnatrlo shadow boundaries. I t ia show in th e work th a t when the in cid en t wave la polarized with the e le c tr ic v e cto r in the plane of incidence the c u rren t d i s t r i bution nasr the boundaries c ited i s expressed through a u n iv ersal (Id e n tic al f o r a l l bodies) function 0 ( f) of the argument f “ - j - , where / ia the d istan ce fro a th e g scaetric shadow boundaries meas ured in th e Incident plane and d I s the width of the half-shadow region. An an aly tlo expression i s derived fo r tho fu n ctio n 0 ( f ) and detailed tables are given. The solution o f th e problaa of th e cu rran t d is trib u tio n i s based e sse n tia lly on the study o f th e so lu tio n of th e In te g ra l equation fo r the c u rrent d en sity ? on th e surface of the p e rfe c t conductor. I f th e aonochrmeatle electromagnetic wave H ■ H** f a l l s on the eonductor and I f th e following n o tatio n is introduced + + + (24) ' - (1 - T - x H « ] +then the follow ing In teg ra l equation le obtained fo r th e su rfa ce cur rent density +(25) +idlers le the u n it v e cto r nonssl to the conductor su rface; "? and r*7a re radius v ecto rs o f fixed p o in ts o f the surface and of p o in ts with the surface element d37 and R “ | ? - "?'] . As an In v estig atio n of th e In te g ra l equation In the case o f very large values of k ( i . e . , sn a il wavelengths A ) shows. I t can be con sidered, with enough accuracy, th a t X “ 2J** on th e illum inated p a rt o f the surface (tdilch corresponds to Fresnel r e fle c tio n theory and J • 0 In the shadow p a rt. In tha neighborhood o f the geom etrical shadow boundaries, th e In te g ra l equation shows th a t In a bandwidth o f +(26) d - R* , +sdiere Bg i s th e rad iu s o f curvature o f a sectio n of th e body surface by the Inciden t plane, the c u rren t d en sity and, th e re fo re , th e f ie l d has an approxim ate value dependent only on th e value o f th e ex tern al f ie l d H** In the p o in t under In v estig atio n , the geometric character^ is t lo s of th e eurfaoe element and on the e le c tr ic p ro p ertie s of the conductor. Such a r e s u lt means th a t u n iv e rsal fo n m las f o r th e cu rren t xvl + + + density on the surface o f • p e rfec t aonduotor in the half-shadow r e fl«B can bo obtained from the so lu tio n of th e d iffre c tio n problen f o r ^ p a rticu la r o im of • oonveac surfaoe, The u n iv ersal formulas h b tlenod oro obUlnod by considering tho probloo of piano wave d if f ra c tion fro* a paraboloid of rorelution. Tho roo u lt la +___ »iC f aK t +(27) t - r w ) - ^ w ~ ) « , +rfioro * ( t) la tho oonplax Alrey fimotion and T la a contour In tho o o ^ lex plana going fro * in f in ity to Mro along tho lin o arg » y IT +and from taro to in f in ity along tho p o sitiv e p a rt of tho r a a l a x is. An investigation of tho asynptotle values of G(f) fo r largo p o sitiv e and Dogatlvo values o f £ shows th a t tho c u rran t d e n sity 3* transforms continuously whan tho tra n s itio n i s made from the half-shadow in to tho lin e -o f-slg h t or in to the shadow regions, in to tho values £3SX and J - 0, respectively. Detailed tables ara constructed for tho function +0(f). Tho r e s u lt of tho preceding work i s generalized in "Field of a Plane Wave Hoar the Surfaoe of a Conducting Body" in th a t, f i r s t , the fie ld i s determined not only on the body surfaoe i t s e l f but also in a certain surface la y e r with thickness —i l l in comparison with th e r a d ii of curvaturej second, the body is considered to bo not a p o rfa et, b at ® ly a good conductor in tho sense th a t th e )M « teentovioh conditions hold f o r tho ta n g en tial f ia l d component* on i t s su rface. Furtheim ore, x rii + + + the p o la risa tio n o f the Inc id ant wave nay be such th a t the e le c tr ic ▼actor Ile a In or la perp* d lo u lar to the plana of Incidence. Let ua dlecuaa the Fock work, "Fresnel D iffrac tio n f rtn Convex Bodies", (1951)7. Considered In th is work la the d if f re e tio n from a sphere, h e r e in re fra o tlo n of the etnoaphere la n o t taken Into account. I t la con sidered th a t the source and the observer a re above th e surfaoe o f th e e arth , where h^ la the source height and h j la the height of th e observation p o in t. The f i e l d I s expressed through th e two so lu tio n s IT and w of the equation A u ♦ k^V - 0. The follow ing notations a re Introduced In a ddition to those used previously: +(aa) r x - ( - ^ ) ' Tich1 , y 2 - 1*2 , +(29) q - ( - I f f (? ♦ U * l j qt - (?) - l / 1 . +The following fornulas bold noar th e su rfsea of th e sphere: +#lka0 (30) D * T y r m v (l< 7 l' 72*q ) * +• +and the atten u a tio n fa c to r 7 Is expressed b j a c e rta in contour in te g ra l containing two Airey fu n ctio n s. A ll these r e s u lts a re contained In the work " F ield fro n a V ertic al and H orizontal Dipole, Raised S lig h tly Above mu + + + th t Bartli1* Surface*, (1949)® and In th a 1951 work, an approxiante «*preoalon la ji^ n i fo r T In th a region af th a ehadow oona. Henoe, i t la ooneid r red th a t tha paraneter defined >7 th a fo rm ic +y^ v7 +0 .) +la la rg e and tha q u a n tity £ ■ x - ~ la f in ite or m a ll. Two funetione are lntrodaoad +(33) +(34) +1 +f(aO - a - 1* 2- 1 ^ ^ j ,K ^ dee | +2^,-1 +ppraxlmate expres aIon T(x^y^f y ^ .q ) la th a follow ing fo r tha ahadow oona +- - • UA p H ft.Q - g(f) ♦ —i - g '( ^ ) l , +W* L J +Me do not c ite tha axprwaalon f o r 4>o . Tha p rin c ip a l ta n s la /* f(£ )> proportional to tha freenel Integral. I t la indepandmt of tha n o ta ria l of tha d if f ra c tin g body. Superlnpoeed 00 th e d iffra c tio n ploture (Praanal d if f ra c tio n ) datamdned h f th ia to m la th e background depandmt on tha function g ( () varleo »lowly in comparison with tha p rin cip al ta rn . Thia background deponda on tha s a te r i a l o f the d if fra c tin g body. + + + UPBBESCS +1 . A tra n s la tio n o f T.A. Pock, ■D iffrac tio n o f RadloiAToa around tha B arth 'a Sorfaea*, la a v alla U o th r o n g Morria D. Priadman, In c.] M ovtooriilo, Kaaaaotraaatt*. 2 . So# Appendix t o tb le e o lleo tlcn o f Pock paper*. 3 . See Chapter VQ o f t h is c o lle c tio n . k . So* Chapter I? o f th is c o lle c tio n . 5. See Chapter ? I o f tbit c o llec tio n . 6. See Chapter I I o f th is o o lle ctlo n . 7. See Chapter IX o f th la c o llec tio n . 8. See Chapter m i o f th la oo lle ctio o . + + + I . NEW METHODS IN DIFFRACTION THEORY +V. A. Foclc +The g e n e ra l problem o f th e th e o ry o f d i f f r a c t i o n o f e l e c t r o magnetic waves o o n a lata In f in d in g a s o lu tio n o f M axw ell'a equations, having p resc rib ed s in g u la r itie s ( fie ld so u rces) and s a tis f y in g p re s c rib e d boundary c o n d itio n s and c o n d itio n s at In fin ity . The s o lu tio n o f th i s problem p r e s e n ts s e rio u s m athe m atical d i f f i c u l t i e s , which a r is e c h ie f ly from th e n e c e s s ity o f talcing In to account th e g e o m etric al shape o f th e o b s ta c le s on w hich th e wave i s f a l l i n g . The p ro b lem I s somewhat s im p lifie d I f only m onochrom atic waves o f g iv e n frequency are considered, b u t the d if f ic u lt ie s are s t i l l so g re a t, th a t th e p roblem h a s n o t y e t b e e n s o lv e d , e x c e p t i n c a s e s when th e o b s ta c l e I s o f a p a r t i c u l a r l y sim p le fo rm . The b e s t known o f these are the cases of a p e rfe c tly re fle c tin g h a lf-p la n e o r a wedge, th e c ase s o f a sp h ere and a c irc u la r c y lin d e r. The c a se s o f an e l l i p t i c and a p a ra b o lic c y lin d e r have • I s o been c o n s id e re d , and th e f i e l d o f a p la n e wave In c id e n t on a p e rfe c tly r e f le c tin g p a ra b o lo id of re v o lu tio n (oblique Incidence) has re c e n tly been o b tain ed by the a u th o r. In the f *w c a a c s e n u m e ra te d a r i g o r o u s s o l u t i o n o f th e p ro b le m I n th e /°* » of an In fin ite s e rie s of In te g ra ls has been o b tained. +{'-) + + + 2 +The aim of a theory la to give a p ic tu re reproducing a l l th e q u a lita tiv e and q u a n tita tiv e fe a tu re e o f th a phenomenon c o n sid e re d . This aim i s not a tta in e d u n t i l the s o lu tio n obtained is of a su ffic ie n tly simple form. I f the rigorous so lu tio n has a com plicated a n a ly tic a l form, i t c o n s titu te s only th e f i r s t s te p ; a second s te p must be made - the d e riv a tio n o f form ulas s u ita b le fo r numerical c alcu latio n s. T his second s te p may be a s d i f f i c u l t as th e f i r s t one. To giv e an example, we may mention th a t th e problem o f d if f r a c tio n o f ele c tro -m a g n e tic waves around a sphere was BOlved rig o ro u sly some 40 y e ars ago (M ie). This problem in clu d es th a t o f the propagation of radio-waves along the surface of the e a rth . Owing to th e slow convergence o f the s e r ie s Involved, th e g en eral s o lu tio n could, however, not be ap p lied to the l a t t e r problem u n t i l 1918, when a tra n sfo rm a tio n o f the o r ig in a l s e r ie s in to an o th e r r a p id ly converging s e r ie s was found (W atson). But th e improved form o f tho s o lu tio n was B t i l l u n s a tis fa c to ry In sornt- re s p e c ts , being very com plicated and a p p lic a b le only In th e re g io n o f the g eom etrical shadow ( f a r beyond th e lin e of h o r iz o n ) . A f a r more s a tis f a c to r y form o f the s o lu tio n , ap plicable in a ll cases of p ra c tic a l importance, has been re c e n tly found by th e a u th o r .1 .:R, where R is the radius of curvature of the o bstacle. I t is convenient to take .netead the quantity +In a d d itio n to the two sm all param eters defined above, th e re may be o th e rs , depending on the p o s itio n of th e p o in t of observation. For instance, in the problem of the propaga tio n of ra d io waves along the e a r th s u rfa c e th e angle of In c lin a tio n o f th e ray to th e h o rizo n may be regarded as sm all. Let us co n sid e r the consequences o f the fa c t th a t the p aram eters 1 :. 4 h and l:m are s m a ll. In th e lim itin g case | i ) |« a o (perfect conductor) a great sim p lificatio n a rises from th e f a c t th a t th e f i e l d i s known beforehand in s id e the conductor ( t h i s f i e l d being equal to z e r o ). Ve can confine ourselves to the space outside th e conductor by prescrib in g +p aram eters of the problem tu e in v erse v a lu e o f |q | o r the qu an tity 1: +(2) +(4) + + + 5 +proper boundary conditions to the fie ld In a ir (the tangential components o f the e l e c t r i c a l v e c to r should vanish a t the su r face). A sim ilar situ a tio n a flse s If - T u T Is very large. The f i e l d In sid e the body Is In t h i s case very small except In a th in surface la y e r (sk in -e ffe c t), and the Influence of th is la y e r may be accounted f o r by s ta tin g boundary conditions f o r th e e x te rn a l f i e l d . These are o f the form +? Jx “ ^ < Ex * nxEn> = V z ' nzHy ' e t c - <’ ) +where ( J x , Jy , J z ) I s th e su rfa c e c u rre n t d e n s ity v e c to r, (nx» riy, n^) th e u n it v e c to r of th e normal to the su rface, Ejj th e normal component o f th e e l e c t r i c f i e l d , th e meaning o f th e o th e r symbols being e v id e n t. These co n d itio n s, f i r s t +e q u a lity sig n ifie s th a t the thickness o f the skin layer should be sm all as compared w ith th e ra d iu s of cu rv atu re of the o b s ta c le . C onditions (3) may be e a s ily g en eralized fo r a r b i t r a r y v alues o f the m agnetic permea b i l i t y m. C onsequently th e sm allness o f 1: J h i perm its us to confin e our a t te n tio n to the f i e l d o u tsid e and on the body, which c o n s titu te s an Im portant s im p lif ic a tio n o f the problem. We now proceed to examine the Influence o f the sm allness +s ta te d by Leontovlch^ In a somewhat d iffe re n t form, apply I f The l a t t e r ln +(5) +of the wave-length. + + + 6 +As w ell known. In th e lim itin g case o f sm all w ave-lengths th e laws of g eom etrical o p tic s become v a lid . P a r tic u la r ly , the boundary of the shadow on th e su rfa c e o f th e body becomes sharp and well d e fin e d . On th e onp sid e of th e boundary — In the illum inated region — the fie ld obeys very nearly F renenel's laws o f r e f le c tio n , and on th e dark sid e the f i e l d ra p id ly decreases to zero. The approxim ation given by the geo m etrical o p tic s I s , however, not s u f f i c i e n t f o r o u r purp o ses. The p o in t o f I n te r e s t f o r us I s the d if f r a c t i o n phenomenon In I t s s t r i c t sense, l . e . , th e bending o f the ra y around th e o b s ta c le . This phenomenon cannot be tr e a te d by th e means of g eo m etrical o p tic s , end to g ive a th eo ry o f th i s phenomenon a more a c c u ra te s o lu tio n o f the fie ld equations Is required. The au th o r succeeded In fin d in g t h i s s o lu tio n by means o f a new p r in c ip le which may be c a lle d "The P rin c ip le o f the Local F ie ld In th e Penumbra Region". This p r in c ip le c o n s is ts In the fo llow ing: - The tr a n s itio n from li g h t to shadow on th e s u rfa c e o f the body tak es p lace In a narrow s t r i p along the boundary o f the g eo m etrical shadow. The w idth o f t h i s s t r i p I s o f th e o rd e r +where R0 I s th e ra d iu s o f cu rv a tu re o f th e normal s e c tio n of th e body by th e plane o f In c id e n c e . . I t may be proved th a t. +(6) + + + 7 +with neglect of email q u a n titie s of the order fie ld In th le s tr ip has a local, character: I t depends only on th e value o f the f i e l d of the In c id e n t wave In the neighbor hood o f th e p o in t c o n sid ered , on th e geom etrical shape o f the body near th e p o in t and on th e e l e c t r i c a l p ro p e rtie s o f the m a terial of th e body. The f i e l d n e a r a given po in t on the s t r i p does not depend cn I t s v alu es a t d is ta n t p o in ts and can be c a lc u la te d s e p a ra te ly . To e s ta b lis h th e p r in c ip le o f th e lo cal f i e l d and to deriv e e x p lic it form ulas f o r t h i s f i e l d we have used two d if f e r e n t methods. One o f th e se (2) a p p lie s to th e case of an ab so lu te con d u cto r and g iv es the v alues o f the f i e l d on I t s su rfa c e . We s ta r t with the In teg ral equation fo r the surface current density J. This i s o f th e form +The v e c to r Jex (e x te rn a l c u rre n t d e n s ity ) Is defined by the ex p ressio n ( 3 ), where H i s rep la c e d by Hex, the magnetic vector of the external fie ld j z is the r a d iu B vector of the point of observation, z ' th at of the point of Integration; +(5) where f - (1 - lKR)e1KB ( 6) +R o | z - z ' | Is the le n g th o f th e chord between z and z '; +(7) + + + I s th e valu e o f th e u n it v e c to r of the normal, a t z. A q u a lita tiv e study of the In te g ra l equation perm its us to e sta b lish the p rin c ip le of the lo c a l f ie ld . This p rin c ip le once e sta b lish e d , we have to fin d a s o lu tio n o f th e d if f r a c t io n problem f o r a con vex body o f a p a r t i c u l a r shape and to d e riv e approximate formulas fo r th e f i e l d on I t s s u rfa c e . In v ir tu e o f th e p r in c ip le o f the lo cal f ie ld , these formulas hold fo r any o th er convex body having a t th e p o in t consid ered th e same v alu es o f the p r in c ip a l r a d ii of c u rv a tu re . (The p a r t i c u l a r body must o f course be s u f f ic ie n tly general to possess points with any prescribed values of p rin cip al r a d ii of curv atu re ; a c tu a lly a paraboloid of re volution has been u s e d ). Proceeding In t h i s way we a r r iv e a t a gen eral formula fo r th e s u rfa c e valu es o f th e ta n g e n tia l components of the m agnetic f i e l d o r, which amounts to th e same, fo r the su rfa c e c u rre n t d e n s ity v e c to r. T his formula I s o f the form +I being th e d is ta n c e f r a n th e boundary o f the geom etrical shadow, measured along the ray ( l . e . , along the lin e of In te rse c tio n of the plane o f Incidence with the surface of the body) and taken p o s itiv e In th e d ir e c tio n o f th e shadow and n eg ativ e in th e o p p o site d i r e c t i o n . The fu n c tio n 0 (« , 0) Is d efin ed by th e In te g ra l +J - Jex a (e , 0) (7) +where th e argument ■ In G d enotes the q u a n tity +(8) +(8 ) + + + (9) +a ( t ’ 0) ^ V ( c r ’ +where C i s a contour in th e complex t-p la n e running from I n f in ity to zero along th e l in e are t • and from zero to in fin ity along the p o sitiv e real a x is. The fu n ctio n "(t) - Uo(t) ( 10) +and by th e asym ptotic beh av io r f o r la rg e n egative values of t +*o(t) - e 1 * ( - t ) ‘ 1/4 • exp [ l | ( * t) 3/ 2] . ( 11) +The fu n c tio n 0 (« ,0 ) tends to the lim it 0 - 2 fo r larg e neg ativ e v alues of c , w hile I t s modulus decreases ex p o n en tially fo r la rg e p o s itiv e v alues o f «. Formula (7) reproduces thus the g radual d ecrease o f th e f i e l d am plitude when p assin g from l i g h t to shadow. The same r e s u l t s may be o btained by an other method** which allow s us to g e n e ra liz e them in two r e s p e c ts . F i r s t l y , th e body need no t be a p e r f e c t conduotor, but nay have a f in ite conductivity. I f only the boundary condltipns (7 ) are a p p lic a b le . Secondly, the f ie ld Is obtained not only on the surface of the body, but also near the aurfaoe ( a t distances th a t a re small a s compared w ith the r a d i i of c u rv a tu re ). The method c o n s is ts In s im p lify in g Maxwell’i'e q u a tio n s and boundary +(9) + + + 10 +c o n d itio n s by n e g le c tin g q u a n titie s of the o rd e r o f the square o f th e sm all param eters 1- J m and 1 : m. The wave equation f o r th e am plitude I s thereb y re p laced by a p ara b o lic equation of S c h ro d ln g e r's ty p e . The sim p lifie d e q u ations are v a lid In a lim ite d re g io n n ear a p o in t on the penumbra s t r i p . The s o lu tio n of th e se eq u atio n s may be performed by means o f th e s e p a ra tio n o f v a ria b le s and y ie ld s the f i e l d In the region co n sid ered and e s p e c ia lly In th e penumbra s t r i p on th e body. In tro d u cin g the complex q u a n tity +*A~ +(th e modulus I q f i s thus th e q u o tie n t o f the two small m e te rs ), we may w rite In ste a d o f (7 ) +(12) +para +j ex 0 (6 , q) , (13) +where +0 ( 6. q) - e f i - r c t r - v f t ) * (14) +th e c o n to u r C being th e same as In (9 ) . These form ulas give th u s th e d i s t r i b u t i o n o f c u rre n ts on th e penumbra s t r i p on the ' body and g e n e ra liz e our prev io u s form ulas (7) and (9$. The form ulas f o r th e f i e l d n ear the s u rfa c e are more complicated and w ill not be w ritte n h ere. I t I s to be noted th a t In th e outward p o rtio n o f the s t r i p , where th e Illu m in a te d re g io n b e g in s, approxim ate expressions can be derived from our formulas th a t coincide w ith expressions fo r +( 10) + + + 11 +the f ie ld obtained by superposing the In cid en t and the re fle c te d wave and u sing F re s n e l's c o e f f ic ie n ts o f r e f le c tio n . On the other hand, In the opposite portion of the s trip the fie ld Is p r a c tic a lly zero. Thus our form ulas c o n s titu te the m issing lin k Join in g the two regions where th e laws o f geom etrical o p tic s may be a p p lie d . Together w ith F r e s n e l's form ulas they allow us to compute th e f ie ld near and on the whole su rface of the d iffra c tin g body. • In some problems t h i s I s a l l th a t 1b re q u ire d . In the problem of p ropagation of waves around the e a r t h 's su rfa c e , fo r In sta n c e , we a re only concerned w ith th e f i e l d on h eig h ts not exceeding ten k ilo m e te rs—a q u a n tity th a t Is sm all as com pared w ith the e a r t h 's ra d iu s ( 6380km .). In th is Instance our form ulas, I f m odified so as to Include the case when the source I s near o r on the s u rfa c e , give the req u ired so lu tio n . In o th er problems, however, the fie ld a t large distances from the s c a tte r in g body I s needed. In s p ite of the f a c t th a t our formulas are v alid only in the region near the surface, they provide a means to c a lc u la te th e f i e l d a t la rg e d ista n c e s a ls o . Indeed, the f i e l d of th e s c a tte r e d wave Is generated by the c u rre n ts Induced on the su rface (In the sk in -la y e r) by the In c id e n t wave. These c u rre n ts a re given by our form ulas. Thus, by applying well-known theorems on th e v ecto r p o te n tia l due to a given c u rre n t d i s t r i b u t i o n , we may, in p r in c ip le , c a lc u la te th e f ie ld fo r a r b itr a r y d is ta n c e s from the r e f l e c t in g body. +(11) + + + 12 +The p r in c ip le o f th e lo c a l f i e l d In th e penumbra region provided thus a b a s is f o r the approxim ate so lu tio n of the problem o f d if f r a c ti o n In th e g eneral case o f a convex body o f a r b itr a r y shape. +1. V. POCK, Jo u rn al o f P h y sics. ix ;.2 5 5 , 1945. 2 . V. POCK, Jo u rn al o f P h y sics, x :130, 1946. +3. M. LEONTOVITCH, B u ll. Academy S cien ces. U .S .S.R ., s e r l e physique, l x ; l 6, 1944, (In R u ssian ), alBO H. LEONTOVITCH and V. POCK, Jo u rn al of P hysics. x:13, 1946. 4. V. POCK, B u ll. Academy S cien ces. U .S .S .R ., e e rie physique, &:171f 1946, (In R u ssian ). +(12) + + + 13 +TT THE DISTRIBUTION OP CURRENTS INDUCED BY A PLANE WAVE +ON THE SURFACE OF A CONDUCTOR +V. Fock +The d is tr ib u tio n of c u r r e n ts . Induced on the +su rface o f an p e r f e c tly conducting body by an In cid en t plane wave Is con sid ered . The body Is supposed to be +convex and to have a contin u o u sly varying c u rv atu re. +The wave length X o f th e I n c id e n t wave la supposed to be small as compared w ith th e dimensions o f the body and w ith the r a d ii o f c u rv a tu re o f I t s s u rfa c e . I t +is shown th a t the c u rre n t d i s t r i b u t io n In the v ic in ity +o f the geom etrical shadow I s e x p re ssib le In terms of +an u n iv e rsa l fu n c tio n 0(%) (th e same fo r a l l b o d ie s), +depending on the argument £ » I / d , where I I s th e d istan c e from the boundary o f the g eom etrical Bhadow, measured In the plane o f Incidence, and d Is the width +o f th e penumbra region (d 16 the rad iu s of +c u rv atu re of the normal s e c tio n o f the body by the plane of IncidenceJ . For the function OU) an an a ly tic a l e x p ressio n Is derived and ta b le s a re computed. +Let us co n sid er a p e r f e c tly conducting body on the su rface o f which a plane electrom agnetic wave I s In c id e n t. The su rface o f th e conductor Is supposed to be convex, w ith a continuously vary in g c u rv a tu re . The In c id e n t wave Induces on the conductor e l e c t r i c a l c u rre n ts , which In t h e i r tu rn become a source o f the s c a tte r e d wave. I f the c u rre n t d i s t r i b u tio n on the conductor Is determined, then the c a lcu latio n of the fie ld of the sc a tte r e d wave may be performed by apply in g th e well-known formulas f o r the v e c to r - p o te n tia l. Hence th e e s s e n tia l ste p In so lv in g th e problem of d if f r a c tio n o f a p lan e wave by a p e rfe c t con ductor Is to find the c u rren ts Induced on I ts su rface. +(1) + + + 1* +The p re se n t paper la a p relim in ary re p o rt on our work ooncam lng the approxim ate s o lu tio n o f th ia problem, +1. Let ub denote by J th e su rfa c e c u rre n t d e n s ity on the con d u cto r. The v eo to r J la d efin ed f o r every p o in t on the s u r fa c e and la d ire c te d alo n g th e tan g en t to th e au rfao e. I t ie com pletely determ ined by I t s two ta n g e n tia l components, th e th i r d component (normal to th e s u rfa c e ) being equal to a ero . I t may be shown t h a t th e v e c to r j s a t i s f i e s the follow ing In teg ral equationt +j - 2J« +J d8, (1<01) +with f - (1 - lkR)elkR . ( 1 . 02) +In t h i s equ atio n R I s th ele n g th of th echord Joining the two p o in ts of th e s u r f a c tt th e fix e d p o in t r ( x ,y , z ) , fo r which the In te g r a l I s e v alu ated , and the v a ria b le po in t r 'f x '. y 'j Z 1) , whose co o rd in a te s are fu n c tio n s o f th e I n te g ra tio n v a ria b le s , n is a u n it vector of the normal to the surface a t the point r , dS1 la th e eurfao e elem ent a t r* and k la the ab so lu te value o f th e wave v e c to r. The q u a n tity Jex i s an " e x te rn a l" c u rre n t d en sity defined by th e formula +["*«“ ] • +where H** i s the value o f th e magnetio f ie ld o f the In cid en t wave on the aurfao e (" e x te rn a l" f i e l d ) . +I f the dependence o f th e e x te rn a l f i e l d upon the co o rd in ates i s giv en by the f a o to r +(a) + + + ,lk(ax+ 0y+-y2 ) +15 +(1 .01) +then the c u rre n t d e n s ity may tje sought In the form o f a product 0f a sim ila r fa c to r w ith a slow ly v arying fu n c tio n o f coordina t e s . The I n te g r a l ( l .O l ) a f t e r d iv id in g by (1.04) tak es the form +i » J elk [R ^ (* , - x ) ^ ( » ,-y)+7 (* , -*)j gag. , (1.05) +where $ I s a slow ly vary in g fu n c tio n . I f the wave len g th la s u f f ic ie n tly sm all as compared w ith th e dimensions o f the body, the value o f th e in te g r a l w ill be approxim ately +I * ^ « , (1 . 06) +:< cos 0 +where th e p o in t x 1 y ' z ' Is connected with the p o in t x y 2 as i t is shown In P ig s. 1 and 2, and 0 I s the angle of Incidence of the ray. +Pig. 1 Fig. 2 +The a n a ly tic a l con n ectio n between the p o in ts x 1 y ' 2 ' and x y 2 Is given by th e fo llo w in g form ulas. Let n ’ denote the u n it v ecto r o f the normal a t the p oint x ' y ’ z ' and l e t +(3 ) + + + 16 +a + 2 n ' cob 6 +0 + 2n^ cos fl +y + Zn'x coe 6 +where +(1.07) +cob ■ (. +In o u r work we have obtain ed th e re q u ire d s o lu tio n f o r th e paraboloid of revolution (p a rtic u la rly the values of the tangential +(6 ) + + + 19 +components o f th e magnetic f i e l d on I t s surface) and have used th is solution to derive the approximate formulas. Let the e q u atio n o f th e p arab o lo id have the form +x2 + y2 - 2az - a2 - 0 . ( J . 01) +If the parabolic coordinates; +u - k ( r ♦ z) ; « « k ( r - a) ; (3.04) ♦ - arc t* JC +(7) + + + (3.05) +20 +with +are Intro d u ced , th e eq u atio n of th e p arab o lo id becomes +« * oQ - ka . (3 .06) +For th e g e n e ra liz e d (c o v a ria n t) ta n g e n tia l components o f the e x te rn a l m agnetic f i e l d we have th e ex p ressio n st +21u H*x + H*x = ^ _Juo e in * , (3.07) +- 21u H®x + H*x «= J u o e ltl ' 10 . (5 . 08) 9k +In the new co o rd in a te s th e ex p ressio n f o r (1 hue the form +0 = i (u - S') cos 6 + J uo s in 4 cos d . (3.09) +For the same componentso f the t o t a l f i e l d ex p ressions In form o f Fourier series with respect to the angle t are obtained. The c o e f f ic ie n ts o f s in s$ and cos s$ In th e se s e r ie s are d e fin ite In teg rals with respect to the parameter t. Involving some com plicated fu n c tio n s o f u, o, 4, s , t . These s e rie s and I n te g r a ls can be transform ed In to double In te g ra ls of th e form +21u H + H = - ° u * 2ir k s in (3 . 10) where the function g ( s ,t ) la defined In the follow ing way. D 5 ( o ,a ,t) be an In teg ral of the d iffe re n tia l equation +(8) + + + 21 +0 4 + * i + ( 1 . • ! « .1\ c . de dp ^ 4 ' 4p 2y +having a t tj-»ooan asym ptotic expressio n +JL t \ s± l « i ^ I t , o +Tf t -1 ir -* + y 1 j +C (» ,s ,t) • . 01 - s - I t +where F2Q I s an asym ptotic s e r ie s o f the form +1 + a - It . l \ 2 ' "V ip to tlc s e r ie s o f the +(Vs. 0 .1 +f&2 +i«2^_&i6±Ui5+... +N (s,t) = | e C‘ ( t / B , - t - l ) + * ( s 2+ t Z) C2 ( 0 , 8 , - t + l ) (3.14) where p I s con sid ered to be th e q u a n tity (3 -06). +g ( s , t ) « e 2 ? (u ,s + l,t) ? ( c , s - l , t ) ( s - lt) N ( s ,t ) . (3 -15) +With g ( s ,t ) having t h i s v a lu e , th e expression (3.10) I s v a lid , I f - it/2 < $ < w/2. In the cases tt/2 < $ < jir/2 and - 3ir/ 2 < ♦ < -w/2 we have to take fo r g ( s ,t ) a somewhat d if f e r e n t e x p re ssio n , which we s h a ll not (9) + + + 22 +w rite down h e re . The In te g r a tio n In (3 .1C) w ith re sp e c t to the v a ria b le t I s to be made along th e r e a l a x is from - oo to + oo and w ith r e s p e o t to s a’.ong th e Im aginary a x is from - 1 ooto + 1 oo. The valu e o f -21u I s o btained from (3 .1 0 ), I f we re p la c e d by -d. The double In te g ra l can be e v alu ated approxim ately under th e assum ption, th a t th e value o f u « lea I s very la rg e . Let us Introduce the quantity Ju o sin A cos d - o cos 0 > '( » « ) ] w (.In . ) W ' (5-l6) +T t is easy to v e r if y t h a t on th e g eom etrical boundary of the shadow t « 0 j bu t In g en eral I w ill be la r g e , o f th e o rd e r of o1^ . T h erefo re, when e v a lu a tin g th e I n te g ra ls we s h a ll con s id e r o to be very la rg e and { to be a r b itr a r y (in g e n e ra l, f i n i t e ) . I t can be shown, th a t under th ese assum ptions the following approximate e x p lo sio n s fo r the in te g ra ls are valid with a re la tiv e e rro r of the order of +Hu + H^ * ^ - T " eUl + 10 0 ( 4) * (?-17) +- 2iu H + H. » — r S . “ - W 0 ({) , (3 . 18) vk +where +0(4) - e1 3 —1= J e l t ---dI (3.19) +4 * J w' (t) rl th e symbol denoting a oontour running from in f i n i t y to the +o rig in along th e ray arc z - 2 /3 it and from th e o r ig in to I n f i n i t y along the ray arc * » 0 (the p o sitive real a x is). (1 0 ) + + + 23 +The f u n c ti o n w(t ) whose d e r i v a t i v e i s in v o lv e d in th e in te g r a n d h a s 'b e e n s t u d i e d i n o u r p r e v io u s p a p e r * . w( t ) s a tis f ie s the d if f e r e n tia l equation +w" ( t ) « tw (1 ) , ( 3 .2 0 ) +and can be w ritte n in th e form o f an in te g r a l +where th e co n to u r denoted by r g runs from I n f i n ity to th e o r i g i n a lo n g th e a rc z « - 2 /3 if and from th e o r ig in to in f in ity along th e p o sitiv e re a l a x is . Com parison o f (3 .1 7 ) and (3 .1 8 ) w ith (3 .0 7 ) and (3 .0 8 ) g iv e s +% “ Ht g 0 ( i ) • (3 -2 2 ) +Thus th e ta n g e n tia l components o f th e t o t a l m agnetic f i e l d a re eq u al to th e ta n g e n tia l components o f th e e x te rn a l f ie l d m u ltip lie d by a c e r ta in complex fu n c tio n o f a s in g le v a ria b le £. A B lm lla r r e la tio n e x is ts between th e to t a l and th e " e x te rn a l" c u rr e n t d e n s ity , namely +J = JCX 0 ( t) . (3.23) +Let us examine th e g eom etrical meaning o f th e v a ria b le ( in more d e t a i l . C onsider th e se c tio n o f th e paraboloid su rface by the plane of incidence passing through the given point ,(F lg . 4 ) . We denote by f the d ista n c e o f th e given p o in t from +* Jo u m . o f P hys., 1945. +(1 1 ) + + + 24 +th e geom etrical boundary o f the shadow, considered p o s itiv e In th e d ir e c tio n o f th e shadow and n e g a tiv e In th e d ire c tio n o f the l i g h t . The d is ta n c e I I s measured In the plan e o f In cidence. Let R be th e ra d iu s o f c u rv a tu re o f th e su rface s e c tio n and k « & r /\ th e ab so lu te value o f th e wave v e c to r. Then th e q u a n tity +£ where d I s th e w idth (2 . 01) o f th e penumbra re g io n J la e a s ily seen to coincide with the quantity (3 . 16) defined fo r a paraboloid o f r e v o lu tio n . Since we know beforehand th a t formulae (3-22) and (3 .23) a re q u ite g e n e ra l, we conclude th a t th ey a re v a lid fo r a l l bodies with a given cu rv atu re. I f $ la given by (3.2 4 ). +(12) + + + 25 +These formulae give the transition from the shadow to the +light +Por large positive values of % the function 0(£) is approxi mately equal to +1 (*~ + bl +dU ) = ce \ 3 / e-b* , (3.25) +where a , b, c a re known numbers; namely +a - 0.5094 ; b « 0.8823 ; c « 1.8325 . (3.26) +Owing to the factor e'b^ the function 0 ( 0 decreased rapidly. This corresponds to the decrease of the amplitude In the Bhadow region. +For large negative values of 6 the function G (0 admits an asym ptotic expansion of th e form +0 ( 0 =■ 2 + + • • • (3 -2 7 ) 20 +and tends to a lim it which I s equal to 2. This lim itin g value corresponds to form ulas (1.11) f o r the Illu m in ated reg io n . The d isco n tin u o u s fu n ctio n (1 . 11) i s thus replaced In our more e x act s o lu tio n by th e continuous fu n c tio n (3 .2 3 ). This en ables us to c a lc u la te the d is tr ib u tio n o f c u rre n ts on the su rface o f a con d u ctin g body w ith s u f f i c i e n t accuracy. In th e Appendix are given ta b le s o f th e fu n c tio n 0 defined by (3 .19) snd of the function g re la te d to 0 by the equation +0 <«) * • ’ « a). S uppressing the tim e-dependent f a c to r e~lu)t In the f i e l d components, we can express th ese components by means o f the Hertz fu n c tio n U which depends on r and 0 o n ly . De n o tin g by k th e ab so lu te v alue o f th e wave v e c to r we o b ta in fo r the f ie ld In the a ir; +(2 ) + + + 33 +the o th e r components b ein g equal to zero. Sim ilar equations hold for the fie ld In the e a rth . The fu n c tio n U s a tlB f le ^ fo r r > a the equation LV + k2U - 0 , ( 1. 02) and the r a d ia tio n co n d itio n a t i n f i n i t y +11m - lk r U ) (1.03) +I f b > a, 1. e. I f the source (dipole) Is located over the e a r t h 's su rfa c e and no t on th e su rface I t s e l f , U must have +a sin g u la rity a t the point r ■ b, 8 * 0, such th a t +_lkR +U * S jp - + u f (1.04) +and U* remains f i n i t e I f kR ■» 0. In th is formula +R = Vr2 + b2 - 2rb cos S (1 . 05) is the d ista n c e IVora the d ip o le . On the e a r t h 's su rfao e the Hertz fu n c tio n U has to s a t i s f y th e boundary conditions which ensure the c o n tin u ity of th e ta n g e n tia l components Eg and H^. I f we denote th e Hei^tl fu n ctio n w ith in the e a rth by Uj th ese boundary c o n d itio n s w ill have th e form: +k2U = k2 U2 ; £ (rU) « (rU2 ) f o r r - a . (1 . 06) +For O ^ r ^ g (w ith in the e a r th ) the fu n ctio n U2 has to s a tis f y an equation sim ila r to (1 . 02) and to remain f i n i t e . The q u a n tity k2 In form ula (1 .0 6 ) and In subsequent form ulas I s determ ined by the equation i,2 = „„2 * , „ (1.07) + + + 3* +and by the c o n d itio n Im(kg) > 0. I t Is u se fu l to Introduce In ste ad of th e co n d u c tiv ity of' the e a r t h 0, a length I which c h a ra c te riz e s the s p e c if ic re s is ta n c e o f th e e a r th . We put +f « c/4sfl. (1.08) +For sea w ater the v alues o f I vary from 0.05 cm (very s a lty w ater) to 0 .5 cm (d careely s a l t y w a te r ) . For th e s o il th is length Is hundreds or thousands times g re a te r. Introducing the complex lndu o tlv e c a p a c ity of. th e e a rth +1 H I 0*09) +, fcg '■ k. J T ( i.io ) The s o lu tio n o f our problem In th e form of s e rie s Is well known. We w rite , down the n e cessary ..form ulas, w ithout giving th eir derivation +*n *V"5 "Jn+* W.». +Cn tx) (*>.■■ +( 1 . 11) +where J y(x) Is th e Beeeel fu n c tio n and H ^ ( x ) I s the Hankel fu n c tio n of th e f i r s t kin d . These fu n c tio n s are; connected by the re la tio n ♦n (*) C^(x) - ^ ( * ) ' C n (x) ■ 'l . ‘ (1.18) +We Introduce a s p e c ia l n o ta tio n f o r the logarith m ic d e riv a tiv e of th e fu n c tio n Fn(* )i *n +. »A(«) *n ( x ) <*) +(1.13) + + + 35 +A8 s e e n rro m ( 1 . 0 1 ) , th e f i e l d on th e e a r t h 's s u r f a c e aay be expressed by the q u a n titie s +° a ” D| r ■ a 5 * 5F (rU> |r - a* ( * • » > For th ese q u a n titie s th e follow ing s e rie s In Legendre p o ly n o m ia ls may be o b ta in e d : +„ - - r V Y (2n + 1) +(1 .1 5 ) +(1 .16) +Our ta s k I s to p erform an approxim ate summation o f th e se se rie s . +2. THE SUMMATION FORMULA +The sums we have to c a lc u la te are o f the form +S - ^ v * ( v ) P y_^(cos 6), (2.01) +where the summation Is tak en over h a lf In te g ra l values o f v. I n th e sum ( 1 .1 5 ) th e f u n c ti o n $ ( v ) ( d i s r e g a r d i n g a c o n sta n t fac to r) is equal to +*(v) .. ----------------- j-i- 2 --------------------------- . (2 .( ‘ X y-i(k2a) +I n th e sura ( 1 .1 6 ) t h i s f u n c t i o n d i f f e r s fro m ( 2 .0 2 ) by th e fa c to r xv_ +(5) + + + 36 +For the d i r e c t com putation o f th e eun I t would be necessary to take th e number o f th e tarm s approxim ately equal to 2ka, 1. e. to double the number o f th e waves which may be p ut around the e a r th circum ference. Since t h i s number la enormous. I t la e v i d e n t, th a t such a d i r e c t summation Is Im possible. For the c a l c u la tio n o f the sum S I t I s n ecessary to make use of th e fa c t t h a t d(v) i s an a n a l y tic a l fu n c tio n and to transform th is sum in to an I n te g r a l, which Is to be ev a lu a ted by some approximate method. Such a tra n s fo rm a tio n was f i r s t l y proposed by Watson^ In 1918 and was th e n used by v ario u s a u th o rs. But a l l th ese a u th o rs aimed to b rin g th e ex p re ssio n o b tain ed by th is tr a n s fo rm ation to the form o f a sum o f re s id u e s , while our aim Is to s e p a ra te out a main term which I s e a s ie r to In v e s tig a te and to estim a te the magnitude o f th e rem ainder. The method of com p u ta tio n of th e main term I s not p redeterm ined th ereb y . When perform ing our tra n sfo rm a tio n we have to b ear in mind th e follo w in g g e n e ra l p ro p e r tie s o f th e fu n c tio n d (v ). I t Is an a n a ly tic a l fu n c tio n o f v meromorphlc In th e r ig h t h a lr -plane. I t has poles only In the f i r s t quadrant and Is holomorphlc In the fo u rth quadrant. I t decreases a t In fin ity In such a way t h a t a l l th e I n te g r a ls co n sid ered converge. The Legendre fu n c tio n s t h a t e n te r (2 .0 1 ) can be expressed by means o f th e fu n c tio n +°v ■ £ {Y r { M t } p ( * ' * ' v + r a r * ) (2 ‘03) +( 6) + + + 37 +where F denotes the hypergeom etrlcal fu n c tio n . Denoting by Gf and by P*_^ the ex p ressio n s which are obtained from G and from Pymj = Py_ j(co s ®) by re p la c in g 0 by 71 - 0 we g e t: +P , ■ — 7= = f e iv 0 ' 1T 0* + e ' lv ®+1? o 1 . (2.0*.) v' s 11V2 s i., 0 I v v J +It. i s seen from (2.03) th a t I f the values of v l i e o u t sid e of a c e r ta in s e c to r , which Includes the n egative re a l a x le , and I f | v s in 0 | I s la rg e , then the fu n ctio n Gy (and a ls o G*) I s approxim ately equal to +Ov ~ t ^ A . (2.05) +S u b s titu tin g (2.05) In (2 .p 4 ) we g et the w ell known asym ptotic ex p ressio n f o r I f we denote by B(v) the f i r s t term in formula (2.C1.) : +B(v) = — -1--------- e lv ®-1¥ G* (2.06) 7i V2 s in 0 +the follo w in g r e la tio n may be proved +P*_j ■ e 1^ - ^ " Pv. j + 21 cos vti B (v). (2.07) +We s h a ll use t h i s r e l a t i o n l a t e r on. We note th a t B(v) Is holomorphic In the rig h t half-p lan e. Let us c o n sid er In th e plane o f th e .complex v a ria b le v th re e c o n to u rs: 1) th e loop which s t a r t s a t i n f in ity on the p o s itiv e r e a l a x is , runs above the r e a l a x is , e n c irc le s the7 +(7) + + + 38 +o rig in counter-clockw ise and retu rn s to the s ta rtin g point a t I n f i n i t y running below the r e a l a x is ; 2) th e broken lin e Cg, which c o n tain s th e f i r s t quadrant and la describ ed (in i t s h o riz o n ta l p a r t drawn s l i g h t l y o v er the r e a l ax le ) from the l e f t to th e r ig h t a id e ; 3) the s t r a i g h t lin e which crosses th e o r ig in and i s in c lin e d a t a sm all angle to the Imaginary a x is. This lin e is described from the top to the bottom and lie 3 in the second and fourth quadrants. He can w rite th e sum S in th e form +S • j J" v$(v) sec vii dv, (2.08) +sin c e th e I n te g r a l on the rig h t-h a n d sid e reduces to the sum o f th e re s id u e s in th e p o in ts v * n + 4. The fu n ctio n d(v) being hdlomorphlc in the fo u rth q u a d ra n t, we may rep la c e the contour Cj by th e contours C2 and and w rite +5■' * J C2 +»♦(») ■ +(2.09) +This tra n sfo rm a tio n o f the sum corresponds to the usual one; the In teg ral along the contour is neglected because of th e sm alln ess o f the odd p a r t o f $(v) (an estim ate o f i t s magni tude w ill be given below ), and th e in te g r a l along Cg is reduced + + + 59 +t o the sum o f re s id u e s . But we s h a ll go a ste p fu r th e r and d iv id e the I n te g r a l along Cg in to two p a r ts : the main term >nd the c o rre c tio n term . I n s e r tin g in the in te g r a l th e ex p re ssio n (2 .0 7 ) f o r P*_£ we s h a ll have +S = Sx + S2 + Sy (2 .1 0 ) ' +where +S1 ’ ] v*(v) B(v) dv. (2.11) C +S9 ■ - $ \ v*(v) sec vn e lvfl Pv . dv (2.12) J C2 +S3 = | j v*(v) sec vn P j_ j dv. (2.13) +C5 +The in teg ran d in S1 has no poles on the re a l ax is (and a ls o in th e fo u rth q u a d ra n t). T herefo re, th ere i s no d iffe re n c e , whether we ev a lu a te the in te g r a l along Cg or along Cj We have denoted by C any contour, which i s e q u iv alen t to Cg o r C y The re p re s e n ta tio n o f S as a sum o f th ree I n te g ra ls (2.10) is e x a c t—th e re was made no n e g le c tio n in our d e riv a tio n . But th e e stim a tio n o f the magnitude o f Sg and shows th a t these in te g r a ls a re n e g lig ib ly sm all a s compared to S1 . In f a c t , i f we ev a lu a te the I n te g r a l Sg as a sum of r e s i dues a t th e p o le s of d(v) we s h a ll see th a t i t s r a t i o to S1 is of the order +(9) + + + (2 .I t) +40 +| #2 iv i (* -« )| +where v1 Is th e pole o f d(v) n e a re s t to the r e a l a x is . The Imaginary p a r t o f Vj I s p o s itiv e and f o r la rg e values o f ka w ill be Im(vj) - c(ka)1/5 , (2.15) +where c I s a pure number o f th e o rd e r of u n ity ( f o r the p e r fe c t conductor c ■ 0 .7 0 ). Since ka Is very la rg e ,o f the order o f a m illio n ( f o r X • 40 m, ka • 10^), I t Is c le a r , th a t the q u a n tity (2 .1 5 ) w ill be la rg e ( f o r In stan ce, equal to 70) and the q u a n tity (2.14) w ill be n e g lig ib ly sm all. (In our problem 6 cannot reach the v alue s sin c e In th is case we have to take Into account the Influence of Ionized layers of the atmosphere and our form ulas cease to be v a l i d .) The v alue of th e I n te g r a l S^ Is determined by the odd p a r t o f $ ( v ). But the odd p a r t o f t h i s fu n ctio n w ill be o f the order | e 21k2a | . (2.16) +S ince th e im aginary p a r t o f kga I s a p o sitiv e and very la rg e , th e v alue o f (2 .1 6 ) w ill be Inconceivably Bmall. The fo llo w in g p h y sic a l p :c .tu r e g jv e s a n o tio n of th e sm alln ess o f the I n te g r a ls S2 and S^. The In te g ra l Sg Is the am plitude o f a wave which tr a v e lle d once o r s e v e ra l times around th e globe w ithout r e f r a c t i o n (by means o f d if f r a c tio n o n ly ) . The in te g r a l S j la the am plitude o f a wave which +(1 0 ) + + + *»1 +traversed a path equal to the diam eter of the globe with the abso rp tio n which ta k e s p la c e w ith in the e a rth . I t Is c le a r th a t both the I n te g r a ls a re nefellglbly small as compared w ith the am plitude o f the wave which reached the o b server through the a i r by the n e a re s t way. T herefore w ith the whole p e rm issib le accuracy ( l . e . with an e r r o r which I s n e g lig ib ly sm all as compared w ith the e rro rs Involved In th e p o s itio n o f our p h y sic al problem) the otu.i S defined by (2.01) may be pu t equal to the In te g ra l Sj alo n e. This In te g r a l may be w ritte n In th e form += ^ v * (v ) e lv0 0 * d v , (2.17) +which follow s from (2.11) when the e x p ression (2 . 06) fo r I Is Inserted. +I f 0(v) I s the fu n c tio n (2 .0 2 ), then the re la tio n between urn S and the q u a n tity Ufl Is +ua ' ' TEafr S> (3.01) approximate ex p ression fo r U& may be +Therefore, w ritten +2e = \ v * { , +V +elvO > d v . +us s (3 .02) + + + 42 +The p o s itio n of the main p a r t of the In te g ra tio n p ath In (3.02) depends on the p o in t fo r which the In te g ra l Is evaluated. In g e n e ra l the main p a r t I s In the v ic i n ity o f the p o in t v = v0 , where (5.03) +The q u a n tity h la th e len g th o f the p e rp en d icu lar dropped from th e e a r t h 's c e n te r on th e ray (1. e.} on the s tr a ig h t lin e which connects th e source and the p o in t o f o b se rv a tio n ). For the approximate evaluation o f the In te g ra l I t Is necessary to obtain the asymptotic expressions for the func tio n s 0* and d(v) v a lid on th e main p a r t o f the In te g ra tio n p a th . Since v0 and vq6 a re la rg e as compared w ith u n ity , we may pu t according to (2.05) +Q* = V w /v . ( 3 .0 4 ) +For th e Hankel fu n c tio n s Involved In ip(v) one may te n ta tiv e l y use the Debye exp ressio n +Cw_4 (P) +V i - ( v2/ p2 ) +(3-05) +where (3.06) +These expressions are v alid provided the condition +I p2 - v2 ! » PV 3 +U2) +(3.07) + + + *»3 +la s a tis f ie d - As to th e fu n c tio n i t s value near the p o in t v * vQ nay be re p re se n te d w ith a s u f f ic ie n t ap p ro x i mation by the e x p ressio n ' +K - i “ - W 1 - T 7 (3-03) +k2 a +In o rd e r to make c l e a r . In which cases the In e q u a lity (3.07) Is s a tis f ie d , le t us Introduce the parameter +(3-09) +where 7 la the angle between the v e r t i c a l d ire c tio n a t the observ atio n p o in t and the d ire c tio n from t h i s p o in t to the source. I t I s e a s ily seen th a t f o r v * vQ, p • ka th e In e q u a lity ( 3 . 07) Is eq u iv a le n t to the c o n d itio n th a t p should be larg e and p o s itiv e . Such values of p correspond to the Illum inated reg io n . The v alues o f p o f the o rd e r of. u n ity (p o sitiv e and negativ e ones) correspond to the reg io n o f penumbras the special value p ■ 0 gives the boundary of the geom etrical shadow (horizon l i n e ) . Large and neg ative values of p c o rre s pond to the shadow re g io n . In t h i s s e c tio n we s h a ll In v e s tig a te the case of a larg e p o sitiv e p (Illum inated region)j other cases w ill be in v e stig a ted in the next sections. We have seen thai, I f p » 1 the Debye expressions fo r the Hankel fu n c tio n s a re v a lid . I n s e r tin g th ese expressions In to +P cos 7, +(13) + + + 44 +(3 .0 2 ) and u sin g (3.04) and (3 .0 8 ) we g et +(3.10) e 119) +For the function W In (3.13) the follow ing approximate expression Is obtained; +(15) +■ <3 -20 > + + + M-0 = h/R (3.21) +J*6 +where +is th e in c lin a tio n o f the ray to the h o rizo n . The contour T i s a s t r a i g h t lin e which crosseB the p o in t u, * u0 p assin g th ere from th e fo u rth to th e second quadrant o f the plane o f n (or of u - u0 to be more e x a c t) . Hie I n te g r a l ( 3 . 20) can be c alcu lated w ithout any f u r th e r approxim ation and g ives the well-known Weyl—van d er Pol form ula. I f we put +<>•»> +we s h a ll have +W » 2 - i(de"((3+T)2 f e*2 1® +(3 .2 » +To o b ta in th e f i e l d components from our ex p ressio n s fo r Uft and we have to d i f f e r e n t i a t e th e se e x p ressio n s by 6 which Is e a s ily done, sin c e we may reg ard a l l f a c to rs in ( 3 . 13) ex cept e lkR, as co nstants. +it. ASYMPTOTIC EXPRESSIONS FOR THE HANKEL FUNCTIONS +In th e follow ing we have to c o n sid e r the case when the p o in t of observation is in the region o f penumbra. T his case is c h a ra c te riz e d by th e values o f th e param eter p (p o s itiv e s o r n e g a tiv e s) o f the o rd e r u n ity . Aa th e in e q u a lity +( 16) + + + U7 +(» 01) is n o t s a t i s f i e d In th lB c a se , the hebye expressions 05) fo r th e Hankel fu n ctio n s are not v a lid on the main p a r t 0f the In te g ra tio n c o n to u r and must be replaced by some o th e rs, jhe new ex pressions f o r the Hankel fu n c tio n s s u ita b le fo r our purpose c»n be o b tain ed from th e asym ptotic expressions which +are given In our p”e v lo u s pap er^, o r from the form ulas given h +in the well-known W atson's t r e a t i s e , b ut i t Is more sim ple to deduce them Independently. Our aim Is to f i n d an approxim ate expression fo r the Hankel fu n c tio n in te rm s of th e fu n c tio n w (t), defined by the In teg ral +w (t) = Ije12-1/ 5*5 dz, (<(.01) +the contour T running frun in fin ity to the origin along the ray arc c » - 2u/3 and from th e o r ig in to In f in ity along the ray arc z ■ 0 (the p o s itiv e r e a l a x is ) . Tne fu n ctio n w (t) sa tis fie s the d iffe re n tia l equation +w "(t) - tw (t) (1. . 02) +with the i n i t i a l conditions: +"(0 ) = ■o / l = 1.0899290710 + 10.6292708b25, 32 /3 r (2/5) +w' (0) - e -i(it/6) . 0,791,5704238 - io.4587**5‘‘,'8 l. 3 / 5 r ( */ « (<<. 03) +(17) + + + 48 +w (t) ie an I n te g r a l tra n sc e n d e n ta l fu n c tio n , which can be ex panded In to a power a e rle a o f the form: +w (t) w(0) 1 1 + 2T^ + (2.5)h-«> ) + (5-5 +; t “ t i t 10 i +(4.04) I f we s e p a ra te In w (t) th e r e a l and the Imaginary p a rts (for re a l values of t) putting +w (tj ■ u (t) + l v ( t) , (4.05) +then u ( t ) and v ( t ) w l l l ’be two Independent I n te g r a ls o f equa tio n ( 4 , 0£) connected by the r e l a t i o n +u ’ ( t ) v ( t ) - u ( t ) v ■( t ) - 1. (4.06) +The asym ptotic expressio n s of th ese fu n ctio n s fo r larg e negative values of t are obtained by separation of the re a l and Imaginary p a r ts In th e form ulas: +For large p o sitiv e values of t the asymptotic expressions u ( t ) , v (t) and th e ir d e riv a tiv e s are of the form +, i t 3/ 2 i ( t ) = t * 1/ " e7 ; +, t t 3/2 += t 1/* e 3 ; +(18) +(4.09) + + + 49 +2 ,.3/2 v ( t) ■ K l/U • ’ 5 . +. a t 3/2 +v , (t) , . l t l / ^ e 3 k . +Prom the s e r ie s (4.04) th e follow ing re la tio n s deduced: w w (te ^ ) • 2elE v (-t). +w (te "5”) = e 5 [ u ( t ) - l v (t ) j . +These r e la tio n s d e sc rib e th e b ehavior, of w(t) In t l t-plane. Ve note th a t w (t) is e x p re s s ib le In terms of th fu n c tio n of the o rd e r 1/5 scco rd ln g to the formula +«(t) (-«)3/2) . +A fter having enumerated '.he main p ro p e rtie s of now proceed to deduce the asym ptotic e x pression fo r fu n c tio n H ^ ( p ) where v and p are la rg e and nearly that the ratio +remains bounded, while p tends to In fin ity . The Hankel fu n c tio n H ^ ( p ) adm its the in te g ra l tatlon +(19) +(*•10) +are easily +(« .ll) +(4.12) +e complex +e Hankel +(*.13) +w (t), we the Hankel eq u al, so +{*1.10 +repreaen + + + (1.15) +50 +< ‘ »w. 4 p +where the contour C c o n sists of a p a rt of the str a ig h t lin e Im(v) = - 7t d e sc rib e d from - n l - onto some p o in t v = v w ith He(v0) < 0 [ e . g . vo * ( - n /V T ) - lw}, a s tr a ig h t lin e Jo in ing vo to the o rig in and, fin a lly , the p o sitiv e re a l axis des c rib e d from th e o r ig in to I n f i n i t y . Let us express v through t , according to (4 .1 4 ), and In tro d u ce a new I n te g r a tio n v a ria b le +z * I T J /Z ’V (4.16) +C onsidering t and z as f i n i t e and p as la rg e , we can ex pand the lntergrand In (4.15) In a a e rie s of negative (fra c tio n a l) powers of p. Since th e re le v a n t p a r t of the tra n s formed contour C c o in cid es w ith contour T we can w rite +- A ( l ) ' 1/5 - & ( f f * * ...]« • +* (4.17) +and ev alu a te th e In te g r a l u sin g (4 .0 1 ). We thus o b tain +(4.18) +In v irtu e of the d iffe re n tia l equation (4.02) the f if th d eriv ativ e equals * ( 5 ) ( t ) = t 2 w' ( t ) + 4 tw ( t) . (4 . 19) +(2 0 ) + + + 51 +In s e rtin g t h i s In (4 .1 8 ) and usin g ( l . l l ) we g et the follow ing ex p ressio n f o r the fu n c tio n ? v- l / 2 (p): +Cv- l / 2 ( p ) = - - ( f ) l / 6| " ( t ) - ^ { | ) * 2/ 3 [t2W ( t) + 4 tw ( tj+ .. | . (4.20) +D iffe re n tia tin g th is expression with respect to p (with account of the dependence o f t on p w ith v co n stan t) we get the following expression fo r the derivative: +t ^ - l / 2 (p)= l ( f ) " l / 6| w ' ( t ) - ^ ( f ) ‘ 2/I?f*+9 )^ (t)-iltw '(t)] + . . . } . ( * . 21) +These ex p ressio n s w ill be used In the next se c tio n . § 5 . The expressions o f th e Herz fu n c tio n v a lid In the penumbra reg io n . We re w rite th e ex p re ssio n (3.02) f o r the Herz fu n ctio n re p la c in g th e r e in the q u a n tity Oj by I t s approximate value V jt/v and th e q u a n tity s i n 6 b efore the In te g ra l by 9. We g et +f +U ( v ) e lve y r a v . (5 .01) 8 kab J +The contour C may be taken Id e n tic a l w ith contour C2 , which was d efin ed In ^ 2 , o r may be re p laced by some contour eq u iv a len t to C? . The main p a r t of th e In te g ra tio n p ath l i e s in our case ( l .e . fo r f in ite values of the parameter p) near +(21) + + + 52 +th e p o in t v = lea. Consequently, th e fu n ctio n _^{k2a) involved in (2 . 02) can be rep la c e d by th e value o f (3 . 08) fo r v = ka. I n t r o d u c e th is In d(v) we o b ta in : +*(v) +____________ t v.j(K b )____________ (5.02) +For ( v j and i t s d e r iv a tiv e we must uee expressions v a lid n ear the p o in t v ■ k a. Such e x p ressio n s were obtained in the p receedlng p arag rap h . R e tain in g In (<*.20) and (X.21) the p rin c lp a l term s only we g e t: +I v ^ O * ) - - i ( j * ) V 6 •<*), (5.03) +Cv.* (k a ) * l ( ^ ) 1/6 w '( t ) . ( 5 .0 0 +where the v a ria b le t 1* connected w ith v by the r e la tio n +(5.05) +The num erator In (5 .0 2 ) la o b tain ed from (5 . 03) by rep lacin g a by b and t by t ', where +(5.06) +Equating (5 . 05) and (5 .0 6 ) we o b ta in th e connection between t and t 1. Since th e r a t i o h /a , where h • b - a , Is a n a ll £we s h a l l c o n sid e r I t o f rhe sane o rd e r aa (ka)"2^ j we must neg le c t I t as compared to u n ity . We may then put +(2 2 ) + + + f = t - y, +where +kh ( 5 . 08) (k a /2 ) ly +Is a quantity proportional to the height of the source over the e a r t h 's s u rfa c e . We may c a ll y the reduced heig h t o f the sou rce. Hence, w ith n e g le c t of terras o f the o rd er h /a o r Oca) -2 /3 a +tv-i(kb) ‘ - 1(!r )1/6w(t • y)* (5.09) +where t la determ ined by (5 .0 5 ). (We have a lso rep laced b by a In the f a c to r b e fo re w.) S u b s titu tio n o f (5 .0 3 ), (5-04) and (5.09) In (5-02) giver, the desired approximate expression fo r ${v). I f we pu t f o r the sake o f b re v ity +' W iq \ (5 -10) +* (v) ■ - ( | r ) /? • +:mberlng formulas (1 . 09) and (1 .1 0 ), v Mty q +- _ , /naN1^ V e - 1 + 1(x/2ti/) +Q' 1W -eTilx/Lf) +(5 .n ) +■may w rite fo r + + + w ith th e same accuracy +54 +q ■ 1 ( ^ ) 1/3 - = = = ? = = = = = = (5.13) +VX / V € + 1 + l(X /2n/) +This form is s l i g h t l y more convenient fo r c a lc u la tio n s . We have now to s u b s titu te th e value o f $(v) from (5-11) in to (5-01) and Intro d u ce th e in te g ra tio n v a ria b le t . Making t h i s s u b s t i t u t i o n , we may re p la c e the q u a n tity V""v"in th e i n t e grand by th e c o n sta n t value V k a and a lso w rite b in ste a d a t a in the f a c to r b efo re the in te g r a l. The r e s u ltin g formula may be w r itte n in th e form: +Ua = e - ^ f e 1Xt I & ( t) d t, (5.14) c' +where x denotes th e q u a n tity +x = ( t ) 1/3®' (5.15) +which may be termed as th e reduced h o riz o n ta l d istan ce from the s o u rc e, while y and q have the values given by (5.08) and (5 .1 3 ). The conto u r C must be such t h a t a l l th e poles o f the in te g ran d are comprised w ith in the contour; as we s h a ll see la te r , they are a ll situ ated in the f ir s t quadrant of the t p la n e . Thus we can c a rry out th e in te g ra tio n in (5-14) from loo to 0 and from 0 to + oa In o rd e r to g e t a more c le a r idea on the r a t i o of the h o r iz o n ta l and th e v e r t i c a l sc a le in the v a ria b le s x and y , we w rite th e e x p ressio n f o r th e param eter p, as defined by (24) + + + 55 +■)), in te rn s o f x and y . Prom th e c o n s id e ra tio n o f the trian g le with v e rtic e s In the e a r th 's c en ter. In the source po in t and In the p o in t o f o b s e rv a tio n , th e follow ing approxlpate expression la ea sily deduced: +I t follows th a t the equation of the horizon lin e Is x = V 7 . Fu rth er we s h a ll need th e r e l a tio n between the d i s tance R from the source as measured along a s tr a ig h t lin e and the h o riz o n ta l d is ta n c e afl as measured along the arc o f a grea^t c i r c l e . Assuming a® >> h, 1. e . (k a)1^ x >> y , th l6 r e la tio n may be w ritte n +kR ■ ka6 + u)o , (5.17) +where +“ o = h + ¥ - h • (5 -18) +6. DISCUSSION OF THE EXPRESSION FOR THE HERTZ FUNCTION +The expression o b tained fo r th e Hertz fu n ctio n Is most conveniently w ritte n In the form: +lka$ +Ua * S-g— V ( x ,y ,q ) , (6.01) +where +- . ' V ? " • (6 -02> c +(25) + + + 56 +The q u a n tity V may be c a lle d a tte n u a tio n fa c to r by analogy with th e q u a n tity W, which waa Introduced e a r l i e r ^see (3 .1 3 )]. Let us determ ine th e connection between V and W. Since In the d e nom inators of ex p ressio n s (3.13) and (6 .01) the q u a n titie s R and aO can be co nsidered as e q u al. I t follo w s from (5-17) +W » Ve-lu)o. (6.03) +We have now to I n v e s tig a te the ex p ressio n (6.02) fo r V. We s h a ll f i r s t co n sid e r the case o f larg e p o s itiv e values o f p(Illum inated reg io n ). This case has been already discussed by a n o th er methcd (f 3 ). B ut, as formula (6.02) w?i obtained f o r the case o f a f i n i t e p . I t seems to be o f I n te r e s t to v e r if y th a t i t 13 a ls o v a lid in th e case o f a larg e p . I f p >> 1, th e I n te g r a tio n p a th may be deformed so as to c ro ss the p o in t where - / T - P- I t s main p a r t w ill be s itu a te d In th e domain o f la rg e n e g a tiv e v alues of t , where expressions (it.07) and (<<.0c) i c r w and w are a p p lic a b le . Using them and applying the method o f th e s te e p e s t d e sc e n t, we o b tain +V ,1 The l a t t e r ex p re ssio n p r a c t i c a l l y coincided w ith (5 .15). We note t h a t in th e case when x i s of the order o f u n ity o r large the condition p » 1 is su ffic ie n t for the a p p lic a b ility +(2 6 ) + + + 57 +0f the method of s te e p e s t d e sc e n t. I f x Is :-mall, the fu rth e r condition y2 » 2x is n e c essary . I f th e l a t t e r co n d itio n Is not s a t i s f i e d bu t l.ie In e q u a lity +x « y « 1/x (6.06) *’ +is s a t i s f i e d I n s te a d , the I n te g r a l can be c a lc u la te d by another method. F u rth er s im p lif ic a tio n s in th e asym ptotic expression f o r w(t - y) can be then made, and th e in te g ra l (6.02) reduces to the form +l£ IT +V =e Vs ] ----------- d t - (6.07) C +Taking V - t as in te g r a tio n v a r ia b le , we are led to an In te g ra l o f the form (5.20) £with V- t - (k a /2 )1^ u ]and we g et again the Weyl-van d er Pol form ula (3-23) w ith the follow ing values of 6 and t : +6 - ¥ q V7 , T - e 1 " — X— . (6.08) +2V x +These valu es p r a c tic a lly c o in cid e w ith (3 .2 2 ). Let us now in v e s tig a te tne most in te r e s tin g case when p is o f th e order o f u n ity ( p o s itiv e or n e g a tiv e ). Vfe know th a t t h i s Is th e region o f the penumbra, where th e d if f r a c tio n e f f e c ts p lay the dominant p a r t . I f the values of x and y are of the order of u n ity , the most e f f e c tiv e method o f e v a lu a tio n o f the in te g ra l (6.02) is th e re p re s e n ta tio n o f t h i s I n te g r a l in form o f a sum of resid u es +(27) + + + 58 +taken a t the poles o f the Integrand. D enoting by t 8 * t g (q) th e ro o ts o f th e e q u atio n +**'(t) - qw (t) - 0 ( 6 . OS) +we o b ta in +(6 . 10) +The ro o ts t 9 (q) are fu n c tio n s o f the complex param eter q. For the value q ■ 0 they reduce to the roots t^ = t g(0) of the d e riv a tiv e w '( t ) and fo r q * oo they reduce to the ro o ts t ° ■ t s (a} o f the fu n ctio n w (t). The phases o f t ; and t ° are equal to n/3» so th a t +We g iv e h e re th e m o d u li o f th e f i r s t f i v e r o o t s t ^ a n d t ° : +s +For la rg e v a lu e s of s we have approxim ately +(28) +(6 .12) + + + 59 +To c a lc u la te th e ro o ts f o r f i n i t e values of q we may use the d iffe re n tia l equation +(6.13) +which can be e a s ily deriv ed from (4 .0 2 ). The root t 8 (q) Is determ ined e ith e r as th a t s o lu tio n o f (6.13) which a t q * 0 reduces to t^ o r as th a t s o lu tio n which a t q ■ coreduces to t®. Both d e fin itio n s a re e q u iv a le n t. S to rtin g from the f i r s t d e f in itio n , a s e r ie s in ascending powers o f q may be e a s ily co n stru cted fo r t B; th i s s e r i e s w ill converge fo r | q | <|)/"t^*|. S ta rtin g from th e second d e f in itio n we may co n stru ct a s e rie s in descending (negative) powers of q; th is w ill converge fo r M > 1 ^ 1 - These s e r ie s s h a l l not be w ritte n down here. I t may be n o ticed t h a t th e v alue o f t , which fo r larg e values of | q | Is clo se to qc , I s no t a r o o t o f equation (6 .0 9 ). I f th e co n d itio n y2 « » I V s l 13 s a t i s f i e d , we have the approximate re la tio n +^■w| t • ch(y sh(y y f t g). (6.14) +This r e la tio n perm its us to e stim a te the value o f remote terms In the se rie s (6.1 0 ). I f s Is 3 0 'larg e th at |q | « I V ^ I . we have approxim ately t g * t g (0) ■ t ^ . I t follow s from th is and from e x p ressio n (6 .1 4 ) t h a t the s e r ie s (6.10) Is always +(29) + + + 60 +convergent. But I f x Is small or I f y Is la rg e , the s e rie s converges slo w ly , and to c a lc u la te I t s sum a larg e number of terms may be re q u ire d . In the shadow re g io n , where p Is la rg e and n e g a tiv e , the s e r ie s (6 .1 0 ) converges very ra p id ly and I t s sum approxim ately reduces to I ts f ir s t term. Our s e r ie s (6.10) corresponds to th a t o f Watson but has the advantage of sim p lic ity . The fundamental form ula (6.02) perm its us to In v e stig a te not only the lim iting cases (large p o sitive values of p -lllu m lr.ated region, large negative values of p-shadow region) but a ls o the In term ed iate c a se s, namely the region of the penumbra. While In the lim itin g cases our form ula leads to an Improvement o f form ulas p re v io u sly known (the r e f le c tio n formula and the Weyl-van der Pol formula f o r th e Illu m inated region and the Watson s e r ie s f o r the shadow r e g io n ). In the tra n s itio n a l penumbra re g io n I t y ie ld s e s s e n t i a l l y new r e s u lts . The case when x and y a re la rg e and p - f l n i t e (s h o rt waves, penumbra) Is o f s p e c ia l I n t e r e s t . This case has not been In v e s tig a te d b e fo re as th e known form ulas are not v a lid h ere. In what follow s we s h a ll d e riv e approximate form ulas, which allow a complete d iscussion of th is case. We In tro d u ce the q u a n tity +* -V 7 . +(?0) +2 = (6.15) + + + 61 +which re p re s e n ts the reduced d ista n c e measured from the boun dary o f the geom etrical shadow (and no t from the so u rc e ). In the region o f geom etrical shadow we have z > 0, In the v lB lble region z < 0. Our p aram eter p , expressed In terms o f z and x, takes th e form +In our case x Is la rg e an z I s f i n i t e ; hence we have ap p ro x i mately p = - z. The main p a r t o f the I n te g r a tio n path In (6.02) c o rre s ponds now to v alues o f t o f th e o rd er o f u n ity ; but I f y Is larg e and t f i n i t e we may use fo r w (t-y) the asym ptotic ex p re ssio n (4 .0 7 ) which g ives +w(t - y) (6.17) +or approximately +1? -1 /4 i f y5^2- 1 V y t . (6.1ft) w(t - y) = e "y e 5 +I n s e r tin g (6 .1 8 ) In to (6 .0 2 ) and rep lacin g In the fa c to r b efore the I n te g r a l the q u a n tity x^ y '^ by u n ity , we g et +yV2 V (x .y .q ) = e 5 V ^ x - V y . i l ) , (6.19) +where +f eizt += J W*(t) - qw(t) d t ‘ +(31) +(6 .20) + + + 62 +The terms n eg lected In (6 .1 9 ) are (fo r a f i n i t e z) o f the order of 1/V "y" (o r of 1 /x ). T herefo re, th e fu n c tio n V (x ,y ,q ) o f two arguments x ,y and o f the param eter q reduces In our ease to a fu n c tio n V1(z,q ) o f a s in g le argument z and of the same p aram eter q. The r e sulting sim plification Is quite e ssen tial. Let us now d e riv e the r e l a t i o n connecting the a tte n u a tio n fu n c tio n Wwith th e fu n c tio n V j. We have the I d e n tity +(6 .21) +where u> has th e v alue (5 .1 6 ). O m itting In (6.21) the la s t term we o b ta in from (6.03) and (6 . 19) +iz ? W ■= e^ V ^ z .q ) . (6.22) +Thus, in our approxim ation function W depends on x and y only through z = x -\J~y". The fu nctio n V1(z ,q ) I s an I n te g r a l tra n sc e n d e n ta l func tio n o f th e v a ria b le z. For a p o s itiv e z we can ev a lu a te the I n te g r a l (6.20) a s a sum o f re s id u e s , and we get +V ^ z .q ) * 12 ^ L i (6.23) +. ( t . - q j w(t_) 8=1 3 (fo r z > 0), where t s a re th e ro o ts o f equ atio n (6 . 09) which were d iscu ssed e a r l i e r . The la r g e r Is z the more ra p id ly converges th e s e rie s ( 6 . 23) . For a s u f f i c i e n t l y la rg e p o s itiv e z I t s sum reduces to +(32) + + + 63 +the f i r s t term. For f in ite negative values of z (e .g . - 2 < z < o) the I n te g ra l (6.20) has to be e v alu ated by q u ad ratu res. For larg e n eg ativ e v alues o f z th i s In te g ra l may be evaluated by th e method o f s te e p e s t d e scen t, and we g et +v i ( z '«> e i V w ^ T ’ (6 ' 21° +According to (6 .2 2 ), th i s gives +W = 2 / ( l + ^ ) . (6.25) +Since approximately z « - p, th is coincides with expres sion (6.05). We note In conclu sio n t h a t our fundamental formula (6.02) can be obtain ed by th e method o f p a ra b o lic eq u ation, proposed by M. Leontovich and ap p lie d by him-' to the d e riv a tio n o f the Weyl-van d er Pol form ula. The a p p lic a tio n o f L eontovich’s method (in a s l i g h t l y Improved form) to our problem w ill be given In a separate paper. +REFERENCES +1 V. Fock, C. R. Acad. S c l . URSS, >43 (19*»5). 2 B. Vvedensky, B u ll. Acad. S c l. URSS, s e r phys. , ^ 415 (19&0). 5 V. Fock, C. R. Acad. S c l. URSS, 1,. 97 (1934). u o. n . Watson, TrcaU.Be an..the..Theory o f B e m i F vnctlona. Cambridge, 1922. ^ M. Leontovich, B u ll. Acad. S c l. URSS, s e r . p h y s., fl, 16 (1 9 « ). +(33) + + + 65 +... SOLUTION o p t h e problem o p pro pag ation o p electromagnetic waves *'■ ALONO THE EARTH'S SURFACE BY THE METHOD OF PARABOLIC EQUATION +The problem o f p ro p a g a tio n o f e le c tro m a g n e tic waves alo n g th e su rfa c e o f th e e a r th is so lv e d by th e m ethod o f p a ra b o lic e q u a tio n p ro p o sed by Leonto v ic h . In the f i r s t se c tio n th e su rfa ce o f the e a rth is co n sid ered as p lane and th e well-know n W eyl-van d e r Pol form ula i s d educed. T h is form ula tu rn s ou t to be th e e x ac t s o lu tio n o f th e pa ra b o lic e q uation w ith corresponding boundary c o n d itio n s. In th e second se ctio n the su rfa ce is co n sidered as sp h e ric a l, and the re s u ltin g form ula co in cid es w ith th a t o b ta in ed by Pock by th e method o f summation o f in fin ite se rie s rep resen tin g the rigorous so lu tio n o f th e problem . +A new form o f th e s o l u t i o n o f th e p ro b le m o f p r o p a g a tio n o f e lec tro m ag n e tic waves from a v e r ti c a l e lem en tary d ip o le +the f ie ld is c a lc u la te d f o r p o in ts on th e su rfa ce of th e e a rth , b u t a cc o rd in g to th e r e c ip r o c ity theorem th e same s o lu tio n gives d ire c tly the f ie ld a t any p o in t above the su rface i f the d ip o le is lo c a te d on th e s u rfa c e I t s e l f . In th e p re s e n t p a p er i t i s shown t h a t P o c k 's s o l u t i o n c a n a l s o be o b ta in e d by a n o th er m ethod, namely by red u c in g th e problem to an e q u atio n of p arab o lic type fo r the "atten u a tio n fu n ctio n ". +*In the sequel these papers w ill be re fe rre d as I . +M. L e o n to v ic h and V. Pock +s itu a te d a t a given h e ig h t above th e s p h e rica l su rfa ce o f the In th is so lu tio n +(1) OiLlL + + + 66 +The method o f p a ra b o lic eq u atio n was proposed by Leontovlch and a p p lied by him to th e s o lu tio n o f th e same problem f o r the case o f a plane earth . Since the considerations of the o riginal paper by leo n to v lc h ( ^ ) * * need some m o d ificatio n s, we s h a ll give In what follow s a new e x p o sitio n o f th e method, applying I t f i r s t l y to the case of a plane earth and considering then the case of a spherical earth. +1. THE CASE OP A PLANE EARTH +We assume th e tim e-dependence o f a l l th e f i e l d components to be o f the form e”lu>t. In th e fo llo w ing th is fa c to r s h a ll be om itted. Let us denote by k th e ab so lu te value of the wave v e c to r and by q th e complex In d u ctiv e c a p a c ity o f the e a rth : +I c - f S j , - e + i M . e + 1 , (i.oi) +The q u a n tity +having the dimensions of a length c h a ra c te rise s the sp ecific re s is ta n c e of th e e a rth ( t h i s le n g th v a r ie s from some ten th s o f a ce n tim ete r f o r sea w ater to te n and more m eters fo r dry s o i l ) . Let U be th e v e r t i c a l component o f the Hertz vecto r (the Hertz fu n ctio n ). This function s a tis f ie s the equation +AU + k2U - 0 . ( 1 . 03) We s h a ll w rite th e H ertz fu n c tio n In th e form +• • T h i s pap - w ill be r e f e r r e d In th e sequel as I I . +(2) + + + 67 +where R la th e d ista n c e from th e p o in t o f o b servation to the *ource and th e fa c to r W le th e s o -c a lle d "atte n u a tio n fu n ctio n ". H3 i t 1® known, f o r kR-*0 th e H e rtz fu n c tio n tends to i n f in ity in such a way th a t W ta k e s a f i n i t e v a lu e . We n o m a llz e U in ( uch a manner t h a t th i s v alue s h a l l be equal to u n ity ( i t being gupposed th a t both th e source and th e o b servation po in t remain above the su rfa c e o f th e e a r th ) . In the follow ing we assume, however, th a t the source la located on th e e a r t h 's s u rfa c e . Let us introduce c y lin d ric a l coord in ates r , z w ith th e o rig in Jr. the dip o le and the z a x is drawn v e r t i c a l l y upwardb . On th e ear t h 's su rface we have z - 0 . The d is ta n c e R w ill be R - - J r 2 + z2 . Hie p rin c ip a l "larg e param eter" of our problem i s the q u a n tity h | . For la rg e In I the attenuation function Wis a slowly varying function of coordinates. In order to c h aracterize the slowness of its v ariatio n i t Is useful to introduce the dimensionless coordinates . +p - JSL . ; C = , (1-05) 2 Ini -J Ini +and to co n sid e r W as a fu n c tio n o f p and ?. The d e riv a tiv e s of W w ith re s p e c t to itB arguments w ill be then o f the same o rd e r of magnitude bb th e fu n c tio n W i t s e l f . S u b stitu tio n of (1.04) in to equation (1.03) gives fo r the fu n c tio n W(p,?) an e q u a tio n , which can be s im p lifie d i f one supposes th a t the i n c lin a tio n angle o f th e ray to the horizon Is small and th a t th e d is ta n c e from the source i s a t l e a s t equal to s e v e ra l wave le n g th s . These assumptions y ie ld the Ineq u alities: +| « 1 ; kR » 1 , (1.06) which a re eq u iv a le n t to +i « 2.JN ; P » • +(3) +(1.07) + + + 68 +Since |i)| la assumed to be la rg e , th e In e q u a litie s (1.07) hold in a wide range of the v alu es o f p and ( (and In any case fo r values of p and C of the order of u n ity ). I f the In eq u a litie s (1.07) are v a lid , th e eq u atio n f o r W (p,() assumes the form +The terms om itted in (1.08) a re of th e o rd er o f l / | q | as compared with those re ta in e d . The boundary co n d itio n f o r Won the e a r t h 's surface Is obtain ed from th e c o n d itio n f o r th e Hertz v e c to r +— * -------- U ( f o r z - 0 ) ( 1 . 09) +az +given by L eontovlch. I t has th e form ++ qxw • 0 (fo r C -0 ) (1.10) 9C where ____ +ql - 1 P f el ^ (l-H) +and « I s th e s o -c a lle d lo ss a n g le , defin ed by +6 - arc tg ; 0 < 6 < | . (l .IP) +In th e lim it |n | —wo th e range o f the v a ria tio n s of p and Cls0 0 . Hence th e d e s ire d so lu tio n o f (1 .0 8 ) h as to s a t i s f y th e c o n d itio n +|w - 2 | —♦ 0 f o r p - * 0 a n d t > 0 . +(6) +(1 . 22) + + + 71 +However, s i n e s p ■ 0 1b a s in g u l a r p o i n t o f th e e q u a tio n f o r V, c o n d itio n (1.20) tu m e o u t to be n o t s u f fic ie n t fo r th e unique d eterm in atio n o f th e s o lu tio n . Ve re p la c e I t , th e re f o re , by • more s tr in g e n t c o n d itio n +f o r p-eO and C > 0 , (1.2 3 ) +which I s , a s I t w ill be seen l a t e r , a s u f f i c ie n t one. Thus, fo r th e d eterm ination o f th e "atten u a tio n fu n ctio n " V we have th e d i f f e r e n t i a l e q u a tio n (1 . 0 8 ) , th e b o u n d a ry c o n d itio n s (1.10) and (1.23) and the co n d itio n o f fln lte n e e s o f U In the region considered (fo r p > 0 ). To s im p lif y th e d i f f e r e n t i a l e q u a tio n , we make t h e su b +stitu tio n r2 Wa . (1 . 2M +Then th e e q u atio n ta k e s th e form +• 0 (1.25) +The boun d a ry c o n d itio n f o r W1 w i l l be +ow, +The c o n d itio n a t p * 0 becomes +1 JT +(for C -0 ). +-♦0 (fo rp -» 0 ). +(1 .26) +(1-27) +Since p - 0 Is a re g u la r p o in t o f the equation fo r «1 (In d i s t i n c t i o n t o th e e q u a tio n f o r W) c o n d itio n ( 1 .2 7 ) 1« • s u ffic ie n t one. +(7) + + + 72 +S o lv in g ( 1 .2 5 ) by means o f s e p a r a t i o n o f v a r i a b l e s , we e a s ily o b ta in a p a r ti c u la r s o lu tio n w hich s a t i s f i e s th e boundary c o n d itio n (1 . 26) ; namely +V1 - e ' lv 2 P (c o s vC - s i n v f) , ( 1 . 2 8 ) +where v i s the param eter o f se p a ra tio n . For r e a l v a lu es o f v th is e x p re ssio n rem ains f i n i t e and s a tis f ie s a ll conditions w ith th e exception of (1 .2 7 ). For complex v a lu es o f v (ex cep t th e c ase v - ± lq ^ ) ex p re ssio n (1 . 28) becomes I n f i n i t e when C-e® and th e r e f o r e , does n o t s a tis fy th e necessary co n d itio n s. I f lq^ th is expression transform s in to th e fo ra +W1 +p - c (1 .29) +A cc o rd in g t o ( 1 .1 1 ) and ( 1 . 1 2 ) , we have +$ < arc qx < f , (1 .30) +and, consequently, +Re ( q x ) > 0 ; Re ( iq * ) < 0 . ( 1 .3 1 ) +Hence th e r e a l p a rte o f th e c o e f fi c ie n ts o f p and ( In (1 .2 9 ) a re n eg ativ e and exp ressio n (1 .28) a lso s a tis f ie s a l l c onditions w ith th e exception o f (1 .2 7 ). 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n +0006860366 00000 n +0006860520 00000 n +0006860564 00000 n +0006860746 00000 n +0006860790 00000 n +0006860923 00000 n +trailer <<615AE3DDA72540EE81EC2A024FBFB591>]/Prev 6854067>> startxref 6860967 %%EOF \ No newline at end of file diff --git a/storage/DWPXRV3K/.zotero-ft-cache b/storage/DWPXRV3K/.zotero-ft-cache new file mode 100644 index 0000000..6c7f0db --- /dev/null +++ b/storage/DWPXRV3K/.zotero-ft-cache @@ -0,0 +1,62 @@ +Skip to main content +Physics > History and Philosophy of Physics +arXiv:2408.02790 (physics) +[Submitted on 5 Aug 2024] +Einstein Against Singularities: Analysis versus Geometry +John D. Norton +View PDF +Einstein identified singularities in spacetimes, such as at the Schwarzschild radius, where later relativists only find a coordinate system assigning multiple values to a single spacetime event. These differing judgments derive from differences in mathematical methods. Later relativists employ geometrical structures to correct anomalies in the coordinate systems used in analytic expressions. Einstein took the analytic expressions to be primary and the geometrical structures as mere heuristics that could be overruled if physical assumptions required it. Einstein's non-geometric methods had a firm base in the history of mathematical methods. They continued the non-geometric orientation of Christoffel, Ricci and LeviCivita. Einstein's insistence that singularities must be eliminated marked a departure from earlier tolerance of singularities. It was founded upon his longterm project of eliminating arbitrariness from fundamental physical theories. However, Einstein was willing to theorize with singularities only temporarily if they were the least arbitrary approach then available. +Subjects: History and Philosophy of Physics (physics.hist-ph); General Relativity and Quantum Cosmology (gr-qc) +Cite as: arXiv:2408.02790 [physics.hist-ph] +  (or arXiv:2408.02790v1 [physics.hist-ph] for this version) +  +https://doi.org/10.48550/arXiv.2408.02790 +Focus to learn more + +Journal reference: Philosophy of Physics 2(1) (2024) 13:1-73 +Related DOI: +https://doi.org/10.31389/pop.91 +Focus to learn more +Submission history +From: John D. Norton [view email] +[v1] Mon, 5 Aug 2024 19:13:41 UTC (4,871 KB) + +Access Paper: +View PDFOther Formats +view license +Current browse context: physics.hist-ph +< prev next > + +newrecent2024-08 +Change to browse by: gr-qc physics +References & Citations +INSPIRE HEP + +NASA ADS +Google Scholar +Semantic Scholar +Export BibTeX Citation +Bookmark +Bibliographic Tools +Bibliographic and Citation Tools +Bibliographic Explorer Toggle +Bibliographic Explorer (What is the Explorer?) +Litmaps Toggle +Litmaps (What is Litmaps?) +scite.ai Toggle +scite Smart Citations (What are Smart Citations?) +Code, Data, Media +Demos +Related Papers +About arXivLabs +Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?) +About +Help +Contact +Subscribe +Copyright +Privacy Policy +Web Accessibility Assistance + +arXiv Operational Status +Get status notifications via email or slack \ No newline at end of file diff --git a/storage/DWPXRV3K/2408.html b/storage/DWPXRV3K/2408.html new file mode 100644 index 0000000..57cae38 --- /dev/null +++ b/storage/DWPXRV3K/2408.html @@ -0,0 +1,360 @@ + +[2408.02790] Einstein Against Singularities: Analysis versus Geometry + + + + + + + + + + + + + + + + + + + + + + + +

+ + + diff --git a/storage/F6L6674P/.zotero-ft-cache b/storage/F6L6674P/.zotero-ft-cache new file mode 100644 index 0000000..a656543 --- /dev/null +++ b/storage/F6L6674P/.zotero-ft-cache @@ -0,0 +1,74 @@ +In this modern age of GPS and +precision long-range radar, it’s difficult to imagine the difficulty of navigating an aircraft at four miles a minute in darkness across blackedout enemy territory using only dead reckoning, star fixes and maps. +Thus it was hardly surprising that during WW2 the Luftwaffe adopted radio methods to guide night bombers to their targets in Britain. The story of the secret and silent ‘battle of the beams’ between the attackers who developed these specialised systems and the defenders who strove to disrupt them is one of the most fascinating in the history of short wave radio. It is a drama in which British radio amateurs played a pivotal role +Lorenz +2Q  2FWREHU  LQ WKH ÀUVW DLU UDLG RQ Britain in WW2, a Heinkel He 111 medium ERPEHU ZDV VKRW GRZQ E\ D 6SLWÀUH RI  Squadron over the Firth of Forth. When the plane’s radio equipment was taken to RAE Farnborough for examination, the technicians ZHUH VXUSULVHG WR ÀQG WKDW WKH /RUHQ] EOLQG approach receiver from the aircraft was a 7-valve superhet of much higher sensitivity than the 2-valve straight set that was adequate for normal service. Later, captured aircrew from another He 111 were overheard saying that no matter how diligently the British searched their plane WKH\ZRXOGQHYHUÀQGWKHLUERPELQJQDYLJDWLRQ equipment, implying that it would be overlooked because it was right under their noses. The blind approach system had been GHYHORSHG E\ WKH /RUHQ] &RPSDQ\ LQ %HUOLQ long before the outbreak of war and it had EHHQLQVWDOOHGDWPDQ\DLUÀHOGVWKURXJKRXWWKH world. The system initially used motor-driven switches to modulate the antenna lobes of a : 0+] 0&: WUDQVPLWWHU ORFDWHG at the end of the runway, such that if an aircraft were to the right of the approach path LWUHFHLYHGDVHULHVRI+]WRQHVHFRQG dashes, whereas if it were to the left it received VHFRQG GRWV 7KH GRWV DQG GDVKHV ZHUH synchronised, so that directly on the correct ÁLJKWSDWKWKH\PHUJHGLQDQHTXLVLJQDO]RQH +Feature Battling the +Radio Beams +80 0D\ +Part 1: Headache and Aspirin +The Knickebein beams from Kleve and Stollberg could be directed to intersect over targets such as the Rolls-Royce aero-engine factory at Derby. (Image: Dahnielson/cc by-sa 3.0). +August 1941 photo of part of a 20m-high Knickebein transmitter antenna, possibly in Halinghen, Hauts-de-France. (Image: Bundesarchiv, Bild 101I-228-0322-04 / Friedrich Springorum / CC-BY-SA 3.0). +. + + + Feature +May 2020 81 +to form a continuous tone. Was it possible that this popular commercial system had been PRGLÀHGWRVHUYHORQJUDQJHPLOLWDU\SXUSRVHV" ,QLWLDOO\WKHUHVSRQVLEOHFLYLOLDQ$LU0LQLVWU\ RIÀFLDOWDOHQWHG\RXQJ$VVLVWDQW,QWHOOLJHQFH 'LUHFWRU5HJLQDOG-RQHVZDVDGYLVHGE\WKH 0DUFRQL&RPSDQ\·VSURSDJDWLRQH[SHUWWKDWD V\VWHPRSHUDWLQJDWIUHTXHQFLHVDERYH0+] FRXOGQ·WEHXVHGWRJXLGHERPEHUVRYHU%ULWDLQ VLQFHVXFKVKRUWZDYHUDGLDWLRQZRXOGQ·WEHQG VXIÀFLHQWO\DURXQGWKHFXUYDWXUHRIWKHHDUWK 3KHQRPHQD VXFK DV WURSRVSKHULF GXFWLQJ ZHUHQRWZHOONQRZQDWWKLVWLPH ,QGHHGWKH PD[LPXPUDQJHRIWKHVWDQGDUG/RUHQ]V\VWHP ZDVRQO\DERXWPLOHVEXWDQHQWKXVLDVWLF UDGLR DPDWHXU 5RZOH\ 6FRWW)DUQLH *), FRQYLQFHG -RQHV WKDW LW VKRXOG EH SRVVLEOH WRH[WHQGWKHUDQJHE\WKHVDPHWHFKQLTXHV WKDWZHUHXVHGE\UDGLRDPDWHXUVWRDFKLHYH '; FRPPXQLFDWLRQV 8VLQJ D PXFK ODUJHU JURXQGDQWHQQDZLWKDQDUURZHUEHDPZLGWK KLJKHUWUDQVPLWWHUSRZHUDQGPRUHVHQVLWLYH UHFHLYHUVKHEHOLHYHGWKDWDWOHDVWKLJKÁ\LQJ SODQHVFRXOGEHDEOHWRXVHDPRGLÀFDWLRQRI WKH V\VWHP LQ WKH UHYHUVH GLUHFWLRQ IRU ORQJ UDQJHQDYLJDWLRQ+HDOVRVXJJHVWHGWKDWWKH 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ZDV QRZ DSSDUHQW DQG WKH 5$) DSSURSULDWHO\ FRGHQDPHG WKH HQHP\ EHDP V\VWHP¶+HDGDFKH·:KHQ)LJKWHU&RPPDQG &KLHI+XJK'RZGLQJZDVDVNHGZKDWVKRXOG EHGRQHKHUHSOLHGLQRQHZRUG ́-DPμ +80 Wing +,Q $XJXVW  D UDGLR FRXQWHUPHDVXUHV XQLW FDOOHG1R 6LJQDOV :LQJZDVIRUPHGE\ VLJQDOV VSHFLDOLVW (GZDUG $GGLVRQ WR SURYLGH +Dr Bruce Taylor, HB9ANY bgtaylor@ieee.org +Restoring an aircraft Knickebein system (foreground). Left: EBL2 signal processing unit; Middle: EBL3 superhet beam receiver; Right: U8 210V HT rotary converter. (CDV&T and Hans Goulooze). + + + Feature +82 May 2020 +electronic intelligence and counter the German beams. Its motto was “Confusion to Our Enemies”. The Wing Headquarters was established in the Aldenham Lodge Hotel in Radlett, a village about 14 miles north west of London in convenient proximity to the London/ Birmingham GPO trunk cable. It was linked directly to the Fighter Command Operations Room at Bentley Priory in Stanmore. The old Lodge was infested with rats and cockroaches but it had a swimming pool, rather a rare asset for a WW2 RAF base! Because of their technical experience, resourcefulness and ability to improvise solutions rapidly, many British radio amateurs served in this unusual unit, with the General Secretary of the RSGB, John Clarricoats, G6CL, acting as a ‘Recruiting Sergeant’. Fifty BBC radio engineers also joined and within a year Addison had built up monitoring and jamming systems at over 120 outstations throughout the country. By September 1941, 80 Wing had a strength of 2000 men and +women of all ranks. A staff of 27 WAAFs was engaged to use 242 telephone lines to connect the Radlett HQ with the outstations. Before specialised systems to counter Knickebein could be built, Addison’s team improvised makeshift jammers by commandeering 150W 27.12MHz diathermy sets from local hospitals. These were converted WR 5) SRZHU DPSOLÀHUV DQG GULYHQ E\ VPDOO transmitters made at the Peto Scott factory to emit radio noise on the Knickebein frequencies. Two sets were installed in vehicles that could rapidly be despatched to any target area. Others were installed in dispersed police stations, which were alerted by telephone from Wing HQ when they were required. One village bobby put a set in his bedroom, where his wife could switch it on if he was out on his beat at the time of a call. The Rediffusion factory in south-west London produced a number of powerful jammers very UDSLGO\E\FRQYHUWLQJWKHN:DXGLRDPSOLÀHUV on their production line into radio transmitters. +:LQJDOVRPRGLÀHGHLJKW5$)/RUHQ]DLUÀHOG approach transmitters to radiate fake beams across the Knickebein ones to induce the attacking planes to stray off course, or to drop their bomb load in open country before reaching the target. The Air Arm of 80 Wing, which later became  6TXDGURQ FDUULHG RXW UHJXODU ÁLJKWV WR locate the radio beams. To narrow the search area for the Ansons, manned receiving stations were set up by lashing garden sheds to the tops of the towers of a few selected Chain Home radar stations. Braving the freezing cold in these high level shacks, the listening operators could indicate to Wing HQ the Knickebein frequencies that were being used on any night, and to which side of each station the beams lay. Knowing the antenna patterns of the Knickebein transmitters and their locations, the information from several such receiving stations could be combined to estimate the bearings of the main lobes. Since the beams were often turned on well before each night attack, this gave time to identify the probable target and set up the jammers. Meanwhile a more sophisticated antidote for Headache was being developed by Robert Cockburn and his team at the Telecommunications Research Establishment (TRE) in Worth Matravers, which included Martin Ryle, G3CY. This countermeasure was aptly named ‘Aspirin’. When a Knickebein raid started, the 500W Aspirins netted on to the frequency and transmitted dashes with the same modulation tone at exactly the same rate as the real transmitter. When the jamming signal was strong enough, pilots on the correct track continued to hear dashes, causing them to diverge from it. This even resulted in several ERPEHUV Á\LQJ LQ FLUFOHV QDYLJDWLRQ EHFDPH so unreliable that by mistake some German bombers landed in England instead of at their home bases. At least one inexperienced young bomber crew, who hadn’t been taught to navigate at night without the Knickebein beams, bailed out from their plane when they found they were jammed. When the start of systematic Aspirin jamming revealed that Knickebein had become well understood by the RAF, many German bomber pilots preferred to keep out of the beam VLQFHWKH\IHDUHG PLVWDNHQO\ WKDWQLJKWÀJKWHUV or aerial mines might be waiting for them all along the route to the target. This psychological effect may actually have caused more disruption than the jamming itself. By the autumn of 1940 raiders no longer considered Knickebein usable HQRXJK IRU WDUJHW LGHQWLÀFDWLRQ DOWKRXJK LW was several months before the young German pilots plucked up the courage to tell Göring that the system was useless. However, as we shall see in Part 2, the German Aviation Research Institute (DVL) had been developing another highly secret and much more accurate VHF radio beam system that would soon be used by the Luftwaffe with devastating effect. +Hallicrafters S-27 amateur radio receivers were used to search for the Luftwaffe beams. +After the occupation of the Netherlands and France, more compact second-generation 45m-wide FuSan721 Knickebein antennas could be used, as they could be sited nearer to Britain. (Model by Michael Kayser) + + + Radio amateurs played a +pivotal role in electronic countermeasures during WW2. +In Part 1 we saw how the RAF used amateur radio receivers to discover the Knickebein system of radio beams that the Luftwaffe employed to guide its night bombers to targets in Britain. ‘Aspirin’ jammers for this ‘Headache’ had been developed by TRE and deployed successfully by 80 Wing, and the system was considered no longer usable for accurate navigation. But the enemy had other tricks waiting in the wings. +X-Gerät +On 6 November 1940 a raiding Heinkel III bomber that had suffered compass failure over England tried to return to its base in occupied France by using a radio beacon at Saint-Malo. But the beacon was being jammed by 80 Wing, so the crew became disorientated and instead of landing in Brittany the plane ran out of fuel and crash landed just offshore from the beach at West Bay in Dorset. British Army soldiers waded into the shallows and secured a rope around the fuselage, but then the Royal Navy arrived and claimed that because the plane was in the sea it was theirs to salvage. When the sailors towed it into deeper water to secure it to a ship, the rope parted and the plane sank to the bottom! In spite of this incident the waterlogged radio equipment on board the aircraft was recovered and sent to RAE Farnborough, where it was found to include a new type of bombing radio navigation aid called X-Gerät. This system was considerably more sophisticated than Knickebein, having both coarse and Àne director beams and 20 operating frequencies in the higher frequency range of 65-77MHz. The X-Gerät system also laid three very narrow crossbeams across the director beam prior to the target, which allowed the aircraft’s ground speed to be determined and the bomb release point to be computed by a special ‘bombing-clock’ +Feature Battling the +Radio Beams +82 June 2020 +Part 2: Bromide, Domino and Benjamin +Locations of the radio beam transmitters in 1941. (Courtesy of Bill Rankin, www.afterthemap.info). +7KHWKUHHGRUVDODQWHQQDPDVWVUHYHDOWKDWWKLV+HLQNHOZDVDQ;*HUlWSDWKÀQGHU + + + Feature +June 2020 83 +mechanism on board the plane. The 0.05q Àne director beam was so narrow that in calculating its bearing 5-Àgure log tables had to be used to take account of the fact that the earth isn’t a perfect sphere (it’s slightly Áattened near the poles). A result of the antenna conÀguration required to achieve this high directivity was that the radiation pattern had 14 lobes, several of which the bombers had to Áy across to Ànd the true guide beam. The crossbeams also had multiple sidelobes, and as the Áight progressed the aircrew had to resolve the ambiguity by counting them until they reached the genuine Àrst marker beam. These sidelobes also complicated 80 Wing’s task of determining the target. Since the X-Gerät system required special equipment and trained aircrew operators, it was Àtted only to the bombers of an elite group of pathÀnders called Kampf Gruppe 100 (KGr100), whose task was to mark the target with hundreds of 1kg thermite incendiaries, on which the main force would bomb visually. But the poor ballistics of these incendiaries resulted in considerable spread and they didn’t have a special Áare colour to distinguish them from Àres caused by misdirected bombs. Learning from experience with Knickebein, the 500W X-Gerät transmitters emitted spoof beams before each raid, while the real ones weren’t turned on until as late as possible, a tactic that sometimes confused the bombers as much as the defenders. Fortunately for the Allies, KGr100 was based at Vannes, far to the west of France and beyond the reach of secure German military landlines, so the unit had to use wireless for ground communications. This allowed the control messages to be intercepted by the Y Service and radio amateur VIs and decrypted at Bletchley Park. With these decrypts, Jones was able to deduce how the operating frequencies were related to the receiver settings that were transmitted to the pathÀnders before each raid. Using this information, Cockburn’s team at TRE rapidly introduced 100W X-Gerät jammers called ‘Bromides’ that were equivalent to the Aspirins for Headaches. Nevertheless, Bromide proved ineffective during the devastating 10-hour raid on Coventry, even though the jammers at Birdlip Hill, near Gloucester, Kenilworth and Hagley were well within range. This was because their modulation tone was set to 1500Hz, whereas the X-Gerät receivers had a sharp audio Àlter centred on 2000Hz. The mistake was corrected before the raids on Birmingham Àve days later, when the Luftwaffe bombers were partially disrupted and dispersed. By April 1941, 80 Wing had enough Bromides to disrupt all the X-Gerät director and crossbeam frequencies +and no other inland British city was to suffer such highly concentrated damage. In spite of at least eight attacks on the Rolls-Royce works at Derby during WW2, only a single bomb actually hit a factory building. Except on moonless or cloudy nights, no radio aids were required to Ànd the sprawling metropolis of London. But speciÀc industrial assets in the city couldn’t be targeted accurately without the help of reliable beams and the enemy bomb loads were scattered over almost 100 boroughs. Although no longer used by raiding bombers, the 6577MHz X-Gerät transmitters were kept functioning as decoys until they were Ànally dismantled in November 1942. +Y-Gerät +As early as mid-1940, when the existence of the Knickebein beams was conÀrmed, Enigma decrypts from Bletchley Park included mention of what appeared to be another system, code-named ‘Wotan’. Since this is the name of a Germanic God with only one eye, Jones guessed that it might refer to a new navigation aid that used only a single beam. It turned out that this reasoning was wrong but the conclusion was perfectly correct! Monitoring stations began to report beam signals between 42.1 and 47.9MHz that had different characteristics, with alternate right and left signals of equal duration transmitted at a high rate, for they were decoded in the aircraft electronically rather than aurally. The bearing analyser was coupled to the modiÀed He 111 autopilot by an automatic Áight control system that was much ahead of its time. This more advanced ‘Y-Gerät’ system reduced the number of confusing sidelobes by switching between a cardioid and a more directive antenna pattern. It achieved very accurate slant ranging by transmitting a 300Hz, 3kHz or 7.5kHz tonemodulated carrier to a transponder in the aircraft +on one frequency, and comparing the phase with the return signal carrying the same modulation sent back from the aircraft on a different one. The range measurement was made by the ground controller, who used a version of the X-Gerät stopclock to determine when to order the aircraft to release its bombs. Since the system was more complex and could only operate with Àve aircraft at a time, Y-Gerät equipped planes were formed into a specialised pathÀnder group (Group III of KG26) that led the main bomber stream. III/KG26 made the error of practising using Y-Gerät for many weeks before trying it on a major bombing raid. So Cockburn’s team had time to analyse the signals and devise a subtle countermeasure called ‘Domino’, which was ready for action on the very Àrst night that the system was used for a large-scale attack on Britain. They borrowed the powerful BBC TV transmitter at Alexandra Palace, which by chance operated in the same frequency band and had been shut down at the outbreak of war lest it be used by the Luftwaffe to home on London. An EMI TV receiver was set up at the former outside broadcast relay station at Swains Lane in Highgate, with its bandwidth enlarged to accept both the ground control transmission on 42.5MHz and the response from the pathÀnder bomber on 46.9MHz. From there, the modulation signal was sent by Post OfÀce landline to Alexandra Palace, together with a subdivision of the carrier frequency that allowed the TV transmitter to zero beat with the ground transmission. At Swains Lane Ewart Farvis sat listening to the German radio communications with his Ànger on a key that controlled Alexandra Palace remotely. At the critical moment, he sent the modulation back to the aircraft on 42.5MHz, using a power that was sufÀcient to give a false range indication but not enough to arouse suspicion of jamming. Thirty years after the event, when Farvis Ànally felt free to tell me about this secret war work, he described the result as hilarious. Being Áuent in German, he could follow the acrimonious radio dialogue between the bewildered young bomber aircrew and their ground controller as they argued about the cause of the perplexing behaviour of their instruments. The aircrew accused the ground station of sending bad signals, while the ground controller attributed the problems to airborne equipment failure, probably due to a loose wire. He even told the distraught operator to “thump the box”, which caused Farvis to remark that he was evidently a real radio man! The jamming was repeated successfully with more pathÀnders before the Luftwaffe abandoned the attack. At TRE, Farvis went on to analyse the signals of the German VHF IdentiÀcation, Friend or Foe +Dr Bruce Taylor, HB9ANY bgtaylor@ieee.org +The X-Gerät ‘bombing-clock’ measured the time WRÁ\EHWZHHQWZRFURVVEHDPVWRGHWHUPLQHWKH bomb release time. (Horst Beck Collection, photo Frank Dörenberg, N4SPP/F4WCN). + + + Feature +(IFF) system, allowing the team to develop the ‘Perfectos’ radio device that RAF night Àghters used to trigger the transponders in enemy aircraft, to determine their positions without using radar. Following the deployment of Perfectos, many Luftwaffe crews Áew with their IFF switched off and were shot down by their own side’s Áak. After the capitulation of Germany, Farvis was given the temporary rank of Squadron Leader (and a revolver) when he was Áown to Munich to interrogate German engineers and scientists. He had a fruitful discussion with the designer of X-Gerät and Y-Gerät, Johannes Plendl. +Benjamin +Having established an effective countermeasure for the ranging system of Y-Gerät, Cockburn lost no time in manufacturing production versions of Domino, which could also deal with rapid frequency changes that were sometimes made in the middle of an operation. Although a Domino station on Beacon Hill near Salisbury was attacked by a small force of bombers it was soon back on the air and, during the Àrst two weeks of March 1941, only 18 aircraft of 89 Y-Gerät sorties received the bomb-release signal. Domino was an effective but complex countermeasure, requiring two-way communication between jammer and aircraft. But Cockburn soon found that Y-Gerät navigation could be disrupted by an even simpler form of jamming. When three Heinkel bombers were shot down during a raid over Liverpool in May 1941, the vulnerability of their Y-Gerät signal analyser was studied in detail at Farnborough. It was found that a short gap between the pair of direction signals was essential for the electronic bearing-analyser to lock to the beam. By Àlling in this gap by transmitting a continuous note on the beam frequency, the analyser unlocked and gave no useful indication. Within three weeks 80 Wing had a new jammer on the air that used this technique, and Àve more were operational before the end of the month. Cockburn called it ‘Benjamin’ (for ‘Ben jamming’, since Benito was the British codename for Y-Gerät). The Luftwaffe eventually realised that Y-Gerät had been compromised from the Àrst day that it was used. Bomber pilots no longer put any faith in wireless navigation aids, making the accurate night bombing of inland targets very difÀcult. In one raid the crews that thought they had bombed Nottingham dropped their weapons in open country 15 miles east of the city, killing two chickens with 230 +Conclusion +In his memoirs on the Battle of Britain, Churchill wrote one sentence about the vitally important role of radar, but eight pages on the German radio beams. Were it not for Jones, Scott-Farnie, Cockburn, Farvis, TRE, 80 Wing and the efforts of numerous dedicated radio amateurs, there would undoubtedly have been many more instances like the destruction of Coventry. Without effective electronic countermeasures, concentrated pin-point bombing might well have destroyed the British aero-engine and SpitÀre factories, changing the course of the war. In a light-hearted tribute at the end of the conÁict, he wrote, “You certainly did pull the crooked leg”. +Correction +The Knickebein antenna shown on page 80 (May) is of the compact type and isn’t 60m high. The total distance from the bottom to the top of the stacked dipoles is less than 10m, which makes the total height of the structure less than 20m above ground. Even the giant antenna at Stollberg Hill was much less than 60m high, although it was 90m wide. The photo on page 82 isn’t a Knickebein antenna, although it does bear a resemblance. The one shown doesn’t have the ‘crooked leg’ angle characteristic of Knickebein. It is instead a photo of a ‘Bernhard’ radio navigational beacon, which had no connection with the bombing beams. +The Alexandra Palace TV transmitter was used to disrupt Y-Gerät on 42.5MHz. (Photo based on Duncan Harris/CC-BY-2.0). +7KH&RDOYLOOH2XWVWDWLRQRI:LQJRQWKHÁLJKWSDWKWR'HUE\KDG$VSLULQ to jam Knickebein, two Bromides for X-Gerät and Benjamin for Y-Gerät. ,Q/RXJKERURXJK$5&RSHUDWHG*%&+*IURPWKHVLWH &KDUOH\ +HULWDJH*URXS%OXHVN\*RRJOH(DUWK  +84 June 2020 +high explosive bombs, one oil bomb and !ve sticks of 36 incendiaries. In some raids bombing was so scattered over the southern counties of England that it was impossible to deduce the intended target until it was revealed by the crews of downed bombers. Meanwhile, the tide of war began to turn. The experience of 80 Wing proved invaluable when the Allies began to take the !ght to the enemy and in the summer of 1942 the RAF used radio beams to guide the bombing of the Krupp arms factory in a precision night attack through ten-tenths cloud. +We apologise to Dr Taylor for the following errors that were introduced into Part 1 of this feature. +A downed Heinkel 111 pathfinder. \ No newline at end of file diff --git a/storage/F6L6674P/Taylor - ,Q $XJXVW D UDGLR FRXQWHUPHDVXUHV XQLW FDOOHG1R 6LJQDOV LQJZDVIRUPHGE VLJQDO.pdf b/storage/F6L6674P/Taylor - ,Q $XJXVW D UDGLR FRXQWHUPHDVXUHV XQLW FDOOHG1R 6LJQDOV LQJZDVIRUPHGE VLJQDO.pdf new file mode 100644 index 0000000..b4e1028 Binary files /dev/null and b/storage/F6L6674P/Taylor - ,Q $XJXVW D UDGLR FRXQWHUPHDVXUHV XQLW FDOOHG1R 6LJQDOV LQJZDVIRUPHGE VLJQDO.pdf differ diff --git a/storage/FHFCL8HL/why the values of cavendish are meaningless for predicting earths mass.docx b/storage/FHFCL8HL/why the values of cavendish are meaningless for predicting earths mass.docx new file mode 100644 index 0000000..12ce6d0 Binary files /dev/null and b/storage/FHFCL8HL/why the values of cavendish are meaningless for predicting earths mass.docx differ diff --git a/storage/HN7IDPXU/Louis Brown - A radar history of World War II_ Technical and Military Imperatives-IOP (1999).chm b/storage/HN7IDPXU/Louis Brown - A radar history of World War II_ Technical and Military Imperatives-IOP (1999).chm new file mode 100644 index 0000000..b0f74fa Binary files /dev/null and b/storage/HN7IDPXU/Louis Brown - A radar history of World War II_ Technical and Military Imperatives-IOP (1999).chm differ diff --git a/storage/J93DU5HH/.zotero-ft-cache b/storage/J93DU5HH/.zotero-ft-cache new file mode 100644 index 0000000..6319d52 --- /dev/null +++ b/storage/J93DU5HH/.zotero-ft-cache @@ -0,0 +1,540 @@ +1 +July 20, 2001; rev. August 16, 2001 +General Covariance, Gauge Theories and the Kretschmann +Objection. +Submitted to Symmetry in Physics: New Reflections, +Katherine Brading and Elena Castellani ( eds), in preparation. +John D. Norton 1 +Department of History and Philosophy of Science +University of Pittsburgh, Pittsburgh PA USA 15260 +jdnorton@pitt.edu +How can we reconcile two claims that are now both widely accepted: +Kretschmann's claim that a requirement of general covariance is physically +vacuous and the standard view that the general covariance of general relativity +expresses the physically important diffeomorphism gauge freedom of general +relativity? I urge that both claims can be held without contradiction if we attend +to the context in which each is made. +1 I thank Carlo Rovelli, John Earman, Elena Castellani and Chris Martin for their discussion +and for forcing me to think this through. I am also grateful for discussion by the participants +in the "International Workshop: General Covariance and Quantum?: Where Do We Stand," +Department of Physics, University of Parma, June 21-23, 2001, organized by Massimo Pauri. + + + 2 +1. Introduction +Two views... +When Einstein formulated his general theory of relativity, he presented it as the +culmination of his search for a generally covariant theory. That this was the signal +achievement of the theory rapidly became the orthodox conception. A dissident view, +however, tracing back at least to objections raised by Erich Kretschmann in 1917, holds that +there is no physical content in Einstein's demand for general covariance. That dissident view +has grown into the mainstream. Many accounts of general relativity no longer even mention +a principle or requirement of general covariance. +What is unsettling for this shift in opinion is the newer characterization of general +relativity as a gauge theory of gravitation, with general covariance expressing a gauge +freedom. The recognition of this gauge freedom has proven central to the physical +interpretation of the theory. That freedom precludes certain otherwise natural sorts of +background spacetimes; it complicates identification of the theory's observables, since they +must be gauge invariant; and it is now recognized as presenting special problems for the +project of quantizing of gravitation. +...That We Need not Choose Between +It would seem unavoidable that we can choose at most one of these two views: the +vacuity of a requirement of general covariance or the central importance of general +covariance as a gauge freedom of general relativity. I will urge here that this is not so; we +may choose both, once we recognize the differing contexts in which they arise. Kretschmann's +claim of vacuity arises when we have some body of physical fact to represent and we are +given free reign in devising the formalism that will capture it. He urges, correctly I believe, +that we will always succeed in finding a generally covariant formulation. Now take a +different context. The theory—general relativity—is fixed both in its formalism and physical + + + 3 +interpretation. Each formal property of the theory will have some meaning. That holds for its +general covariance which turns out to express an important gauge freedom. +To Come +In Section 4 I will lay out this reconciliation in greater detail. As preparation, in +Sections 2 and 3, I will briefly review the two viewpoints. Finally in Section 5 I will relate the +reconciliation to the fertile "gauge principle" used in recent particle physics. An Appendix +discusses the difficulty of making good on Kretschmann's claim that generally covariant +reformulations are possible for any spacetime theory. +2. Einstein and Kretschmann's Objection +Einstein... +In November 1915 an exhausted and exhilarated Einstein presented the +gravitational field equations of his general theory of relativity to the Prussian Academy of +Science. These equations were generally covariant; they retained their form under arbitrary +transformation of the spacetime coordinate system. This event marked the end of a seven +year quest, with the final three years of greatest intensity, as Einstein struggled to see that a +generally covariant theory was physically admissible. 2 +Einstein had several bases for general covariance. He believed that the general +covariance of his theory embodied an extension of the principle of relativity to acceleration. +This conclusion seemed automatic to Einstein, just as the Lorentz covariance of his 1905 +formulation of special relativity expressed its satisfaction of the principle of relativity of +2 Over the last two decades there has been extensive historical work on this episode. Earlier +works include Stachel (1980) and Norton (1984); the definitive work will be Renn et al. (in +preparation). + + + 4 +inertial motion. 3 He also advanced what we now call the "point-coincidence" argument. The +physical content of a theory is exhausted by a catalog of coincidences, such as the coincidence +of a pointer with a scale, or, if the world consisted of nothing but particles in motion, the +meetings of their worldlines. These coincidences are preserved under arbitrary coordinate +transformations; all we do in the transformations is relabel the spacetime coordinates +assigned to each coincidence. Therefore a physical theory should be generally covariant. Any +less covariance restricts our freedom to relabel the spacetime coordinates of the coincidences +and that restriction can be based in no physical fact. +...and Kretschmann +Shortly after, Erich Kretschmann (1917) announced that Einstein had profoundly +mistaken the character of his achievement. In demanding general covariance, Kretschmann +asserted, Einstein had placed no constraint on the physical content of his theory. He had +merely challenged his mathematical ingenuity. For, Kretschmann urged, any spacetime +theory could be given a generally covariant formulation as long as we are prepared to put +sufficient energy into the task of reformulating it. In arriving at general relativity, Einstein +had used the "absolute differential calculus" of Ricci and Levi-Civita (now called "tensor +calculus.") Kretschmann pointed to this calculus as a tool that made the task of finding +generally covariant formulations of theories tractable. 4 +Kretschmann's argument was slightly more subtle than the above remarks. +Kretschmann actually embraced Einstein's point-coincidence argument and turned it to his +own ends. In his objection, he agreed that the physical content of spacetime theories is +3 The analogy proved difficult to sustain and has been the subject of extensive debate. See +Norton (1993). +4 For further discussion of Kretschmann's objection, Einstein's response and of the still active +debate that follows, see Norton (1993) and Rynasiewicz (1999) + + + 5 +exhausted by the catalog of spacetime coincidences; this is no peculiarity of general +relativity. For this very reason all spacetime theories can be given generally covariant +formulations. 5 +Kretschmann's objection doe s seem sustainable. For example, using Ricci and Levi +Civita's methods it is quite easy to give special relativity a generally covariant formulation. +In its standard Lorentz covariant formulation, using the standard spacetime coordinates (t, +x, y, z), special relativity is the theory of a Minkowski spacetime whose geometry is given by +the invariant line element +ds2 = c 2dt2 - dx2 -dy2 - dz2 (1) +Free fall trajectories (and other "straights" of the geometry) are given by +d2x/dt2 = d2y/dt2 = d2z/dt2 = 0 (2) +We introduce arbitrary spacetime coordinates x i, for i = 0,...,3 and the invariant line element +becomes +ds2 = gik dxi dxk (3a) +where the matrix of coefficients g ik is subject to a field equation +Riklm = 0 (3a) +with Riklm the Riemann-Christoffel curvature tensor. The free falls are now governed by +d2xi/ds2 + {kim} dxk/ds dxm/ds = 0 (4) +where {kim} are the Christoffel symbols of the second kind. +5 Rhetorically, Kretschmann's argument was brilliant. To deny it, Einstein may need to deny +his own point-coincidence argument. However a persistent ambiguity remains in Einstein's +original argument. Just what is a point-coincidence? Einstein gives no general definition. He +gives only a list of illustrations and many pitfalls await those who want to make the +argument more precise. For example, see Howard (1999). + + + 6 +Examples such as this suggest that Kretschmann was right to urge that generally +covariant reformulations are possible for all spacetime theories. While the suggestion is +plausible it is certainly not proven by the examples and any final decision must await +clarification of some ambiguities. See Appendix 1: Is a Generally Covariant Reformulation +Always Possible? for further discussion. +3. The Gauge Freedom of General Relativity +Active General Covariance +Einstein spoke of general covariance as the invariance of form of a theory's equations +when the spacetime coordinates are transformed. It is usually coupled with a so-called +"passive" reading of general covariance: if we have some system of fields, we can change our +spacetime coordinate system as we please and the new descriptions of the fields in the new +coordinate systems will still solve the theory's equations. Einstein's form invariance of the +theory's equations also licenses a second version, the so-called "active" general covariance. It +involves no transformation of the spacetime coordinate system. Rather active general +covariance licenses the generation of many new solutions of the equations of the theory in the +same coordinate system once one solution has been given. +For example, assume the equations of some generally covariant theory admit a scalar +field φ(xi) as a solution. Then general covariance allows us to generate arbitrarily many more +solutions by, metaphorically speaking, spreading the scalar field differently over the +spacetime manifold of events. We need a smooth mapping on the events—a +diffeomorphism—to effect the redistribution. For example, assume we have such a map that +sends the event at coordinate x i to the event at coordinate x' i in the same coordinate system. +Such a map might be a uniform doubling, so that x i is mapped to x' i = 2. xi. To define the +redistributed field φ', we assign to the event at x' i the value of the original field φ at the event + + + 7 +with coordinate x i.6 If the field is not a scalar field, the transformation rule is slightly more +complicated. For further details of the scalar case, see Appendix 2: From Passive to Active +Covariance. +Why it is a Gauge Freedom +The fields φ(xi) and φ'(xi) are mathematically distinct. But do they represent +physically distinct fields? The standard view is to assume that they do not, so that they are +related by a gauge transformation, that is, one that relates mathematically distinct +representations of the same physical reality. That this is so cannot be decided purely by the +mathematics. It is a matter of physics and must be settled by physical argumentation. +A vivid way to lay out the physical arguments is through Einstein's "hole +argument."7 The transformation on the manifold of events can be set up so that it is the +identity everywhere outside some nominated neighborhood of spacetime ("the hole") and +comes smoothly to differ within. We now use the transformation to duplicate +diffeomorphically all the fields of some generally covariant theory. Do the new fields +represent the same physical reality as the old? It would be very odd if they did not. Both +systems of fields agree completely in all invariants; they are just spread differently on the +manifold. Since observables are given by invariants, they agree in everything observable. +Moreover, the two systems of field will agree everywhere outside the hole, but they differ +only within. This means that, in a generally covariant theory, fixing all fields outside this +neighbor fails to fix the fields within. This is a violation of determinism. In short, if we +assume the two systems of fields differ in some physical way we must insist upon a difference +6 To visualize this redistribution in the two dimensional case, imagine that the original field +is represented by numbers written on a flat rubber membrane. If we now uniformly stretch +the rubber membrane so it doubles in size, we have the new field. +7 See Earman and Norton (1987), Norton (1999). + + + 8 +that transcends both observation and the determining power of the theory. The ready +solution is that these differences are purely ones of mathematical representation and that +the two systems of fields represent the same physical reality. +Its Physical Consequences +Accepting that this gauge freedom has important consequences for the physical +interpretation of a theory such as general relativity. 8 The theory is developed by positing a +manifold of spacetime events which is then endowed with metric properties by means of a +metric tensor field g ik. The natural default is to take the manifold of events as supplying +some kind of independent background spacetime in which physical processes can unfold. The +gauge freedom makes it very difficult to retain this view. For, when we apply a +diffeomorphism to the field and spread the metrical properties differently over events, the +transformation is purely gauge and we end up changing nothing physical. So now the same +events are endowed with different properties, yet nothing physical has changed. The simplest +and perhaps only way to make sense of this is to give up the idea of an independent existence +of the events of the manifold. In so far as we can associate an event of the manifold with real +events in the world, that association must change in concert with our redistribution of the +metrical field over the manifold. +Our notion of what is observable is affected by similar considerations. What is +observable is a subset of the physically real and that in turn is expressed by the invariants of +a theory. Might an observable result consist of the assertion that an invariant of some field +has such and such a value at some event of the manifold? No. The invariance must also +include invariance under the gauge transformation and the assertion would fail to be +invariant under the gauge transformation. In redistributing the fields, the transformation +8 For further discussion of these and related issues and their import for the quantization of +gravity see Rovelli (1997). + + + 9 +might relocate that invariant with that value at quite another event of the manifold. If some +result is eradicated by a gauge transformation, it cannot have been a result expressing +physical fact since the gauge transformation alters nothing physical. We must resort to more +refined ways of representing observables. For example, they may be expressed by an +assertion that two invariants are equal. The event at which the equality resided may vary +under gauge transformation; but the transformation will preserve the equality asserted. +4. Reconciliation +The Context in which Kretschmann's Objection Succeeds +Kretschmann's objection s ucceeds because he allows us every freedom in +reformulating and reinterpreting terms within a theory. Thus we easily transformed special +relativity from its Lorentz covariant formulation (1), (2) to a generally covariant formulation +(3a), (3b), (4). In doing so, we introduced new variables not originally present. The are the +coefficients of the metric tensor g ik and the Christoffel symbols { kim}. +With this amount of freedom, it is plausible that we can arrive at formulations of any +theory that have any designated formal property. 9 Imagine, for example, that we wanted a +9 I am distinguishing the formalism of the theory (and its formal properties) from its +interpretation. The formalism of a theory would be the actual words used, if the theory +consisted of an English language description, independently of their meanings. Formal +properties would include such things as the choice of English and the number of words. More +commonly physical theories use mathematical structures in place of words. These structures +can be considered quite independently of what we take them to represent in the world. The +properties we then consider are the purely formal properties. A real valued field on some +manifold is just a mathematical structure until we specify what it may represent in the +world. That specification is the job of the interpretation. See next footnote. + + + 10 +formulation of Newtonian particle mechanics in which the string of symbols " E=mc2" +appears. (This is a purely formal property since we place no conditions on what the string +might mean.) Here is one way we can generate it. We take the usual expression for the +kinetic energy K of a particle of mass m moving at velocity v, K=(1/2) mv2. We introduce a +new quantity E, defined by E = 2K, and also a new label "c" for velocity v, so that c=v. Once +we substitute these new variables into the expression for kinetic energy, our reformulated +theory contains the string " E=mc2". +The physical vacuity arises because we are demanding the formal property of general +covariance (or some other formal property) without placing further restrictions that would +preclude it always being achievable. The vacuity would persist even if we demanded a fixed +physical content; we must simply be careful not to alter our initial physical content as we +adjust its formal clothing. In the case of the discovery of general relativity, Einstein did not +keep the physical content fixed. It became fully fixed only after he found a generally +covariant formulation that satisfied a number of restrictive physical limitation. +The Context in Which the Diffeomorphism Gauge Freedom has Physical Content +Matters are quite different if we fix the formalism of the theory and its +interpretation. So we might be given general relativity in its standard interpretation. 10 If a +theory has any content at all, we must be able to ascribe some physical meaning to its +assertions. A fortiori there must some physical meaning in the general covariance of general +10 By "interpretation" I just mean the rules that tell us how to connect the various terms or +mathematical structures of the theory with things in the physical world. These rules can +vary from formulation to formulations and theory to theory. So, in ordinary formulations of +special relativity, "c" refers to the speed of light. In thermodynamics "c" would refer to +specific heat. + + + 11 +relativity. It may be trivial or it may not. 11 Consulting the theory, as we did in Section 2 +above reveals that the content is not trivial. +Things are just the same in our toy example of forcing the string " E=mc2" into a +formulation of Newtonian particle mechanics. Let us fix the formulation to be the doctored +one above. We had forced the string " E=mc2" into it. But now that we have done it, the string +uses symbols that have a meaning and, when we decode what it says about them, we +discover that the string expresses something physical, the original statement that kinetic +energy is half mass x (velocity) 2. Mimicking Kretschmann, we would insist that, given +Newtonian particle mechanics or any other theory, some reformulation with the string is +assuredly possible; so the demand for it places no restriction on the physically possible. But, +once we have the reformulation, that string will express something. +The analogous circumstance arises in the generally covariant reformulation of special +relativity. The existence of the reformulation is assured. Once we have it, its general +covariance does express something. In this case, it is a gauge freedom of the geometric +structure just like that of general relativity. The Lorentz covariant formulation of (1) and (2) +admits preferred coordinate systems. In effect, some of the physical content of the theory is +encoded in them. They specify, for example, which are the inertial motions; a body moves +inertially only if there is a coordinate system in which its spatial coordinates do not change +with the time coordinate. In the transition to the generally covariant formulation, this +11 Indeed the assertion may prove to be a logical truth, that is, it would be true by the +definition of the terms it invokes or it may amount to the definition of term.While their truth +is assured, such assertions need not be trivial. For example in a formulation of special +relativity we may assert that that coefficients of the metric tensor are linear functions of the +coordinates. This turns out to place no physical restriction on the theory; it merely restricts +us to particular coordinate systems. It is what is known as a coordinate condition that +defines the restricted class of coordinate systems in which the formulation holds. + + + 12 +content is stripped out of the coordinate systems. We can no longer use constancy of spatial +coordinates to discern which points move inertially. This content is relocated in the +Christoffel symbols, which, via equation (4) determine whether a particular motion is +inertial. The general covariance of (3a), (3b) and (4) leave a gauge freedom in how the metric +gik and the Christoffel symbols { kim} may be spread over some coordinate system. In one +coordinate system, they may be spread in many mathematically distinct but physically +equivalent ways. +To summarize +There is no restriction on physical content in saying that there exists a formulation of the +theory that has some formal property (general covariance, the presence of the string of +symbols " E=mc2", etc.) But once we fix a particular formulation and interpretation, that very +same formal property will express something physical, although there is no assurance that it +will be something interesting. +5. Gauge Theories in Particle Physics +This summary generates a new puzzle. One of the most fertile strategies in recent +decades in particle physics has been to extend the gauge symmetries of non-interacting +particles and thereby infer to new gauge fields that mediate the interaction between the +particles. Most simply, the electromagnetic field can be generated as the gauge field that +mediates interactions of electrons. This power has earned the strategy the label of the "gauge +principle." How can this strategy succeed if Kretschmann is right and there is no physical +content in our being able to arrive at a reformulation of expanded covariance? In the particle +context, this corresponds to a reformulation of expanded gauge freedom. So why doesn't +Kretschmann's objection also tell us that the strategy of the gauge principle is physically +vacuous? + + + 13 +The solution lies in the essential antecedent condition of Kretschmann's objection. +The physical vacuity arises since there are no restrictions placed how we might reformulate a +theory in seeking generally covariance. It has long been recognized that the assured +achievement of general covariance can be blocked by some sort of additional restriction on +how the reformulation may be achieved. Many additional conditions have been suggested, +including demands for simplicity and restrictions on which extra variables may introduced. +(For a survey, see Norton, 1993, Section 5; Norton, 1995, Section 4.) The analogous solution +is what gives the gauge principle its content. In generating gauge fields, we are most +definitely not at liberty to expand the gauge freedom of some non-interacting particle field in +any way we please. There is a quite precise recipe that must be followed: we must promote a +global symmetry of the original particle field to a local symmetry, using the exemplar of the +electron and the Maxwell field, and the new field arises from the connection introduced to +preserve gauge equivalence. 12 +There is considerably more that should be said about the details of the recipe and the +way in which new physical content arises. The recipe is standardly presented as merely +expanding the gauge freedom of the non-interacting particles, which should mean that the +realm of physical possibility is unaltered; we merely have more gauge equivalent +representations of the same physical situations. So how can physically new particle fields +12 The transition from special relativity in (1) and (2) to the generally covariant formulation +(3a), (3b) and (4) can be extended by one step. We replace the flatness condition (3a) by a +weaker condition, a natural relaxation, R ik = glmRilmk = 0. The result is general relativity in +the source free case. Arbitrary, source free gravitational fields now appear in the generalized +connection { kim}. We have what amounts to the earliest example of the use of the gauge +recipe to generate new fields. The analogy to more traditional examples in particle physics is +obvious. + + + 14 +emerge? This question is currently under detailed and profitable scrutiny. See Martin (2000), +(manuscript) and contributions to this volume. +Appendix 1: Is a Generally Covariant Reformulation Always +Possible? +As Earman (manuscript, Section 3) has pointed out, it is not entirely clear whether a +generally covariant reformation is always possible for any spacetime theory. The problem lies +in ambiguities in the question. Just what counts as "any" spacetime theory? Just what are +we expecting from a generally covariant reformulation? Let me rehearse some of the +difficulties and suggest that for most reasonable answers to these questions generally +covariant reformulation will be possible though not necessarily pretty. +The Substitution Trick... +Let us imagine that we are given a spacetime theory in a formulation of restricted +covariance. It is given in just one spacetime coordinate systems X i. Let us imagine that the +laws of the theory happen to be given by n equations in the 2n quantities A k, Bk +Ak(X i) = Bk(X i) (5) +where k = 1, ..., n and the A k and Bk are functions of the coordinates as indicated. Consider +an arbitrary coordinate system x i to which we transform by means of the transformation law +xi = xi(X m) (6) +We can replace the n equations (5) by equations that hold in the arbitrary coordinate system +by the simple expedient of inverting the transformation of (6) to recover the expression for +the X m as a function of the x i, that is X m = X m(xi). Substituting these expressions for X m into +(5), we recover a version of (5) that holds in the arbitrary coordinate system +Ak(X i(xm)) = Bk(X i(xm)) (5a) + + + 15 +We seemed to have achieved a generally covariant reformulation of (5) by the most direct +application of the intuition that coordinate systems are merely labels and we can relabel +spacetime events as we please. +...Yields Geometric Objects +While (5a) is generally covariant, we may not be happy with the form of the general +covariance achieved—one of the ambiguities mentioned above. We might, as Earman +(manuscript, Section 3) suggests, want to demand that (5a) be expressed in terms of +geometric object fields. The standard definition of a geometric object field is that it is an n +tuple valued field of components on the manifold, with one field for each coordinate system, +and that the transformation rule that associates the components of different coordinate +systems have the usual group properties. +While this definition may appear demanding, it turns out to be sufficiently +permissive to characterize each side of (5a) as a geometric object field. For example, in each +coordinate system x m, the geometric object field A has components A k(X i(xm)), which I now +write as Ak(xm). The transformation rule between the components is induced by the rule for +coordinate transformations. That is, under the transformation x m to yr(xm), Ak(xm) +transforms to A k(xm(yr)), where xm(yr) is the inverse of the coordinate transformation. With +this definition of the transformation law for A k, the components will inherit as much group +structure as the coordinate transformations themselves have; that is, it will be as much of a +geometric object field as we can demand. 13 For example, assume the transformations of +13 Why the hedged "as much group structure as the coordinate transformations themselves +have"? These general coordinate transformations may not have all the group properties if the +domains and ranges of the transformations do not match up well. Assume T 1 maps +coordinates x i on a neighborhood A to coordinates y i on a neighborhood B that is a proper +subset of A and T 2 maps coordinates y i on B to coordinates z i on A. Then the composition + + + 16 +coordinate systems z p to yr and yr to xm conform to transitivity. Then this same transitivity +will be inherited by A. We will have A k(xm(zp)) = A k(xm(yr(zp))) since the transitivity of the +coordinate transformation yields x m(zp) = xm(yr(zp)). +But areThey the Geometric Objects We Expect? +While the components A k turn out to be geometric object fields, they are probably not +the ones we expected. In brief, the reason is that the transformation rule induced by the +substitution trick does not allow any mixing of the components. That precludes it yielding +vectors or tensor or like structures; it turns everything into scalar fields. To see how odd this +is, take a very simple case. Imagine that we have special relativity restricted to just one +coordinate system X i. Our law might be the law governing the motion of a body of unit mass, +Fi = A i, where Fi is the four force and A i the four acceleration. Under a Lorentz +transformation +Y0 = γ(X 0 – vX 1) Y1 = γ(X 1 – vX 0) Y3 = X 3 Y4 = X 4 +with velocity v in the X 1 direction, c=1 and γ = (1-v2)-1/2.The usual Lorentz transformation for +the components A i of the four acceleration would be +A' 0 = γ(A 0 – vA1) A' 1 = γ(A 1 – vA0) A' 3 = A 3 A' 4 = A 4 (6) +Note that the transformed A' 0 and A' 1 are linear sums of terms in A 0 and A1. For this same +transformation, the substitution trick merely gives us +A' i = A i(X m(Yr)) (6a) +That is, A' 0 is a function of A 0 only and A' 1 is a function of A 1 only. +This oddity becomes a disaste r if we apply the substitution rule in a natural way. +Instead of starting with Ai in one fixed coordinate system X i, we might start will the full set +T2T1 cannot coincide with the direct transformation of x i to zi since the composition has lost +that part of the transformation outside B. + + + 17 +of all components of A i in all coordinate systems related by a Lorentz transformation to X i. If +we now try and make this bigger object generally covariant by the substitution trick, we will +end up with two incompatible transformation laws for the transformation X i to Yi when we +try to transform the components A i—the law (6) and law (6a). We no longer have a geometric +object field since we no longer have a unique transformation law for the components. +The escape from this last problem is to separate the two transformation groups. We +consider A i in coordinate system X i and A' i in coordinate system Y i separately and convert +them into distinct geometric object fields by the substitution trick. As geometric object fields +they have become, in effect, scalar fields. The Lorentz transformation then reappears as a +transformation between these geometric objects. +The Coordinates as Scalars Trick +If this is our final goal, then another general trick for generating generally covariant +reformulations could have gotten us there much faster. We return to A k(X i) of (5). We can +conceive the X i as scalar fields on the manifold—that is really all they are. 14 Scalar fields are +geometric object fields already. The A i are functions of X i, that is, functions of scalar fields. +Therefore they are also geometric objects. So we can conceive of the entire structure A k(X i) as +a geometric object field. We have gotten general covariance on the cheap. We cannot avoid a +cost elsewhere in the theory however. Our reformulation is overloaded with structure, one +geometric object field for each of what was originally a component. There is clearly far more +mathematical structure present than has physical significance. So the theory will need a +careful system for discerning just which parts of all this structure has physical significance. +14 Ask, what is the X 0 coordinate in coordinate system X i of some event p? The answer will be +the same number if we ask it from any other coordinate system y i as long as we are careful to +ask it of the original coordinate system X i. That is, each coordinate can be treated as a scalar +field. + + + 18 +Temptations Resisted +These devices for inducing general covarianc e are clumsy but they do fall within the +few rules discussed. We might be tempted to demand that we only admit generally covariant +formulations if their various parts fall together into nice compact geometric objects. But what +basis do we have for demanding this? Are we to preclude the possibility that the theory we +started with is just a complicated mess that can only admit an even more complicated mess +when given generally covariant reformulations. (Newtonian theory has been accused of this!) +And if we are to demand only nice and elegant reformulations, just how do we define "nice +and elegant"? +My conclusion is that generally covariant reformulations are possible under the few +rules discussed and that efforts to impose further rules to block the more clumsy ones will +cause more trouble than they are worth elsewhere. +Appendix 2: From Passive to Active Covariance +As above, assume the equations of some generally covariant theory admit a scalar +field φ(xi) as a solution. We can transform to a new coordinate system by merely relabeling +the events of spacetime; x i is relabeled x' i, where the x'i are smooth functions of the x i. The +field φ(xi) transforms to field φ'(x'i) by the simple rule φ'(x'i) = φ(xi). Since the equations of the +theory hold in the new coordinate system, the new field φ'(x'i) will still be a solution. The two +fields φ(xi) and φ'(x'i) are just representations of the same physical field in different +spacetime coordinate systems. +This is the passive view of general covariance. It can be readily t ransmogrified into +an active view, a transition that Einstein had already undertaken with his 1914 statements +of the "hole argument". What makes φ'(x'i) a solution of the theory under discussion is +nothing special about the coordinate system x' i. It is merely the particular function that φ' +happens to be. It is a function that happens to satisfy the equations of the theory. We could + + + 19 +take that very same function and use it in the original coordinate system, x i. That is, we +could form a new field φ'(xi). Since this new field uses the very same function, it retains every +property except the mention of the primed coordinate system x' i. Thus it is also a solution of +the equations of the theory. +In short, the passive general covariance of the theory has delivered us two fields, +φ(xi) and φ'(xi). They are not merely two representations of the same field in different +coordinate systems. They are defined in the same coordinate system and are mathematically +distinct fields, in so far as their values at given events will (in general) be different. Active +general covariance allows the generation of the field φ'(xi) from φ(xi) by the transformation xi +to x'i. +References +Earman, John (manuscript) "Once More General Covariance." +Earman, John and Norton, John D. (1987): "What Price Spacetime Substantivalism? The +Hole Argument," British Journal for the Philosophy of Science. 38, pp. 515-25. +Howard, Don (1999) "Point Coincidences and Pointer Coincidences: Einstein on the Invariant +Content of Space-Time Theories," in H. Goenner, J. Renn, J. Ritter, T. Sauer (eds.) +The Expanding Worlds of General Relativity (Einstein Studies volume 7) pp. 463 +500. +Kretschmann, Erich (1917): "Über den physikalischen Sinn der Relativitätspostulat, A +Einsteins neue und seine ursprünglische Relativitätstheorie," Annalen der Physik, +53, 575-614. +Martin, Christopher (2000) "The Gauge Argument," Talk at the Philosophy of Science +Association Biennial Meeting, Vancouver, 2-5, November, 2000. +Martin, Christopher (manuscript) Dissertation, Department of History and Philosophy of +Science, University of Pittsburgh. + + + 20 +Norton, John D. (1984) "How Einstein found his Field Equations: 1912-1915," Historical +Studies in the Physical Sciences, 14, 253-316; reprinted in Don Howard and John +Stachel (eds.) Einstein and the History of General Relativity: Einstein Studies, Vol. +1 Boston: Birkhäuser, 1989, pp.101-159. +Norton, John D. (1993), "General Covariance and the Foundations of General Relativity: +Eight Decades of Dispute," Reports on Progress in Physics, 56, pp. 791-858. +Norton, John D. (1995) "Did Einstein Stumble? the Debate Over General Covariance," +Erkenntnis 42, pp. 223-45. +Norton, John D. (1999) "The Hole Argument," Stanford Encyclopedia of Philosophy +http://plato.stanford.edu/entries/spacetime-holearg/ +Renn, Jürgen; Sauer, Tilman; Janssen, Michel; Norton, John D. and Stachel John (in +preparation) General Relativity in the Making; Einstein's Zurich Notebook. +Rovelli, Carlo (1997) "Halfway through the Woods: Contemporary Research on Space and +Time," pp. 180-223 in J. Earman and J. D. Norton (eds.) The Cosmos of Science: +Essays of Exploration. Pittsburgh: University of Pittsburgh Press. +Rynasiewicz, Robert (1999) "Kretschmann's Analysis of General Covariance and Relativity +Principles," in H. Goenner, J. Renn, J. Ritter, T. Sauer (eds.) The Expanding +Worlds of General Relativity (Einstein Studies volume 7) pp. 431-462. +Stachel, John (1980): "Einstein's Search for General Covariance," paper read at the Ninth +International Conference on General Relativity and Gravitation, Jena; printed in +Don Howard and John Stachel (eds.) Einstein and the History of General Relativity: +Einstein Studies, Vol. 1 (Boston: Birkhäuser, 1989) pp.63-100. \ No newline at end of file diff --git a/storage/J93DU5HH/Norton - 2003 - General covariance, gauge theories and the Kretschmann objection.pdf b/storage/J93DU5HH/Norton - 2003 - General covariance, gauge theories and the Kretschmann objection.pdf new file mode 100644 index 0000000..d1c73e5 Binary files /dev/null and b/storage/J93DU5HH/Norton - 2003 - General covariance, gauge theories and the Kretschmann objection.pdf differ diff --git a/storage/JCISVT2H/.zotero-ft-cache b/storage/JCISVT2H/.zotero-ft-cache new file mode 100644 index 0000000..8ce5b54 --- /dev/null +++ b/storage/JCISVT2H/.zotero-ft-cache @@ -0,0 +1,1001 @@ +CORRESPONDING AUTHOR: +John D. Norton +Department of History and Philosophy of Science, University of Pittsburgh, US +jdnorton@pitt.edu +TO CITE THIS ARTICLE: Norton, John D. 2024. "Einstein Against Singularities: Analysis versus Geometry." Philosophy of Physics 2(1): 13, 1–73. DOI: https://doi.org/10.31389/ pop.91 +Einstein Against Singularities: Analysis versus Geometry +JOHN D. NORTON +ABSTRACT +Einstein identified singularities in spacetimes, such as at the Schwarzschild radius, where later relativists only find a coordinate system assigning multiple values to a single spacetime event. These differing judgments derive from differences in mathematical methods. Later relativists employ geometrical structures to correct anomalies in the coordinate systems used in analytic expressions. Einstein took the analytic expressions to be primary and the geometrical structures as mere heuristics that could be overruled if physical assumptions required it. Einstein’s non-geometric methods had a firm base in the history of mathematical methods. They continued the non-geometric orientation of Christoffel, Ricci and LeviCivita. Einstein’s insistence that singularities must be eliminated marked a departure from earlier tolerance of singularities. It was founded upon his longterm project of eliminating arbitrariness from fundamental physical theories. However, Einstein was willing to theorize with singularities only temporarily if they were the least arbitrary approach then available. +RESEARCH + + + COREOPS 2 Philosophy of Physics DOI: 10.31389/pop.91 +1. INTRODUCTION +Einstein’s treatment of spacetime singularities in his general theory of relativity has presented significant challenges to later commentators. His work elicits both admiration and exasperation. The work is admired for creating a new realm of physical theory within which a century’s work on gravity and cosmology would unfold. It is exasperating for its treating of singularities in ways that later relativists judge to be novice errors. It is all the more exasperating since this treatment persisted even after the problems were pointed out to Einstein. John Earman and Jean Eisenstaedt’s (1999) survey give the most thorough recounting and appraisal of Einstein’s work on singularities. They summarize the tensions as: +... Einstein was forced to fight a number of skirmishes with singularities, and more often than not he lost. The losses exhibit a strange asymmetry: he was unreasonably disturbed by (what today we would classify as) apparent singularities to the extent that he was prevented from embracing some of the most revolutionary consequences of his theory; but on the other hand he was not at all concerned about (what today we would call) real singularities, and as a result he pursued for over twenty years an ill-founded research programme on the problem of motion (186). +Their puzzlement persists throughout their narrative: +...his 1935 paper with Rosen may strike the modern reader as bizarre and nearly incomprehensible (230). +It was not just Einstein. Even David Hilbert, under Einstein’s sway, was apparently unable to discern when singularities are merely artefacts of a singular coordinate transformation: +How Hilbert, one of the great mathematical minds of the century, could have failed to appreciate this elementary point defies rational explanation (193). +Klaas Landsman, in his survey of the foundations of general relativity, echoes their concern: +Even Hilbert and Einstein were initially confused about the meaning of these apparent or real singularities, but today it is clear that rr r rrr [Schwarzschild radius] and rr r rr [mass horizon] are just singularities of the coordinate systems in which the Schwarzschild and de Sitter solution are expressed (2021, 125). +This paper will seek to show that Einstein’s treatment of spacetime singularities conformed with a consistent program of research. It may now appear willfully capricious, but only because the presumptions of Einstein’s program are no longer ours. His analysis was not an instance of baffling mathematical incompetence. Rather, it employed mathematical methods different from those we now use and that now appear opaque to us. They were, in turn, guided by physical assumptions that were, in their time, cogent but are now discarded, often for solid empirical reasons. The ultimate failure was not a consequence of arbitrary opportunism, but the reverse: a dogged adherence to methods and assumptions that failed. +For concreteness, this paper will focus on two apparent anomalies in Einstein’s treatments of spacetime singularities: +1. Einstein’s Apparent Misidentification of Mere Coordinate Singularities. The Wedge. +If a coordinate system is poorly adapted to the spacetime geometry, quantities expressed as functions of the coordinates may become singular. They are not true pathologies of the spacetime geometry but merely artefacts of a coordinate + + + COREOPS 3 Philosophy of Physics DOI: 10.31389/pop.91 +system that has “gone bad” and can be remedied by adopting a new coordinate system. Three prominent cases in Einstein’s work are his identification of singularities in a uniformly accelerated coordinate system in a Minkowski spacetime; at the “rr r rrr” Schwarzschild radius of a Schwarzschild spacetime; and what was then called the “mass horizon” in a de Sitter spacetime. They all have the same form: Coordinate systems fail since they assign multiple coordinate values to the same event in a construction that appears as a wedgelike formation in a spacetime diagram. +2. Einstein’s Vacillations Over the Formal Admissibility of Spacetime Singularities. +At times, Einstein portrayed spacetime singularities in calamitous terms. He wrote (Einstein and Rosen, 1935, 73) “For a singularity brings so much arbitrariness into the theory that it actually nullifies its laws.” He was even willing to modify his celebrated gravitational field equations to eliminate them or to argue that physical processes prohibit their formation. Yet, on other occasions he entertained field singularities as models for light quanta; as essential to understanding de Sitter’s solution to his λλ-augmented gravitational field equations; and as a means to derive the equations of motion of a free particle from his gravitational field equations. +Einstein (1949, 684) famously described himself as a “type of unscrupulous opportunist” when compared to the systematic epistemologist. The temptation is to extend the description to his program in physics. The goal of this paper is to argue otherwise. There is, it will be argued, a deeper coherence underlying these apparent anomalies. It derives from two elements in Einstein’s thinking. One is methodological. The other is an enduring and controlling heuristic within his worldview. +1. Einstein privileged analytic expressions over synthetic geometry. +It has long been recognized that Einstein was not a geometrical thinker, after the modern manner.1 His privileging of analytic expressions was not a personal aberration. There were, in Einstein’s time, two distinct mathematical traditions, which will be described in Section 6 below. One was a synthetic, geometrical tradition emerging from Gauss and Riemann’s theory of curved surfaces. The other was analytic and derived from Christoffel and Riemann’s work on the invariants of quadratic differential forms. In formulating his general theory of relativity Einstein aligned with the second, analytic tradition. +While both these traditions contributed to the mathematics of Einstein’s general theory of relativity, they differ in which are the primary objects of study. +• For synthetic geometry in the tradition of Gauss, the primary object of study is the geometric surface or space. Quadratic differential forms are a means of describing their properties. • For the methods in the analytic tradition of Christoffel, the primary objects of study are mathematical expressions or formulae, that is, quadratic differential forms defined over variables and their transforms. +That quadratic differential forms could be used in geometry was an incidental application of the analytic methods. It was a fact to be acknowledged but not allowed to control the method. +1 See, for example, Norton (1993, §2), Reich (1994, 210). + + + COREOPS 4 Philosophy of Physics DOI: 10.31389/pop.91 +These differences were generally unimportant in Einstein’s work on general relativity. The pertinent exception came when spacetime singularities arose from a misbehaving coordinate system. The synthetic, geometry tradition can escape them. The analytic tradition struggles with them. For each “wedge” example above, the pathology in the coordinate system is that, geometrically understood, it assigns multiple values to a single event. The new, regular coordinate system must assign a single value to each single event. That means that the new coordinate system cannot be generated from the pathological coordinate system by a one-to-one mapping. This presents no difficulty of principle for the synthetic, geometric tradition. The intrinsic geometry of the space guides construction of the new coordinate system. It does not need and cannot use a one-to-one mapping from the old coordinate systems. +That a one-to-one mapping cannot be used is, however, troublesome for the analytic approach within which Einstein worked. Its basic objects of study are analytic expressions and their one-to-one, differentiable transformations. Once an expression has a “wedge” type singularity in one set of variables, none of the admissible transformations can eradicate it. The analytic expressions are irreparably singular. The difficulty can be escaped in this analytic tradition only by weakening this basic conception of the primary objects of study. Einstein was, on occasion, willing to make the compromise. We shall see that, in a natural concession to the geometry, he allowed that the irregularities at the origin of polar coordinate systems are not pathological. However, absent the motivation of an underlying intrinsic geometry, he clearly felt no compulsion to make this same concession in other cases. Of course, the geometric picture has heuristic value. What would decide whether it was to be used was Einstein’s non-geometric, physical interpretation of his equations. Prominent amongst these was an expectation that the analytic expressions are static in their time coordinate. These physical interpretations fitted better, we shall see, with the singularities. +It is surely surprising to modern relativists that Einstein would forgo the geometric picture that now proves so fertile. Here Dennis Lehmkuhl’s (2014) study provides an essential recalibration. It documents how Einstein was dismissive and even scornful of the now familiar idea that general relativity had “geometrized” gravity. In correspondence in 1926, he even disparaged geometrical conceptions as an Eselsbrücke [“donkey bridge”], that is, roughly speaking an artificial crutch, a convenience for novices. +We now turn to the second element in Einstein’s work. +2. Einstein used the elimination of arbitrariness as a guide in theory construction. +That we recover better theories by eliminating arbitrariness was an enduring heuristic that figured prominently in Einstein’s opposition to spacetime singularities. While the heuristic had played a part in much of Einstein’s earlier physical theorizing, its presence was easy to overlook, perhaps even by Einstein himself, since it found expression in many different forms, according to the physical problem addressed. It drove his search for the most general relativity of motion. Anything less required us to designate arbitrarily which is the ether state of rest or which are the inertial frames of reference. Indeterministic quantum mechanics introduced arbitrariness not present in deterministic theories. The ultimate physics, Einstein foretold, is one without any arbitrary constants. +We are now apprehensive of spacetime singularities, since they arise in extreme regimes where we expect our present theories to fail. Prior to Einstein’s deprecation of them, their + + + COREOPS 5 Philosophy of Physics DOI: 10.31389/pop.91 +presence in physical theories was generally untroubling and required only a brief mention in passing. Einstein, however, made their elimination a core requirement of his long-sought unified field theory. His aversion to singularities was unlike our modern apprehensions. Rather he likened singularities to boundary conditions in field theories. They are elements that can be chosen freely. It is a harmful freedom since it expands the set of solutions of a theory’s fundamental equations in a way that merely reflects our arbitrary choices. For this reason, in 1917, he rejected a cosmology that stipulates that special relativity obtains at spatial infinity. Admitting singularities, Einstein feared, allowed similar, unjustified freedoms in theorizing. +While finding a final theory without arbitrariness was Einstein’s ultimate goal, his day-today work sought to move towards this goal by reducing arbitrariness wherever feasible, even if it could not be eliminated completely. General relativity, as originally formulated, had two independent laws: the gravitational field equation for the configuration of the metric field; and the geodesic law for the motion of free bodies or, more generally, an independent matter theory. To derive the geodesic law from the source-free gravitational field equations would eliminate the arbitrariness of two independent laws in favor of the lesser arbitrariness of one law. Such a derivation seemed within Einstein’s reach if he represented particles as singularities in a source free field. It was a temporary expedient that replaced a greater by a lesser arbitrariness. +There are many more facets to Einstein’s engagement with spacetime singularities than can be covered here. This paper is limited to reporting just those fragments of the history that bear directly on the two elements described above. A fuller accounting of the history may be found in the existing literature, such as the synoptic account of Earman and Eisenstaedt (1999) and in the editorial notes to Einstein’s correspondence of 1917 and 1918 in Schulmann et al. (1998). Lehmkuhl (2017; 2019) provides an illuminating account of Einstein’s earlier treatments of the problem of motion. +The three sections of Part I below deal directly with the three cases of singularities identified by Einstein, the modern reaction to them, and an account of how Einstein’s views did not cohere with it. The related Appendix B defends with a simple example the viability of Einstein’s prioritizing of analytic expressions. Part II provides an historical perspective on Einstein’s mathematical methods. Sections 5 and 6 recount the mathematical tradition upon which Einstein drew. Section 7 recounts how this tradition was incorporated by Einstein and Grossmann into their early sketch of the general theory of relativity. Details of their novel use of the term “tensor” are in Appendix A. Section 8 reports how Einstein’s suppression of geometrical notions appeared in his theorizing in general relativity. Section 9 of Part III recounts the presence of singularities in the literature prior to Einstein. Section 10 then reviews how Einstein’s goal of eliminating arbitrariness from fundamental theories called for an elimination of singularities; and how his temporary use of singularities was a choice of the least arbitrary of the avenues available. +A final, concluding Section 11 summarizes the coherence of Einstein’s program, but notes that it has not proven productive. The alternative of giving priority to the geometry is the basis of modern advances in both black hole physics and cosmology. These advances show that Einstein’s program of research failed. It did not fail, however, because of elementary errors, but because Einstein, like the rest of us, cannot foresee what future research may bring. + + + COREOPS 6 Philosophy of Physics DOI: 10.31389/pop.91 +PART I: THREE SINGULARITIES +2. EINSTEIN’S SIMPLEST SPACETIME SINGULARITY +2.1 THE SINGULARITY +To grasp Einstein’s understanding of spacetime singularities, we can do no better than to recount the elementary example that Einstein himself used. It was developed in his collaborative work with Rosen (Einstein and Rosen 1935) specifically for the purpose of explaining his view of the role of singularities in his physical theories. The example starts with the familiar line element of special relativity: +dddd2 = −dddd12 − dddd22 − dddd32 + dddd42, (1) +where ξξ1, ξξ2, ξξ3 are the Cartesian coordinates for space and ξξ4 is the time coordinate, with cc c c. They introduce a uniformly accelerated coordinate system, adapted to the hyperbolic motion of uniform acceleration in the +ξξ1 direction, by the transformation: +ξξ1 = xx1cosh(ααxx4) ξξ2 = xx2 ξξ3 = xx3 ξξ4 = xx1sinh(ααxx4). (2) +Under this transformation, the line element (1) becomes: +dddd2 = −dddd12 − dddd22 − dddd32 + αα2dd12dddd24. (3) +Free bodies moving on geodesics have a non-zero coordinate acceleration in the -x1 direction. Recalling Einstein’s principle of equivalence, this acceleration is to be interpreted as due to a homogeneous gravitational field acting in the −xx1 direction. Here is Einstein and Rosen’s formulation of this interpretive principle: +... “Principle of Equivalence”: If in a space free from gravitation a reference system is uniformly accelerated, the reference system can be treated as being “at rest,” provided one interprets the condition of the space with respect to it as a homogeneous gravitational field (1935, 74). +Einstein and Rosen identify the hyperplane xx1 = 0 as “a singularity of the field” so that Einstein’s source free gravitational field equations, RRkkkk = 0, for RRkkkk the Ricci tensor, fail to be satisfied. This conclusion is justified by: +... the fact that the determinant of gg of the ggμμμμ vanishes for xx1 = 0. The contravariant ggμμμμ therefore become infinite and the tensors RRiikkkkkk and RRkkkk take on the form 0/0. From the standpoint of Eqs.[(3)] the hyperplane xx1 = 0 then represents a singularity of the field (1935, 74). +They then offer an interpretation of the significance of the singularity. Einstein’s original gravitational field equations, with stress-energy sources represented by the tensor TTiiii, is +RRiiii − (1/2)ggiiiiRR R −RRiiii. (4) +To apply this equation to the line element (3), they consider a modification of the line element: +dddd2 = −dddd12 − dddd22 − dddd32 + (αα2dd12 + σσσdddd24. +Applying the field equations (4), the stress-energy tensor2 can be computed and has nonzero terms they write as: +TT22 = TT23 = αα2/σσ/σσ σ αα2xx12/σσσ2. + + + COREOPS 7 Philosophy of Physics DOI: 10.31389/pop.91 +As σσ approaches zero, the original line element (3) is approached in the limit. In this limit, the non-zero terms of the stress-energy tensor exhibit a singularity at xx1 = 0. These terms diverge at xx1 = 0 but converge to zero for non-zero xx1.3 This divergence is interpreted as: +... the solution [(3)] contains a singularity which corresponds to an energy or mass concentrated in the surface xx1 = 0 (1935). +2.2 THE MODERN REACTION +It surely understates matters to say that modern readers find this analysis “astonishing,” to use Earman and Eisenstaedt’s (1999, 215) word. The entirety of the results Einstein and Rosen report is due to artifacts of the coordinate system introduced by the transformation (2). A mere change of coordinates introduces no singularities in the spacetime geometry. It remains everywhere flat with vanishing curvature and Ricci tensor. All this is made transparent by plotting the new coordinate system in a spacetime diagram, shown in Figure 1, where coordinates ξξ2 and ξξ3 have been suppressed: +The diagram shows that the accelerated coordinate system “goes bad” at xx1 = 0. That is, for fixed xx2 = ξξ2 and xx3 = ξξ3, the infinitely many events xx1 = 0, −∞ < xx4 < ∞ are mapped, many-to-one to the single event at ξξ1 = ξξ4 = 0. The singularity Einstein and Rosen report is due entirely to this pathology of the coordinate system. +The diagram also shows the worldlines of two geodesics, AAAA′ and BBBB′. Since their worldlines have vanishing four-acceleration, that invariant fact remains so even after the +2 It is designated parenthetically as “fictitious.” +3 The order of operations in the expression for TT22 as given by Einstein and Rosen is ambiguous. To recover the singularity claimed, the expression should be read as αα2/[σσσσ σ αα2xx12/σσσ2] = αα2/[σ√σσ σ αα2xx12/√σσσ2] +Figure 1 Einstein and Rosen’s accelerated coordinate system. + + + COREOPS 8 Philosophy of Physics DOI: 10.31389/pop.91 +we adopt a new coordinate system. The “falling” is an illusion arising as a coordinate effect. Another coordinate effect is that the falling point would require infinite xx4 coordinate time to complete its fall through all values of position xx1 > 0; and infinite xx4 coordinate time to rise through all values of position xx1 > 0. The coordinate surface xx1 = 0 seems to represent an unachievable horizon. It is a coordinate effect only, since both motions are completed in finite proper time. +2.3 WHY WE MUST TAKE EINSTEIN’S EXAMPLE SERIOUSLY +This modern appraisal now seems so natural and so at variance with Einstein and Rosen’s claims that is easy to suppose that Einstein and Rosen were poorly informed or simply hasty or both. Surely even a brief acquaintance with modern views would have elicited a retraction from them.4 This supposition must be resisted. There is ample evidence that the view presented was Einstein’s well-considered and enduring view. +To begin, the example was not hastily chosen. It is the basis of his formulation of the principle of equivalence, which was, for Einstein, one of the most enduring foundational elements of his general theory of relativity. It initiated his first steps towards the theory in 1907 and remained unaltered throughout all his writings.5 It was and remained at the core of Einstein’s understanding of his theory. +Next, Einstein and Rosen’s paper came two decades after the completion of Einstein’s theory and after the nature of singularities in his theory had been closely examined by the physics community. The sorts of considerations we now consider as modern had been developed and understood. They were communicated to Einstein by correspondents. We shall see below that no lesser figure than Felix Klein had pointed out to Einstein the pathology of his coordinate system in the case of the mass horizon of the de Sitter solution. The considerations had also appeared in the physics literature from the pen of a figure known personally to Einstein. We shall see again that Lemaitre had shown that the singularity Einstein and Rosen presumed in a Schwarzschild solution was, likewise, an artefact of a pathology in the coordinate system. We may infer that Einstein chose not to adopt this understanding, but the idea that he did not know of it in 1935 is unsustainable. +Further, the notion that a singularity is a surrogate for matter had already been explored seriously in the same way in the context of the de Sitter solution, to be discussed below. With Einstein’s assent and approval, Hermann Weyl had there sought to justify this interpretation of a singularity by the same artifice used by Einstein and Rosen in 1935. That is, he had sought to understand a singularity as the singular limit of a regular matter distribution. Einstein and Rosen’s artifice was not a hasty, ad hoc expedient, but an application of approach already present in the literature. Finally, the physics and geometry of the example is transparently simple. Einstein and Rosen acknowledged explicitly that their new coordinate system covers only the two wedges shown in Figure 1. They wrote +It is worth pointing out that this metric field [(1)] does not represent the whole of the Minkowski space but only a part of it ... only those points for which ξξ12 ≥ ξξ42 correspond to points for which [(1)] is the metric (1935, 74). +4 Even if one does not know that the line element (3) was produced by a coordinate transformation from a familiar Minkowskian line element, Wald (1984, 149–153) shows how efforts to geodesically extend the line element (3) would lead back to the full Minkowski line element (1). +5 For a survey, see Norton (1985). + + + COREOPS 9 Philosophy of Physics DOI: 10.31389/pop.91 +They clearly knew how their accelerated coordinate system is distributed over the Minkowski spacetime. They knew that the surfaces of constant xx4 intersect at ξξ1 = ξξ4 = 0. There, in those coordinates, the Riemann curvature tensor of the Minkowski spacetime vanishes. Einstein had emphasized that, if a tensor is a zero tensor in one coordinate system, it remains so for all. In his review article of 1916, written upon completion of the general theory, his synopsis of the “Mathematical Aids to the Formation of Generally Covariant Equations” included this fact as fundamental for the development of the laws of his theory: +The things hereafter called tensors are further characterized by the fact that the equations of the transformation for their components are linear and homogeneous. Accordingly, all the components in the new system vanish, if they all vanish in the original system. If, therefore, a law of nature is expressed by equating all the components of a tensor to zero, it is generally covariant (1916a, 121). +In short, there was no simple error in the illustrative example given by Einstein and Rosen. It was transparent, well-informed, and quite purposefully chosen. They meant what they said. +2.4 WHAT EINSTEIN MEANT: ANALYTIC EXPRESSIONS OVER GEOMETRY +The key to discerning what Einstein meant is that his methods were not those of modern treatments. There are two elements in the treatments: the geometry intrinsic to a spacetime, and the analytic expressions that can be used to describe that geometry. +The modern approach privileges the geometry over the analytic expressions. When there is a mismatch, the analytic expressions are to be corrected against the geometry. Einstein and Rosen’s accelerated coordinate system produces the line element (3) that fails adequately to represent the intrinsic geometry of the Minkowski spacetime at xx1 = 0. The geometry is upheld and the line element is regarded as defective at xx1 = 0. Its coordinates have “gone bad” there. +In Einstein’s approach, the analytic expression (3) itself is primary. The Minkowski spacetime played a heuristic role in its construction. Einstein can draw on its geometry to discern the properties of the analytic expression. The geometry is pertinent only in so far as it serves that purpose. When there is a mismatch, such as at xx1 = 0, there is no automatic presumption that the analytic expression is at fault. Which of the geometry or analytic expressions requires a correction is a matter to be decided by the intended physical interpretation. +The principle of equivalence provided that interpretation: The line element (3) is to be associated with a homogeneous gravitational field in which free bodies undergo accelerated fall. From this perspective, the singularity identified at xx1 = 0 proves to be congenial. Einstein and Rosen’s analysis interprets it as an energy or mass concentration. It would, presumably, serve as a natural source of the homogeneous field. That the singularity should be interpreted in this way fits with Einstein’s larger research agenda. As we shall see below, these sorts of singularities were routinely interpreted as proxies for the matter distributions that a successful unified field theory would put in their place. +This alternative is only sustainable as long as Einstein and Rosen do not treat their accelerated coordinates as pathological at xx1 = 0. Rather, for fixed coordinate values xx2 and xx3, they must treat as distinct events all those with xx1 = 0, but differing xx4. To collapse all + + + COREOPS 10 Philosophy of Physics DOI: 10.31389/pop.91 +these events to a single event so that the original geometry of the Minkowski spacetime is respected would render untenable the identification of energy or mass at xx1 = 0. +It is quite incongruous with Einstein’s mode of presentation to draw a spacetime diagram for this alternative interpretation. However, we can better picture Einstein and Rosen’s interpretation if we see how such a diagram, given in Figure 2, differs from the familiar one of Figure 1. +The figure shows the spacetime for xx1 ≥ 0, with the singularity at xx1 = 0 represented not by a point but a line with all possible xx4 coordinates. The geodesics ξξ1 = kk, for various constants kk, of Figure 1 are now represented by bell-like curves. It follows from the transformation equations (2) that their trajectories in xx1, xx4 coordinates are +xx1 = kkkcosh(ααxx4). +A small amount of algebra shows that for small xx4 times, each trajectory exhibits, in close approximation, the expected parabola of free fall: +xx1 = kkkk k kkkkkkkkxx4k2k. +For large xx4 times, positive and negative, the trajectory approaches asymptotically the horizon at xx1 = 0 that is unattainable in xx4 times. This effect is the origin of the gravitational red shift Einstein first inferred from the principle of equivalence in 1907. +Einstein and Rosen do not mention this horizon. However, since it will return explicitly in later examples, we should note that there is no elementary confusion here. It is transparent from the construction of the example that a freely falling body will traverse the wedge ξξ12 ≥ ξξ42 and leave it in finite proper time. It would be a complete novice folly to think +Figure 2 Einstein and Rosen’s homogeneous gravitational field. + + + COREOPS 11 Philosophy of Physics DOI: 10.31389/pop.91 +otherwise. The horizon exists in the different sense that it is the limit of events covered by the accelerated coordinate system xxii. Motions described by the line element (3) using these coordinates will never reach it. +Once the independence of the line element (3) from the Minkowski spacetime geometry is recognized, it is no longer puzzling that Einstein and Rosen report that tensors RRiikkkkkk and RRkkkk take on the singular form 0/0. For, they are not the tensors of the original line element (1), but of the new line element (3) that differs from (1) at xx1 = 0. That there is no one-toone mapping between the original xxii coordinates and the new xxii coordinates is essential for the difference. For otherwise, their vanishing in one coordinate system would necessitate their vanishing in the other. +How can Einstein interpret the line element (3) as associated with a homogeneous gravitational field when its spacetime curvature for all xx1 > 0 remains flat, just like the Minkowski spacetime? The question raises issues that cannot be fully addressed here. Briefly, once again it is a matter of how the equations are to be interpreted. +When this objection was put to him by Laue in correspondence of 1950, Einstein replied that +... what characterizes the existence of a gravitational field from the empirical standpoint is the non-vanishing of the [non-generally covariant coefficients of the connection] Γiillii, not the non-vanishing of the [Riemann curvature tensor] RRiiiiiiii.6 +Thus, the line element (1) with vanishing Γiillii, is interpreted as gravitation-free, whereas the line element (3) with non-vanishing Γiillii, harbors a gravitational field. +What is noticeable here and in all of Einstein’s writings on general relativity is that it is not geometrical in its expressions. Where the geometrical approach talks of a “Minkowski spacetime” and a “Schwarzschild spacetime,” Einstein’s analytic approach talks of “solutions” to equations, where the term designates analytic expressions such as (1) and (3). The term “solution” appears 40 times in the five pages of Einstein and Rosen’s paper. The term “space-time” and “space” each appear only once. +3. SINGULARITY AT THE SCHWARZSCHILD RADIUS +This last example serves Einstein’s and our purpose well. For, Einstein’s understanding of the more complicated examples is the same, but just harder to see because the physics is less transparent. We shall see this in two cases: the singularity in the Schwarzschild solution in this section; and the “mass singularity” in the de Sitter solution in the next section. +3.1 THE RADIUS AS A SINGULARITY +Einstein and Rosen (1935, 75) wrote the Schwarzschild solution in a form that Eisenstaedt (1989, 216) identified as using “Droste coordinates” after the version of the solution given in Droste (1916): +As is well known, Schwarzschild found the spherically symmetric static solution of the gravitational equations +dddd2 = − 1 +(1 − 2mm +rr ) dddd2 − dd2(dddd2 + sin2ddddθθ2) + (1 − 2mm +dd )dddd2 +(5) +6 See Norton (1985, §11) and Lehmkuhl (2022, §9.3.6) for details; and for further discussion, Section 8.2 below. + + + COREOPS 12 Philosophy of Physics DOI: 10.31389/pop.91 +(rr r rrr, θθ from 0 to ππ, φφ from 0 to 2ππ); ... The vanishing of the determinant of the ggμμμμ for θθ θ θ is unimportant, since the corresponding (spatial) direction is not preferred. On the other hand, gg11 for rr r rrr becomes infinite and hence we have there a singularity. +The character of the singularity is elaborated in Einstein’s later paper that argues against the physical possibility of gravitational collapse beyond the Schwarzschild radius. He employed an isotropic coordinate system to present the Schwarzschild solution: +If one considers Schwarzschild’s solution of the static gravitational field equations of spherical symmetry +(1) dddd2 = −(1 + μμ +2rr )4(dddd12 + dddd22 + dddd32) + ( 1 − μμ +2rr +1+ μμ +2rr +) +2 +dddd2 +it is noted that +gg44 = ( 1 − μμ +2rr +1+ μμ +2rr +) +2 +vanishes for rr r rrrr. This means that a clock kept at this place would go at the rate zero. Further it is easy to show that both light rays and material particles take an infinitely long time (measured in “coördinate time”) in order to reach the point rr r rrrr when originating from a point rr r rrrr. In this sense the sphere rr r rrrr constitutes a place where the field is singular. (μμ represents the gravitating mass.) (1939, 922). +These remarks from the 1930s reflect what had already become a standard view amongst physicists after the completion of Einstein’s theory in 1915 and Schwarzschild’s presentation of his solution. There is a singularity at the Schwarzschild radius “rr r rrr.” In his influential, two-part memo, “Foundations of Physics,” Hilbert (1917, 70) noted the irregularity in the solution. In his Teubner Encyklopädie article, Pauli (1921, 728) also mentioned it in passing; as did Laue (1921, 215) in his relativity textbook. +3.2 THE MODERN REACTION +This standard view did not persist. Lemaître (1933, 52, 82) showed how the singularity could be eradicated by a change of the coordinate system and was thus “fictive.”7 Almost three decades passed before the idea of eliminating the singularity by a mere coordinate transformation had attracted enough of a following to enter the mainstream. Finkelstein (1958), Szekeres (1959), and Kruskal (1960) showed how a single coordinate system could be found that covered the entire Schwarzschild solution such that there is no singularity at the Schwarzschild radius. +We can plot the Droste coordinates of Einstein’s Schwarzschild’s solution (5) in a diagram of the fully extended Schwarzschild spacetime based on Kruskal-Szekeres coordinates, as shown in Figure 3 below, with two angle coordinates suppressed. Kruskal (1960) replaced the tt and rr coordinates of (5) with coordinates vv and uu such that light propagates along the diagonals ddddddddd d dd. (The trajectories of light are represented by the cross-hatching with diagonal lines in Figure 3.) +7 For a recounting of Lemaître’s analysis, see Eisenstaedt (1993). + + + COREOPS 13 Philosophy of Physics DOI: 10.31389/pop.91 +The Droste coordinates cover a wedge in the figure and, as Einstein and Rosen recognized, a duplicate set of Droste coordinates cover a second wedge on the other side of the figure. There are further parts of the fully extended Schwarzschild solution not covered by these two Droste coordinate systems. They are the regions inside the Schwarzschild radius. They are bounded above and below by a future and a past curvature singularities at vv2 − uu2 = 1. +The modern reaction to Einstein and Rosen’s identification of a singularity at the Schwarzschild radius can be read directly from the figure. The Droste coordinates map many values of the coordinate tt to a single event at the apex of the wedges. There is no singularity at that event in the spacetime; there is only a pathology of the coordinate system. That the spacetime is regular at this radius is commonly affirmed by noting, as does Kruskal (1960, 1743), that “the curvature invariants of the Schwarzschild metric are perfectly finite and well behaved at [rr r rrr].” +There is a remarkable similarity to the accelerated coordinate system of Einstein and Rosen (1935) in a Minkowski spacetime. Both cover only a wedge of the full spacetime; both have a special place for hyperbolas, which are invariant figures for hyperbolic rotations; and both have a coordinate pathology at the apex of the wedge. There, both coordinate systems map many values of the “tt” coordinate to a single spacetime event. The analogy between the two cases was explored by Rindler (1977, §8.6) and became an important stimulus to further work on black holes and their horizons. For this reason, the wedge is often called a “Rindler wedge” and Einstein and Rosen’s accelerated coordinates “Rindler coordinates.” +3.3 WHAT EINSTEIN MEANT +The modern view privileges the spacetime geometry over the analytic expressions. From this perspective, Einstein’s assertions about the Schwarzschild solution are incomprehensible. He has mistaken a pathology of his coordinate system for a true singularity of the spacetime geometry. This was not Einstein’s view. He privileged the analytic expression over the geometry. There is no one-to-one mapping that takes the quadratic differential form (5) into the corresponding quadratic differential form for the Schwarzschild spacetime in Kruskal coordinates. One has to abandon such mappings and use the geometry of the fully extended Schwarzschild spacetime to correct the Droste coordinates. While that is the modern procedure, it was not Einstein’s. He was not willing to compromise the quadratic differential form (5) by privileging the geometry and using it to eliminate the singularity. +Once we recognize that Einstein’s remarks about the Schwarzschild solution refer specifically to this quadratic different form (5), they are not confusions, but quite +Figure 3 Droste coordinate curves in the fully extended Schwarzschild spacetime in Kruskal coordinates. + + + COREOPS 14 Philosophy of Physics DOI: 10.31389/pop.91 +consistent. First, we saw above that Einstein (1939, 922) remarked that a clock kept at the Schwarzschild radius “would go at a rate zero.” That is read trivially from the vanishing of the “gg44” component the metric of (5). It also conforms with the spacetime geometry. For a clock, kept at the Schwarzschild radius in Droste coordinates, would be kept at a single event in the spacetime, where no proper time elapses, even though many different values of the time coordinate tt are assigned to the event. +Second, we have Einstein’s remark (1939, 922) “that both light rays and material particles take an infinitely long time (measured in ‘coördinate time’) in order to reach [Schwarzschild radius].” This is not a confused assertion that these systems can never reach the Schwarzschild radius. Einstein is not confusing an infinite coordinate time with an infinity of proper time. There can be no doubt of that since Einstein explicitly specifies “coordinate time.” The distinction is foundational in the theory he devised and he is, among all physicists, the least likely to confuse the two. Rather, Einstein is pointing out a limitation in the reach of the quadratic differential form (5). Its time coordinate tt can only cover motions outside the Schwarzschild radius. While it is a natural project to ask how the motion might continue past the reach of the coordinate system, it is one that likely did not interest Einstein. His 1939 paper argued that no spacetime could form with a bare Schwarzschild radius. Bodies falling towards it would first strike source matter. +This expectation about the limit of motions physically realizable by the Schwarzschild solution was not a novelty of 1939. Einstein had long presumed it. We learn from reporting by Charles Nordmann (1922, 154–156) that the presumption had figured prominently in discussions about relativity theory when Einstein had made a visit to the Collège de France in Paris.8 In discussion on April 5, 1922, Hadamard has asked Einstein what would happen if a mass were condensed enough so that its exterior field included the singular Schwarzschild radius. Einstein seemed to be taken aback by the suggestion. “It would be,” Nordmann quoted Einstein as saying, “an unimaginable misfortune [malheur] for theory...” The quote continued with Einstein seeming to suggest that even in this case the Schwarzschild solution would break down: “...it is very difficult to say what would happen physically, for then the formula ceases to be applicable.” Nordmann continued his report that Einstein light-heartedly called the problem the “Hadamard catastrophe.” It seems that Einstein had then simply assumed that a bare Schwarzschild radius was impossible, but he had not really worked through the physics needed to sustain its impossibility. For, he was otherwise unable to give a more cogent response. He needed time. That response came in the next meeting of April 7. Einstein argued that a mass, sufficiently condensed to bring about the Hadamard catastrophe, was physically impossible. He recalled Schwarzschild’s earlier calculation that the pressure inside the mass would become infinite at the center, before the Hadamard catastrophe was realized, and also that clocks there would halt. +Once again, contrary to Einstein’s methods, we can draw a spacetime diagram that represents how Einstein conceived the quadratic differential form (5). On the right, Figure 4 shows the many, distinct events it attributes at the Schwarzschild radius for the differing values of the time coordinate tt. The left of the figure shows corresponding part of the Schwarzschild spacetime in Kruskal coordinates. +Both show the worldline of a body that maintains a constant rrrrrr r rrrr coordinate position in the Droste coordinates of (5). The worldline is vertical in the Droste coordinates +8 For editorial discussion see Kormos Buchwald et al. (2012, xlviii). + + + COREOPS 15 Philosophy of Physics DOI: 10.31389/pop.91 +shown on the right and a hyperbola in Kruskal coordinates shown on the left. The worldlines of light propagating towards and away from the rr r rrr radius are shown on the right in Droste coordinates. They pass through events tt t t, rrrrrr r rrrr rrrr. Both of the worldlines are asymptotic to the Schwarzschild radius rr r rrr. The same trajectories are shown on the left in Kruskal coordinates as straight, diagonal lines. These fully extended trajectories pass through the Schwarzschild radius, shown as dashed diagonal lines, and continue to contact either the past or future singularity. +3.4 EINSTEIN’S DEFINITION OF A SINGULARITY +Einstein’s remarks in these two papers (1935; 1939) enable us to identify more precisely what he meant by a singularity in these contexts. +First, we can say what his conception is not. It is not the modern conception of a failure of the intrinsic geometry, such as the divergence of curvature invariants. Is it a zerovalued component of the metric tensor? In (5) we have a zero-valued metrical component, gg44 = (1 − 2mmmmmm = m at rr r rrr, the events that Einstein and Rosen identify as singular. However, we shall see in Einstein and Rosen’s treatment of their “bridge” that the mere fact of a zero-valued component of the metric tensor is insufficient for a singularity. This is not unexpected. A vanishing component of the metric tensor may be completely benign, as is commonly the case with off-diagonal components. Vanishing diagonal components, however, can be associated with a degeneracy of the metrical structure. A degeneracy is not a singular breakdown. The familiar example is the spatial metric of a Newtonian spacetime. Using ordinary Cartesian coordinates for space and absolute time as the time coordinate, the metric has the form +hiiii = +⎢⎢⎣⎡⎢ +1000 0100 0010 0000 +⎥⎥⎦⎤⎥ +. +It assigns ordinary Euclidean lengths to separations in space, but zero length to separations between events at one point in space but with different absolute time coordinates. +Figure 4 Falling light in Kruskal and Droste coordinates. + + + COREOPS 16 Philosophy of Physics DOI: 10.31389/pop.91 +Correspondingly, we shall see that a diverging metrical component is also insufficient for there to be a singularity.9 In Einstein and Rosen’s analysis of their “bridge” (below), they show that the diverging gg11 = −1/(1 − 2mm/mmm = m at rr r rrr can be regularized by a oneto-one coordinate transformation. +What further conditions are needed for Einstein to identify a singularity? Einstein and Rosen specified them above in their discussion of the line element (3) in accelerated coordinate systems: +... the fact that the determinant of gg of the ggμμμμ vanishes for xx1 = 0. The contravariant ggμμμμ therefore become infinite and the tensorsRRiikkkkkk and RRkkkk take on the form 0/0. +It is not the vanishing or the divergence of components of the metric tensor, but the fact that their extreme values propagate through the theory, generating more infinite quantities or indeterminate quantities of the form 0/0 elsewhere. In particular, the quantities used to define the source-free field equations, the Riemann tensor RRiikkkkkk and its contraction RRkkkk are compromised. +3.5 HILBERT’S DEFINITION OF A SINGULARITY +Einstein and Rosen’s formulation appeared roughly two decades after Schwarzschild’s solution was found. A similar but not identical characterization was published earlier by Hilbert in his 1916 “Foundations of Physics” and an equivalent version was given in his lectures from that summer. In the second part of his highly influential December 1916 communication on general relativity, Hilbert (1916) affirmed that the Schwarzschild line element (5) is singular at both radial coordinate positions, rr r r and rr r rr, where rr r rr, corresponds to the Schwarzschild radius rr r rrr of (5). He then gave the applicable definition of regularity, that is, of non-singularity: +That is, I call a metric or a gravitational field ggμμμμ, at a position, regular, if it is possible, through reversible, one-to-one [eindeutig] transformation, to introduce such a coordinate system, that, for it, the corresponding functions gg′μμμμ, are regular at that position, i.e. in it and in its neighborhood [they] are continuous and arbitrarily often differentiable and have a determinant gg′ different from zero (1916, 70, his emphasis). +Earlier that year, in lectures given over Göttingen’s summer semester, Hilbert gave another version of his characterization: +We call a gravitational field or a metric “regular”—this definition was still to be added—if it is possible to introduce such a coordinate system that the functions ggμμμμ are regular at every position in the world and have a determinant different from zero. We further designate an individual function as regular if it is finite and continuous along with all its derivatives. This is, incidentally, always the definition of regularity in physics, while in mathematics it is required that a regular function be analytic. The metric [(5)] has singularities for αα α α and, correspondingly, αα α α, at the position rr r r and rr r rr, and correspondingly at r = 0. If we consider that these singularities arise in the absence of masses, then it seems also plausible that they cannot be eliminated by coordinate transformation(1916, 252). +9 We saw above that Einstein and Rosen (1935, 75) found the Schwarzschild solution (5) in Droste coordinates to be singular since “ gg11 for rr r rrr becomes infinite and hence we have there a singularity.” I read this formulation as tacitly presuming that the infinity produces problems elsewhere when it propagates through to other quantities. + + + COREOPS 17 Philosophy of Physics DOI: 10.31389/pop.91 +The singularity identified by Hilbert in these characterizations is specifically one arising in analytic expressions, such as the Schwarzschild line element (5), when they are understood to belong to a set of expressions closed under one-to-one coordinate transformations. The definition was not a means of impugning the Droste coordinate system as a preliminary for further analysis of the geometry of the spacetime at the Schwarzschild radius. The singular character of the line element at the Schwarzschild radius was, for Hilbert, a failure of the physics directly. Immediately after presenting the Schwarzschild solution in Droste coordinates and prior to giving the above definition of regularity in his 1916 lecture notes, Hilbert (1916, 251) had declared: +According to our understanding of the nature of matter, we can consider as physically realizable solutions ggμμμμ of the [source-free gravitational] differential equations KKμμμμ = 0 only those which are regular and free from singularities. +The same sentiment appears after the corresponding definition in his published communication “...in my opinion, only regular solutions of the physical fundamental equations represent reality immediately...” (1916a, 70). +These formulations are important. First, in the 1910s, when Einstein was completing his discovery of general relativity, there was no higher standard of mathematical excellence than David Hilbert in Göttingen. We might not now favor the characterization of singularities that he advanced. We cannot now dismiss it as a confusion of an Einstein, who, we would suggest, had brilliant physical intuitions but was prone to novice errors of mathematics. +Second, precisely because of his leading position, Hilbert’s formulation was authoritative. When Laue identified the Schwarzschild radius as singular, it was in conformity with Hilbert’s definition. He wrote, +... the singularity of the metric ([5]) at [rr r rrr] cannot be eliminated by the introduction of other coordinates, but lies entirely in the nature ofthings (1921, 215). +3.6 THEIR DIFFERENCES +Einstein and Hilbert’s definitions of a singularity are similar but not identical. The main difference is that Hilbert adds an explicit consideration: “... it is possible, through reversible, one-to-one [eindeutig] transformation, to introduce such a coordinate system, that ...”. This condition fails at rr r r for an ordinary Euclidean space with radial coordinates rr and θθ and Euclidean line element dddd2 = dddd2 + dd2dddd2. It certainly seems perverse now to offer a definition that would render the simplest of geometries singular. However, we should not presume that Hilbert was guilty of so trivial a mathematical oversight. As long as his criterion is applied to mathematical expressions, it may be uncongenial now, but it commits no mathematical blunder. It simply asserts the singularity of the expression dddd2 = dddd2 + dd2dddd2 at rr r r, but allows the regularity everywhere of the expression dddd2 = dddd2 + dddd2, where xx and yy are the familiar Cartesian coordinates. +Einstein, however, was not committed to this level of mathematical purity. Presumably, Einstein would have agreed with Hilbert’s definition in generic circumstances. However, he was willing to make exceptions, uncongenial to a rigorous mathematician, when his physical intuition called for it. Hilbert’s definition of regularity fails for the Schwarzschild solution (5) at θθ θ θ.10 We saw, above, that Einstein and Rosen (1935, 75) dismissed this failure with: +The vanishing of the determinant of the ggμμμμ for θθ θ θ is unimportant, since the corresponding (spatial) direction is not preferred. +10 The coefficient of dddd2, rr2sin2θθ, vanishes at θθ θ θ and leads to gg g g. + + + COREOPS 18 Philosophy of Physics DOI: 10.31389/pop.91 +Here they are deferring to the geometry, but without giving a more precise mathematical foundation for their reasons. This is an interesting contrast. Hilbert’s mathematical precision gives us a result we do not now like. Einstein’s mathematical imprecision gives us the result we do now like. +We now almost automatically would regularize a line element like dddd2 = dddd2 + dd2dddd2 by introducing a new coordinate system, such as (xx, yy), that is not related by a one-toone mapping with the original coordinate system (rr, θθ). Einstein supposes that this sort of regularization is not compelled mathematically, but must be supported by physical considerations. This supposition is central to Einstein’s rejection of the geometric regularizations that we might now apply to all three examples discussed here. Appendix B offers a simple example to show that the regularization of the line element dddd2 = dddd2 + dd2dddd2 is not a mathematical necessity, but requires a physical basis. +I set aside a complication with Hilbert’s definition for regularity. He does not specify whether it is merely a sufficient condition or both necessary and sufficient. If it is merely sufficient, then it does not preclude regularity at the origin of radial coordinates in a Euclidean space. The natural reading is to include necessity: that systems failing his definition of regularity are singular. I will read it that way. +3.7 EINSTEIN-ROSEN BRIDGES +The principal function of Einstein and Rosen’s paper was to offer an account of particles that would foreshadow Einstein’s long-standing goal: a theory with a single unified field that embraces all atomic forms of matter. The Einstein-Rosen proposal was, at best, an intermediate on the way to this goal. It did not posit a single unified field, but employed two fields: the metric field ggiiii of general relativity and the Maxwell four-vector potential φφii of electrodynamics. The Maxwell field vector was needed to endow the particles with charge. However neutral particles could be represented with the metric tensor alone. The proposal was a development of the idea that the Schwarzschild radius in the Schwarzschild solution was an unrealizable surrogate for matter that would have a regular representation in a successor theory. +The core novelty of the Einstein-Rosen paper was a means of regularizing the singularity at the Schwarzschild radius so that the Schwarzschild solution could represent a particle. That singularity, it was noted above, did not arise from the vanishing or divergence of the coefficients of metric tensor at rr r rrr. It arose from the vanishing of the determinant gg. For division by its zero-value propagated through the formalism, yielding indeterminate quantities of the form 0/0. The contravariant metric ggiiii is equal to [ggiiii]/gg, where [ggiiii] is the co-factor of the metric tensor ggiiii. This contravariant metric would then be used to contract the Riemann tensor to form the Ricci tensor, RRiiii, for the gravitational field equations. Following a remark by W. Mayer, Einstein and Rosen realized that they could avoid division by the troublesome determinant gg if they replaced the source-free field equations, RRiiii = 0, by RRii∗ii = gg2RRiiii = 0. +An appeal of the new field equations was that the Schwarzschild line element (5) remained a solution and the line element ceased to be singular at rr r rrr. To see its regularity, Einstein and Rosen rescaled the rr coordinate of (5) by introducing a new coordinate uu, where uu2 = rr r rrr. In the new coordinate system, the Schwarzschild solution became +dddd2 = −4(uu2 + 2mmmdduu2 − (uu2 + 2mmm2(dddd2 + sin2ddddθθ2m + ( uu2 +uu2 + 2mm ) dddd2. (6) + + + COREOPS 19 Philosophy of Physics DOI: 10.31389/pop.91 +The troublesome gg11 = −1/(1 − 2mm/mmm = m at rr r rrr of (5) had been transformed to a benign gg11 = −4(uu2 + 2mmm = −mmm at the Schwarzschild radius uu u u. The corresponding zero-valued coefficient of (5), gg44 = (1 − 2mmmmmm = m at rr r rrr, remained zero-valued as gg44 = uu2/(uu2 + 2mmm = m at uu u u. While this zero value would lead to gg g g, its zero value was no longer troublesome for the modified field equations. Einstein and Rosen (1935, 75) could declare the solution “free from singularities.” +In his more popular writing, “Physics and Reality,” Einstein (1936) was more explicit about the elimination of the singularity. After reviewing his work with Rosen, he concluded of the Schwarzschild solution in the form (6): +This solution behaves regularly for all values of [uu]. The vanishing of the coefficient of dddd2 (i.e., gg44) for [uuu u u results, it is true, in the consequence that the determinant gg vanishes for this value; but, with the methods of writing the field equations actually adopted, this does not constitute a singularity (321). +For our purposes, what matters is how the regularity of the Schwarzschild solution was established. The coordinate transformation uu2 = rr r rrr is a one-to-one mapping (assuming that the positive square root is taken for uu). The requirement that coordinate transformations must be one-to-one had not been relaxed. Einstein and Rosen were still assigning all values of the tt coordinate to events with uu u u (and each fixed θθ and φφ). That is, they are still representing, as infinitely many events, what is treated as a single event in the fully extended Schwarzschild spacetime represented in Figure 3. This requirement of one-to-one mapping must be abandoned if the Kruskal coordinate system shown in Figure 3 is to be adopted. +With this in mind, we can review what Einstein and Rosen have established with their bridge. The structure they called a “bridge” arises when the Schwarzschild solution (6) is considered for all values of −∞ < uu < ∞. It was their representation for a single, uncharged particle. Even though they allowed all values of their coordinates in (6), their bridge only covered the two wedges of the exterior Schwarzschild spacetime of Figure 3. The interior was untouched. While they did not draw any figures, it is now common for us to find, such as in Kruskal (1960), that their bridge represented by figures akin to Figure 5. +Figure 5 Einstein-Rosen bridge. + + + COREOPS 20 Philosophy of Physics DOI: 10.31389/pop.91 +This figure shows a spacelike surface within the solution, spanned by the coordinates −∞ < uu < ∞ and 0 ≤ φφ φ φφφ. In the fully extended Schwarzschild spacetime, an event with uu u u (or equivalently, rr r rrr) at the neck of the bridge corresponds to a single event at the apex of the two wedges shown in Figure 3.11 For Einstein and Rosen, however, there were infinitely many such events, distinguished by different values of the tt coordinate. For them, a better picture would be something like Figure 6. It shows a single bridge, as Einstein and Rosen would have conceived it, extended according to the development of the tt time coordinate. +The key difference is how events at the Schwarzschild radius are treated. In the fully extended Schwarzschild spacetime, shown at the left, for a given set of angular coordinates, there is a single event picked out by the Droste coordinates at rr r rrr, for all values of tt. In Einstein and Rosen’s conception, shown at the right, different values of tt pick out different events at rr r rrr. That is, the set of events at rr r rrr for all tt, forms a curve in the spacetime, for Einstein and Rosen, where it is just a single event in the fully extended Schwarzschild spacetime. +3.8 THE STATIC LINE ELEMENT +Finally, there is a single word throughout Einstein’s discussions of the Schwarzschild solution that may appear innocent, but actually has a controlling influence on his analysis. All the forms of the solution Einstein discussed are identified as “spherically symmetric static solution of the gravitational equations.” That they must be “static” means that Einstein sought a line element in which all the ggμμμμ are independent of the xx4 time coordinate; and gg14 = gg24 = gg34 = 0. +The physical intuition behind the condition is plausible: the symmetric field surrounding an idealized mass like the sun should not change as time advances; and it should be possible to foliate the field into distinct moments of time (which would fail for constant time coordinate surfaces, if the gg14, gg24, gg34 were non-zero). Because of its naturalness, +Figure 6 Einstein-Rosen Bridge with tt degrees of freedom. +11 This familiar figure should be read with caution. It represents well the topology of the two-dimensional, spatial surface spanned by the coordinates rr and φφ. It is poorer at representing metrical relations, in so far as we expect them to be induced by embedding in a three-dimensional Euclidean space. For such an embedding, rr might be a Cartesian coordinate in the vertical direction and xx a Cartesian coordinate in the horizontal direction with an origin at the midpoint. A metrical distance dddd in the rr r rr plane must satisfy dddd2 = [1/(1 − 2mm/mmmmddmm2 = ddmm2 + dddd2. Solving the resulting differential equation for xx, we find that the horizontal displacement of the surface from the midpoint is xx x xxx√ +rr +2mm − 1 . That is, the curve of bridge is a parabola. The asymptotically flat surfaces on either end are fictitious surfaces at infinite Euclidean distance from the midpoint. + + + COREOPS 21 Philosophy of Physics DOI: 10.31389/pop.91 +this condition was assumed automatically from the first moments. It was stated explicitly in Einstein’s celebrated communication of November 19, 1915 (833). In it, he gave the first approximate solution for the spacetime of the sun in his near complete general relativity and used it to explain the anomalous 43 seconds of arc in Mercury’s orbit. Schwarzschild (1916, 190), in his first derivation of his solution, repeats the conditions, citing Einstein’s 1915 assertion of them. Droste (1916, 198) began with a stipulation of this static form for his line element. Both Weyl (1918, §30) and Laue (1921, §21) in their early texts on general relativity proceeded with the assumption of the same static form. +The effect of requiring this static condition, however, is severe. It precludes Einstein and these later relativists from finding a non-singular representation of the fully-extended Schwarzschild spacetime. The coordinate systems that are capable of covering the fullyextended spacetime, such as Kruskal’s, violate the condition. +3.9 IN RETROSPECT +What can we say in retrospect concerning Einstein’s treatment of the Schwarzschild solution? In a limited sense, it was adequate for the practical issues of solar system astronomy that drew only on the Schwarzschild solution outside the rr r rrr event horizon. However, as research in gravitational physics progressed, Einstein’s algebraic approach to the Schwarzschild solution and his insistence on a static line element proved infertile. The geometric approach proved productive. The full extension of the Schwarzschild spacetime, past the event horizon at rr r rrr, has provided some of the most important developments. A black hole with its curvature singularity has become the favorite testing ground for theories of quantum gravity. Advances in observational astronomy include the detection through gravitational wave astronomy of the coalescence of two black holes and the visual imaging of the event horizon of a black hole. In this regard, Einstein’s insistence on algebraic methods proved to be his own personal event horizon beyond which his gaze could not pass. +4. THE MASS HORIZON IN A DE SITTER SOLUTION +Einstein’s work in cosmology of the late 1910s triggered an earlier debate over just what counts as a true singularity in general relativity. The debate is especially interesting for present concerns since, in its course, Einstein was forcefully presented with the geometric deflation of what he had identified as a singularity; we can be sure that Einstein knew of the extended geometry and we can follow how he argued against it. +The debate developed before and around Einstein’s celebrated 1917 paper, “Cosmological Considerations on the General Theory of Relativity.” Einstein’s goal was to find a cosmological solution of his theory that conformed with what he came to call “Mach’s principle.” It is the requirement he later summarized, that “the gg-field is determined by the masses of bodies without residue” (1918, 241, his emphasis). The principle has the consequence that “according to the gravitational field equations, no GG-field is possible without matter” (243). +Einstein’s gravitational field equations of 1915 admit the spacetime of special relativity as a matter-free solution, an impossibility according to Mach’s principle.12 Einstein’s 1917 paper introduced a new cosmological solution that depicts a static, spherical space with a uniform matter distribution. Einstein found that he had to add a cosmological term λλ to his +12 This is given as a motivation for modifying his gravitational field equations in Einstein (1918, 243). + + + COREOPS 22 Philosophy of Physics DOI: 10.31389/pop.91 +gravitational field equations so that they would admit the new solution. Mach’s principle was upheld in the sense that the modified field equations no longer admitted the matterfree solution of special relativity. +Einstein’s proposal ran into grave difficulties. Almost immediately, De Sitter found a matter-free solution of the λλ-augmented gravitational field equations. One of the great debates of modern physics erupted. At its core was the question of whether certain singular expressions identified by Einstein could be surrogates for source masses; and whether they were singularities at all. +The details of this episode and the resulting debate have been recounted elsewhere in greater detail and with greater insight than is possible here. A thorough recounting is found in editorial apparatus of the Collected Papers, Schulmann in the headnote “The Einstein-de Sitter-WeylKlein Debate” (1998, 351–357) and numerous footnotes elsewhere; in Earman and Eisenstaedt (1999, §3), in Janssen (2014, 198–208), and in Smeenk (2014). Below I will focus just on the specific aspects of the debate concerning the singularities pertinent to present concerns. +4.1 EINSTEIN ON THE SINGULARITY IN THE DE SITTER SOLUTION +Einstein (1918a) provided a synopsis of his then stable view of the de Sitter solution in a short note, “Critical Comment on a Solution of the Gravitational Field Equations Given by Hr. De Sitter,” communicated to the Prussian Academy on March 7, 1918. He formulated the solution to his source free, λλ-augmented gravitational field equations in a coordinate system (rr, ψψ, θθ, tt) as: +dddd2 = −dddd2 − RR2sin2(ddrRRrrddrr2 + sin2rrddψψ2] + cos2(ddrRRrrr2dddd2, (7) +where RR is the constant radius of curvature of a tt = constant space. De Sitter had presented this line element in exactly matching notation as one version of his solution in de Sitter (1917a, 7, eqn. 8B). Einstein had selected this version of de Sitter’s solution because it has the key property of being static. That is, gg44 = cos2(rrrrrr is independent of tt, which means that (in geometrical language)13 the constant tt hypersurfaces all have the same spatial geometry, which Einstein presumed on astronomical evidence to be the case for our universe. +Einstein proceeded to specify with considerable care why he judged there to be a singularity at the value rr r rrrrrr of the rr coordinate for which gg44 = cos2(rrrrrrrr2 vanishes. He first laid out the conditions required for non-singularity:14 +... it is a requirement of the theory that the [λλ-augmented gravitation field] equations hold for all finite points. This can then only be the case if both the ggμμμμ as well as the associated contravariant ggμμμμ (together with their first derivatives) are continuous and differentiable; therefore in particular the determinant gg g gggμμμμg must disappear nowhere in the finite (1918, 270). +This plausible condition, however, faced the same problem as the Schwarzschild solution in Droste coordinates: According to it, the de Sitter solution is singular at the origin rr r r of the spherical coordinates. It is, presumably, with this difficulty in mind, that Einstein introduced a clarification: +13 And gg14 = gg24 = gg34 = 0. +14 Einstein’s concern with the finitude of the points derives from his disagreement with an assertion by de Sitter in a letter to Einstein of April 1, 2017 (Schulmann et al. 1998 , Doc. 321) that the singular points are at infinity. + + + COREOPS 23 Philosophy of Physics DOI: 10.31389/pop.91 +Further, the continuity condition for the ggμμμμ and ggμμμμ is not to be understood as requiring that there must be a choice of coordinates in which it [the continuity condition] is satisfied in the whole space. Obviously it must only be required that there is a choice of coordinates for the neighborhood of each point for which the condition of continuity is satisfied in this neighborhood; this restriction on the requirement of continuity arises naturally out of the general covariance of the [λλ-augmented gravitation field equations] (1918, 271). +Einstein then used this weakened condition to eliminate the apparent singularity at the origin: +For the de Sitter solution now, according to [(7)] +gg g ggg4sin4(rrrggrsin2ψψcos2(rrrggr +Thus to begin with, gg vanishes for rr r r and for ψψ ψ ψ. This relation, however, implies only an apparent violation of the condition of continuity, as can easily be shown through an appropriate change in the choice of coordinates (1918). +While Felix Klein would soon conclude that the singularity at rr r rrrrrr should be treated similarly, Einstein insisted otherwise. He continued: +However gg vanishes also for rr r rrrrrr, and indeed here is a discontinuity that cannot be eliminated through any choice of coordinates. ... Until proven otherwise, it is therefore to be assumed that the de Sitter solution has a real singularity in the surface located at rr r rrrrrr, that is does not conform with the [λλ-augmented gravitational] field equations for any choice of coordinates (1918). +While Einstein took the analytic formula of line element (7) as the subject of analysis, for comparison purposes again, we can give a geometric picture of Einstein’s understanding. For constant tt, the line element (7) reduces to a three-dimensional spherically curved space with radius of curvature RR, divided in half by a singular surface at rr r rrrrrr. Suppressing the θθ angle variable, one half of this space is shown in Figure 7 as a hemisphere with the singularity at its equator. The space is static, so that the hemisphere evolves forward, unchanged in time, as shown by the vertical tt axis, and carries the singularity with it through time. +Figure 7 Einstein’s Conception of the de Sitter Solution. + + + COREOPS 24 Philosophy of Physics DOI: 10.31389/pop.91 +De Sitter sent Einstein a summary of his new, proposed solution in a letter of March 20, 1917 (Schulmann et al. 1998, Doc. 313). Einstein responded four days later on March 24. De Sitter’s new solution was inadmissible as a serious candidate for cosmology for physical reasons: the singularity itself was problematic, as well as the solution’s matter-free character. Einstein summarized his concerns: +Therefore it seems to me that your solution does not correspond to a physical possibility. The ggμμμμ and ggμμμμ (together with their first derivatives) must be continuous everywhere. +In my opinion, it would be unsatisfactory if a world without matter were conceivable. Rather, the ggμμμμ-field should be fully determined by matter and not be able to exist without the matter. This is the core of what I mean by the requirement of the relativity of inertia (Doc 317, Einstein’s emphasis). +The “relativity of inertia” would shortly be given the more familiar title “Mach’s principle.” +Einstein’s objections to de Sitter’s solution continued in their correspondence. Einstein objected, for example, that at the singularity rr r rrrrrr, since gg44 = 0, the velocity of light drops to zero, the energy of a mass point would be zero and masses would have minimal gravitational potential, so they would accumulate there (Einstein to de Sitter July 22, 1917 Doc. 363; Schulmann et al. 1998). Such a singularity is “in my opinion to be excluded as physically not coming into consideration.” For these reasons, Einstein remained recalcitrant. In a letter to de Sitter on July 31, 1917 (Schulmann et al. 1998, Doc. 366), he wrote that he could not “grant your solution any physical possibility” and:15 +For rr r rrrrrr, the mass point has no energy; it does not exist there any more at all, but has eaten itself up completely on the way there. The admission of such cases appears to me to be absurd [sinnwidrig]. This will naturally always be true, regardless of how we may choose the variables. +4.2 THE MASS HORIZON +Einstein’s opposition to de Sitter’s solution soon softened, but did not disappear. He found a way to accommodate de Sitter’s solution to Mach’s principle. The idea was to identify the singularity as a concentration of matter at the singular surface. It was a “mass horizon,” as it soon came to be called,16 and responsible for the spatiotemporal properties of the world, in accordance with Mach’s principle. The proposal concluded Einstein’s March 7, 1918, with a critical comment on the de Sitter solution. He wrote: +In fact, de Sitter’s system [(71)] solves the [ λλ-augmented gravitational field equations] everywhere, only not in the surface rr r rrrrrr. There—as in the immediate vicinity of a gravitating mass point—the component gg44 of the gravitational potential becomes zero. The de Sitter solution must in no way [be seen as] the case of a matter-free world, but much more as corresponding to the case of a world whose matter is all concentrated in the surface rr r rrrrrr: this could indeed be demonstrated through a limiting process from a spatial to a surface-like distribution of matter (Einstein 1918a, 272). +15 Einstein use of the term “variables” and not “coordinates” conforms with his focus on analytic expressions formulated with variables as opposed to geometries with coordinates. +16 The term “mass horizon” appears, for example in Weyl (1918, 226; 1919, 34) as Massenhorizont. + + + COREOPS 25 Philosophy of Physics DOI: 10.31389/pop.91 +In foreshadowing this proposal in a letter to de Sitter of August 8, 1917, (Schulmann et al. 1998, Doc. 370), Einstein explained more fully that “... the falling of the gg44 (to zero) in the approach to rr r rrrrrr is to be thought of as caused through matter, just like the falling of gg44 in the approach, f.[or] e.[xample] to the sun.” +Einstein’s proposal included a supposition that the mass horizon could be produced by a limiting process. Einstein reported with obvious satisfaction to de Sitter in a letter of April 15, 1918 (Schulmann et al. 1998, Doc. 506) that Hermann Weyl, in his new relativity text Raum-Zeit-Materie, had done just the requisite calculation.17 Einstein, however, soon found he was not satisfied with the details of Weyl’s calculation and the two exchanged letters and proposals in April to June 1918 until Weyl’s corrections were acceptable to both.18 +Hermann Weyl was a mathematician of the first rank. He was a student of Hilbert and became Hilbert’s successor in Göttingen. His active engagement provided a mathematical ratification to Einstein’s assessment of the singular character of de Sitter’s solution. +4.3 THE GEOMETER’S REACTION +It took several decades before concerted opposition arose to Einstein and Hilbert’s judgment of the singular nature of the Schwarzschild radius. In the case of the de Sitter solution, that repudiation arose more quickly. Einstein and de Sitter’s proposals in cosmology attracted the attention of Felix Klein, a colleague of Hilbert’s at Göttingen, and perhaps the foremost geometer of his era. His 1872 “Erlangen program” sought to unify many disparate geometries in one system. Its leading idea was that each geometry could be characterized by a group. His approach fared poorly with the Riemannian spacetimes of variable curvature of Einstein’s general theory of relativity since the groups with which Klein worked there were, in general, trivial.19 The exceptions were the geometrically more symmetric Minkowski spacetime of special relativity and the two cosmologies of Einstein and de Sitter. They were homogenous enough to admit a non-trivial group structure. Hence, it was not surprising that Klein took an interest in them. He repeatedly and clearly presented the geometer’s objection that Einstein’s singularity was a mere artefact of his choice of coordinate system. +Klein reported his geometric analysis of Einstein’s and de Sitter’s cosmological solutions in lectures in Göttingen of May 7 and June 11, 1918. Their content was summarized in Klein (1918) and he subsequently published more expansive versions with the same essential content. Klein (1919) reported a version communicated to the Amsterdam Academy of Science in a meeting of September 29, 1918. Klein (1918a) reported a still more elaborate version communicated in Göttingen on December 6, 1918. +Klein’s analysis was set in a five-dimensional extension of the familiar four-dimensional Minkowski spacetime. Its line element was20 +dddd2 = dddd2 + dddd2 + dddd2 − dddd2 + dddd2. (8) +The coordinates ξξ, ηη, ζζ and ωω are spatial and the coordinate νν is temporal. Within this five-dimensional space, he introduced an hyperboloid with radius of curvature RRRRR whose four-dimensional surface is the space of the de Sitter solution: +17 See Weyl (1918, §33) and a subsequent clarification in Weyl (1919). +18 See Docs. 511, 513, 525, 535, 544, 551 in Schulmann et al. 1998. +19 For discussion of the contrast, see Norton (1999). +20 Klein included considerably more geometry in his full discussion than is relevant to the treatment of the singularity. He made contact with his work in projective geometry and suggested that, spatially, the solution should not employ spherical geometry, but elliptical geometry in which antipodal points are identified. + + + COREOPS 26 Philosophy of Physics DOI: 10.31389/pop.91 +ξξ2 + ηη2 + ζζ2 − νν2 + ωω2 = RR2/cc2. (9) +Klein then sought to recover the de Sitter solution in the form (7) employed at times by de Sitter and by Einstein in his communication of Einstein (1918a). To this end he introduced four spacetime coordinates, rr, ψψ, θθ and tt, through the relations21 +ξξ ξ ξξ (rrrξξr ψψ (10) +ηη η ηη (rrrηηr ψψ θθ +ζζ ζ ζζ (rrrζζr ψψ ψψψψψψψψ +νν ν νν (rrrννr (ccccrννr +ωω ω ωω (rrrωωr (ccccrωωr +Transformation (10) replaces Klein’s original five coordinates by four. It follows that transformation (10) induces a relation among the new coordinates. Forming the sum of squares ξξ2 + ηη2 + ζζ2 − νν2 + ωω2 using (10) affirms that the formula for the hyperboloid (9) holds as an identity among the four new coordinates. That is, these coordinates are restricted by their definitions to the surface of the hyperboloid. +This new coordinate system fails to cover the entire hyperboloid. To see this, form the ratio of the expressions for νν and ωω in (10) and recover +νν ν tanh(cccccccc ccc (11) +For a fixed value of the coordinate tt, relation (11) identifies a plane in the five-dimensional space: νν ν constantωω. Each of these planes intersects the hyperboloid in a threedimensional geometrically spherical space of constant tt. As tt varies from −∞ to +∞, the factor tanh(cccccccc varies from -1 to +1. It follows that these constant tt spaces all lie between the two planes νν ν ννν and νν ν ννν, to which the hyperboloid is asymptotic. These planes are shown in Figure 8, in which two of the five dimensions have been suppressed. The new coordinates will cover the part of the hyperboloid lying within by the two-sided wedge formed by the planes νν ν ννν and νν ν ννν. +Figure 8 Two-sided wedge in the de Sitter hyperboloid. +21 For continuity with Einstein’s notation of (7), I have relabeled Klein’s variables according to θθ θ θθθθθ, φφ φ φφ and ψψ ψ ψψ. + + + COREOPS 27 Philosophy of Physics DOI: 10.31389/pop.91 +It now follows that the new coordinates introduced in (10) become singular at antipodal points νν ν νν ν ν, where the two asymptotic planes intersect. The surfaces of constant tt and their intersection are shown in Figure 9. The circles of constant tt in the figure are, more fully, three-dimensional spherical spaces whose two angle coordinates, ψψ and θθ, are not shown. The intersection of all surfaces of constant tt appear as two antipodal points on each of these circles. These two points are the projection onto the circles of a twodimensional spherical surface within the full three-dimensional spherical space spanned by the coordinates r, ψψ, and θθ. +This sphere of intersection of all spaces of constant tt is the singularity identified by Einstein that becomes the mass horizon. It is evident that, if the full spacetime is the geometrically homogeneous hyperboloid (9), then the singularity is simply an artifact of the new coordinate system introduced in (10). Indeed, if we take the hyperboloid to underlie de Sitter’s solution, then any judgement of special, singular regions contradicts the homogeneity of the hyperboloid. From this perspective, Einstein’s claim of a singularity must be mistaken. +In each of his presentations, Klein made this point of the spurious character of the singularity. He did not emphasize it, but was sure to make it. In his first reported publication, he concluded: +Thereby, the criticism which Einstein recently leveled against the de Sitter dddd2 (Berlin Academy of March 7 1918) is reduced to its true value. The singularity, which the de Sitter dddd2 has at ωω ω ω and νν ν ν depends only the arbitrariness with which the tt is introduced (Klein, 1918, 44). +In his 1919 paper, he remarked that, at ωω ω ω and νν ν ν, “tt becomes undetermined” (615). A footnote remarks: “However this is only a singularity of the coordinate tt, not of the underlying manifold [(8), (9)].” Earlier, Klein had characterized the singularity at this point in the surface in a slightly different manner: “... it appears as something singular, that is, +Figure 9 Einstein’s static coordinate system for the de Sitter solution. + + + COREOPS 28 Philosophy of Physics DOI: 10.31389/pop.91 +as the location of a world point for which tt adopts the value 0/0” (1918a, 421). Here, Klein presumably drew on the inverse of relation (11), which Klein had written as22 +tt t ttttt log[(ωω ω ωωωt(ωω ω ωωωω (ωωωωωωω ωωωω +When ωω ω ωω ω ω, the argument of the log function takes the indeterminate form 0/0. Klein’s 1918 writing was perhaps most dismissive: +For the general analytic conception, one has thereby no singularity present other than that of the polar angle φφ at the origin of a common (polar-)coordinate system (1918a, 418). +Einstein’s assertion of a singularity is here compared to a simple error in understanding how polar coordinates work at the origin of a polar coordinate system. The polar angle coordinate does take on all values or an indeterminate value at the origin without impugning the geometry of the surface to which it is applied. Only a geometrical novice, we might suppose, would confuse this with a singularity. +4.4 ASSESSING THE GEOMETER’S REACTION +Modern commentators have celebrated Klein’s intervention as introducing the decisive insight into how singularities are to be treated in general relativity. Earman and Eisenstaedt assess it as: +The importance of Klein’s contribution can hardly be overemphasised: for the first time in the history of GTR, what had been taken to be a real singularity had been shown to be merely apparent; and as well Klein had provided a paradigm for demonstrating the fictitious character of a singularity by getting rid of it by extending the spacetime; and his paradigm contained the realisation that the extension may have to be done by means of a non-regular coordinate transformation to non-static coordinates (1999, 195). +That Klein was an accomplished geometer intervening on a novice is suggested by Klein’s closing remarks in his letter of May 31, 1918. There, he emphasized the geometrical foundation of his understanding of the de Sitter solution: +With this, I would like to close today. My entire letter is intended to be only a precisification of my earlier, related communication. If I now give definite formulae in the place of geometrical considerations, that is done since with their help clearer expression is possible. However, geometrical considerations remain still the source of the whole train of thought (Schulmann et al. 1998, Doc. 552). +While this may now be the modern assessment, it was not shared then widely by mathematicians of the first tier who worked on de Sitter’s solution. They fully understood Klein’s analysis and merely treated it as an alternative to Einstein’s. If anything, they favored Einstein’s view. For example, in his discussion of “de Sitter’s world,” Lanczos reported Klein’s view: +Now, since all points of this pseudosphere are equivalent and regular, any singularity of the line element can only derive from the coordinate system used(1921, 540). +However, he immediately retreated from Klein’s position by recalling Weyl’s supposition of a layer of matter around the singularity. +It is a completely independent assertion and involves a singularity that cannot be removed by a transformation (1921). +22 Klein’s formula omits a factor of 1/2 found in standard expressions for the inverse of the function tanh(xxx. The factor was added silently in the reprinting of the paper in Klein’s collected papers (1921, 609). + + + COREOPS 29 Philosophy of Physics DOI: 10.31389/pop.91 +The primary burden of Lanczos’ note was a close analysis of Weyl’s proposal. +Similarly, Weyl’s (1921) treatment of cosmology in his 4th expanded edition of Raum-ZeitMaterie elaborated his own proposal for a mass horizon in the de Sitter solution. It then only briefly sketched Klein’s alternative in the closing pages of the section (256), without naming Klein. The alternative was introduced with a neutral “One recovers a metrically homogeneous world if ...” Weyl left open the decision between the two systems. It is to be decided by their differing physical properties. +The question arises whether it is the first or the second co-ordinate system that serves to represent the whole world in a regular manner. In the first case, the world would not be static as a whole, and it is consistent with the laws ofnature that it is empty of mass: de Sitter proceeds with this assumption. In the second case, we have a static world that is not possible without a mass-horizon; this assumption, which we have discussed more fully here, is preferred byEinstein (1921). +4.5 EINSTEIN’S TOPOLOGICAL RESPONSE +We can be sure that Einstein was well-informed of Klein’s geometrical analysis from the outset. Klein informed him of his work in letters of May 31 and June 16, 1918, roughly coincident with Klein’s 1918 presentations of May 7 and June 11 in Göttingen on de Sitter’s solution.23 (Schulmann 1998, Docs. 552, 566). In the second, Klein gave a compact summary of the main analysis, comparable to the content of his communication of September 26 to the Amsterdam Academy (Klein, 1919). There was enough of the formulae for a reader of the letter to reconstruct the full analysis. Reporting on his recent communication in Göttingen, Klein introduced the analysis with a simple summary, +I arrived at the result that the singularity you have noted in fact can be simply transformed away (1919). +Einstein’s reply came four days later in a letter to Klein of June 20, 1918 (Schulmann et al. 1998, Doc. 567). His tone was conciliatory and unruffled. His letter began: +You are quite right. De Sitter’s world is, in itself, free of singularities and its world points are all equivalent. A singularity only comes about through the substitution that affords the transition to the static form of the line element. This substitution alters the analysis-situs relations. That is, two hypersurfaces +tt t tt1 +and tt t tt2 +intersect in the original representation, while they donot intersect in the static [representation]. This is related to the fact that one must have masses for the static conception, but not in contrast in the first [one]. +Einstein’s direct reply to Klein’s assertion is illustrated in the difference between Figures 7 and 9 above. Einstein made a point in topology, a field whose older name was “analysis situs.” In the static de Sitter solution of (7) depicted in Figure 7, the singularity consists of many two-dimensional spheres, each distinguished by a different t coordinate. In the hyperboloid of Figure 9 recounted by Klein, the singularity consists of a single twodimensional sphere. All the t coordinates of (7) are assigned to this one sphere, since the hypersurfaces of each value of t intersect in the one sphere. It follows that the two singularities differ in their topology: Einstein’s is three-dimensional and Klein’ is two +23 In the versions of (8) and (9) in the June 16 letter, in a minor aberration in his notation, Klein assigned the minus sign to ωω and not νν. + + + COREOPS 30 Philosophy of Physics DOI: 10.31389/pop.91 +dimensional. They cannot be related by a one-one coordinate transformation. Klein’s full hyperboloid, Einstein argued here, is distinct from the de Sitter solution of (7). +Einstein’s response to Klein was brief given what later assessments judged to be devastating criticism. However, it was brief since Einstein needed only to add the topological consideration. In an earlier letter to Klein, sometime before June 3, he had already explained in greater detail why he dismissed de Sitter’s solution. He summarized his dismissal in that earlier letter as: +From a physical point of view, I believe that I can assert quite definitively that this mathematically more elegant, four-dimensionally unified conception of the world does not correspond to reality. That is, the world seems to be constituted such that its finely distributed matter can remain at rest in a suitably choice of the coordinate system (Schulmann et al. 1998, Doc. 556). +He then gave the details. De Sitter’s line element (7) at least gave a static spacetime. However, its matter must be located in the mass horizon that Weyl had analyzed. In contrast, Einstein’s own cosmology of 1917 had the requisite uniform matter distribution. Einstein was eager to be understood. He drew small pictures illustrating the matter distributions in space in his 1917 cosmology and in the mass horizon of de Sitter’s solution. +To later commentators who interpret Klein’s letter as the intervention of an expert in geometry pointing out the error of a novice in geometry, Einstein’s response is fragile and unconvincing. Einstein’s patient tone indicates that he did not see it that way. He had no need to see it that way. Einstein regarded the primary element of his theorizing to be analytic expressions, such as (7). That the expression can be generated as a solution to his field equations by means of the hyperboloid is merely an artefact of its construction. It does not establish that the full hyperboloid is the physically applicable solution of Einstein’s gravitational field equations. Which that is, whether expression (7) or not, is a matter of physics. As we shall see below, the physics, in Einstein’s view, directed the selection of (7). +Klein accepted Einstein’s response. The full hyperboloid was unobjectionable, mathematically, as a solution to Einstein’s gravitational field equations. However, its physical applicability to our universe was to be decided by physical considerations. Klein deferred to Einstein’s assertion that these considerations spoke against the full hyperboloid. Klein reported this assessment at the end of his December 6 communication in Göttingen. He noted that his analysis contradicted Weyl’s proposal of a mass horizon and continued: +I have not checked the correctness of Weyl’s calculations. However, I am happy to adopt the understanding that Einstein has expressed in correspondence that the difference in our mutual results must be based on the difference in the coordinates used. What I designate as a single point of intersection with the application of the [coordinates] ξξ, ηη, ζζ , νν and ωω, is a simply extended region with the use of the [coordinates]24 θθ, φφ, ψψ , tt (because of the undetermined, remaining values of t). It should not be hard to arrive at a full elucidation here(Klein, 1918a, 423). +Having accepted Einstein’s narrow topological argument, Klein then gave his final assessment: +My concluding vote on de Sitter’s claims, however, is that mathematically—up to that one still not fully clarified point—everything is in order. However, one is led to physical consequences that contradict our familiar way of thinking and, in any case, the agenda pursued by Einstein with the introduction of the spatially closed world (1918a). +24 [JDN] Corresponding to r/R, ψψ, θθ, tt in (7) + + + COREOPS 31 Philosophy of Physics DOI: 10.31389/pop.91 +If Einstein had committed some novice blunder, Klein did not see it. Indeed, Klein’s criticism seems hasty. His barb was that Einstein’s singularity is no different from the singularity at the origin of polar coordinates suggests a negligence on Einstein’s part. The barb is incompatible with Einstein’s earlier writing. For, as we saw above, Einstein (1918a) had addressed just this problem in his critical comment on de Sitter’s solution. He had noted the presence of just this sort of apparent singularity at the origin of the coordinates of the line element (7) and had explained why he found it to be eliminable in a way that the singularity at rr r rrrrrr was not eliminable. +Einstein’s topological argument was a minor consideration in his thinking. In the next two subsections, we shall see that he was well acquainted with the issues Klein had raised and had well developed means to address them. +4.6 EINSTEIN AND THE HYPERBOLOID +It is perhaps tempting to imagine that, with his fixation on analytic expressions like (7), Einstein was unaware that de Sitter’s solution was represented most simply by the hyperboloid. The view is unsustainable. That de Sitter’s solution derives from the hyperboloid had been present, prominently, from the start. The hyperboloid is the second most simple relativistic spacetime and the simplest solution of Einstein’s augmented gravitational field equations. +To see its simplicity, it is helpful to consider the analogous case of an ordinary threedimensional space. The simplest case is just a flat, Euclidean space of vanishing curvature. The next simplest case is of a homogeneous, spherical space with the same positive curvature elsewhere. This second case can be constructed by the artifice of considering a four-dimensional Euclidean space with Cartesian coordinates ξξ1, ξξ2, ξξ3, and ξξ4 and the line element +dddd2 = dddd12 + dddd22 + dddd32 + dddd42. (12) +This line element induces a constant, positive metrical curvature on a spherical, threedimensional hypersurface defined by +RR2 = ξξ12 + ξξ22 + ξξ32 + ξξ42. (13) +An explicit expression for the metric on this hypersurface is recovered by using (13) to eliminate25 ξξ4 from the line element (12) and to arrive at the line element and metric of the hypersurface26 +dddd2 = γγiiiiddddiiddddii γγiiii = δδiiii + ddiiddii/(RR2 − ρρ2), (14) +where iii ii i ii ii i and ρρ2 = ξξ12 + ξξ22 + ξξ32. +This construction, if promoted to a five-dimensional Minkowski spacetime, is the construction Klein employed for the de Sitter hyperboloid. Line element (13) and hypersphere (14) are the direct analogs of Klein’s line element (8) and hyperboloid (9). The main difference, aside from dimensionality, is that a hyperbola in a Minkowski spacetime is the curve of constant curvature analogous to the circle of constant curvature in a Euclidean space. Moving to higher dimensions, the hypersphere is a three-dimensional homogenous +25 By substituting ξξ4ddξξ4 = −ξξ1ddξξ1 − ξξ2ddξξ2 − ξξ3ddξξ3 and ξξ42 = RR2 − ρρ2 from (13). +26 No single coordinate system can be mapped one-one to the surface of a sphere, so there must be some anomalies. Writing (13) as ξξ42 = RR2 − ξξ12 + ξξ22 + ξξ2, we find that each set of values of ξξ1, ξξ2 and ξξ3 corresponds to two points on the sphere, according to whether positive or negative root of ξξ42 is taken. The metric expression (14) is singular at the equatorial sphere +where ξξ4 = 0 and RR2 = ξξ12 + ξξ22 + ξξ32, so that RR2 − ρρ2 = 0 . + + + COREOPS 32 Philosophy of Physics DOI: 10.31389/pop.91 +surface in a four-dimensional Euclidean space. Its analog is the de Sitter hyperboloid, which is a four-dimensional, homogenous hypersurface of constant curvature in a fivedimensional Minkowski spacetime. +We can have no doubt that Einstein was fully aware of the construction of the spherical space through (12), (13), and (14). These are the equations Einstein used in his 1917 cosmology paper (149–150) to introduce the spherical space of his 1917 cosmology. It is not possible that Einstein could have overlooked the analogy between his work of 1917 and the construction of the de Sitter hyperboloid, for de Sitter (1917) motivated his original derivation of his solution precisely by means of this analogy. Lest his readers could have any doubt of his use of the analogy, de Sitter employed the presentation (1917, 1219), typographically taxing in the era of hot metal typesetting, of displaying the two derivations side by side, as shown in Figure 10. +Case A is the three-dimensional space of Einstein’s 1917 cosmology. The closely analogous case B is de Sitter’s first presentation of his new solution to Einstein’s augmented gravitational field equations. Klein’s analysis employed a Minkowskian line element (8) with an indefinite signature. To bring the two cases even closer together, de Sitter employed the then familiar device of an imaginary time coordinate xx4 = iiiiii so that his line element and metric were positive definite and his hypersurface was a hypersphere. De Sitter recognized that the artifice of an imaginary time coordinate was dispensable and did not alter the results. His footnote at the word “symmetry” is “We can also take xx4 = cccc. Then the four-dimensional world is hyperbolical—instead of spherical, but the results remain the same.” +Finally, we can be sure that Einstein was fully informed of the analogy used by de Sitter. De Sitter’s results were communicated to the Amsterdam Academy on March 31, 1917. Days earlier, on March 20, de Sitter had already communicated his results to Einstein in a letter (Schulmann et al. 1998, Doc. 313). The letter employed the same side-by-side presentation of Einstein’s case A and de Sitter’s case B and reported the presentation of the hyperboloid in two further coordinate systems. This letter and de Sitter’s (1917) paper marked the start of an energetic correspondence between Einstein and de Sitter on the physical cogency of the new solution, and de Sitter followed up with several more publications elaborating on the solution. +For our purposes, what matters is that Klein, in 1918, had little new to tell Einstein. for Einstein was already well aware that the de Sitter solution was generated by means of a fully homogeneous hyperboloid whose geometry was everywhere regular. It is not +Figure 10 De Sitter’s Case A and Case B. + + + COREOPS 33 Philosophy of Physics DOI: 10.31389/pop.91 +credible that Einstein had somehow overlooked the fact that the singularity of the mass horizon arose as an artifact of the way the coordinates were applied to the hyperboloid. Einstein’s (1918a) earlier published critique of de Sitter’s solution has already compared the coordinate singularity at the origin rr r r with that at rr r rrrrrr and decided that they had a different character. That decision suggests that Einstein already had in hand his topological rejoinder to Klein. In any case, the whole issue was incidental to Einstein for his interest was the line element (7), independently of how it related to the hyperboloid. +The modern diagnosis of a geometrically sophisticated Klein correcting a geometrically naïve Einstein would appear to have the history inverted. In its place, we have Klein the geometer, whose vision is restricted to purely mathematical matters of geometry, corrected by an Einstein, who was willing to see beyond pure matters of geometry to a larger class of solutions of his gravitational field equations in the service of his physics. +4.7 EINSTEIN’S PHYSICAL OBJECTIONS TO THE FULL HYPERBOLOID +In Einstein’s view, at best, de Sitter’s analysis was an exercise in mathematics that uncovered new solutions of Einstein’s augmented gravitational field equations. What mattered to Einstein was not just the abstract mathematics, but which solutions satisfied physical conditions appropriate to our universe. To this end, Einstein provided two physical conditions that precluded de Sitter’s solution in all their forms. These two conditions controlled his analysis and he insisted repeatedly on them. +The first was the Machian intuition that had underpinned Einstein’s investigations into general relativity from the start and had figured prominently in his cosmological paper of 1917: The metric field is determined completely by the masses of bodies, without which no spacetime is possible. In 1918, he gave the condition the name Mach’s principle, where he reaffirmed forcefully his commitment to it with +... the necessity of retaining it is in no way supported by all colleagues. However, I myself view its satisfaction as unconditionally necessary (1918, 242). +That commitment immediately ruled out de Sitter’s (1917) proposal of the full hyperboloid since it is a matter-free spacetime. +Einstein recalled his commitment to Mach’s principle in many places. We saw above that, only four days after de Sitter had informed Einstein of his new solution, on March 24 Einstein gave it as a reason for rejecting the physical admissibility of de Sitter’s solution (Schulmann 1998, Doc 317, Einstein’s emphasis): +In my opinion, it would be unsatisfactory if a world without matter were conceivable. Rather, the ggμμμμ-field should be fully determined by matter and not be able to exist without the matter. This is the core of what I mean by the requirement of the relativity of inertia. +De Sitter found Einstein’s remark so significant that he included it in a postscript to his 1917 presentation (1225). Only two days later, in a letter of March 26, Einstein repeated the point to Klein, this time most likely in the context of Einstein’s 1917 cosmology (Schulmann et al. 1998, Doc. 319): +Whoever is not disturbed if the existence of a ggμμμμ field without field producing matter is possible according to the theory, and if a single mass (conceived as alone in the world) can possess inertia—that is someone not to be convinced of the necessity of the new step. + + + COREOPS 34 Philosophy of Physics DOI: 10.31389/pop.91 +Einstein’s commitment to Mach’s principle remained firm after all the deliberations concerning the de Sitter solution had been settled. He reaffirmed it in his 1921 Princeton lectures (Einstein 1923). Over several pages, he repeated his Machian-inspired cosmological analysis at length (110–119). It included his formulation of Mach’s principle: +If we think these ideas consistently through to the end we must expect thewhole inertia, that is, the whole ggμμμμ-field, to be determined by the matter of the universe, and not mainly by the boundary conditions at infinity (113, his emphasis). +The second physical condition was that an admissible cosmology must have a static line element in which, in particular, gg44 is constant. This condition had been carefully deduced in his 1917 cosmology paper from what he took to be the most basic of astronomical observations. He gave its starting point as +The most important fact that we draw from experience as to the distribution of matter is that the relative velocities of the stars are very small as compared with the velocity of light (Einstein, 1917a, 184). +Proceeding step by step from this observational foundation, Einstein deduced that, to close approximation, the metric for spacetime on a cosmic scale must be static, that is, in some coordinate systems, satisfy +gg44 = 1 aaaaaa gg14 = gg24 = gg34 = 0. +The added condition of the constancy of gg44 follows since, in the first approximation, it is the variability of gg44 alone that controls the acceleration of free bodies.27 A constant gg44 in the first approximation precludes any significant accelerations for the stars. The vanishing of the remaining metrical coefficient is not explained beyond “as always with static problems.” Presumably the intent is to preclude rotating coordinate systems in which Coriolis forces would appear. +This second condition completed the case for the rejection of the de Sitter hyperboloid as a viable cosmology. With the singularity of (7) reinterpreted as a mass concentration, this form of the de Sitter solution was compatible with Mach’s principle. The line element (7) was static in the sense that the metrical coefficients were independent of the time coordinate xx4 and conformed with gg14 = gg24 = gg34 = 0. However, its gg44 = cos2(rrrrrrrr2 was not constant and dropped to zero as the mass horizon was approached. The outcome was that free masses, such as stars, would be accelerated towards the cosmic masses at the mass horizon, just as we would expect from Newtonian intuitions. +This second condition was repeatedly stressed by Einstein as precluding the de Sitter line element of (7) as a viable cosmology. He wrote to de Sitter on June 14, 1917: +It seems to me that a reasonable interpretation of the world before us necessarily requires the approximate spatial constancy of the gg44, on account of the fact of the small relative motion of the stars (Schulmann et al. 1998, Doc. 351). +Einstein gave the same argument against the de Sitter line element (7) and in favor of his original 1917 cosmology in his letter of early June 1918 to Klein (Schulmann et al. 1998, Doc. 556):28 +If the world were really so [as (7) depicts], then the fixed stars must have tremendous speeds, so that their statistical distribution could be maintained [sich erhalten], on account of the colossal differences of gravitational potential which must be present between the different points of such a world. The non +27 As shown for example in Einstein (1923, 89). +28 It is unclear to me how Einstein imagines that a rapid motion could maintain the observed uniform distribution. + + + COREOPS 35 Philosophy of Physics DOI: 10.31389/pop.91 +existence of great star speeds compels us to believe that matter in the large is not distributed unduly non-uniformly over the world. +Einstein did not waver from this second condition. A careful recapitulation of it forms the second part of the case Einstein made for his cosmology in his 1921 Princeton lectures (Einstein, 1923, 113–119). +The combination of these two conditions finally elucidates a puzzle in Einstein’s (1918) discussion of March 6 of Mach’s principle and his λλ-augmented gravitation field equations. He there expressed his expectation that (243): +A singularity-free space-time-continuum with everywhere vanishing energy tensor of matter appears not to exist according to [λλ-augmented gravitational field equations]. +This is a curious remark for Einstein to make a year after de Sitter had shown that just such a solution exists in the full hyperboloid. We might charitably guess that Einstein was tacitly including a further condition that the solution sought must be static, for then the full de Sitter hyperboloid would be excluded. +That this was the case is indicated by the correction to this remark that Einstein made to Klein in his letter of June 20, 1918 (Schulmann et al. 1998, Doc. 567). We saw above his concession in that letter that “de Sitter’s world is, in itself, free of singularities.” That concession was immediately followed by recalling the condition that imposes a singularity onto the solution: “A singularity only comes about through the substitution that affords the transition to the static form of the line element.” A few lines later, Einstein elaborated: +My critical remark about the de Sitter solution requires a correction; there is in fact a singularity-free solution of the gravitational equations without matter. However, this world may in no way come into consideration as a physical possibility. For there can be no time tt specified so that the three-dimensional slicestt = const. do not intersect, and so that these slices are equal (metrically) to one another. +4.8 IN RETROSPECT +For all his certainty, Einstein’s position proved fragile. The astronomical affirmation of the expansion of the nebulae came within a decade by the end of the 1920s. It is fitting that Einstein and de Sitter (1932) co-authored a note in which the requirement of a static line element and the added λλ term in the gravitational field equations were both retracted. They posited a non-static, expanding Einstein-de Sitter spacetime, distinct from the 1917 de Sitter solution. Einstein’s defense of Mach’s principle collapsed by the time of the writing of his “Autobiographical Notes.” He dismissed Mach’s analysis (1949, 29) as inappropriate for a consistent field theory. Einstein’s λλ outlived him. More recent work in cosmology has found that it is needed to accommodate our astronomical observations. Our current λλ CDM model of cosmology indicates that, in the distant future, a λλ driven expansion of the universe will bring our cosmos ever closer to a rapidly expanding, de Sitter spacetime with asymptotically depleted matter. Einstein would surely not be pleased. +PART II: THE HISTORICAL CONTEXT +To examine Einstein’s treatment of these three singularities in isolation gives an incomplete picture of Einstein’s understanding of them. His work, as we shall see in this Part II, cohered with an analytic tradition in mathematics that has long fallen from favor in modern work in relativity; we shall see in the next Part III that his treatment of singularities conformed with one of the most enduring themes of Einstein’s work in physics, his sustained efforts to eliminate arbitrariness from physical theories. + + + COREOPS 36 Philosophy of Physics DOI: 10.31389/pop.91 +5. ANALYTIC AND SYNTHETIC GEOMETRY +Einstein’s privileging of the analytic approach was not a capricious partition of a homogeneous body of mathematics in distinct parts. For centuries, two traditions—the analytic and the synthetic—had cohabited in geometrical writings in a fertile synergy. The existence of the two traditions was a commonplace of mathematics when Einstein began his work on general relativity. The leading geometer of his time, Felix Klein, wrote a series of volumes intended for mathematics teachers in the high schools. The second volume on geometry derived from lectures Klein gave in the summer semester of 1908. In them, he wrote:29 +However, I should like to add to this account an explanation of the difference between analytic and synthetic geometry, which always plays a part in such discussions. According to their original meaning, synthesis and analysis are different methods of presentation. Synthesis begins with details, and builds up from them more general, and finally the most general, notions. Analysis, on the contrary, starts with the most general, and separates out more and more the details. It is precisely this difference in meaning which finds its expression in the designations synthetic and analytic chemistry. Likewise, in school geometry, we speak of the analysis of geometric constructions: we assume there that the desired triangle has been found, and we then dissect the given problem into separate partial problems. +In higher mathematics, however, these words have, curiously, taken on an entirely different meaning. Synthetic geometry is that which studies figures as such, without recourse to formulas, whereas analytic geometry consistently makes use of such formulas as can be written down after the adoption of an appropriate system of +coordinates. Rightly understood, there exists only a difference of gradation between these two kinds of geometry, according as one gives more prominence to the figures or to the formulas. Analytic geometry which dispenses entirely with geometric representation can hardly be called geometry; synthetic geometry does not get very far unless it makes use of a suitable language of formulas to give precise expression to its results. Our procedure, in this course, has been to recognize this, for we used formulas from the start and we then inquired into their geometric meaning (1909, 110–112, emphasis in original). +The difference sketched here by Klein is the age-old difference between Euclid’s and Descartes’ geometries. It is so important to the present paper that we give a banal example to illustrate it and to show how it can become problematic. +We recover the same result in Cartesian geometry by means of the two variables xx and yy and a linear relation over them: +AAAA A AAAA A A (15) +for real constants AA and BB. If the variables xx and yy are understood to be the coordinates of a Euclidean two-dimensional surface, this is the equation of a straight line through the origin (0,0). The isotropy of the possible dispositions of such lines is recovered from the leading idea of Klein’s “Erlangen Program”: each geometry is defined by the invariants of its characteristic group. The group of affine transformations: +xx′ = aaxx a aaaa aa′ = ccxx a ccaa (16) +29 The English translation here from the third edition ( 1939, 55) matches the German of the first 1909 edition in this passage. + + + COREOPS 37 Philosophy of Physics DOI: 10.31389/pop.91 +for real constants aa, bb, cc and dd, is sufficient to characterize the isotropy of the disposition of these lines. Under the action of this group, the line represented by (15) is mapped to every other possible straight line passing through the origin. The totality of the lines is an invariant structure that is mapped to itself by the affine transformations (16). That fact is expressed most compactly as a formal property of a symbolic equation: the covariance of the equation (15) under the affine transformations of the variables (16). +We can see how easily the compatibility of the two approaches can be disturbed. Assume that, instead of representing straight lines by the linear relations (15), we had proposed a functional dependence of the variable yy on xx: +yy y yyyy (17) +for a real constant C. In this representation, the line along the yy-axis corresponding to xx x x becomes anomalous. It corresponds to something like the constant C taking an infinite value, or, perhaps, more carefully, all possible values of y must correspond to the single value of the variable xx x x. The condition that (17) is a function is violated. The anomaly persists, even allowing for the covariance of (17) under affine transformations, in so far as an affine transformation would need to contradict the functional property of (17) to eradicate the anomaly. There is, of course, no corresponding anomaly in the Euclidean representation. +For definiteness, we summarize the key ideas of the two approaches. They share the same elements: the notion of a geometric space or surface; and algebraic equations in variables adapted to the surfaces. The key difference is which takes priority: +Synthetic approach: The geometric surfaces or spaces are the primary subject of investigation. The equations serve as an analytic means of describing them and anomalies in the equations may be neglected if they do not correspond to anomalies in the spaces. +Analytic approach: The equations and their transformations are the primary subject of investigation. The geometric surfaces and spaces are supplementary and sometimes merely have an heuristic role in aiding in the construction ofsuitable equations. +The two approaches are complementary. It would be difficult to pursue modern work in spacetime theories without employing both. However different theorists will differ in the emphasis placed on each. In the most extreme example of the analytic approach, the geometric connections are all but completely suppressed. This happens so routinely that we now scarcely notice it. The volume VV and temperature TT of an ideal gas are related linearly, with the constant of proportionality fixed by the mass of the gas sample. Geometrically, each of these linear relations are represented by a straight line in VVVV space. This geometric fact is relegated to elementary didactics, if it is noticed at all. We would dismiss tensions between the geometry and analysis as anomalies of the geometry. The straight line along the TT-axis where VV V V does not represent a sample of gas of zero mass that retains its zero volume at all temperatures. Rather it represents no gas at all. +Einstein, we have seen, favored the analytic approach heavily and gave its equations priority over the geometrical surfaces investigated in the synthetic approach. +6. TWO TRADITIONS IN EINSTEIN’S TIME +In the early twentieth century, when Einstein was developing his general theory of relativity, he drew on two manifestations of the analytic and the synthetic approaches. + + + COREOPS 38 Philosophy of Physics DOI: 10.31389/pop.91 +Synthetic geometry contributed to his theory through Gauss’ theory of surfaces, and the analytic approach contributed through Christoffel’s theory of the invariants of quadratic differential forms. While the connections between them were obvious, the two had developed as independent mathematical traditions.30 +6.1 GAUSS’ THEORY OF SURFACES +Gauss’ theory of surfaces provided the geometrical component of the foundations upon which general relativity is built. It was developed by Gauss in several documents in Latin in the 1820s. They are collected and translated into English as Gauss (1902). The theory considered a two-dimensional surface of varying curvature with coordinates p and q, embedded in a three-dimensional Euclidean space, with coordinates xx, yy, and zz. The distance between neighboring points in the Euclidean space was given by the linear element √dddd2 + dddd2 + dddd2 and the corresponding linear element in the curved surface was given by (e.g., 1902, 20, 47): +√EEEEEE2 + 2FFEEEEEEFF + FFEEFF2 (18) +for EE, FF and GG suitable functions of pp and qq. Gauss then computed the curvature at each point of the surface from the radii of curvature of sections by normal planes (1902, 15, 97) and also the curves of shortest distance (e.g., 1902, 97). The embedding in the Euclidean space was only an artifice used by Gauss to derive the geometrical self-contained properties of the two-dimensional curved surface, which could be understood without reference to the embedding space. +The extension of Gauss’ theory to higher dimensional spaces was undertaken at Gauss’ instigation in Riemann’s (1854) celebrated Habilitationsvortrag, “On the Hypotheses which lie at the Foundations of Geometry.” Gauss had embedded his two-dimensional curved surfaces in a higher dimensional Euclidean space. Riemann sought to extend Gauss’ analysis without using the artifice of an embedding space. Lacking a serviceable notion in then existing mathematics, Riemann struggled awkwardly to introduce the key concept: an nn dimensional manifold of points (n fach ausgedehnten Mannigfaltigkeit = nn-fold extended manifold). He would then turn to the metrical relations defined on these manifolds. +When Einstein was developing general relativity, Gauss’ theory had developed into what had then come to be called “differential geometry.” The authoritative work was “BianchiLukat” (Lukat 1910). It is Max Lukat’s authorized German translation of the second expanded edition of Luigi Bianchi’s Lezioni di geometria differenziale. While it introduces now familiar analytic mathematics associated with quadratic differential forms, it is a work of synthetic geometry. The analytic methods are secondary to its primary focus, the geometry of spaces and surfaces. What are their metrical properties? What are their curvature and geodetic properties? Which coordinate systems are usefully adapted to them? Which are the conformal transformations of the coordinates? It is an expansive work that continues in this vein for 24 chapters and over 700 pages. +6.2 THEORY OF QUADRATIC DIFFERENTIAL FORMS +Through Gauss’ introduction of the line element (18), quadratic differential forms became the foundational analytic structure of the geometry of spaces of variable curvature. The mathematics of these differential forms could, however, be investigated independently of +30 See Reich (1994, 184) for more discussion of how the two programs of research in geometry and analysis remained distinct at the time of Einstein’s discovery of general relativity, even though connections between the two programs were then recognized. + + + COREOPS 39 Philosophy of Physics DOI: 10.31389/pop.91 +their application in geometry. Such investigation provided the analytic component that figured prominently in the mathematics used by Einstein in his general theory of relativity. +A foundational work historically in these investigations is Christoffel’s (1869) “On the transformations of homogeneous differential expressions of the second order.” The project of the paper is laid out in its first paragraphs. +In the differential expression +FF F ∑ ωωiiiii∂∂∂∂ii∂∂∂∂ii; iii ii F ii ii iiiiii +the coefficients ωω are arbitrary functions of the variables xx1, xx2, ... xxnn that are independent of one another. If, instead of the latter, one introduces a system of functions of the new variables xx′1, xx′2, ... xx′nn that are [also] independent of one another, then FF goes over into a new differential expression +FF′ = ∑ ωω′iiiii∂∂∂∂ii′∂∂∂∂′ii +that is equal to the original by virtue of the substitution carried out. +Conversely if the differential expressions FF and FF′ are given, then one can pose the question of which conditions are necessary, such that the one could be transformed into the other, and in case this is possible, which substitutions bring about the required transformation. +What is notable is what is present and what is not present in this opening statement. +The project is formulated fully within analysis in terms of formulae for FF and FF′, expressed as functions of the variables xx1, ... xxnn, It is to find substitutions of the variables under which the quantities FF and FF′ are equal, so that FF is invariant; and to determine conditions necessary for the existence of the substitutions. +The project is not formulated as one in geometry. The variables are not coordinates of a geometric surface; the invariant FF is not the metrical line element of such a surface; and the associate coefficients ωωiiiii are not coefficients of a metric tensor. They are simply functions of the variables indicated and the project is to ascertain their behavior under substitutions of the variables. +The analysis continues without any explicit connection to geometry. What we now know as the “Christoffel symbols” are introduced. What we now call the “Riemann-Christoffel curvature tensor” is introduced without any special fanfare or name. It is simply a quantity, denoted by four indices “(gkhi)” (1869, 54), that has a role in determining which transformations leave F unchanged. It is only in the last paragraph of the last page that a connection to geometry is made. Christoffel mentions that his quantity F is also known as the “square of the line element belonging to the space of three dimensions” and he directs his readers for details to Riemann’s celebrated, posthumously published Habilitationsvortrag of 1854. +This attribution marked the beginning of the now long-standing tradition of associating the origin of this four-index symbol “(gkhi)” with Riemann’s efforts to extend Gauss’ theory of curved surfaces in his address of 1854. As readers of Riemann’s Habilitationsvortrag know, this poses a historical puzzle. The quantity does not appear in the Habilitationsvortrag. For a work of such importance in geometry, it is striking for having few analytic expressions. Readers who persist in the quest for Riemann’s formulation of this quantity are directed to a later work in thermal physics, Riemann’s (1861) Commentatio. The quantity that comes to be known as the “Riemann-Christoffel curvature tensor” appears on page 95, in an + + + COREOPS 40 Philosophy of Physics DOI: 10.31389/pop.91 +equation that is labeled “(I).” The vanishing of the quantity in (I) is the condition under which a general quadratic differential form, written as ∑ bbιιιι′ ddddιιddddιι′, can be transformed into a simplified form, written as ∑ (ddddιι′ )2. +While later literature commonly presents this equation (I) as a direct development of the geometric ideas of Riemann’s Habilitationsvortrag, a study of this literature by Farwell and Knee (1990) finds no sound basis for this interpretation. Rather, they find that the equation is developed independently of the geometry. They locate it in the development of what they call “tensor analysis” and conclude: +Riemann did not consider the equivalence of forms in relation to geometry, but rather in the context of heat conduction. Riemann’s mathematical derivations in the second part of the “Commentatio” contain no reference to heat conduction, but equally they contain no reference to geometry. The one allusion to geometry is an illustration, which is not linked to heat conduction and does not obviously therefore serve as a ‘useful addition’ (237). +No doubt Riemann recognized the importance of his equation (I) in differential geometry. However, his development of it proceeded independently of the geometry and belongs within the tradition of the analysis of quadratic differential forms. +Ricci and Levi-Civita’s (1900) “Methods of the Absolute Differential Calculus and their Applications” continues in the analytic tradition of Christoffel. Its purpose is to present what it calls the “absolute differential calculus” as a method with many applications. Einstein’s use of the calculus in general relativity has led to it coming to be known as “tensor calculus” and for it to be connected almost inseparably with Einstein’s theory. Hermann’s (1975, ix) English translation, for example, renders Ricci and Levi-Civita’s “systèmes covariants et contrevariants” as “Covariant and Contravariant Tensors” and their “Quadrique fondamentale” [fundamental quadratic differential form] as “RiemannianMetrics.” (See Appendix: Einstein and Grossmann Generalize the Term “Tensor.”) +Ricci and Levi-Civita did not conceive their calculus as a theory of differential geometry. It was conceived as a general, analytic tool, one of whose applications lay in geometry. Modern readers, expecting a work in differential geometry, should pause at the opening sentence: +Let us denote by T a completely general transformation of variables (1) xxii = xxii(yy1, yy2, ..., yynn) +that is bijective and regular in the domain we will consider; ...(1900, 128) +The analysis concerns variables. These xx’s and yy’s are not, in general, coordinates. They are only identified as such when later sections apply the methods to geometry. Much of the article reviews applications outside geometry. Chapter III considers applications in analysis. Chapter V treats applications in mechanics, which we would now identify as Lagrangian and Hamiltonian mechanics. Chapter VI is labeled as applications in physics. It investigates various field equations, such as Laplace’s equation for a potential, vector formulations involving the divergence and curl, and the differential equations of electrodynamics and heat conduction. +The article does make many connections to geometry. Chapter II “Intrinsic geometry as an instrument of the calculus,” seeks to re-express the concepts of the calculus in geometric terms. It starts by identifying the quadratic differential form, expressed in terms of variables, with the line element of a geometry, expressed in terms of coordinates. A connection to Gauss’ theory of surfaces, however, is not made until Chapter IV “Geometric Applications.” Gauss’ theory is treated as something independent of the calculus. Ricci and + + + COREOPS 41 Philosophy of Physics DOI: 10.31389/pop.91 +Levi-Civita lament that the expositions of Gauss’ theory lack a unified method. Their goal is to apply their calculus to provide one: +The absolute differential calculus, on the contrary, leads to [a unified method] without any effort, by giving the theory as simple a form as possible (1900, 165). +We find a similar separation of the mathematics of quadratic differential forms in Wright’s treatise on quadratic differential forms. Its first “historical” chapter introduced the notion of a quadratic differential form through the line element of Gauss’ theory of surfaces. The chapter concludes by separating the general theory from this one application: +Thus far it is suggested that the invariants [of quadratic differential forms] are essentially connected with differential geometry. This is by no means the case. They are connected with a certain form, and any interpretation of this form leads to a corresponding interpretation for the invariants (1908, 4). +To illustrate other interpretations, Wright notes that kinetic energy in Lagrangian mechanics is expressed by a quadradic differential form in the mechanics generalized coordinates. +Decades later, after Einstein’s general theory of relativity had become the most prominent application of Ricci and Levi-Civita’s calculus, Levi-Civita still presented the absolute differential calculus as a method, distinct from differential geometry, which was one of its principal applications. Levi-Civita’s (1926) Absolute Different Calculus was given the parenthetic subtitle “(Calculus of Tensors).” This separation is marked by its care in distinguishing the variables of the calculus from the coordinates of a space. Chapter IV is devoted to problems in analysis. It opens with: +This chapter is devoted to the study of the effect on some analytical entities of a change of variables (61). +It continues with the specification of the notion of a transformation of variables: +Consider nn independent variables xx1 , xx2, ... xxnn, which we shall as usual denote collectively by xx, and suppose a transformation applied to them which leads to another set of nn independent variables xx; ... (61). +That this notion is, in principle, more general than the purely geometric notion, LeviCivita then explained: +The geometrical name for this operation is of course change of co-ordinates; ...” (1926, Levi-Civita’s emphasis). +7. EINSTEIN AND GROSSMANN ADOPT THE ABSOLUTE DIFFERENTIAL CALCULUS +We learn from later autobiographical recollections how Einstein came to the mathematical methods used in his general theory of relativity. He had by 1912 an already well-developed program of research that sought a generalization of the principle of relativity and a theory of gravitation. In it, extending coordinate transformations beyond the Lorentz transformation would figure centrally.31 After Einstein’s return to Zurich in August 1912, he approached a friend from his university days, the mathematician Marcel Grossmann, for assistance. Einstein’s description (1956, 16) of the problem posed to Grossmann is likely somewhat anachronistic: how could he find generally covariant equations that would govern the metric tensor ggiiii of spacetime. Grossmann searched the literature and found the work of Riemann, Ricci and Levi-Civita, that, Einstein recalled, extended Gauss’ theory of curved surfaces. Most important +31 See Norton (2020) for details. + + + COREOPS 42 Philosophy of Physics DOI: 10.31389/pop.91 +was what Grossmann soon called the “Riemann differential tensor” (Einstein and Grossmann 1913, 35) and, in slightly variant form, the “Christoffel four-index-symbol of the first kind” (36). +Einstein and Grossmann’s collaboration resulted in the first sketch of the general theory of relativity, the “Entwurf ...” or “Sketch ...” paper, Einstein and Grossmann (1913). It contained the first published exposition of the mathematical methods to be used in the developing theory. Einstein delegated the exposition of these methods to Grossmann’s “Mathematical Part.” Grossmann made quite clear at the outset that his exposition would be analytic in its orientation, reflecting Ricci and Levi-Civita’s approach. He began his exposition by acknowledging his primary sources, Christoffel’s (1869) and Ricci and Levi-Civita’s paper (1900, 23): +The mathematical aids for the development of the vector analysis of a gravitational field, which is characterized by the invariance of the line element +dddd2 = ∑ +μμμμ +ddddμμddddμμ, +goes back to the fundamental paper byChristoffel [(1869)] on the transformation of quadratic differential forms. Proceeding from Christoffel’s results,Ricci and LeviCivita [(1900)] have developed their methods of the absolute differential calculus, i.e. [absolute in the sense] of independent of the coordinate system. It enables the differential equations of mathematical physics to be given an invariant form. +The exposition that follows focused on analytic expressions and how they transform under coordinate transformations. The topics covered are standard and familiar to modern readers: the transformation rules for covariant and contravariant tensors, the conversions among covariant and contravariant tensors, the formation of new covariant quantities by covariant differentiation, and eventually the Riemann tensor. +Once one looks for it, it is striking that there is essentially no explicit mention of any geometrical ideas. The focus is narrowly on the transformation properties of various analytic expressions. The omission was no oversight, as Grossmann made clear, in an admission that modern readers might find startling: +... I have deliberately set aside geometrical aids, since, in my opinion, they contribute little to the intuitive understanding [Veranschaulichung] of the formation of concepts of the vector analysis (1913, 24). +This treatment by Grossmann became the template used by Einstein in his subsequent developments of the mathematical methods needed by his new general theory of relativity. It is used in Einstein’s (1914) review of the still incomplete general theory of relativity; his triumphant (1916) review of the completed theory; and his text-book like exposition (1923). +These expositions followed Grossmann’s approach of focusing on the transformation properties of analytic expressions and shared its aversion to geometrical aids. Presumably, this reflected Einstein’s comfort with the analytic approach. It conforms with the question within the analytic approach that Einstein put to Grossmann at the outset in 1912. He asked after an equation and its transformation behavior: +Is there a differential equation for the ggiiii that is invariant under non-linear coordinate transformations? (Einstein 1956, 15). +He did not ask the synthetic question of what spacetime geometry might generalize the principle of relativity and accommodate gravity. +There was an eclectic character to Grossmann’s exposition. He sought to use the methods of Ricci and Levi-Civita to subsume an existing literature of the vector analysis of four dimensional spacetimes. This vector analysis originated with Minkowski and was + + + COREOPS 43 Philosophy of Physics DOI: 10.31389/pop.91 +developed by Sommerfeld and Laue. One trace of this subsumption is the idiosyncratic use of the term “tensor” from vector analysis in the “Entwurf ...” paper. Its use subsequently became standard in both physics and mathematics. (For details, see Appendix: Einstein and Grossmann Generalize the Term “Tensor.”) In his introductory remarks, Grossmann sought to reassure his readers of the success of the subsumption: +... the greater generality of the concepts formed in [the new general vector analysis] gives it a clarity that the special cases often lack (1913, 23). +That the subsumption was successful may well be correct from Grossmann and Einstein’s perspectives. However, it had all but eradicated the synthetic-geometric perspective that Minkowski himself had advanced. In his celebrated popular lecture, “Space and Time,” Minkowski sought to suppress the analytic, that is, the emphasis on the transformation properties of the equations. He favored an elevation of the synthetic geometry in the concept of his four-dimensional world of spacetime. He wrote: +... the word relativity-postulate for the requirement of an invariance with the [Lorentz] group GGcc seems to me very feeble. Since the postulate comes to mean that only the four-dimensional world in space and time is given by phenomena, but that the projection in space and in time may still be undertaken with a certain degree of freedom, I prefer to call it the postulate of the absolute world (or briefly, the world-postulate) (1908, 83, his emphasis). +Einstein made clear that he eschewed Minkowski’s geometric conception of special relativity in the introduction to his 1916 review article on his general theory. He characterized the advance made by Minkowski as:32 +The generalization of the theory of relativity was facilitated greatly through the conception the special theory of relativity was given by Minkowski. This mathematician first recognized clearly the formal equivalence of the spatial coordinates and the time coordinate and made it usable for the construction of the theory (Einstein 1916, 769). +What is notable in Einstein’s characterization of the advance is Einstein’s omissions of the idea of spacetime and its geometry. He has reduced Minkowski’s contribution to one that is expressible in the analytic language of “formal equivalence” of coordinates. +8. EINSTEIN PRIVILEGES THE ANALYTIC +The methods Einstein and Grossmann introduced were an eclectic mix of ideas: geometrical ideas from Gauss’ theory of surfaces; analytic ideas from Christoffel’s treatment of the invariants of quadratic differential forms; and vectorial ideas from the mathematics used in electrodynamics and special relativity. All are present in one form or another. However, when Einstein had to choose among the ideas, he favored the analytic. In addition to the cases noted above, here are just a few more examples of this favoring that permeates Einstein’s treatments of general relativity. +8.1 VARIABLES OR COORDINATES? +We noted above that Ricci and Levi-Civita called their xx’s and yy’s “variables” when they were part of a general analysis of expressions. It was almost only when they applied their methods +32 This passage is from the first page of Einstein’s review article. This page was omitted from Einstein (1916a) in the later, widely read collection, The Principle of Relativity . + + + COREOPS 44 Philosophy of Physics DOI: 10.31389/pop.91 +to geometry that these variables were relabeled as “coordinates” (coordonnées). Einstein’s xx ’s and yy’s were almost always called “coordinates” (Koordinaten). On one occasion of critical importance in the physical interpretation of the general relativity, he slipped back into the language of variables. In his review article, Einstein (1916, 776–777) offered his “pointcoincidence” argument for the physical basis of a requirement of general covariance. We need not rehearse the content of the argument,33 but only note how he represented his xx’s: +... We allot to the universe four space-timevariables xx1, xx2, xx3, xx4, in such a way that for every point-event there is a corresponding system of values of the variables xx1 ... xx4. To two coincident point-events there corresponds one system of values of the variables xx1 ... xx4, i.e. coincidence is characterized by the identity of the coordinates. If, in place of the variables xx1 ... xx4, we introduce functions of them, xx′1, xx′2, xx′3, xx′4, as a new system of co-ordinates, ... (1916a, 117–118, my emphasis). +Correspondingly, the variables are not “transformed” as coordinates usually are said to be. The new variables are introduced as functions of the old variables. We find a similar reversion to variable language when Einstein formulates his requirement of general covariance. He wrote in emphasized text: +The general laws of nature are to be expressed by equations which hold good for all systems of co-ordinates, this is, are co-variant with respect to any substitutions whatever (generally covariant) (1916a, 117). +The term “substitutions” connotes the analytic operation of replacing one variable in an equation by another functionally dependent on it. +8.2 THE PRINCIPLE OF EQUIVALENCE +Einstein’s principle of equivalence played a central role both in Einstein’s discovery of his general theory of relativity and in his interpretation of the physical content of the theory. The principle, however, has proven quite recalcitrant to univocal interpretation. There is an expansive literature on the principle both struggling to understand its content and offering alternative versions of it.34 Here is the principle in Einstein’s review article: +For, if we now assume the special theory of relativity to apply to a certain fourdimensional region with the co-ordinates properly chosen, then the ggσσσσ have the values given in (4) [diagonal form]. A free material point then moves, relatively to this system, with uniform motion in a straight line. Then if we introduce new space-time co-ordinates xx1, xx2, xx3, xx4, by means of any substitution we choose, the ggσσσσ in this new system will no longer be constants, but functions of space and time. At the same time the motion of the free material point will present itself in the new co-ordinates as a curvilinear non-uniform motion, and the law of this motion will be independent of the nature of the moving particle. We shall therefore interpret this motion as a motion under the influence of a gravitational field. We thus find the occurrence of a gravitational field connected with a space-time variability of the ggσσσσ (1916a, 120). +This formulation asserts that a Minkowski spacetime in one set of coordinates has no gravitational field, but in another set of coordinates it does. This understanding has proven unintelligible to many later commentators. Synge’s lament is now classic. He described his role: +33 For details, see Giovanelli (2013). +34 See Norton (1985) and Lehmkuhl (2022) for a variety of attempts to provide a cogent reading of Einstein’s formulations. + + + COREOPS 45 Philosophy of Physics DOI: 10.31389/pop.91 +It is to support Minkowski’s way of looking at relativity that I find myself pursuing the hard path of the missionary (1960, ix). +Einstein’s principle of equivalence was singled out for exasperated disdain: +... I have never been able to understand this Principle. ... In Einstein’s theory, either there is a gravitational field or there is none, according as the Riemann tensor does not or does vanish. This is an absolute property; it has nothing to do with any observer’s world-line. Space-time is either flat or curved, ... +Synge’s lament gives pithy expression to the understanding of a synthetic geometer who takes the geometry of the spacetime to be primary: there is just one spacetime. Changing the coordinate system does not alter it physically. +Einstein’s account becomes intelligible if we allow that his was not the synthetic approach. What mattered to him were the analytic expressions. In one coordinate system, the analytic expressions represent the motion as a linear relation among the coordinates. In the other coordinate system, the analytic expressions represent the same motion as a non-linear relation among the coordinates. Since he was not proceeding in the synthetic approach, the spacetime geometry has merely a supplementary role and does not control the physical interpretation of the analytic expressions. Thus, Einstein can assign a different physical interpretation to each of the these differing analytic expressions. And he does. One corresponds to a gravitation-free case, the other to the presence of a gravitational field. +That analytic expressions related by a simple coordinate transformation can represent different physical situations will surely seem untenable if one takes the geometry of the spacetime as primary. A manuscript on special and general relativity by Einstein (1920), written but not published in 1920, shows how Einstein conceived the separation physically of the two expressions. After a lengthy discussion of special relativity, he turned to general relativity. His introduction of “The Basic Idea of the Theory of General Relativity in Its Original Form” in Part II, Section 15, took an unexpected turn. He recalled the thought experiment of the magnet and conductor from his discovery of special relativity. In an inertial frame in which a magnet is at rest, the magnet is surrounded by a pure magnetic field. If one transforms to an inertial frame moving with respect to the magnet, a new entity, an electric field, is produced by the time varying magnetic field in the new inertial frame.35 He concluded (his emphasis): +... the existence of the electric field was therefore a relative one, depending on the state of motion of the coordinate system used; and only the electric and magnetic fields combined could be granted a kind of objective reality, aside from the state of motion of the observer or, corr[espondingly], the coordinate system. +Einstein then recalled the “happiest thought of [his] life” that, in 1907, inspired the principle of equivalence and set him on the pathway to general relativity: +The gravitational field only has a relative existence, in a way similar to the electric field produced by magneto-electric induction (1920). +That is, the gravitational field of the accelerating coordinate system should be treated in the same way as the induced electric field. It has a relative existence depending on the coordinate system chosen, even if only the perspectives of both coordinate systems combined should be accorded objective reality. +35 For discussion of the importance of this thought experiment in Einstein’s discovery of special relativity, see Norton (2004). + + + COREOPS 46 Philosophy of Physics DOI: 10.31389/pop.91 +We need not labor too hard to convince ourselves of the cogency of these attributions of reality. All that matters here is that Einstein was convinced of their cogency. He was quite comfortable relating attributions of reality to observers’ states of motion. In his defense of the reality of the Lorentz length contraction, he summarized its status as: +... it [Lorentz contraction] is not “real” in so far as it does not exist for a comoving observer; however, it is “real” for a non-co-moving observer, i.e. [it is real] in that it can be demonstrated in such a way by physical means (Einstein 1911). +8.3 THE RIEMANN-CHRISTOFFEL TENSOR +Einstein’s treatment of the Riemann-Christoffel tensor again illustrates his privileging of the analytic expressions and their transformations over the geometry of the spaces. He wrote in his 1916 review article:36 +The mathematical importance of this tensor is as follows: If the continuum is of such a nature that there is a co-ordinate system with reference to which the ggμμμμ are constants, then all the [components of the Riemann-Christoffel tensor] BBμμρρμμμμ vanish. If we choose any new system of co-ordinates in place of the original ones, the ggμμμμ referred thereto will not be constants, but in consequence of its tensor nature, the transformed components of BBμμρρμμμμ will still vanish in the new system. Thus the vanishing of the Riemann tensor is a necessary condition that, by an appropriate choice of the system of reference, the ggμμμμ may be constants. In our problem this corresponds to the case in which,*[37] with a suitable choice of the system of reference, the special theory of relativity holds good for a finite region of the continuum (1916a, 141, his emphasis). +Here, Einstein’s interpretation follows closely the analytic understanding of Christoffel and Riemann in his analytic mode. The quantity provided necessary and sufficient conditions for one analytic expression—a quadratic differential form—to be transformed into another. +It also reaffirms Einstein’s interpretation of the principle of equivalence. Special relativity is recovered only after a coordinate system is adopted in which the metric is diagonalized. In other coordinate systems, such as those that are adapted to acceleration, a real gravitational field is present and we have left special relativity. +What matters for our purposes is this privileging of the analytic expressions. What matters also is what is missing: There is no mention of the geometry of spaces. Gauss’ treatment of the same result, in the case of a two-dimensional, positive definite geometry, directly expresses it in terms of the geometry of surfaces. It is his “remarkable theorem” (theorem egregium) Gauss wrote:38 +THEOREM. If a curved surface can be developed onto any other surface, the measure of curvature at every point remains unchanged. It is also evident that any finite part of a curved surface, after developing on another surface, will retain the same curvature. +36 Reich (1994) has also emphasized how Einstein’s article avoided the geometrical connotations of the Riemann-Christoffel tensor. She remarked, for example, on Einstein’s discussion of the tensor (210) “The word curvature does not even appear.” +37 Einstein’s footnote, his emphasis: “The mathematicians have proved that this is also a sufficient condition.” +38 My translation corrects the English translation of (Gauss 1902, 47) which combines sentences and drops some text from the original Latin. + + + COREOPS 47 Philosophy of Physics DOI: 10.31389/pop.91 +A special case, to which geometers have hitherto restricted their investigations, is that of surfaces developable onto a plane. Our theory automatically teaches that the measure of curvature of such surfaces at any point is = 0 (1828, 24–25, his emphasis). +Here, the older expression to be “developed” means to be mapped in a way that preserves metrical properties. A cylinder, for example, can be mapped onto a flat plane by unrolling the cylinder. +Gauss’ theorem egregium can be promoted to the spacetimes of special and general relativity. A version of it expresses the significance of the vanishing of the RiemannChristoffel tensor for those who privilege the geometry. An example arises in Eddington’s (1923) relativity text in Chapter 3, Section 36 (Eddington’s emphasis): +Hence the vanishing of the Riemann-Christoffel tensor is a necessary condition for flat space-time. This condition is also sufficient—if the Riemann-Christoffel tensor vanishes space-time must be flat. +Others gave essentially similar formulations at this time, such as in Tolman (1934, 186). +8.4 EINSTEIN ON MINKOWSKI +That Einstein’s understanding of the Riemann-Christoffel tensor so avoids geometrical conceptions is no aberration of the one example. We saw it already in Einstein’s assessment of the advance brought by Minkowski’s reformulation of Einstein’s 1905 special theory of relativity as a theory of spacetime (1916, 769). This striking assessment was repeated elsewhere. +We would now say that Minkowski’s contribution fundamentally reconfigured what we take the theory to be. In Einstein’s original formulation, it was a theory of the Lorentz transformation of physical quantities. Minkowski’s formulation introduced a new concept, spacetime, and special relativity became the theory of its geometry. That theory introduced geometric structures that were not present in Einstein’s formulation. They include the light cones that divide spacetime displacements into timelike, spacelike, and lightlike; a notion of four-dimensional distance in the spacetime, the interval; that moving bodies trace out four-dimensional, timelike worldlines; that hyperbolas are the geometric figures analogous to circles in Euclidean geometry; and so on. +In his popular Relativity, Einstein reported these geometric conceptions in a brief 17th chapter, after 16 chapters that recount the theory without them. When that already brief chapter came to report what was important in Minkowski’s reformulation of his theory, it identified nothing geometrical in conception. Rather, it identified how Minkowski’s work enabled a clarification of the formal expressions used in the theory: +But the discovery of Minkowski, which was of importance for the formal development of the theory of relativity, does not lie here. It is to be found rather in the fact of his recognition that the four-dimensional space-time continuum of the theory of relativity, in its most essential formal properties, shows a pronounced relationship to the three-dimensional continuum of Euclidean geometrical space. ... In order to give due prominence to this relationship, however, we must replace the usual time co-ordinate t by an imaginary magnitude √−1cccc proportional to it. Under these conditions, the natural laws satisfying the demands of the (special) theory of relativity assume mathematical forms, in which the time co-ordinate plays exactly the same ro1e as the three space coordinates. Formally, these four co-ordinates correspond exactly to the three space co-ordinates in Euclidean + + + COREOPS 48 Philosophy of Physics DOI: 10.31389/pop.91 +geometry. It must be clear even to the non-mathematician that, as a consequence of this purely formal addition to our knowledge, the theory perforce gained clearness in no mean measure (Einstein 1921, 38–39). +8.5 EINSTEIN AGAINST GEOMETRIZATION +One needs only a cursory review of Einstein’s writings on general relativity to see that he privileged analytic expressions over geometric conceptions. Geometric curvature is rarely mentioned. The transformations of analytic expression get thorough attention. Thus, it is the “Riemann-Christoffel tensor” whose significance lies in its control over which analytic expressions can be transformed into which others. It is not, as it soon came to be called,39 the “Riemann-Christoffel curvature tensor” that measures the geometric curvature of space or spacetime. +It was plausible that this emphasis in Einstein’s writing merely reflected a disinterest in geometric conceptions. Lehmkuhl (2014) has shown that this is not so. In several writings, Einstein took issue with the idea that general relativity had in some sense “geometrized” gravity. For example, Einstein wrote a review of Émile Meyerson’s La deduction relativiste. In it, Einstein rebuked Meyerson for seeing in relativity a program of “the reduction [Zurückführung] of all concepts of the theory to spatial, or rather geometrical, concepts” (Lehmkuhl 2014, 318).40 On the contrary, Einstein found that the idea of physics tracing back [“führe...zurück”] to geometry has no clear meaning. He concluded: +The fact that the metric tensor is denoted as “geometrical” is simply connected to the fact that this formal structure first appeared in the area of study denoted as “geometry”. However, this is by no means a justification for denoting as “geometry” every area of study in which this formal structure plays a role, not even if for the sake of illustration, one makes use of notions which one knows from geometry. Using a similar reasoning Maxwell and Hertz could have denoted the electromagnetic equations of the vacuum as “geometrical” because the geometrical concept of a vector occurs in these equations. +Einstein offered an alternative conception. The goal of his relativistic work is unification, such as the unification of gravity and electricity then attempted by Weyl and Eddington (and of course Einstein’s own efforts at a unified field theory). Lehmkuhl illustrated how general relativity itself was regarded by Einstein as unifying earlier ideas of gravity and inertia. +Einstein’s treatment of the same issue a year earlier shows his impatience with the idea of geometrization. Hans Reichenbach had been working on Hermann Weyl’s efforts to extend general relativity to electromagnetism.41 In a letter to Einstein of April 24 1926, Reichenbach had argued that the “geometrical representation of electricity” is “nothing more than a graphical representation and amounts, therefore, to nothing physical at all” (Kormos et al. 1918, 412). Einstein agreed and reinforced Reichenbach’s deflation in a letter to him ofApril 8, 1926: +You are completely right. It is preposterous to believe that “geometrization” means something essential. It is for me a kind of novice aid [Eselsbrücke] for the discovery of numerical laws. Whether one attaches a “geometrical” conception to a theory is an inessential private matter. The essential thing with Weyl is that +39 For example in Bergmann (1942. Part II, Ch. XI). +40 The French text for these passages is in Einstein and Metz (1928, 164–165). Lehmkuhl (2014, 318) has located Einstein’s original German text that was translated into French by Metz. My extracts are from Lehmkuhl’s translation of this German text. +41 For further details of Reichenbach’s negative views about geometrization, see Giovanelli (2022; 2023, §2) and Lehmkuhl (2014). + + + COREOPS 49 Philosophy of Physics DOI: 10.31389/pop.91 +he subjects the formulas to a new condition (“gauge invariance”) as well as invariance with respect to [spacetime] transformations (Kormos et al. 2018, 424). +Einstein’s reaction, once again, suppresses the geometry in favor of privileging the transformational behavior of formulae. +Einstein’s description of geometrization as an “Eselsbrücke” requires some reflection. It is literally “donkey bridge” and its meaning in Einstein’s time and now is an artificial aid, such as (presently) a mnemonic. It has a geometric connection that may be important. It is the German translation of the Latin pons asinorum. The term designates Theorem 5 in Book 1 of Euclid’s Elements. It owes its name to the bridge-like form of the figure and its reputation as the theorem whose understanding would first defeat someone without good geometrical abilities. A geometrical donkey could not pass over the bridge to the rest of Book 1. To reflect all these considerations, the term is translated here as “novice aid.” +The sense in which Einstein took geometrical considerations to be such a novice aid might be well captured by his use in his 1917 cosmology paper, described above, of a fictional four-dimensional space to introduce the line element of the spherically curved threedimensional space of his new cosmology. It is an artifice that speeds us to the result, but is no basis for concluding that there is factually a higher dimensional space into which the three-dimensional space curves. He wrote of it: +The four-dimensional Euclidean space from which we started serves only to define conveniently [zur bequemen Definition] our hypersurface (1917, 149). +The same point is made again of this construction in Einstein’s Princeton lectures: +The aid of a fourth dimension has naturally no significance except that of a mathematical artifice (1923, 115, fn). +The notion of geometrization assailed in these exchanges with Meyerson and Reichenbach by Einstein may well be stronger than that of the synthetic conception outlined in this paper. If Einstein’s “reduction” [Zurückführung] has the same meaning as “reduction” in the more recent literature in philosophy of physics, then the reduction of gravitation to geometry would be akin to Maxwell’s reduction of light to electromagnetic radiation. If that notion is what Einstein intended, then he was well within his rights to reject it. +The modern, synthetic conception of geometrization is weaker. It is just that the interval s and the metric tensor ggiiii are properties of an independently existing structure. It is called “geometrical” since it generalizes the structure that is the subject of Euclidean geometry. Einstein may well be right that a careful examination would find this terminology to be meaningless. But that does not dismiss the idea of the structure itself and that it is the primary object of investigation in general relativity. His exchanges with Meyerson and Reichenbach gave Einstein the opportunity to recognize the structure and endorse the corresponding synthetic viewpoint. He did not. Instead, he recalled analytic expressions and their transformations. +PART III. EINSTEIN, SINGULARITIES, AND ARBITRARINESS +9. SINGULARITIES IN MATHEMATICS AND PHYSICS +The term “singularity” has powerful connotations today. We believe that the entirety of our universe sprang explosively from a singular big bang. The greatest menace offered by our physics is the voracious singularity at the heart of a black hole. At both, we expect + + + COREOPS 50 Philosophy of Physics DOI: 10.31389/pop.91 +physical conditions so extreme as to outstrip all imagination. The term has proliferated in the popular conscience. “The singularity” is foretold as the moment when self-reinforcing technological change transforms human civilization in unforeseeable ways. The idea is yet another touched by the great John von Neumann. According to Stanislaw Ulam (1958, 7), he contemplated “...the ever accelerating progress of technology and changes in the mode of human life, which gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue.” +The apocalyptic or perhaps just radical aura surrounding the notion of a singularity was not present in the mathematics and physics of Einstein’s time. In technical contexts,42 the notion figured primarily in mathematical work. There was no sense of a catastrophic threat or ominous breakdown. Rather a division into singular and non-singular behavior was part of the routine taxonomy of mathematical structures. To be non-singular was merely a frequent antecedent condition in useful theorems. +A result now familiar was also familiar then. As reported in Bocher (1907, 66),43 in linear algebra, a linear transformation of variables is many-to-one and has no inverse if the determinant of the matrix of transformation coefficients is zero. Then, the transformation and the matrix are both said to be “singular.” Of relevance to metrical geometry is a result shown later in Bocher (1907, Ch. X). A quadratic form of rank rr, Σ1nnaaiiiixxiixxii, can always be reduced to a sum of squares by a non-singular transformation of the variables. +In this benign vein, talk of singularities was pervasive in the literature in differential geometry in the first decades of the twentieth century. Fowler gave a general characterization of them in curves in which the usually applicable, general treatments break down (his emphasis): +These cases of exception correspond to exceptional points on the curve, usually such that there are only a finite number in any finite region, at which the curve has some peculiar property such as a stationary tangent, a point of inflexion, exceptionally high order contact with its circle of curvature or its envelope, etc. All such points at which the curve possesses peculiar properties may be considered to be singular points on the curve... (1920, 80). +He continued to note that it is usual to restrict the term to cases in which certain first derivatives vanish. +One index of the ubiquity of the notion in geometry is provided by Volume 3, Part 3, of the authoritative Teubner Encyclopedia, Meyer and Mohrmann, (1902–1927) that is devoted to differential geometry. The terms “singular” and “singularity” (singulär, singularität) appear 162 times in a volume of over 800 pages.44 They are used to describe singular points and their higher dimensional analogs, singular lines and surfaces. +Discussion of singularities was almost entirely restricted to the mathematical literature. While they arose also in physical applications in field theories, their presence commonly produced little if any comment. When they were recognized, they were not found to be so troublesome +42 The most common use of the term, however, was in non-technical discourse where it just designated a form of uniqueness. For example, Taylor’s (1813, 261) inventory of synonyms records it in the context of human personality types as: “The word singularity is applied by a natural hyperbole to any rare form of behaviour; to any unusual degree of peculiarity.” +43 The condition that matrices be non-singular is so important that the term “non-singular” appears 472 times in the text; and the term “singular” appears 142 times. +44 The volume consists of article spanning two decades. They are dated 1902, 1902, 1903, 1903, 1903, 1914, 1920, 1921 and 1923. + + + COREOPS 51 Philosophy of Physics DOI: 10.31389/pop.91 +as to require any remedial action. Chapter IX on Spherical Harmonics of Maxwell’s Treatise begins with a lengthy section “On Singular Points at which the Potential becomes Infinite.” In the simplest case, Maxwell (1873, 157) considered the potential VV at a place rr distant from electricity ee condensed to a point with spatial coordinates (aa, bb, cc). The potential VV is given by his equation “(1)” and is VV V VVVVV. Maxwell reported the singular behavior: +At the point (aa, bb, cc) the potential and all its derivatives become infinite, but at every other point they are finite and continuous, and the second derivatives of VV satisfy Laplace’s equation (1873, 157). +He then reflected on the troublesome character physically of this result: +Hence, the value of VV , as given by equation (1), may be the actual value of the potential in the space outside a closed surface surrounding the point (aa, bb, cc), but we cannot, except for purely mathematical purposes, suppose this form of the function to hold up to and at the point (aa, bb, cc) itself. For the resultant force close to the point would be infinite, a condition which would necessitate a discharge through the dielectric surrounding the point, and besides this it would require an infinite expenditure of work to charge a point with a finite quantity of electricity (1873, 157). +Maxwell’s solution was, in effect, to ignore any oddity at the infinite point itself and confine consideration to the region surrounding it and approaching arbitrarily closely to it (Maxwell’s emphasis): +We shall call a point of this kind an infinite point of degree zero. The potential and all its derivatives at such a point are infinite, but the product of the potential and the distance from the point is ultimately a finite quantity e when the distance is diminished without limit. This quantity ee is called the charge of the infinite point. +Maxwell’s tame treatment of singularities seems, however, to be the exception. They were otherwise largely ignored in the German electrodynamics literature. “Abraham-Foeppl” (1918) was the standard German language textbook on Maxwell’s electrodynamics in Einstein’s time. It made no mention of singular points in its fields. In its treatment of point sources (Quellpunkte) in Chapter 14, it noted that the radially-directed, vector force due to a point source of charge ee diminishes with distance rr from the source as eeeee2. The text remarks that this quantity “becomes infinite, if one enters the source point,” but says nothing more. There is no suggestion that this infinity might be troublesome. Sommerfeld (1904–1922) is the volume of the Teubner Encyclopedia that treats electrodynamics. Articles from 1902 to 1906 occupy the first five hundred pages.45 The term “singular” appears just twice in incidental roles. +I have found one exception from Einstein’s time. Mie (1912/1913) developed a theory of matter based on a modification of Maxwell’s electrodynamics. A major goal was to find a solution of the theory’s equations for the static, spherically symmetric field for an electron. The bulk of the second part of Mie’s paper is devoted to examining the singularities that appear in the static spherically symmetric solutions, especially at radial coordinate rr r r and rr r r. His goal, according to Pauli (1958, 192) was an everywhere regular solution, which he failed to recover. +45 The next article is Pauli’s review of relativity theory of 1920 and then, finally, a 1921 article on the electron theory of metals. + + + COREOPS 52 Philosophy of Physics DOI: 10.31389/pop.91 +Einstein surely knew of this work of Mie, a prominent physicist whose work was taken up by David Hilbert. Einstein entered into a correspondence with him in 1917 and 1918.46 Mie’s work is discussed briefly in Einstein’s (1919, 349) early attempt to use gravitation theory in a theory of elementary particles and again in Einstein and Grommer (1927, 3). Einstein judged Mie’s theory as unsatisfactory. I have found no evidence that Mie’s treatment of singularities played any role in Einstein’s thought. In any case, Einstein had no need of Mie’s theory to suggest to him the idea of representing particles as singularities. Einstein (1909, 824–825) had already speculated that light quanta could be incorporated into electromagnetic theory if the quanta were themselves to singularities in the field. +10. EINSTEIN AGAINST AND FOR SPACETIME SINGULARITIES +Einstein’s treatments of singularities poses two puzzles. The first—“against”—arises from the discussion of the last section. Until Einstein’s work on general relativity, singularities had little presence in physical theorizing. They were certainly not the theoretical anathema portrayed by Einstein. Why did Einstein choose to vilify them? +The second puzzle—“for”—is why, in spite of his vilification of singularities, they made several appearances in his theorizing. This second puzzle attracted comment from Earman and Eisenstaedt: +... it should be emphasised how flexible and adaptable, how much of an opportunist Einstein was with respect to singularities. At first singularities were to be regarded with such horror that the presence of a singularity in the De Sitter solution was sufficient to disqualify it from serious consideration. But shortly thereafter singularities that correspond to mass concentrations are to be welcomed (at least on a provisional basis), for then De Sitter’s solution can be accommodated without compromising the precious Mach principle (1999, 194). +Elsewhere (1999, 186), they describe Einstein’s use of singularities in his collaborative treatment of the problem of motion in Einstein, Infeld and Hoffmann (1938). Einstein is, they report, “always an opportunist” and the result is an unsuccessful “pact with the devil.” +This section will offer solutions to both puzzles. To the first, Einstein’s antipathy to singularities derived from an enduring and deep-seated presumption, fundamental to all his work in relativity. It is the requirement that arbitrariness must be eliminated from physical theory. To the second, we recall that general relativity was, for Einstein, only an intermediate theory on the way to his unified field theory. General relativity, by itself, did not represent matter adequately. Its singularities can mark where general relativity fails and the unified field would be needed to represent matter. Until that unified field theory was secured, the singularities could serve as a surrogate for that matter. Even then, Einstein’s decision to admit singularities provisionally was made within the confines of the ultimate goal of eliminating arbitrariness. We shall see that the limited use of singularities was, in Einstein’s estimation, the least arbitrary of the options available. +These issues are developed mostly within Einstein’s search for his unified field theory. For helpful surveys of Einstein work on his unified field theory, see Sauer (2014) and van Dongen (2010). +46 Schulmann et al. 1998, Docs. 346, 348, 407, 410, 416, 421, 456, 460, 465, 470, 488, 493, 532. + + + COREOPS 53 Philosophy of Physics DOI: 10.31389/pop.91 +10.1 AGAINST SINGULARITIES +Einstein did not initially harbor an aversion to singularities. Rather, his attitude agreed with the generally untroubled acceptance noted above in his contemporary literature that radially symmetric fields have a singularity at the source point. Such acceptance was implicit in Einstein’s (1909, 824–825) speculation that light quanta may themselves be singularities of the field. Einstein himself made the connection to this earlier literature in a letter to Henrik Lorentz of May 23, 1909 (Klein et al. 1993, Doc 163): +Rather I believe that light is grouped around a singular point in a way similar to how we are used to assuming for electrostatic fields. +He glossed the supposition to Jakob Laub in a letter of May 19, 1909 (Klein et al. 1993, Doc 161) as “Linear differential equations with singularities.” The supposition of linearity is important. Einstein’s light quantum hypothesis was that, thermodynamically, in the high frequency Wien regime, light quanta are mutually independent. This independence is directly recoverable if the field equations are linear, since multiple solutions can be superposed by simple addition4.7 +A change in Einstein’s attitude coincided with the completion of his general theory of relativity and the move towards a unified field theory. It changed in time to ground Einstein’s criticism of de Sitter’s solution to his λλ-augmented gravitational field equations. Prior to the singularity’s recharacterization as a “mass-horizon,” its presence was sufficient grounds for Einstein to dismiss the solution. His letter to de Sitter of July 31, 1917 (Schulmann et al. 1998, Doc. 366) began: +However I may conceive it, I cannot ascribe any physical possibility to your solution. The difficulty has to do with the fact that in the (naturally measured) finite the ggμμμμ assume singular values. +We saw above that, in 1922, in response to a query from Hadamard, Einstein characterized the realization of the singular Schwarzschild radius as “an unimaginable misfortune [malheur] for theory...” In their joint paper, Einstein and Rosen (1935, 73) deplored singularities as nullifying the laws of a theory. (Their formulation is quoted in Subsection 10.3 below.) The search for singularity-free solutions was a prominent, stable feature of Einstein’s attempts at a unified field theory. He wrote, +The most important question related to the (strict) field equations is that of the existence of singularity-free solutions, which could represent electrons and protons (1930, 23). +Similarly, Einstein and Mayer wrote: +According to our conviction, a satisfactory field theory must manage with a singularity-free description of the total field, therefore also of the field inside corpuscles (1932, 130). +In his popular, “Physics and Reality,” Einstein expressed it this way: +What appears certain to me, however, is that, in the foundations of any consistent field theory, the particle concept must not appear in addition to the field concept. The whole theory must be based solely on partial differential equations and their singularity-free solutions (1936, 306–307). +47 As Einstein and Infeld (1949, 210) note, the failure of linearity becomes important in Einstein’s later attempts to represent particles by singularities, for otherwise interactions between particles would be impossible. +48 The series of dashes is an older German convention to mark the end of a section. I include the German here since the standard translation in the Schilpp volume is weak. It is: “The question is: What are the everywhere regular solutions of these equations?- - -” + + + COREOPS 54 Philosophy of Physics DOI: 10.31389/pop.91 +We can gauge the importance to Einstein of these singularity-free solutions by his choice of the question that closes the final page of his “Autobiographical Notes” (Einstein 1949, 94).48 +Die Frage ist: Was für im ganzen Raume singularitatsfreie Losungen dieser Gleichungen gibt es?- - +The question is: what sort of singularity-free solutions are there of these equations?- - +It is a poignant question, since it is written with the understanding that his decades of work towards his unified field theory were incomplete. +That Einstein opposed singularities in field theories is clear. What remains to be answered is the question of why he opposed them. The answer comes from an enduring supposition in Einstein’s thought. We should be striving for physical theories free of arbitrariness, he held. Einstein’s aversion to singularities is simply part of that project. +This supposition may seem less important compared to the more visible demands Einstein made on physical theories: the principles of relativity, Mach’s principle and determinism in quantum systems. However, a closer look at all of these more visible demands shows that they share a common aversion to arbitrariness. This commonality is not emphasized in Einstein’s earlier writings and it is quite plausible that he did not recognize its importance or even its presence. It emerges explicitly in Einstein’s later writings. Presumably it did so since it served his needs in addressing the physical issues of his later theorizing. The abandoning of Mach’s principle in his later years also made it possible for the aversion to arbitrariness that lay behind it to become a more explicit concern. +This aspect of Einstein’s thought has attracted less attention from historians. An exception is Don Howard’s (1992) study of the Eindeutigkeit [uniqueness] principle in philosophical work contemporary with Einstein. This demand for uniqueness, Howard argued, underlies Einstein’s insistence that we not admit a violation of determinism in general relativity in the context of the “hole argument.” A failure of uniqueness, we might note, amounts to the introduction of arbitrariness into our physical theorizing. +Perhaps the most explicit formulations came in his “Autobiographical Notes.” Einstein listed two conditions for the evaluation of physical theories. The first was compatibility with empirical facts. The second he found much harder to articulate. We favor “naturalness” and “logical simplicity,” where he used quotation marks for both terms in deference to the difficulty of precisely defining them. The related “inner perfection” of a theory, Einstein noted, is enhanced if the theory is not chosen arbitrarily: +The following I reckon as also belonging to the “inner perfection” of a theory: We prize a theory more highly if, from the logical standpoint, it is not the result of an arbitrary choice among theories which, among themselves, are of equal value and analogously constructed (1949, 23). +A later version revealed that Einstein’s discomfort with arbitrariness was so deeply rooted that he could provide no deeper foundation for it.We have come to the deepest of his convictions: +... I would like to state a theorem which at present can not be based upon anything more than upon a faith in the simplicity, i.e., intelligibility, of nature: there are no arbitrary constants of this kind; that is to say, nature is so constituted that it is possible logically to lay down such strongly determined laws that within these laws only rationally completely determined constants +￿￿.￿ EINSTEIN AGAINST ARBITRARINESS + + + COREOPS 55 Philosophy of Physics DOI: 10.31389/pop.91 +occur (not constants, therefore, whose numerical value could be changed without destroying the theory)- - - (63, Einstein’s emphasis). +Once we know to look for it, we find the elimination of arbitrariness figuring in many places in Einstein’s thought. Here are some examples that, retrospectively, can be seen to share the commonality, although we cannot assume that this was explicitly recognized by Einstein at the time. +Einstein used the elimination of arbitrariness in characterizing the motivation for the 1905 special theory of relativity. Its key innovation was the recognition of the relativity of simultaneity; and that was possible, Einstein recalled,49 only after an arbitrariness in earlier theories were identified: +... all attempts to clarify this paradox [of the chasing of light] satisfactorily were condemned to failure as long as the axiom of the absolute character of time, viz., of simultaneity, unrecognizedly was anchored in the unconscious. Clearly to recognize this axiom and its arbitrary character really implies already the solution of the problem (1949, 53). +What became Mach’s principle was, for Einstein, a way of eliminating the idea of inertial systems of reference or inertial spaces as primitive posits in physical theories prior to general relativity. They were, as Einstein put it, “bloss fingierte Ursache”—“merely fictitious causes” (1916, 771, his emphasis). Earlier, Einstein explained his concern as, +What is unsatisfactory is that it remains unexplained how inertial systems could be distinguished from all other systems (1913, 1260). +That is, their designation is an arbitrary element in these prior theories. In a letter to Lorentz of January 15, 1915, he was forceful in his insistence on the elimination of this arbitrariness: +Of two things KK1 and KK2 that are equally justified in their definitions, one is distinguished without a physical basis (that is in principle accessible to observation)—My confidence in the logical consistency of natural events bristles against this most strongly [sträubt sich ... aufs kräftig[st]e]. In my view, a world picture that does without this sort of arbitrariness is preferable (Schulmann et al. 1998, Doc. 47). +This form of unacceptable arbitrariness arose in Einstein’s cosmological reflections through the possibility of stipulating boundary conditions for the metric field at spatial infinity. It is worth examining his concerns here in more detail since he will elsewhere treat the arbitrariness of singularities as being of the same type. +In his cosmology paper (Einstein 1917), he considered the case in which the metric field might be stipulated to adopt special relativistic limiting values as spatial infinite is approached. This might be the case, for example, if the cosmology consisted of a central collection of masses in an otherwise empty space. Such boundary conditions, Einstein continued, would violate the principle of relativity, in so far as they introduce a preferred reference system; and it would be unstable according to statistical physics (1917, 147). The objection that attracted most discussion, however, was that it would violate what he would soon call Mach’s principle: +... we fail to comply with the requirement of the relativity of inertia. For the inertia of a material point of mass mm (in natural measure) depends upon the +49 Complaints about the arbitrariness of theories appear elsewhere in Einstein’s (1949) recollections, such as 31, 37 (arbitrariness of older field theories) and 55 (arbitrariness in assumption of existence of rigid bodies). + + + COREOPS 56 Philosophy of Physics DOI: 10.31389/pop.91 +ggμμμμ; but these differ but little from their postulated values, as given above, for spatial infinity. Thus inertia would indeed be influenced, but would not be conditioned by matter (present in finite space). If only one single point of mass were present, according to this view, it would possess inertia, and in fact an inertia almost as great as when it is surrounded by the other masses of the actual universe (1917a, 183, Einstein’s emphasis). +In his Princeton lectures, Einstein had put a quantitative measure on how much arbitrariness is introduced by stipulating these boundary conditions: +The hypothesis that the universe is infinite and Euclidean at infinity, is, from the relativistic point of view, a complicated hypothesis. In the language of the general theory of relativity it demands that the Riemann tensor of the fourth rank RRiiiiiiii shall vanish at infinity, which furnishes twenty independent conditions, while only ten curvature components RRμμμμ, enter into the laws of the gravitational field. It is certainly unsatisfactory to postulate such a far-reaching limitation without any physical basis for it (1923, 110). +Einstein then gave a terser formulation: +If we think these ideas consistently through to the end we must expect the whole inertia, that is, the whole ggμμμμ -field, to be determined by the matter of the universe, and not mainly by the boundary conditions at infinity (1923, 114, his emphasis). +10.3 AGAINST THE ARBITRARINESS OF SINGULARITIES +Why did Einstein so oppose singularities in his theories? Einstein and Rosen gave the answer. After recalling the presence of singularities in present theories, they wrote in a revealing passage:50 +... writers have occasionally noted the possibility that material particles might be considered as singularities of the field. This point of view, however, we cannot accept at all. For a singularity brings so much arbitrariness into the theory that it actually nullifies its laws. ... Every field theory, in our opinion, must therefore adhere to the fundamental principle that singularities of the field are to be excluded (1936, 73). +Thus, elsewhere in his popular “Physics and Reality,” after discussion the prospects of matter-free theories, Einstein continued: +How are we to proceed from this point in order to obtain a complete theory of atomically constituted matter? In such a theory, singularities must certainly be excluded, since without such exclusion the differential equations do not completely determine the total field (1936, 312). +50 The ellipses contain an embarrassing oversight. Einstein and Rosen justify their conclusion by recalling a solution of the gravitational field equations with two singularities at relative rest and thus not able to represent particles that attract. It was an embarrassing oversight since Einstein had earlier determined that the solution’s singularity filled an axis connecting the points. For details see Lehmkuhl (2019 , §5, fn. 61). This oversight may have strengthened Einstein and Rosen’s resolve in choosing the strong verbiage of “nullify.” However, the aversion to singularities did not weaken in later work, after Einstein presumably had the occasion to recognize the oversight. + + + COREOPS 57 Philosophy of Physics DOI: 10.31389/pop.91 +Several pages later, he asserted the positive result: +As a matter of fact, up to now we have never succeeded in a field-theoretical description of corpuscles free of singularities, and we can, a priori, say nothing about the behavior of such entities. One thing, however, is certain: if a field theory results in a representation of corpuscles free of singularities, then the behavior of these corpuscles in time is determined solely by the differential equations of the field (320, his emphasis). +If we reflect on familiar examples of singularities in spacetime theories, Einstein’s point is straightforward. Most simply, singular solutions are associated with parameters that must be set externally. In modern cosmology, for example, to recover a specific matter content of the universe, we need to augment a big bang cosmology by fixing the early density of matter emerging from the initial singularity.51 That fixing is done empirically by projecting backwards from present conditions. +While singularities may introduce some arbitrariness,52 uncontrolled by the theory’s differential equations, how did Einstein and Rosen come to conclude the far stronger claim that they nullify the laws of a theory? The answer is that Einstein equated the introduction of singularities into a theory with the arbitrary stipulation of boundary conditions. The connection was made explicitly by Einstein in a later appendix on the theory of the nonsymmetric field, added to his Princeton lectures, Meaning of Relativity. The appendix is poignant, since it concludes with a recognition by Einstein in his final years, that then present mathematical methods were simply not adequate to developing his long-sought goal: a theory of particles whose exact solutions are free from singularities. In the midst of this concession, Einstein equated singularities with boundary conditions, which he regarded as then ineliminable: +A field theory is not yet completely determined by the system of field equations. Should one admit the appearance of singularities? Should one postulate boundary conditions? As to the first question, it is my opinion that singularities must be excluded. It does not seem reasonable to me to introduce into a continuum theory points (or lines, etc.) for which the field equations do not hold. Moreover, the introduction of singularities is equivalent to postulating boundary conditions (which are arbitrary from the point of view of the field equations) on ‘surfaces’ which closely surround the singularities. Without such a postulate the theory is much too vague. In my opinion the answer to the second question is that the postulation of boundary conditions is indispensable (1956a, 164). +First, we can see how this equation can be sustained. Consider the Schwarzschild line element above +dddd2 = − 1 +1 − 2mm +rr +dddd2 − dd2(dddd2 + sin2ddddθθ2) + (1 − 2mm +dd ) dddd2. (5) +51 Einstein, as we might expect, took a dim view of the singularity (1956a, 124): “The introduction of a such a new singularity seems problematical in itself.” +52 Perhaps Einstein also drew on the result that, in general, including singularities in a field greatly increases the size of the solution space of its governing differential equation and thus the extent of stipulations needed to identify the solution sought. The simplest example is that Laplace’s equation ∇2φφ φ φ, for a potential φφ, has a unique solution φφ φ φ if we assume φφ vanishes at spatial infinity. Non-trivial solutions are only possible if we introduce singularities that play the role of charges. Einstein certainly knew this elementary result and used it in his solving of his weak field gravitational field equations in Einstein (1913, 1259). + + + COREOPS 58 Philosophy of Physics DOI: 10.31389/pop.91 +It represents a one-parameter family of line elements satisfying the usual set of symmetry conditions and boundary conditions. If the parameter mm is set to zero, we recover the line element of special relativity. Some other stipulation is needed to designate a different solution. We would now just specify a non-zero value for mm. We could alternatively proceed as Einstein indicated. We could stipulate as another boundary condition that the sphere at radius rr r rr for all tt, εε ε ε, has the metrical component ggtttt = (1 − 2mmm(mm m mmm). +Another way to see the similarity that Einstein does not give is merely to replace the radial coordinate rr by an impact coordinate uu u uuuu. Then the Schwarzschild line element becomes53 +dddd2 = − 1 +uu4(1 − 2mmuum dduu2 − 1 +uu2 (dddd2 + sin2ddddθθ2m + (1 − 2mmuumddmm2, +The usual boundary condition is that as rr r r, ggtttt → 1 and ggrrrr → −1. This same boundary condition is now relocated to the origin at uu u u, where it reappears as a singularity in which gguuuu → −∞. +If Einstein treated the introduction of a singularity in the same way as the boundary conditions at infinity in cosmology, we can see why the introduction of such singularities might nullify the laws, for that nullification occurred in the cosmology. If we posit special relativistic boundary conditions at infinity, in Einstein’s example, that arbitrary boundary condition all but completely determines the inertial properties of bodies in the spacetime. +10.4 FOR SINGULARITIES: SINGULARITIES AS SURROGATES FOR MATTER +Given Einstein’s view of the corrupting role of singularities, we must ask why, in some contexts, he seemed quite comfortable with singularities. Einstein’s tolerance for these singularities is explained by two factors. First—to be discussed in this subsection—they were not to be taken seriously, physically, but merely marked where the source-free theory of spacetime failed and an unarticulated matter theory would take over. Second—to be discussed in the next subsection—Einstein tolerated singularities temporarily as the less arbitrary choice on the way to his long-term goal, a singularity free, unified field theory. +The use of singularities as surrogates for matter is a repeated device in Einstein’s work. Einstein and Rosen (1936) identified the singularity in a uniformly accelerated coordinate system as representing matter. Einstein reconciled himself to the singularity in the de Sitter solution by identifying it as a matter concentration. Elsewhere, Einstein sought to recover the equations of motion of free, massive particles without positing the geodesic equation by investigating the motions associated with singularities according to his source-free gravitational field equations. An earlier attempt was in his collaboration with Jakob Grommer (Einstein 1927; Einstein and Grommer 1927). A later attempt came in his collaboration with Leopold Infeld and Banesh Hoffmann (Einstein, Infeld and Hoffmann 1938). +The justification for treating singularities as a surrogate for matter was simple: As long as the matter was spatially concentrated in a small volume, then the space outside this matter filled volume would be governed by Einstein’s source-free gravitational field equations. The plausible supposition was that collapsing an already concentrated matter distribution into a singular point would not greatly alter the surrounding spacetime. Thus, the spacetime surrounding a singularity could be used as a serviceable approximation for the spacetime surrounding a concentrated matter distribution. +53 Using dddd d dddddd2)dddd. + + + COREOPS 59 Philosophy of Physics DOI: 10.31389/pop.91 +This justification was given by Hilbert in his lectures from the summer semester of 1916. He wrote: +These mathematical difficulties [of solving the gravitational field equations] impede us, already f[or] e[example] in the construction of a single, neutral point mass. If we could construct such a neutral mass and if we could know the course of the in the neighborhood of this position, and if we let the neutral mass degenerate ever more towards a point mass, then the gg would turn out to be a singularity at this point. We would have to regard such [a thing] as allowed in the sense that the ggμμμμ outside the immediate vicinity of the singularity correctly returns the process truly realized in nature. Now we must have before us such a singularity in [line element (5)]. Furthermore, we can say that the construction of a neutral point mass, even if it becomes possible later, will turn out to be so complicated that, for the applications in which one does not consider the immediate vicinity of the point mass suffering from a singularity, it has become possible already now to calculate with sufficient accuracy the approximately correct gravitational potentials (1916, 253, his emphasis). +Hilbert included a similar, briefer assessment in his influential 1916 “Foundations of Physics”: +Although, according to my understanding, only regular solutions represent immediately the reality of the physical, fundamental equations, solutions with non-regular points are still directly an important mathematical means for approximating characteristically regular solutions. In this sense, according to the processes of Einstein and Schwarzschild, the non-regular measure [line element (5)] at rr r r and rr r rrrrr is to be seen as the expression for the gravitation of a centrally symmetrically distributed mass in the vicinity of the null point. ... In the same sense, a point mass is also to be conceived as the boundary case of a certain distribution of electricity around a point. Indeed, I foresee in this place deriving the equations of motion of them from my physical fundamental equations (1916a, 70–71). +In keeping with Hilbert’s view, it became standard in early expositions of general relativity to treat the singularity at the Schwarzschild radius as sufficiently problematic physically as to be physically impossible. The routine response was that real masses must always have a size larger than this radius. For example, after announcing that the singularity at the Schwarzschild radius cannot be eliminated by a coordinate transformation, Laue continued: +One must indeed conclude from this that each mass mm, if of spherical form, necessarily has a radius greater than that corresponding to the value rr r rrrrrrr2 [Schwarzschild radius]. And in fact we so far know of no contradictory case, also not with atomic nuclei (1921, 215). +Eddington’s text drew a similar conclusion: +There is a singularity at rr r rrr, so that the particle must have a finite perimeter not less than 4ππππ (1923, 186). +Einstein’s attempts, in his collaboration with Grommer and with Infeld and Hoffmann, clearly depend on this orientation.54 That is, they suppose that a singularity will behave +54 The cogency of Einstein’s approach has been debated. Tamir (2012) has elaborated the critique that it is nonsensical to talk of the motion of a singularity, since a singularity is not a locus of events in the spacetime. Lehmkuhl (2017) has sought to vindicate Einstein’s approach by arguing that the motions traced in Einstein’s constructions do not need to be that of a true singularity but only a highly concentrated matter distribution. + + + COREOPS 60 Philosophy of Physics DOI: 10.31389/pop.91 +sufficiently like a free mass to enable the recovery of the equations of motion of the free mass. Lehmkuhl (2017; 2019) has given an extensive analysis of Einstein and Grommer’s collaborative work and of further issues surrounding it. He concluded that: +... the singularity should be interpreted to signify a placeholder or a blind spot of the theoretical treatment, rather than something that should be interpreted literally, as referring and approximately true (2017, 212). +Einstein, Infeld, and Hoffmann proceeded explicitly with the same understanding. They recognized that the surrogacy of singularities for masses is an empirical assumption that may fail: +It is of significance that our equations of motion do not restrict the motion of the singularities more strongly than the Newtonian equations, but this may be due to our simplifying assumption that matter is represented by singularities, and it is possible that it would not be the case if we could represent matter in terms of a field theory from which singularities were excluded (1938, 66). +They identified the security of their results in the security of the theory in the surrounding matter- and singularity-free regions: +For, although the equations of the field are undefined at the singularities, their validity in the regular region is sufficient to determine the motion of these singularities (80). +We see the same attitude elsewhere in Einstein’s reaction to what became known as the “big bang” singularity in expanding universe cosmologies. Einstein and de Sitter (1932) had presented a simple expanding universe cosmology. In it, the scale factor increases with cosmic time tt as tt2/3, so that there is a curvature and matter density singularity at t = 0. In their paper, Einstein and de Sitter made no mention of this time dependence or of this initial singularity. Presumably, it did not attract their serious attention. The time dependency is only given later by Einstein in a little-known 1933 article on cosmology, reported by O’Raifeartaigh et al. (2015). There, Einstein presumed that a breakdown in the assumption of the uniform distribution of matter would mean that their equations no longer apply close to the initial timett t t. +In an appendix to the 1937 second edition of his Princeton lectures, Einstein now included a more reflective assessment: The present general theory of relativity would likely break down in the early universe so that a singularity is not assured:55 +The theoretical doubts are based on the fact that for the time of the beginning of the expansion the metric becomes singular and the density, ρρ, becomes infinite. In this connexion the following should be noted: The present theory of relativity is based on a division of physical reality into a metric field (gravitation) on the one hand, and into an electromagnetic field and matter on the other hand. In reality space will probably be of a uniform character and the present theory be valid only as a limiting case. For large densities of field and of matter, the field equations and even the field variables which enter into them will have no real significance. One may not therefore assume the validity of the equations for very high density of field and of matter, and one may not conclude that the ‘beginning of the expansion’ must mean a singularity in the mathematical sense. All we have to realize is that the equations may not be continued over such regions (Einstein 1956a, 129). +55 A footnote a few pages earlier gave a terser assessment (Einstein 1956a, 124): “It may be plausible that the theory is for this reason inadequate for very high density of matter. It may well be the case that for a unified theory there would arise no singularity.” + + + COREOPS 61 Philosophy of Physics DOI: 10.31389/pop.91 +10.5 SINGULARITIES AS THE LESSER ARBITRARINESS +In using singularities as surrogates for matter, Einstein had not abandoned his enduring goal of eliminating arbitrariness from his physical theorizing. His goal remained a unified field theory of matter in which particles were represented within regular solutions, free from the arbitrariness of singularities. We saw, above, through the 1936 proposal of Einstein-Rosen bridges, that Einstein was even willing, at least temporarily, to alter his source-free gravitational field equations if it would lead to a singularity-free account of particles. +The enduring difficulty for Einstein was that this prized unified field remained tantalizingly beyond his reach. If he could not realize a theory free of arbitrariness, then, as a practical matter, he could seek to reduce the arbitrariness in his theories. His treatment of singularities conformed with this practice. +Einstein’s assimilation of the singularity in de Sitter’s cosmological solution as a mass horizon lay loosely within this conception. It was not a problem he had sought. De Sitter had pressed it on him. The singularity arose, we saw, through Einstein seeking a static gravitational field within de Sitter’s solution. Then, through the concept of the mass horizon, Einstein could conform the singularity with Mach’s principle and thereby to his goal of limiting arbitrariness, even if the de Sitter solution itself was not Einstein’s choice for a cosmology. +The project of a more sustained investigation of singularities that was chosen by Einstein concerned the use of singularities to recover the motion of free bodies. There is some evidence that Einstein came to this use of singularities as surrogates for matter after an early reluctance. In the text of his Princeton lectures of 1921, he reflected on the failure of then present theories to produce a serviceable theory of the inner structure of charged particles. A footnote abjured the use of singularities to represent the charged particles: +It has been attempted to remedy this lack of knowledge by considering the charged particles as proper singularities. But in my opinion this means giving up a real understanding of the structure of matter. It seems to me much better to give in to our present inability rather than to be satisfied by a solution that is only apparent (Einstein 1923, 55). +These hesitations were gone by the time of his collaboration with Grommer.56 Their joint paper, Einstein and Grommer (1927, 3) described the state of electrodynamics and other field theories as disturbing (“störend”) and blemished (“Schönheitsfehler”) in having two foundational laws. A partial differential equation governs the fields and a total differential equation governs the motions of particles. While arbitrariness is not mentioned explicitly, the goal is to reduce the arbitrariness by eliminating one of the foundational laws. +Einstein and Grommer then consider whether the same “duality,” as they call it, is to be found in general relativity. They described three approaches. The first was just to duplicate the duality by positing, as an independent law, that material points move on geodesics. The second was to introduce an energy tensor for matter. It follows from the gravitational field equations that such a tensor must obey a conservation law in the form of its vanishing divergence. They abandoned this approach, they reported, since it had been unable to account for elementary particles using continuous fields; and for other unspecified reasons. The third approach was to conceive of elementary particles as singularities. In his +56 Lehmkuhl (2019, §4) attributes a leading role in the transition to Einstein’s correspondence with the physicist, Yuri Rainich. + + + COREOPS 62 Philosophy of Physics DOI: 10.31389/pop.91 +review of them, Lehmkuhl called the second and third the “TT approach” and the “vacuum approach” (2017, 1204). +This third approach is the one Einstein and Grommer pursued. They summarized their project in emphasized text: +However, it has turned out that the law of motion of the singularities is completely determined by the field equations and by the character of the singularities, +without needing supplementary assumptions. To show this is the goal of the present investigation (Einstein and Grommer 1927, 4). +If Einstein and Grommer succeed in this goal, they have reduced the arbitrariness in the duality of fundamental laws. +A little over a decade later, Einstein’s collaborative efforts with Infeld and Hoffmann proceeded on the same basis. This time, they rejected Lehmkuhl’s “TT approach” because of the uncontrolled arbitrariness it introduces. The paper states this in its first sentences: +In this paper we investigate the fundamentally simple question of the extent to which the relativistic equations of gravitation determine the motion of ponderable bodies. +Previous attacks on this problem ... have been based upon gravitational equations in which some specific energy-momentum tensor for matter has been assumed. Such energy-momentum tensors, however, must be regarded as purely temporary and more or less phenomenological devices for representing the structure of matter, and their entry into the equations makes it impossible to determine how far the results obtained are independent of the particular assumption made concerning the constitution of matter (Einstein, Infeld, Hoffmann 1938, 65). +That is, choosing a specific stress-energy tensor means that the final results are not general, but depend on the particular form of matter represented; and these particulars may in turn not be fundamental, but merely reflect the superficial appearance of the matter at hand (“phenomenological”). This hesitation over the TT approach had already been reported by Einstein in his 1936 “Physics and Reality.” There he expressed it in the form of a celebrated metaphor: +It [general relativity with a stress energy tensor TT] is sufficient-as far as we know-for the representation of the observed facts of celestial mechanics. But it is similar to a building, one wing of which is made of fine marble (left [geometric] part of the equation), but the other wing of which is built of low-grade wood (right [matter] side of equation). The phenomenological representation of matter is, in fact, only a crude substitute for a representation which would do justice to all known properties of matter (1936, 311). +In his “Autobiographical Notes,” Einstein later summarized how the project had eliminated an arbitrariness from general relativity that had to be removed: +In the relativistic theory of gravitation, it is true, the law of motion (geodetic line) was originally postulated independently in addition to the field-law equations. Afterwards, however, it became apparent that the law of motion need not (and must not) be assumed independently, but that it is already implicitly contained within the law of the gravitational field (Einstein 1949, 79). + + + COREOPS 63 Philosophy of Physics DOI: 10.31389/pop.91 +Einstein both sought to eliminate singularities from his theorizing and, at the same time, found them useful in theorizing. We may well wonder if Einstein recognized that this could give his theorizing a capricious appearance. He did recognize the problem and we have his answer, again in his “Autobiographical Notes”: +Now it would of course be possible to object: If singularities are permitted at the positions of the material points, what justification is there for forbidding the occurrence of singularities in the rest of space? This objection would be justified if the equations of gravitation were to be considered as equations of the total field. [Since this is not the case], however, one will have to say that the field of a material particle may the less be viewed as a pure gravitational field the closer one comes to the position of the particle. If one had the fieldequation of the total field, one would be compelled to demand that the particles themselves would everywhere be describable as singularity-free solutions of the completed field-equations. Only then would the general theory of relativity be a complete theory (Einstein 1949, 81, Einstein’s emphasis). +Lehmkuhl’s concluding remarks give a quite serviceable recounting of Einstein’s answer, drawing on Einstein’s earlier work: +Finally, we now understand how Einstein could have allowed for singularities to account for matter in GR, yet be adamant that no singularities were allowed to occur in the sought-after unified field theory. It was the hybrid character of GR that allowed for this double standard: it was exactly because it was not supposed to be an adequate theory of matter that it was acceptable to allow for singularities as place-holders of matter. But it was not acceptable to allow for singularities in the domain about which GR was supposed to be fundamental, correct: regions of spacetime with only gravitational fields, free of matter. Accordingly, a unified field theory of gravity and matter would have to live up to these latter, stricter standards: no singularities anywhere (2019, 189). +11. CONCLUSION +In their synoptic analysis of Einstein’s treatments of spacetime singularities, Earman and Eisenstaedt, in a moment of exasperation, prescribe the challenge taken up in this paper: “But as we will see, much of the early work on spacetime singularities seemingly defies explanation” (1999, 193). What I hope this analysis has demonstrated is that Einstein’s treatment of singularities was not capricious and ill-informed. Rather, it was part of a well thought out research program that did not turn out to be productive. +Einstein followed an established tradition in mathematics that took analytic expressions to be the primary subjects of analysis; geometric notions play only an heuristic role. A geometric structure could suggest corrections to the analytic expressions, but those corrections need only to be accepted if they conformed with other physical facts. In both cases of the singularities Einstein identified at the Schwarzschild radius and in the de Sitter solution, the geometry suggested a correction in which events distinct in the analytic expressions were to be identified. From the geometric perspective, the coordinate systems used had “gone bad.” However, both corrections required Einstein to give up something he believed was required by the physical facts of the two cases, the static character of his line elements. The analytic expressions prevailed and the singularities remained. + + + COREOPS 64 Philosophy of Physics DOI: 10.31389/pop.91 +In retrospect, the more productive approach would have been to accept the geometric correction and discard the static requirement as Einstein had formulated it. That this approach would prove to be more productive could not be known a priori. It is only with the later advances in physics and astrophysics that its superiority becomes apparent. Contrary to Einstein’s supposition, there is no pathology in a Schwarzschild spacetime at the Schwarzschild radius. Rather, that radius merely marks an event horizon. The physics within it has attracted considerable attention. Similarly, de Sitter’s solution turns out not to represent a static spacetime. The full de Sitter hyperboloid recovered from the geometry is the simplest case of an expanding universe, whose expansion is driven by the cosmological constant λλ. In present cosmologies, it may prove to be the fate of our universe in the distant future. +Puzzlement over how Einstein could neglect these geometrical directives has obscured what may well be the more interesting question historically: How did singularities play a role in Einstein’s research? There was little concern prior to Einstein about singularities in physical theories. It was Einstein who identified them as troublesome and developed a program of research that demanded their elimination. His goal was distinctively and even idiosyncratically Einstein: an elimination of arbitrariness from physical theory. His fiercely defended and then abandoned Mach’s principle was just one instrument serving this larger goal. Singularities, Einstein argued, introduced unacceptable arbitrariness into physical theories, comparable to that introduced by arbitrary boundary conditions. They had to go. +While never abandoning the hope for a unified field theory, free of singularities, Einstein sought to minimize the arbitrariness in his physical theories as an intermediate towards that final theory. This minimization underwrote Einstein’s use of singularities to represent point masses in his attempts to identify the equations of motion that governed them. While these singularities would be unacceptable in his final, unified field theory, Einstein judged them to introduce less arbitrariness into the analysis than the available alternatives: simply positing the geodesic law as an independent law; or seeking an energy tensor to represent matter separately from the metric field. +APPENDIX A: EINSTEIN AND GROSSMANN GENERALIZE THE TERM “TENSOR.” +Where Ricci and Levi-Civita (1900) had used the terms “covariant and contravariant systems” (systèmes covariants et contrevariants), Einstein and Grossmann used the term “tensor” as a generic replacement for “system” and applied it in the now familiar way to all systems transforming linearly under first derivatives of the coordinates (1913, 25).57 That this was a novel use of the term “tensor” was noted in contemporary literature, such as Budde (1914, 246) and later by Veblen (1927, 28). How Einstein and Grossmann chose this idiosyncratic substitution remains an open question. The term tensor was used by Hamilton in his work on quaternions as a measure of the unsigned magnitude of quantities. It was chosen by Hamilton to reflect the idea that a length in space is extended if a tension is applied (1853, 56–58). This seems to have been the common use of the term in mathematics in the nineteenth century. Föppl’s introduction to Maxwell’s electrodynamics followed Hamilton’s usage (Föppl 1894, 6). “Tensor” designated the scalar magnitude of vectors. Since this scalar magnitude is of great importance in Maxwell’s theory, it is not surprising that the term appears 72 times in Föppl’s volume. Given the youthful +57 Reich (1994) is an expansive and detailed study of the development of what became known as the “tensor calculus” and also of the introduction and use of the term “tensor.” + + + COREOPS 65 Philosophy of Physics DOI: 10.31389/pop.91 +Einstein’s early fascination with Maxwell’s theory, it is quite likely that he had contacted the volume. It was the premier German language exposition of Maxwell’s theory during Einstein’s youth.58 This prolific use of the term “tensor” did not survive long in treatises on electrodynamics. In Abraham’s (1904) “completely reworked” (vollständig umgearbeitet) second edition of Föppl’s 1894 volume, this use of tensor is replaced by the more familiar “scalar” (Skalar) (4–6). The term “tensor” played only a minor role in the new exposition through the notion of a “tensor triple” (Tensortripel), which corresponds to the modern notion of a 3x3 Cartesian tensor. It figured in rotational mechanics (§14) and fluid flow (§17). This novel use of the term “tensor” had been introduced explicitly by Voigt (1898) in his work on the mechanics of crystals. He recognized (vi, 20) the prior use of the term in the theory of quaternions but felt that the extension to the multi-component quantity was admissible, since this quantity would be used to represent stresses and strains in materials three-dimensional materials. +APPENDIX B: A FANCIFUL FIELD THEORY +The line element +dddd2 = dddd2 + dd2dddd2, (B1) +with 0 ≤ rr r r and 0 ≤ θθ θ θθθ, where we assume the expression cyclic in θθ, such that, for each rr, θθ and θθ θ θθθ designate the same point. It is one of the simplest cases in which we routinely judge that a coordinate system has “gone bad.” For, when this line element represents the metrical geometry of a Euclidean surface, the one point at the origin at rr r r is assigned all the angular coordinates 0 ≤ θθ θ θθθ. Correspondingly, we have singular behavior in the coefficients of the metric tensor. While ggθθθθ = 0, we have the more troublesome ggθθθθ = ∞. The singularity is dismissed as a mere coordinate artefact. +Are we compelled to this dismissal? Might rr r r identify an infinity of distinct points, according to the different values of 0 ≤ θθ θ θθθ? The example of the Euclidean surface is so familiar that it is easy to assume that such an identification is simply a novice blunder in mathematics whenever the analytic expression (B1) appears. Familiarity is not the same as mathematical necessity. That the coordinate system in an analytic expression of the form (B1) has “gone bad” at rr r r is not a mathematical necessity. Whether it has gone bad depends on how the variables are interpreted physically and, in this case, the physical assumption that a Euclidean surface is represented. +To see that the physical interpretation of the variables really does control whether rr r r is a singularity in expression (B1), we merely need to concoct a physical scenario in which rr r r does represent a singularity in the physics. The following fanciful physical theory is not intended as a serious physical theory but merely to demonstrate that, under some interpretations, rr r r in (B1) is singular. +The theory is set in a two-dimensional space that is topologically R≥0 × SS, that is, a truncated cylinder, shown in Figure 11. No presumption is made about the spatial metric for the space. It will not be needed. What matters is that each coordinate pair (rr,θθ) identifies a unique point in the space, including when rr r r. There are point charges in the space that interact through retarded potentials. That is, the action of one charge upon another is delayed by a time that is a function of the distance between the charges. In such theories, the retardation time is commonly isotropic in distance and is given by (distance)/cc. +58 Frank’s (1979, 38) biography asserts positively that Einstein did read the Föppl volume. + + + COREOPS 66 Philosophy of Physics DOI: 10.31389/pop.91 +In this fanciful theory, the retardation times are defined in terms of coordinate differences and are anisotropic. In the rr coordinate direction, the retardation time dddd for a coordinate differential dddd, with dddd d d, is just dddd d dddd. In the θθ coordinate direction, the retardation time dddd for a coordinate differential dddd, with dddd d d, is just dddd d dddddd. We stipulate that the general case is governed by the line element of the same form as (B1)59 +dddd2 = dddd2 + dd2dddd2. (B2) +This line element specifies a temporal distance between points in the space that mimics a spatial, metrical distance. +As rr approaches 0, the retardation times exhibit extreme behavior. That is, if we pick two points separated by Δθθ θ θ, with Δrr r r, the retardation time decreases with rr as +Δtt t ttΔtt +as shown in Figure 11 for Δθθ θ θ. +At rr r r, the retardation time is Δtt t t. The line element (B2) has become singular. As before, the associated metrical coefficients are ggθθθθ = 0 and ggθθθθ = ∞. However, we cannot escape the singularity by declaring that the coordinates (rr,θθ) have “gone bad” at rr r r. By stipulation, they have not. Indeed, the singularity is an essential part of the physics. For, while is it mathematically inconvenient, the singularity has a natural physical interpretation: At rr r r, the interaction has become an instantaneous action at a distance with zero retardation time. +ACKNOWLEDGMENTS +My special thanks are owed to Harrison Payne, who read and commented extensively on drafts of this text. I thank Diana Kormos Buchwald, Michel Janssen, and Dennis Lehmkuhl for helpful comments. +Figure 11 Retardation Times in a Fanciful Field Theory. +59 This formula is not the same as assuming that the velocity components of the retarded action sum by the Pythagorean formula. + + + COREOPS 67 Philosophy of Physics DOI: 10.31389/pop.91 +COMPETING INTERESTS +The author has no competing interests to declare. +AUTHOR AFFILIATIONS +John D. Norton orcid.org/0000-0003-0936-5308 Department of History and Philosophy of Science, University of Pittsburgh, US +REFERENCES +Abraham, Max, and August Föppl. 1904. Theorie der Elektrizität. Vol. 1. Einführung in die Maxwellsche Theorie des Elektrizität. 2nd ed. Leipzig: B. G. Teubner. Bergmann, Peter G. 1942. Introduction to the Theory of Relativity. Englewood Cliffs, NJ: Prentice-Hall. +Bocher, Maxime. 1907. Introduction to Higher Algebra. New York: MacMillan. Budde, Emil. 1914. Tensoren und Dyaden im Dreidimensionalen Raum. Braunschweig: Friedr. 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This is an open-access article distributed under the terms of the Creative Commons Attribution 4.0 International License (CC-BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. See http:// creativecommons.org/ licenses/by/4.0/. +Philosophy of Physics is a peer-reviewed open access journal published by LSE Press. +Weyl, Hermann. 1919. “Über die statischen kugelsymmetrischen Lösungen von Einsteins ’kosmologischen’ Gravitationsgleichungen.” Physikalische Zeitschrift, 20: 31–34. Weyl, Hermann. 1921. Raum-Zeit-Materie. 4th ed. Berlin: Julius Springer. DOI: https:// doi.org/10.1007/978-3-662-02044-9 +Wright, J. Edmund. 1908. Invariants of Quadratic Differential Forms. Cambridge: Cambridge University Press. \ No newline at end of file diff --git a/storage/JCISVT2H/Norton - 2024 - Einstein Against Singularities Analysis versus Geometry.pdf b/storage/JCISVT2H/Norton - 2024 - Einstein Against Singularities Analysis versus Geometry.pdf new file mode 100644 index 0000000..592369e Binary files /dev/null and b/storage/JCISVT2H/Norton - 2024 - Einstein Against Singularities Analysis versus Geometry.pdf differ diff --git a/storage/LX54A5Z7/.zotero-ft-cache b/storage/LX54A5Z7/.zotero-ft-cache new file mode 100644 index 0000000..6b2d62b --- /dev/null +++ b/storage/LX54A5Z7/.zotero-ft-cache @@ -0,0 +1,190 @@ +Archaeological Discovery, 2023, 11, 189-202 https://www.scirp.org/journal/ad ISSN Online: 2331-1967 ISSN Print: 2331-1959 +DOI: 10.4236/ad.2023.114009 Sep. 26, 2023 189 Archaeological Discovery +The German Radio Guidance Station K11, Stp +Mo 44c at Saint-Fiacre (Lanmeur-FR) +Giancarlo T. Tomezzoli +Faculté de Lettres et Sciences Humaines, Université de la Bretagne Occidentale, Brest, France +Abstract +It is common opinion that the Battle of Britain during the WWII was principally characterised by the role of the British radars and the RAF aircrafts in detecting and destroying incoming German bombers. This is partially true, because it ignores the role played by German installations of advanced technology for guiding German bombers during their missions over Great Britain and the British attempts to jam the German bomber guiding beacons. The German radio guidance station K11, StpMo44cat Saint-Fiacre (Lanmeur) is one of the best examples of German radio guidance station in France. The visits on the site, permitted to identify some K11,StpMo44c components and to determine their preservation state at about eighty years from the end of the WWII. +Keywords +Knickebein, K11, Mo44c, Lanmeur, Saint-Fiacre, Battle of England, Luftwaffe, Wassermann, See-Elefant +1. Introduction +It is common opinion that the Battle of Britain during the WWII was principally characterised by the role of the British radars and the RAF aircrafts in detecting and destroying incoming German bombers. This is partially true, because it ignores the role played by German installations of advanced technology, in particular the Knickebein systems, for guiding the German bombers during their mission over Great Britain and the British attempts to jam the German bombers guiding beacons. +2. History +The information about the Knickebein (Bent Leg) system came to the British +How to cite this paper: Tomezzoli, G. T. (2023). The German Radio Guidance Station K11, StpMo44c at Saint-Fiacre (Lanmeur-FR). Archaeological Discovery, 11, 189-202. https://doi.org/10.4236/ad.2023.114009 +Received: August 13, 2023 Accepted: September 23, 2023 Published: September 26, 2023 +Copyright © 2023 by author(s) and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access + + + G. T. Tomezzoli +DOI: 10.4236/ad.2023.114009 190 Archaeological Discovery +scientific, military intelligence through a note on a paper saved a day of March 1940 from the shot down German Heinkel aircraft 1H + AC belonging to the Kampfgeshwader26Löwen. Its translation was:” Navigational Aid: ... Radio Beacon Knickebein from 0600 hours on 315 ̊”. Radio beacons were normally used by navigators for figuring out the position of their aircrafts. The radio beacon 315 ̊ was unusual because it pointed north-west and appeared to have been pre-set before the beacon itself. Knickebein appeared as a beamed beacon set in that day for transmitting in a north-west direction. The interrogation of one of the prisoners allowed to establish that Knickebein was something similar to the German radio-guidance X-Apparatus, developed at the same time and, because of the short wave used, the British experts estimated that the beacon was not wider than a km in diameter over London. Further, a rumour arrived from France, according to which the Germans had set up a kind of radio beam station on their frontier (Kleve-Dutch border, Stollberg-Schleswig-Holstein, Lörrach-Baden, Trenkle, 1979) that the experts evaluated as having surprisingly narrow beacon. Such a narrow beam would have required very short wavelengths. The German attack exercises against Great Britain of March 1940 were followed by other exercises in June/July 1940. The beacons, surprisingly were directed against England although there was enough exercise space over France. Consequently, from early June, the British had the possibility to investigate such directional beams by means of one aircraft equipped with a radio landing system developed in Germany, and to prepare quickly countermeasures by means of diathermy transmitters (high frequency electric current devices) in the hope to jam the beacons by sending noise on the Knickebein frequencies (coded Headache), but with little effect (Jones, 2009). A secret weapon report update (Jones, 2009) for the new Prime Minister Churchill, who had taken over the same day as the German invasion of Holland and Belgium, warned: “It is possible that [the Germans] have developed a system of intersecting radio beams so that they can locate a target such as London sufficiently accurately for indiscriminate bombing. ..., but the accuracy expected by the Germans is something like a 1/2 mile over London from the western frontier of Germany. Efforts are still being made to determine the possible wavelengths so that counter measures can be employed”. The British Y Service intercepted German radio signals and a message from the Chief Signal Officer of the FliegerKorpsIVon 5th June at 1455, decoded at Bletchley which was successful in decoding some of the Enigmamessages, which informed: “Cleves Knickebein is confirmed (or established) at position 53 ̊24' north and 1 ̊ west”. It was now obvious that the Germans had an intersecting beam system for bombing England. The bombers of the FliegerKorpsIV were Heinkel111of KampfGeschwadern4 and 27, equipped with a receiver E.Bl.I (Empfanger Blind I—blind landing receiver type I), normally used for blind landing, improved for receiving Knickebein frequencies. Knowing the frequencies at which the receiver could be tuned allowed the identification of the Knick + + + G. T. Tomezzoli +DOI: 10.4236/ad.2023.114009 191 Archaeological Discovery +ebein emission frequencies. Another prisoner informed that Knickebein was a bomb-dropping device which involved two intersecting radio beams and which was developed in Germany at Rechling. He drew a sketch of what he thought to be a transmitting tower. In a ministry high-level meeting, it was taken the decision to jam these emission frequencies. Five British radar stations were equipped with signal receivers on radar towers, a RAF unit received the duty of detecting the beams in the air and new receivers and jamming systems were investigated (Jones, 2009). On 1940 a small Knickebein system version was developed by the German company Telefunken, comprising a rail ring of 45 m in diameter. Its antenna, on a turntable, was turned on the rail. In the middle, it comprised 2 × 4 half-wave dipoles each associated with a reflector. Because thick dipole tubes were used, a system, without changes to the antenna, was able to be tuned from 30.0 to 31.5 MHz and from 31.5 to 33.3 MHz. The systems were used against Great Britain from May to September 1940 but always disturbed and finally they could no longer be used. For recognizing the distance from the target each bomber was provided with a X-device. The system beacons served primarily to recognize the approach and return routes on the sea about 30 - 80 km parallel to the English coast outside the range of jammers. To indicate turning points, at the beginning, another Knickebein beacon was used and later other types of radio beacons. One system beacon was directed to the target indicating the pathway and it was crossed over the target by a second beacon used as signal for the bombing (Trenkle, 1979). The Knickebein beacon worked according to the Lorentz beam principle consisting in transmitting two fairly blunt beams, pointing in slightly different directions but overlapping one another in a relatively narrow region which was the beam along which the aircraft had to fly. The two overlapping beams were generated by two aerial systems pointing in slightly different directions and mounted together on a turntable. The radio transmitter was switched from one of these aerials to the other and back again in a repetitive sequence so that one aerial transmitted for a short time transmitting a dot beam, followed by a longer interval, while the other aerial transmitted for a longer time transmitting a dash beam followed by a short interval. On a receiver for the two aerial signals on an aircraft a dot signal was immediately followed by a dash signal giving rise to an equi-signal giving a continuous note. As the aircraft moved on one side toward the dot beam the dot signals became stronger above the continuous note and vice versa with the dash signals. This indicated to the pilots the direction to steer for bringing the aircraft back in the equi-signal beam. The turntable was turned so that the aerials were set in a direction such that the equi-signal beam crossed the target. In case of a bomber, a second system transmitted a beam crossing the equi-signal beam few kilometres before the target. On 1940 nine small Knickebein systems were installed along the coasts of Norway, Germany, Holland, and France. On 27th June 1940 another Knickebein information arrived through an Enig + + + G. T. Tomezzoli +DOI: 10.4236/ad.2023.114009 192 Archaeological Discovery +ma message “it is proposed to set up Knickebein and Wotan installations near Cherbourg and Brest” (Jones, 2009). Correspondingly, on the other side of the English Channel, a company working for the German Luftwaffe on the aviation camp of Morlaix was the first German unit to reach Lanmeur. The Luftwaffeinstalled one of the small Knickebein system at Saint-Fiacre, near Lanmeur (Figures 1-3). The system was defended by the 3rd battery of the group Flak752(Unit L32 999). The gunners were lodged at the ancient gendarmerie (Flock, 2012). From 13th August 1940 (AdlerTag) began large-scale operations of German bombers using Knickebein systems. So, Liverpool, among other, was attached from 28th to 30th August (Jones, 2009). +Figure 1. aerial oblique view of the radio guidance station K11, StpMo44cof Saint-Fiacre around 1947. Distinguishable are: the access road, the reinforced, buried bunker, concrete barracks or exhaust vents near the bunker, Flakemplacements, the Knickebein ring with two nearby constructions, a ditch for one shack or cistern; the Wasserman/SeeElefant antenna (Rapport Pinczon du Sel, 1947-1948a). +Figure 2. radio guidance station K11, StpMo44c of Saint-Fiacre (Rapport Pinczon du Sel, 1947-1948b)—a, tobruck; b, unburied concrete bunker; c, listening post; d, concrete cover for Flakgun—small model—20 mm; e unburied thick concrete bunker R622(11), flanked by a tobruck for machine gun; f barbed wire and mines; g farm. + + + G. T. Tomezzoli +DOI: 10.4236/ad.2023.114009 193 Archaeological Discovery +Figure 3. radio guidance station K11, StpMo44c of Saint-Fiacre—1, tobruck; 2, reinforced, buried bunker; 3, concrete barracks or ventilation towers; 4, three concrete barracks or ventilation towers; 5, possible light Flak emplacement or tobruck; 6, L409Flak emplacement; 7, Knickebein single rail ring; 8, possible light Flak emplacement or tobruck; 9, pit for shack or cistern; 10, possible Flak emplacement or tobruck; 11, R622. C0515-0021_1966_F0515-0915_0110, n ̊ 110, ech. 1/23364, Argentique, 16/05/1966. +The German site of Saint-Fiacre was fortified assuming the code name StpMo 44c and became an important Luftwaffe radio guidance station (Funk-SendeAnlage—FuSAn) coded Dora/Knickebein K11. It was built by the Organisation Todt(O.T.) dependent directly from the High Kommandanturand allowed the driving of the German bomber wings during night raids on Great Britain (Flock, 2012). It was equipped with: 1 × FuSAn721 Knickebein; 1 × FuMG402Wassermann; 1 × See-Elefantand 1 × FuSE(Funk-Sende-Empfänger—emitter) 62A (Lécuillier, 2003). Table 1 adds some more convergent information about the site. Ameliorated, more powerful jam senders (Aspirin) were successfully used from 7th September. These transmitted dash signals like those emitted by the Knickebein systems so that the German bomber navigators flying along the equi-signal beams, hearing the dash signal would be confused depriving them of navigation accuracy. In October the jammers were so powerful that the Knickebein beacons on England were almost worthless for insufficiently trained bomber crews and could only be used for marking approach routes across the sea including turning points (Trenkle, 1979). Apart from the accidental bombing night of 24th August, London was saved from attack up to the afternoon of 7th September, when London docks were touched and gone in fire visible from the British coast, facilitating the German night bombers. From 7th September to 13th November each night, except one, 160 bombers were sent against London (Jones, 2009). + + + G. T. Tomezzoli +DOI: 10.4236/ad.2023.114009 194 Archaeological Discovery +Table 1. Dora/Knickebein K11(Lippmann, 2021). +ID F3 Type Cover name Location Order/Duty Equipment +334 FuSAn Dora St. Fiacre/ 1 × FuSAn721Knickebein +Knickebein Nw Lanmeur (1944 dismantled) +K11 1 × FuMG402Wassermann +1 × See-Elefant +1 × FuSE62A +The Saint-Fiacre site was attached several times by allied bombers, but only +one bomb damaged the ring rail of the Knickebein system. +The FuMG402was formed by a square frame of ten meters length mounted +on a pivot at the extremities and a roll ring. On 1944, this emitter was replaced +by a device See-Elefant linked to a pylon forty-meter hight supporting the an +tennae. A reinforced, buried bunker (Figures 3-5) was built, comprising a three meters thick coverage, four garage cells for special tracking trucks, one electrical power plant, one data exploitation and transmission room to the wings in flight and rooms and depots for the troop. +Four bunkers two of which provided with a machine gun tobruck and two +other tobrucks (one nowadays destroyed) were located on the site. The anti-air +defence was composed by three emplacements each provided with a 20 mm Flak +30gun. The station was protected by a large net of barbed wires and mine fields +(Lécuillier, 2003). +Lanmeur was liberated on 9th August 1944 (Flock, 2012). +After the Liberation, the site, favourable for radar installations, was preserved +by the French Armée and Marine Nationale. The reinforced, buried bunker, +judged practically indestructible, was used as garage and agricultural depots by +the field proprietors. +Recently, the site has been transformed in a “stand de tir”—shooting range +and the large garages cells still preserve their original orange camouflage (Lécuil +lier, 2003). +3. The Visits +The visits took place on 20 July 2023 and 22 July 2023. The K11, StpMo44c (48 ̊39'58.31"N, 3 ̊43'48.7"W, height 120.69 m) identified structures (Figure 3) were the following. A tobruck(1) (48 ̊39'54.36"N, 3 ̊43'46.44"W, h. 115.58 m) (Figure 6) disposed as defence of the site entrance road, buried in the terrain. The exposed external concrete structure was well-preserved, without damages due to combats or bombardments. It presented green painted entrance walls due to a restauration attempt. The entrance gave access to a clean combat room preserving formwork board traces. The combat room aperture was obstructed by a blue metallic plate. + + + G. T. Tomezzoli +DOI: 10.4236/ad.2023.114009 195 Archaeological Discovery +(a) +(b) (c) +(d) (e) (f) +Figure 4. Reinforced, buried bunker—(a) Coverage three meters thick; (b) Entrances of the electrical power plant; (c) Entrance square and four garage cells for special vehicles with orange camouflage; (d) Entrance of the rooms and depots for the troop; (f) Internal telephone; (g) Watertight insulation. +A reinforced, buried bunker (2) (48 ̊39'54.62"N, 3 ̊43'47.6"W, h. 114.45 m), 14 × 9 m, Sonderkonstruktion, facing three sides of an entrance square (Figure 5). On its coverage were several meters of terrain and vegetation. The entrances of the electric generator room and the fuel depot faced the square left side. The four entrances of the garage cells faced the middle, larger square side. The entrance of the troop rooms and depots faced the square right side. All the entrances were obstructed by recent metallic, bleu painted doors, so that the interior remained inaccessible. The bunker external concrete structure appeared well-preserved without damages due to combats or bombardments. It preserved the traces of the formwork boards typical of the German masonry and the original orange camouflage on the garage cells entrances. A group of concrete barracks or ventilation towers (3) (48 ̊39'54.69"N, + + + G. T. Tomezzoli +DOI: 10.4236/ad.2023.114009 196 Archaeological Discovery +3 ̊43'48.24"W, h. 121.56 m) for the generator room and the garage cells, near the bunker coverage, disappeared or buried in the terrain. A three concrete barracks or ventilation towers (4) (48 ̊39'55.43"N, 3 ̊43'47.52"W, h. 121.26 m) for the garage cells and the troop rooms and depots, inaccessible (Figure 6). The visible coverages appear in good preservation state without damages due to combats or bombardments. A television antenna on the coverage of the larger one indicated a possible squat. A possible light Flakemplacement or tobruck(5) (48 ̊39'56.82"N, 3 ̊43'47.86"W, h. 117.31 m) disappeared or buried in the terrain. A FuMG402Wassermann(48 ̊40'54.49"N, 3 ̊43'51.52"W, h. 116.23 m) disappeared. Its basement was not identified because it was probably demolished or buried in the terrain. No concrete anchor blocks for the antenna on the terrain were identified. +Figure 5. reinforced, buried bunker plan—(a) Entrance square; (b) Electric generator room; (c) Fuel depot; (d) Workshop; (e) Garage cells; (f) Troop rooms and depots (Lécuillier, 2003; Peeters, 2003). +(a) (b) (c) +Figure 6. (a) Tobruck(1) entrance; (b) Aperture of the combat room; (c) Concrete barracks or ventilation towers (4). + + + G. T. Tomezzoli +DOI: 10.4236/ad.2023.114009 197 Archaeological Discovery +A See-Elefant (unknown position) disappeared. Its basement was not identified proba bly because it was demolished or buried in the terrain. No concrete anchor blocks for the antenna were identified on the terrain. A FuSE62A radar (unknown position) disappeared. Its possible concrete platform was not identified because it was probably dismantled or buried in the terrain. An L409 (6) (48 ̊39'57.25"N, 3 ̊43'50.08"W, h. 120.05 m), with one possible nearby other Flakemplacement, disappeared or buried in the terrain. A FuSAn721 Knickebein (7) (48 ̊39'58.39"N, 3 ̊43'49.4"W, h 120.76 m) disappeared. A possible light Flakemplacement or tobruck(8) (48 ̊39'58.98"N, 3 ̊43'50.13"W, h. 120 m) disappeared or buried in the terrain. A 7 × 10 m pit for shack or cistern (9) (48 ̊39'58.33"N, 3 ̊43'48.14"W, h. 120.45 m) disappeared. A possible Flak emplacement or tobruck (10) (48 ̊39'58.17"N, 3 ̊43'46.57"W, h. 117.6 m) disappeared or buried in the terrain. An R622(11) (48 ̊40'1.38"N, 3 ̊43'46.97"W, h. 117.22 m) buried in the terrain and covered by vegetation (Figure 7) (Appendix). The visible portion did not let possible to estimate its preservation state. Two elements of the electrified protection barrier (48 ̊39'57.05"N, 3 ̊43'48.11"W, h. 117.32 m) (Figure 8) each comprising an original, concrete support and five insulation glass elements some of them still in place. +Figure 7. R622(11) ruins. +(a) (b) +Figure 8. electrified protection barrier—(a) Remains of two concrete supports; (b) Glass insulation element, details. + + + G. T. Tomezzoli +DOI: 10.4236/ad.2023.114009 198 Archaeological Discovery +4. Discussion +K11 is sometime erroneously indicated in literature as located at Plestin-lesGrèves (N/O Morlaix) (Trenkle, 1979). The listening post (c) in Figure 2 might correspond to the Knickebein system. Two theories concern the vehicles parked in the reinforced, buried bunker cells. The first assumes that they were four trucks (Meßfahrzeugen) each provided with a shelter containing sensor devices for measuring the strength (Tomezzoli, 2019) of the Knickebein signals at different distances (Lécuillier, 2003). The second assumes that they were three trailers each provided with shelter containing radar instrumentation and a tractor. The tractor moved the trailers on the entrance square site to allow the cooling down of the instrumentation in the shelters. In case of attack the tractor would have pushed the trailers inside the garage cells. The same type of bunker, including the camouflage painting was constructed at K9(Beaumont-Hague-West Cherbourg). The Knickebein operators were probably lodged in the rooms and depots for the troop (f) of the bunker so as to have easy access to the data exploitation and transmission room. The location of this room inside the bunker is unknown. It is also possible that operators were lodged in the constructions near the Knickebein ring or in the nearby R622originally intended for two groups of soldiers. +The internal telephone (Figure 4(e)) bearing the inscription: ACHTUNG! +FEIND HORT MIT!—Danger! Enemy hears with!—has been indicated as a false +one. +The bombing missions managed by K11are unknown. The electric generator was similar to a Diesel motor of a ship. It supplied electricity not only to the Knickebein and the radar systems but also to the electrified protection barrier (Figure 7). +The K11rail ring was demolished on 1975 after some people had accidents on +it. The aerial systems were already dismantled on 1944. +The pit might have hosted and protected a shack for personnel lodgement as +those at Cap Fréhel (Tomezzoli, 2021), Qu500and Qu13at the Pointe du Raz +(Tomezzoli, 2021), on the Menez Hom (Tomezzoli, 2017) and at Flescou (To +mezzoli, 2022) or was a cistern/pool as those at Murs Érigné (Tomezzoli, 2016) +and the Domaine de Pignerolle (Tomezzoli, 2019) for providing relax to the per +sonnel in service and water in case of fire to the components on the site. The commissioning of FuMG402Wassermannstarted about on 1942, therefore that of K11 did not participate to the Battle of Britain as possible ranging system for detecting the German bombers positions on the equi-signal beam so as to allow the transmission of the second beam indicating the target. The FuMG 402 and the See-Elefant were long-range, early warning radars (range of about 300 km) intended for detecting incoming enemy aircrafts and alert the Flakemplacements not only those of the site but also those around Brest (Tomezzoli & Dupont, 2009). The FuSE62Awas a movable, short-range radar (range of about 30 km) able to detect azimuth and height of incoming enemy aircrafts so as to + + + G. T. Tomezzoli +DOI: 10.4236/ad.2023.114009 199 Archaeological Discovery +direct the fire of the gun batteries of the site and possible nearby other batteries. It is still recognizable here the coupling on the same site of long-range, early warning and short-range radars remarked also at the radar stations at Cap Fréhel (Tomezzoli & Moser, 2021), Pointe du Raz (Tomezzoli, 2021), Saint-Pabu (Tomezzoli & Colliou, 2017), Monterfil (Dupont et al., 2007) and Les Mées (Tomezzoli & Pottier, 2015). +The mast actually claimed as 40 m height of the See-Elefant radar-system +(Figure 2) was added on the site on 1944. The site included aFuSE62AWürzburg +with a circular antenna and a Wassermannradar at different times—though not +necessarily at the same time. +A photogrammetric analysis of Figure 1 revealed that the mast was actually 60 +m height and was not pointed at the bottom. Based on this, it appears to be the +mast of a WassermannS (Schwehr—heavy) without the antenna elements. The +See-Elefant was not a complete radar system. It was only the half of a bi-static +radar system: the radar transmitter (See-Elefant, with a twin mast (!) antenna) +was not collocated with the associated radar receiver (“Russel”). They had large +antennas separated by about one km. No antenna system had a mast that looked +like the one in Figure 1. +A decoy-Knickebein (“Schein Knickebein” typically a wooden contraption) +was located 3.5 km North of K11, at Saint-Jean-du-Doit (Döremberg, 2004 +2016). A search on satellite images for such a decoy actually permitted to identify +a circular structure of about 30 m in diameter at Guernevez (48 ̊42'14.02"N, +3 ̊46'19.22"W) in the municipality of Saint-Jean du Doigt, but the visit on the +site on 8th August 2023 and the information of the owner allowed to ascertain +that it was a waste water dump built on free terrain in the 1950s. The owner also +declared that no structure of the WWII was located at Guernevez. +The choice to place the Wassermann and after of the See-Elefant at the site +was rather obvious. In fact, the site already offered an elevated position (121 m), +a reinforced, buried bunker, an electric generator, a data exploitation room and +personnel lodgements. +The K11Site map, based on RAF Photographic Reconnaissance Unit (P.R.U.) +sorties in July 1940-Sept. 1941 (Döremberg, 2004-2016), identifies six more guns +light batteries around the site. +5. Conclusion +The development of the shooting range preserved the K11 reinforced, buried bunker, one cell of it is actually used as shooting training room and the troop rooms and depots (f) used as administration rooms. But it imposed also a deep alteration of the site by the erection, because of the neighbouring inhabitants protestations (Baudier, 2021), of terrain barriers to muffle the gunfire shots, which caused the covering or destruction of site structures like tobrucks(Figure 2) and concrete barracks or ventilation towers (3). The utilisation of the reinforced, buried bunker, at the moment, ensures its preservation and its survival in + + + G. T. Tomezzoli +DOI: 10.4236/ad.2023.114009 200 Archaeological Discovery +the near future. However, no classification as monument or architectural heritage of the site is foreseen. Moreover, no tourist board gives information about its existence, history and structures. In any case, the hope is that this article will attract the attention of archaeologists, scholars and a large public about the study and preservation of German installations of advanced technology operating in France during the WWII. +Acknowledgements +I am grateful Mr Döremberg for his explanations about the Knickebeinsystem, the first parked vehicle theory and his kind permission of using information about K11 coming from his internet site, to Mr. Denis for his explanations during a visit of the K11 site and about the second parked vehicle theory, to Mr. Peeters for his kind permission to insert in the article the reinforced, buried bunker plan and to Mr Fleuridas for his kind permission to insert in the Appendix the plans of the R622 bunker. +Conflicts of Interest +The author declares no conflicts of interest regarding the publication of this paper. +References +Baudier, L. (2021). ÀLanmeur,letorchonbrûleautourdustanddetir. Le Télégramme. https://www.letelegramme.fr/finistere/lanmeur-29620/a-lanmeur-le-torchon-brule-aut our-du-stand-de-tir-3765034.php +Döremberg, F. (2004-2016). “Knickebein”StationsKN-1-KN-13. https://www.nonstopsystems.com/radio/hellschreiber-modes-other-hell-RadNav-knick ebein.htm#Kn11 +Dupont, P. H., Fresil, Y., & Tomezzoli, G. (2007). Deutsche Militärbauten bei Rennes. DAWANachrichten,49,56-66. +Flock, A. (2012). L’OccupationAllemandedansles162CommunesduNordFinistère19401944. +Jones, R. V. (2009). MostSecretWar.BritishScientificIntelligence1939-1945. Penguin Books. +Lécuillier, G. (2003) StationdeRadionavigation(Mo48c)puisstanddetir,Saint-Fiacre (Lanmeur). Association Pour l’Inventaire de Bretagne. http://patrimoine.bzh/gertrude-diffusion/dossier/station-de-radio-guidage-codee-k11-emet teur-knickebein-puis-see-elefant-en-1944-mo-48c/2d3c3f06-98a4-48d2-ab0e-531098d9b013 +Lippmann, H. (2021).Funkmeß(ortungs)stellungeninFrankreich. Bretagne West mit Brest. http://www.atlantikwall.info/radar/france/rf_.htm#Bretagne_West +Peeters, D. (2003) Stationderadionavigation(Mo48c)puisstanddetir,Saint-Fiacre(Lanmeur). Association Pour l’Inventaire de Bretagne. http://patrimoine.bzh/gertrude-diffusion/dossier/station-de-radio-guidage-codee-k11-emett eur-knickebein-puis-see-elefant-en-1944-mo-48c/2d3c3f06-98a4-48d2-ab0e-531098d9b013 +Rapport Pinczon du Sel (1947-1948a). Brest.CollectionGellat. Service Historique de la Marine. +Rapport Pinczon du Sel (1947-1948b). LeMurdel’AtlantiquelaCotedelaMancheetde + + + G. T. Tomezzoli +DOI: 10.4236/ad.2023.114009 201 Archaeological Discovery +l’AtlantiqueduMontSaint-MichelàLaita.Service Historique de la Marine. Brest, Livre IV. Plan n° 62_IV. +Tomezzoli, G. T. (2016). The German Base “the Bank” at Mûrs-Érigné (Anjou-FR). ArchaeologicalDiscovery,4,37-47. https://doi.org/10.4236/ad.2016.41004 +Tomezzoli, G. T. (2017). The WW II German Stützpunkt on the Menez-Hom (FinistèreFR). ArchaeologicalDiscovery,5,224-237. https://doi.org/10.4236/ad.2017.54013 +Tomezzoli, G. T. (2019). The Monitoring Mast of the WW II German W/T Station Be-2. ArchaeologicalDiscovery,7,224-237. https://doi.org/10.4236/ad.2019.72005 +Tomezzoli, G. T. (2021). The German Radar Stations at the Pointe Du Raz (FR). ArchaeologicalDiscovery,9,198-222. https://doi.org/10.4236/ad.2021.93011 +Tomezzoli, G. T. (2022). The Heer Küste Artillerie Abteilung 1161. ArchaeologicalDiscovery,10,193-214. https://doi.org/10.4236/ad.2022.104007 +Tomezzoli, G. T., & Colliou, S. (2017). The WW II Saint-Pabu German Radar Camp and the Stützpunkte Re 03, Re 04. ArchaeologicalDiscovery,5,142-162. https://doi.org/10.4236/ad.2017.53009 +Tomezzoli, G. T., & Moser, J.-L. (2021). The German Radar Station La 318 Frosch. ArchaeologicalDiscovery,9,113-134. https://doi.org/10.4236/ad.2021.92006 +Tomezzoli, G., & Dupont, Ph. (2009). Die Flak Batterien der Festung Brest. DAWANachrichten,Ausgabe,54,4-43. (In German). +Tomezzoli, G., & Pottier, L. (2015). Die deutschen militärlogistischen Anlagen westlich von Mamers. DAWANachrichten,65,14-27. +Trenkle, F. (1979). DiedeutschenFunk-Navigations-undFunk-Fürungsverfahrenbis1945. Motorbuch Verlag. + + + G. T. Tomezzoli +DOI: 10.4236/ad.2023.114009 202 Archaeological Discovery +Appendix +Figure A1. R622twin group shelter—plan: 2 gas lock, 5 - 6 crew rooms (Courtesy Fleuridas P.). \ No newline at end of file diff --git a/storage/LX54A5Z7/Tomezzoli - 2023 - The German Radio Guidance Station <i>K11<i>, <i>Stp Mo 44c<i> at Saint-Fia.pdf b/storage/LX54A5Z7/Tomezzoli - 2023 - The German Radio Guidance Station <i>K11<i>, <i>Stp Mo 44c<i> at Saint-Fia.pdf new file mode 100644 index 0000000..6221ab9 Binary files /dev/null and b/storage/LX54A5Z7/Tomezzoli - 2023 - The German Radio Guidance Station <i>K11<i>, <i>Stp Mo 44c<i> at Saint-Fia.pdf differ diff --git a/storage/PI6XT8IJ/1996-GPS and Relativity_ An Engineerin-Fliegel.pdf b/storage/PI6XT8IJ/1996-GPS and Relativity_ An Engineerin-Fliegel.pdf index 1f94858..a1565db 100644 Binary files a/storage/PI6XT8IJ/1996-GPS and Relativity_ An Engineerin-Fliegel.pdf and b/storage/PI6XT8IJ/1996-GPS and Relativity_ An Engineerin-Fliegel.pdf differ diff --git a/storage/PMBL5MRJ/.zotero-ft-cache b/storage/PMBL5MRJ/.zotero-ft-cache new file mode 100644 index 0000000..bc2a88b --- /dev/null +++ b/storage/PMBL5MRJ/.zotero-ft-cache @@ -0,0 +1,322 @@ +1 +July 27, 2001; Revised August 15, 2001 +Einstein's Triumph over the Spacetime Coordinate System: +A Paper presented in Honor of Roberto Torretti +John D. Norton1 +Department of History and Philosophy of Science +University of Pittsburgh +Pittsburgh PA 15260 +1. Introduction +Each student of Einstein must eventually make his or her their peace with Einstein's +pronouncements on relativity and spacetime coordinate systems. Einstein saw the +development of relativity as the ultimately successful struggle to overcome certain spacetime +coordinate systems and thereby to implement a generalized principle of relativity. This +signal achievement of relativity is embodied in its general covariance. We now hold +spacetime coordinate systems merely to be convenient devices for smoothly labeling events. +The selection of a coordinate system amounts to little more than a conventional choice of +1 Dr. Torretti has inspired my generation: in scholarship, by setting the standard in his +researches in history and philosophy of space and time; and in humanity with his generosity +and kindness. I take this opportunity to thank him personally for the stimulating model of +scholarship in his Relativity and Geometry and related writings and for his encouragement, +patience and instruction when I first worked in history and philosophy of space and time, +especially during a year we shared at the Center for Philosophy of Science, University of +Pittsburgh, in 1983-1984. He helped make it one the most exciting years intellectually of my +life. + + + 2 +numbers, much like the selection of definition. How can one proclaim victory over a +definition? If we are offended by a definition, the more appropriate attitude is just to decide +quietly not to use it. +Dr. Torretti's celebrated Relativity and Geometry and related writings represent a +landmark of scholarship. They provide our most detailed account of how Einstein's work in +relativity theory changed physical geometry. It is presented in a comprehensive historical +context with the uncompromised insistence that every geometric conception must be +explicated to the highest standards of mathematical rigor. So when Dr. Torretti makes his +peace with the problem of Einstein and spacetime coordinates in Section 5.5 "General +Covariance and the Einstein-Grossmann theory," this latter insistence ensures that the +peace will be uncomfortable—for Einstein. He takes Einstein's formulation of the postulate of +general covariance and rephrases in language that mimics Einstein's 1905 statement of the +principle of relativity of special relativity. Calling it the "principle of general relativity," Dr. +Torretti explains why the similarity of the two relativity principles is only superficial. Unlike +the case of the special principle, the general principle does not assert a physical equivalence +of states of motion. Dr. Torretti's analysis is careful, thorough and leaves no room to quibble. +So we are left with a puzzle. How could Einstein be so confused about the fundamentals of +his own theory? +My goal in this paper is small. I do not want to dispute Dr. Torretti's careful analysis. +Rather I offer an extended footnote to it. I want to try to explain what Einstein intended in +his remarks about coordinate systems. There is, I believe, a natural reading for Einstein's +claims that do make perfect sense. They require us to adopt a physical interpretation of +relativity theory that is now no longer popular, so the natural reading will no longer have +intrinsic interest. It will, however, allow us to make sense of Einstein's claims and his +program. + + + 3 +2. "The Vanquishing of the Inertial System" +A Letter to Besso +When we face claims that are unintelligible in the writing of an Einstein, we are +often tempted to dismiss them as remarks made in haste in the frenzied first moments of +great discovery. Might they not be retracted or qualified in some essential way as time brings +sober distance from those heady moments? While time mellowed Einstein, we can be sure +this was not the case with his proclamations over coordinate systems. He brought the general +theory of relativity to a generally covariant formulation in November 1915. Nearly 40 years +later, after his theory had been much celebrated and its foundations subject to minute +scrutiny, Einstein wrote to his lifelong friend and confidant, Michele Besso. +His letter of August 10, 1954, lays out a brief account of the essence of the general theory of +relativity, explicitly intended to be free of entanglement with the history of the theory. +(Speziali, 1972, p.525)2 +Your characterization of the general theory of relat.[ivity] characterizes the +genetic side quite well. It is also valuable afterwards, however, to analyze the +whole matter logically-formally. For as long as one cannot determine the +physical content of the theory on account of temporarily insurmountable +mathematical difficulties, logical simplicity is the only criterion of the value of +the theory, even if it is naturally an insufficient one. +The special th.[eory] of r.[elativity] is really nothing other than an adaptation +of the idea of the inertial system to the empirically confirmed conviction of the +constancy of the velocity of light with respect to each inertial system. It does not +vanquish the epistemologically untenable concept of the inertial system. (The +2 I thank Karola Stotz for help in this translation. + + + 4 +untenability of this concept was brought to light especially clearly by Mach and +was, however, already recognized with lesser clarity by Huygens and Leibniz.) +The core of this objection against Newton's fundamentals is best explained +through the analogy with the "center point of the world" of Aristotelian physics: +there is a center point of the world, towards which heavy bodies strive. This +explains, f[or] e[xample], the spherical shape of the earth. The ugliness in it is +that this center point of the world acts on all others, but that all these others +(i.e. bodies) do not act back on the center point of the earth. (One-sided causal +nexus.) +It is just like this with inertial systems. They determine the inertial relations +of things everywhere, without being influenced by them. (Really one ought better +to speak of the aggregate of all inertial systems; however this is inessential.) The +essence of the gen.[eral] th.[eory] of rel.[ativity] (G. R.) lies in the vanquishing +[Ueberwindung] of inertial systems. (This was still not so clear at the time of the +setting up of G. R., but was subsequently recognized principally through Levi +Civita.) In the setting up of the theory I had chosen the symmetric tensor gik as +the starting concept. It provided the possibility of defining the "displacement +field" Γlik... +Einstein briefly explained the notion of the displacement field and its independence from the +metric gik. He continued: +But how is it that the displacement field really led to the vanquishing of +inertial systems? If one has vectors with the same components at two arbitrarily +distant points P and Q in an inertial system, then this is an objective (invariant) +relation: they are equal and parallel. On this rests the circumstance that one +obtains tensors again through differentiation of tensors with respect to the +coordinates in an inertial system and that e.g. the wave equation represents an +objective expression in inertial systems. The displacement field now allows such + + + 5 +tensor formation by differentiation in relation to an arbitrary coordinate system. +Therefore it is the invariant substitute of inertial systems and thereby--as it +appears--the foundation of every relativistic field theory. +Einstein then continued to explain how the metric and displacement field are used to +formulate general relativity and his unified field theory. +Its Unusual Treatment of Coordinate Systems +Einstein finds the essence of the general theory to lie in the vanquishing of inertial +systems, that is, inertial coordinate systems. Part of his account is that these systems have +the objectionable feature of acting without being acted upon. That aspect has been subject to +much discussion and analysis. It is usually explicated by the notion of "absolute object," +geometric objects that act but are not acted upon. In special relativity, the pertinent absolute +object is the Minkowski metric.3 Here I pass over the problem of explicating the absoluteness +Einstein raises; I am interested in just one other aspect. Einstein's notion of the absolute +inertial [coordinate] system has been transmogrified into an absolute geometric object, the +Minkowski metric. +It is so tempting to say that this transformation is what Einstein really intended. But +then we must be amazed at his tenacity in avoiding the assertion. His remarks to Besso +mention the metric field and the displacement field, both geometric objects, but condemns +the inertial system for its absolute character—and this forty years after his achievement of +general covariance.4 +3 For discussion see Norton (1993, Section 8). +4 Similar remarks on inertial systems span Einstein's life. They appear, for example, as early +as Einstein (1913, pp. 1260-61) and as late as a letter to George Jaffé of January 19, 1954 +(Einstein Archive, document with duplicate archive control number 13 405). + + + 6 +2. Einstein's use of Coordinate Systems +Their Physical Content +There is a simple way to understand Einstein's remarks.5 He did not regard +coordinate systems as we now do, as essentially arbitrary systems of numerical labels of +events. In his theorizing, they initially carried significant physical content. The journey to +the completion of general relativity required the systematic elimination of this content. +That coordinate systems can be used to represent significant physical content is not +the modern view and it is tempting to think that no other view is possible. But that +narrowmindedness is quite incorrect. Our physical theories use mathematical structures to +represent aspects of interest of the physical world. We routinely use a manifold that is +topologically R4 to represent the set of physical events in special relativity. Nothing prevents +us using the structurally richer number manifold of quadruples of reals as this manifold. If +we do use a number manifold in this way, then we are assigning quadruples of reals to +events in spacetime. That is just what a coordinate system does. +A number manifold has considerably more structure than we use in standard +theories of spacetime. It has a preferred origin (0,0,0,0), for example. How are we to interpret +that? Does this preferred origin correspond to a real physical center point of the world? +Whether it does or not cannot be decided purely by the mathematics of the theory. The +mathematics can only affirm that (0,0,0,0) is indeed different from all other points in R4, but +not that the differences amount to nothing physically. This last judgment must be made by +the physical interpretation we supply for the mathematical structures. The modern view is to +discount it as physically insignificant. Einstein's default was the opposite. The various +5 I have developed the approach to Einstein's use of coordinate systems sketched below in +greater detail in Norton (1989, 1992). + + + 7 +features of coordinate systems represent physical features of the world. Most crudely, the +origin (0,0,0,0) is a physical center point. In Einstein's program, we must find a way of +depriving coordinate systems of this default physical content. +...and How it is Systematically Denied +Einstein used a single technique that was not his own invention. He used a strategy +codified by Felix Klein in the nineteenth century.6 Each geometric theory would be +associated with a class of admissible coordinate systems and a group of transformations that +would carry us between them. The cardinal rule was that physical significance can be +assigned just to those features that were invariants of this group. In special relativity, that +group is the Poincaré group. The origin (0,0,0,0) is not an invariant; under translations +within the group, the origin is not mapped back to itself. Thus it has no physical significance. +But the light cone structure –the complete catalog of the pairs of events that are lightlike +separated7—is invariant and thus has physical significance. +3. The Development of Relativity Theory +The Default Interpretation of Spacetime Coordinate Systems... +Einstein's natural starting point is to assign physical significance to the natural +features of a coordinate system. Using the familiar (t, x, y, z) as the spacetime coordinates, +we can list some of them: +6 For a more detailed account of the connection to nineteenth century geometry, see Norton +(1999). +7 In coordinate terms, the pair satisfies the condition ∆t2 - ∆x2 - ∆y2 - ∆z2 = 0, where (t, x, y, z) +are the usual spacetime coordinates, ∆ represents the coordinate differentials and the speed +of light is set to unity. + + + 8 +(a) The origin (0,0,0,0) corresponds to a central point; the distinction between the x, y and z +coordinates makes space anisotropic. +(b) The curves picked out by constant values of x, y and z are a state of rest. +(c) In a Lorentz or Galilean covariant theory, the set of all curves picked out by (b) for all +coordinate systems are the inertial states of motion. +(d) Coordinate differences have metrical significance; they represent the possible results of +clock and rod measurements by observers in the state of rest picked out by (b). +...and Their Loss of Physical Significance +The development of relativity theory brings the systematic elimination of these +default physical interpretations. As our starting point, we might imagine a one-coordinate +system theory. It would have all the physical structures of the list above (a)-(e). The first step +had already been taken in the nineteenth century. The spatial sections of the spacetime are +covered by coordinates x, y, z. The Euclidean character of space entails that we can use many +coordinate systems related by translations, rotations and reflections. None of the structures +of (a) are invariants of these transformations. They lose physical significance. +The Relativity of Motion +The theory would retain an absolute state of rest (b), however. That is eliminated by +the transition to a Newtonian spacetime, with the characteristic group the Galilean group, or +to special relativity with the characteristic group the Poincaré group. The states of rest (b) +are no longer invariant. + + + 9 +The next step marks the starting point of Einstein's 1907 quest for his general theory +of relativity.8 Einstein sought to expand the covariance of his theory further so as to deprive +the inertial states of motion (c) of physical significance. This, he believed, was achieved with +his postulation of the principle of equivalence which now allowed him to extend the Poincaré +group with transformations that represented uniform acceleration, although in only limited +circumstances. Einstein immediately interpreted the expansion as representing an extension +of the principle of relativity to acceleration. In this account, we see why: the inertial motions +of (c) are no longer invariants of the admissible transformations. +Metrical Significance +Presumably this much was all Einstein expected in 1907. In 1912, Einstein realized +that the development of his theory required him to take another step in depriving +coordinates of physical significance. He saw an analogy between the problem of gravitation +and relativity and the theory of curved surfaces of Gauss. The latter has led to a new +mathematics in which one could use arbitrary coordinate systems and in which coordinate +differences cease to have the direct metrical significance of (d).9 +8 There has been very considerable investigation in recent decades of Einstein's passage to +the general theory of relativity. They span from early work including Torretti (1983), Norton +(1984) and Stachel (1980) to Renn (in preparation). +9 Here I will report Dr. Torretti's repeated lament that the group structure—or lack of it—of +Einstein's expanded coordinate systems brought many unintended problems apparently +ignored by Einstein. For example (Torretti, 1983, p. 153) observes that the ranges of two +coordinate charts may not overlap, so that the point transformation by induced the +corresponding coordinate transformation may have degenerate properties. Einstein largely +maintained a physicist's silence on these mathematical niceties. + + + 10 +Independent Existence +With this development, Einstein's quest for depriving coordinate systems of their +default physical significance has taken an unanticipated turn. It proved to be a trifle in +comparison to the final hurdle that Einstein needed to overcome in arriving at a generally +covariant formulation of his general theory of relativity. Having failed to find what he +thought were admissible generally covariant gravitational field equations in 1912 and 1913, +Einstein eventually found a way to discount the failure. He developed arguments that +purported to show that general covariance would be physically uninteresting, were it to be +achieved. The best known and most important of these was the "hole argument." +The error of Einstein's argumentation is now well known. He had generated two +intertransformable metric fields gik(xm) and g'ik(xm) in the same coordinate system, xm. He +had assumed that the two fields represented two distinct physical possibilities. That proved +to be the elusive error that took several years to find. Einstein presumed that it made sense +to say that the two fields were in the same coordinate system. That tacitly accorded an +existence to the coordinate system independent of the metric field defined on it. Figuratively, +it meant that it makes sense to say that we can remove the first field from the coordinate +system, leave a bare coordinate system behind and then deposit the second fieldin the very +same coordinate system. +One of the final stages of Einstein's development of a generally covariant theory was +to recognize that coordinate systems have no such independent existence. He described his +error to Besso in a letter of January 3, 1916:10 +10 Schulmann et al. (1998) Papers, Vol. 8A, Doc. 178; Einstein's emphasis. I have argued +elsewhere that Einstein's according independent reality to coordinate systems may have had +catastrophic effects at an earlier stage of his quest for general covariance. See "What Was +Einstein's Fatal Prejudice?" in Renn et al. (in preparation). + + + 11 +There is no physical content in two different solutions G(x) [gik(xm)] and G'(x) +[g'ik(xm)] existing with respect to the same coordinate system K. To imagine two +solutions simultaneously in the same manifold has no meaning and the system +K has no physical reality. +4. Conclusion +These considerations, however, have little force with modern readers. We now +proceed from a quite different starting point. We do not accord default physical significance +to coordinate systems. If we wish to endow a spacetime with inertial structures, absolute or +otherwise, we start where Einstein ended. We start by endowing a manifold with an affine +connection (displacement field) whose natural straights are the inertial motions. In all this, +coordinate systems are little more than convenient labels for spacetime events. +For Einstein, however, matters looked quite different. His default was to load +physical content into the coordinate systems. The conceptual development through special to +general relativity is characterized by depriving coordinate systems of their default physical +significance in progressively greater measure. He had initially intended to end up just +depriving coordinate systems of absolute inertial motions. Once Einstein had started the +process, it could not be stopped. The natural development of the theory ended up forcing +much more. The coordinate systems lost their metrical significance and, after much +suffering, he finally recognized the need to dispense with a notion of independent existence +he had tacitly accorded them. +References +Einstein, Albert (1913a) "Zum gegenwärtigen Stande des Gravitationsproblems," +Physikalische Zeitschrift, 14, pp.1249-1262. +Norton, John D. (1984) "How Einstein found his Field Equations: 1912-1915," Historical +Studies in the Physical Sciences, 14, 253-316; reprinted in Don Howard and John + + + 12 +Stachel (eds.) Einstein and the History of General Relativity: Einstein Studies, Vol. 1 +Boston: Birkhäuser, 1989, pp.101-159. +Norton, John D. (1989) "Coordinates and Covariance: Einstein's view of spacetime and the +modern view," Foundations of Physics, 19, 1215-1263. +Norton, John D. (1992) "The Physical Content of General Covariance" in J. Eisenstaedt and +A. Kox eds., Studies in the History of General Relativity: Einstein Studies, Vol.3, +Boston: Birkhauser. +Norton, John D. (1993), "General Covariance and the Foundations of General Relativity: +Eight Decades of Dispute," Reports on Progress in Physics, 56, pp. 791-858. +Norton, John D. (1999) "Geometries in Collision: Einstein, Klein and Riemann." in J. Gray, +ed., The Symbolic Universe . Oxford University Press, pp.128-144. +Renn, Jürgen; Sauer, Tilman; Janssen, Michel; Norton, John D. and Stachel John (in +preparation) General Relativity in the Making; Einstein's Zurich Notebook. +Schulmann, Robert; Kox, A. J.; Janssen, Michel; and Illy, József (eds.) (1998) The Collected +Papers of Albert Einstein. Volume 8. The Berlin Years: Correspondence, 1914-1918. +Part A: 1914-1917. Part B: 1918. Princeton: Princeton University Press. (“Papers, +Vol. 8”) +Speziali, Pierre (ed., trans.) (1972) Albert Einstein Michele Besso: Correspondance 1903-1955. +Paris: Hermann. +Stachel, John (1980): "Einstein's Search for General Covariance," paper read at the Ninth +International Conference on General Relativity and Gravitation, Jena; printed in +Don Howard and John Stachel (eds.) Einstein and the History of General Relativity: +Einstein Studies, Vol. 1 (Boston: Birkhäuser, 1989) pp.63-100. +Torretti, Roberto (1983) Relativity and Geometry. Oxford: Pergamon. \ No newline at end of file diff --git a/storage/PMBL5MRJ/Norton - 2001 - Einstein's triumph over the spacetime coordinate system.pdf b/storage/PMBL5MRJ/Norton - 2001 - Einstein's triumph over the spacetime coordinate system.pdf new file mode 100644 index 0000000..fe14600 Binary files /dev/null and b/storage/PMBL5MRJ/Norton - 2001 - Einstein's triumph over the spacetime coordinate system.pdf differ diff --git a/storage/QR6V9JN7/.zotero-ft-cache b/storage/QR6V9JN7/.zotero-ft-cache new file mode 100644 index 0000000..78689b1 --- /dev/null +++ b/storage/QR6V9JN7/.zotero-ft-cache @@ -0,0 +1,736 @@ +i +: + + + LIBRARY +OF THF. +UNIVERSITY OF CALIFORNIA, +GIFT OF" +Jl +Accession No. 836.9-U-. +>\0vta{/yvv< +Received ,190 + + + + + J + + + TRAVERSE TABLES +WITH AN INTEODUCTOEY CHAPTEE ON +CO-ORDINATE SURVEYING +BY +HENEY LOUIS, M.A, A.E.S.M., F.I.C., F.G.S., ETC. +i\ +PROFESSOR OF MIXING AND LECTURES ON SURVEYING, DURHAM COLLEGE OF SCIENCE, NEWCASTLE-ON-TYNE EXAMINER IN MINE SURVEYING TO THK CITY AND GUILDS OF LONDON INSTITUTE +AND +GEOKGE WILLIAM CAUNT, M.A. +LECTURER IN MATHEMATICS, DURHAM COLLEGE OF SCIENCE, NEWCASTLE-ON-TVNE +LONDON +EDWAED ARNOLD +37 BEDFORD STREET. STRAND +1901 + + + a + + + PKEFACE. +THE publication of this little work is due to the writer's +conviction, gained in many years of miscellaneous surveying +practice, as well as in some spent in the teaching of surveying, that the co-ordinate method of plotting traverses is far preferable +to any other, on the score of both accuracy and expedition. There are, of course, several traverse tables already in existence ; but +whilst some of these are calculated with a degree of accuracy +greater than is required in ordinary surveying, and more +especially in ordinary mine surveying, others are not accurate enough, inasmuch as their calculations are not extended to +every minute of the degree. The price of the former works is, +moreover, somewhat prohibitive, at any rate as far as the +ordinary mine surveyor is concerned. +At the present day it is usual to employ, in ordinary underground and surface work, instruments divided into single +minutes, so that the tables must be calculated for this unit to be +of any real use. In ordinary chaining it may be taken that it +is rare for any traverse to exceed ten chains in length, whilst the +limit of accuracy for such lengths is about one link. The tables +are therefore calculated to five significant places (four places of +decimals), so that their accuracy is about ten times as great +as is attained in ordinary actual work. This limit is therefore +sufficiently near for all practical purposes, and, at the same time, does not involve any undue amount of arithmetical work. + + + iv PREFACE. +These tables are not intended for cadastral surveys, for which +seven decimal places are required, or at times even more. The +arrangement of the tables is one which the writer finds in +practice to be convenient for rapid work, all the figures needed +for any given angle being found at one opening of the pages and in one line. The tables have been entirely recalculated by +Mr. Gaunt, and checked in all possible ways, and every +precaution has been taken to ensure accuracy in printing, so as to warrant the hope that they may be found free from +error. The writer ventures to hope that their publication may +serve to popularize this most convenient method of working out +traverse surveys in this country, HENEY LOUIS. +NEWCASTLE-ON-TYNE, December, 1900, + + + TBAVEESE TABLES. +CO-ORDINATE SURVEYING. +CO-ORDINATE surveying, or, to speak more precisely, co-ordinate plotting, is the name given to a method of recording the results +of traverse surveys in which the draughtsman represents each draft of the survey by means of its rectangular co-ordinates. It cannot well be applied to any other than traverse surveying, hence its utility is mainly restricted to such forms of survey work +as depend upon traverses, that is to say, mine surveys, surveys of roads, rivers, or railways, and surveys of areas. In a traverse survey the lengths and directions of the various traverses or drafts are determined in the field by methods with which all +surveyors are familiar; it need only be here observed that, however determined, the direction of any traverse is the angle which it makes with any determinate direction ; the latter may +either be an absolutely fixed direction, such as the terrestrial +meridian, or it may be comparatively fixed, as the magnetic meridian, or it may be purely arbitrary, such as the direction of the first draft of the survey, or of any other traverse, or of one of +the main directions in which the survey extends, e.g. the main +road of a large colliery, the principal street of a town, etc. In mining surveys it is customary in this country to refer all directions to the magnetic meridian, in spite of several obvious +inconveniences to which this practice is subject; although it is certainly better to use the terrestrial meridian, yet the +method of plotting by co-ordinates is exactly the same whatever a2 + + + vi TRAVERSE TABLES. +be the line of reference that is used. For the sake of sim +plicity it will here be supposed that a method of surveying +has been adopted by which the angle which each traverse makes with the terrestrial meridian can be accurately determined. +Thus, in Fig. 1, let the traverse line of length OA (= I) +make an angle a with the meridian line YY' through 0, and +let XX' be drawn at right +angles to TOY'. Draw Aa +and Aa' perpendicular respec +tively to the lines XX' and +YY' ; then Aa = Oa' = I cos a, +and Aa' = Oa = I sin a, are +**f +"" the co-ordinates of the point A referred to its origin 0, or the co-ordinates of the traverse OA. +Oa', the meridian co-ordinate, +*' is usually spoken of as the difference of latitude (generally abbreviated into latitude), and Oa, the equatorial co-ordinate, is generally called the departure of the traverse OA, and these words, latitude and departure, are adhered to even when the +reference lines, YY' and XX' , do not correspond with either the terrestrial or the magnetic meridian and equator respectively. It is obvious that the co-ordinates of any traverse can +be calculated by the aid of a table of sines and cosines, but this is a laborious and slow operation. Traverse tables are merely tables in which the results of these calculations are recorded so as to save time; in the present traverse tables the latitude and departure are given for every minute of angle and for all lengths from 1 to 10, so that the co-ordinates for any desired length can be taken out by simple addition, at the same +time moving the decimal point as may be required. Thus, required the co-ordinates of a traverse 1638 links long, making an angle of 27 49' with the meridian line. Entering the table headed 27, the minutes are found in the column at the left +hand (headed Min.), and looking horizontally along the line corresponding to 49', the several figures are taken out under the unit distances (Dist.) which head each double column of lati +tude (Lat.) and departure (Dep.), thus + + + TRAVERSE TABLES. vii +27 ,49' Dist. Lat. Dep. 1000 884-5 466-6 600 530-7 280-0 30 26-5 14-0 8 7-1 3-7 +1638 1448-8 764'3 +So that the required latitude is 1449 links, and the required departure 764 links. It will be noticed that the figures are +only taken out to the first decimal place ; in ordinary surveying fractions of links are not recognized, so that the co-ordinates are merely required to be correct to the nearest unit ; there is +therefore no object in using more than one decimal place. Whenever the angle given exceeds 45, the angle must be sought for at the bottom right-hand corner, and the minutes +read upwards in the last right-hand column; care must be taken also to read the latitudes and departures upwards in accordance with the respective designations at the bottom of the page. In this connection it is worth remembering that +when the angle is less than 45, latitudes are greater than departures, and when the angle exceeds 45, latitudes are less +than departures, A useful check is also obtained by noting +that +(Distance)2 = (Latitude)2 + (Departure)2 +When one traverse only has to be plotted, but little is gained by the use of co-ordinates ; but when a number of successive traverses have to be laid down, as is the case in an ordinary +traverse survey, the advantage is evident, as the various latitudes +and departures can be added together arithmetically, and thus the exact position of the end point determined before the survey +is plotted. Thus, let OA, AB, and BC (Fig. 2) be three traverses, of which the lengths and the angles which they make with the meridian are known. Then Oa' and Oa are, as before, the +co-ordinates of the traverse OA or of the point A referred to +its origin ; similarly, J93/ and AM are the co-ordinates of B +referred to its origin A. But Ob = Oa + ab = Oa -J- AM, and +Ob' = Oa' -f- a'V = Oa' -f MB; therefore the co-ordinates of +the point B referred to the origin are the sums of the re +spective latitudes and departures of the two traverses OA and AB. In the same way Oc and Oc', the co-ordinates of the point + + + Vlll TRAVERSE TABLES. +C referred to the origin 0, are the sums of the co-ordinates OA, +AB, and BC, it being noted that BG runs in the opposite +direction to OA and AB} and its latitude is therefore negative. +In other words, the meridian and equatorial co-ordinates of any +point that is reached by a series of traverses, are the algebraical sums of the respective latitudes and departures of each one of the component traverses. It is usual to treat the directions +OJC and OY as positive, and OX' and OY' as negative; in other +words, northerly latitudes and easterly departures are treated +as + quantities, and southerly latitudes and westerly departures as quantities. In loose-needle surveys either meridian or quadrant angles +may be read at the will of the surveyor. In ordinary theodolite +surveys and in " racking " or " fixed-needle " surveys with the Vernier dial, the angles are determined that any given traverse makes with the meridian (or other arbitrary direction), so that +any angle may be registered from to 360. The fii'st step is therefore to reduce these meridian angles (or azimuths, as they +are often called) to quadrant angles by the following rules : If the meridian angle is letween and 90, the quadrant is +N.E., and the quadrant angle = meridian angle. + + + J. V J^JTVOJ. +TRAVERSE TABLES. ix +If the, meridian angle is between 90 and 180, the quadrant +is S.K, and the quadrant angle = 180 meridian angle. +If the meridian angle is between 180 and 270, the quadrant +angle is S. W., and the quadrant angle = meridian angle 180. +If the meridian angle is between 270 and 360, the quadrant +is N. W., and the quadrant angle = 360 meridian angle. +For example, to find the quadrant angles corresponding to +the following meridian angles : (a) 17 23' ; (6) 141 44' ; (c) 250 +21'; (d) 339, 08'. +Meridian angle. Quadrant angle. (a) 17 23' N. 1723'E. +(6) 141 44' S. (180 - 141 44') E. = S. 38 16' E. +(c) 250 21' S. (250 21' - 180) W. = S. 70 21' W. , +(d) 339 08' N. (360 - 339 08') W. = N. 20 52' W. +Sometimes these angles are simply written +17 23' + , -38 16'+, -70 21'-, +20 52'-, this method being specially convenient when any arbitrary line is selected as the direction of reference in preference to a meridian ; it is under +FIG. 3. +stood that the first sign always refers to the latitude and the +last to the departure. The successive stages in working out a traverse survey by +co-ordinates, preparatory to plotting, are best illustrated by an +example. Let Fig. 3 represent a traverse survey of an area + + + x TRAVERSE TABLES. +bounded by straight lines, executed by the " double fore-sight +" +method with an ordinary theodolite, the area forming a seven +sided polygon. The first two columns (see p. xii), namely the measured lengths of the sides and the observed theodolite readings, are obtained in the field and taken from the field-book in which they were entered.1 At the beginning of the survey +the theodolite is supposed to be pointed due north; the first reading gives therefore the meridian bearing of the first traverse +OA; the meridian bearings, or azimuths, of the subsequent traverses are obtained by the well-known rule : Add the observed theodolite reading to the last meridian bearing and subtract 180 from, or add 180 to, the sum, according as that sum is greater or less than 180. The result in this ca.se is as +follows : +Meridian bearing of OA 295 12' +Theodolite reading of AB 72 13' +367 25' 180 +Meridian bearing of AB 187 25' +Theodolite reading of B C 135 37' +323 02' 180 +Meridian bearing of B C 143 02' +Theodolite reading of CD 87 20' +230 28' 180 +Meridian bearing of CD 50 28' +Theodolite reading of DE 240 05' +290 33' 180 +Meridian bearing of DE 110 33' +Theodolite reading of EF 41 26' +151 59' 180 +Meridian bearing of EF 331 59' +Theodolite reading of FO 79 10' +411 09' 180 Meridian bearing of FO 231 09' +The meridian bearings thus obtained are entered in their +1 It goes without saying that the closing angle at 0, which in this case +should be equal to 244 03', is observed and noted in the field-book as a check, though it is not required for these calculations. + + + TRAVERSE TABLES. xi +proper column, and then the column of quadrant bearings is at once filled in (see p. xii), in accordance with the rules already given. By reference to the tables, the latitudes and departures are then determined by simple addition ; the first two may be +given in full by way of example : +64 48' DUt. Lat. Dep. 1000 425-78 904-83 400 170-31 361-93 8 3-41 7-24 +1408 599-5 1274-0 +7 25' 800 793-31 103-27 40 39-67 5-16 7 6-94 0-90 +847 839-9 109-3 +The latitudes and departures are entered in their re +spective columns. As this is a closed survey, returning to the starting point 0, the total north and south latitudes and the +total east and west departures ought to be respectively equal to each other, and it will be seen that such is practically the +case, fractions of a link being disregarded. The last two columns, headed total latitudes and departures, are really the successive co-ordinates of each of the survey stations ; they are obtained by the successive algebraical additions of the latitudes and departures respectively, the sum or difference taking the same sign as the larger of the two +figures. Thus, to take the latitudes, the latitude of the point +A +is evidently 599*5 links N; then we have : +Latitude of point B = 599'5 N. + 839-9 S. = (839-9 - 599-5) S. = 240-4 S. +Latitude of point C = 240'4 S. + 1428*6 S. = 1669*0 S. +Latitude of point D = 1669-0 S.+ 1059-2 N. = (1669-0 - 1059-2) S. = 609'8 S. +Latitude of point E = 609-8 S + 347-9 S. = 957-7 S. +Latitude of point F = 957-7 S. + 1743-6 N. = (1743-6 - 957-7) N.= 785-9 N. +Latitude of point = 785'9 N. + 786-0 S. = (786-0 - 785-9) S. = 0-1 S. +The total departures are calculated in precisely the same way. The clerical work of the addition is checked by adding up the two columns of latitude and the two of departure ; the differences between these respective pairs should be equal to the final total latitudes and departures. + + + Xll TRAVERSE TABLES. +3s +FABCDEOODCABEF + + + TRAVERSE TABLES. xiii +the irregular expansion and contraction of even the best drawing paper 1 is more than enough to introduce grave inaccuracies into the best drawn plan. As an example of the method of calculation, let it be +required to determine the distance and bearing of station E +from station B. From the column of total latitudes and departures we have +Station B. Lat. S. 240-4. Dep. W. 1383-3 Station E. Lat. S. 957-7. Dep. E. 1903-2 +Therefore E is 717-3 links S. and 3286'5 links E. of B. +Bearing of line BE = S. tan -1 -~j E. = S. 77 41' 15" E. +Distance EB = . = . +*ep'. = */tep* + lat.* = ' +.* . , +cos bearing sin bearing cos 77 41 15 +sn + 3286-5* = 3364 links +These calculations are best made in the usual way by the aid of tables of logarithms. In case of need, the traverse tables +can be used for them, as the departure column for distance += +1, is practically a table of natural sines, whilst the corresponding latitude column is practically a table of natural +cosines, and these evidently give all the elements required for the calculation. In ordinary practice it is, however, far better to use any good table of logarithms for this portion of the work. The above survey is an imaginary one, and there is therefore no closing error. In actual closed traverse surveys there is +of course usually some error. By working out the co-ordinates, +and by adding up the observed angles (including the closing angle), it is at once obvious whether the error is in the linear +or in the angular measurements ; in the latter case, if it is only +the closing angle that has been read wrong, the co-ordinates will close, though the angles do not. If the error falls within the required limits of accuracy, it is easily distributed between the co-ordinates, and the plotting is done from the co-ordinates thus rectified. +The following is an example from actual practice, of a survey +in a coal mine. A survey was started from a peg in the " flat," +1 Those interested in this matter should consult an important paper by +Mr. C. C. Leach. Transactions of the North of England Institute of Mining +Engineers, Vol. xxxiv., 1884-85, p. 175. +I + + + XIV TRAVERSE TABLES. +and was extended to a point in a " back place +" to which it was desired to drive a road from the peg in the flat. The theodolite was set up in the flat, using the centre line of the flat as the axis +of direction to which the survey was to be referred. A copy of the field-book is given below, many of the minor details +being, however, omitted. += + + + TRAVERSE TABLES. xv +The co-ordinates are worked out as previously explained, and the total latitudes and departures obtained as follows : + + + XVI TRAVERSE TABLES. +becomes one of quite secondary importance. All that is required to be known is already determined before the plotting is commenced. It may also be remarked that all the opera +tions up to and including the taking out of the total latitudes +and departures are of the utmost simplicity, involving no higher +S cede % inch - 1 Chcdrv +FIG. 4. +arithmetical knowledge than the addition and subtraction of decimals, and may hence be entrusted to any moderately intelligent lad, instead of occupying the time of the surveyor himself. The advantages of the use of co-ordinates are, however, + + + TRAVERSE TABLES. xvn +most evident when it is necessary to determine the area included in a closed traverse. Unless co-ordinates are used the +only method of determining such areas accurately is by an involved trigonometrical method, consisting of cutting the area up into triangles the apices of which meet in any assumed point. +The angles of each triangle have then to be calculated, the triangles solved, and the sum of their areas thus determined. This method is so laborious that it is never used in practice. Unless this or the method of co-ordinates is used, however, the determination of the area can only be made by first plotting the survey, by which a number of errors of more or less importance are necessarily introduced. +By the use of co-ordinates, all these difficulties are avoided, +and the area of any closed traverse can be calculated directly +and easily from its latitudes and departures, without any +plotting at all. The principle of the calculation is best seen from a simple example : +Let the five sided figure OABCD (Fig. 5) be the plan of +a traverse survey situated wholly on one side of the meridian +through the point 0, and let it be required to determine the area of the figure. The total latitudes and departures are calcu +lated in the usual manner, and we have for the respective survey stations : + + + xviii TRAVERSE TABLES. +Total latitude. Total departure. +00 +A Oa'( = -y) Oa( = 'x) +B Ob'( = - yi) Ob( = *:) +C Oc'( = ya) Oc( = x,} +D Od'( = #3) Od( = a?8) +Then the area of the figure +OABCD = d'DCSAa' - d'DO - OAa' +d'DCBAa' = d'DCc' + c'CBV + VBAu' +d'DCc' = UDd' + Cc'}d'c' += H+0)(-y-0) Hence += J[(0 + 3 )(0 - 2/ 3 ) + (aJ 3 + a; a) +/(dep. of + dep. of D)(lat. of - lat. of D) +(dep. of D 4- dep. of (7)(lat. of 7) - lat. of (7) +/. the area OABCD = J ( (dep. of (7 + dep. of 5) (lat. of C' - lat. of 5) +(dep. of 5 + dep. of -4)(lat. of B - lat. of A) +((dep. of A + dep. of 0)(lat. of A - lat. of 0) +The rule for the calculation of the area contained by a closed traverse is therefore as follows : +The algebraic sum of the total departures of each pair of adjacent angular stations is multiplied by the algebraic difference of their total latitudes ; the products thus obtained are added +together, and the sum divided by two gives the area required. In applying this rule it must be borne in mind that the station points must always be taken in strict order.1 To each +total latitude or departure the correct algebraic sign must be prefixed, and regard must be had to it in the arithmetical +1 It makes no difference whether the points be taken in the order in which they have been surveyed, or in the opposite order; the essential point +is that one regular order shall be adhered to. If the points are taken in the +opposite order the only difference will be that the area will have a instead +of a 4- sign. This is easily seen; for in the above calculation if the points +be taken in the opposite order, the signs of the sums of the departures will be +unaltered, and the signs of the differences of latitudes will be changed (e.g. +(y2 ?/3 ) instead of (y3 y2 )> etc.), so that the sign of the area will be +changed, its numerical value being unaffected. The sign obtained for the area of any closed traverse depends upon the direction of the first traverse, +and upon that in which the points are taken ; it is always considered as positive. + + + TRAVERSE TABLES. xix +operations involved. The result will be expressed in squares of the unit of measurement employed, square links if the survey was made in links, square feet or square metres if the distances were measured in feet or metres, etc. The above rule is occasionally stated in a different way, which is sometimes more convenient for calculation. The total latitude of each station is multiplied by the +algebraic sum of the departure of that traverse, and of the one next +following ; 1 the sum of the products thus obtained, divided by 2, +gives the area required. The departure here referred to is not the total departure +referred to the origin of the survey, but the departure of the traverse referred to its own starting station. It can easily be shown that these two rules are practically the same. For in Fig. 5, taking the values given above, we shall have for the departures of each traverse +Departure of point D referred to O +C +1 *7') +> ^" ^^ +Then according to the second rule +Twice area OABCD = +x +l - x.2 +X -Xxl +Again, according to the first rule, we have seen that +Twice area OABCD = +*s - s/3 - + 0*3 + s2)(ys - 2/2) + (a?2 + i)(y +- XIJ\ + Xl*J the same result as that given by the second rule. All that has been said of the first rule holds equally good of the second. In both of them the words latitude and +departure may also be interchanged without altering the result, so that there are really four different arithmetical operations +that can be employed indifferently. Yet another method is sometimes employed, known as that of +the " double meridian distance." In this the successive latitudes +are multiplied by multipliers obtained from the departures ; a +1 It is evident that the suras of the departures of any two traverses is +equal to difference between the total departures of the point before and the +point after the one being worked. + + + XX TRAVERSE TABLES. +column of " double departures " is formed by adding each +departure to the preceding one ; from these double departures the multipliers are obtained by adding each double departure to the last multiplier, the first multiplier being always zero. +By way of example, the area of the figure OABCD may be +calculated, the values of the departures and latitudes being as follows : + + + TRAVERSE TABLES. xxi +In both cases the results are of course identical, namely 49,910 square links or 0*4991 acre. It will be seen that the second method of calculation here produces a negative sign ; this would have been positive had the points been taken in the opposite order. +The following is an example of the application of the second rule to the same area : +Total latitudes. + + + XX11 TRAVERSE TABLES. +Latitude. + + + TRAVERSE TABLES. xxin +Stations. + + + XXIV TRAVERSE TABLES. +to select the traverse lines so as to equalize as nearly as possible the offset areas on either side ; this has to be done by inspection, +on the ground, and of course requires a good deal of practice. It occasionally happens that some of the points in a survey are determined by methods of triangulation instead of by +traversing. Broadly speaking, the term triangulation may be applied to the determination of any point by angular measure +ments from, the two ends of a base-line of known length ; the triangle is then solved, and the lengths of the two unknown sides calculated. This calculation is simply and easily performed by means of co-ordinates. +The problem in its most general form is shown in Fig. 7. +Suppose the points A,B have been already determined, their +CL' +Y' FIG. 7. +departures Oa and 01 being x and ^ and their latitudes Oa' +and Ob' being y and ^ respectively. The angles AC(= a) +and ABC( = &) are determined by observation ; from these data the latitude and departure of have to be calculated. Let +the quadrant bearing of the line BA be N". a E. ; then the +quadrant bearing (]3) of the line EC = 1ST. (a + 6) E., and the +quadrant bearing (y) of the line A C = S. (a a) E. Care must be taken in every case that the signs are correct according to +the particular quadrant. +Then tan 7=-^-= +a'c' y +tan * ~ + +b'c Oc' yl +Whence Oc' = * tan ? + x +tan 7 + tan y8 + + + TRAVERSE TABLES. xxv +The departure Oc may be calculated from the corresponding formula : QC _ *i cot & + V + x cot 7 yt +cot /3 + cot 7 +The above is the method generally employed, and is perhaps the most convenient when the ordinary mathematical tables are +available. It is, however, possible to use a method to which the traverse tables can be applied, and the work thus consider +ably simplified. For in Fig. 7 Oc = Oa + ac = x + OK +... Qc = x sin (a + b) +which may be written +n AB sin b . 10 sin y +10 sin (a + b) +All these values can now be taken from the traverse tables +because +AB sin b is the departure of distance AB for the angle b +10 sin 7 is the departure of distance 10 for the angle 7 +10 sin (a 4- &) is the departure of distance 10 for the angle a -f Z>; if +a + b is greater than 90, the angle 180 (a + b) should be used instead. +Another form for the above expression is +n +, AB sin a . sin +:a?1+ *in(a + b) +For the latitude Oc', either of the two following expressions may be used: +^ +, , AB sin a . cos fl +1 +sin (a + i) s^n ^ C08 +sin (a + b) +Any of these may be used with the traverse table as above +indicated, by multiplying numerator and denominator by 10, or by any other convenient number so that in the last case the second term of the formula for Oc would read +(dep of AB for angle &) x (lat. of 10 for angle 7) +dep. of 10 for angle (a + 6) +As an example of these calculations let the co-ordinates of the two points A,B of a traverse survey be as follows : + + + XXVI TRAVERSE TABLES. +Lat. ofJ. ... N. 87 links Dep. of^L ... W. 204 links +Lat. of ... S. 85 Dep. of B ... E. 89 +Quadrant bearing of AB = S. 59 35' E. Length of AB - 340 links. +From A and B, Fig. 8, the angles between the direction AB +and the lines joining these points with the two points C and D, +Scale inch,<-1 Chain. +which it is desired to fix, have been observed, and found to be as follows : +Angle CAB = 40 28' += 69 13' +Angle ABC = 68 59' +Angle A BD = 38 05' +Then, to determine the point C, we have by the first method +Meridian bearing of AC = 180 00' - 59 35' - 40 28' = 79 57' +Quadrant bearing of AC = N. 79 57' E. +Meridian bearing of BC = 360 00' - 59 35' + G8 59' = 369 24' +Quadrant bearing of BC = N. 9 24' E. +T} , (87 x tan 79 57') + (85 x tan 9 24') + 89 + 204 +tan 79 57' - tan 9 24' = N. 146 And Oc = ( 2Q4 x cot 7 9 57') + (89 x cot 9 24') + 87 + 85 += E. 127 +cot 9 24'^- cot 79 57' +As a check upon the arithmetical work of the calculations +we have +Tan 9 24' = I27 +n +"" 89 = 0-1 G5 +14G + 85 +To determine the point D, we have + + + TRAVERSE TABLES. xxvii +Meridian bearing of AD = 180 - 59 35' + 69 13' = 189 38' +Quadrant bearing of AD = S. 9 38' W. +Meridian bearing of BD = 360 - 59 35' - 38 05' = 262 20' +Quadrant bearing of BD = S. 82 20' W. +T +, n r _ (87 x tan 9 38') + (85 x tan 82 20') + 204 + 89 +tan 82 20' - tan 9 38' = S. 129 . d , = (204 x cot 9 38') + (89 cot 82 20? +) + 87 + 85 cot 9 38' cot 82 20' = W. 240 +In applying these formulas special attention must be paid to the signs of the departures and latitudes. Using now the second method given above +O -201 + (34 ' sin 68 59/ )( 10 sin 79 57/) +10 sin (68 59' + 40 28') +From the tables +Departure of 300 = 280-04 for angle G8 59' +Departure of _40 = 37-34 +Departure of 340 = 317-38 +Departure of 10 for angle 79 57' = 9'8466 +Departure of 10 for angle 109 27' = departure for angle 70 33' = 9-4293 += -204 + 331-4 = +127-4 +, = 87 , (340 . sin 68 59') x (10 cos 79 57') +10 sin (68 59' + 40 28') +From the tables +Latitude of 10 for angle 79 57' = 1-7451 , . 7 317-38 x 1-7451 9-4293 = 87 + 58-7 = +145-7 +Od = -904 - (34 sin 38 05') x (10 . sin 9 38') +10. sin (69 13' + 38 05') 9fu _ 209-71 x 1-6734 9-5476 = -(204 + 36-7) = -240-7 +Od' = 87 (340 . sin 38 05') x (10 . cos 9 38') +10 . sin (69 13' + 38 O5'j~~ 209-71 x 9-859 9-5476 = 87-216-5 = -129-5 +UNIVERSITY +CALIF01 + + + xxviii TRAVERSE TABLES. +The results obtained are of course practically the same if the calculations are made with a sufficient degree of accuracy, but the use of the traverse tables even in such triangulation +problems is seen to very much shorten the calculations. + + + TRAVERSE TABLES. + + + Degrees. +Dist. + + + e + + + 1 Degree. +Dist. + + + 6 + + + 2 Degrees. +Dist. + + + 8 + + + 3 Degrees. +Dist. + + + 6 + + + 4 Degrees. +Dis + + + t + + + 5 Degrees. +Dist. + + + 6 + + + 6 Degrees. +Dist + + + + + 7 Degrees, +Dist + + + 6 + + + 8 Degrees. +Dist + + + 6 + + + 9 Degrees. +Dist. + + + e + + + 10 Degrees. +Dist + + + e + + + 11 Degrees. +Dist. + + + e + + + 12 Degrees. +Dist. + + + + + 13 Degrees. +Dist. + + + 6 + + + 14 Degrees. +Dist. + + + e + + + 15 Degrees. +Dist. + + + e + + + 16 Degrees. +Dist + + + ( + + + 17 Degrees. +Dist. + + + 6 + + + 18 Degrees. +Dist. + + + 6 + + + 19 Degrees. +Dist. + + + 6 + + + 20 Degrees. +Dist. + + + 6 + + + 21 Degrees. +Dist. + + + 6 + + + 22 Degrees. +Dist. + + + + + 23 Degrees. +Dist. + + + 6 + + + 24 Degrees. +Dist + + + 6 + + + 25 Degrees. +Dist + + + 6 + + + 26 Degrees. +Diet. + + + I UNIVERSITY I +Vog . -*\*-S + + + 27 Degrees. +Dist + + + 6 + + + 28 Degrees. +Dist. + + + 6 + + + 29 Degrees +Dist. + + + 6 + + + 30 Degrees. +Dist, + + + ( + + + 31 Degrees. +Dist. + + + 6 + + + 32 Degrees. +Dist. + + + 6 + + + 33 Degrees. +Dist. \ No newline at end of file diff --git a/storage/QR6V9JN7/traversetableswi00louirich.pdf b/storage/QR6V9JN7/traversetableswi00louirich.pdf new file mode 100644 index 0000000..43d3ae4 Binary files /dev/null and b/storage/QR6V9JN7/traversetableswi00louirich.pdf differ diff --git a/storage/RJEQ5ZPF/.zotero-ft-cache b/storage/RJEQ5ZPF/.zotero-ft-cache new file mode 100644 index 0000000..3960553 --- /dev/null +++ b/storage/RJEQ5ZPF/.zotero-ft-cache @@ -0,0 +1,2514 @@ +1 +Einstein’s Investigations of Galilean Covariant +Electrodynamics prior to 1905 +John D. Norton1 +Department of History and Philosophy of Science +University of Pittsburgh +jdnorton@pitt.edu +Einstein learned from the magnet and conductor thought experiments how to use field +transformation laws to extend the covariance to Maxwell’s electrodynamics. If he +persisted in his use of this device, he would have found that the theory cleaves into two +Galilean covariant parts, each with different field transformation laws. The tension +between the two parts reflects a failure not mentioned by Einstein: that the relativity of +motion manifested by observables in the magnet and conductor thought experiment does +not extend to all observables in electrodynamics. An examination of Ritz’s work shows +that Einstein’s early view could not have coincided with Ritz’s on an emission theory of +light, but only with that of a conveniently reconstructed Ritz. One Ritz-like emission +theory, attributed by Pauli to Ritz, proves to be a natural extension of the Galilean +covariant part of Maxwell’s theory that happens also to accommodate the magnet and +conductor thought experiment. Einstein's famous chasing a light beam thought +experiment fails as an objection to an ether-based, electrodynamical theory of light. +However it would allow Einstein to formulate his general objections to all emission +theories of light in a very sharp form. Einstein found two well known experimental +results of 18th and19th century optics compelling (Fizeau’s experiment, stellar +aberration), while the accomplished Michelson-Morley experiment played no memorable +role. I suggest they owe their importance to their providing a direct experimental +grounding for Lorentz’ local time, the precursor of Einstein’s relativity of simultaneity, +and do it essentially independently of electrodynamical theory. I attribute Einstein’s +success to his determination to implement a principle of relativity in electrodynamics, +but I urge that we not invest this stubbornness with any mystical prescience. +1 I am grateful to Diana Buchwald, Olivier Darrigol, Allen Janis, Michel Janssen, Robert Rynasiewicz and +John Stachel for helpful discussion and for assistance in accessing source materials. + + + 2 +1. Introduction +Although we have virtually no primary sources, the historical scholarship of the last few decades +has painstakingly assembled clues from many places to give us a pretty good sketch of Einstein’s route to +special relativity. He had a youthful interest in electrodynamics and light with no apparent skepticism +about the ether. As a sixteen year old in the summer of 1895, he wrote an essay proposing experimental +investigation into the state of the ether associated with an electromagnetic field.2 The skepticism emerged +later along with a growth of his knowledge of electrodynamics. By the end of 1901, he was writing +confidently of work on a “capital paper” on the electrodynamics of moving bodies that expressed ideas +on relative motion.3 Later recollections stress the guiding influence of his recognition that the electric field +induced by a moving magnet has only a relative existence. His pursuit of the relativity of inertial motion +led him to reject Maxwell’s theory and its attendant constancy of the velocity of light with respect to the +ether in favor of investigation of an emission theory, somehow akin to Ritz’ later approach, in which the +speed of light was a constant with respect to the emitter. These investigations proved unsatisfactory and +Einstein was brought to a crisis in the apparent irreconcilability of the relativity of inertial motion and the +constancy of the velocity of light demanded by Maxwell’s electrodynamics. The solution suddenly came +to Einstein with the recognition of the relativity of simultaneity and a mere five to six weeks was all that +was needed to complete writing the paper, which was received by Annalen der Physik on June 30, 1905. +My understanding of this episode is framed essentially by the historical researches of John +Stachel, individually and in collaboration with the editors of Volume 2 of the Collected Papers of Albert +Einstein; and by Robert Rynasiewicz and his collaborators. See Stachel (1987, 1989), Stachel et al. (1989a), +Rynasiewicz (2000) and Earman et al. (1983) and the citations therein for their debts to other scholarship. +In addition to the arduous scholarship of discovering and developing our present framework, they have +supplied particular insights of importance. For example, Rynasiewicz and his collaborators have pointed +out that Einstein must have known of field transformations akin to the Lorentz transformation for fields +years before he adopted the novel kinematics of the Lorentz transformation for space and time, so that +the historical narrative must somehow account for a development from field transformation to the space +and time transformations they necessitate. In addition to his work as editor of the Einstein papers in +finding source material, Stachel assembled the many small clues that reveal Einstein’s serious +consideration of an emission theory of light; and he gave us the crucial insight that Einstein regarded the +Michelson-Morley experiment as evidence for the principle of relativity, whereas later writers almost +universally use it as support for the light postulate of special relativity.4 +My goal in this paper is not to present a seamless account of Einstein’s path to special relativity. +That is an ambitious project, hampered by lack of sources and requiring a synthesis with Einstein’s other +2 Papers, Vol. 1, Doc. 5. +3 Papers, Vol. 1, Doc. 128. +4 Even today, this point needs emphasis. The Michelson-Morley experiment is fully compatible with an +emission theory of light that contradicts the light postulate. + + + 3 +research interests at the time.5 Rather I seek to extend our understanding of several aspects of Einstein’s +path to special relativity: +• The outcome of the magnet and conductor thought experiment. This thought experiment showed Einstein +that electric and magnetic fields might transform between inertial frames under rules that mix both +fields and he hoped that this device might somehow enable Maxwell’s electrodynamics to be made +compatible with the principle of relativity. In Section 2, I will map out the prospects for the Galilean +covariance of Maxwell’s theory opened by this new device. They are promising but prove not to yield a +single theory. A full exploration of the possibilities yields two partial theories with different field +transformation laws and I call them the “magnet and conductor partial theory” and the “two charge +partial theory”. Each is associated with one part of Maxwell’s theory and the tension between them +reflects an awkwardness that Einstein did not mention, but was mentioned by Föppl, a possible source +for Einstein’s magnet and conductor thought experiment. It is that the relativity of motion of +observables of the magnet and conductor thought experiment is not reflected throughout Maxwell’s +theory. Föppl illustrated the failure with his two charge thought experiment. That failure, captured +formally in the existence of two incompatible partial theories each with its own defects, would have +been a pressing problem for Einstein’s program of relativizing electrodynamics and, perhaps, fatally +discouraging to a less stubborn thinker. +• Einstein’s speculation on an emission theory of light. In Section 3, I show why Einstein’s remarks that he +had held to Ritz’s view on an emission theory of light cannot be taken literally. Ritz’s work depended +essentially on a skepticism about fields, which Einstein did not share and which led Ritz to seek action +at a distance laws as the fundamental laws of electrodynamics. However a folk version of Ritz’s view, +articulated most clearly by Pauli, is a good candidate for an emission theory that Einstein might have +entertained. It can be grafted directly onto the stronger one of the two partial theories mentioned above +(“magnet and conductor partial theory”) and would be initially appealing since would promise to +preserve the gains of the analysis of the magnet and conductor while also accommodating an emission +theory. Since the resulting theory still does not escape the defect of that partial theory, it was at best a +brief way station for Einstein as he proceeded to develop quite general objections to any emission +theory of light that I outline in Section 4. +• Einstein’s chasing a light beam thought experiment. In his Autobiographical Notes,6 Einstein emphasized the +importance of this thought experiment, first devised when he was 16 years old. In Section 5, I will argue +that its original significance lay in arousing a visceral suspicion towards ether based theories, while not +giving any cogent reasons for disbelieving such theories. The fertility of its basic idea—investigating +how observers moving with light see the waveform—was proven later in Einstein’s work, justifying the +prominence Einstein accorded it in his recollections. In Section 6, I will suggest it enables strong +5 How could we ignore the possibility of a connection between Einstein’s reflections on an emission +theory of light and his 1905 postulation of the light quantum hypothesis? But what might that connection +be? See Rynasiewicz, 2000, Sections 6 and 7. +6 Einstein (1949), pp. 48-51. + + + 4 +arguments against any emission theory of light, giving powerful yet simple grounding for his +complaint that no emission theory could be formulated as a field theory. +• Fizeau’s experiment on the velocity of light in moving water and stellar aberration. Einstein was scarcely able +to remember if he knew of the most accomplished of the 19th century experiments on light +propagation, the Michelson-Morley experiment, prior to his writing of the 1905 paper. In its place, +Einstein singled out Fizeau’s experiment and stellar aberration as the more memorable and compelling +experiments. In Section 7, I will suggest their importance derives from their giving direct experimental +foundation to Lorentz’ notion of local time without requiring any detailed electrodynamical theory or +Lorentz’s theorem of corresponding states. I expect this last point to be evident to anyone who has fully +understood the relevant section of Lorentz’s 1895, Versuch, and how directly local time is expressed in +the experimental results. Since the notion of local time becomes the relativity of simultaneity, when +reinterpreted in the context of the principle of relativity, I suggest that these experiments earned their +place in Einstein’s thought by providing an experimentally grounded pathway to the relativity of +simultaneity. +• In section 8, I remark that what is distinctive about the deliberations reported throughout this paper is +that the effect of the motion of an observer on light is investigated in terms of its effect on the waveform +of the light. While the historical evidence available is small, essentially none of it gives importance to +Einstein reflecting on light signals used to synchronize clocks. So we must even allow the possibility +that these reflections only entered in the last moments of years of work, when the essential results, +including the relativity of simultaneity, were already established, but in need of a vivid and compelling +mode of presentation. I warn of the danger of illicitly transferring the prominence of light signals and +clocks in our thought to Einstein’s historical pathway to special relativity. +It might seem perverse to persist in efforts to reconstruct Einstein’s path to special relativity when the +source material is so scant. However I think the effort is justified by the continuing fascination that +Einstein’s discovery exerts both inside and outside history of science. It has encouraged all manner of +speculation by scholars about the relationship between Einstein’s discovery and their special fields of +interest, be they modes and methods within science; or Einstein’s broader social and cultural context; just +about everything in between; and many things that are not in between. As this literature continues to +grow, it would seem perverse to me not to persist in efforts to reconstruct what was surely most directly +relevant of all to the discovery, Einstein’s own antecedent theorizing. And I’d really like to know what +Einstein was thinking on the way to special relativity! In these efforts, I am fully aware of the +historiographical pitfalls so well described by Stachel (1989, pp. 158-59), so that I need only refer the +reader directly to that discussion and to endorse Stachel’s analysis. + + + 5 +2. What Einstein Learned from the Magnet and Conductor +Thought Experiment +Themagnetandconductorthoughtexperiment +Einstein began his celebrated 1905 “On the Electrodynamics of Moving Bodies,” by describing +how then current, ether based electrodynamics treated the case of a magnet and conductor in relative +motion. The full theoretical account distinguished sharply between the case of the magnet at rest in the +ether and the conductor at rest in the ether. In the first case, a simple application of the Lorentz force law +yields the measurable current. In the second, the time varying magnetic field of the moving magnet +induces, according to Maxwell’s equations, a new entity, an electric field, and this field brings about the +measurable current. What is curious is that the currents arising in each case are the same. The theory +distinguishes the two cases but there is no observable difference between them; the measurable current +depends only on the relative velocity. Cases like these, Einstein suggested, indicate that the ether state of +rest is superfluous and that the principle of relativity ought to apply to electrodynamics.7 +In a manuscript from 1920, Einstein recalled how this simple reflection had played an important +role in the thinking that led him to special relativity. The essentially relevant parts of his recollection +read:8 +In setting up the special theory of relativity, the following ... idea concerning Faraday’s +magnet-electric induction [experiment] played a guiding role for me. +[magnet conductor thought experiment described]. +The idea, however, that these were two, in principle different cases was unbearable for me. +The difference between the two, I was convinced, could only be a difference in choice of +viewpoint and not a real difference. Judged from the magnet, there was certainly no electric +field present. Judged from the electric circuit, there certainly was one present. Thus the +existence of the electric field was a relative one, according to the state of motion of the +coordinate system used, and only the electric and magnetic field together could be ascribed +a kind of objective reality, apart from the state of motion of the observer or the coordinate +system. The phenomenon of magneto-electric induction compelled me to postulate the +(special) principle of relativity. +[Footnote] The difficulty to be overcome lay in the constancy of the velocity of light in a +vacuum, which I first believed had to be given up. Only after years of [jahrelang] groping +did I notice that the difficulty lay in the arbitrariness of basic kinematical concepts. +7 Einstein (1910, pp. 15-16) gives a slightly elaborated version of the original 1905 statement of the thought +experiment. +8 Einstein (1920). Einstein’s emphasis. + + + 6 +Einstein’s other recollection of the importance of this thought experiment is in a typescript note in +English, with handwritten German corrections, in honor of Albert A. Michelson’s 100th birthday and +dated December 19, 1952.9 In the struck out typescript, Einstein discounts the influence of the Michelson +Morley experiment on him “during the seven and more years that the development of the Special Theory +of Relativity had been my entire life.” The handwritten notation expands and corrects the struck out +typescript:10 +My own thought was more indirectly influenced by the famous Michelson-Morley +experiment. I learned of it through Lorentz’ path breaking investigation on the +electrodynamics of moving bodies (1895), of which I knew before the establishment of the +special theory of relativity. Lorentz’ basic assumption of a resting ether did not seem +directly convincing to me, since it led to an [struck out: to me artificial appearing] +interpretation of the Michelson-Morley experiment, which [struck out: did not convince +me] seemed unnatural to me. My direct path to the sp. th. rel. was mainly determined by +the conviction that the electromotive force induced in a conductor moving in a magnetic +field is nothing other than an electric field. But the result of Fizeau’s experiment and the +phenomenon of aberration also guided me. +These recollections leave no doubt of the importance of the magnet and conductor thought experiment in +directing Einstein’s work towards special relativity. It is significant that Einstein calls it to mind in a +tribute to Michelson at a time when the lore held that the Michelson-Morley experiment played a decisive +role in leading Einstein to special relativity. Einstein corrects this lore and puts the magnet and conductor +thought experiment in its place. +The recollections put no date on when the thought experiment compelled Einstein to postulate +the special principle of relativity. The strong suggestion in both is that it was early in Einstein’s +deliberations. That early timing is made more concrete by the footnote to the 1920 recollection. After the +thought experiment, much must still happen. He still faces years of years of groping and will still give +serious thought to abandoning the constancy of the velocity of light—presumably referring to Einstein’s +deliberations on an emission theory of light—before he arrives at the 1905 insight of the relativity of +simultaneity. +Thetransformationoftheelectricandmagneticfield +The magnet and conductor thought experiment not only compelled Einstein to postulate the +special principle of relativity, it also gave him an important new device for realizing it: as we transform +between inertial frames, the electric and magnetic fields transform by rules that mix the two fields +linearly. What might manifest as a pure magnetic field in one frame of reference will manifest as a +combination of electric and magnetic fields in another. This device enabled Einstein to see how the +9 Document with control number 1 168, Einstein Archive. Available in facsimile at the Einstein Archives +Online as http://www.alberteinstein.info/db/ViewImage.do?DocumentID=34187&Page=1 +10 Part of translation from Stachel (1989a, p. 262). + + + 7 +relativity of motion in the observables of electrodynamics could be extended to the full theory. The +induced electric field surrounding a moving magnet does not betoken the absolute motion of the magnet. +It only betokens the motion of the magnet in relation to an observer, who judges the field generated by +the magnet to have both magnetic and electric components. +This device of field transformation persists in Einstein’s theorizing. It is central to the +demonstration of the relativity of motion in electrodynamics in his 1905 “On the electrodynamics of +moving bodies,” with the full expression for the Lorentz transformation of the electric and magnetic field +given in its Section 6. +Whichtransformation?11 +Years before, when Einstein first learned the device of such field transformations from the +magnet and conductor thought experiment, upon which transformation did Einstein settle? Surely it was +not the full transformation equations of 1905, but something a little less. What was it? +The thought experiment gives us just one special case that is easily reconstructed, as I have done +in Appendix A. In the (primed) rest frame of a magnet, we have a magnetic field H’ and no electric field +(E’=0). If a charge e moves at velocity v in this magnetic field, then the Lorentz force law in vacuo (L, +below) tells us that the force f’ on the charge is f’/e = (1/c)(vxH’). Einstein now expects that this same +force must arise in the (unprimed) rest frame of the charge from the transform of E’, the electric field +E = (1/c)(vxH’). That is, the field E’=0 in the magnet rest frame transforms into the field E = (1/c)(vxH’) +in a frame moving at v. Schematically: +E’=0  E = (1/c)(vxH’) (1) +The natural linear generalization of this rule is just +E = E’ + (1/c)(vxH’) (2) +(and I will argue below that this is more than just a natural choice; it is forced in certain circumstances). +What rule should apply to the transformation of H? There is a single answer to which modern readers are +understandably drawn. Because of the symmetrical entry of E and H fields into Maxwell’s equation, +would not Einstein presume a similar transformation law for H so that the combined law is +E = E’ + (1/c)(vxH’) H = H’ – (1/c)(vxE’) (3) +11 What follows is limited to investigation of the prospects of the device of field transformations in the +context of Lorentz’ version of Maxwell’s theory, which is based on just two fields as the basic quantities. +This became Einstein’s preferred version of Maxwell’s theory and he had announced his intention to +study it as early as December 28, 1901. (Papers, Vol. 1, Doc. 131.) John Stachel has pointed out to me that +the two field transformations of Table 1 arise naturally in versions of Maxwell’s theory based on four +fields, E, B, D and H, such as Hertz’ theory, which we know Einstein had studied earlier. (Papers, Vol. 1, +Doc. 52.) E and B are governed by transformation (5) and D and H are governed by transformation (4). +For a modern explication of the two transformations, see Stachel (1984). We might also modify Maxwell’s +theory so that just one field transformation applies. Jammer and Stachel (1980) drop the ∂H/∂t term in +(M4) to recover a modified theory that (excepting the Lorentz force law (L)) is covariant under (4). + + + 8 +This transformation is the field transformation law Einstein presented in his 1905 paper up to first order +quantities in v/c; and it is the very field transformation law that Einstein would have found when he +read Lorentz’s (1895) presentation of his theorem of corresponding states. +While it is possible that Einstein may have inferred to this transformation, I do not think that +there are good grounds to expect it.12 The symmetry of E and H in Maxwell electrodynamics is only +partial. They do not enter symmetrically in the Lorentz force law and the E field couples to sources +whereas the H field does not, so symmetry is not a compelling reason to proceed from (2) to (3). Of course +we know in the long run that cultivation of (3) will bear great fruit. But, to use it in the short run, requires +some prescience. Use of the first order Lorentz field transformation (3) requires the use of Lorentz’ local +time in transforming between frames of reference; otherwise covariance of Maxwell’s equations fails even +in first order and the whole exercise is for naught. It is one thing to use the first order Lorentz +transformation and local time as Lorentz did: as a computational device for generating solutions of +Maxwell’s equations and, carefully, on a case by case basis, to show that various optical experiments +admit no (first order) detection of the earth’s motion with respect to the ether. But Einstein’s quest is for +the transformation that implements the relativity group. That is quite another thing. If he is able to use +the first order Lorentz transformation and local time to implement that group, then he would have +already to recognize that Lorentz’ local time is more than a computational convenience. He must see it is +the real time of clocks, the time of an inertial frame, every bit as good as the time of the frame from which +he transformed. That requires him already to have his insight into the relativity of simultaneity. Further, +since the first order Lorentz transformation preserves the speed of light to first order, there would seem +little scope to doubt the constancy of the speed of light and toy with an emission theory of light. +Thus it is unlikely that Einstein inferred directly to the first order Lorentz transformations (3) +from the magnet and conductor thought experiment; or, if he did, that he retained them in the core of his +theorizing. For his recollections require years of reflection to pass before he arrived at the moment when +his insight into simultaneity was decisive; and the above recollections suggest that the time period in +which he entertained an emission theory of light was in those intervening years. Curious also is that the +1952 recollection contrasts Lorentz’ 1895 work, which is criticized for its treatment of the ether, with +Einstein’s reflections on the magnet and conductor that provided the “direct path.” That is an unlikely +contrast if the magnet and conductor thought experiment brought Einstein directly to the essential +content of Lorentz’ work. +TheprospectsofaGalileancovariantelectrodynamics +So what transformation was the immediate outcome of the magnet and conductor thought +experiment for Einstein? We read directly from his recollections that it compelled him to seek an ether +free electrodynamics compatible with the principle of relativity and one that may exploit some sort of +12 The transformation is incomplete; it forms a group only if quantities of second order and higher are +ignored. That can be remedied, of course, by the adjustments of 1905; but that presupposes sufficient +commitment to the equations to want to remedy the problem. + + + 9 +field transformation law akin to (2) or (3). We know that as early as December 1901, Einstein was hard at +work on a paper on a theory of the electrodynamics of moving bodies whose novelty included some ideas +on relative motion.13 So presumably he was in possession of some sort of novel theory, although +evidently it was not sufficiently coherent for him to proceed all the way to attempt publication. +While we have no direct statement of what that theory might have looked like, it is a matter of +straightforward calculation to determine what the possibilities were. If we presume that Einstein’s +kinematics of space and time remain Galilean, then the field transformation laws associated with +Maxwell’s electrodynamics are given uniquely in Table 1. The table shows the four Maxwell field +equations in vacuo, in Gaussian units, with charge density ρ and electric current flux j=ρv, for a charge +distribution moving with velocity v. +13 Einstein wrote to Mileva Maric on December 17, 1901: “I am now working very eagerly on an +electrodynamics of moving bodies, which promises to become a capital paper. I wrote to you that I +doubted the correctness of the ideas about relative motion. But my doubts were based solely on a simple +mathematical error. Now I believe in it more than ever.” (Papers, Vol. 1, Doc. 128). See also Einstein to +Maric, December 19, 1901, for a report by Einstein on discussions with Alfred Kleiner on “my ideas on the +electrodynamics of moving bodies” (Papers, Vol. 1, Doc. 130). The possessive “my” here seems to have +eclipsed Einstein’s earlier remark to Maric, March 27, 1901, “How happy and proud I will be when the +two of us together will have brought our work on the relative motion to a victorious conclusion!” (Papers, +Vol. 1, Doc. 94; translations from Beck, 1983.) + + + 10 +∇.E = 4πρ (M1) ∇.H = 0 (M2) +€ +∇ × H = 4cπ j+ 1c +∂E +∂t (M3) +€ +∇ × E = − 1c +∂H +∂t (M4) +Lorentz force law +f/e = E + (1/c)(vxH) (L) +covariant under +covariant under +Galilean time and space transformation +t=t’ r=r’–ut’ +Field transformations +E = E’ H = H’ – (1/c)(uxE’) (4) +Galilean time and space transformation +t=t’ r=r’–ut’ +Field transformations +E = E’ + (1/c)(uxH’) H = H’ (5) +The Two Charge Partial Theory The Magnet and Conductor Partial Theory +Defect +• A moving magnet does not induce an electric +field. +• The Lorentz force law is not included, so +observable effects of electric and magnetic fields +are not deducible. +Defect +•A moving charge does not induce a magnetic +field. +Table 1. Extent of Galilean Covariance of Maxwell’s Electrodynamics +The table divides neatly into two columns. The two equations (M1) and (M3) are Galilean +covariant if the field transformation (4) is invoked. The two equations (M2) and (M4) along with the +Lorentz force law (L) are Galilean covariant if the field transformation (5) is invoked.14 (The +demonstration of covariance is standard and sketched in Appendix B.) Unlike the first order Lorentz +transformation (3), all these covariances are exact; they hold to all orders in v/c and they form a group. +There is a lot to be read from the way the table divides. +It is shown in Appendix A that the content of the right hand column-- Maxwell equations (M2) +and (M4) and the Lorentz force law (L)—are all that is needed to treat the magnet and conductor thought +experiment in a Galilean covariant calculation. Hence I have labeled the equations in the right hand +column the “magnet and conductor partial theory” since it is all that is needed to treat the theory of the magnet +and conductor thought experiment in a manner compatible with the principle of relativity of inertial motion. This +14 I adopt the obvious conventions. The Galilean transformation maps a coordinate system (t’, r’=(x’, y’, +z’)) to another (t, r=(x, y, z)), moving with velocity u. + + + 11 +was Einstein’s stated goal for all electrodynamics and here it is already for the case he found +inspirational. +What mars the success of this partial theory, however, is that forces empirically incorrect results +when it is applied to other cases. Take the case of a charge at rest. It is surrounded by an electrostatic field +but no magnetic field, so H’=0. If we now view this charge from another frame, the transformation H=H’ +(5) assures us that there is still no magnetic field surrounding the charge. But that contradicts Oersted’s +famous result that an electric current—charges in motion—are surrounded by a magnetic field. +Föppl’stwochargesthoughtexperiment +What are we to make of the other column in Table 1? Here is the remainder of Maxwell +electrodynamics and it is Galilean covariant, but under a different field transformation law! This +difference is the formal expression of a problem that Einstein did not mention in his celebrated discussion +of the magnet and conductor thought experiment. In the case of a magnet and conductor, a +straightforward application of Maxwell’s theory shows that the observables depend only on the relative +motion. But one can readily construct other thought experiments in which the observables do depend on +absolute motions—or that they actually do not would require exploitation of the full apparatus +developed by Lorentz that gets its final expression in Einstein’s theory of relativity. +That there were other problematic thought experiments readily at hand had been pointed out +clearly by August Föppl (1894) in the first of a venerable lineage of electrodynamics texts. Föppl’s (1894, +Part 5, Ch.1) text includes a favorable discussion of the relativity of motion and inquires into the extent to +which it may be realized in Maxwell’s electrodynamics. The magnet and conductor thought experiment is +presented (pp. 309-10) as a case in which the relativity of motion is respected. As Holton (1973) shows in +his discussion of this aspect of Föppl’s work, there is some reason to believe that Einstein had read the +Föppl volume, with its version of the thought experiment Einstein would make famous. Föppl +immediately proceeded to warn his readers that the relativity of motion was not always respected and +one might not always get the same results when systems are set into uniform motion. He made good on +the warning with an even simpler thought experiment (pp. 310-11) that I will call the “two charges +thought experiment.” +One recognizes all the more that such a careful analysis [as given to the magnet and +conductor] really was required from the fact that analysis does not yield the same result in +all cases. Consider, for example, two electrically charged particles (material points) that +move off next to one another in parallel paths with the same speed. They are at rest relative +to one another. However they act on one another with quite different forces than they +would if they were at absolute rest. Motion through the medium [ether] now leads to +electrical convection and displacement currents and, in connection with them, to a +magnetic field that is not present in the state of absolute rest. So this will still be true, if we +also keep all external, disturbing influences distant and imagine both particles alone in an +ether filled space, so that there are absolutely no reference bodies present, against which +we could observe motion. Absolute motion already manifests a quite definite influence on + + + 12 +them, whereas that [absolute motion] could not be distinguished at all from a state of rest +according to the axiom of kinematics discussed in the previous section. In cases of this type, +therefore, the action of the bodies on each other does not depend solely on their relative +motion. +The thought experiment is very simple. Consider two charges at rest in the ether. Their interaction is +determined by ordinary electrostatics. They exert forces on each other according to Coulomb’s inverse +square law. Now set them into uniform motion. The interaction becomes very complicated. The moving +charge becomes an electric current that will generate a magnetic field; and the time varying electric field +around the moving charges will also generate a magnetic field. This magnetic field will act on the charges +moving through it. In the case of the magnet and conductor, the analogous induced electric field is almost +miraculously of just the right magnitude to obliterate any observable effect that might reveal which of the +magnet or conductor is in absolute motion. The same miracle does not happen with the two charges. The +extra forces due to the induced magnetic field are simply added to those already due to the electric field. +The result is that the forces acting and thus the motions resulting would allow a co-moving observer to +distinguish whether the pair of charges is moving through the ether or is at rest.15 +Appendix C gives the calculations needed to show that the principle of relativity fails for the +observables in the case of the two charges. The appendix calculates the general case of any static +distribution of charges whatever that is then set into uniform motion, since it proves to be no more +complicated. In the general case, new forces appear in the moving system as a result of the induced +magnetic field, although the forces are second order in v/c small. What is important for our purposes, as +Appendix C shows, is that Maxwell’s equations (M1) and (M3) are all that is needed to compute the +original field and the new magnetic field arising when the charges are set in motion. These equations are +used to infer that the E field of the charge distribution induces a magnetic field H = –(1/c)(vxE) when +the system is set into uniform motion with velocity –v. It is easy to see that this very same induced +magnetic field could have been inferred directly from the field transformation law (4). The upshot is that +the theory of the left hand column of Table 1, the “two charges partial theory” is all that is needed to treat the +fields of the two charges thought experiment in a manner compatible with the principle of relativity of inertial +motion. +The crucial omission is that the treatment extends only to the fields but not to the forces and +accelerations associated with them. For the two charges partial theory does not include the Lorentz force +15 To see that a straightforward analysis will not save the principle of relativity for observables, note that +Föppl’s case of the two charges is, in its essentials, the same as the problem of determining the behavior +of Lorentz’s spherical electron when it is set in motion. In Lorentz’ case, he must now deal with each of +the infinitely many parts of the electron interacting with all the other parts by exactly the interaction that +Föppl calls to mind for two point charges. Lorentz (1904, §8) is able to give an account that conforms to +the principle of relativity (for observables) only by using the full apparatus of his theorem of +corresponding states, including the contraction hypothesis in its generalized form that applies as well to +the non-electromagnetic forces that hold the charges of the electron together. + + + 13 +law. Once that law is invoked for the thought experiment of the two charges (or any static charge +distribution set into uniform motion) different forces are inferred for the cases of rest and motion and the +principle of relativity is violated. This defect cannot be remedied easily. It is shown in Appendix B that +field transformation (5) is the unique transformation under which the Lorentz force law (L) is covariant. +Since Maxwell’s equations (M1) and (M3) are not covariant under this transformation, a theory of +processes governed by these two equations and the Lorentz force law cannot be given a Galilean +covariant formulation. +The two charge partial theory suffers an additional defect analogous to that of the magnet and +conductor theory. It precludes the induction of an electric field by a moving magnet. In the magnet’s rest +frame, we will have E’=0. Since its field transformation law (4) requires E=E’, there can be no induced +electric field associated with a moving magnet, in contradiction with Faraday’s experiments on induction. +Whatthedeviceoffieldtransformationbrings +Let us take stock. In the magnet and conductor thought experiment, there are no observable +consequences of absolute motion and Einstein reported the importance of this result in his early thinking +on relativity theory. What Einstein would surely also have known was that that observable consequences +could be recovered from absolute motion in other thought experiments in electrodynamics. Indeed if he +read Föppl’s account, as we have reason to believe he did, then he would have had just such a thought +experiment brought to his attention as failing where the magnet and conductor thought experiment +succeeded. +So the magnet and conductor thought experiment does not show satisfaction of the principle of +relativity for all observables in electrodynamics. It shows them only in one part of electrodynamics and +suggests a device, field transformations, that might bring the principle of relativity to that part of +electrodynamics and perhaps more. +We do not know how Einstein applied the device when he first conceived it. However we can +map out the space of possibilities that he would have to explore if he began to use the device within +Maxwell’s electrodynamics. The terrain is quite fixed; it is as described in Table 1. It is what Einstein +would find just as long as he was willing to complete the exploration, although he might not present it or +conceive it in quite the way I have. Maxwell’s electrodynamics can be made Galilean covariant, but only +if it is cleaved into two parts, each with its own field transformation law. The two parts complement each +other. Each is able to give a Galilean covariant account of processes governed by two of Maxwell’s +equations; but the field transformation each invokes fails to conform to the processes accommodated by +the other partial theory. The tension between the two thought experiments is now reproduced in the +tension between the two partial theories. +The device of field transformations has not extended the partial conformity of the observables of +Maxwell’s theory to the principle of relativity. What it has done, however, is to extend the conformity of +the theoretical structures, the fields, to the principle of relativity and that is noteworthy progress. Perhaps +it was sufficient progress to figure in what the Einstein of December 1901 thought might become a + + + 14 +“capital paper.” If so, the nagging defects of the two partial theories might also have been sufficient to +prevent writing or publishing just such a paper. +Thepathahead +How might Einstein proceed with these results in hand? If he had to choose between the two +partial theories, the choice would be obvious. The magnet and conductor partial theory was superior in +so far as it supplied satisfaction of the principle of relativity for both fields and observables. But why +force a choice? The obvious goal would be to unify the two partial theories. However, prior to insights +about the relativity of simultaneity, there would be no way to do this. The tension between the two +partial theories is readily recognizable as reflecting the most obvious problem facing attempts at a +Galilean covariant electrodynamics: Maxwell’s theory entails a constant speed c for light and that result +cannot be Galilean covariant. Either of the two parts of Maxwell’s theory alone is insufficient to entail the +speed of propagation of waves, so each may admit a Galilean covariant formulation. But once the two +parts are combined, the constant speed for light can be derived; a single Galilean covariant formulation +will no longer be possible. “The difficulty to be overcome,” as Einstein added in a footnote to his 1920 +recollection of the magnet and conductor thought experiment, “lay in the constancy of the velocity of +light in a vacuum, which I first believed had to be given up.” +One way to proceed is to attempt to modify Maxwell’s theory in some way to enable Galilean +covariance under a single field transformation law. It is obvious that a Galilean covariant electrodynamics +must be an emission theory of light, that is, a theory in which the velocity of the emitter is vectorially +added to the velocity of the light emitted. If an emitter at rest emits light with velocity c, then Galilean +kinematics entails that the emitter, moving at velocity v, must emit the light at velocity c+v. So an +emission theory of light is necessary in a Galilean covariant electrodynamics. (But it is certainly not +sufficient for Galilean covariance of the electrodynamics—and we will see an overlooked failure of +sufficiency below in a well know emission theory!) So consideration of an emission theory of light will +inevitably arise as long as one’s exploration of Galilean covariant electrodynamics is thorough enough. +Thus it is not at all surprising that Einstein would proceed to investigate an emission theory of light in a +later phase of his work. In the following section, I will review the little we know of Einstein’s +investigations into an emission theory. I will also point out a connection between the partial theories +considered here and our best guess for Einstein’s emission theory: if one takes the strongest of the two +partial theories, the magnet and conductor partial theory, it turns out it can be extended without +modification to this emission theory. +3. Einstein’s Efforts towards an Emission Theory of Light +Even with the insight afforded by the magnet and conductor thought experiment in hand, the +footnote to Einstein’s 1920 recollection quoted above shows that years of theoretical groping were still +needed to make good on the principle of relativity and that they included serious consideration of +abandoning the constancy of the speed of light. Later Einstein (1909, p. 487) remarked that the + + + 15 +abandoning of the ether led naturally to an emission theory of light: “Then the electromagnetic fields that +constitute light no longer appear as states of a hypothetical medium, but as independent structures, +which are emitted by light sources, just as in Newton’s emission theory of light.”—and it is impossible for +modern readers to fail to connect this remark to Einstein’s work on light quanta. As we shall see below, +on quite a few occasions Einstein identified his own approach to an emission theory to be akin to that of +Walter Ritz. +Ritz’sview. +What was Ritz’s view? It is laid out in a 130 page article (Ritz, 1908), which is summarized in +another shorter paper (Ritz 1908a).16 In one sense, the view laid out is a great deal more than a theory; it is +a synoptical view of the present state of electrodynamics, dissenting strongly from some of the +mainstream views. But it is also something less than a complete theory. Rather it is an elaborately +articulated program for the development of a theory along with quite extensive implementation of the +program. Further implementation of the program was terminated by Ritz’s failing health and death in +July 1909 of tuberculosis. +Ritz’s (1908) paper was divided into two parts. The first developed a series of skeptical +viewpoints, each of which led more or less directly to a revision of then present electrodynamical theory. +Those of relevance here included: +Fields and other quantities. Ritz expressed skepticism about the many quantities used in electromagnetic +field theory, most notably the electric and magnetic fields. He urged a return to laws expressing the +interaction between two charges of the type developed by Weber and others in the 19th century. These +action at a distance laws expressed the force exerted by one charge on another in terms of the distance +between them and their motions. Ritz even urged that this force could be eliminated in favor of the +charges’ motions. +Ether. Ritz laid out objections to the existence of the electrodynamical ether. He urged it should be +eliminated from electrodynamics and that the principle of relativity should be restored. +Einstein’s special theory of relativity. Ritz criticized Einstein’s way of implementing the principle of +relativity. He felt that Einstein’s insistence on retaining Lorentz’s electrodynamics insufficient grounds to +support the strange kinematical notions Einstein introduced. +Retarded potentials. Ritz urged that the presentation of Lorentz’s electrodynamics in terms of Maxwell’s +differential equations was incomplete. Instead he favored the more restricted formulation in terms of +retarded potentials. This restriction eliminated the advanced solutions of Maxwell’s equations, which, +Ritz felt, violated energy conservation, in so far as they represented a never seen convergence of radiation +from spatial infinity. +The second part of Ritz’s paper sought to develop the program implicit in the first part through +the following strategy. In the first part he had laid out a progression of results in the then standard +theory. He now sought to replicate these results, but modifying them in such a way as to bring them into +16 For discussion and an English translation of the shorter Ritz (1908a), see Hovgaard (1931). + + + 16 +accord with the principle of relativity. The progression of the first part began with a statement of +Maxwell’s equations (M1)-(M4) and the Lorentz force law (L), drawn from Lorentz’ formulation of +Maxwell’s theory. He then introduced a scalar potential φ and a vector potential A in the usual way. They +are defined implicitly by: +E = –∇φ – (1/c) ∂A/∂t H = ∇xA (6) +Maxwell’s equations, reexpressed in terms of these potentials, can then be solved by retarded potentials. +These retarded potentials arise when the scalar and vector potentials φ(x,y,z,t) and A(x,y,z,t) at position +(x,y,z) and time t are expressed in terms of an integral over what we would now call the past light cone of +the event (r,t); that is over all events (x’,y’,z’,t’), where the time t’ is retarded according to +t’ = t – r/c (7) +with r the distance between points (x,y,z) and (x’,y’,z’). The integrals are +€ +φ(x, y, z,t) = [ρ′] +r +∫∫∫ dτ′ +€ +A(x, y, z, t) = 1c +[ρ′v′] r +∫∫∫ dτ′ (8) +where the notation “[ρ’]” designates that ρ is computed at (x’,y’,z’,t’=t-r/c) and similarly for [ρ’v’].17 +These retarded potentials were only an intermediate for Ritz. He then proceeded to report with approval +work of 1903 in which Schwarzschild found the corresponding expression for the retarded force acting on +a charge due to the charge distribution in space (Ritz, 1908, p. 326). The expression was so unwieldy that, +in the shorter paper, Ritz (1908a, p. 432) stated frankly that “it is a rather complicated expression which +we will not write down” and I will follow his good sense. Ritz then proceeded to simplified versions of +Schwarzschild’s result for special cases, such as two interacting charges with small velocities and +accelerations (Ritz, 1908, p. 348, 1908a, p. 433). +The starting point of Ritz’s modification in the second part of his paper was the retarded action +implicit in the time (7) used in Lorentz’s theory. The distance r was measured in a coordinate system at +rest in the ether; so this retardation time expresses the constancy of the velocity of light and +electromagnetic effects with respect to the ether. In its place, Ritz (1908, p. 373) proposed that +electromagnetic action propagates with a velocity c with respect to the source. To make it easy to +visualize his proposal, he imagined that electric charges constantly emit infinitely small, fictitious +particles in all directions with a radial velocity c with respect to the source. These fictitious particles +model the dissemination of the electromagnetic action of one charge onto another and of light. In accord +with his skepticism about the ether, he preferred to call it projection, which connotes ballistics, rather +than propagation, which connotes transmission by a medium. The clearest comparison between the older +view of the propagation of electromagnetic action and his view of its projection came in the following +expressions. In Lorentz’ theory, in a coordinate system at rest in the ether, the radius of the sphere R at +time t emanating from an event at (x’,y’z’) at time t’=t–R/c is +c2(t – t’)2 = R2 = [x – x’(t–R/c)]2 + [y – y’(t–R/c)]2 + [z – z’(t–R/c)]2 (9) +17 Ritz (1908, p. 325). I have simplified Ritz’s notation slightly by substituting a single boldface vector for +the three components Ritz wrote out individually. + + + 17 +This represents an expanding sphere whose center remains at one point at rest in the ether. In its place, +Ritz proposed that the radius of the expanding sphere r at time t would be given by18 +r2 = [x – x’(t–r/c) – (r/c)vx’(t–r/c)]2 + [y – y’(t–r/c) – (r/c)vy’(t–r/c)]2 ++ [z – z’(t–r/c) – (r/c)vz’(t–r/c)]2 (10) +The velocity v’ is the velocity of the source and v’(t–r/c) is the velocity of the source at the moment of +emission. Equation (10) describes an expanding sphere whose center is no longer at rest in the coordinate +system; if the source were to continue to move uniformly with velocity v’, it would remain the center of +the sphere. This geometrical description was favored by Ritz. We might now just say that the velocity of +the source at the instant of emission is added vectorially to the velocity of the action. +With this model in mind, Ritz proceeded directly to the expressions developed by Schwarzschild, +such as for the interaction of two charges, and sought ways to eliminate any absolute velocities in them, +as required by the principle of relativity. Note that he does not explicitly address the expressions (8) for +the retarded potentials, but proceeds directly to modifying expressions for the interaction of two charges. +The results are far from simple and not unique. It is helpful to see the expression Ritz presents for the +interaction of two charges e and e’, if only to see just how complicated it is. It is given (Ritz, 1908, p. 380) +as +€ +Fx = ee′ +r2 1 − rw′r +c2 +  +  +cos(r, x)φ ur +c , u2 +c2 + + + + + + − uxur +c2 ψ ur +c , u2 +c2 + + + + + + − rw′x +c2 χ ur +c , u2 +c2 + + + + + + + + +  + + + +, +Fy = ... +€ +φ=1+ 3− k +4 +u2 +c2 + 3(1 − k) +4 +ur2 +c2 + a1 u4 +c4 +L +€ +ψ= k+1 +2 + b1 u2 +c2 + b2 ur2 +c2 +L +€ +χ = 1 + c1 u2 +c2 + c2 ur2 +c2 +L (11) +The achievement of this expression is that all the velocities that enter, u, ur, ux, are relative velocities, +although the accelerations, wr, wx, are not relative and, of course, need not be if all that is sought is the +relativity of inertial motion. The expression contains many underdetermined constants (K, ai, bi, ci), +which are to be determined by experience. Ritz then proceeded to more specialized cases such as when +the speeds and accelerations of the charges are small. +The above gives only a flavor of the range of material in Ritz’s paper, which also includes an +electromagnetically based theory of gravitation, in which gravitational action also propagates at c. +18 In the above formulae (9) and (10), “x’(t–R/c)” is to be read as “the value of the x’ coordinate of the +source at time t–R/c”; and similarly for the remaining terms. + + + 18 +HowwasRitz’stheoryreported? +While Ritz’s view could not be described as a theory but was really an elaborate program of +research, very little of this entered the literature in which Ritz’s name is invoked.19 The reason, I am +presuming, is that this literature was largely devoted to empirical testing of different views about light. +What could be tested most directly of Ritz’s views was whether the velocity of the emitter is actually +added to the velocity of the light emitted. Since that proposition was so central to Ritz’s theory and open +to test, it needed to be decided before more detailed investigation of Ritz’s views was warranted.20 A +paper by Ehrenfest (1912) calls attention to Ritz’s work on an emission theory. His discussion is devoted +essentially to empirical testing and is spare in the details he gives of Ritz’s views. He displays assertions +(p. 317): +[B] A light pulse emitted by a non-accelerated light source L travels in a concentric sphere, +whose radius increases with the constant speed V and whose center remains coincident +with L. +... +[C] An observer ascertains a greater speed of light for a light source approaching him than +for one at rest with respect to him. +He later glosses Ritz as having a theory in accord with these assertions (p. 318): +It is well known that Ritz developed such an emission theory of light [footnote includes +citation of Ritz (1908)]. In this theory, electrons emit retarded potentials according to (B) +and (C) and with rejection of the postulate (D) [Einstein’s light postulate]. +What is striking is that Ehrenfest’s gloss encapsulates Ritz’s view as a theory concerning retarded +potentials, while Ritz at best regarded them as intermediates to Weber-like action at a distance laws. The +19 The significant exception is the continuing literature that is unconvinced of the necessity of adopting +special relativity. O’Rahilly (1938) includes a fairly detailed exposition of Ritz’s real views (Ch. XI), urges +that they have been slighted in discussions of Einstein’s relativity theory (Ch. XIII, §5) and concludes the +Epilogue with a provocative “We therefore reject the false dilemma: Aut Einstein aut nullus!” [Einstein or +nothing!] +20 De Sitter’s (1913) very short note reported a disproof of Ritz’s proposition by observing the light from +double stars, which seemed to be unaffected by the velocities of approach and recession of the stars as +they orbited each other. He reported only as much of Ritz’s view as was needed for the test: “If a light +source has a speed u...then, according to Ritz’s theory, the speed of the emitted light in the same +direction is C+u, where C is the speed of light emitted from a source at rest.” Tolman (1912) includes +Ritz’s view with discussions of other emission theories of light. He allows (p. 137) that Ritz has proposed +“a very complete emission theory of electromagnetism.” But he recites just enough of Ritz’s views to +enable testing, for example (p. 137): “According to this theory, light retains throughout its whole path the +component of velocity which it obtained from its original moving source, and after reflection light +spreads out in a spherical form around a center which moves with the same velocity as the original +source.” + + + 19 +idea that Ritz’s theory was centrally concerned with retarded potentials was solidified by Pauli’s 1921 +Encyklopädie article, which has become the standard citation for Ritz’s theory and the ensuing empirical +investigations that refuted it. Pauli (1921, p.6) wrote of efforts to construct a theory of light within +electrodynamics that relinquishes the constancy of the velocity of light: +Only Ritz has succeeded in doing this in a systematic theory. He retains the equations +€ +curlE + 1c +∂H +∂t = 0 div H = 0 [(M4’), (M2’)] +so that the field intensities can be derived, just as in ordinary electrodynamics, from a +scalar and vector potential +€ +E = −gradφ- 1c +∂A +∂t H = curlA [(6’)] +The equations +€ +φ(P, t) = ρdVP′ +rPP′ +[ ]t′=t−r/c +∫ +€ +A(P, t) = (1/c)ρvdVP′ +rPP′ +[ ]t′=t−r/c +∫ [(8’)] +of ordinary electrodynamics are now, however, replaced by +€ +φ(P, t) = ρdVP′ +rPP′ +[ ]t′=t−[r/(c+vr )] +∫ +€ +A(P, t) = (1/c)ρvdVP′ +rPP′ +[ ]t′=t−[r/(c+vr )] +∫ [(12)] +While Pauli does not identify the variable, presumably vr is the velocity of the source at time t’ in the +direction of the point P. With this summary, Ritz’s program has now been reduced to the simplest +modification of standard electrodynamics. Lorentz’s retardation time t’=t–r/c (7) in the retarded potential +integrations (8), (8’) are simply replaced by the retardation time accompanying Ritz’s views on the +velocity of propagation of electromagnetic action: +t’ = t – [r/(c+vr)] (13) +The transition from retarded potentials (8), (8’) to (12) is exactly the transition called for by Ritz’s proposal +that we replace the motions (9) for the propagation of electromagnetic action with (10) for its projection. +Natural as Pauli’s formulation of Ritz’s theory may be, I have not found its central expression for +the projected potentials (12) in Ritz’s papers. Ritz proceeded directly to action at a distance expressions +such as (11) since they were the fundamental goals of his program; expressions in retarded potentials +were at best intermediaries, but as such would be in keeping with his thought. However it is not hard to +understand why Pauli and perhaps Ehrenfest would present Ritz’s views as they did. While Ritz had a +program in electrodynamics, it is very hard to state a simple end point that is the proposed replacement +of then standard electrodynamics. Rather Ritz’s papers are filled with expressions like (11), valid only for +special cases. What Pauli recognized, presumably, is that this difficulty in Ritz’s views derives from his +insistence that electrodynamics return to Weber like action at a distance laws. The difficulty is not a result +of that aspect of Ritz’s work that was of interest to Pauli in writing a review article on relativity theory; +that is, Ritz’s proposal that the velocity of light depend on the velocity of the emitter. So perhaps Pauli +felt he was serving his readers well by shielding them from the unnecessary complications of Ritz’s other +views. Or perhaps he had not sifted Ritz’s papers for the final result but had been informed by an + + + 20 +unreliable source. With commendable lack of concern for the quibbles of later historians of science, Pauli +reported what Ritz would surely have concluded if only he could suppress his skepticism about fields. +We now have three Ritzes: +The Real Ritz. This is the Ritz of Ritz (1908), enmeshed in an elaborate project to reconfigure +electrodynamics. +Pauli-Ehrenfest’s Ritz. This is the Ritz who merely sought to reconfigure electrodynamics with retarded +potentials that use a projected, retardation time (13) in order to restore Galilean relativity to +electrodynamics. +The Experimentalists’ Ritz. This is the Ritz that merely proposed that the velocity of the source should be +added vectorially to the velocity of light. +EinsteinonthesimilaritybetweenRitz’sandhisownemissiontheory +The earliest remarks we have by Einstein relating his own ideas on an emission theory of light +and those of Ritz arise from Einstein’s reaction to Ehrenfest’s (1912) paper. In a letter from mid 1912 to +Ehrenfest responding to the paper, Einstein wrote: 21 +I was not annoyed in the least by your article. On the contrary. Such considerations are +quite familiar to me from the pre-relativistic time. I certainly knew that the principle of the +constancy of the velocity of light is something quite independent of the relativity postulate; +and I considered what would be more probable, the principle of the constancy of c, as was +demanded by Maxwell’s equations, or the constancy of c, exclusively for an observer sitting +at the light source. +In his initial response to Ehrenfest’s paper in an earlier letter of 25 April 1912 (Papers, Vol. 5, Doc. 384), +Einstein allowed that this own thinking on an emission theory was akin to Ritz’s: +I believe that there are quite simple experiments to test Ritz’ conception, which, +incidentally, was also mine before rel. theory. +What is important is the timing and context of Einstein’s letter. He wrote less than a decade after his own +work on an emission theory and, as remarked in the later (June 1912) letter, still had a comfortable +memory of that earlier work. Ehrenfest’s paper was raising the question of empirical tests that might +distinguish Einstein’s theory of relativity from a theory attributed to Ritz. In spite of Einstein’s cheer (“not +annoyed in the least”), he could not overlook that this was a challenge to his theory. Ehrenfest was +apparently standing in for Ritz, whose death in 1909 precluded Ritz defending his own work. Einstein +would surely want to be circumspect over claims made in this context and not assert lightly that he had +already conceived of Ritz’s view. +Although written much later,22 a more revealing statement is in the draft of a response written on +the back of a letter dated 1 February 1952 to Einstein from C. O. Hines. (Einstein Archive 12 250, 12 251.) +21 Einstein to Ehrenfest, “before 20 June 1912,” Papers, Vol. 5, Doc. 409. Einstein proceeds immediately to +say that he chose the first, so this recollection immediately jumps over the time he spent developing and +assessing his emission theory. + + + 21 +Hines reported difficulties in his study of Ritz’s treatment of light and pressed Einstein for assistance, +hoping that Einstein had had discussions with Ritz on the subject. Einstein replied, now addressing Ritz’s +ideas directly: +Ritz’s ideas on electrodynamics and optics are not so far developed that one can call them +a “theory.” What is special in them is that there does not exist a definite speed for light +propagation at a position and in a given direction, but that this [speed] depends on the +state of motion of the light source. Then one cannot trace light propagation back to +differential equations, but one must introduce “retarded potentials,” which is a kind of +action at a distance. +Before setting up the special theory of rel., I had myself thought of investigating such a +possibility. +It is revealing that Einstein corrects Hines’ supposition that Ritz really had a theory and not merely, as I +have suggested above, a well advanced program of research. That shows that Einstein had some real +familiarity with Ritz’s work. I would also suppose that this familiarity was in place when Einstein +responded to Ehrenfest’s (1912) paper. Where Ehrenfest (1912) talks of Ritz’s “theory,” Einstein replies by +calling it Ritz’s “conception.”23 +22 Other later remarks by Einstein affirm the kinship of Einstein’s early ideas with Ritz’s. With a cover +letter dated 21 March 1922, Mario Viscardini sent Einstein an article for his opinion. It was described as +providing a new solution to the Michelson experiment. Einstein responded (Einstein Archive 25-302; +translation, Rynasiewicz, 2000, p. 168): +The hypothesis articulated in the article, that in free space light has the constant velocity c, +not with respect to the coordinate system but relative to the light source, was discussed for +the first time in detail by the Swiss physicist W. Ritz and was seriously taken into +consideration by myself before the formulation of the special theory of relativity. +Einstein wrote on the back of a letter from A. Rippenbein of 25 August 1952 that once again proposed a +novel theory of the motion of light (Einstein Archive, 20-046; translation from Stachel, 1982, p. 189): “Your +attempt to replace special relativity with the assumption that the velocity of light is constant relative to the +source of light was first advocated by Ritz....even before setting up the special theory of relativity, I +rejected this way out...” Shankland (1963/73) reported that Einstein “told me that he had thought of, and +abandoned the (Ritz) emission theory before 1905.” +23 At the time of Einstein’s discussion with Shankland in the 1950s, Einstein seemed to have sufficiently +detailed recollection of Ritz’s theory to dispute Shankland’s (1963, p. 49) praise of the theory: +When I [Shankland] suggested that Ritz’s theory was the best of the several emission +theories of light, he shook his head and replied that Ritz’s theory is very bad in spots. +[footnote: citation to Einstein, 1909a] But he quickly added, “Ritz made a great contribution +when he showed that frequency differences are the crucial thing in spectral series.” + + + 22 +The more revealing remark, however, comes after. Having pointed out that Ritz did not have a +definite theory, Einstein extracts the important part of Ritz’s program and formulates it as the idea that +one must introduce retarded potentials. He then proceeds to assert that this was the sort of possibility he +had investigated himself. +WhichwasEinstein’sRitz? +That is, what did Einstein mean when he remarked to Ehrenfest in 1912 that Ritz’s conception has +been his own? We can immediately rule out the Real Ritz. Einstein’s sensibilities are well known. He was +uninterested in Weber style action at a distance laws as the fundamental laws of electrodynamics. We +shall see below that one of the complaints Einstein levels against an emission theory was that he could see +no way of converting the theory into a field theory. That is precisely the reverse of Ritz’s program, which +was to convert field theories into action at a distance laws, even at the cost of extraordinary complications +in the laws. +What of the Experimentalists’ Ritz? Again it is unlikely this is Einstein’s Ritz. I have already given +grounds for believing that Einstein knew details of Ritz’s work—specifically their complicated, +programmatic nature. There are more reasons to believe this. By 1912, Einstein had read some of Ritz’s +work (though not necessarily the relevant papers) and had had some interactions with him. Ritz (1908, +Part 1, §3; 1908a, pp. 434-35) had urged that Lorentz’s electrodynamics should be restricted to retarded +potentials and the advanced potential solutions disallowed. Ritz (1909) then urged that this restriction +would resolve the thermodynamic difficulties surrounding thermal radiation (out of which quantum +theory emerged). Einstein (1909, pp. 185-86) disputed Ritz’s solution, arguing for the admissibility of both +retarded and advanced solutions. This attracted a response from Ritz (1909a); and the matter was +resolved with a polite statement of their differences in a jointly signed article, Ritz and Einstein (1909). +Einstein may never have seen Ritz (1908, 1908a); he may have read Ritz (1909) only because it appeared in +a journal in which Einstein sought publication, Phyikalische Zeitschrift. Perhaps Einstein could engage in +all these interactions with Ritz without learning that Ritz (1908, 1908a) contained outspoken even +polemical assaults on his special theory of relativity. What makes that blissful ignorance extraordinarily +unlikely is that Ritz happened to be the major competing candidate for Einstein’s first academic position +at the University of Zurich. The committee favored Ritz over Einstein, but chose Einstein only because of +Ritz’s incurable ill-health. Alfred Kleiner, the professor at Zurich who had fostered the position, initially +favored Ritz as well. (See Fölsing, 1997, p. 249 for further details.) While the popular image is of an other +worldly, absent-minded Einstein, the real Einstein of 1909 was eager and ambitious and surely not likely +to want to be uninformed of the outspoken criticism of his work from someone who proved to be his +principal professional rival. And if Einstein somehow did not know that Ritz was his rival and had even +not heard of Ritz’s criticism, all this would be likely to change once he was installed at the University of +From his interviews with Einstein, Wertheimer (1959, p.216) reports that work by Einstein on a modified +set of Maxwell’s equations that might admit a variable speed for light persisted “for years.” Ritz was not +mentioned. + + + 23 +Zurich. A committee of eleven had voted on the appointment. Might not one of those, perhaps Kleiner +himself, ask Einstein to respond to Ritz’s criticism? And this would not be the occasion for an uninformed +response. +So Einstein’s Ritz lay somewhere between the Real Ritz and the Experimentalists’ Ritz. We can +certainly imagine many Ritzes in between. They would all be characterized by efforts to use the emission +prescription of (10) for the propagation of electromagnetic action to relate the electromagnetic quantities +at one point in space and to the distibution and motion of electric sources throughout space. Pauli and +Ehrenfest have conveniently supplied us with a description of the intermediate Ritz that seems naturally +to have sprung to their minds. That this was also Einstein’s Ritz is strongly suggested by Einstein’s +remarks to Hines quoted above. Einstein explicitly does what Pauli and Ehrenfest do tacitly: reduce and +reformulate Ritz’s program into a proposal relating to retarded potentials. So I conclude that Einstein’s +Ritz was the Pauli-Ehrenfest’s Ritz, or something closely related. +How should we read Einstein’s remark to Ehrenfest and others that his conception agreed with +Ritz’s? We should read it in its context in which Ritz’s program had come to be understood as something +like Pauli’s reduced version. For example, Einstein responded to a paper in which Ehrenfest (1912) +characterizes Ritz’s theory as one in which “electrons emit retarded potentials according to [emission +theory of light].” We should understand Einstein to be saying to Ehrenfest, “Ritz’s conception (as you +have misdescribed it) was also mine” and to be tactfully reserving the parenthetic reprimand on +Ehrenfest’s misdescription. +Apathfromthemagnetandconductortotheretardedpotentials +One other consideration makes it plausible that Einstein’s speculation on an emission theory +passed through consideration of Pauli’s retarded potentials (12) and perhaps even lingered there. It turns +out that there is a natural and direct path to them from the device of field transformations suggested by +the magnet and conductor thought experiment. Here is how it arises. +We have seen above that the four Maxwell equations divide uniquely into two pairs, each +associated with a Galilean covariant theory with a different field transformation law. The two charge +partial theory is based on Maxwell’s equations (M1) and (M3). The magnet and conductor partial theory +is based on (M2) and (M4). The latter is clearly superior in that it also incorporates the Lorentz force law +(L) and accommodates the thought experiment Einstein found so motivating. So, if he conceived these +partial theories at all, he might well be tempted to retain the magnet and conductor partial theory and +seek to modify the two charge partial theory in an attempt to find a unified theory. +This path would lead directly to the emission theory Pauli ascribed to Ritz. The important fact +about (M2) and (M4) is that field sources--charge density ρ and flux j--do not appear in them. The sources +appear only in the other two equations (M1) and (M3). Since emitters are merely accelerating charges and +light the propagating waves they generate, these two equations (M1) and (M3) are the natural candidates +for modification if an emission theory of light is sought. But can such a modification of (M1) and (M3) be +found that would not compromise (M2) and (M4)? It can. Einstein merely needs to reformulate the theory +in terms of retarded potentials as in (6), (6’) and (8), (8’) above. As Pauli suggests, one immediately + + + 24 +incorporates the emission theory by merely altering the retardation time accordingly. Yet Maxwell’s +equations (M2) and (M4) are left untouched, for, by familiar theorems, those two equations are equivalent +to the assertion of the existence of the scalar and vector potentials.24 That is, assuming the magnet and +conductor partial theory entails the existence of the potentials φ and A; this is the path from magnet and +conductor partial theory to the retarded potentials. The path back is just as easy; by assuming a retarded +potential formulation of electrodynamics that uses potential φ and A defined by (6), (6’) entails Maxwell’s +two equations (M2) and (M4). +ThefataldefectofthetheoryPauliattributedtoRitz +This is an harmonious extension of the magnet and conductor theory. If Einstein had entertained +extending the magnet and conductor partial theory towards an emission theory of light, we could readily +imagine him finding it. Unfortunately we could equally well imagine him finding the fatal defect in the +theory, a defect that Pauli did not mention. The original tension between the two partial theories, as +captured by the conflicting field transformation laws (4) and (5), remains unresolved. +To see the problem we need to determine the transformation laws for the potentials φ and A. As +shown in Appendix B, the field transformation (5) can be extended to the potentials φ and A by assuming +that they transform according to +φ = φ’ – (1/c)u.A’ A = A’ (14) +Unfortunately these transformations are incompatible with the covariance of the retarded potential +integrals (12). The quickest way to see the incompatibility is to take the case of a source charge +distribution that is at rest. Since we have v=0 everywhere, it follows from (12) that A=0. If we now +transform to another frame using the above transformation law, we have A’=0. That is a disaster. In the +new frame, the charges will no longer be at rest and thus by (12) will produce a non-vanishing H’ field, so +that A’ cannot vanish. The transformation (14) for the potentials φ and A simply replicates the defect of +the magnet and conductor partial theory and its field transformation H=H’, which also precludes a +moving charge from inducing an electric field. +There is no simple repair. One might wonder whether the alternative field transformations (4) +might be called upon in some way, since they do not include H=H’. Or one might inspect the retarded +potential integrals (12) and notice that they would be covariant under the transformation φ’ = φ and +24 Maxwell’s equation ∇.H = 0 (M2) asserts that H is divergenceless; so there must exist another vector +field—let us call it A—such that H = ∇xA. Substituting this expression for H into Maxwell’s equation +(M4), we learn that ∇x[E + (1/c)(∂A/∂t)]=0. That is E + (1/c)(∂A/∂t) is irrotational, so there must exist a +scalar field φ, such that E + (1/c)(∂A/∂t) = –∇φ. These are equivalent to the expressions for E and H in (6). +This shows that the equations (M2) and (M4) entail the existence of the scalar and vector potentials; the +converse entailment follows just by reversing the above argumentation. + + + 25 +A’ = A + (1/c)φu. All this is to no avail.25 We must recall that the mere existence of the potentials as +defined in (6) entails Maxwell’s equations (M2) and (M4). As Appendix B shows, the transformation (14) +is the one associated with transformation (5), under which (M2) and (M4) are covariant. Any other +transformation for φ and A would be incompatible with the covariance of (M2) and (M4) and thus with +the covariance of the definitions of φ and A themselves. +Thus, if Einstein followed this path to its end, he would have been disappointed. Indeed what we +have found is that the theory Pauli attributed to Ritz in (6’) and (12) is not Galilean covariant after all! The +definitions (6’) require field transformations (5) and (14); but the integrals (12) are not covariant under +these field transformations. Presumably Pauli (1921, p.8) overlooked this since he proceeded to aver that +“the relativity principle is automatically satisfied by all such [emission] theories.” Conformity to an +emission theory of light is necessary for a Galilean covariant electrodynamics; but, as this example shows, +that conformity is not sufficient to assure Galilean covariance. +Insum... +In sum, it is not so easy to recover a clear statement of just what Einstein is claiming for his earlier +view when he equates it with “Ritz’s conception.” Setting the remark in its context, the view claimed +would use an emission prescription akin to (10) for the propagation of electromagnetic action using some +sort of non-local field law. The most plausible, concrete formulation at hand is Pauli’s retarded potentials +(12) with a projected retardation time. While we certainly cannot preclude other formulations of an +emission theory by Einstein, Pauli’s proposal fits well with Einstein’s remark to Hines that a Ritz inspired +emission theory must be formulated in terms of retarded potentials. There is also a natural path to this +same formulation directly from the magnet and conductor partial theory, but, contrary to appearances, it +turns out not be Galilean covariant. +4. Einstein’s Objections to Emission Theories +Einstein’sanalysisof1912 +Einstein abandoned his efforts to find an emission theory of light. The reasons seem not to relate +to defects in one or another particular emission theory. Rather they derive from a concern that an +emission theory of light must contradict some quite secure properties known empirically for light. +Einstein gives us his most extensive expression of these concerns in 1912 in his correspondence with +Ehrenfest and also in a long unpublished manuscript on special relativity. Our problem will be to try to +25 Might an escape lie in the fact that A and φ need only be determined up to a gauge transformation, so +that we can be more lenient in the transformations allowed, as long as the measurable E and H fields +conform to Galilean covariance? The escape fails since whatever transformation we might envisage for +the potentials, it must return observable fields that conform to the transformations (5) for the fields E and +H used in their definition and those transformations includes the fatal transformation H=H’. + + + 26 +disentangle which of the objections to an emission theory played a role in Einstein’s thought prior to his +1905 paper and which were now being advanced by Einstein in 1912 as a contribution to the then current +debate over emission theories—although I will conclude it cannot be done cleanly. +In a long unpublished exposition of special relativity written in 1912-1914, Einstein (1912-14, pp. +35-35; translation Beck, 1996, p. 26) Einstein explained why an emission theory of light would be +unsatisfactory: +[In one possibility] the velocity of light in [the medium of Fizeau’s experiment, which +measures the velocity of light in moving water] M depends on the velocity of motion of the +light source with respect to M (Ritz [deleted: and Ehrenfest]). This being so, light rays of all +possible propagation velocities, arbitrarily small or arbitrarily large, could occur in M. +Intensity, color, and polarization state would not suffice to define a plane light wave; one +would have also to add the determinative element of velocity, which, however, should not +make itself felt in any effects of the first order (which would be proportional to the first +power of velocity of the light source). For the light coming from stars that are in motion +relative to the Earth has—as far as our experience extends—the same properties as the light +from terrestrial sources of light. To do justice to that, one is forced to make the most +peculiar assumptions if one pursues this point of view, as for example the following: if +light of velocity c+v strikes a mirror perpendicularly, then the reflected light has the +velocity c–v. These complications make it seem understandable why it has not proved +possible so far to set up differential equations and boundary conditions that would do +justice to this conception.- +The concerns described here are a digest of issues raised in the 1912 exchange between Einstein and +Ehrenfest following the latter’s publication of Ehrenfest (1912). The main import of Einstein’s first +reaction (Einstein to Ehrenfest, 25 April 1912, Papers Vol. 5, Doc. 384) was to suggest to Ehrenfest that +Ritz’s conception was open to simple experimental test. The test depended on which of two cases was +assumed. +In the first case, one might assume that light from a moving source retains the motion of the +source when it passes through a medium at rest or is reflected from a substance at rest. For this case, +Einstein observed, the wavelength of the light would be unaffected by the motion of the source, but the +frequency would be affected. So a Doppler shift would not be experimentally detected by devices that +measure wavelength directly (such as diffraction gratings); but it would be detected by processes that +measure the frequency directly. Here he named dispersion processes that depend on resonance.26 In the +26 Einstein’s intent is clear. If light emitted from a source at rest has the waveform f(k.r–ωt), then the effect +of a velocity v of the source is to boost the waveform according to the Galilean rule r  r - vt, so that the +waveform becomes f’(k.r–(ω+k.v)t). The boost has left the wave number k unaffected, but the frequency +has been altered (Doppler shifted) from ω to ω+k.v. Diffraction gratings form interference patterns by +reassembling light that has followed paths of different lengths to the observing screen, so the resulting +patterns depend only on the wavelength of the light and will not reveal the Doppler shift in this case + + + 27 +usual understanding, such as supplied by relativity theory, since wavelength λ and frequency ν are +always related by c=λν, with c constant, a Doppler shift in frequency can only arise if there is a +corresponding Doppler shift in the wavelength. +In the second case, light that interacts with matter is transformed so that it loses the motion +imprinted by the moving source; presumably it adopts the velocity c with respect to the intervening +matter. Einstein proposed an experiment that would reveal this effect. One of two coherent light rays +from a moving star would pass through a foil. The effect of the foil on the velocity of one ray would be +evident in a phase difference between the two rays. +In the exchanges that followed, misunderstandings were resolved. To get the result Einstein +reported in the first case, it was essential that, if light from a source moving at v attains velocity c+v, it +must retain this velocity in all directions upon deflection. This is not the case described above in the 1912 +14 manuscript in which light with velocity c+v reflecting as light with velocity c–v. So when Ehrenfest +mistook this last rule for the first of the two cases, it took a few exchanges to resolve the matter. (Einstein +to Ehrenfest, 2 May 1912, Doc. 390; Ehrenfest to Einstein, after 16 May, 1912, Doc. 394; Einstein to +Ehrenfest, 3 June 1912, Doc. 404; all in Papers, Vol. 5.) In his June 3 letter, Einstein explained that +Ehrenfest’s alternative would still have untenable, observable consequences: the different velocities of +incidence and reflection would now mean that angles of incidence and reflection would no longer be +equal. However Einstein also needed to concede to Ehrenfest (Doc. 409, Papers, Vol. 5 “before June 1912”) +that there would be no first order effect in some experiment involving reflection.27 +Einstein’s letter of June 1912 identifies one further problem for an emission theory of light. +Einstein wrote: +In support of the independence of the speed of light from the state of motion of the light +source one can, of course, quote its simplicity and ease of realization. As soon as one gives +up this hypothesis, then, even to explain shadow formation, one must introduce the ugly +assumption that light emitted from a resonator depends on the type of excitation +(excitation through “moving” radiation or excitation of another kind). +Einstein’s point is hard to interpret. Shadow formation is usually the province of simple, geometric +optics, with diffraction at hard edges handled by Huygens constructions. It is hard to see how re +radiation from resonators could be involved unless Einstein is considering the shadows cast by semi +transparent bodies. Their transparency depends upon the frequency of the incoming light not arousing +resonant responses in the atoms of the bodies, with these atoms modeled as resonators. Perhaps the point +is that, in an emission theory of light, whether a pane of glass is transparent to light or casts a shadow +(assuming the speed of light remains isotropic). Light interacts with suitable resonators, such as bound +charges, according to the light’s frequency. So dispersion phenomena that depend on the latter will be +sensitive to the changes in frequency and will reveal this Doppler shift. +27 It is not clear to me to which experiment he referred. In the proposed experiment of the second case of +his letter of April 25, Einstein had claimed an effect that depends on the foil-screen distance in quantities +of first order, but this experiment did not involve reflection. + + + 28 +would no longer depend on just the wavelength and polarization of the light, but the relative velocity +between the source and the glass as well. +How much of these considerations played a role in Einstein’s evaluation of emission theories +prior to the 1905 paper? How much were later elaborations for the debate of 1912? This last letter gives +the answer. In the full passage quoted partially above in Section 3, Einstein wrote: +I was not annoyed in the least by your article. On the contrary. Such considerations are +quite familiar to me from the pre-relativistic time. I certainly knew that the principle of the +constancy of the velocity of light is something quite independent of the relativity postulate; +and I considered what would be more probable, the principle of the constancy of c, as was +demanded by Maxwell’s equations, or the constancy of c, exclusively for an observer sitting +at the light source. I decided in favor of the first, since I was convinced that each light [ray] +should be defined by frequency and intensity alone, quite independently of whether it +comes from a moving or a resting light source. Moreover it did not occur to me to consider +whether the radiation deflected at a point could behave differently in propagation +compared to newly emitted radiation from the point concerned. Such complications +seemed to me far less justified than those brought by the new concept of time. +The decisive consideration, Einstein tells us, that spoke to him against an emission theory prior to his +1905 paper was his conviction that light should be characterized by frequency and intensity (and +polarization) alone. He was then rather uninterested in the fussy details of how a variety of distinct +emission theories might be devised to accommodate to various sorts of processes of deflection or +reflection. They seem to have come to the fore in the literature emerging around 1912 that sought to test +an emission theory experimentally, for just those details decide how the experiments are to be done. (See +Tolman, 1912, for example.) +Laterremarks +Later remarks augment the comments from 1912, but not always univocally. The earliest of them +contradicts Einstein’s 1912 assertion of lack of interest in specific hypotheses about deflected radiation. +He wrote to Mario Viscardini (April 1922, Einstein Archive, 25-301; translation in part from Rynasiewicz, +2000, p. 182) in direct continuation of the part quoted above: +I rejected this [emission] hypothesis at the time, because it leads to tremendous theoretical +difficulties (e.g., the explanation of shadow formation by a screen that moves relative to the +light source). However the Dutch astronomer de Sitter has given the most convincing +refutation of this hypothesis, in that he pointed out that the light from a component of a +double star must be emitted with a time changing speed that is absolutely not in agreement +with what is given by observation. +Another repeats earlier remarks. In a 1952 draft written on the back of a letter from A. Rippenbein, +Einstein wrote (Einstein Archive, 20-040; translation based on Stachel, 2002, p. 189): +Your attempt to replace special relativity with the assumption that the velocity of light is +constant relative to the source of light was first advocated by Ritz. This assumption is + + + 29 +compatible with Michelson’s experiment and with aberration...[Einstein then refers to De +Sitter’s refutation of Ritz’s theory]. In addition this theory requires that light waves with +different velocities of propagation shall be possible everywhere and in each definite +direction. It would be impossible to set up any sort of reasonable electromagnetic theory +that accomplishes this. This is the principal reason why, even before setting up the special +theory of relativity, I rejected this way out, although it is intrinsically conceivable.” +In his Shankland (1963, p. 49) report of discussion with Einstein in the early 1950s, Shankland described a +new objection by Einstein to an emission theory. It would allow light phases to get mixed up and for light +even to reverse itself: +... he told me that he had thought of, and abandoned the (Ritz) emission theory before +1905. He gave up this approach because he could think of no form of differential equation +which could have solutions representing waves whose velocity depended on the motion of +the source. In this case, the emission theory would lead to phase relations such that the +propagated light would be all badly “mixed up” and might even “back up on itself.” He +asked me, “Do you understand that?” I said no and he carefully repeated it all. When he +came again to the “mixed up” part he waved his hands before his face and laughed, an +open hearty laugh at the idea! +Then he continued, “The theoretical possibilities in a given case are relatively few and +relatively simple, and among them the choice can often be made by quite general +arguments. Considering these tells us what is possible but does not tell us what reality is.” +Presumably mere repetition along with some gymnastic hand waving did not help Shankland figure out +what Einstein intended. Fortunately another letter by Einstein from the same time adds the missing piece +that makes sense of it all. Einstein’s above quoted response to Hines from February 1952 continues +(Einstein Archive, 12-250, 12-251): +...Then one cannot trace light propagation back to differential equations, but one must +introduce “retarded potentials,” which is a kind of action at a distance. +Before setting up the special theory of rel., I had myself thought of investigating such a +possibility. At that time I had only a weighing of the plausibility of theoretical arguments at +my disposal. I did not then think of the use of the evidence on double stars. I deliberated as +follows: If a suitably accelerated light source emits light in one direction (e.g., the direction +of the acceleration), then the planes of equal phase move with different speed, and one can +set it up like this, +so all the surfaces of equal phase coincide at a particular place, so that the wavelength there +is infinitely small. Moreover the light will be so turned around that the rear part overtakes +the front. + + + 30 +If we imagine a light source to be accelerating sufficiently rapidly in the direction of the emitted light, +then the increasing phase velocity may allow light emitted later to catch up with light emitted earlier and +then overtake it, so the light emitted later arrives before that emitted earlier. If one programs the +acceleration just right, all the waves will catch up at just the same moment, producing a superposition of +continuously many waves at one point. That some sort of singular behavior arises is evident, but it is not +clear to me why Einstein characterized it as an infinitely small wavelength. My supposition is that the +emitted light waves all have the same wavelength in an emission theory but different frequencies, so the +singularity would be in the frequency at the point in question. Einstein continued, repeating a description +of the experiment he proposed to Ehrenfest in 1912 and returning to familiar themes: +Further an ever so thin, diaphanous film will change the speed of “moving” light by a +finite contribution, so that interference, e.g. in the case +would give rise to quite incredible phenomena. +But the strongest argument seemed to me: If there is no fixed velocity for light at all, then +why should it be that all light emitted by “stationary” bodies has a velocity completely +independent of the color? This seemed absurd to me. Therefore I rejected this possibility as a +priori improbable. +De Sitter’s argument concerning emission from double stars is—as far as I can +see—sufficient by itself as contrary evidence. +The last remark was apparently responding to Hines’ remark that double star observations provided the +only objections properly raised against Ritz’s optical theories and, Hines felt, “even that may be explained +away.” +Apuzzle:whynodifferentialfieldequationsforanemissiontheory? +This collection of remarks by Einstein on the inadmissibility of an emission theory of light clearly +mixes objections conceived prior to his 1905 paper with those developed later when he discussed the +issue of empirical testing of emission theories. I find it quite plausible that Einstein’s deliberations prior to +the 1905 paper did not depend much on considerations of particular hypotheses on how deflected light +might move (just as Einstein writes to Ehrenfest in June 1912, above). The mere fact that many velocities +for light were possible seemed incompatible with observations: accelerating sources might lead to light +reversing itself, a phenomenon never seen; and Einstein concluded from it that there could be no field +theory based on differential equations for light. But I also find it plausible that Einstein may not have had +a perfect memory of deliberations that were undertaken years before and possibly never committed to +writing; and that in his later recollections and reports in letters he might be less concerned to lay out an + + + 31 +accurate report as a resource for historians of what he had thought and when, rather than to convince a +possibly argumentative correspondent of the untenability of an emission theory. +Instead of continuing to try to sort out just what might have belonged to which time, I want to +point out the puzzling character of the principal thread. Einstein’s repeated concern with an emission +theory is that there seems to be no way to formulate it in a field theory based on differential equations.28 +One reason given is that an emission theory allows waves of different velocities. A light wave of velocity +c+v can reflect as one of c–v. Light from accelerating sources can overtake and even form singular points. +This “many velocities” argument is simply not cogent. It takes very little effort to find differential +equations that admit just this behavior for waves. They are now quite familiar to us from quantum +theory, for example. Both the ordinary Schrödinger equation and the Lorentz covariant Klein-Gordon +equation admit waves with many different phase velocities. Since they are linear equations, we can +readily construct fields consisting of the superposition of many waves propagating at different velocities. +We will even find Einstein’s example of overtaking waves with velocities contrived so that a singular +point momentarily forms. We should not be so troubled by such points. They are otherwise known in +analogous cases in optics as caustics and are not regarded as fatal to our present wave theories of light. +So perhaps Einstein was just hasty and blundered. Before we accept that possibility, I want to +recall the other remark he makes repeatedly about emission theories: that such a theory makes it +impossible to characterize light solely by the usual parameters of intensity, color and possibly +polarization. That remark, which has so far been uninterpreted, seems decisive to me. For I believe that it +is impossible to give an electromagnetic field theory specified by differential equations of the type +familiar to us that is: (a) an emission theory of light; (b) Galilean covariant, even with field transformation +laws; and (c) characterizes light waves by intensity, color and polarization alone. +This claim might seem to need some significant computation for support. It turns out not to. There is a +very simple thought experiment that makes it transparent. That thought experiment is primally attached +to Einstein’s name and to the discovery of special relativity. +5. Einstein Chases a Light Beam +Athoughtexperimentofunclearimport +After yielding to the “invitation and earnest request” and “quite some persuasion” of its editor +(Einstein, 1949, preface), in 1946, Einstein put his autobiographical reminiscences of a life in science on +paper for the volume Albert Einstein: Philosopher-Scientist. On other occasions, he had stressed the +28 This objection has entered the standard lore. Becker (1964, p. 313) writes: “...the [Ritz hypothesis of an +emission theory] is completely untenable from the theoretical standpoint of a field concept which describes +the motion of light by a differential equation, because it cannot be understood how the velocity of +propagation of light from a source located at a point of space should be related to the condition of the +light source.” Alas, no justification is given. + + + 32 +importance of the magnet and conductor thought experiment in bringing him to special relativity. In this +account, however, it is not mentioned. Instead another thought experiment is given the central role. +Einstein reformulated the problem as the search for a universal formal principle akin the principles of +thermodynamics. He continued (p. 49-50) +After ten years of reflection such a principle resulted from a paradox upon which I had +already hit at the age of sixteen: If I pursue a beam of light with the velocity c (velocity of +light in a vacuum), I should observe such a beam of light as an electromagnetic field at rest +though spatially oscillating. There seems to be no such thing, however, neither on the basis +of experience nor according to Maxwell’s equations. From the very beginning it appeared +to me intuitively clear that, judged from the standpoint of such an observer, everything +would have to happen according to the same laws as for an observer who, relative to the +earth, was at rest. For how should the first observer know or be able to determine, that he is +in a state of fast uniform motion? +One sees in this paradox the germ of the special relativity theory is already contained. +Today everyone knows, of course, that all attempts to clarify this paradox were condemned +to failure as long as the axiom of the absolute character of time, or of simultaneity, was +rooted unrecognized in the unconscious. +This thought experiment has proven immensely popular in accounts of the discovery of special relativity. +Who could not fail to be charmed by the image of a precocious sixteen year old whose innocent +imaginings lay the groundwork for a great discovery? +What is rarely mentioned, however, is that the thought experiment does not quite make sense.29 +Usually Einstein’s thought experiments are models of lucid argumentation, quite compelling to the +29 Banesh Hoffmann (1982, pp. 93-97), a former collaborator and biographer of Einstein, is one of the few +to discuss the problem. His explanation is that the sixteen year old Einstein tacitly applied the principle of +relativity to rule out frozen light and that some kind of subconscious, psychological block precluded him +conceiving that light might even be slowed by the motion of an observer. Darrigol (1996, pp. 289-90) +resolves the problem by suggesting that we simply doubt the veracity of Einstein’s recollection since +Einstein believed in the existence of the ether as late as 1901. He concludes, “we should therefore regard +the wide-spread belief that Einstein had an inborn trust in the relativity principle as a myth.” This +reaction seems to me over eager to dismiss a recalcitrant historical datum. Einstein’s recollection does not +require an inborn trust in the relativity principle at age 16. It merely requires that he, as an ether theorist, +be disturbed by one consequence of his theory, that it allows a moving observer to catch light. Surely we +must allow a precocious 16 year old a visceral reaction that something is wrong with one consequence of +his theory without demanding that he then discard the theory or even have a cogent argument behind the +reaction. However I do agree with Darrigol that we should not allow the story of the premonitions of a 16 +year old to invest him with mysteriously prescient powers, as is the wont of popularizers. We cannot say +what significance is to be accorded to such anticipations until we know what other anticipations were felt + + + 33 +reader. But this one, if it intended to be an objection to an ether theory of light, does not bear scrutiny. +Using ordinary kinematical notions, if we sped fast enough through the ether after a beam of light, we +would bring it to rest. The fact that we do not experience such a thing merely reflects the fact that we +happen not to be moving very fast through the ether. What of Maxwell’s equations? Using the standard +kinematical notions associated with an ether theory, it is trivial to show that rapid motion would bring +the light to rest. Maxwell’s equations (M1)-(M4) admit plane wave solutions of frequency ω propagating +in the direction of the wave number vector k +E = E0 sin (ωt–k.r) H = H0 sin (ωt–k.r) (15) +where the field vectors are transverse to the direction of propagation (k.E = k.H = 0) and orthogonal to +each other (kxE/|k| = H); and the frequency ω and wave number vector k relate as ω = |k|c. We +transform from the unprimed ether frame (t,r) to a primed frame (t’,r’) using t=t’ and r = r’ + vt’, where +the condition that the velocity v matches the velocity of propagation of the wave entails30 k.v = ω. The +wave in the new frame is +E’ = E’0 sin (–k.r’) H’ = H’0 sin (–k.r’) (16) +since the argument in the waveform is ωt–k.r = ωt’–k.(r’ + vt’) = (ω–k.v)t’–k.r’ = –k.r’. (The primes on the +field vectors allow for the possibility of some sort of transformation of the field quantities. We need not +concern ourselves too much with that possibility since we merely seek to describe the waveform in +another frame but not establish any sort of Galilean covariance for the laws governing the descriptions.) +The wave has been brought to rest; it is a frozen sine wave (“spatially oscillating”). +Thedoubtsofasixteenyearold +We can quickly resolve another apparent problem with the thought experiment. While Einstein +attaches the thought experiment to himself as a sixteen year old, the mention of Maxwell’s equations is +unlikely to come from that time. He was then a high school student and the formal study of Maxwell’s +theory did not come until his university studies, around 1898 (see “Einstein on the Electrodynamics of +Moving Bodies,”pp. 223-35 in Papers, Vol. 1). Einstein’s wording in his Autobiographical Notes, clearly +allows the original thoughts of the 16 year old Einstein to gestate and develop over a ten year period and +we should surely imagine Maxwell’s equations entering the reflection in the course of this process. Or if +Maxwell’s equations played any part in the 16 year old’s reflections, they were hesitant and incomplete, +reflecting his own incomplete knowledge of Maxwell’s equations. +That the original thought experiment was more a visceral reaction of disbelief to a striking +possibility, frozen light, is suggested by the two other accounts we have of the thought experiment. Both +are more clearly localized to a young Einstein at age 16 in the year 1895-96 he spent at a high school +(gymnasium) in the Canton of Aarau, Switzerland. In 1916, the psychologist Max Wertheimer met with +by the young Einstein but came to nothing. A poor predictor can be made into a profound seer by +selective reporting of his few successes. +30 A point of constant phase moves according to k.r = ωt. Differentiate with respect to t to recover k.v = ω. + + + 34 +Einstein in order to probe the psychology of his work. Later, in a work first published posthumously in +1945 after his death in 1943, Wertheimer (1959, pp. 214-15) reported: +The problem began when Einstein was sixteen years old, a pupil in the Gymnasium +(Aarau, Kantonschule)... +The process started in a way that was not very clear, and is therefore difficult to +describe—in a certain state of being puzzled. First came such questions as: What if one +were to run after a ray of light? What if one were riding on the beam? If one were to run +after a ray of light as it travels, would its velocity thereby be decreased? If one were to run +fast enough, would it no longer move at all?...[W’s ellipses] To young Einstein this seemed +strange. +...When I asked him whether, during this period, he had already had some idea of the +constancy of light velocity, independent of the movement of the reference system, Einstein +answered decidedly: “No, it was just curiosity. That the velocity of light could differ +depending upon the movement of the observer was somehow characterized by doubt. +Later developments increased that doubt.” +The same thought experiment is recounted in an autobiographical sketch written shortly before Einstein’s +death. While reminiscing of his year at the gymnasium in Aarau, he wrote (Einstein, 1956, p. 10) +During this year in Aarau the following question came to me: if one chases a light wave +with the speed of light, then one would have before one a time independent wave field. But +such a thing appears not to exist! This was the first child-like thought experiment related to +the special theory of relativity. Discovery is not a work of logical thought, even if the final +product is bound in logical form. +Both these reports portray the thought experiment in its original form as much less of the well reasoned +and polished display pieces that characterize Einstein’s scientific writing. Rather it was more an account +of a psychological event in his personal history, the instinctive sense of a sixteen year old Einstein that +something was not right in a theory that allows light to be brought to rest. This is surely the import of +Einstein’s insertion of a remark (“Discovery is not a work of logical thought...”), in the midst of cozy +recollections of a happy year of his youth. They recall a familiar theme in his more philosophical writing, +that discovery in science inevitably involves creative steps that cannot be reconstructed logically. +6. The Importance of the Thought Experiment +Aproposal +The instincts of a sixteen year old Einstein were just the first step. Einstein’s recollection in his +Autobiographical Notes clearly accords the light chasing thought experiment an importance that endures +well into the work that eventually yields special relativity. The mention of Maxwell’s equations tells us +that it was invoked when he knew Maxwell’s equations and that part of its use involved Maxwell’s +equations. Further, its function in the narrative of Autobiographical Notes is to bridge the gap between the + + + 35 +early sensing of a problem to do with relative motion through to his insight into the relativity of +simultaneity. +My goal in this section is to propose an account of how such broad importance might be possible +so that thought experiment merits pride of place in an autobiographical statement that he recognized +would be definitive. (He called it, “my obituary”(p.3).) Beyond sowing the initial seed of doubt in his +sixteen year old mind, I do not think we will be able to identify a single result in which the primary +importance of the thought experiment can be found. If that were the case, Einstein would likely have +mentioned it in his own accounts; and, even if such an import were there, we have too meager resources +to locate it. Instead, what we can do is map out a period we know occurred in Einstein’s research in +which the thought experiment could be peculiarly effective in advancing his investigations. This was the +time when Einstein weighed emission theories of light and found them wanting. Below I will propose +three ways in which the thought experiment could be used to cast doubt on an emission theory of light in +ways compatible with Einstein’s remarks. +More generally, however, I suggest that the thought experiment reflects the standard way that +Einstein investigated the interaction of light and the motion of an observer in the years leading up to the +1905 paper: the effects of that motion were to be understood in terms of how it affected the waveform of +the light, just as the 16 year old Einstein had done. Such deliberations gave mounting reasons to doubt +ordinary kinematical assumptions. I will suggest in Section 8 that our present fascination with light as a +clock synchronizing signal as opposed to light as a propagating electromagnetic waveform may reflect +only a very small part of the thinking that led him to special relativity. +Problemsforanemissiontheoryoflight +Let us place Einstein at a time in which he is entertaining the possibility of an emission theory of +light that conforms to the principle of relativity. Any such theory would allow a sufficiently rapidly +moving observer to catch light. +Observational problem: “There seems to be no such thing, however, neither on the basis of experience...” +The ether theorist’s rejoinder was that we do not see such a thing since we happen not to be +moving that fast through the ether. In an emission theory that is no longer as viable an objection. All that +is required for us to see light frozen or significantly slowed in its propagation is for there to be a light +source moving rapidly enough away from us. The ether theorist’s explanation required slow motion for +just one entity, our earth. The emission theorists’ explanation requires slow motion for many more: every +object that transmits light to us. If we allow independence in their motions, the chances that this can be +the case decrease exponentially with the number of objects considered. +Theoretical problem: “...nor according to Maxwell’s equations.” +An emission theory of light must still harbor propagating light waves, such as the sinusoidal +waves (15) or something with similar undulations—that is one of our most familiar observations +concerning light. In an emission theory of light, an inertially moving observer would be able to observe +the frozen fields (16) or something with similar undulations. Because the theory is supposed to satisfy the +principle of relativity, these fields must also satisfy the basic equations of the theory, an additional + + + 36 +condition the ether theorist did not need to meet. That is, the two sinusoidal field (16) or something like +them must be added to the repertoire of fields admissible in electrostatics and magnetostatics. But that is +a very dubious outcome. While we may not know the precise form that an emission theory might take, it +is surely reasonable to expect it to agree quite closely with older theories in domains in which the older +theories have been extensive explored. One of the most secure of these domains is electrostatics and +magnetostatics. But such fields are simply unknown in standard 19th century electrostatics and +magnetostatics. All known static fields are well captured by the condition that they be time independent +and solutions of Maxwell’s equations (M1) and (M3) and they do not admit the sort of spatially oscillating +fields characterized by (16). In short, the fact that Maxwell’s equations do not admit a spatially oscillating +field at rest is a serious problem for an emission theory of light that satisfies the principle of relativity. +Failure of differential equations: “For how should the first observer know or be able to determine, that he is in a state +of fast uniform motion?” +Let me ask Einstein’s question in a slightly narrower fashion. Imagine that you are given the +instantaneous state of a waveform. How are you to determine whether it belongs to a waveform speeding +past you (i.e. you are “at rest”); or whether your share the waveform’s motion (i.e. you are “in a state of +fast uniform motion”)? The answer is routinely given by the field equations of the theory in question. +Take for example Maxwell’s equations (M1)-(M4). They are first order partial differential equations. As a +result, the state of fields at some instant specified how they will develop in time. You feed in the E and H +fields at some instant; use the field equations to read off their first derivatives; and finally integrate the +first derivatives to find the time development of the fields. +There is no reason to doubt that a similar procedure would be possible for an emission theory +until we add in one condition repeatedly mentioned by Einstein as decisive in his evaluation of emission +theories: a plane light wave must be fully specified by its intensity, color and, possibly, polarization. +What that means is that the waveform is given by (15). The intensity is given by magnitude of the vectors +E0 and H0. The color is given by one or another of the frequency ω or (scalar) wave number k, where +fixing one fixes the other, since they are related by ω=kc. The polarization is determined by the direction +of the vectors E0 and H0. (The waveform (15) is the simplest case of linear polarization; circular and +elliptical polarization arises when waveforms of the same frequency but different phases are +superimposed.) It is of course entirely understandable why Einstein would insist on these few parameters +being all that is needed to characterize a light wave. As Einstein explains in the 1912-14 manuscript (as +quoted above), it is an experimental matter; these are the only properties that have been found, even after +light from both celestial and terrestrial sources has been subject to extensive experimental investigation. +Now the problem is acute. For the two waveforms are identical at an instant. The waveform that +speeds past, (15), evaluated at t=0, is identical with the frozen waveform, (16). If the theory is +deterministic, given that waveform as its initial state, only one future time development will be possible +according to the field equations. So the field equations will be unable to determine correctly whether the +waveform is destined to propagate rapidly as in (15) or whether it is frozen as is (16) and represents the +wave for all time. For field laws expressed as differential equations to capture an emission theory of light, +the waveform must have some distinguishing characteristic encoded within it, so that the initial states + + + 37 +presented to the field equations are different in the case of propagating or frozen light. That +distinguishing characteristic would enable the field equations to return different time developments. The +motion of its source must somehow be imprinted onto light as an additional property. But just such an +additional property is what Einstein denies exists on the basis of experimental evidence. +This argument for the failure of any formulation in terms of differential equations is quite general +and quite robust. I have stated it as an objection to any set of first order differential equations, they being +the natural choice if one seeks laws modeled after Maxwell’s equations. One might well wonder if higher +order differential equations would be able to capture an emission theory, such as second order +differential equations. The idea would be that the initial state supplied to the second order differential +equations would be the fields E and H along with their first time derivatives, ∂E/∂t and ∂H/∂t. While the +propagating and frozen waveforms may agree on E and H at the instant in question, the motion of the +first would be encoded in non-zero time derivatives not manifested by the second. But the very idea of +fields that agree in their intensities but not their derivatives is precluded, exactly because these first +derivatives encode an additional property that makes a physical difference. The first derivatives would +add an additional physical parameter exactly of the type denied by Einstein. This problem could not be +escaped with differential equations of still higher order. +Or perhaps as a last effort, one might look to field transformation laws of the type (4) and (5). The +idea would be that these transformations alter the relative magnitude of the E and H vectors and that the +velocity of the wave’s source might somehow be imprinted in differences of those ratios. If the +transformation of the wave from (15) to (16) is accompanied by field transformation (5), then the effect is +to annihilate the transformed wave’s E’ field entirely, while leaving the H’ field unchanged. Might we use +this to distinguish propagating wave (15) from the frozen wave (16)? Once again, the idea founders on +the limited number of properties allowed a light wave. In addition to intensity, color and polarization, +one would have to add another property representing different ratios of the magnitude of the E and H +fields. (Such difference would surely be evident in experiments measuring interference; waves with +different ratios of field intensities would not annihilate in the same way.) +Finally, it is instructive to review an example that shows that the difficulty is not merely forming +differential equations that satisfying the principle of relativity and that admit waves with their velocity of +propagation somehow encoded within. That by itself is easily achieved. Take the Lorentz covariant Klein +Gordon equation for some particle of imaginary mass, im. Setting the units conveniently (c=1, h/2π=1) +and taking the simplest case of one spatial dimension, the equation is +€ +∂2 +∂t2 − ∂2 +∂x2 − m2 + + + + + +φ= 0 (17) +Its plane wave solutions are φ = exp i(ωt–kx) where m2 = k2–ω2. Since the speed of propagation is just +v=ω/k, waves with speeds from zero to arbitrarily close to one are admissible. The case of the wave of +zero velocity concerns us. It is just φ = exp i(mx) or φ = exp i(–mx). If this is supplied as an initial +condition to the Klein Gordon equation (17), the equation will tell us that this wave does not propagate. +That can happen because the wave number k=m encodes the crucial velocity information. The condition + + + 38 +m2 = k2–ω2 guarantees that any wave with exactly the wave number k=m is a frozen wave. No +propagating wave can bear that wave number. No analogous escape is possible for an emission theory of +light. What is essential is that the particle of imaginary mass im of this Klein Gordon equation (17) has the +characteristic parameter m for which there is no analog in light. +This example might also explain a remark Einstein makes in his draft letter to Hines in 1952: +“...why should it be that all light emitted by “stationary” bodies has a velocity completely independent of +the color? This seemed absurd to me....”It follows immediately from the above that the speed v of the +waves admitted by this Klein Gordon equation satisfies v2 = (ω/k)2 = 1–(m/k)2. That is, there is a fixed +relationship between the speed of the wave and its wavelength k, which also fixes its color. Presumably +Einstein had hoped that the color of a light wave in an emission theory would encode its velocity, +analogously. Evidently light does not admit such encoding since, empirically, there seems to be no +connection between the colors possible for light and the velocity of its source. +This completes the argument, associated with the chasing the light thought experiment, that +demonstrates that no field law expressed in differential equations can be (a) an emission theory of light; +(b) Galilean covariant, even with field transformation laws; and (c) characterize light waves by intensity, +color and polarization alone. +7. Stellar Aberration and Fizeau’s Experiment +TheopticalexperimentsthatmatteredtoEinstein +In spite of the lore that places the Michelson-Morley experiment at the center of Einstein’s +thoughts as he worked on the problems that would lead to special relativity, it has long been known that +the experiment played only a small role. See Stachel (1987) for a recent appraisal that draws on the +correspondence between Einstein and Mileva Maric brought to light in the 1980s. Einstein did however +give a clear statement of the optical experiments that were significant to him. In the note written in +Michelson’s honor and quoted from in Section 2 above, Einstein had first written (Einstein Archive 1-168): +I am not sure when I first heard of the Michelson experiment or its more precise repetition +by Michelson and Morley. I was not conscious that it influenced me directly during the +seven and more years that the development of the Special Theory of Relativity had been +my entire life; for I had taken it for granted as being true. +That English typescript had been struck out and replaced by the handwritten remark (quoted above) that +he learned of the experiment through reading Lorentz’ 1895 Versuch. It led up to the reaffirmation of the +importance of the magnet and conductor thought experiment and ended in a statement of the optical +experiments that did matter to him: +But the result of Fizeau’s experiment and the phenomenon of aberration also guided me. +Similar remarks were also reported by Shankland, with a little dismay. He had first approached Einstein +“to learn from him what he really felt about the Michelson-Morley experiment, and to what degree it had + + + 39 +influenced him in his development of the Special Theory of Relativity.” (Shankland, 1963, p.47) Instead he +found Einstein telling him that he only learned of the experiment after 1905: +“Otherwise,” he said, “I would have mentioned it in my paper.” He continued to say the +experimental results which had influenced him most were the observations of stellar +aberration and Fizeau’s measurements on the speed of light in moving water. “They were +enough,” he said. ... when I added that it seemed to me that Fizeau’s original result was +only qualitative, he shook his pipe and smiled, “Oh, it was better than that!” +In a follow up report, Shankland (1973, p. 896) once again recounted how Einstein sought to direct +discussion away from ether drift experiments to stellar aberration and Fizeau’s experiment: +...Prof. Einstein volunteered a rather strong statement that he had been more influenced by +the Fizeau experiment on the effect of moving water on the speed of light, and by +astronomical aberration, especially Airy’s observations with a water filled telescope, than +by the Michelson-Morley experiment. +It is not hard to understand the small role Einstein accorded to the Michelson-Morley experiment. +Stachel (1982, p.179) made the decisive remark that, in all later accounts in which it is mentioned, Einstein +offered the experiment as evidence for the principle of relativity, not the light postulate, as is now the +routine practice. If this was Einstein’s attitude prior to 1905, then the experiment would be relevant only +at the earliest stages of Einstein’s explorations. Einstein had decided that the principle of relativity must +hold by the time of the magnet conductor thought experiment. From then on, the Michelson-Morley +experiment could be of little assistance. Its null result was a foregone conclusion, entailed by the principle +of relativity. It could not assist Einstein in deciding between “the principle of the constancy of c, as was +demanded by Maxwell’s equations, or the constancy of c, exclusively for an observer sitting at the light +source [emission theory],” the options he recalled to Ehrenfest that he had weighed. In either case, a null +result is expected. An emission theory would only predict a positive result if the experiment used a light +source moving with respect to the interferometer. +But what of stellar aberration and Fizeau’s experiment? How could these long known first order +experiments be more informative than the newer Michelson-Morley second order experiment? This is the +answer I will develop here: If one looks carefully at how both experimental results are accommodated in +Maxwell’s electrodynamics by the then standard analysis of Lorentz, one finds that they supply direct +experimental evidence for Lorentz’s local time and that they do this essentially independently of +Maxwell’s theory. I urge that this is precisely what Einstein realized. +Lorentz’stheoremofcorrespondingstates31 +Lorentz’s (1895) Versuch is a tour de force. It develops a unified theoretical framework in which to +treat electromagnetic and optical processes in moving bodies and to demonstrate that, even though +Maxwell’s electrodynamics depends essentially on a resting ether, optical processes will depend only on +31 For a account of nineteenth century ether drift experiments and their analysis in Lorentz’s work, see +Janssen and Stachel, forthcoming. + + + 40 +relative velocities at least to first order in v/c. The centerpiece of Lorentz’s work is his theorem of +corresponding states. (pp. 85-86) It amounts to a computationally simple prescription for constructing +new solutions of Maxwell’s equations from old solutions, where the new solutions represent the old, set +into uniform motion. More exactly, it enabled a new solution as close to a uniformly moving copy of the +old solution as Maxwell’s theory allowed and, in the early versions of the theorem of 1895, the new +solution would satisfy Maxwell’s equations only up to quantities of the first order in v/c. The theorem +reduced a difficult problem, finding solutions of Maxwell’s equations for systems in motion, to a much +easier one, finding solutions of Maxwell’s equations for systems at rest. The basis of the theorem was a +transformation for field and other quantities and the coordinates (t, r=(x,y,z)) of the ether rest frame that +included: +E’ = E + (1/c)(uxH) H’ = H – (1/c)(uxE) t’=t–u.r/c2 r’=r–ut (18) +where the term u.r/c2 gave an artificial-looking place dependence to the time variable t’, so Lorentz (p. +50) called it “local time.” To use the theorem, one finds a solution of Maxwell’s equations in the ether +frame, designating the field and coordinates with primes; the primed quantities are replaced with +unprimed quantities by means of the transformation (18); and the resulting formulae are assured by the +theorem of being solutions of Maxwell’s equations up to first order quantities in the ether frame. They +represent the corresponding state of the original solution. +This gloss greatly simplifies Lorentz’s own development, which included a multistep +transformation to arrive at (18). For a thorough treatment, see Janssen (1995, Ch. 3) and also Rynasiewicz +(1988). I will continue with this simplified treatment since it contains all that is needed for the point to be +made. In similarly reduced fashion, I will review how Lorentz (1895, §37, §§60-78) treated three optical +processes: Doppler shift, stellar aberration and the velocity of light in moving media. In each, the +transformations of the field quantities turn out to play no role in the final result. All that matters to track +the velocity of a wave are the locations at which the field intensity drops to zero; these are unaffected by +the field transformations. As a result, I will simply represent a propagating wave as f(ωt–k.r), where ω is +the frequency and k the wave number vector and f stands for the multivalued field intensities. I will also +suppress accompanying transformations of the field intensities. +Doppler shift. If a source emits a plane light wave in the +x direction, its waveform is f(ωt–kx). The wave +propagates with speed V=ω/k, which need not be c. Setting u = (u,0,0) so we “boost” in the x-direction, +the corresponding state is a light wave emitted by a source moving at u in the x-direction. Its waveform is +f(ωt’–kx’) = f(ω(t–ux/c2) – k(x–ut)). That is, the transformation is +f(ωt–kx)  f(ω(1+u/V)t – k(1+uV/c2)x) (19) +From it, we read that the velocity boost has increased the frequency from ω to ω(1+u/V). +Stellar Aberration. The simplest case arises for starlight arriving from a star lying in a direction +perpendicular to the earth’s motion. To arrive at the result, assume we have light propagating in the +y +direction. Its waveform is f(ωt–ky). We presume propagation in a vacuum, so we have c=ω/k. We arrive +at the same result if we imagine the earth boosted in the –x direction or the star boosted by velocity + + + 41 +u=(u,0,0) in the +x direction. Take the latter case. The waveform now becomes f(ωt’–ky’) += f(ω(t–ux/c2) – ky). That is, the transformation is +f(ωt–ky)  f(ωt–kux/c–ky) (20) +One sees that this transformation has deflected the direction of propagation from the perpendicular +toward the direction of motion of the star by the small angle of (u/c) radians.32 This result illustrates the +general result for stellar aberration: for first order quantities in (u/c), the direction of the light propagating +from a star is given by the direction of the vector sum of the velocity of the light and the relative velocity +between the earth and the star. +Fizeau’s Experiment. In this experiment, Fizeau measured the speed of light in moving water. When the +water is at rest, light propagates through it with a speed c/n, where n is the refractive index of the water. +When the water moves at speed u in the direction of the light, the question was how much of that speed +would be added to that of the light. If the moving water was conceived as fully dragging the ether along +with it, then the resulting speed would be c/n + u. If the ether was not dragged along at all, the speed +would remain at c. Fizeau found experimentally a result compatible with partial dragging of the ether: +c/n+ u(1-1/n2). This was the result originally proposed by Fresnel for just these circumstances and the +coefficient (1-1/n2) is the Fresnel drag coefficient. +While Lorentz’s theory supposed a fixed ether that was not dragged at all, he could still recover +the Fresnel drag from an application of his theorem of corresponding states. The waveform for light +propagating in the +x direction for water at rest is f(ωt–kx), where c/n = ω/k. For the case of the water +moving at u=(u,0,0), the theorem of corresponding states gives the transformed waveform f(ωt’–kx’) += f(ω(t–ux/c2) – k(x–ut)). That is, the transformation is +f(ωt–kx)  f(ω(1+un/c)t – k(1+u/cn)x) (21) +We read from it that the frequency is Doppler shifted to ω(1+un/c) and the wave number to k(1+u/cn). +The speed of propagation is given by their ratio: +€ +ω(1+ un/c) +k(1 + u/cn) ≈ cn + u 1 − 1 +n2 + +  + (22) +where the equality holds to quantities first order in u/c. This last result is an astonishing triumph for +Lorentz’s theory. The velocity that light adopts in moving water results from a massively complicated +interaction between charged ions of the moving water and the light wave propagating in the spaces in +between. Yet all Lorentz needs to recover the experimentally observed effect is his theorem of +corresponding states and a small amount of algebra on the space and time variables in the argument of +the waveform. +32 To see this, note that a surface of constant phase for the deflected wave is given by the constancy of +(ωt–kux/c–ky) = k(ct–(u/c)x–y) = k(ct– b.r), where b=(u/c,1,0) is a vector normal to the surface. For +(u/c) << 1, this vector b is deflected (u/c) radians from the +y direction towards the +x direction. To see +that b is normal to the surface, note that for any two points on the surface r and s, we have b.(r–s)=0, +which just asserts that b is orthogonal to any vector (r–s) lying in the surface. + + + 42 +Einsteinabandonsanemissiontheoryoflight.Whatnow? +The decision to abandon the search for an emission theory of light would have created great +difficulties for Einstein in his efforts to realize the principle of relativity in electrodynamics. Without later +insights into simultaneity, a simple consequence of the principle of relativity is that the velocity of a +source must be added to the velocity of the light. Yet no adequate electrodynamics could accommodate it +exactly because it also meant that a suitable velocity between the emitter and observer would allow the +observer to see light slowed or even frozen. Once again, let us chase a beam of light. Assume the +waveform of the light, propagating at c in the +x direction, is f(ωt’–kx’), with c=ω/k. Then a Galilean +transformation to an observer moving at u in the +x direction is t’=t and x’=x+ut and the transformation +between the two observers is: +f(ωt’–kx’) = f(ω(1-u/c)t–kx) (23) +The light frequency is Doppler shifted to ω(1-u/c) at the same time as the light is slowed to a speed of +(ω/k)(1–u/c) = c–u. Einstein’s original idea of field transformations could be of no further assistance in +avoiding this slowing of light. Transformations of the field, such as (4) and (5), did not affect the speed of +the wave, since they did not change the position of points of zero field intensity. +In retrospect it is so clear that Lorentz had precisely the theoretical machinery needed to solve +this problem. A quick comparison of the Galilean transformation (23) with Lorentz’s analogous (19) +shows it. Had Einstein used Lorentz’s local time in the transformation, then, he would have retained the +correct result for the Doppler shift and the velocity of the light wave would have remained c. For V=c, +Lorentz’s waveform (19) is f(ω(1+u/c)t – k(1+u/c)x), so its speed of propagation is simply c=ω/k. In a +1907 review article, Einstein (1907, p. 413) made just this point, writing +One needed only to realize that an auxiliary quantity that was introduced by H. A. Lorentz +and that he called “local time” can simply be defined as “time.” +Yet at the time it would be anything but an obvious connection. Indeed, even after Einstein showed the +connection, Lorentz never felt it was the correct view. Lorentz’s local time was an artificial mixture of +time and space coordinates justified solely by its utility as an auxiliary quantity in the process of +generating new solutions from old by means of the theorem of corresponding states; it simply was not the +true time of the ether. The time that Einstein sought was the real time of his observers in relative motion. +The recognition that local time might well just be this time would be easier for someone who approached +Lorentz’s work with a goal of realizing the principle of relativity. Even then the connection proved hard +to make. Einstein read Lorentz’s Versuch well before he had the crucial insight into the correct +interpretation of local time.33 He also had just the ability to adopt the sort of unorthodox views needed, +for he had been quick to conclude that a magnetic field transforms to a mixture of magnetic and electric +field merely under a change of state of motion of the observer. +33 On 28 December 1901, Einstein wrote to Mileva Maric of his plan to read what both Lorentz and Drude +had written on the electrodynamics of moving bodies. (Papers, Vol. 1, Doc. 131). Drude’s (1900, Ch. 8) +also contained an account of aberration, Fizeau’s experiment and the theorem of corresponding states. + + + 43 +We may never know the precise path that led Einstein from his rejection of emission theories of +light to Lorentz’s local time and whether that path led through a rereading of parts of Lorentz’s Versuch +or an independent recreation of their content. However I want to point out one quite plausible possibility. +First note that the phenomenon of stellar aberration raises no special problem for an ether-based, +wave theory of light. Take the simple case considered above of a star located in a direction perpendicular +to the earth’s motion through the ether. The light from the distant star arrives on earth as plane waves +propagating perpendicular to the earth’s motion. Earth-borne astronomers, however, must compensate +for the earth’s motion if they wish to center the star’s image in their telescopes. Their telescopes must be +tilted forward slightly by the very small angle of u/c radians to accommodate the earth’s velocity u. The +result is captured in an analogy given routinely in textbooks even today. The starlight is analogous to a +rain shower with the raindrops falling vertically. If we run across the shower with a narrow, deep hat and +try to catch the raindrops, we will need to tilt the hat slightly in the direction of our motion, so that the +trailing side of the hat does not intercept the raindrops before they strike the hat’s base. What holds for +the raindrops entering the hat is also true for the portion of the starlight wave front that enters the +telescope. The telescope must now be tilted if the wave front is to remain centered in the telescope barrel +as it propagates along its length. +Stellar aberration does, however, raise serious problems for a wave theory of light if we ask in +addition that the theory conforms to the principle of relativity. If the direction of starlight from a resting +star is deflected by the earth’s motion, then the principle of relativity demands a second effect, arrived at +merely by redescribing this result in the earth’s frame of reference. If the earth is at rest, then the apparent +direction of starlight from a distant star must be affected by the star’s motion u and by the usual angular +deflection of u/c, for small u/c. It is not at all obvious how a wave theory of light can accommodate this +result. To see the problem, begin with the star at rest. Its light will arrive at the earth as plane waves +propagating perpendicular to the wave fronts. Let us say the waveform is f(ωt’–ky’) so that it propagates +along the y-axis to the earth. Now use a Galilean transformation to set the star and its light into uniform +motion u in any direction perpendicular to the direction to the earth. Define the x-axis so that this +transformation is t’=t, x’=x+ut, y’=y. The transformed waveform is just f(ωt–ky), which still propagates in +exactly the same direction. The Galilean transformation is unable to turn the direction of the normal to +the wave fronts and thus unable to replicate the change of direction of propagation demanded by a +relativized stellar aberration.34 In short, the principle of relativity demands that stellar aberration depends +34 One might try to escape the problem by supposing that the direction of propagation is not always given +by the normal to the wave front. We might, as Born (1962, p.141) proposed, identify the direction of +propagation with the direction of energy propagation, supposing the latter to transform differently from +the wave normal under Galilean transformation. Whatever may be the merits of such proposals, they are +unavailable to someone trying to implement a principle of relativity. If the direction of propagation of a +plane wave is normal to the wave fronts in one inertial frame—say the “ether” frame—then that must +true in all inertial frames. Or again: a simple Huygens construction tells us that plane waves propagate in +a direction normal to their wavefronts. If that construction works in one inertial frame of reference, it + + + 44 +only on the relative velocity of the earth and the star; but the simple analysis suggests that the effect only +arises when the earth is moving. (For an informal account of this problem, see Norton, manuscript.) +An emission theory of light would hold the promise of solving this problem, since it would seem +to be well adapted to stellar aberration already. Here is the empirically validated rule for computing +stellar, expressed in terms of relative velocities to conform to the principle of relativity. We add +vectorially the velocity of the star with respect to the earth to the velocity of the starlight with respect to +the star; the direction of the resulting vector is the apparent direction of the starlight on earth. An emission +theory of light merely adds that this resulting vector gives not just the direction of the starlight, but its +speed as well. It would seem that the observed phenomenon of stellar aberration almost directly +expresses the central principle of an emission theory of light. +With his rejection of emission theories, if he had not already done so, Einstein would have to +solve the problem of developing an account of stellar aberration that depends only on the relative +velocity of the earth and the star. But then he might recall that Lorentz had recovered the essential result +in his Versuch. Even in his ether-based theory, it turned out that stellar aberration did depend only on the +relative velocity and not the absolute velocities of the earth and the star. It would have been a simple +matter to consult the Versuch or Drude’s Lehrbuch der Optik to recall how this was possible. +WhatstellaraberrationandFizeau’sexperimentshow +Consider how Lorentz’s transformation (20) may be read by someone seeking to realize a +principle of relativity in electrodynamics. The waveform f(ωt–ky) represents light emitted by a star at +rest. The waveform f(ωt–kux/c–ky) represents light emitted by the star when that star moves at u +perpendicular to the direction of the emission of the light. For a relativist, that same motion could arise +merely through an observer moving at u in the opposite direction. So the two waveforms could equally +be just the same wave but viewed by observers in relative motion. Then one simply recovers the +transformation between the two frames by reversing Lorentz’s calculation f(ωt–kux/c–ky) += f(ω(t–ux/c2) – ky) = f(ωt’–ky’). Identifying the two arguments in the waveforms we have +ω(t–ux/c2) – ky = ωt’–ky’ +From this we read off the partial transformation +t’ = t–ux/c2 y’ = y. +This last step involves a small complication since we must divide one equation into two. The ωux/c2 term +could in principle be incorporated in the y transformation equation. That possibility proves to be +unphysical.35 +must work in all. Stellar aberration must be accommodated by turning the wave fronts, if the principle of +relativity is to be respected. +35 If the term is located in the y transformation equation, that equation would be y’ = y + (u/c)x. Thus a +boost in the x direction would take an arbitrary point (x,0) on the x-axis and shift it in the +y direction, + + + 45 +What is important about viewing the calculation in reverse is that it requires no electrodynamical +theory and no theorem of corresponding states to recover the above transformation. On the contrary, it is +driven empirically. The observations associated with stellar aberration tell us that a waveform f(ωt–ky) +will be deflected by an angle (u/c) if there is a relative motion u< 30 km. => 18 miles), a number taken from Fig. 1 in his article, there is no trouble in explaining wireless reception on the far side of the mountain. By the time Tesla published this piece, the subject of diffraction of electromagnetic waves had become sophisticated and had engaged the attention of a number of distinguished mathematicians. If the mountain is modeled as a hemispherical impediment to the wave, and if the earth is a good conductor, then the problem of scattering +by the mountain can be attacked using the method of images. The problem becomes that of a plane wave incident upon a sphere. This problem had been solved in the period 1908–9 by Debye and Mie and would also show a signal in the optical shadow cast by the hemispherical mountain.19 In the period beginning in 1889 and ending in the era of Tesla’s writing, the Scottish mathematician H. M. Macdonald had treated waves from a Hertzian dipole diffracted from the earth, which he modeled as a perfectly conducting sphere.20 His work was improved by the great French scientist and philosopher, Henri Poincaré, who in the period 1909–1912 converted Macdonald’s series of Bessel functions into a definite integral that could be better evaluated. The German mathematical physicist Arnold Sommerfeld, unlike his predecessors, treated the earth as an imperfectly conducting surface, although he simplified matters by making the earth flat. He placed a vertical, electrically short dipole above the earth and derived an expression for the resulting electric and magnetic fields. His results of 1909 were expressed in terms of an integral that he evaluated asymptotically for an observer far from the antenna. He found that a surface wave had been generated, and his theory nicely supported that of another German, Jonathan Zenneck, whose less rigorous work had led to what became known as the Zenneck wave, which existed on the ground at some distance from the antenna. The latter turned out to be the asymptotic solution + + + Volume 30, 2017 9 +Wunsch +of Sommerfeld’s theory. In 1919, the German mathematician Herman Weyl solved Sommerfeld’s configuration and ended up with a different approach that did not contain Zenneck’s wave. This result caused Sommerfeld to rework his solution, and his new findings did not agree with Zenneck. In short, the first two decades of the 20th century was a lively and sometimes contentious period in the theory of radio wave propagation, but there is no hint of this in Tesla’s paper. Nor is there any indication in anything he wrote that he had the sophisticated mathematical skills to comprehend what was being written by the people cited above. There were, of course, great inventors with minimal knowledge of higher mathematics (think of Edison, Morse, Bell) but these largely belonged to the 19th century, and one does see Tesla as part of that tradition. His clinging to a sketchy circuit theory explanation seems pathetic. Incidentally, as early as 1904, a textbook of Henri Poincaré had addressed the primacy given to currents flowing through the earth in Tesla’s model of wireless telegraphy. He points out that if a coherer is placed in a hole in the ground “it will operate [as a detector of wireless telegraphy] when uncovered; if the hole be filled with earth, the oscillations produce no effect. We must look for something more than earth currents to explain the phenomena.”21 Recall that the most common detector in use at that time was the Branly coherer. Putting aside theoretical considerations, Tesla’s paper is notable for the +omission of major empirical findings contained in the famous and practical Austin-Cohen formula, a concise expression that describes the strength of the electric field experienced by a receiving antenna when both receiver and transmitter are over the ocean. Louis Winslow Austin and Louis Cohen had worked for the U.S. Navy in the early 1910’s, making shipboard electrical measurements of the field radiated from various transmitters manufactured by Reginald Fessenden’s company, the National Electric Signaling Company, or NESCO. By 1911, the two men had devised a successful empirical formula that gives the received field.22 +Ir = 4.25 Ish1h2 e-ad/√λ. +dλ +Here Ir is the current received by an antenna driving an impedance of 25 ohms, Is is the transmitting antenna’s current, h1 and h2 are the lengths of the two vertical antennas, l is the wavelength, d is the distance separating the antennas, and a = .0015. Lengths are in kilometers and currents in amperes. The formula was effective only during the day and was so useful that it became the basis for testing new theoretical predictions of received fields. The presence of the square root of the wavelength in the exponent was later derived theoretically by the English mathematician G. N. Watson and published in 1919, only a few months after Tesla’s paper.23 Interestingly, Tesla, speaking of the formula, states unequivocally “... the actions at a distance cannot be proportionate to the + + + 10 The AWA Review +Paradigm Lost: Nikola Tesla’s True Wireless +height [length] of the antenna and the current in the same,” which is in direct contradiction to what the much-used equation asserts. Tesla’s statement “the current in the same” is especially puzzling, not only because it had been established experimentally but also because he has essentially been using alternating circuit theory, in a strange form, and the device he is employingan antenna, and a conducting earthare mathematically linear and should, according to linear circuit analysis, create a response in linear proportion to the current exciting the antenna. Strange to say, Tesla then uses Austin-Cohen to reject Hertzian waves, saying that, “...I cannot agree with him [Austin] on this subject. I do not think that if his receiver was affected by Hertz waves he could ever establish such relations as he has found.” So, on +the one hand, he rejects the famous formula but then embraces it as a means to argue against Hertzian wave theory. Let us now study Fig. 18, in Tesla’s paper, reproduced here in Fig. 5. He has now introduced a second mountain that is further from the transmitter than the one in the previous figure. He argues that if Hertzian wave theory were true, then the second mountain “could only strengthen the Hertz wave [at the receiver] by reflection, but as a matter of fact it detracts greatly from the received impulses because the electrical niveau between the mountains is raised...” [niveau is a French word for level surface]. What Tesla fails to understand here is that without knowing the wavelength of the radiation, the separation of the two mountains, and the position of the antenna between them, we can make +Fig. 5. Tesla considers the effect of two hills. (True Wireless, Fig. 18) + + + Volume 30, 2017 11 +Wunsch +no statement about the enhancement or reduction of the signal at the receiver caused by the presence of the second mountain. In fact, using elementary wave theory or a transmission line analog, we can argue that if the two mountains are separated by half a wavelength and if the receiver is midway between them, and if the soil is of reasonably high conductivity, then we have what is called a standing wave between the mountains. In this case, the effect of the more distant mountain is to enhance the signal at the receiver. There are waves moving from right to left and vice-versa between the mountains. Such an arrangement, when set up in a room, as Hertz did in his famous experiment published in 1888, is known as an interferometer.24 +Kuhn tells us that if we want to see what constitutes “normal science” and the paradigms it embraces, we should look at the textbooks of that era.25 By 1904, we can say confidently that the paradigm shift created by Maxwell and Hertz had taken hold and was part of normal science. This was the date of publication of Poincaré’s book, whose chapters 7, 8 and 9 are devoted to the propagation of waves along wires, dielectrics, and air. It seems evident that Tesla was not reading the textbooks of his epoch. +Tesla and Antenna Theory +Another puzzling segment of Tesla’s anti-Hertz diatribe is his Fig. 16, shown below as Fig. 6. Tesla would have us believe that the antenna on the right +Fig. 6. Tesla considers a straight and bent antenna. (True Wireless, Fig. 16) + + + 12 The AWA Review +Paradigm Lost: Nikola Tesla’s True Wireless +(which nowadays is called “an inverted L”) is just as effective as a receiver or transmitter as the straight antenna on the left. He claims that he has performed an experiment that supports this conclusion. He also asserts that the experiment proves that “currents propagated through the ground, and not ... space waves” is the reason for true wireless telegraphy. In 1919, an understanding of the theory of receiving antennas was still fairly primitive.26 And it was only in 1924, with the work on reciprocity of John R. Carson at Bell Labs, that the tools that had been developed to analyze transmitting antennas could be brought to bear on receiving antennas.27 So, we must not be harsh in condemning Tesla for his wrongful assertion. However, it was known as early as 1898 that if antennas are placed above a flat highly conducting earth, one can invoke the method of images for analyzing them.28 It was well known before 1919 that if the earth is a good conductor, the electric field of a propagating radio wave would be primarily perpendicular to the earth, and the field strength would be proportional to an integral of the current along the vertical portion of the antenna. It should have been apparent to Tesla that if a transmitting vertical wire antenna is small, measured in wavelengths, and has the shape of the antenna on the left of Fig. 6, and if it is now bent into the shape shown on the right, then the electric field normal to a flat highly conducting earth is reduced.29 However, the situation here +is potentially quite complicated. The difficulty occurs with an imperfectly conducting earth. Marconi, in 1906, described to the Royal Society an array he built consisting of inverted L antennas and observed that the array broadcasts most effectively in the direction of the arrow shown below, i.e., away from the horizontal element.30 Fig. 7 is taken from Principles of Wireless Telegraphy by G. W. Pierce, published in 1910.31 Jonathan Zenneck, in the same era as Pierce, describes the work of H. von Hoerschelmann, a student of Arnold Sommerfeld, who apparently was the first to explain the directive properties of Marconi’s antenna. His earth is assumed to be imperfectly conducting. He includes the vertical portions of the current induced in the earth directly under the horizontal wires of the array.32 The upshot is that whether one assumes a highly conducting earth or one of imperfect conductivity (as is required for Marconi’s antenna), Tesla’s assertion “that the antennas can be put out of parallelism without noticeable change in action on the receiver” is utterly wrong. Marconi’s inverted L was constructed in the year 1905, and the explanation by Hoerschelmann was +Fig. 7. Marconi’s directional inverted L antenna. (G. W. Pierce, Principles of Wireless Telegraphy, 1910, p. 298) + + + Volume 30, 2017 13 +Wunsch +published in Zenneck’s book, which came out in German in 1912, both well before Tesla’s paper.33 +Skin Effect +Tesla repeatedly speaks of his system of wireless telegraphy implemented by sending messages through the earth. Here he displays his ignorance of what is now referred to as “skin effect”: that alternating currents have a marked tendency to cling to the outside (skin) of conductors. Knowledge of this goes back to the work of the Englishman, Sir Horace Lamb, in 1883 and was advanced further by his countryman, Oliver Heaviside, in 1885.34 The results showed that the higher the frequency in use, the greater the tendency for the current to adhere to the outside of the conductor. It is especially puzzling that Tesla does not mention this phenomenon as he took advantage of it in arranging for photographs of himself enveloped by sparks.35 The frequency of the generator he was using was such that the energy would not penetrate deeply into his body, which meant that although he might have been burnt, he would not have been electrocuted. In an 1893 lecture before the Franklin Institute in Philadelphia, he sought to explain his not being shocked with a confused discussion.36 By 1919, skin effect and the concept of skin depth (the depth of penetration of the current) would have been in the better electrical engineering textbooks.37 We can calculate how far a wave might penetrate into a mountain +in the United States where typical soil conductivity, s = .005 mhos/meter and the relative permittivity, er = 10.38 We will assume a frequency f = 100 kHz. Using the standard formula for skin depth that applies when conduction current greatly exceeds displacement current,39 we have +δ=√ 1 +π f μσ +Here d is the skin depth and m is the permeability of the soil, assumed here to be nonmagnetic. The skin depth for the numbers chosen here is about 22 meters. It is virtually impossible for the signal that Tesla imagines to penetrate a mountain having these typical parameters. +Dismissal of Gliding Waves +Let us now focus on Tesla’s Fig. 13 (shown here as Fig. 8) and his accompanying discussion. At the very top of his figure Tesla has the caption, “Hertz’s waves passing off into space through the earth’s atmosphere.” To someone acquainted with even elementary antenna theory, the picture is a puzzle. It depicts what appears to be a vertical antenna fed by a generator connected between the base of the antenna and the earth. In 1919, such an antenna would likely be of small height when measured in the wavelengths in use. Using the method of images and antenna analysis dating from the turn of that century, it should have been apparent that no radiation propagates along the axis of the antenna; instead, the radiation + + + 14 The AWA Review +Paradigm Lost: Nikola Tesla’s True Wireless +tends to be focused along the ground. In fact, if the current in amperes along the antenna is I0, then elementary antenna theory establishes that the strength of the electric field is at a distance r from the antenna, above the earth, is given by +Eθ = I0120πh sinθ for 0 ≤ θ ≤ π / 2 , +λr +where h is the length of the antenna, l is the wavelength in use and r is the distance of the observer from the antenna.40 All the distances are in meters. The meanings θ and Eθ should be evident from Fig. 9. Observe that directly above the antenna corresponds to q =0, so that sinq = 0, which indicates there is no radiation normal to the earth, while along the earth q = 90 degrees, and the radiation is maximum, which might +suggest a wave gliding along the surface of the earth, provided we are close enough to the antenna to neglect the earth’s curvature. This result would have certainly been known well before 1919. The book Robison’s Manual of Radio Telegraphy and Telephony for +Fig. 8. Tesla condemns the “Gliding Wave.” (True Wireless, Fig. 13) +Fig. 9. Electric field and spherical coordinates. + + + Volume 30, 2017 15 +Wunsch +the use of Naval Electricians, published in 1918, contains the following diagram showing the direction of electric lines (see Fig. 10).41 It illustrates that a monopole antenna radiating above a flat perfectly conducting ground tends to radiate in a direction parallel to the ground and not in a direction along the axis of the antenna. This is not a polar plot of the field strength vs. angle but a picture showing the direction of the electric field at various locations. Incidentally, one can argue that there is no radiation along the axis of the antenna even if the ground has imperfect conductivity.42 Tesla specifically condemns any theory that claims “[space waves] pass along the earth’s surface and thus affect the receivers. I can’t think of anything more improbable than this ‘gliding wave’ theory which... [is] contrary to all laws of action and reaction.” Of course, this gliding wave concept that we would now call a “surface wave” did describe daytime radio propagation and was central to the work of such theorists as Sommerfeld, Zenneck, and Watson.43 +Tesla Debunks the Ionosphere +Warming to the task of diminishing other theorists, Tesla then damns what was then only a conjecture: the belief in what was then known as the KennellyHeaviside layer. We now call this the ionosphere—a set of layers of three or more ionized gases in the earth’s upper atmosphere. It was first postulated, as a single layer, in 1902 by Arthur Kennelly and Oliver Heaviside, working independently, as a way of explaining how radio waves propagate beyond the horizon.44 Although its existence and height were not verified experimentally until 1924 by the Englishman Edward Appleton, for which he was later awarded the Nobel Prize, its presence was generally accepted in 1919, especially as a means to explain the long distances that radio waves would propagate at night.45 Tesla tells us, “I have noted conclusively that there is no Heaviside layer, or if it exists it is of no effect.” One wonders if he recanted this statement after Appleton’s experiment. +Communication with Airplanes +Among the more perplexing aspects of Tesla’s article is his discussion tied to his Fig. 15. He is showing here in Fig. 11 a “Hertz oscillator” suspended in the air, and uses this arrangement to explicate something that became well known during World War I: an airplane could communicate with a wireless receiver on the ground. Also known, but not discussed by Tesla, was that two airplanes in the air might experience radio contact with each other. +Fig. 10. Electric field lines of a short monopole antenna. (Manual for U.S. Navy Electricians, 1918) + + + 16 The AWA Review +Paradigm Lost: Nikola Tesla’s True Wireless +What Tesla must explain is how his transmitter in the air might communicate with the receiver on the ground in spite of its not having a direct connection to the earth that would be capable of effectively launching his crucial earth currents. His explanation is that “we are merely working through a condenser.” Stating incorrectly there is a capacity that “is a function of a logarithmic ratio between the length of the conductor and the distance from the ground,” he says the receiver is affected in the same manner as with an ordinary transmitter. Evidently, we are to believe that the capacitance between earth and ground makes possible the earth currents crucial to his argument. The formula for the capacity of a wire that he is most likely referring to would have been well known by the 1910s when it already had appeared in textbooks and handbooks:46 +C = 1.111 L picofarads. +2h +2 ln ( r ) +This expression is the capacity of a wire of length L above, and parallel to, the earth’s surface, which is assumed to be highly conducting. An airplane in flight dragging a wire antenna behind itself would create this situation. The wire is at height h above the earth, and its radius is r. All dimensions are in centimeters, and the logarithm is base e. Note that the capacity is proportional to the wire length L, not to the logarithm of L as Tesla asserted.47 Using the well-known formula for capacitive reactance X = 1/(2p f C), where f is the operating frequency, we could in principle obtain the impedance between the wire and earth. Dividing the voltage of the antenna, with respect to the earth, +Fig. 11. Tesla denies there is “Space Wave” transmission in wireless telegraphy. (True Wireless, Fig. 15) + + + Volume 30, 2017 17 +Wunsch +by this impedance, we might think we have obtained the current on the earth. But what voltage are we to use? Because the antenna illuminates the earth with an electromagnetic wave, the concept of voltage difference or potential difference cannot be applied. It was known in the late 19th century that electric potential difference between two points is calculated by the line integral of the electric field along a path between those points. When there is a time varying electromagnetic field between these points the result will depend on the path taken and so the concept of voltage difference ceases to be of use.48 Note that Tesla skirts entirely the phenomenon of airplane-to-airplane wireless communication, which had been observed during the war.49 Such communication could not possibly involve earth currents if the transmission took place over a desert or dry sandy soil. +The Hertzian Wave Discourse +The publication of Maxwell’s Treatise on Electricity and Magnetism in 1873, which described his work of the previous decade, together with Hertz’s experiments of 1886–9, created the paradigm shift which Tesla was unable to accept. We might be a little indulgent here—the new paradigm was slow to be accepted—consider Marconi for example. By the late 19th century Marconi was being lionized in the British press because of his demonstrations of wireless telegraphy, but an interview in McClure’s magazine from 1899 has him +declining to say what sort of waves he was using: “What kind of waves they were Marconi did not pretend to say; it was enough for him that they did their business well.”50 When asked about the difference between his waves and those used by Hertz he replied “I don’t know. I am not a scientist, but I doubt if any scientist can tell you...”51 What seemed to impede the connection of Marconi’s waves to those of Hertz’s was that it was known by 1897 that the former’s radiation could pass through the walls of a building while Hertz’s, which was based on a model of radiation as visible light, would apparently not perform such a feat.52 Marconi’s first British patent, number 12039, which was filed in 1896, speaks of an arrangement that he calls “a Hertz radiator” producing effects “which propagate through space [as] Hertzian rays.” But he also talks of electrical actions or manifestations “...transmitted through the air, earth, or water by means of electrical oscillations of high frequency.” For a while, Marconi’s manifestations in the ether were known in some circles as Marconi waves, but the term soon died. Some further indication of the confusion, circa 1900, is a question raised by the historian of early wireless, J. J. Fahie, in his publication of 1901, “... is the Marconi effect under all circumstances truly Hertzian...?”53 After 1899, we find that Marconi began to refer more frequently in his work to “Hertzian waves.” In a speech given before the Institution of Electrical Engineers (now the IET) in + + + 18 The AWA Review +Paradigm Lost: Nikola Tesla’s True Wireless +England on March 2, 1899, he says, “I think it desirable to bring before you some observations and results I have obtained with a system of Hertzian wave telegraphy, which was the first with which I worked....”54 His U.S. patent 676,332 of 1901 refers to “a transmitter producing Hertz oscillations.” And, following Kuhn, we can say that Hertzian waves entered the discourse of “normal science” because we find extensive references to them in a textbook, e.g., Poincaré, cited above. In fact, studying the index of Poincaré, we find that he uses Hertzian waves and electromagnetic waves as synonyms. John Ambrose Fleming, who was the first Professor of Electrical Engineering at University College, London, and who did major work for Marconi beginning in 1899, published a textbook titled Hertzian Wave Wireless Telegraphy in 1903, in which there is not the slightest doubt that wireless telegraphy relies on the waves of the title. Interestingly, Tesla, in certain of his turn-of-the-century U.S. wireless patents, refers to Hertzian waves, or “radiations,” being “brought into prominence” by Heinrich Hertz.55 In all of these instances, such waves are disparaged as being of an outmoded or less desirable way of transmitting signals, or energy, which should be discarded in favor of one that either uses extremely strong electric fields and high antennas to ionize a layer of the earth’s atmosphere which is to then act as a conductor of a transmission system (which includes the earth’s crust)—or of another that uses +wavelengths so long as to make the earth into a conducting sphere that has been brought to a resonant condition. In the later case, he recommends using frequencies lower than 20,000 cycles per second (cps) and asserts one might go as low as 6 cps (patent 787,412, lines 260–270). +Maxwell and Einstein: Difficulties for Tesla +When Tesla wrote his True Wireless paper he was not a young man—he was 63. Male life expectancy in the United States was then 54. His formal education in science and engineering had taken place many years before. He had studied for somewhat less than three years at the Austrian Polytech in Graz Austria in the late 1870’s. In 1880 he audited courses at Charles Ferdinand University in Prague but was not enrolled. His course work should have given him a solid grounding in electric circuit theory, and it was in school that he developed a great interest in alternating currents, especially for motors.56 It is highly unlikely that Tesla would have studied Maxwell’s theory while at school. As first presented in 1873, it was so difficult that few could understand it; nowhere will you find in Maxwell’s treatise the four succinct equations studied today by all electrical engineering and physics students. His analysis is based entirely on potentials, not the electric and magnetic fields used now. He used 20 equations and 20 variables, and it was only through the efforts of such people as Hertz, Heaviside, and Willard Gibbs + + + Volume 30, 2017 19 +Wunsch +in the late nineteenth century that the equations were to assume the form we find them in today.57 Even with their simplifications, we know that Maxwell’s theory was not systematically taught at Cambridge University until after around 1900.58 Because Hertz’s famous experiment was inspired by Maxwell’s work, which Tesla most likely did not understand, it seems plausible that Tesla might cling to an electric circuit theory paradigm in explaining what was called wireless communication. Note however, this was not canonical circuit theory—Tesla had added some bizarre features of his own to force it to explain wireless telegraphy. Maxwell’s theory and its experimental verification by Hertz is not the only paradigm shift in Tesla’s era that he was unwilling to accept and understand. Throughout his life, he spoke often of particles that moved faster than light—a direct contradiction of Einstein’s theory of relativity.59 In an interview with Time magazine on the occasion of his 75th birthday in 1931, he claimed to have “split atoms” with no release of energy—again a contradiction of relativity. He also asserted that he had, using “pure mathematics,” come up with a theory that “tend[s] to disprove the Einstein theory.” There is no indication that Tesla ever had the knowledge to derive a competing theory. Circa 1930, Tesla wrote a poem for his friend George Sylvester Viereck in which he muses about science.60 One stanza addresses Newton and contains these lines: +“Too bad, Sir Isaac, they dimmed your renown And turned your great science upside down. Now a long haired crank, Einstein by name, Puts on your high teaching all the blame. Says: matter and force are transmutable And wrong the laws you thought immutable.” +Note the “long haired crank”—Tesla’s name for the man who overthrew the Newtonian paradigm of mechanics. Much has been written about opposition to Einstein’s theory of relativity; this hostility reached its peak in the two decades following the confirmation of the general theory of relativity via the measurement of the bending of starlight by the sun’s gravitational field in 1919.61 Some of this opposition was rooted in anti-Semitism, as the preceding reference shows, and we do know that Tesla had anti-Jewish tendencies.62 In addition, Hertz, whom he diminishes, was, like Einstein, of Jewish origin,—only partly in Hertz’s case—but it seems more likely that the statement to Time magazine derives more from an almost pathological narcissism that compelled him to be in the public eye. Tesla has been called a scientist, engineer, and inventor. While the confusion and angst that can befall a scientific community having difficulty in adapting to a paradigm shift has been much written about, especially after Kuhn’s seminal publication, the effect of a scientific paradigm shift on + + + 20 The AWA Review +Paradigm Lost: Nikola Tesla’s True Wireless +inventors, as opposed to scientists, has been less explored.63 When we study the lives of individual inventors or engineers we can find failure to adapt to a paradigm change. +Shifting Paradigms in Invention +Besides Tesla, whose inability to absorb a new paradigm should be evident, we have the example of yet another great inventor, Thomas A. Edison. Edison had little formal teaching in schools and was largely educated by his mother and by his own readings. His first important work experiences and inventions were in the field of the [wired] telegraph, which operates using direct currents, and it is clear that he obtained a strong intuitive grasp of DC theory. It is understandable that his subsequent system of generating and distributing electric power was all based on DC. Paul Israel, the esteemed biographer of Edison and editor of the Thomas Edison papers, remarks, “While experimenting with generators, Edison again relied on his experience with telegraph technology to provide a useful analogy that guided laboratory research.” Israel points out how Edison and his workers sometimes envisioned direct current generators as “carbon battery elements.”64 Historians have written about Edison’s unwillingness to adapt to the newly introduced system of AC electric power, which posed a direct economic threat to his own DC system.65 We will probably never know for sure if his objection to AC was truly based on his concern that it was more lethal +than DC, or whether he was acting out of pride, inertia, economic self-interest, or an inability to grasp a phenomenon requiring some mathematical sophistication that eluded him. His statement in 1891 to Henry Villard, President of Edison GE, “The use of alternating current instead of direct current is unworthy of practical men,” has proved to be as fatuous as Tesla’s notion that Hertzian wave theory is “an aberration of the scientific mind.”66 +Age and Vanity +We are left to wonder why Tesla wrote this long paper displaying a wealth of ignorance. One clue might come from an article about him that appeared in the New York Times of January 9, 1943, a few days after the inventor’s death. The generally admiring piece observes, “His practical achievements were limited to the short period that began in 1886 and ended in 1903. And what achievements they were.” By 1919, Tesla’s last important work had taken place more than half a generation before. Studying a list of Tesla’s patents, we find that about 90% of them were filed on or before 1903, and all of his important ones were granted before this date.67 +Resurrecting Tesla’s Reputation +His Electrical Experimenter piece can be read as a rather sad effort to resurrect his reputation. Moreover, his denigration of Hertzian waves and promotion of the primacy of earth currents may be seen as an attempt to preserve respect for his construction of a 187-foot tower (capped with a sphere) in 1901–1903 on + + + Volume 30, 2017 21 +Wunsch +Shoreham, Long Island, whose purpose was to produce a “World Wireless System” that would radiate “several thousands of horsepower” and permit the connectedness of all the telephone and telegraph exchanges in the world by wireless means. The system was to use currents in the earth but was never demonstrated.68 Consider his allusion in “The True Wireless” to a speech he gave in 1893 at the Franklin Institute where there is a portion entitled “Electrical Resonance.” He remarks in 1919, “This little salvage from the wreck has earned me the title of ‘Father of Wireless’ from many well-disposed workers ...” Perusing the speech, we wonder who these well-disposed workers are. In his Institute lecture he asserted, “I do firmly believe that it is practicable to disturb by means of powerful machines the electrostatic condition of the earth and thus transmit intelligible signals and perhaps power... We know now that electrical vibration may be transmitted through a single conductor. Why then not try to avail ourselves of the earth for this purpose [italics added]?”69 Notice the use of the word electrostatic. His proposal is not based on any use or understanding of electromagnetic waves. As further proof of this, he goes on to wonder what the electrical capacitance of the earth might be and “the quantity of electricity the earth contains.” None of this thinking proved germane to communication by wireless telegraphy nor is his obsession in the article with determining the period of oscillation +of currents that might be induced in a resonant earth. +Strengthening Tesla’s Claims +In a further attempt to strengthen his claims to invention in wireless, Tesla lays claim to discovering the forerunner of the Audion in the caption to his Fig. 9 (reproduced here as Fig. 12). The captions reads, “The Forerunner of the Audion—the Most Sensitive Wireless Detector Known, as described by Tesla in His Lectures Before the Institution of Electrical Engineers, London, February, 1892.” It is instructive to read the text of the talk where he discusses his “forerunner.”70 He begins by paying homage to Professor Crookes and his invention, the Crookes tube. Like Crookes, Tesla is not using thermionic emission. He employs a cold evacuated glass bulb, like a lamp bulb, but with no filament. The bulb, which has a “high vacuum,” contains some conducting powder, which in turn is connected by a wire to one terminal of a high frequency, high voltage induction coil. The bulb has a sheet of metal foil on its surface that is also connected to the coil for some experiments, but not others. The +Fig. 12. Tesla’s “Forerunner of the Audion.” (True Wireless, Fig. 9) + + + 22 The AWA Review +Paradigm Lost: Nikola Tesla’s True Wireless +straight lines that you see in the figure he calls a “brush”; it gives off a glow that he calls luminosity—whose shape and form he reports is very sensitive to the presence of objects or nearby electric or magnetic fields. However fascinating his demonstration, Tesla still has not produced the forerunner of the Audion. The latter, we recall, was invented by Lee de Forest, and was the first working three-element vacuum tube. His patent application is dated January 29, 1907, and it issued on February 18, 1908. Despite de Forest’s confused understanding of his invention, within the next half dozen years it was proving its worth as both an amplifier and an oscillator. If we want to see the forerunner of the Audion we must look to the work of Fleming and Edison, whose devices, like de Forest’s, relied on thermionic emission. The distinguished historian of the vacuum tube, Gerald Tyne, makes no mention of Tesla in his well-regarded opus.71 This is not surprising—Tesla’s bulbs responded by glowing only in the presence of strong, quasi-electrostatic fields produced by his machines. It is regrettable that Tesla’s narcissism caused him to write this paper—it can only provide difficulty for his acolytes and apologists. The ignorance he displays of classical electromagnetic theory, which by 1919 was a mature subject, can only diminish his reputation. +Gernsback and His Magazine +If Tesla’s True Wireless is so utterly wrong, and if it conflicts with the paradigms used by engineers and scientists +of 1919, how did he get his article published? To answer this, we must focus on the magazine where it appeared and its editor/publisher Hugo Gernsback (1884–1967).72 Almost a generation younger than Tesla, Gernsback had certain things in common with him: they were both inventors with substantial lists of patents—Gernsback had 22, Tesla 112; both came from groups that placed them in small minorities in the United States (Gernsback was a Jew from Luxemburg); both studied science and engineering on the European continent; and both occupied a kind of nether world bridging science and fantasy.73 They apparently had a lasting friendship that would tend to counter suspicions that Tesla was an anti-Semite. Gernsback pressured the Westinghouse Company, which had benefited greatly from Tesla’s work in three phase power and induction motors, to give the near destitute inventor a pension in 1934.74 +Gernsback’s Electrical Experimenter +The Electrical Experimenter, started by Gernsback in 1913, is where we find Tesla’s article six years later.75 Although the term “science fiction” did not exist until coined by Gernsback in 1929, his magazine Modern Electrics carried a serialized story of that genre in 1911–12, written by Gernsback—something to keep in mind when we look at the Electrical Experimenter, where Tesla was to publish abundantly in the 7-year life of that magazine.76 What sort of magazine was the Electrical Experimenter? It was dense + + + Volume 30, 2017 23 +Wunsch +with ads for radio hardware, e.g., Murdock headphones and audio interstage transformers as well as Grebe and De Forest radios. Mainly, it carried stories of new inventions, especially those with an electrical basis, such as a new radio compass, a method of abolishing smoke electrically, new electric stoves, and quack medicine—anesthesia via electricity and an electrical cure for tuberculosis using the Tesla coil.77 Much of the magazine was given over to what we would now call “techno-euphoria”—a belief that technology would bring us wonderful things in the not-too-distant future. One example was the Thought Recorder, shown in Fig. 13. The author of the article is none other than Gernsback himself. He imagines a man in an office who is connected to a halo on his forehead. The halo is supporting an Audion amplifier tube that detects and amplifies the +man’s thoughts. They are then sent to an instrument on his desk that converts his thoughts to an inscription on a moving tape. The latter is supplied to the man’s secretary who is capable of reading the information on the tape and who can now write letters or memos based on what the boss has been thinking. The article appears in the same issue as Tesla’s, and Tesla, in an introduction, gives some measured support to the idea. Interestingly, Greenleaf Whittier Pickard, a distinguished electrical engineer who helped develop what we would now call the crystal radio, circa 1904, also comments and employs the term “Hertzian waves,” illustrating how commonly the phrase was used. +The Electrical Experimenter does seek to explain legitimate recent advances in the sciences. For example, Einstein’s special and general theory of relativity and the general theory’s +Fig. 13. The “Thought Recorder.” (Electrical Experimenter, May 1919) + + + 24 The AWA Review +Paradigm Lost: Nikola Tesla’s True Wireless +confirmation by the observed bending of light are carefully described in the January 1920 issue by an unusual person for the era: a female astronomer, Isabel M. Lewis, M.A, who was a regular contributor and the first woman astronomer to be hired at the U.S. Naval Observatory.78 The magazine also published pure science fiction stories, such as “At War with the Invisible” appearing in the March and April 1918 issues, which described a war between the planets Mars and Earth in the 21st century.79 +Science Fiction, Nostalgia for the Future Unfortunately, a magazine mixing techno-euphoria, future studies, science fiction and real science is playing dangerous games: the boundaries became diffuse. The March 1918 Electrical Experimenter has an article by Gernsback starting on page 743 entitled “Can Electricity Destroy Gravitation?” The author asserts it can, and describes the work of a Prof. Francis E. Nipher of the Saint Louis Academy of Science. The professor’s experiment is described thusly: He suspends a small lead ball from a string. It is placed in proximity to a very heavy lead ball that rests on a bench. The small ball and string are seen to be deflected toward the heavy ball because of the force of gravitational attraction—a straightforward replication of the famed Cavendish experiment of 1797–8.80 The professor then passes a direct current through the large ball. Nothing has changed. But then he applies an AC current, et voilà, the small ball moves away from the +large one, thereby proving that gravity has been weakened by electricity. Anyone with a modicum of knowledge of electromagnetic theory would see what was happening here. The AC creates a time varying magnetic field that induces eddy currents in the small ball. These currents interact with the magnetic field to push the small ball away from the large one. The clue that Faraday’s law of induction and the induced current serve as the explanation should have been the failure of the experiment to work with a direct current. The gravitational field, like DC and its resulting fields, is static. A direct current cannot induce a voltage or current in a neighboring circuit, while alternating currents have that ability. Eddy currents were well understood by 1919. One wonders how much real science Gernsback knew; it is no surprise that he permitted another paper based on dubious physics to be published the next year: Tesla’s “The True Wireless.” The Electrical Experimenter morphed into another Gernsback magazine: Science and Invention, in 1920.81 This publication, although it did in some ways live up to its title, increasingly carried science fiction and proved so successful that Gernsback was able to introduce more magazines (e.g., Amazing Stories, Wonder Stories) that were wholly devoted to the science fiction genre, and he is best known as a publisher of science fiction. At least one historian has suggested that many of the ideas in Gernsback’s science-fiction stories promoted Tesla’s “still unrealized ideas” for inventions.82 + + + Volume 30, 2017 25 +Wunsch +Endnotes +1. Nicholson Baker and Margaret Brentano, “The World on Sunday: Graphic Art and Joseph Pulitzer’s Newspaper (1898–1911),” (Bullfinch Press, Boston, 2005) pp. 102–103. 2. Nikola Tesla, “The True Wireless,” Electrical Experimenter, vol. 7, no. 3, May 1919, pp.22–23, 61–63, 87. The following website has images of the original pages: http://w w w.free-energ y-nfo.com/Tesla TrueWireless.pdf. Other sources of the paper can be found by Googling the search term “Tesla True Wireless.” Vendors of CD’s having a complete run of the issues of the Electrical Experimenter can be found on eBay. +3. Thomas Kuhn, The Structure of Scientific Revolutions, 3rd ed., (University of Chicago Press, Chicago, 1996). 4. R.P. Feynman, R. B. Leighton, and M. Sands, “The Feynman Lectures on Physics, vol. 2,” (Addison-Wesley, Reading, MA, 1964) pp. 1–6. 5. Jed Buchwald, The Rise of the Wave Theory of Light, (University of Chicago Press, Chicago, 1989); With the birth of quantum theory circa 1900–26, a particle theory of light based on photons was to reemerge, but it did not undermine Maxwell’s work thanks to the concept of the wave-particle duality. See for example Ian Walmsley, Light: A Very Short Introduction, (Oxford University Press, Oxford, 2015). +6. Hugh Aitken, Syntony and Spark: The Origins of Radio, (Princeton University Press, Princeton, 1985), Chapter 3. +7. Hugh Aitken, Syntony and Spark. +8. Interestingly, we have only Tesla’s word that this meeting took place. There is no supporting entry in Heinrich Hertz: Memoirs, Letters, Diaries by Mathilde Hertz and Charles Süsskind, 2nd edition (San Francisco Press, San Francisco, 1977). As Tesla was a famous inventor by the time of the meeting, it is puzzling that he was not mentioned by Hertz. Also, no meeting is described by Bernard W. Carlson in his definitive biography of Tesla: Tesla: Inventor of the Electrical Age, (Princeton University Press, Princeton, 2013). +9. Tom Lewis, Empire of the Air: The Men Who Made Radio, (Harper-Collins, New York, 1991), p 136. +10. Paul Schubert, The Electric Word: The Rise of Radio, (Macmillan, London, 1928) pp. 166–168. +11. It was not until 1893, well after Tesla had completed his education, that the great simplification in AC circuit analysis made possible by the use of complex quantities began to be adopted, thanks to the work of C. P. Steinmetz. See, for example, Charles Proteus Steinmetz, “Complex Quantities and their Use in Electrical Engineering,” AIEE Proceedings of International Electrical Congress, July 1893, pp. 33–74. 12. Alfred Hay, The Principles of Alternate Current Working, (Biggs and Co, Boston, 1897) pp. 137–148. Available at Google Books; for other 19th century engineers who used fluid analogies—or rejected them—see Paul J. Nahin. Oliver Heaviside: Sage in Solitude, (IEEE Press, Hoboken, NJ) 1988, p. 59 (note his footnote 3 and the derisive comment “drainpipe theory”). 13. There is a stern critique of using mechanical explanations for explaining electrical phenomena in Henri Poincaré, Maxwell’s Theory and Electrical Oscillations, (McGraw-Hill, NY, 1904) Chapter 1, pp. 1–2. This book is available at Google Books. Tesla was so committed to hydraulic analogies that he supplied one for his high voltage, high frequency invention, the Tesla coil. See N. Tesla, My Inventions. This series of articles originally appeared in the Electrical Experimenter in 1919. They have been republished in his book My Inventions (Barnes and Noble, NY, 1995). See especially pp. 76–77. The analogy is so complicated that one is better served by studying the original electrical device and applying the laws of AC circuit theory and resonance. 14. Interestingly, in U.S. patent 645,576, Tesla has not yet discarded the return wire in a communication/power distribution system he is proposing. Part of his circuit consists of a path through an atmospheric layer that his powerful transmitter will, he asserts, succeed in ionizing. The earth is also employed in the circuit. The patent was granted in 1900, but by 1919 he has dispensed with the return part of the circuit. 15. For an explanation of the concept of Whig history, as it applies to the history of science, see Steven Weinberg, “Eye on the Present, The Whig History of Science,” New York Review of Books, vol. 62, no. 20, Dec. 17, 2015. 16. J. Zenneck and A. E. Seelig (translation), Wireless Telegraphy, (McGraw-Hill, NY 1915) + + + 26 The AWA Review +Paradigm Lost: Nikola Tesla’s True Wireless +pp. 258–259. This book provides an idea of how textbooks, circa 1910–1920, explained waves received on the far side of the mountain. 17. See the article on diffraction in the 11th edition of the Encyclopedia-Britannica, vol. 8, 1911. https://en.wikisource.org/wiki/1911_Encyclop %C3%A6dia_Britannica/Diffraction_of_Light /11. Also, for a modern treatment see Y. T. Lo, Y. T and S. W. Lee, Antenna Handbook, (Van Nostrand-Reinhold, NY, 1988) sec. 29. 18. R. W. P King and S. Prasad, Fundamental Electromagnetic Theory and Applications, (Prentice Hall, Upper Saddle River, New Jersey 1986) chapter 7. +19. Jules Stratton, Electromagnetic Theory, (McGraw-Hill, New York. 1941), secs. 9.22–9.24. +20. Chen-Pang Yeang, Probing the Sky with Radio Waves (University of Chicago Press, Chicago. 2013). I am greatly indebted to this source. 21. Henri Poincaré and F. King Vreeland (translation), Maxwell’s Theory and Wireless Telegraphy, (McGraw-Hill, New York, 1904) p. 161. Tesla might have countered by asserting that the Branly coherer responds to the electric field—not the magnetic field—and the earth weakens the former. 22. L. W. Austin, “Some Quantitative Experiments in Long Distance Radio Telegraph,” Reprint No. 159, Bulletin of Bureau of Standards, vol. 7, no. 3, Feb. 1, 1911; see also Robison, 1918, p. 228. 23. Watson, G. N. “The Transmission of Electric Waves Around the Earth,” Proc Royal Society (London) Series A, vol. 95, July 15, 1919, pp. 546–553. 24. Heinrich Hertz, Electric Waves, (Dover Books, Mineola NY, reprint of Macmillan book 1893) chapter 8 (dating from 1888, especially Fig. 26). 25. Kuhn, page 43. +26. Samuel Robison, Robison’s Manual of Radio Telegraphy and Telephony for Naval Electricians (U.S. Naval Institute, Annapolis, MD, 1918) p.131. He asserts that the directivity behavior of the “flat top antenna” attributed to Marconi, which involves a long piece of wire or wires parallel to the ground, is still not understood. 27. L. J. Chu, “Growth of the Antennas and Propagation Field Between World War 1 and World War 2. Part 1, Antennas,” Proceedings of the IRE, vol. 50, no. 5, May 1962, pp. 685–7. +28. Charles Burrows, “The History of Radio Propagation up to the End of World War I,” Proceedings of the IRE, vol. 50, no. 5, May 1962, pp. 682–684. 29. Note that Marconi had described arrays formed from inverted L antennas as early as 1906, as noted in G. W. Pierce below. The horizontal elements were much longer than the vertical ones, a configuration not suggested in Tesla’s Fig. 16. G. W. Pierce, Principles of Wireless Telegraphy, (McGraw-Hill, New York, 1910) Chapter 25. See also Practical Wireless Telegraphy, Elmer Bucher, Wireless Press, 1917, sec. 233. Here, the horizontal portion of the antenna is nearly a mile long. 30. See G. Marconi, “On Methods Whereby the Radiation of Electric Waves May Be Mainly Confined to Certain Directions, and Whereby the Receptivity of a Receiver May Be Restricted to Electric Waves Emanating from Certain Directions,” Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 77.518 (1906): 413–21; Electrician, vol. 60, 1908, p. 883. 31. Pierce, p. 298. 32. Zenneck and Seelig, Sec. 202–204. The book contains the reference to Von Hoerschelmann, which was published in German as a dissertation in 1911. 33. Aitken, p. 267. 34. Nahin, pp. 142–143. +35. Bernard Carlson, Tesla: Inventor of the Electrical Age, (Princeton U. Press, Princeton NJ, 2013) p. 200–202; note that some images were the result of multiple exposures where Tesla was not present when the sparks were being generated, see pp. 297–299. +36. T. C. Martin, editor, The Inventions, Researches and Writings of Nikola Tesla, 1893; republished by (Barnes and Noble, NY, 1992) Chapter 6. From the lecture: “The reason why no pain in the body is felt, and no injurious effect noted, is that everywhere, if a current be imagined to flow through the body, the direction of its flow would be at right angles to the surface; hence the body of the experimenter offers an enormous section to the current, and the density is very small, with the exception of the arm, perhaps, where the density may be considerable...The expression of these views, which are the result of long continued experiment and observation, both with steady and + + + Volume 30, 2017 27 +Wunsch +varying currents, is elicited by the interest which is at present taken in this subject, and by the manifestly erroneous ideas which are daily propounded in journals on this subject.” Tesla misses the essential point here—the very shallow depth of penetration of the energy. The arm plays no special role. Notice that he takes a swipe at other workers’ “erroneous ideas.” 37. Indeed, it was in Poincaré’s book of 1904 (see above). 38. E. C. Jordan and K. Balmain, Electromagnetic Waves and Radiating Systems, 2nd ed., (Prentice-Hall. NJ, 1968) p. 655. 39. Note that this is a simplification of a formula derived by Heaviside in 1888. See Nahin, who also gives the formula we are using here, p. 176 40. King and Prasad, section 5.9. The sinθ variation was derived by Hertz in the 19th century (see Hertz, Electric Waves, p. 143 above) and was popularized by Louis Cohen in a paper written for engineers in 1914. See his “Electromagnetic Radiation,” Journal of the Franklin Institute, April 1914, vol. 177, no. 4, pp. 409–418. 41. Robison, 1918, p. 62. Notice that the same picture appears in an even earlier edition of Robison, dating from 1911, on page 76. This book is available from Google Books. 42. R.W.P King, Theory of Linear Antennas, (Harvard University Press, Cambridge, MA, 1956) chapter 7. Note that this work is based in part on Sommerfeld’s work of 1909. 43. Burrows. 44. Ibid. 45. The ionosphere, although not called by that name, could be found in electrical engineering handbooks as early as 1915; see for example W. H. Eccles, Wireless Telegraphy and Telephony: A Handbook of Formulae, Data and Information. (Electrician, London, 1915), pp. 162–3. 46. Eccles, p. 120. 47. In the unlikely event that the wire hangs straight down from the aircraft, the preceding formula does not apply. However, it would still be incorrect to say that the capacitance varies with the logarithm of the length of wire. The required formula shows a more complicated behavior. See Eccles p. 120. 48. James Clerk Maxwell, A Treatise on Electricity and Magnetism, vol. 1.(Clarendon Press, Oxford 1891) p. 76. This has been reprinted by Dover Books, NY, 1954. For a modern treatment that emphasizes the limitations of the +concept of voltage difference see Edward.C. Jordan and Kenneth. Balmain, Electromagnetic Waves and Radiating Systems, second ed., (Prentice-Hall, New Jersey 1968) p. 36. 49. ht t p:// blogs.m hs.ox .ac.u k /i n novat i ng incombat/ See also R. W. Burns, Communications: An International History of the Formative Years, (IEE Press, UK, 2004) p. 407. 50. http://earlyradiohistory.us/1899marc.htm, McClure’s Magazine, (London), June 1899, pp. 99–112. +51. Sungook Hong, Wireless: From Marconi’s Black Box to the Audion, (MIT Press, Cambridge, MA, 2001) p. 205. See Aitken, his footnote 12 page 195. Note (same page) that even Fleming, Marconi’s well-regarded consulting engineer, was at first misled by the misuse of analogies drawn from the theory of light. 52. Aitken, pp. 285–286 and Hong p. 42, footnote 48. +53. J. J Fahie, A History of Wireless Telegraphy, (Blackwood, Edinburgh, 1901) p. 216. 54. Guglielmo Marconi, “Wireless Telegraphy,” Journal of the Institution of Electrical Engineers, vol. 28, 1899, pp. 273–291. 55. U.S. Patent 685,955 of 1901, 685,954 of 1901, 685,956 of 1901, 787,412 of 1905. 56. Carlson, chapter 2. 57. Nahin, chapters 7 and 9. 58. Bruce Hunt, The Maxwellians, (Cornell U. Press, Ithaca, NY, 1991) p. 202. +59. Marc Seifer, Wizard: The Life and Times of Nikola Tesla, (Citadel Press. New York, 1998) p. 423. 60. Margaret Cheney & Robert Uth, Tesla: Master of Lightning, (Barnes and Noble/Metro Books, NY, 2001) pp. 138–139. +61. Milena Wazeck , Einstein’s Opponents, The Public Controversy about the Theory of Relativity in the 1920’s. (Cambridge University Press, Cambridge, UK, 2014). 62. Seifer, p. 212. 63. For an example of writing on the subject of paradigm shifts in physics after Kuhn, see Jaume Navarro, “Electron Diffraction Chez Thomson: Early Responses to Quantum Physics in Britain.” The British Journal for the History of Science, vol. 43, 2010, pp. 245–275. 64. Paul Israel, Edison: A Life of Invention, (John Wiley & Sons, New York, 1998) p. 176. 65. Thomas Parke Hughes, Networks of Power: Electrification in Western Society, (Johns Hopkins University Press, Baltimore, 1983). + + + 28 The AWA Review +Paradigm Lost: Nikola Tesla’s True Wireless +66. Matthew Josephson, Edison: A Biography, (Wiley, New York, 1992) p. 359. 67. The web site https://en.wikipedia.org/wiki/ List_of_Nikola_Tesla_patents lists 111 or 112 U.S. Tesla patents (depending on how they are counted). 68. Nikola Tesla, “My Inventions,” Electrical Experimenter, 1919, see chapter 5, available on the Internet http://www.teslasautobiography .com/ See also Carlson, chapter 15. 69. T. C. Martin, pp. 346–7. In the late 19th century, Tesla spoke repeatedly of disturbing the electrostatic condition of the earth as a means of sending intelligence. See also Martin p. 292 for an example used in a speech before the British IEE in 1892. 70. This tube appears in a speech he gave in 1892 to the Institution of Electrical Engineers (London). See T. C. Martin ed. pp. 225–229. +71. Gerald Tyne, Saga of the Vacuum Tube, (Antique Electronic Supply, Tempe AZ. 1977). 72. Mike Adams, “Hugo Gernsback: Predicting Radio Broadcasting, 1919–1924,” Antique Wireless Association Review, vol. 27, August 2014, pp. 165–192. 73. For a listing of the Tesla U.S. patents see http:// web.mit.edu/most/Public/Tesla1/alpha_tesla. html. The number for Gernsback was obtained from a search of Google Patents using his name as the inventor. Footnote 64 above also gives a source of Tesla’s patents. 74. Carlson, p. 379. 75. K. Massie, and Stephen Perry, “Hugo Gernsback and Radio Magazines: An Influential Intersection in Broadcast History,” Journal of Radio Studies, vol. 9, no. 2, 2002. Note that the magazine was originally titled The Electrical Experimenter. The title was shortened during 1917. 76. The term was apparently first used in Gernsback’s magazine Wonder Stories in the issue of June 1929; Gernsback had earlier coined the term “scientifiction.” See Leon Stover, Science Fiction from Wells to Heinlein, (McFarland Publishers, Jefferson, NC, 2002) p. 9. 77. Frederick Strong, “The Home Treatment of Tuberculosis by High Frequency Currents,” The Electrical Experimenter, vol. 5, no. 10, Feb. 1918. 78. http://maia.usno.navy.mil/women_history/ lewis.html. 79. M Ashley and R. Lowndes, The Gernsback +Days, (Wildside Press, Rockville, MD, 2004) p. 51–2. 80. https://en.wikipedia.org/wiki/Cavendish_ experiment. 81. Ashley, above, p. 53. 82. Stover, p. 175. In 1923 Gernsback produced a book, Radio for All, published by Lippincott. The work was designed to introduce people to what was still in many ways a hobby. Thus, there were instructions for building simple radios—crystal and one-or two-tube sets, as well as transmitters. It is puzzling that the book makes no mention of the work of Tesla, given his friendship with Gernsback, although there are numerous allusions to Marconi as well as single references to such inventors as Poulsen, Pickard, Fessenden, and Dunwoody. +Acknowledgements +I would like to thank Dr. Elizabeth Bruton of the University of Manchester, Jodrell Bank Discovery Centre, for reading this paper and offering useful advice. And I would also like to thank Prof. Karl Stephan of Texas State University, San Marcos, for giving me a valuable library of early textbooks on wireless telegraphy. I would like to thank Prof. Chen-Pang Yeang of the University of Toronto, a distinguished historian of early 20th-century wave propagation theory, for his comments. I am indebted to this journal’s editor Dr. Eric Wenaas for many useful suggestions that resulted in my paring down this paper and making it clearer. +About the Author +A. David Wunsch was born in Brooklyn, NY, on December 15, 1939. He grew up in the same Flatbush neighborhood of red diaper babies as Bernie Sanders. David studied electrical engineering at Cornell and later earned his Ph.D. at + + + Volume 30, 2017 29 +Wunsch +Harvard where he was a student in the Antenna Group directed by Professor R.W.P. King. David has spent most of his professional life at the University of Massachusetts, Lowell which is located in Lowell, Massachusetts. He is now Professor of Electrical Engineering Emeritus. In 1995 he started the course for liberal arts majors at Lowell, Principles and History of Radio. It is described in the article “Electrical engineering for the liberal arts: radio and its history,” IEEE Transactions on Education, vol.41, no.4, pp.320–324, Nov 1998. David is the book review editor of the IEEE Magazine Technology and Society. He is the author of two textbooks: Complex Variables with Applications (Pearson), currently in its third edition, and the recently published A MATLAB Companion to Complex Variables (Taylor and Francis). +David recently rebuilt the Heathkit oscilloscope that he constructed in 1957. He thought it would make him 17 again but his beard remains white. +David Wunsch + + + + + Volume 30, 2017 31 +Zeh Bouck, Radio Adventurer +Part 1: The Pilot Radio Flight to Bermuda +© 2017 Robert M. Rydzewski, KJ6SBR +Zeh Bouck (2PI, W4FCP, W8QMR), born John W. Schmidt (1901–1946), was an early radio pioneer, engineer, writer, and adventurer who represented amateurs in Washington, D.C. and met with President Hoover. He helped design the Pilot Super Wasp, was one of the first newspaper radio columnists, penned stories and radio plays, and was an associate editor for journals such as Radio Broadcast and CQ: The Radio Amateur’s Journal. An IRE Fellow and member of the Radio Club of America, he was most famous in his day for his role aboard the airplane Pilot Radio, a “flying laboratory.” In 1930 the plane made two historic journeys: the first flight from the United States to Bermuda and the first flight of any land plane around the South American continent. This article provides a brief biography of Bouck to 1930 and summarizes the history of the Pilot Radio Company of Brooklyn and its interest in aircraft radio. Along the way, other figures such as Reginald Fessenden, Hugo Gernsback, and Milton Sleeper are encountered. A detailed account of Bouck’s famous and hazardous Bermuda flight with pilot William Alexander and navigator Lewis Yancey follows, focusing on the role of radio communications. Remarkably, Bouck, who remains largely forgotten today, accomplished all this in spite of a serious disability caused by childhood polio. +Zeh Bouck +Accomplishments +Zeh Bouck visited the White House in 1930 and met with President Hoover, and at one point he represented the Hoover administration, acting as an unofficial U.S. ambassador to foreign nations.1 Alongside Hiram Percy Maxim and Edwin Howard Armstrong, he advocated for radio amateurs at the Third National Radio Conference in Washington in 1924. He was one of the first radio columnists, writing for the New York Sun by 1922, and a +newsmaker himself. He wrote hundreds of articles for magazines ranging from Boys’ Life to Radio News to Cosmopolitan, plays for the radio, technical pamphlets, and books. Largely selfeducated in radio engineering from a childhood spent chasing DX (longdistance communication) in the days of spark, he became a Fellow of and served on committees for the Institute of Radio Engineers and was a Member of the Radio Club of America. He contributed to the design of the Pilot Super Wasp and early receivers made by the National Radio Company. He helped + + + 32 The AWA Review +Zeh Bouck, Radio Adventurer +edit several journals, including Radio Broadcast, Aero News & Mechanics, and the radio amateur’s journal CQ. He was an aircraft radio pioneer, spending more than a thousand hours in the air and many more in the lab trying to solve the many problems involved in aircraft communications. He served as radioman aboard the Pilot Radio, a “flying laboratory,” on the very first flight from the U.S. mainland to the speck in the ocean known as Bermuda. Soon after, he served on the first flight of any land plane around the South American continent, surviving a plethora of emergency landings, mishaps, and one hellacious crash landing that took the Pilot Radio to its watery grave. +Despite an array of achievements worthy of a real-life Indiana Jones, today Zeh Bouck is an obscure footnote to radio history. One might have read his fate in the tealeaves of his later years. He was no Horatio Alger; if anything he went from riches to rags—not uncommon in those years of the Great Depression. By World War Two, he had seen his fame and fortune rise and fall. Time would not allow him to reach those heights again. Most people who have seen a picture of Bouck have come across it in the pages of old Radio News accounts of his aeronautical adventures. There he is, standing next to that vintage Stinson airplane in some exotic locale, a short, +Fig. 1. From left to right: Emile Burgin, Zeh Bouck, and Lewis Yancey. Photo taken at Roosevelt Field, New York, May 14, 1930. (Author’s collection) + + + Volume 30, 2017 33 +Rydzewski +pipe-smoking, broad-shouldered man with a boyish face, Harry Potter-like glasses, and upswept dark hair, looking a bit old-fashioned even then with his signature cravat, and perched conspicuously on a pair of crutches (see Fig. 1). Most readers probably assumed he had just been injured in his adventures. Not so. Like a more famous American of the time, Franklin D. Roosevelt, day in and day out Zeh Bouck stared down a major disability that would have left most people satisfied to just be able to get around the house, much less the cockpit of a plane or the jungles of the Amazon. But Bouck was different. His was a spirit and determination that few possess. He didn’t try to conceal his handicap, nor did he curse the rotten card that fate had dealt him in the form of childhood polio. In what may have been his greatest achievement of all, he simply ignored it and did what he set out to do, struggling along step by step. +A Short Biography +The story of Zeh Bouck has many chapters, the aerial adventure recounted here being just one of them. He was born John W. Schmidt in New York in 1901, the son of John A. Schmidt, a German dry goods merchant, and Alice White, whose maternal grandparents had the Dutch surnames Zeh and Bouck.2 The Boucks had produced a governor of New York. His mother’s brother had changed his name from Charles White to Bouck White and was famous (or infamous) as a firebrand revolutionary and writer who was, at various times, jailed, tarred and feathered, and driven +out of town.3 The Zeh and Bouck clans hailed from rural Schoharie County in upstate New York, where Zeh Bouck would later live and where Zehs and Boucks still live to this day. By the mid1920s, his parents had divorced, and he lived with his mother in New York City. John “Jack” Schmidt wrote under the pen name Zeh Bouck and later legally changed his name to that as well. Possible reasons for the name change could include the anti-German sentiments prevailing in the years around World War One, a preference to be associated with his mother’s side of the family, or just the more distinctive sound of the name. Unfortunately, his reasoning on this is unknown. Despite the thousands of available documents by and about Zeh Bouck, many blank spots on the map of his life remain. Writing about himself in the third person, he said that he had “blossomed forth as an operator in the heyday of the E.I. Co. to the crackling tune of the one-inch spark coil and the rat-tattat of the decoherer. His first call was issued by Gernsback in his Wireless League of America, and his first code was Morse.”4 All of this was before he had reached the ripe old age of 11. He attended Townsend Harris High School in New York City and took classes at the City College of New York, although he never received a degree.5 In 1928 Zeh Bouck married Charlotte Bosse, with whom he would have a daughter who, sadly, lived for only a few weeks, and a son, Paul. A natural born writer as well as a superb radio operator and experimenter, his works began appearing in + + + 34 The AWA Review +Zeh Bouck, Radio Adventurer +newspapers and magazines shortly after World War One. His earliest known article is a short story he wrote around the time he graduated high school, which was called “A Ham on the Telephone.” This appeared under the pen name of “Tewpieye” (a play on his callsign, 2PI) in the August 1920 issue of QST.6 By early 1922, he was penning a regular radio feature for the Saturday New York Globe (which later was merged into the New York Sun), thereby becoming one of the world’s—not just the Globe’s—very first newspaper radio columnists. His column reflected radio enthusiast interests of the day, the earlier ones being more technical (like how to build your own resistance-coupled amplifier), while later ones in the 1930s included critiques of popular radio shows, guides to listening in on shortwave bands, and observations on European shortwave propaganda broadcasts.7 In all, Bouck probably wrote several thousand articles in his short life, many of which can still be found. He also worked in various capacities for a number of radio parts manufacturers at times including Daven, Amsco, Arcturus, and later, Pilot Radio & Tube Corporation of Brooklyn (see Fig. 2). Ever busier, he wrote some fiction for national magazines including Cosmopolitan and Argosy, a few radio plays, books (one of them with a chapter on how to write radio plays),8 and he was a contributor, editor, or associate editor for a number of magazines, including Radio News, All-Wave Radio, Boys’ Life (which had some remarkably technical +articles for youths), Radio Broadcast, and Aero News & Mechanics. At one point he even helped organize a radio department for an advertising agency.9 Looking at his circumstances in those decades, like many another, it is likely that his jobs in the 1920s represented burgeoning opportunities, while those in the 1930s had more to do with keeping the wolves at bay. Back in the early 1920s, when more radio receivers were “homebrewed” than commercially manufactured, more money could be made selling radio parts than factory-assembled sets. Close ties existed between parts manufacturers, their engineers, salesmen, copywriters, publicity agents (who might all be the same guy), and magazine and newspaper publishers. “Every Saturday, The New York Sun published a 32-page supplement on how to build various circuits. Everyone followed the writings of Stuart Blyden, the radio editor at The Sun,” explained Harry Kalker, an M.I.T. educated engineer. “I was a salesman for Amperite... If I wanted to live well the following week, I regularly called on Thursday to see if Blyden of The Sun and Casson of The Telegram had specified my Amperite parts by name in the ‘Circuit of the Week’ for that issue.”10 It wasn’t unusual, then, for Bouck to “kill two birds with one stone” and write articles on circuits featuring Daven or Amsco resistors or Arcturus tubes in those years. But from the time he joined Pilot Radio in 1928, his job was different—and considerably more interesting. + + + Volume 30, 2017 35 +Rydzewski +Fig. 2. Advertisement for the Pilot Radio & Tube Corporation. (Radio Design, Vol. 2, No 4, Winter, 1929, inside back cover) + + + 36 The AWA Review +Zeh Bouck, Radio Adventurer +Pilot Radio of Brooklyn +Management +The Pilot Electric Manufacturing Company made and sold parts as well as complete kits, the latter being something like the Heathkits of their day, if not as easy to assemble. Pilot ran the full gamut of activities, including manufacturing primary parts, designing circuits, publishing schematics, advertising in their house organ, Radio Design, and selling by mail order through their distributor, “the fastest radio mail order service in the world,” Speed, Inc.11 “Pilot was one of the very few real fabricators of the radio industry,” wrote former Pilot employee Robert Hertzberg. “In a crowded factory in Brooklyn, NY, it made its own tools and dies and manufactured all the bits and pieces of its components and assemblies. It did all its own turning, stamping, winding, plating, forming, etc.”12 Pilot’s pilot, so to speak, was Isidor Goldberg, who was raised in an orphanage on New York’s Lower East Side. Goldberg had been exposed to the possibilities of wireless by the age of 16 when he worked at Hugo Gernsback’s Electro Importing Company (E.I. Co.) factory.13 Later, he managed to construct a radio parts empire out of nothing but hard work, savvy, and determination. Goldberg had big ideas and knew how to take chances. His company, Pilot Electric Manufacturing Company, morphed into the Pilot Radio and Television Corporation, and then the Pilot Radio and Tube Corporation +in 1929; all will be referred to as “Pilot Radio.” Pilot Radio didn’t confine itself to just manufacturing parts for homebrew or manufactured radios; the company also explored promising new areas like television and aeronautical radio communication. Much later, it would be a pioneer in the new “high fidelity” audio field. +Pilot Radio and Early TV +Pilot Radio’s foray into television, back in those spinning disk days, may have contributed to the forced bankruptcy of former boss Hugo Gernsback’s publishing empire early in 1929.14 The year before, in a U.S. first, Gernsback had collaborated with Pilot Radio and its brilliant young chief engineer, John Geloso, to broadcast televised images for five minutes at the top of each hour (after a much more ambitious schedule had been abandoned) over his New York City radio stations, WRNY (920 kHz) and W2XAL (9700 kHz). One could watch “faces of living people, the WRNY placard... a moving toy monkey, and a moving ‘roly poly man.’”15 The Pilot television receiver used in the first public demonstration of wireless television in the United States is shown in Fig. 3. What could one see on the television that Pilot developed? According to Bouck, “One gazed hopefully through the window in the upper center and saw all sorts of things with zig-zags of dull red light predominating... Occasionally an image could be seen—the fringy call letters of the broadcasting station, or an equally fringy head and shoulders. + + + Volume 30, 2017 37 +Rydzewski +This would float with varying degrees of rapidity across the field of vision and disappear in parts or wholly like the Cheshire cat.” There was a control for synchronization, but “this was usually accomplished far more satisfactorily by the rule of thumb—i.e., by placing the thumb against the periphery of the scanning disk as a light brake. You could always tell a television engineer... by the callous on his right thumb.”16 The images, of course, were unaccompanied by sound, except for the drone of the motor. The equipment and broadcasting costs involved probably helped push Gernsback’s own empire into the red at the time. Gernsback wrote in his +autobiography, “Indeed, the experiment, the first of its kind, cost a small fortune, with no income whatsoever even contemplated.”17 But mere bankruptcy couldn’t keep the futuristic Gernsback down, and a new series of magazines like Radio-Craft quickly rose from the ashes to compete with his old ones like Radio News. But the television venture hadn’t done much good for Pilot either. “I betcha I must have paid to have the darn things [Pilot television sets] thrown away in ’29,” Goldberg said decades later. “If I’d kept up all those programs, I’d have gone broke.”18 Television back then was definitely not ready for prime time. “After a few rounds,” concluded Bouck a while +Fig. 3. Rear and front view of the Pilot television receiver used at New York University in the fall of 1928 in a successful demonstration of images broadcast from Hugo Gernsback’s radio station, WRNY. Note the motor and large disk. The screen measured 1.5 inches. (Radio Design, Vol. 4, No. 1, Fall, 1931, p. 23) + + + 38 The AWA Review +Zeh Bouck, Radio Adventurer +later, “television never even came out of the corner.”19 When it finally did, after decades had passed and cathode ray tubes had supplanted spinning disks, Pilot Radio would have better luck, if more competition. +Wasps and Super Wasps +In late 1920s, it was in a different arena that Pilot Radio proved to be a quite a contender—that of shortwave receivers. Its introduction of the 3-tube, regenerative Pilot Wasp shortwave receiver in 1928 tapped into the burgeoning shortwave and amateur long-distance reception (DX) markets in a big way. With a $21.75 price in kit form including plug-in coils (around $300 today!), +it represented a good balance of economy and performance, and it became a popular choice for young amateurs and DXers. According to QST, by 1930 more amateurs were using Pilots than any other receiver. Adding a fourth tube, a screen-grid 224, in a front-end-tuned RF section was expected to improve its performance considerably. To this end, Goldberg assembled an all-star team including Robert Hertzberg, chief engineer John Geloso, Alfred Ghirardi, Zeh Bouck, and Robert S. Kruse. According to Hertzberg, the circuit was designed largely by Kruse (see Fig. 4), and the packaging was done by Geloso, while he himself did the field testing and manual writing. The roles of the others are less +Fig. 4. Pilot Super Wasp original schematic hand drawn by Robert Hertzberg in 1929. (Courtesy of son Paul Hertzberg, K2DUX) + + + Volume 30, 2017 39 +Rydzewski +clear, but Bouck is credited with having an input into the design of the final product, the Pilot Super Wasp (see Fig. 5), which, gratifyingly, ended up living up to everyone’s expectations. It was an instant success, which Hertzberg attributed to its bulletproof design, favorable sunspot conditions, and the growing popularity of programs from the BBC in Chelmsford and PCJ in Eindhoven, Holland, with its star Edward Startz. The set was popular both in America, where one could either order the kit from Pilot Radio or buy it at Kresge’s, and abroad, where Pilot did a surprisingly large amount +of its business. Hertzberg himself personally installed a set in New York for the King of Siam (and he was).20 The success of the Super Wasp ensured that the AC Super Wasp, Universal Super Wasp, and eventually a very strange superhet cathedral set called the Super Wasp Allwave would follow. As for Bouck, he had previously designed circuits published in Radio Broadcast, and later he would have a hand in the design of some National shortwave receivers, along with Robert Kruse (again) and David Grimes.21 Based on his own choice of receivers in later years, Bouck would remain partial +Fig. 5. Robert Hertzberg at the controls of the Pilot AC Super Wasp in 1929. (Courtesy of son Paul Hertzberg) + + + 40 The AWA Review +Zeh Bouck, Radio Adventurer +to National sets for life. But in 1928, it was Pilot Radio that offered young Zeh Bouck truly soaring career opportunities as it entered a field where “the sky’s the limit” and let its Super Wasp fly. +Aircraft Radio +Utility +There were many reasons for airplanes to carry radios. Air-to-ground communications could greatly increase aviation safety. Bad weather might be avoided, flights tracked, emergency messages sent, aerial navigation improved, lives saved. As runways became crowded, hop-offs and landings could be coordinated to avoid accidents. Flight safety was not then what it is now; accidents were appallingly common, especially among small planes with fearless (or clueless) pilots. Improving flight safety was mostly a concern of commercial airlines that conducted regular flights, such as Pan American Airways and United Airlines. They preferred to keep their expensive planes and pilots intact and had to convince potential passengers that buying an airline ticket was not a form of assisted suicide. Manufacturers of small planes were more laissez-faire about it, as they were essentially selling the thrill—not the safety—of flying: “A half hour in flight on a bright sunny day will dispel all those memories of the difficulties of flying in a storm or fog.”22 But only if you made it through the storm or fog. Improving aerial navigation was another important use of aircraft radio. Early flight navigation relied mostly on +visual landmarks. In some states, towns over a certain size (e.g., a population of 4,000 in Maryland) were required to paint their names prominently on a roof or large tank for the benefit of flyers. Amelia Earhart herself wrote, “An arrow pointing the direction to the nearest landing field is also desirable.”23 According to Bouck, “Piloting a plane across country... is a tiresome undertaking, requiring constant vigilance of the man at the controls. Winds move much more rapidly than sluggish ocean currents, and the plane travels so fast that it requires only small errors in compass or judgment to throw the flyer off his course.”24 Worst of all, visual landmarks could not help at night, with low clouds or fog, or at sea. Navigation by radio waves would have no such limits. A. K. Ross noted, “No longer will it be necessary for the long-distance flyer, crossing the trackless ocean or fog-hidden land, to be isolated from those on land and sea as effectively as though he were on a different planet.”25 Radio beacons would point the way—literally. Using a system developed by the National Bureau of Standards in the mid-to-late 1920s, a central radio tower would support the tops of two large, side-by-side triangular loops, each of which would broadcast an aero band signal (315–350 kHz). Both would use the same frequency, but one would be modulated with a 65-cycle tone and the other at 85 cycles. The setup would allow these signals to propagate in figure-eight patterns at right angles to each other. Using a goniometer (an “overgrown variometer”), + + + Volume 30, 2017 41 +Rydzewski +the orientations of the two figure eights could be rotated to any desired compass bearing without physically moving the antenna. The 65-cycle and 85-cycle signals would be of equal strength only at the centerlines of the four areas of overlap (see Fig. 6). A plane using a nondirectional antenna (often a 5- or 10-foot vertical rod) would receive the signals, which would be amplified and detected; the signals would ultimately cause two mechanically resonant reeds (one resonating at 65 cycles, the other at 85 cycles) to vibrate up and down rapidly, tracing out apparent white lines side-by-side on a black background. The lines would be of equal length when the signals were of equal strength, indicating an approach (or departure—beacons could be used for both) along the desired course (see Fig. 7). A shorter line on one side meant that the plane +was off course in that direction and the pilot would turn in the direction of the longer line until the two were equal.26 This visual indication enjoyed some advantage over a competing system that had used audio signals sending letters in code (A and N—with the di dah and dah dit starting at the same time so that it came out as a long dah or T, along the centerline). The pilot or navigator would have a hard time hearing these above engine noise (which he would rather listen to for signs of malfunction) and interference, even with the best headphone-equipped helmet.27 All of which points out just a few of the many problems that needed to be overcome in developing aircraft radio systems. +Aircraft Radio Challenges +Bouck describes various problems that had to be addressed in the design of radios for aircraft in an article entitled “The Problems of Aircraft Radio” +Fig. 6. Field characteristics of radiating loop antenna system for radio beacon. The two signals are of equal strength only along the crosshatched area. (Radio Design, Vol. 1, No. 4, Fall 1931, p. 127) +Fig. 7. Radio beacon indicator for panel mounting in plane. The instrument was “about the size of a pack of cigarettes.” (Radio Design, Vol. 1, No. 4, Fall 1931, p. 125) + + + 42 The AWA Review +Zeh Bouck, Radio Adventurer +published in Radio News. He writes, “A plane is capable of lifting a certain gross weight.”28 After subtracting out the machine itself, pilot, fuel and oil, “what is left is payload, and comprises passengers and express or mail.” Every pound added in radio equipment, antenna, and radio operator, including the effective poundage added by wind resistance of externally placed radio accessories like a generator, was one pound less that the plane could carry for profit. Aerial radiotelephony (voice) had an advantage over telegraphy (code) in that the radio operator’s weight would be eliminated and the pilot didn’t need to transmit and receive code, which required the use of hand and brain. Most pilots were not proficient in code and didn’t want to deal with it.29 But even after adding in the weight of an operator, telegraphy was still more efficient than telephony. As Table 1 shows, after including the operator’s weight for telegraphy (assumed to be 150 pounds here), pound-for-pound a readable code signal would still reach further than voice. With either method, +making the apparatus as lightweight as possible helped maximize payload, and aircraft radio found extensive use for aluminum in place of iron and steel wherever possible. Perhaps the biggest problem to confront aircraft radio designers in those days was noise caused by the ignition system with its multitude of spark generators and the audible noise of the engines themselves. Both were much worse than for autos and far harder to deal with. The U.S. Navy as well as many radio companies had found that the entire ignition system including plugs, high-tension wires, magnetos, and even the magneto switches needed to be shielded. This was best done at the time the plane was built, but unfortunately aircraft manufacturers didn’t seem too concerned with this. The audio noise generated by aircraft engine was another problem, and vibration of the plane could wreak havoc on vacuum tubes and create loud microphonics. Shock mounting the sets to the rack with just the right degree of rigidity and the use of special tubes helped with the +Table 1. Airplane Radio Ranges at 300 kc. (Z. Bouck, Radio News, July 1929, p. 20) +Power (W) Telephone Telegraph +(Antenna) Weight +(lbs) +Distance (mi) +Weight* (lbs) +Distance (mi) +50 100 50 250 200 +100 175 100 300 300 +150 200 120 325 350 +200 250 135 350 400 +250 275 150 375 450 +*Including 150 pound weight of operator + + + Volume 30, 2017 43 +Rydzewski +latter. According to Bouck, who had worked for Arcturus, the heavy-cathode AC Arcturus tubes were the best. The vibrations also affected variable condenser plates, causing rapid fluctuations in capacitance and therefore wavelength. Larger or more numerous, thicker (0.0025 inch) plates with wider spacing were called for. For ground-based applications, raising the antenna up high enough is never easy, but getting a good ground usually is. Aloft, the problem is strangely reversed. The metal fuselage (or frame with canvas-covered planes such as the Pilot Radio) could be used as a counterpoise surrogate for ground, but that required special preparation. All metallic parts not rigidly fastened together had to be bonded into a single electrical structure to provide a good counterpoise and reduce noise caused by rubbing together and sparking at imperfect contacts.30 Again, this was something best done during aircraft manufacture, but that often didn’t happen. Bouck tells of his own experience where a radio serviceman bonding structural elements accidentally bonded a rudder cable to a flipper control tube putting both rudder and elevator out of commission, which resulted in a narrow escape from what could have been a fatal crash caused by a radio serviceman improperly installing the ignition shielding.31 For airborne antennas of the late 1920s, the trailing wire type then in use came with a host of problems. The advantages were that the length of antenna reeled out could be adjusted to resonate at the desired frequency, +aerodynamic drag was modest, space and weight allocations were small, and there was no drag when not in use. But there were many disadvantages aside from a flyer forgetting to reel them out (or reel them in before landing). The line was typically terminated with a one or two pound lead “fish” to keep it from flapping around and tearing itself to bits or wrapping itself around the wings. If it were let out too quickly, the wind could take it, causing the whole antenna to snap off. A drag mechanism similar to that used on a fishing reel was called for, and more sophisticated antennas came with a centrifugal clutch to keep the release rate even. Still, things went wrong—farmers complained that their houses or barns were “beaned” by lead weights falling from the sky. Trailing wire antennas weren’t much use for planes on the ground. Another problem was the directionality of a relatively long wire antenna. This made it unsuitable for use with directional beacons mentioned previously. Loop antennas could be used and could even provide radio direction finding (RDF) for transmitters like broadcast radio stations, but they had to be mounted externally (that drag factor again), were low gain, and couldn’t be used to transmit. Bouck noted that a loop used with a superheterodyne broadcast band receiver was much less perturbed by ignition noise than other arrangements. Various configurations of dipoles strung from wingtips, fuselage, and tail were sometimes used, but were too short to have much gain on a small plane, particularly at the long + + + 44 The AWA Review +Zeh Bouck, Radio Adventurer +aero band wavelengths then in use. The best antenna to use seemed to be “up in the air.” +The Flying Laboratory +At the time Pilot Radio entered the field, the idea of airborne radio was not new. As noted by Arthur Lynch, radio and aviation grew up at about the same time and even in the same neighborhood. He observed that Professor Fessenden “conducted much of his preliminary work on radio on Roanoke Island, just about three miles from where the Wright brothers were doing their first work with gliders at Kitty Hawk, at the same time.”32 Aircraft wireless telegraphy from the plane to ground by spark transmission predated World War One, primarily due to its “eye in the sky” military potential for aerial reconnaissance and artillery spotting.33 Airborne wireless equipment had played an important role in the first transatlantic crossing by the U.S. Navy flying boat NC-4 in 1919,34 and a lesser one in Admiral Richard Byrd’s 1926 flight to the North Pole.35 Although the market for aircraft radio among explorers would always be miniscule, the markets for military aviation, airmail and airfreight, and the expanding passenger air service were huge. The fact that radio in those days had been tied to exploration and adventure in the public’s mind offered a way of increasing sales of whatever the company happened to manufacture. After all, Eugene McDonald hadn’t outfitted the MacMillan expedition with his company’s equipment with the goal +of marketing it to the Inuit peoplesalthough if anyone could do that he could. Instead, he provided a way for ordinary Americans to make a vicarious connection to the thrill of Arctic exploration without risking frostbite or having to eat their dogs—simply by buying a radio marked “Zenith.”36 Others in the radio business had tapped into the romance and adventure of flying for promotional purposes as well, including Powel Crosley, who sometimes supplied his radios to selected dealers in well-publicized flights of his personal plane.37 His company even manufactured a plane for a while, the Crosley Moonbeam.38 In short, an association with airplanes or exploration could sell radios—or anything else. Whether Pilot Radio ever seriously aimed to build and sell receivers and transmitters for the small plane market (where most pilots didn’t want to be bothered with what they’d initially see as another complication), or the commercial flight or military aircraft markets (which corporate giants like RCA, GE, and Western Electric had already sunk their talons into) is debatable.39 More likely, the impetus behind Pilot Radio’s efforts had to do with Goldberg’s aerial enthusiasm. He had previously sold aeronautical parts and even model planes. In 1909 and 1910 he had worked with Glenn Curtiss at Curtiss Field. As Pilot’s president, Goldberg had a landing strip built near his home in Westchester County, and his use of the Pilot Radio for business travel no doubt allowed for tax advantages to help defray its expense.40 + + + Volume 30, 2017 45 +Rydzewski +A second and more practical reason for Pilot’s involvement in aero communications was to use Pilot Radio flights, which involved constant air-to-ground HF contact, to generate publicity and boost sales of their popular shortwave Super Wasp receivers, a Bouck-modified version of which their plane carried. Whatever the reasons, between 1928 and 1930 Pilot Radio acquired, maintained, equipped, and flew a “flying laboratory,” a Stinson Detroiter monoplane aptly christened the Pilot Radio. Other companies had their own flying laboratories as well, including RCA, which also used a Stinson Detroiter and flew it cross-country, awarding prizes to the amateurs who communicated with it at the greatest distances.41 Pilot Radio’s interest in airborne radio likely began in 1927, the year of the Lindbergh transatlantic flight. An article in the Brooklyn Standard Union on May 15 states that Milton B. Sleeper, a “well known radio engineer and originator of the transatlantic receiving tests in 1919,” had joined Pilot as Chief Research Director.42 Sleeper, who was four years older than Bouck, had also started out in amateur radio before World War One. Soon he was writing about the latest radio circuits and kit building for magazines such as Everyday Engineering. He later founded his own magazines, including Radio and Model Engineering, and, much later, High Fidelity. Like Bouck, he was a prolific writer and a colorful figure in radio history. Although Alan Douglas refers to him as “primarily a writer” in Radio Manufacturers of the 1920’s,43 +Sleeper’s technical abilities must have been considerable as well since he not only had his own radio company in the early 1920s, but he also had been a radio engineer for Western Electric.44 He would later go on to serve as editor of the Proceedings of the Radio Club of America.45 His plunge into aviation may have begun with his decision to volunteer for the Royal Flying Corps (RFC) during World War One. He had ground training in Toronto and the fascinating accounts he published about it in Everyday Engineering may be the only known documentation of that process.46 Sleeper was discharged from the RFC, which had an overabundance of volunteers, after only five months, and he apparently never flew in combat.47 A Popular Aviation article in early 1929 identified Sleeper as overseeing the f lying laboratory.48 Curiously, although the Pilot Radio name and logo can be seen painted on the plane behind him in an accompanying photo, the article never once mentions Pilot Radio, which could not have pleased Goldberg. It would not be the last time Pilot’s pricey sponsorship would be unreported, its public relations and promotional value lost. How long Sleeper stayed at Pilot Radio is unclear; a month after that article appeared, his primary affiliation was with his own Sleeper Research Laboratories, from which he penned an article deriding the type of spinning disc television that Pilot had worked on.49 Although correct about the limits of that technology, it seems he chose to rub salt in Goldberg’s wound. + + + 46 The AWA Review +Zeh Bouck, Radio Adventurer +Bouck and Sleeper must have known each other, since both were early amateurs, engineers, writers, and members of New York’s Radio Club of America, and Bouck had taken over as editor of Radio Engineering magazine following Sleeper’s departure in 1927. Bouck began his affiliation with Pilot Radio the following year, overlapping with Sleeper for a time. Their hierarchical relationship at that point is not known. Aviation Week reported that both Bouck and Sleeper oversaw Pilot’s radio engineering.50 But then again, they also reported that they were working on aero television. After Sleeper’s departure from Pilot, however, there is no doubt that Bouck, with the title of Engineer in Charge of Aeronautics, led its aerial efforts.51 +Aerial Feats +By 1930, many dazzling aerial feats had already been accomplished by deathdefying (if they were lucky), leatherhelmeted, flying idols—the rock stars of their day. Charles Lindbergh had successfully soloed the 3,500 miles across the Atlantic from New York to Paris three years earlier, becoming a national hero and the most famous man in America overnight. About three months later, pilot Roger Q. Williams and able navigator Lewis “Lon” Yancey attempted the 4,000+ mile transatlantic flight from Maine to Rome.52 Their first attempt ended in a plane wreck, but some people never learn. They set out again in the Bellanca monoplane The Pathfinder, and by flying blind part of the way, they were able to reach that +destination after an emergency landing in Spain. Arriving in Rome, they were greeted by Air Marshal Italo Balbo, cheered by admiring throngs, and decorated by Il Duce (Mussolini) himself.53 New York Times headlines and a parade down Broadway followed upon their return. Two weeks earlier, on the opposite side of the United States, two Army Air Corps flyers, Lieutenants Albert Hegenberger and Lester Maitland (in whose honor two streets near the Oakland, California, airport are still named), accomplished the first nonstop “hop” from the U.S. mainland across the Pacific to the Hawaiian Islands. Starting from Oakland, they set down their Fokker C-2 trimotor, Bird of Paradise, some 2,400 miles away at Wheeler Field on Oahu the next morning (see Fig. 8).54 Interestingly, although radio beacons had been installed at both fields, because of spotty reception and limited range at both ends,55 the oldfashioned, visible beacon of the Kilauea lighthouse proved more useful in guiding the flyers to their destination.56 By April of 1930, many of the biggest feats in long distance aviation had already been accomplished. But one peculiar challenge remained: no one had ever flown a plane from the U.S. mainland to the tiny islands of Bermuda, just over 700 miles away. Bermuda had neither runways nor radio beacons, and unlike the European continent (almost 4 million square miles) or the Hawaiian Island chain (4000 square miles), at 20.5 square miles it was truly “a dot in the ocean.” In those + + + Volume 30, 2017 47 +Rydzewski +days before LORAN, GPS, or Google Maps, when aerial navigation (or “avigation” as it was sometimes called) was via compass, sextant, and other dated methods, a deviation of just a few degrees could mean never seeing land and being stranded at sea, far from help, or worse, as befell Amelia Earhart in the Pacific seven years later. So the challenge remained. Bermuda was a British dependency, and therefore not subject to U.S. Prohibition, making it a very popular destination for wealthy American tourists in those years. A two-day trip by steamer was the only way to get there. The island’s merchants, however, realized the economic opportunities that tourists arriving by air could present, and just getting a plane to reach the islands was the obvious first step. +Armstrong’s Seadromes +Interestingly, Armstrong had an idea that would convert that step into two +shorter ones—that is, Edward R. Armstrong, an engineer and former aviator. He proposed that a giant (1,100 foot long, 28,000 ton) floating mid-ocean platform be constructed about halfway between Bermuda and the United States.57 This would ride 80 feet above the surface, anchored to the sea floor with steel cables, and it would come complete with a landing strip, radio and visible light beacons, a weather station, service and refueling facilities, and a hotel equipped with a Prohibition-free bar for nervous passengers and thirsty aviators.58Armstrong had met with, and received encouragement from, Bermudian officials. The first seadrome, the Langley, was to be anchored 395 miles southeast of New York. Although a concept endorsed by many, including Igor Sikorsky,59 the Armstrong seadrome fell victim to the unpredictable (poor financial timing) as well as the totally predictable (planes with extended ranges). Armstrong attempted for years to revive +Fig. 8. Arrival of the Bird of Paradise, the first flight from the United States to Hawaii, at Wheeler Field, Oahu, June 29, 1927. (Photo on display at the Kilauea lighthouse in Hawaii, credited to U.S. Air Force Museum) + + + 48 The AWA Review +Zeh Bouck, Radio Adventurer +the seadrome idea in the interest of patriotism (boosting jobs during the Depression, bringing bits of America closer to Europe whether they wanted them there or not), or in a seedier form, as a tourist destination “beyond the reach of the 18th Amendment,”60 which would only have to be “free from practices that would shock the conscience of mankind.”61 But the Langley and its kin would be at sea only in the figurative sense. The technology Armstrong pioneered, though, would later enable the development of offshore oil rigs. +Bermuda Safety Prize +To encourage efforts to reach it by air, with or without seadromes, the Bermuda Trade Development Board had offered a prize of £2,000 (about $140,000 today) to be awarded to the first flyer to reach it from the United States.62 Although it was termed the Bermuda Safety Prize (see Fig. 9) and would supposedly be awarded based on the safety measures employed rather +than speed, doubts were raised that it might instead only serve to lure reckless flyers to their doom. Lost at sea or crash-and-burn would be bad for business, not to mention the airmen. At the behest of the Director of the National Aeronautical Society in the United States, the prize offer was withdrawn before anyone tried for it.63 But the lure of being the first remained. Prize or no prize, there was the glory that went along with the risk, and to many flyers that was enough. On October 28, 1928, the Ireland N-2B Neptune amphibian Flying Fish, with pilot W. N. “Bill” Lancaster, navigator Henry W. “Harry” Lyon, and passenger George Palmer Putnam, publisher and future husband of Amelia Earhart, attempted the nonstop flight from Long Island Sound, with Amelia herself waving goodbye from shore. Other than Putnam, this was an experienced crew. Lancaster was a pioneering aviator and Lyon a legendary character who had recently been the navigator on +Fig. 9. Bermuda Safety Prize announcement and map. (Aero Digest, September 1927, p. 276) + + + Volume 30, 2017 49 +Rydzewski +the first flight from the United States (Oakland) to Australia (via Hawaii and Fiji).64 But great expectations couldn’t lift the ship. Placid waters made for too much surface tension, making it impossible for the heavily laden flying boat to take flight. The ship was later able to hop off from Hampton Roads, Virginia, but various problems including water in the gas were blamed for it ultimately setting down off Atlantic City, New Jersey, rather than Hamilton, Bermuda.65 The flight of the Flying Fish to Bermuda was postponed and later rescheduled, but it never took place.66 Among those who thought they could do better was Captain Lewis Yancey (see Fig. 10), the navigator on +the much-publicized Williams flight to Rome. A native Chicagoan, he had enlisted in the U.S. Navy at 16, had been a lieutenant in World War One, received master mariner certification in civilian life, then joined the U.S. Coast Guard, becoming interested in aviation and especially the application of the science of navigation to flying. A true navigator’s navigator, Yancey went on to write a book on aerial navigation.67 He found the challenge of locating that dot in the ocean irresistible, and publicly announced that given just 48 hours’ notice he could guide any good plane and pilot to Bermuda.68 William H. Alexander was one good pilot. A World War One flyer and flight instructor who had trained at the Wright brothers’ aviation school, he held the Fédération Aéronautique +Internationale, or FAI (an international organization based in Paris), flying license No. 1.69 But unlike Yancey, Alexander had recently experienced more ignominy than adulation. On Saturday, September 7th of the fateful year 1929, after dropping off six passengers from his Coastal Airways plane at North Beach he took off again but soon ran out of fuel. Taking his seaplane down off Coney Island in the fog, he landed among the shocked bathers at Seventh Street, killing two children and wounding ten other people. Alexander, “haggard and grief-stricken,” held that his water landing would have injured no one had not a wing accidentally struck a warning sign, deflecting the plane into the bathers. Nevertheless, his pilot’s license was revoked and he was charged +Fig. 10. Captain Lewis Alonzo “Lon” Yancey, navigator on the historic flight of the Pilot Radio to Bermuda. (Aero News and Mechanics, Vol. 2, No. 1, Feb. 1930, p. 9) + + + 50 The AWA Review +Zeh Bouck, Radio Adventurer +with homicide.70 In what now seems too far-fetched for even a Perry Mason courtroom drama, the judge agreed to fly with Alexander in a reenactment, after which he suggested further safety regulations for aviators and not only cleared him of all charges but noted that it was “a marvelous experience.”71 Alexander’s license was soon reinstated. How navigator Yancey, pilot Alexander, and radioman Bouck came together on the Pilot Radio for the historic first flight to Bermuda and exactly what their hierarchical relationship was are not exactly clear. Bouck was no stranger to Bermuda; he had already visited the islands ten times,72 including at least once with his wife Charlotte,73 and he had friends there. A document providing important clues to the origin of the Bermuda flight can be found in the Bermuda Archives.74 On January 9, 1930, Zeh Bouck wrote to J. P. Hand, the chairman of the Bermuda Trade Development Board, that a friend, Allan Thompson, suggested that he contact Hand about flying to Bermuda. Bouck said he was “seriously contemplating” flying to Bermuda from New York within the next month “if it is worth while.” “Can you,” he asked, “get the Board of Trade to put up a cash price [sic] for the first flight to the Islands?” He must have been aware of the previously withdrawn prize, and was hoping to get it reinstated. “I should like to know what the Board of Trade can offer me and my co-pilot for the first and necessarily historic flight to your beautiful islands.” This, and a later reference (“I am flying my ship to +Miami. . .”) would seem to indicate that Bouck, who needed crutches to walk due to what one newspaper account said was “infantile paralysis” (childhood polio),75 could still fly a plane. A number of other accounts over the years suggest this as well,76 and reports of Bouck driving a car can also be found. A recent search was not able to uncover a pilot’s license for Bouck, but these can be hard to find, and in those days some flyers (including Lewis Yancey) apparently considered them optional.77 So for now, this remains yet another unknown in the story of his life.78 Another surprising thing about Bouck’s letter is his affiliation. His letterhead was from Mackinnon Fly Publications, Inc., the publisher of Aero News & Mechanics, of which he was the Managing Editor. Neither his employer, the plane’s owner (Pilot Radio), nor radio in general is mentioned at all. In the letter, Bouck noted that his secondary purpose was to arrange for a series of annual air races to Bermuda, to be sponsored “more or less” by Aero News & Mechanics (see Fig. 11). Bouck mentioned that manufacturers (aircraft, instrument, or radio?) and pilots were enthusiastic about this, and informed Hand that he was tentatively scheduling the races for May! This letter and a few other available documents on Bouck’s private business dealings give the impression that, rather than being meek and mild as one might expect from his photos, Bouck’s was a hardnosed, “take-charge” personality that would put Alexander Haig to shame. Being crammed into a confined space + + + Volume 30, 2017 51 +Rydzewski +Fig. 11. Cover of Aero News and Mechanics, Volume 2, Number 1, Feb. 1930. Zeh Bouck was Managing Editor for this magazine, published by Experimenter Publications, and originally envisioned it sponsoring a first flight to Bermuda followed by annual races to the island. + + + 52 The AWA Review +Zeh Bouck, Radio Adventurer +(the Pilot Radio) on stressful missions with two other gentlemen similarly not lacking in ego or self-proclaimed authority surely had interesting consequences, but unfortunately little about this remains in the historical record. In writing to Hand, Bouck didn’t fail to note that “we all appreciate the publicity and trade that would accrue to Bermuda as a result of my primary flight and the subsequent annual races.” Bouck did receive a reply to his letter—a negative one. He was advised to “abandon any such idea until proper navigational and meteorological facilities exist.”79 Bermuda had already voted funds for the construction of a meteorological station and planned to eventually install a radio beacon, but the government was slow to act, which may, in fact, have prompted the flyers to hurry up and reach the islands while doing so was still a challenge. Replying to the Bermudian objections, the ever-resourceful Bouck wrote back, suggesting that Bermuda station BZB could be used as a navigational aid (RDF). Permission to land, required by international convention, was never granted,80 the prize was not reinstated, and the proposed races would never take place, but the proposed first flight to Bermuda did... “more or less.” +The Flight to Bermuda +Preparations +Financial support for the flight came from a variety of companies. Isidor Goldberg, provided the lion’s share by providing the Pilot Radio, the radio +equipment, and payments for the crew. Goldberg no doubt anticipated his company’s name being featured nationwide in news accounts of the flight. Richfield Oil provided the fuel and oil. The Pioneer Instrument Company was a sponsor. The Edo Corporation, named from the initials of founder Earl Dodd Osborn, fitted the “ship” with the pontoons that would allow for water takeoff and landing. This was carried out in secret lest someone else beat them to the punch. Aero News & Mechanics was apparently not involved,81 but other publications, notably the New York Times, were. In fact, Bouck would be pounding out exclusive in-flight dispatches to the Times radio station WHD on 43rd Street in Manhattan and its chief engineer and crack operator, R. J. Iverson, thus reducing to practice the idea of constant two-way air-toground HF communication. WHD already had an impressive record of DX communications with explorers and flyers (although not necessarily continuous contact) and would build on this in coming years.82 The Pilot Radio itself was a recently manufactured, modified 6-seat Stinson SM-1FS “Detroiter” high-wing monoplane (NR 487H) powered by a 9-cylinder, 300 horsepower Wright “Whirlwind” (J-6) engine, with brakes by Harley Davidson (see Fig. 12). The ship, acquired in mid-to-late 1929 to replace an earlier Pilot Radio flying lab (a Stinson SM-1B, NC 4876),83 was specially equipped with extra gas tanks in the wings, for a total fuel capacity of 200 gallons, enough to cruise at 100 + + + Volume 30, 2017 53 +Rydzewski +mph for 12 hours. Oil could be added from inside the plane. It had a maximum speed of 135 mph and a service ceiling of 17,000 feet.84 Its rated carrying capacity was 4,700 pounds, but the fully laden plane at takeoff would weigh 5,200 pounds.85 The plane would carry two transmitters, one longwave (600–1100 meters) for the old aero beacon/emergency band and the other a shortwave transmitter (35–50 meters) for anticipated in-flight communications. Both were housed in a single unit, and both employed a Hartley oscillator. Communications would be entirely radiotelegraph. All of the radio equipment had been built by Pilot Radio under Bouck’s direction. The receiver was a modified AC Super Wasp that used Arcturus AC tubes, which, with heavy cathodes, were less prone to microphonics than DC tubes. Special coils allowed it to be tuned between 14 and 1200 meters. Receiver and transmitters were combined in a single unit suspended from the top of the plane’s frame. An Exide “non-spillable,” 12-volt, lead-acid aircraft battery supplied filament voltage +to both receiver and transmitters and powered an Esco dynamotor that fed 1000 volts at 100 milliamps to the plate of the De Forest 510A transmitting tube. The Exide, in turn, was continuously charged (except when receiving) by a wind-driven generator mounted on the plane. Receiver B and C voltage was supplied by Eveready batteries. A trailing antenna of variable length was used. Communications would be carried out with the antenna spooled out to 90 feet to work the third harmonic on 41 meters. When not in the air, an emergency antenna could be strung up between the wingtips or flown via kite, +Fig. 12. The Pilot Radio, Pilot’s “flying laboratory,” a Stinson SM-1FS Detroiter that made the historic first trip from the U.S. mainland to Bermuda. (Aero News and Mechanics, Vol. 2, No. 1, Feb. 1930, p. 52) +Fig. 13. Zeh Bouck at his station aboard the Pilot Radio. (Radio News, July 1930, p. 12) + + + 54 The AWA Review +Zeh Bouck, Radio Adventurer +and Bouck estimated there would be enough power to communicate for ten hours without charging.86 The entire radio setup weighed 140 pounds, and the plane’s callsign was W2XBQ (see Fig. 13). +The Bermuda Short Hop +It was April Fool’s Day, 1930, but the mission that day was dead serious. The flyers were eager to hop off as soon as possible to forestall possible competition for the title of first to fly from the United States to Bermuda, but weather was a major factor. For advice on weather, they turned to Dr. James H. Kimball, chief meteorologist at the New York Weather Bureau, whom Bouck referred to as “that Palladium of oceanic flyers”87 (i.e., their protector). He had prognosticated weather conditions for Lindbergh for his famous transatlantic flight and for Byrd on his flight to the North Pole.88 At 11 p.m. on March 31, Kimball’s report had come in: calm weather was predicted the next +day for the entire area between New York and Bermuda. The hop was on (see Fig. 14). In the wee small hours of the morning at Bouck’s New York apartment “provisions had to be packed and other domestic arrangements completed, much to the annoyance of the folks living below. They rapped viciously and repeatedly on their ceiling with some variety of battering ram. After eighteen hours of a hard day’s work, this was an amusing interlude, and I responded, in my kindly way, by dropping encyclopedias on the floor at judicious intervals.”89 After just a couple of hours of sleep, Bouck went to pick up the battery that he had left at a battery station for charging after specifically warning the attendant not to top them off. Batteries meant for airplane use were constructed differently from car batteries to compensate for in-flight sloshing; the cells were not meant to be filled completely. Of course, after a +Fig. 14. The Pilot Radio being towed from its hangar into the water at College Point, Queens, the morning of April 1, 1930, for its historic first flight from the U.S. to Bermuda. (Author’s collection) + + + Volume 30, 2017 55 +Rydzewski +shift change the new attendant took a look, saw the low level, and proceeded to top them off. “I discovered this at 6 a.m. with our takeoff scheduled for a half an hour later,” wrote Bouck. “There was only one thing to do: empty out most of the electrolyte and add sulfuric acid. Unfortunately, there was no sulfuric acid to be found. I tried frantically for a half hour to locate an open drug store without success.” He finally located some at 7:30, dumped the old electrolyte and filled each cell with 24 hydrometers full, one by one. “We blew through the gates at North Beach a quarter hour later, held up for a moment by an importunate member of the press who was clamoring for a story. We explained that we were somewhat busy at the moment, whereupon he sweetly expressed himself with the following sentiment: ‘I hope — — plane sinks!’ This didn’t bother me at the time, though I did recall this touching farewell that night.”90 Because of the battery, Bouck was nearly two hours late for the “hop off” and out of contact with Alexander, Yancey, and others who were probably searching for him the whole time. Usable daylight hours, important for this long flight, had burned away. The greeting he received from his fellow crewmembers can only be imagined; about it he wrote nothing. The plane was afloat on Long Island Sound at Clason Point where the takeoff was attempted. Inauspiciously, the takeoff failed four times in a row because the fair weather had left the waters too calm, which made for high surface +tension, which produced significant drag on the pontoons of the heavily laden plane. This was the same problem that had beset the earlier Bermuda attempt by Lancaster and Lyon. Even the big 300-horsepower Wright Whirlwind engine struggled with this. Takeoffs in choppy water were easier. To lighten the load, the weight needed to be reduced, and it wouldn’t be surprising if the idea of jettisoning Bouck and his batteries came up. Instead, a sea anchor, spare pontoon plates, and some extra fuel were discarded. The fifth attempt again failed, but the sixth was a charm. This time they took advantage of the wakes created by two ferryboats and some helpful waves created by an assisting Edo seaplane. “Bill Alexander gave her the gun,” chronicled Bouck. “In another second the Pilot Radio was on the step, the bumps becoming sharper and sharper as the air speed indicator rose from fifty to fifty-five, sixty, sixtyfive miles an hour. One more sharp rap on the pontoons and we were off. We gained altitude rapidly and cleared the bridges in good style.” Yancey remembered it differently. “I saw the Hells Gate Bridge straight ahead. I pointed it out to Bill. He nodded and said he saw it. Meanwhile, when destruction seemed certain and it appeared we were going to crash into it, Zeh Bouck, calmly oblivious, proceeded to reel out his fishing line antenna . . .”91 The oblivious Bouck then began his radiotelegraph dialog with the New York Times station WHD. “What provisions were they carrying?” asked the + + + 56 The AWA Review +Zeh Bouck, Radio Adventurer +Times. “Rations on board consist of two broiled chickens, four boxes wholewheat crackers, five pounds of chocolate, twelve oranges, five gallons water, one quart Scotch,” he radioed back. In those Prohibition days, the last item seemed to create some excitement, but Bouck noted that it was for medicinal use only—later observing that they were probably the only ones ever bringing whiskey to Bermuda. Yancey took sightings by sextant after sliding back a plastic (pyralin) window at the top of the cabin, letting in 100 mph winds. Sightings taken through the pyralin would have been more comfortable, but they would have been in error because of its refraction.92 Yancey carried three Longines chronographs so that if one got out of whack the other two would give a consensus on which one was in error. The plane sped on its way at an altitude of 2,000 feet. Bouck communicated with WHD regularly the whole way, and the station relayed his messages.93 At 1:55 p.m. Bouck sent a message, “Greetings from mid-Atlantic to you, mother....JACK.” WHD was asked to relay hotel reservations to BZB in Bermuda. Yancey asked Bouck to tap out, “The sky is partly cloudy and we hope it will get no worse, as it might prove hard to find the islands.” At 5:20 p.m. the message from the Pilot Radio was, “If we don’t see the islands pretty soon, we will set her down for the night. If we have to set her down for the night, don’t let anyone worry about us. The sea is like a lake.” Fifteen minutes later the update was, “we may make it and +we may not.” It was getting dark and they had been fighting headwinds. The morning’s delay loomed larger and larger. Had Yancey really steered them on the correct course? At 5:50 PM a decision was reached: “Setting her down right now. Position sixty miles north of Bermuda. Tell everyone not to worry... Will continue to Bermuda in the morning.” GN (good night) followed. The New York Times would tell its readers the next morning: “TwoHour Delay in Taking Off Is Blamed for Failure to Reach Objective.” Bouck decided that after landing on the water, he would let his notorious batteries rest until morning rather than string up an emergency antenna and run them down overnight. Fully charged batteries would be most useful in case of problems taking off in the morning. While the Pilot Radio had been fitted out with pontoons for water takeoff and landing, actually being able to land on the open, rolling sea and then take off again the next morning after the engine had potentially been sprayed with brine all night was not assured. And with the sea anchor left behind, there was the possibility of drifting into a coral reef overnight that could sink the plane (after all, there was that reporter’s curse). In fact, to that date no plane forced down in the middle of the ocean had ever successfully taken off again. For one thing, as Bouck was to note, “water is a hard thing to hit at 60 miles per hour.” But Alexander, an experienced seaplane pilot, managed to set her down and the Edo pontoons held. Seen up close, the + + + Volume 30, 2017 57 +Rydzewski +sea turned out to be rather unlike a lake. The sea anchor having been jettisoned, a couple of 10-quart pails were strung together to provide some stability, but these proved useless for much of the time. Afloat, the flyers endured swells and pitches. “‘Gentlemen, I’m going to be sick,’ Alexander said. And he was.” The plane was too far away from Bermuda for it to have been spotted, and the flyers rather conspicuously made no attempt to contact the Bermudian authorities, who had pointedly denied them permission to land there in the first place.94 Bermudians were therefore unaware of the plane’s presence off their shores until a cable from New York reached them after 8 p.m. The sound reasons behind denying landing permission then became apparent. With incomplete information from New York and nothing from the plane, Bermudian authorities had to assume that it was in distress and mobilize their resources for assistance. Much to their credit, this they did, fully and immediately. Bermudian authorities tried to communicate with W2XBQ (the Pilot Radio) at the 600 meter (500 kHz) international emergency frequency from their St. George’s wireless station, which was kept open all night, but received only silence in return. A little-publicized consequence of the Pilot Radio’s silence was that U.S. East Coast radio stations briefly shut down at about 5:52 p.m. Eastern time per protocol to “clear the airwaves” for a possible 500 kHz SOS transmission.95 Upon learning that the plane had been working 41 meters, the Bermu +dians attempted to reach the flyers on that band as well, but the De Forest 510A tube remained unlit, perhaps unlike the flyers with their bottle of Scotch. Searchlights were switched on. A lookout was kept at the Gibb’s Hill lighthouse. All ships anywhere in the vicinity were asked to be on the lookout. Arrangements (which included insurance issues and financial considerations) were made to have a steam tender, the Mid-Ocean, leave Hamilton at dawn to search for them.96 In short, the Bermudian authorities went to great lengths to aid the aviators perceived to be in distress, who had given them no notice, intentionally remained silent, had been warned not to attempt it, and were pointedly informed that no assistance would be offered if they did. Three times during the night the flyers spotted the lights of a ship in the distance. After considering the possibility that it might be out looking for them, at 3:15 a.m. they fired off the “Very pistol” (a flare gun). The ship, which turned out to be the Canadian steamer Lady Sommers, hove to and headed towards them. They could have communicated with her at some distance by code using a flashlight, but Yancey had lost the plane’s only flashlight while inspecting the pontoons. Fortunately, this was a problem that even the dullest of the Radio Boys—much less Zeh Bouck himself—could easily solve. Gathering together a spare bulb, a couple of wires, and an extra flashlight battery he tapped out Morse messages, touching wire to battery terminal. The Lady Sommers had in fact been sent out to + + + 58 The AWA Review +Zeh Bouck, Radio Adventurer +look for them and offered to take them aboard. Its captain was surprised at the flyers’ reply; they did not wish to be rescued. They would weather the swells for the rest of the night and proceed to Hamilton in the morning, asking Captain Armit to kindly relay the message. +Land Ho! +At daybreak, around 5:40 a.m., despite the swells and seasickness, “Bill [pilot William Alexander] showed his mastery of a ticklish job, and for the first time in the history of flying, a plane forced down in the middle of the ocean took off again.” Five minutes later the antenna was out again, the 50-watt transmitter and modified Pilot Super Wasp receiver fired up, and there on 41 meters was the radio operator at WHD New York, “as loud and clear as when we were over the East River,” happy to find the adventurers alive and well and approaching Bermuda. He informed them that some +other New York papers had already written them off as dead, “which news amused the lads up forward [Alexander and Yancey].” A copy of the message they sent to Edo 10 minutes after taking off praising the quality of their pontoons is shown in Fig. 15. At 6:15 a.m., an island was spotted dead ahead—Yancey had made good on his boast, guiding them on a beeline to Bermuda. Bouck would go on to chronicle this flight in at least four publications: Radio News, Radio Design, The New York Sun, and Yachting.97 These accounts differ slightly in length and a few minor details, but for the most part are quite consistent, even using the same text—recycling copy having always been popular among writers. The first three of these, however, end with the sighting of Bermuda in the distance that April morning and Bouck calling Yancey “the finest aerial navigator in the world.” The reader is left +Fig. 15. Part of an advertisement for EDO pontoons. Note that the telegram’s letterhead refers to the South American Good Will flight, which would not take place until later, but had apparently been in preparation for some time. Also note that Bouck is listed as navigator and Yancey’s name is absent from the letterhead. (Aero Digest, June, 1930, p. 101) + + + Volume 30, 2017 59 +Rydzewski +with the impression that from there it was just a matter of setting her down in Hamilton Harbor—presumably to loud huzzahs—to complete their historic flight. In fact, the end of the journey was quite a bit more complicated, as Bouck related only in his article in Yachting. Since then, many secondary accounts of the journey either contain differing accounts of this stage or leave it out entirely. But of all the reports at the time or since, Bouck’s eyewitness account most has the “ring of truth” to it and consequently is presented here. With the islands in sight, Bouck asked Alexander how much fuel was left. “About one hour,” he replied. But a few minutes later, “‘Putt . . . putt . . . putt,’ says the motor, and conked . . . Once having heard that sound, it is as easily forgotten as the shake of a rattlesnake’s tail. We were definitely out of gas.” An overly optimistic fuel gauge had deceived them. They had been spotted from shore by Commander Landman, the pilot warden, but they wouldn’t know this until later. Alexander again set Pilot Radio down at sea, this time in an emergency landing about five miles short of the islands “just inside of the reefs.” In fact, their improvised sea anchor actually caught on the rocks just a few feet below the pontoons, temporarily anchoring the plane in place. Bouck began stringing up an emergency antenna, but before they could call for help, the frayed anchor line snapped and the current caused the plane to drift west, “toward New York City,” as Bouck said, but by way of the pontoon-piercing reef. +The story continues at that point: “Bill’s genius rose to the situation. He figured that rocking around out there, as we had been doing for the past half hour, we might have sloshed a quart of gasoline down into the equalization tank. Lon [navigator Lewis Yancey] cranked the engine. She took instantly and Bill gave her the gun with Lon climbing through the door, and ten fathoms of rope and radio antenna streaming out behind. We had two minutes of gas—enough to set down definitely in the steamer channel just off Shelley’s Bay.” Here they were met by Messrs. Tucker and Meyer in a speedboat, the first two from Bermuda to contact the new arrivals. Informed of their dry tanks, they soon went back to get the flyers some gas. In the meantime, along came a more official delegation from Bermuda aboard the Golden Wedding (see Fig. 16). The flyers’ arrival was commemorated on a Bermuda postage stamp many years later (Fig. 17). Mr. J. P. Hand, who had personally been involved in refusing Bouck permission to land in Bermuda, various newsmen, photographers, and others gathered around to gawk at and document the historic spectacle. +Arrests and Celebrations +Amid smiles, handshakes, and slaps on the back, Hand welcomed the crew (see Figs. 18 and 19), and then he proceeded to put them under arrest “for flying over Bermuda without a permit and similar diplomatic necessities.” It wouldn’t be the last time Bouck would be arrested in the course of his adventures. When + + + 60 The AWA Review +Zeh Bouck, Radio Adventurer +Fig. 16. The Pilot Radio arrives in Bermuda on April 2, 1930. Bouck is sitting atop the plane with “Pilot Radio” showing on his back. (Roddy Williams Collection, Bermuda Archives) +Fig. 18. Another view of the Pilot Radio’s arrival in Bermuda. On the plane: Lewis Yancey, William Alexander, Zeh Bouck, and J. P. Hand. (Roddy Williams Collection, Bermuda Archives) +Fig. 17. Commemorative postage stamp issued by Bermuda in 1983 based on the figure above. (Author’s collection) + + + Volume 30, 2017 61 +Rydzewski +the other boat arrived with the gas, Hand and a Mr. Richardson joined the crew on board the plane as it again went aloft, this time for a quick aerial tour of the islands, after which at last on April 2 at 8 a.m., the plane alighted in Hamilton Harbor (see Fig. 20) in a landing “so smooth that one could not have told that the plane was hitting water.98 When asked if they wanted anything, Yancey replied, “Anything, as long as it’s alcoholic.” Obligingly, a boatload of cocktails and ale from the famous Inverurie Hotel, a favorite of Bouck’s, was brought out to “liven up our brief period of incarceration.” Soon “pratique” was granted, diplomatic rough +Fig. 19. Front: William Alexander, Zeh Bouck (sitting on wing strut), and J. P. Hand. Person on the rear pontoon wearing spats is probably a Mr. Richardson. (Roddy Williams Collection, Bermuda Archives) +Fig. 20. The Pilot Radio arrives in Hamilton and is greeted by officials and spectators. Yancey, Alexander, and Bouck can be seen on the plane near the wing struts. (Roddy Williams Collection, Bermuda Archives) + + + 62 The AWA Review +Zeh Bouck, Radio Adventurer +spots smoothed over, and the silly arrest forgotten “through a mist of Martini drys.” Later the crew was presented with flowers at the Inverurie Hotel in Hamilton (see Fig. 21). The Bermuda Governor would eventually go on to grant them post hoc landing permission. +Thus began the next phase of their trip, a grueling series of dinners, celebrations, toasts, and speeches. Bouck celebrated his 29th birthday in cocktailladen Bermudian glory. At a dinner in honor of the flyers he was introduced as “outstanding among radio experts +Fig. 21. The flyers are presented with a bouquet of fresh lilies at the Inverurie Hotel in Hamilton on April 2, 1930. Left to right: Miss Kathleen Jones, Lewis Yancey, Zeh Bouck, and William Alexander. (Roddy Williams Collection, Bermuda Archives) + + + Volume 30, 2017 63 +Rydzewski +in the United States, and regarded as the young Fessenden.”99 In fact, Bouck took the occasion to make a pilgrimage to see the real Professor Fessenden and his wife, who were living in Bermuda. She wrote: “We counted it a fine tribute that Mr. Bouck devoted the better part of an afternoon of his short stay on the island to a call at ‘Wistowe’ to pay his respects to the man who had done so much to advance radio. When this call revealed to us the fact of his great physical handicap, it revealed too that the courage which led him to choose his profession must be of a very high order.”100 While the receptions continued in Bermuda, back home the sponsors’ PR machines had sprung to life. Yancey had made a promotional deal with Richfield Oil, which proceeded to praise the aviators for conserving fuel by landing at night rather than trying for the island in the dark. “And the famous Partners in Power, Richfield—California’s famous gasoline and Richlube—100% pure Pennsylvania Motor Oil had scored another triumph.”101 Isidor Goldberg of Pilot Radio, of course, expressed his admiration of the consistency with which the flyers were able to keep in touch at all times using his company’s equipment. Osborn of pontoon-maker Edo was especially pleased with the ocean landings. Pioneer Instruments, manufacturers of the plane’s navigation equipment, noted that the water landing (only one or two were mentioned in American news reports) “served to dispel popular beliefs that sea landings +are always disastrous unless saved by an unusual stroke of luck.”102 The Times in its inimitable way pontificated on lessons learned from the flight, finding the radio signals “remarkable for their clarity all along the 759-mile stretch” and concluding that there should certainly be radio beacons and radio direction finders installed in Bermuda to make flights routine rather than dependent on extraordinary navigation. It found that “what aviation needs is compact, light equipment in the form of receivers, transmitters and radio direction finders.”103 But it said nothing about Pilot Radio equipment—the publicity value of the flight for Pilot was minimal. Most accounts referred to it as “Yancey’s flight” and not “Pilot Radio’s flight”; almost none of them mentioned the Super Wasp. Again, the spotlight had been directed elsewhere. In Bermuda, the flyers met with local U.S. and British officials, which must have been anticlimactic for Yancey after his audiences with Mussolini and the Pope in Rome. Now that the airmen had actually made the journey and lived, the Bermuda Board of Trade, the organization that had earlier offered and then withdrawn the £2,000 Bermuda Safety Prize, voted $1,000 to each of the crewmen to express their gratitude, which must have seemed something like the Bermuda Consolation Prize, but was no doubt still welcomed. Alexander applied for permits to fly local officials around and then fly back home.104 As to how Bermudians viewed the flight, editorials suggest excitement over what it augured for + + + 64 The AWA Review +Zeh Bouck, Radio Adventurer +eventual connection with North America and Europe by air, but also plenty of caution. “The fact remains that a forced landing happened under favourable conditions and converted what might have been a disaster into a mere unfortunate incident.”105 The extraordinary nature of their flight underscored the need for a radio beacon. “I hope no one else will try this flight until we put in radio beam facilities here, and I believe Captain Yancey would say the same,” Hand concluded.106 Those facilities were a long time in coming, but were in place seven years later when Pan American Airways and Imperial Airways began regular service to Bermuda, employing constant radiotelegraph communications just as Bouck had proposed. +The Heroes Return +The Pilot Radio was inspected by British Navy mechanics, who found a serious problem: the landings at sea had damaged one of the pontoon struts. Lacking the special equipment needed to weld the duralumin alloy they could try fixing it, but couldn’t guarantee that the weld would hold when the again heavilyladen plane took off. There were also other potential problems. No aviationgrade fuel was available in Bermuda, and it would take three weeks to ship some in. The regular gasoline that the plane used for the last few miles would do in a pinch but not for a long flight. And after everything that the Bermudians had already gone through, they were none too keen on the prospect of potentially mounting another search-and-rescue mission, especially for the same flyers. +So the plane was partly dismantled and hauled up onto the deck of the SS Araguaya (see Fig. 22), which sailed for New York with plane and crew. They arrived to a festive reception featuring flyovers by fellow aviators including Emile Burgin, a friend of Yancey’s who had flown the Pilot Radio before and would soon do so again. They shook hands with officials, were photographed, were met by their wives, and feted at the Majestic Theatre that night. Guests of Isidor Goldberg and 200 others at the Biltmore the following evening, they spoke of their overnight ocean experience, which they all agreed was “not bad,” over the NBC radio network via station WJZ. As far as their having made a stop en route (actually, from one to three stops, depending on how you defined the destination), they were satisfied that they had still met their primary but unstated objective, proving conclusively that an air service between New York and Bermuda would be feasible with the proper equipment. When a newspaperman (perhaps the one who laid the unsuccessful curse on Bouck?) tried to spoil the party by telling Alexander of a bootlegger who claimed to have already made regular flights to Bermuda, he dismissed the claim. “I don’t think anyone ever flew there before,” he said.107 A few weeks later Bouck, speaking over WGBS in New York, summarized what their flight had proven: 1) that it was possible to “come down in the middle of the ocean, spend a night, and then take off again,” 2) that it was the first time any plane was able to find + + + Volume 30, 2017 65 +Rydzewski +Bermuda, and 3) that a two-way wireless conversation (in code) could be carried out over the whole route by HF.108 In fact, he was pleasantly surprised that there was no sign of a “skip distance effect,” which at some point (they had estimated 500 miles) would cause the signal to be lost. Quite to the contrary, Bouck had needed to attenuate the overly strong signal at times. In light +of these successful communications, it made little sense to add the weight of a longwave set. He again emphasized that planes making the journey should be in constant contact with a land station.109 When asked whether shortwave communications could be carried out from a plane by “phone” (voice) he said that it could, but would require heavier equipment.110 +Fig. 22. Crew and plane returning to the United States aboard the steamer Araguaya. Left to right: Lewis Yancey, William Alexander, and Zeh Bouck. (Collection of Tom Singfield) + + + 66 The AWA Review +Zeh Bouck, Radio Adventurer +While the dinners and speeches, toasts, interviews, and photos continued, the Pilot Radio was quietly being overhauled. Workers removed her pontoons and gave the plane back her land legs (wheels). She would soon depart on a marathon journey that would make her last adventure seem like a short stroll in the park. To be continued. . . . +Endnotes +1. The South American flight of the Pilot Radio (to be addressed in Part 2) was sponsored by the Hoover administration, and as a member of that party, Bouck was something of an unofficial U.S. ambassador. +2. Thirteenth Census of the United States (1910), Essex County, NJ; Fourteenth Census of the United States (1920), New York, NY; Fifteenth Census of the United States (1930), New York, NY; Enumeration of Inhabitants, New York State (1925), New York City. 3. For general overview, see Bouck White entry in Wikipedia. For writing, see B. White, The Mixing: What the Hillport Neighbors Did (Doubleday, Garden City, NY, 1913). For scandals, see New York Times archives. 4. Z. Bouck, “Hamfest,” All-Wave Radio, Mar. 1937, p. 139. +5. Who Was Who Among North American Authors 1921–1939, Volume I (Gale Research Co., Los Angeles, 1976), p. 185. 6. Tewpieye (Zeh Bouck), “A Ham on the Telephone”, QST, Aug. 1920, p. 6. 7. Hundreds of articles by and about Zeh Bouck including many of his regular New York Sun columns are available online at the website Fultonhistory.com/Fulton.html, a valuable resource for this and many other topics. +8. Z. Bouck, Making a Living in Radio (McGrawHill, New York, 1935). 9. “Among Our Authors,” Radio Broadcast, Jun. 1924, p. 188. 10. N. B. Kim, “The Early Radio Days of Harry Kalker,” Antique Radio Classifed, Jul. 1994, p. 8. 11. Radio Design, Vol. 1, No. 4, Winter 1928, p. 132. +12. R. Hertzberg, “Super-Wasp Shortwave Set,” Old Timers Bulletin, Dec. 1970, p. 16. +13. H. Gernsback, “The Old E.I. Co. Days,” Radio News, Mar. 1938, p. 632. 14. “Radio News Publisher in Hands of Receiver,” New York Times, Feb. 21, 1929. +15. R. Hertzberg, “Successful Television Programs Broadcast by Radio News Station WRNY,” Radio News, Nov. 1928, p. 415. 16. Z. Bouck, “Channel Echoes,” All-Wave Radio, May 1937, p. 237. +17. L. Steckler, ed. Hugo Gernsback: A Man Well Ahead of His Time (Poptronix, Inc., Marana, AZ, 2007) p. 327. 18. “Once He Paid to Throw Them Away, Now He Seeks 1928 Vintage Television Sets,” San Bernardino Sun, Apr. 14, 1950. +19. Z. Bouck, “Channel Echoes,” All-Wave Radio, Jan. 1937, p. 19. 20. Robert Hertzberg, “Super-Wasp Short-Wave Set,” Old Timers Bulletin, Vol. 11, No. 3, Dec. 1970, p. 17. 21. D. F. Plant, “Designed for Application: The Story of James Millen, W1HRX,” CQ, Jul. 1967. 22. Quotation from aviation magazine provided by Ed Lyon. My thanks to Ed for this and other valuable insights into early flying and radio communications. 23. A. Earhart, The Fun of It (Harcourt Brace, New York, 1932) p. 91. 24. Z. Bouck, “Making the Air Safe for Traffic,” Radio News, Jun. 1929, p. 1068. 25. A. K. Ross, “Making Radio Easier for Aviators,” Radio News, Sep. 1928, p. 202. 26. S. R. Winters, “Radio Progress,” Popular Aviation, Jul. 1928, p. 36; Z. Bouck, “The Airplane Radio Beacon,” Radio Design, Vol. 1, No. 4, Winter 1928, p. 125; “And NowRadio Guides Airplanes,” Radio News, Feb. 1930, p. 748. 27. S. R. Winters, “Radio Beacons to Guide Planes Across Continent,” Radio Age, Sep. 1926, p. 15. Adopted by the military, the A-N system came to dominate. https://en.wikipedia. org/wiki/Low-frequency_radio_range. 28. Z. Bouck, “The Problems of Aircraft Radio,” Radio News, Jul. 1929, p. 18. 29. Milton Sleeper, who had trained as a cadet in the Royal Flying Corps, noted that cadets would sometimes break the training transmitter to get out of code practice, which they detested. See A. Perry, “The Flying + + + Volume 30, 2017 67 +Rydzewski +Laboratory,” Popular Aviation & Aeronautics, Feb. 1929, p. 26. 30. See M. F. Eddy, Aircraft Radio (Ronald Press, New York, 1931), Chapter 8. +31. Bouck, Making a Living in Radio, p. 37. +32. A. Lynch, “Radio and Aviation,” Radio News, May 1929, p. 985. 33. See, for example I. M. Philpott, The Birth of the Royal Air Force (Pen and Sword Military, South Yorkshire, UK, 2013), pp. 304–306. For early radio experiments on U.S. Navy planes, see L. S. Howeth, History of CommunicationsElectronics in the United States Navy, chapter XIV, available at http://earlyradiohistory .us/1963hw14.htm. 34. D. Crocker, “Radio and the Historic Flight of the NC-4,” Antique Radio Classified, Jan. 2008, p. 14. +35. S. Bart, Race to the Top of the World: Richard Byrd and the First Flight to the North Pole (Regnery History, Washington, D.C., 2013). 36. For one account of the Commander, a true marketing genius, and the 1925 MacMillan expedition, see J.H. Bryant and H.N. Cones, Dangerous Crossings (Naval Institute Press, Annapolis, MD, 2000). 37. D. Crocker, “The Dolphin: Crosley’s Personal Plane,” Antique Radio Classified, Nov. 2005, p. 22. 38. D. Crocker, “Crosley Takes to the Air: The Moonbeam,” Antique Radio Classified, Aug. 2004, p. 9. 39. For a perspective on the state of aircraft radio and the companies involved at the time, see M.F. Eddy, Aircraft Radio, and “Aircraft Radio Communications,” Aero Digest, March 1929, p. 66. 40. Letter from E. Meyer, Secretary to Mr. Goldberg, to Mr. W. L. Hamberger, publisher of the International Cyclopedia of Aviation Biography dated July 28, 1931. Available through Wright State University Special Collections. 41. Ross, Radio News, p. 202; “Flying Radio,” Popular Aviation, Jun. 1928, p. 23. 42. Brooklyn Standard Union, May 15, 1927, p. 12. +43. A. Douglas, Radio Manufacturers of the 1920’s (Sonoran Publishing LLC, Chandler, AZ, 1991), Vol. 3, p. 99. 44. World War One draft registration card for Milton Blake Sleeper, Serial No. 705, Order No. 803, Sep. 12, 1918. 45. Previous editors included Austin Lescarboura +and Carl Dreher. See D. Bart, Comprehensive Index to the Proceedings of the Radio Club of America For 1913-2013, p. xv, available at http://radioclubofamerica.org/wp-content/ uploads/2015/07/proceedings-index-opening-pages.pdf. 46. “Sleeper to Be Birdman With the Allies,” Everyday Engineering, Dec. 1917, p. 131; M.B. Sleeper, “Experiences of an R.F.C. Cadet,” Everyday Engineering, Jul. 1918, p. 162; Aug. 1918, p. 201; Oct. 1918, p. 27; and Dec. 1918, p. 125. 47. Neither did Sleeper ever acquire a pilot’s license, as far as a search at the Smithsonian’s National Air and Space Museum could determine. +48. Perry, Popular Aviation, p. 26. +49. M. B. Sleeper, “What Price Television?,” QST, Mar. 1929, p. 48. 50. “Stinson Detroiter for Radio Research,” Aviation Week, Jul. 9, 1928. 51. Z. Bouck, “W2XBQ Flies to Bermuda,” Radio News, Jul. 1930, p. 12. 52. H.A . Bruno; W. S. Dutton, “The OceanHopping Bug,” Liberty, May 6, 1933, p. 32. 53. A. Cortesi, “Italians ‘Rush’ Pathfinder,” New York Times, Jul. 11, 1929. +54. M. Maurer, Aviation in the U.S. Army, 19191939 (U.S. Government Printing Office, Washington, D.C.). Available at http://media. defense.gov/2010/Sep/23/2001330114/-1/1/0/AFD-100923-007.pdf. 55. “Pacific Fliers Led by Radio Beacon,” Science and Invention, Nov. 1927, p. 623. 56. Check out the display inside the Kilauea lighthouse on Kauai, if you can take your eyes off the incredible surrounding landscape and seascape. 57. “The Armstrong Seadrome,” Aero Digest, December 1929, p. 152; Sherwin L., “Seadrome for Atlantic Flyers Will Be Completed in a Year,” New York Evening Post, April 6, 1931. 58. W. Raleigh, “Seadromes,” Flying, February 1930, p. 22. 59. I. I. Sikorsky, “Airplanes of the Future,” Aero Digest, Dec. 1929, p. 54. 60. Unidentified newspaper, “Building of 1st Seadrome Starts Within 90 Days,” Mar. 26, 1931. Available through Wright State University Special Collections. 61. Unidentified newspaper, “Airport at Sea Legal, Inventor Asserts,” Mar. 27, 1931. + + + 68 The AWA Review +Zeh Bouck, Radio Adventurer +Available through Wright State University Special Collections. 62. “Bermuda Safety Flight Contest,” Aero Digest, Sep. 1927, p. 276. +63. C. A. Pomeroy, The Flying Boats of Bermuda (Colin A. Pomeroy, 2000) p. 10. 64. Lyon was a U.S. Admiral’s son and mariner, and was alleged to also be a bootlegger, gun runner, and many other things besides. See, for example, http://www.mainememory.net/ sitebuilder/site/272/page/531/display?use_ mmn=1. Accessed Jan. 8, 2017. 65. “Putnam and Fliers Hop for Bermuda,” New York Times, Oct. 29, 1928; “Putnam Airplane Arrives at Norfolk,” New York Times, Oct. 30, 1929; “Postpones Flight,” Daily Independent (Murphysboro, Illinois), Nov. 7, 1928. 66. See E. Partridge, T. Singfield, Wings Over Bermuda: 100 Years of Aviation in the West Atlantic (National Museum of Bermuda Press, Old Royal Naval Dockyard, Bermuda, 2014). This meticulously researched, lavishly illustrated volume is the definitive book on Bermudian aviation history, must have been a true labor of love for its authors, and is highly recommended reading. 67. Anyone who thinks that aerial navigation must have been simple in those simpler times is invited to try working out the problems in that book. See L.A. Yancey, Aerial Navigation and Meteorology (Norman H. Henley Publishing, New York, 1929). 68. C. V. Glines, “First Flight to Bermuda,” Aviation History, Jul. 2001. Available at http:// www.historynet.com/aviation-history-firstflight-to-bermuda.htm. Accessed Jan. 8, 2017. 69. See his account of WWI combat, W. Alexander, “Dawn Patrol—A True Story of the R.F.C.,” Aero News and Mechanics, Vol. 2, No. 3, June–July 1930, p. 17. 70. B. Gould, “Yancey Nearing Bermuda on Hop,” New York Evening Post, April 1, 1930. 71. “Pilot of Coney Disaster Hero of Bermuda Flight,” Standard Union (Brooklyn, New York), Apr. 2, 1930, p. 1. 72. “Dinner in Honour of the Fliers,” Royal Gazette and Colonial Daily (Hamilton, Bermuda), Apr. 9, 1930. 73. List of United States Citizens, S.S. Bermuda, sailing from Hamilton to New York, arriving May 3, 1928. 74. Z. Bouck, letter to J.P. Hand, Jan. 9, 1930. Bermuda Archives document CS 3056/8:10. +My thanks to Thomas Singfield who originally unearthed this document. 75. “Zeh Bouck at Summer Home,” The Enterprise (Altamont, New York), May 27, 1932, p. 3. 76. See Z. Bouck, “The First Airplane Reaches Bermuda,” Yachting, Jun. 1930, p. 53, where Bouck says that he could take over for navigator or pilot in an emergency. Also see “Plane Carries Stowaway Back to Maine Home,” Scranton Republican (Scranton, Pennsylvania), Jun. 27, 1929, p. 24, and “Dinner in Honour of Fliers,” Royal Gazette and Colonial Daily. 77. Yancey, who piloted The Pathfinder for most of the flight from Maine to Rome, later admitted to not having a pilot’s license at the time, and later still, in 1931, received his first license. See “Lawyer’s Queries Incense Yancey,” New York Times, May 13, 1930; “Yancey, Rome Flier, Wins Pilot’s License,” unidentified newspaper, Jun. 5, 1931, available from Wright State Special Collections. 78. Attempts to confirm the reason for Bouck’s disability through his own accounts or medical records, or to find descendants or living friends and neighbors who could provide these kinds of details were, sadly, unsuccessful. 79. Quoted in Partridge & Singfield, Wings Over Bermuda, pp. 32–33. 80. Bouck was warned that “no sanction could be given nor assistance offered.” See “The New York-Bermuda Flight,” Royal Gazette and Colonial Daily (Hamilton, Bermuda), Apr. 4, 1930, p. 2. See also Yancey’s statement in “Out of Fuel, Yancey Landed Off St. Georges to Get Gas,” New York Times, Apr. 3, 1930. 81. The only reference to the flight in that journal that this author could find was an editorial by Arthur Lynch crediting Bouck with conceiving of and directing the flight and praising the flyers for their accomplishment. See “The Bermuda Hop,” Aero News and Mechanics, Vol. 2, No. 3, Jun.–Jul. 1930, p. 5. 82. E. Matlack; R. Matlack, “The Paper, the Station, and the Man—A Brief History of the New York Times Radio Stations,” 73, Feb. 1980, p.54. 83. Z. Bouck, “How High is Up?,” Radio Design, Vol. 2, No. 4, Winter 1929, p. 31; “Pilot Radio Firm Acquires Flying Laboratory,” Aero Digest, Sep. 1929, p. 120. + + + Volume 30, 2017 69 +Rydzewski +84. Bouck, Yachting, p. 53. See also Jane’s All the World’s Aircraft, 1930, p. 317c. +85. “Yancey Starts Bermuda Flight,” New York Times, Apr. 1, 1930. 86. Bouck, “W2BXQ Flies to Bermuda,” p. 12; Z Bouck, “How the ‘Pilot Radio’ Made the First Bermuda Flight,” Radio Design, Vol. 3, No. 2, Summer 1930, p. 42. 87. Z. Bouck, “The Story of Three Men in a TubOn Wings,” New York Sun, Apr. 10, 1930. 88. J.H. Kimball, “Telling Ocean Flyers When to Hop,” Popular Science, Jul. 1928, p. 16. 89. Bouck, “The Story of Three Men in a Tub—On Wings.” 90. Ibid. 91. “Yancey and His Aides Honored at Dinner,” New York Times, Apr. 12, 1930. 92. Bouck, Yachting, p. 53. 93. Z. Bouck, “The Log of the Seaplane, the Pilot,” New York Times, Apr. 2, 1930. +94. “The New York–Bermuda Flight,” Royal Gazette and Colonial Daily (Hamilton, Bermuda), p. 2. See also “Out of Fuel, Yancey Landed Off St. Georges to Get Gas,” New York Times, Apr. 3, 1930. 95. “Zeh Bouck, Well Known Here, in Plane that Flies to Bermuda,” Schoharie Republican (New York), Apr. 3, 1930 says that WGY programs were interrupted. “Plane Flying New York–Bermuda Comes Down in Calm Sea Sixty Miles North of Here,” Royal Gazette and Colonial Daily (Hamilton, Bermuda), Apr. 2, 1930 lists WEAF among the stations maintaining radio silence. 96. “Plane Flying New York-Bermuda Comes Down in Calm Sea Sixty Miles North of Here,” Royal Gazette and Colonial Daily (Hamilton, Bermuda), Apr. 2, 1930. 97. Zeh Bouck, “W2XBQ Flies to Bermuda;” Bouck, “How the Pilot Radio Made the First Bermuda Flight;” Bouck, “The Story of Three Men in a Tub—On Wings;” and Bouck, “The First Airplane Reaches Bermuda,” all cited above. 98. “Three Aviators Arrive in Nick of Time,” Royal Gazette and Colonial Daily (Hamilton, Bermuda), Apr. 3, 1930. 99. “Dinner in Honour of Fliers,” Royal Gazette and Colonial Daily (Hamilton, Bermuda). 100. H. M. Fessenden, Fessenden—Builder of Tomorrows (Coward-McCann, New York, 1940), p. 337. 101. Richfield Gasoline advertisement, Reading +Times (Reading, Pennsylvania), Apr. 9, 1930, p. 8. 102. “Wives Unworried During Long Vigil,” New York Times, Apr. 3, 1930. 103. “On the Way to Bermuda,” New York Times, Apr. 6, 1930. 104. “Delay Repairs by Yancey,” New York Times, Apr. 5, 1930. 105. “The New York—Bermuda Flight,” Royal Gazette and Colonial Daily. +106. “Dinner in Honour of the Fliers,” Royal Gazette and Colonial Daily. +107. “Bermuda Fliers Return on Liner,” New York Times, Apr. 11, 1930. 108. “Bouck Lauds Yancey,” New York Times, Apr. 19, 1930. 109. “Radio Devices Aid Safety in Flying,” New York Times, May 4, 1930; Bouck, “How the ‘Pilot Radio’ Made the First Bermuda Flight,” Radio Design. +110. “Bouck Lauds Yancey,” New York Times. +Acknowledgments +This paper would not have been possible without the gracious help of the following people: Mike Adams and Bart Lee (California Historical Radio Society); Colleen Ayers (Radio Club of America); Carl Bobrow, Dr. Peter Jakab, Roger Connor, and Elizabeth Borja (National Air and Space Museum); John Guttman and Karl Vonwodtke (Aviation History Magazine); Kieron E. Hall (Bermuda National Library); Karla Ingemann (Bermuda National Archives); Ellen Keith (Chicago History Museum Research Center); Steve and Anne Lamont (Middleburgh Library); Rick Leisenring (Curtiss Museum); Mrs. John McCabe; David Miller (FlightLine Designs, Inc.); Patrizia Nava (U. Texas at Dallas Eugene McDermott Library); Bernd Neumann; Ludwell Sibley; and Bill Stolz (Wright State University Special Collections). + + + 70 The AWA Review +Zeh Bouck, Radio Adventurer +Special thanks go to Phillip Krejci for incredible photographic restorations involving many hours of work; to Paul Hertzberg, K2DUX, for much useful information on Pilot Radio along with the photo of and schematic hand-drawn by his father, the late Robert Hertzberg; to Ed Lyon (Mid-Atlantic Antique Radio Club) for informative discussions about the challenges of early aircraft radio; to Andrew Pentland for guidance on finding and interpreting Milton Sleeper’s RFC records; to Thomas Singfield, co-author with Ewan Partridge of the outstanding book Wings Over Bermuda, for access to details on the Pilot Radio’s flight that would otherwise be unfindable; and to Bob Winn for help with Zeh Bouck genealogy. +About the Author +Bob Rydzewski, KJ6SBR, is a native of Chicago, Illinois, where his parents had worked at various times for Teletype Corporation, Belmont Radio, and Zenith. One of his earliest memories is of looking up to the eerie green magic eye of a 1930s Zenith console. His interest in electronics as a hobby began about the time he assembled an Eico 460 oscilloscope in a high school physics lab. Around 2000 he developed an interest in collecting and restoring old radios. Inspired by Alan Douglas’s +Radio Manufacturers of the 1920’s, he began searching out the fascinating and often forgotten stories behind the early days of wireless. Bob received an MS in chemistry from DePaul University and went on to a 25-year career in pharmaceutical and biotech R&D, eventually penning a textbook on drug discovery. His writing abilities came to the fore in his current career as a professionally accredited medical writer, helping doctors present clinical trial results through journal articles and congress presentations. Bob and his better half live in the San Francisco Bay Area where he is a proud member of the California Historical Radio Society. +Bob Rydzewski + + + Volume 30, 2017 71 +A Soviet Era Broadcast Receiver System of +the 1950s for Remote Locations +© 2017 Robert Lozier +For nearly 20 years I have taken a special interest in studying how the various national broadcast systems of the world have developed. These variations have often resulted in the development of very different hardware to serve these systems. I was recently given a Russian made thermoelectric generator of the 1950s in very poor condition prompting me to research its significance before investing time in restoration. I was already aware of their existence for powering small broadcast receivers in remote locations of the former USSR and English language Google searches produced links to basic information. Examination of serial numbers found in Google Images searches lead me to believe that these generators were at least made in the tens of thousands and not just a novelty. With little to lose in trying to make my unit presentable, I started preservation and restoration activities. After about 15 to 20 hours work, I concluded that it could be made presentable for exhibition; this prompted me to locate an appropriate radio that would have been powered by these generators. A fellow collector provided me with a fine example that turned out to have one surprising construction method, perhaps making a virtue of necessity, and several other very interesting features that prompted a new round of research. This paper describes my research into this broadcast receiving system, and provides a narrative of how these artifacts were prepared for conservation and exhibition. Many aspects of this receiving system and these artifacts will be largely unfamiliar to American readers. +Introduction +Based on 20 years of study, it became obvious that very different types of hardware were developed to support the various national broadcast systems of the world. I wrote two papers on this subject for the AWA Review describing various aspects of broadcast receiver development outside of the United States, the first treating Italian systems and the second treating radios from a number of other western European countries.1 This paper addresses several +unique broadcast radio systems in the Soviet Union. Beginning in the early 1920s and into the early 1930s, the Soviet Union recognized the value of establishing a broadcast radio system to unite, indoctrinate, and educate the populace. At that time, the primary means of providing radio reception to the populace was accomplished by placing radios in administrative buildings with loudspeakers distributed along city and + + + 72 The AWA Review +A Soviet Era Broadcast Receiver System of the 1950s for Remote Locations +town streets or by centralized receivers with wire lines going to subscriber apartment buildings, factories, public halls, schools, etc., which were operated much like telephone exchanges. The same type of receiver could be placed in an apartment block, dormitory, factory, or school to drive 50 to 250 small speakers. This distribution from a single receiver to multiple loudspeakers in an area was referred to as “radio-diffusion exchanges,” “cable radio,” or “wired radio.” People paid a small subscription fee for the service. At least from the late 1940s, these wired networks distributed program content from 6 a.m. to midnight. The number of receivers in the Soviet Union reported in census figures during the 1930s are considered to be highly suspect by Western historians. The official claim of 170.6 million people in the 1939 census is believed to be inflated by 10 to 20 million. Reports of Soviet statistics in 1940 claim 1.1 million radios at that time, but that is actually the tally of radios manufactured since 1932.2 According to the research of Alex Inkeles, the whole of the Soviet Union possessed 650,000 receiving sets in 1936; of these, 270,000 were crystal receivers, and about 200,000 were considered outmoded types in need of replacement.3 The Radio Committee was able to claim only 500,000 sets as being “ready” to broadcast Stalin’s address before the Supreme Soviet on November 25, 1936. The number of broadcast receivers in operation as of 1940 was reported to be 760,000, with more than five million wired speakers +of the cable radio systems. After the ravages of World War II, less than 18% of listeners in 1947 were said to be receiving their programming via individual receivers. It should be noted that in the rural areas, only a small percentage of the population heard any radio programming on a regular basis. In any case, the penetration of broadcast radio reception via individual receivers lagged far behind most modern industrialized countries that the Soviets were trying to surpass. The government realized that postwar efforts to manufacture broadcast receivers would have to be dramatically increased, and so design bureaus within ministries, universities, and a few radio factories were tasked to develop new designs for low-cost, mass-produced radios. These designs were reported in detail to the public in the pages of the Soviet magazine Радио (Radio) beginning in the very late 1940s.4 Actual volume production was low and did not begin to increase significantly until after 1953, due in large part to the deemed higher priority of rebuilding the electrical, electronic, and communications resources of the Red Army. It was not until the latter half of 1956 that all radio assembly plants were reportedly operating on a continuous assembly-line basis.5 Rural electrification in the Soviet Union lagged behind that in the United States by some 25 or 30 years, such that there was still a significant need for battery-powered broadcast receivers into the 1970s. Adequate distribution of expensive dry batteries to remote + + + Volume 30, 2017 73 +Lozier +locations was at times unreliable and, of course, a continuing expense. Many people remember magazine, newsreel, and television coverage of long lines of Soviet citizens in seeming endless queues for basic goods. Consequently, the Soviet Union began to develop thermoelectric generators as an optional power source. I recently obtained a Russian-made thermoelectric generator of the 1950s in very poor condition, which prompted additional research to determine its significance before investing in a restoration project. English language Google searches for thermoelectric generators that powered small broadcast receivers in remote locations of the former USSR produced links to basic information. Examination of serial numbers found in Google Images searches determined that these generators were made at least in the tens of thousands—not just as a novelty. After 15 to 20 hours +of preservation and restoration work, it became apparent that it could be restored to a condition suitable for presentation. It was obvious that a presentation of the generator would be much enhanced by connecting an appropriate Soviet radio to the generator. A fellow collector provided a fine example of a Soviet radio that turned out to have one surprising feature and several other very interesting features that prompted a new round of research. These features will be described in Part II herein addressing Soviet receivers powered by thermoelectric generators. This paper combines my research into thermoelectric generators in particular and Soviet broadcast receiving systems in general. A description of how these artifacts were prepared for conservation and exhibition is also included. A great deal of this information will be new to most American readers. +PART I. THERMOELECTRIC GENERATORS +Early Thermoelectric Generators +The fact that heated junctions of dissimilar metals can create a magnetic field was discovered by Seebeck in 1821. Seebeck thought that the phenomenon he observed was that of conversion of heat into magnetism. It was left to Ørsted to correct this misperception and properly describe it as creation of an electric current, and in doing so he coined the term “thermoelectricity.” The electrical output of individual dissimilar metallic junctions is very +small, generally seldom more than 3 to 15 millivolts. The first patent for the use of thermoelectricity instead of batteries for useful work in electroplating was by Moses Poole in 1843.6 By the middle 1860s, thermopiles (assemblages of multiple thermocouple junctions to provide useful voltages and currents) were being noted in journals of scientific societies. The junctions were of metals and metallic alloys with junction potentials well under 20 millivolts. + + + 74 The AWA Review +A Soviet Era Broadcast Receiver System of the 1950s for Remote Locations +These early thermopiles were said to have been unsuccessful for continuous work because of oxidation of the metals and junctions as well as stress fracturing of constituent metals during cooling or heating. By 1874, a gas fired commercial version of the Clamond Thermopile was reported to be in operation at the printing works of the Banque de France, presumably for electroplating copper in the electrotyping print process.7 In 1876 the (British) Government Telegraph Service under the direction of Sir W. H. Preece issued a contract to the Thermo Generator Company to supply thermopiles as a replacement for the usual system of electrochemical batteries, but the project was in short order declared a failure. Preece indicated it was his opinion that the faults could be corrected, but the company collapsed before they were able to complete the contract.8 There were a number of investigators in the last quarter of the 19th Century that attempted to overcome the deterioration of junctions and improve efficiency, but the development of practical small dynamos for electroplating virtually eliminated the primary market for thermopiles. In 1909, engineer Edmund Altenkirch is credited with expressing a mathematic relationship between physical properties of thermoelectric materials and the efficiency of a simplified thermopile.9 +Thermoelectric Generator Applications to Wireless Sets +The Science Museum in London has exhibited a Thermattaix gas-fired ther +mopile designed circa 1925 for charging “wireless set accumulators” (vacuum tube radio receiver filament supply batteries) over the range of 2 to 10 volts (see Fig. 1). The magazine Amateur Wireless for April 1929 carried an ad for a Thermattaix, claiming that it could work your wireless set by gas, petrol, steam, or electricity. . . . Electricity? On the surface, this claim to operate a radio by electricity seems to be an oxymoron, but it is one way to convert high-voltage alternating mains to the low-voltage direct current required for charging accumulators. Or, if the high voltage mains came from a jittery onecylinder motor/generator outfit, it could act as a voltage stabilizer. The ad goes on to claim that amongst their customers were gas companies, the Italian Air Force, architects of note, and guides for big game expeditions in Africa and India. It is not known how many units were manufactured, but very few, if any, are in the hands of collectors. +Fig. 1. Thermattaix gas powered generator for charging filament batteries. (Science Museum, London) + + + Volume 30, 2017 75 +Lozier +In the mid-1930s, the Cardiff Gas Light & Coke Company (South Wales, UK) placed the ad shown in Fig. 2 that advertised “THE THERMO-ELECTRIC GENERATOR which makes your Battery Set Independent of Batteries of any kind.” There were mentions of this outfit in Wireless World, and the son of a dealer reports his father having sold a number of these. The advertisement shows a radio of a style that would leave us to presume the thermopiles must have produced 2 volts at 0.5 amps for the valve filaments and 90 to 120 volts at 10 milliamperes for the plate circuits. But again, neither the actual number placed in service nor the cost is known, and there appear to be no surviving examples. Four articles on thermoelectric generators to power radio receivers and radiotelephones have been found in the Russian language magazine Radio (Радио), which began publication in 1946. The February 1952 issue states that under the direction of the prominent Soviet physicist and academician Abram F. Ioffe, investigations in the 1930s turned towards a search for semiconductor materials such as a zinc–antimony alloy (SbZn) bonded to a copper–nickel alloy (constantan) that could produce significantly greater potentials (55 mV in production devices) at higher thermal efficiencies (still, well under 4%). It was stated that the first claimed Soviet use of thermocouples using semiconductors was in “The Great Patriotic War” (WW II) to power small—presumably headphone-only—radio receivers used by partisan forces. One very small line +drawing shows a hanging cast metal pot with a flat bottom. The thermocouples are bonded to the bottom of the pot, and the pot is suspended over an open campfire. Water boiling in the pot becomes the “cold” side for this primitive thermopile. +TGK Series of Soviet Thermoelectric Generators +Later, in 1949–1956, Ioffe derived a “ZT” value parameter as a figure of merit to indicate how efficiently a material converts heat into electricity. He +Fig. 2. Dating from circa 1934, this thermo-electric generator may have been the first product to supply all the power needs of a conventional battery powered broadcast receiver. It was built only in very small quantities. (http://www .douglas-self.com/MUSEUM/POWER/thermo electric/thermoelectric.htm#ca) + + + 76 The AWA Review +A Soviet Era Broadcast Receiver System of the 1950s for Remote Locations +used the new parameter to calculate the practical efficiency of thermoelectric generators.10 A team of engineers then developed a thermoelectric generator powered by a kerosene lamp burner that was capable of delivering 3 watts—enough to power a low-power vacuum tube radio with loudspeaker (see Fig. 3). These generators were made at the Metallamp factory in Moscow. A TGK-3 version of the generator described in the February 1954 issue had two thermopile circuits; one circuit supplied 2 volts at 2 amperes to a synchronous, mechanical, vibrator-type of DC-to-DC converter. It provided 90 VDC for the plate circuits of the radio and -9 VDC for grid bias. The other +thermopile circuit provided 1.2 VDC at a nominal load of 300 mA for lighting the vacuum tube filaments. No storage battery was used in this power system. The February 1956 issue of Radio announced an improved generator, TZGK-2-2, that eliminated the need for a vibrator power supply with its inherent RFI emissions.11 This was a matter of considerable importance because many of these generator-powered radios were in weak signal areas at considerable distances from broadcast transmitter sites. This new generator provided the 90 VDC for plate circuits and -9 VDC for grid bias directly from a series string of approximately 2600 pairs of hot and cold junctions. In the same year, another low-voltage version of the generator, designated TGK-10, was announced in the September issue of Radio (see Fig. 4). This unit did not serve the double purpose of providing room lighting in addition to radio power. This somewhat higher power version, 10–12 watts, was only for battery charging service. A vibrator type power supply sourced by a storage battery was still needed to deliver the peak power requirements of the KRU-2 “cooperative radio center,” which used a multi-band broadcast receiver designed to drive up to 50 low-power loudspeakers in apartment buildings, dormitories, etc. This was for the “cable radio” scheme of distributing broadcast programming in “off-the-grid” communities or collectives. This generator was also employed to power the “Vintage U-2” and “Harvest-1” low-power, 2–3 MHz, AM radio +Fig. 3. The TGK-3 generator powered a DC-toDC mechanical converter to provide +90 and -9 volts for a vacuum tube receiver. (TGK-3 Instruction Manual) + + + Volume 30, 2017 77 +Lozier +telephones used on large agricultural collectives, etc. An article published on the www.radionic.ru web site states that 20,000 of the Harvest radio telephones would be manufactured in 1956, with another 25,000 scheduled to be built in following years. The article states that 70,000 radiotelephone stations will be in service.12 It is unknown if those production goals were ever achieved, and there are no comments on how many were powered from the thermoelectric generators. +Small Thermoelectric Generators to Power Broadcast Receivers +The thermoelectric generator in my possession is stamped ТЭГК-2-2 (1958), which translates to TZGK-2-2 in English (see Fig. 5). The “2-2” of the part number is the guaranteed minimum power output of the generator (i.e., 2.2 watts). This generator seems to have the same outward appearance as the one described in the February 1956 issue of Radio. Web searches of images indicate that the 1958 in parenthesis +Fig. 4. This TGK-10 generator was used to charge batteries in “Harvest-1” low-power HF radio telephones. (Radio, No. 8, 1956, p. 7) +Fig. 5. A TZGK-2-2 (1958) Thermoelectric Generator. (Author’s collection) + + + 78 The AWA Review +A Soviet Era Broadcast Receiver System of the 1950s for Remote Locations +does not represent the year of manufacture; instead, it is an indication of a new model. I have not been able to determine what changes were made internally that would have caused the model number to change. The operating instructions give specific requirements for placement of the generator in a room. It must be near a window and hang from its supplied chains at a minimum distance of 10 cm from the ceiling and at least 1.5 m from any wall. The generator provides 1.2 volts to light the filaments of 7-pin miniature tubes, which are in many ways electrically and dimensionally interchangeable with the miniature tubes introduced by RCA in 1939 and first used in the RCA Victor BP-10 pocket portable radio of 1940 (see sidebar). Another bank of thermocouples provides a nominal 9 volts for grid bias, and a third bank produces 90 volts at a maximum of 10 mA for the plate circuits. These thermopiles are built around a cast aluminum core with six prismaticcross-section channels at the center for the hot gasses to pass through. A sheet metal flue at the top improves draft. +The thermopile is heated by a kerosene lamp burner of the Argand type to raise the temperature of the hot junctions to about 400°C.13 In the case of the TGK-3 and TZGK-2-2, the clear glass globe allows it to serve double duty as room lighting that should produce something approaching 200 lumens. The font holds enough kerosene for about eight hours of operation. Russian language publications provide extensive analyses of various thermocouple materials and thermocouple theory but provide no information on how the thermocouples are actually fabricated for these generators. English language Google Images searches produced no internal construction photographs of these generators. Eventually, I was able to use Google Translate to craft Russian language queries that produced links to a number of dissected generator photographs made by a former Soviet region vintage radio enthusiast in 2009. Even these photographs shed little light on how these junction slabs were fabricated. It is apparent from inspection that the thermocouples were fabricated in many multi-layer monolithic slabs, +How Did the Soviets Develop Their “Finger Lamp” Technology? +How the Soviets acquired the vacuum tube technology described here is an interesting question. Was it acquired directly from RCA or via Lend-Lease agreements with the Soviets during World War II. RCA had indeed entered +into contracts with the Soviets during the 1930s but they were completed by 1938. Most notable was the contract providing a complete electronic TV broadcast system in Moscow. There were attempts to renew agreements + + + Volume 30, 2017 79 +Lozier +during the war and shortly thereafter, but deteriorating government relations ended cooperation by 1949. The LendLease policy enacted in March 1941 did not have in its scope the transfer of technology—only goods. Alex Magoun of the IEEE History Center commented to me in a 2016 e-mail: “American officials were puzzled and frustrated by Soviet refusal to let them observe the use of equipment on the Eastern Front so that they could ensure the Soviets were getting the right goods or using them effectively. I suspect that you’ll know better than me if these tubes were in standard military radios and other electronic combat devices. If the U.S. didn’t ship tubes separately and the glass-based tube was not part of the RCA contract, it certainly would not have been hard for the Soviets to remove tubes from the radio equipment shipped under Lend-Lease and reverse engineer it.” In 2009, the RKK Radio Museum of Veleriy Gromov in Moscow exhibited radios identified as having been provided to the Soviets via various Lend-Lease agreements. One showcase holds a BC-611-B handy-talkie containing the 7-pin miniature tubes developed by RCA. Close examination of Soviet made miniature tubes do show different internal construction details, although by the 1950s, a number of the tubes were carrying dual part numbers that include 1R5, 1T4, 1S5, etc. However, some tubes they made do not have electrically identical specifications to U.S. tubes. Therefore, it seems likely that their “finger lamps” are indeed the +product of reverse engineering. The same could be said for the immediate post-war agreements between RCA and the Soviets, as outlined in a speech by Alex Magoun in 2004: “This [agreement] was apparently signed, and new Russian engineers appeared at RCA’s factories. They gained access to the licensing bulletins and craft knowledge behind RCA’s electron microscope, a device championed by Zworykin as another, more beneficial means of “distant vision;” the latest in cathode-ray tube technologies for radar and television displays; radio-frequency heating for various industrial processes; the beginnings of electronic computer memory; and RCA’s image orthicon, developed for guided missiles during the war and converted to commercial cameras 100 to 1,000 times more sensitive than the pre-war iconoscope. The sale of information and technology came to a halt when the U.S. Commerce Department established an export control system in 1949 to go into effect by midnight, Monday. Between the announcement Saturday and the deadline, an American Amtorg official located a cargo ship and arranged for the loading of $5 million of machinery. This included RCA cameras and electron microscopes, useful in the processing of materials for nuclear weapons. By the time the FBI arrived to impound the goods, the ship was already in international waters.” (Alex Magoun, “Adding Sight to Sound in Stalin’s Russia,” speech presented at the Society for the History of Technology (SHOT), Amsterdam, October 8, 2004). + + + 80 The AWA Review +A Soviet Era Broadcast Receiver System of the 1950s for Remote Locations +but without having slabs to dissect, the method of fabrication could not be determined. A small line drawing appearing in several contemporary articles purports to show a side face of an assembly, but it does not look anything like the photographed assemblies (see Fig. 6). The outside of the cast aluminum core has 14 flats. Each surface is covered by a mica insulating sheet, and one edge of the junction strip is in contact with the mica. This becomes the HOT side of the junctions. Another mica sheet covers the outer face of the junction strip and is in contact with a dual-fin soft aluminum radiator, thus becoming the COLD junctions. A heavy gauge steel U-channel bar clamps the dual-wing radiator fin to the core end caps. There is no evidence of any type of “thermal grease”; that +type of material did not enter the market until the early 1960s. The bottom junction strip pictured in Fig. 6 is part of the 1.2-volt, 300-mA circuit to light the tube filaments. Each junction strip has 18 pairs of hot and cold junctions, and these are mounted to 5 of the 14 flats of the thermopile core. The top junction strip pictured is actually four smaller scale 50-pair junction strips bonded together and connected in series to form the 9-volt bias supply circuit (see Fig. 7). The 90-volt plate circuit supply is made of the same small-scale, 50-junction pairs as the 9-volt bias supply but they are bonded in groups of six and mounted to the eight remaining faces of the thermopile core in the same fashion. There are wedges of corrugated asbestos between each bank of thermocouple slabs. The area between each bank of junctions is +Fig. 6. The two configurations of thermocouples for low- and high-voltage circuits. (Author’s collection) + + + Volume 30, 2017 81 +Lozier +topped off with an asbestos-filled caulk. By the nature of this construction, the asbestos is well protected from any possible abrasion. Note the void highlighted by the arrow in Fig. 6. There is a space of about 4 mm between the aluminum central core casting and the bottom heavygauge steel end plate of the thermopile, which forms a necessary thermal break. There was evidence of random gaps in the caulking of the thermal break that would allow flue gasses to condense onto the end connections of the junction slabs. Heavy corrosion is evident at these gaps. It would be interesting to know if this was a common defect such that few or none of these generators actually put into general service are still operational. An article in Radio for September 1956 describing the TGK-10 version of these generators designed to charge the batteries of the KRU-2 “cooperative radio center” states that the thermocouples last for about 4,000 hours +before the internal resistance of the thermopile becomes too high to service the load.14 This referenced 4000 hours would suggest that the generators may have had a practical lifetime of 3 years or less if in continuous service, but that is not necessarily the case. The KRU-2 was initially designed to accept power from a wind generator to charge the batteries, in which case the thermoelectric generator would have been a backup device. An article found on the Internet states that the TZGK-2-2 generator was rated for 5,000-hour service life.15 The article also describes a lower-power generator designated TZGK-9 (9-volt output at 300 mA) with a service life of 10,000 hours, which was developed to power transistor radios. It may not have been produced in significant quantities since rural electrification had grown considerably by the time Soviet transistor radios reached significant production levels. No other references to the TZGK-9 have been found. +Fig. 7. Bundles of TC slabs in groups of 4 and 6. (www.mobipower.ru) + + + 82 The AWA Review +A Soviet Era Broadcast Receiver System of the 1950s for Remote Locations +New old-stock (NOS) TZGK-2-2 generators have been found in South America, Africa and Eastern Europe. These were most likely used at Industrial Trade Shows, available for retail sale and maybe also for distribution as aid to Communist Party affiliated activities. They rarely show up for sale on eBay, but when they do, asking prices are well above $800 and shipping to the United States can add another $250. However, they don’t seem to attract many bids. The TZGK-2-2 and TGK-3 generators are stamped with serial numbers. Images found on the Internet have shown numbers ranging from 43,000 to 84,000. There were also three examples that use a letter plus a 5-digit number. Therefore, something around 50,000 may have been manufactured over a ten-year period. (This does not include other models.) +Conservation and Restoration of the Generator +The TZGK-2-2 generator was in very poor condition when it was acquired, and there was little expectation of being able to make it presentable for exhibition. Resistance measurements revealed that the 9-volt bias-circuit thermocouples were almost open circuited. The 90-volt circuit measured an erratic 20kΩ to 50kΩ and the 1.2-volt circuit measured a few hundred ohms. In order to determine if it was possible to generate an electric current, the 1.2-volt and 90-volt circuits were connected in series, and heat was applied to the core with a 1,100-watt heat gun. After 5 or +10 minutes of blowing heat through the core, the open circuit voltage climbed to about 15 volts. At that point a single white LED was connected to the circuit and the LED did light! But not very brightly. The series resistance of the circuit was simply too high, perhaps due to the heavy corrosion at the ends of the thermocouple slabs. It was clear that restoring the electrical connections would require the total disassembly of a thermopile filled with asbestos sheeting and asbestos filled caulking. The generator certainly appeared to have been in service for a considerable period of time, so that the thermocouples were probably nearing their end of life anyway. Since there was no point in trying to make it service as a practical source of current, the goal changed to preserving the unit as a historical artifact. At the time of acquisition, the lamp burner was heavily rusted with the nickel plating almost completely gone from some parts (see Fig. 8). The rusted kerosene font had a 2mm pin hole rusted in the bottom. The original flue had been replaced by a scrap length of aluminum pipe. The original nickelplated “sash chain” from which the generator hangs was missing and replaced with incorrect welded-link chain. The lamp burner is made of four stampings that are swaged together. Some of the rust could be scraped off to the point that it could be re-plated with nickel, but other parts of the same swaged assembly were so heavily rusted that virtually no good metal existed on which to plate. Consequently, the assembly was scraped and wire brushed, + + + Volume 30, 2017 83 +Lozier +cleaned with a solvent in an ultrasonic cleaner, sprayed with a zinc-rich cold galvanize paint, and finished off with a coat of decorative nickel lacquer. The metal around the pin-hole in the bottom of the font was sound enough to scrape down to bare steel, insert a fragment of copper braid into the hole, and flare the braid on the inside by fashioning a steel-rod tool that could be worked from the kerosene filler opening. The braid was then flooded with low-temperature silver solder and the bump was filed down to an almost flush surface. There was no point in filling the lamp since electrical tests indicate that the generator thermocouple connections have corroded to the point it surely cannot deliver the minimum of approximately 1.6 watts to operate the 4 to 6 tube radios intended to be powered by the generator. One can find two versions of the kerosene font on the Internet. One is +silver colored and the other is green. Fortunately there were traces of the original paint visible on perhaps 5% of the font and a few small spots where the remaining paint was thick enough to scrape with a razor knife to reveal the true color. It is a spruce-green enamel that is easy to match with commonly available spray lacquers. There was very heavy rusting on both the nickel-plated steel thermopile end caps and most of the U-channel steel clamp bars holding the radiator fins in place. After soaking the clamp bar screws overnight with Liquid Wrench penetrating oil and using light hammer blows, the screws came loose. Two of the clamp bars still had more than 95% of the original nickel plate, so after cleaning, they were given a coating of high-temperature clear lacquer to attest to the fact that these were indeed originally nickel plated. The other clamp bars were so heavily rusted that they were simply cleaned in an ultrasonic cleaner, sanded level, sprayed with a coat of the cold galvanized paint, and finished with a coat of the decorative nickel colored lacquer. Because of their placement at the bottom of the radiator fins, the difference between the original nickel plate and the nickel colored lacquer is only noticeable under critical inspection. The screws and lock washers were cleaned in the ultrasonic cleaner as well, but as an added step, the parts were then soaked in a Sunbelt Chemicals Corp. SMART #3000 “Rust Converter & Metal Treatment.” This was necessary because the very fine metric threads could not +Fig. 8. Burner made of four swaged stampings, some too rusted to be re-plated. (Author’s collection) + + + 84 The AWA Review +A Soviet Era Broadcast Receiver System of the 1950s for Remote Locations +be cleaned effectively with a wire brush. This phosphate conversion solution produces an excellent bonding surface for primers and paints. The fasteners were coated with a high-temperature clear lacquer before installing the screws, and the screws were then painted with a clear lacquer as they were screwed into the tapped holes of the thermopile end caps. Afterwards, the threads were painted again with the clear lacquer to maximize delay in new rusting. The top of the glass globe was sealed and cushioned by a thick but soft asbestos gasket that was missing. A replacement was fabricated of ceramic fiber matting engineered to replace asbestos in just such applications. Fortunately small sheets are available on e-Bay at low cost. Had the original asbestos gasket remained, it would have to be removed for safety reasons because it is positioned so as to be subject to considerable abrasion every time the generator is disassembled for transport or cleaning—unlike the protected asbestos on the generator radiator fins. The pure aluminum radiator fins were first cleaned in solvent to remove cooking grease and then sprayed with a full strength caustic cleaner named SuperClean “Cleaner-Degreaser.” After a rinse, it was washed down with a cloth saturated in a weak acid solution of sodium bisulphate in water, followed immediately with a hot rinse in tap water and a quick force-dry with a hot air gun. This produces a clear matte finish that must be protected by spraying with high-temperature clear lacquer. Sodium bisulfate in granular form is +added to spas and swimming pools to increase the acidity (lower ph); therefore, it is widely available in retail stores and very inexpensive. While the correct 60-cm top suspension chains were missing, the lower chains, springs, spiral wire rings, and flat rings were present, and although very grimy with cooking grease and rust, they cleaned up well enough. Exact duplicate rings were made for the top suspension chains using a scrap piece of steel salvaged from the cabinet of an old microwave oven and then nickel plated to match the originals. I searched for chain that I eventually learned is called “sash chain.” It comes in three different metal gauge thicknesses. This lamp requires the lightest gauge but is apparently only available in 160 foot long bulk reels at about $95. I opted to spend $24 for a 10-foot length of much heavier gauge chain but of the same pattern and scale. The original sheet metal flue was missing. Photos on the Internet indicate that there were two variations of the flue. One is a rolled sheet of steel riveted closed at one end only, and the other is brass, or possibly steel, thin-wall tubing that is nickel plated. Both styles of flue have rolled beads at each end. Finding the correct metric specification tubing would be difficult here in the United States. Fortunately, a local sheet metal shop had an old bead-rolling tool small enough to do the job with rolled sheet steel. The precise length of the flue is only a guess. There appears to be a variation in length from picture to picture in photos found on the Internet. + + + Volume 30, 2017 85 +Lozier +The more than four-meter-long power cord and the termination box are original, but they were in a sorry state requiring radical cleaning, filling of rusted metal with glazing putty, and spray painting (see Fig. 9). The original vinyl insulated wires were filthy, but the vinyl insulation was able to withstand cleaning with the SuperClean brand caustic cleaner. The cable was completely unwrapped to gain access for cleaning. The careful cleaning and application of paints and clear coatings will preserve the appearance for a very long time if exhibited in controlled environments. +More Recent Thermoelectric Generators From time to time in the age of transistor-equipped radios, and in other parts of the world, there have been attempts to make kerosene lantern-powered thermoelectric generators. The argument for this power source is the continuing expense of batteries for radios receiving educational instruction in +areas of extreme poverty. With transistor radios, the generator need only deliver a half a watt of power. From the 1960s onward, developers attempted to use semiconductor base junctions because of their higher efficiencies, but in practice they were apparently not able to develop a cost-effective means of limiting the maximum temperature to which the junctions could be subjected in such lanterns. In bringing these generators to market, there has been little indication that the developers received significant government-sponsored engineering support, subsidized manufacturing, or assistance in distribution, all of which occurred in the former USSR. The net result is that none of the products to date have proved reliable enough or cheap enough to sell into the marketplace. One can search for consumer-grade thermoelectric generators today on the Internet and find a number of products designed to charge cell phones, but in +Fig. 9. The generator termination box duplicates receptacles of standard dry batteries. (Author’s collection) + + + 86 The AWA Review +A Soviet Era Broadcast Receiver System of the 1950s for Remote Locations +evaluating the literature it appears that all these products have the same high vulnerability to excess heat damage. Also, the price of these devices can easily exceed that of a cheap cell phone. Thus, the generators remain more of a novelty for “gadgeteers” with disposable income than a practical solution +for the needy and isolated of the world. However, there are still viable applications for thermoelectric generators. Generators using radioisotopes as a heat source power all deep-space satellites, and there are highly specialized applications for powering remote instrumentation here on earth today. +PART II. SOVIET BROADCAST RECEIVERS POWERED BY THERMOELECTRIC GENERATORS +The second part of this article addresses receivers that could be powered by thermoelectric generators in lieu of a set of non-rechargeable dry batteries. According to the book Reference Broadcasting Receivers, there are at least 12 Soviet battery-powered receivers that were “plug compatible” with the receptacles of the TGK-3 or TZGK-2-2 generators (see Table 1).16 One of these radios now in my collection is a 4-tube Iskra (Искрa) +radio made in 1958 (see Fig. 10), which presents a proper load for the thermoelectric generator described in Part I. The word Iskra translates to Spark, and Spark (1958) is the designation that will be used for this model in the remainder of the paper. Other than having no tubes, this radio is in very good condition with no obvious modifications. Fortunately, the correct Soviet-made tubes were available at a modest cost. +Table 1. Twelve Soviet battery powered receivers that were “plug compatible” with the TGK-3 or TZGK-2-2 generators. +Radio Model a.k.a. Description +Iskra 49 Spark 49 Stamped metal cabinet +Iskra-53 Spark-53 Molded resin cabinet table model +Iskra (1958) Spark (1958) Molded resin cabinet table model +Nov Molded resin midget mantel set +Voronezh Molded resin cabinet portable +Voronezh Molded resin cabinet table model; +3 and 4 button versions +Rodina Wood cabinet table model: +52, 52A, 52M, 52U, 58 + + + Volume 30, 2017 87 +Lozier +This Spark (1958) receiver released for mass production in 1958 is the second update to the ARZ-49 reference design released for production as the Spark 49. The first radio series designed to be equipped with Soviet-made, battery-powered, 7-pin miniature, all-glass envelope vacuum tubes commonly referred in Russian slang as “finger lamps.” The reference design identified as “ARZ-49” came from engineers and designers at the Alexandrov Radio Factory of the Ministry of Communications Industry of the USSR under the direction of A. K. Kulesheva with the +help of the Institute of Broadcasting and Acoustics, also known as the IRPA (see Fig. 11).17 The ARZ-49 reference design was released for limited production as the Spark 49, the first entry in Table 1. A detailed description of the Spark 49 and a follow-on description of circuit changes made for the Spark-53 update appear in the Russian magazine Radio.18 At the same time, a new set of standardized batteries with an unusual configuration was developed to provide the most efficient powering of the radio for 1,000 hours, then considered +Fig. 10. This Spark battery-powered receiver was made in 1958. Note plugs for connection to standard batteries. (Author’s collection) + + + 88 The AWA Review +A Soviet Era Broadcast Receiver System of the 1950s for Remote Locations +to be about a year of typical use. A few years later, another standardized set of batteries is configured to power these “finger lamp” sets for 300 hours. These were designated as a “holiday pack.”19 +The Spark 49 Receiver +The Spark 49 has a three-piece sheet metal cabinet. The front and rear panel were die stamped, and a single folded sheet formed the top, bottom, and sides. Spot welds are used to attach the front panel to the folded sides and small welded brackets support the chassis. For better acoustic properties a thick wood baffle board provides mounting for the loudspeaker. The cabinet is painted in +a textured lacquer to hide sheet metal blemishes. The four-tube superheterodyne circuit uses a 1A1P (1R5) for the mixer frequency changer, 1K1P (1T4) for the intermediate amplifier, 1B1P (1S5) for the detector, AGC and first audio, and a 2P1P for audio power output. (There is no direct U.S. equivalent for the 2P1P.) The tuning range is in two bands: long wave—150 to 410 kHz (2000 to 732 meters) and medium wave—520 to 1600 kHz (577 to 187 m). The performance of the receiver generally meets the electric and acoustic parameters for battery operated broadcast receivers of the 3rd class (the State standard for broadcast receivers GOST 5651-51 effective January 1, 1952).20 In this classification scheme, the “1st Class” receivers were the best with the most features, usually made in limited quantities and often exported to raise hard currency. The 4th Class receivers were the absolute basic 1- to 3-tube “local” receivers and the only ones not using some form of superheterodyne circuit. +Key Spark 49 Receiver Parameters +■ Sensitivity: better than 400 μV. Selectivity at detuning at 10 kHz: 15-20 dB. Image rejection: 20 dB. ■ Rated power to the speaker: 0.15 watt. ■ Acoustic frequency response of the entire receiver path allows the passage of frequencies between 200 and 3000 Hz at no more than 15 dB variation. ■ Harmonic measured sound pressure is not higher than 15%. +Fig. 11. From left to right: V. M. Khakharev, Chief Designer of Alexander radio factory and Stalin Prize winner; I. A. Averin, chief designer; and A. K. Kuleshov, chief designer of the “Iskra” receiver. (Radio, No. 12, 1950) + + + Volume 30, 2017 89 +Lozier +■ The AGC allows the output voltage to change by no more than 10 dB when the input voltage changes 26 dB. ■ Filament current: 0.3 A. Anode current: 6 mA with no signal; average: 12 mA. +Spark 49 Schematic +When choosing a receiver circuit, the main focus was on simplicity and reliability of design as well as obtaining sufficiently high electrical parameters and power efficiency. The receiver is a superheterodyne with a rather low intermediate frequency (IF) of 110 kHz. The IF amplifier has the usual dualcircuit input filter and a single-circuit output filter with aperiodic coupling to the detector. A series resonant circuit is connected to the antenna input to suppress the IF frequency. The local oscillator and IF coils have carbonyl iron cores. Surely the most significant functional feature of this receiver circuit is the provision for a “creeping point” bias voltage for the audio output tube. This is achieved by using a copper oxide diode that rectifies a portion of the audio output obtained from the plate circuit of the output tube. The loudness-dependent audio voltage subtracts from the nominal negative 9-volt “C” bias from the battery pack, allowing maximum amplification while significantly reducing the quiescent plate current of the audio output vacuum tube at low volume. This action significantly reduces the perception of background noise in the receiver because, at low audio signal +levels, the gain of the output tube is reduced. The RC time constant of the circuit is such that distortion caused by having the audio abruptly increase without optimum bias is limited to about 10 milliseconds which is said not to be objectionable. The receiver gives undistorted output power of 0.15 W at rated nominal power supply of 90 volts and 1.2 volts. However, to use the pair of “B” batteries to a final voltage of 60 volts and the filament “A” battery to 0.95 volts at the end of its service life, the listener must be content with much lower power of 80 mW. Therefore, the receiver circuit employs a particularly sensitive dynamic speaker, 1GD-2, which develops an average sound pressure of at least 4 bars at a distance of 1 meter with input power of 0.1 W.21 +Design Revisions Made for the Introduction of the Spark 53 +According to articles in Radio, the metal cabinet of the Spark 49 was replaced by a compression-molded, single-piece cabinet made of a thermosetting resin similar to Bakelite. This same cabinet was also used for the AC-powered Moskovich and again circa 1956 in a demonstration model of a broadcast receiver using Soviet-made transistors.22 The dial scale previously tilted upwards by about 15 degrees was then mounted in the plane of the cabinet front face. Metal tube shields were eliminated, and a two-pin receptacle was added for connection to the “Cable Radio” local network so that the radio loudspeaker could be used to play the + + + 90 The AWA Review +A Soviet Era Broadcast Receiver System of the 1950s for Remote Locations +network audio. There was no switching arrangement within the radio for this input; the listener simply plugged in or unplugged from the receptacle. The “creeping point” bias circuit was revised to employ a third winding on the output transformer to create a bias voltage dependent on the audio signal level that subtracts from the fixed -9 volt bias supply in a presumably more effective manner (see Fig. 12). There were few other electrical circuit +changes made between the two models. However, between 1956 and 1958, the chassis layout and general construction for the Spark-53 was radically revised. This new chassis version was then simply called Spark (again). While the Spark 49 and Spark-53 used traditional coil formers for the RF and oscillator coils, the new mechanical design made use of self-supporting bobbins wound onto thin plastic spools with an internal thread to accept screwdriver-adjustable, +Fig. 12. In the Spark-53 version, a third winding on the output transformer provides the voltage to control quiescent plate current. Also, note primary winding connections for “cable radio” service. (Spark users manual from author’s collection) + + + Volume 30, 2017 91 +Lozier +carbonyl-powdered iron cores. These bobbins are cemented on one side to a die-punched, phenol resin-impregnated, paper board sheet about 1.5mm thick that also serves to hold the wave change switch contacts. The same type of self-supporting coil structure is used for the input and output IF transformers. +Observations of My Spark (1958) Manufactured in 1958 +Cabinet +The molded phenol resin cabinet is very similar to the Spark-53 but different in that a top-center, front face crest feature +has been eliminated. Examination of this receiver from the opened back shows little that is very surprising to the American eye other than the apparent uncommon structure of the IF transformer and the lack of a metal shell to contain it (Fig. 13). +Welding of Joints – a Surprising Discovery +What really caught my eye is the underside of the chassis. In order to remove the cotton braid that covers the battery supply cable for cleaning, it was necessary to unsolder the connections on the underside of the chassis. I was surprised to find that the (presumed) +Fig. 13. Back cover removed on 1958 version of Spark receiver. (Author’s collection) \ No newline at end of file diff --git a/storage/SCRU5YBV/Vol.-30.pdf b/storage/SCRU5YBV/Vol.-30.pdf new file mode 100644 index 0000000..224e773 Binary files /dev/null and b/storage/SCRU5YBV/Vol.-30.pdf differ diff --git a/storage/SGT3IJIQ/Eckersley - ULTRA-SHORT-WAVE REFRACTION AND DIFFRACTION.pdf b/storage/SGT3IJIQ/Eckersley - ULTRA-SHORT-WAVE REFRACTION AND DIFFRACTION.pdf index 9f0bb49..e715fc8 100644 Binary files a/storage/SGT3IJIQ/Eckersley - ULTRA-SHORT-WAVE REFRACTION AND DIFFRACTION.pdf and b/storage/SGT3IJIQ/Eckersley - ULTRA-SHORT-WAVE REFRACTION AND DIFFRACTION.pdf differ diff --git a/storage/TWTVEKE9/.zotero-ft-cache b/storage/TWTVEKE9/.zotero-ft-cache new file mode 100644 index 0000000..8ca88d4 --- /dev/null +++ b/storage/TWTVEKE9/.zotero-ft-cache @@ -0,0 +1,565 @@ +Instruments of Darkness + + + + + Instruments of Darkness +The History of Electronic Warfare, 1939–1945 +Dr Alfred Price +Frontline Books + + + Instruments of Darkness The History of Electronic Warfare, 1939–1945 +A Greenhill Book +First published in 1967 by William Kimber & Co., London Expanded edition published in 1977 by Madonald and Jane’s Publishers, London +Revised hardback edition published in 2005 by Greenhill Books, Lionel Leventhal Limited www.greenhillbooks.com +This paperback edition published in 2017 by +Frontline Books an imprint of Pen & Sword Books Ltd, 47 Church Street, Barnsley, S. Yorkshire, S70 2AS +For more information on our books, please visit www.frontline-books.com, email info@frontline-books.com or write to us at the above address. +Copyright © Alfred Price, 1967, 1977, 2005, 2017 +ISBN: 978-1-47389-564-5 +All rights reserved. No part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any form, or by any means (electronic, mechanical, photocopying, recording or otherwise) without the prior written permission of the publisher. Any person who does any unauthorized act in relation to this publication may be liable to criminal prosecution and civil claims for damages. +CIP data records for this title are available from the British Library +Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY + + + FOR JANE + + + + + Contents +List of Illustrations 9 +List of Maps and Diagrams 10 +Foreword 11 +Author’s Acknowledgements 15 +Prologue 19 +Chapter 1 The Battle of the Beams 21 +Chapter 2 The Instruments 51 +Chapter 3 Discovery 62 +Chapter 4 Towards the Offensive 97 +Chapter 5 The Coming of the Yanks 109 +Chapter 6 Doubts and Decisions 117 +Chapter 7 The ‘Window’ Controversy 124 +Chapter 8 The Pace Hots Up 135 +Chapter 9 Operation ‘Gomorrah’, and After 155 +Chapter 10 Approaching the Climax 179 +Chapter 11 In Support of the Invasion 207 +Chapter 12 The Final Months of the War in Europe 220 +Chapter 13 Climax in the Pacific 240 +Chapter 14 In Retrospect 251 +Appendix A: Main Types of German Surface Radars 259 +Appendix B: Main Types of Japanese Surface Radars 261 +Appendix C: Air Forces, Equivalent Ranks 264 +Glossary: Code-Names, Equipment Designations +and Unit Terms 265 +Index 269 + + + + + Illustrations +The airship LZ-130 Graf Zeppelin (Breuning) 81 Dr Ernst Breuning (Breuning) 81 Knickebein transmitter (Trenkle) 82 Heinkel 111 with Y-Gerät equipment (von Lossberg) 82 Wing Commander Edward Addison (Addison) 82 Heinkel 111 of Kampfgruppe 100 (Trenkle) 83 X-Gerät beam transmitter (Trenkle) 83 Dr R. V. Jones (Jones) 83 The Graf Spee and its Seetakt radar (IWM) 84 Reconnaissance photo of Auderville radar station (IWM) 84 Freya radars at Auderville (IWM) 84 Messerschmitt Bf 110 with Lichtenstein radar (Trenkle) 85 Wassermann early-warning radar at Bergen aan Zee (Chisholm) 85 Derek Jackson (Jackson) 85 Würzburg radar (Trenkle) 86 Generalmajor Josef Kammhuber (Studiengruppe der Luftwaffe) 86 Bruneval radar station (IWM) 86 Giant Würzburg radar on the island of Walcheren 86 (Crown Copyright) +German radar site with barbed-wire defences 87 (Crown Copyright) Himmelbett station (Heise) 87 H2S radar picture and map of Hamburg (Crown Copyright) 88 H2S indicator on a Lancaster bomber (Crown Copyright) 88 Aerial of a Korfu ground direction-finding station (Cockburn) 89 Generalfeldmarschall Erhard Milch (Milch) 89 Oberst Dietrich Schwenke (Schwenke) 89 Generalmajor Joseph Schmid (Studiengruppe der Luftwaffe) 90 Major Hajo Herrmann, with Hermann Göring (Herrmann) 90 Lancaster bomber over Berlin, 16 December 1944 (IWM) 90 B-17 Flying Fortress jamming escort aircraft (IWM) 91 Dr Robert Cockburn (Cockburn) 91 ‘Jostle’ communications jammer (IWM) 91 Junkers 88 night-fighter with SN-2 radar (Crown Copyright) 92 + + + Upward-firing 20-mm cannon in a Junkers 88 (Chisholm) 92 Tail-mounted aerial for SN-2 radar in a Junkers 88 92 (Crown Copyright) +Jagdschloss fighter-control radar (Trenkle) 93 ‘Mandrel’ jamming on a Jagdschloss radar (Trenkle) 93 B-17 bombers being engaged by a flak battery (USAF) 94 The APQ-9 ‘Carpet III’ jamming equipment (USAF) 94 ‘Tuba’ jamming equipment (USAF) 95 B-29 bombers on one of the Marianas islands (USAF) 95 B-29 ‘Guardian Angel’ jamming escort aircraft (USAF) 96 ‘Little Boy’, the atom bomb dropped on Hiroshima (USAF) 96 +Maps and Diagrams +The Lorenz Beam 23 Knickebein beam stations 38 X-Gerät beams during the attack on Coventry 44 The Seeburg Table 57 Himmelbett fighter control stations 60 The ‘Oboe’ system 120 Buck Ryan 128 ‘Serrate’ picture 145 Attack on Hamburg: 24/25 July 1943 159 Attack on Kassel: 3/4 October 1943 180 Attack on Nuremburg: 30/31 March 1944 201 The ‘Ghost Fleet’ 212 Deception operations: night of 5/6 June 1944 215 The Klein Heidelberg system 223 Attack on Bohlen: 20/21 March 1945 234 The Bernhard display 239 +10 Illustrations + + + Foreword +by Sir Robert Cockburn, KBE, CB +(Written in 1967) +World War II was dominated by air power, which permeated every phase of the conflict. The aircraft became a major instrument of offence and defence in the air and a vital weapon in support of ground forces, in maritime warfare, in reconnaissance and in transport. This expansion of air power was stimulated by, and became critically dependent on, a series of remarkable developments in the fields of radar and radio communications. Both sides committed large resources to successive systems of early warning and detection, navigation, target identification and weapon guidance. Under the stimulus of war, technology advanced rapidly and each new system provided greater range, greater precision and greater capacity. Yet by modern standards they were still relatively naïve in concept and were soon found to be vulnerable to interference, deception and manipulation. It was a rude shock to designers to discover how quickly performance demonstrated in the laboratory was nullified in operation against a resourceful enemy; and as the war progressed scientists and engineers pitted their wits against one another to preserve their own systems, and to discover and exploit the weaknesses in those of their opponents. It is this story which Alfred Price describes in Instrument of Darkness. +Alfred Price is a serving officer in the Royal Air Force, at present with Bomber Command; and he has been able to recapture the excitement and drama of a struggle in which new techniques and tactics could have such immediate and catastrophic consequences. But he is also an electronics specialist well qualified to deal with the technical aspects of his subject and to appraise the relative importance of the various countermeasures of World War II. Rarely before or since has it been possible for the scientist in the laboratory to make such a direct impact on military operations. A few black boxes based on a new piece of intelligence, a revealing reconnaissance photograph or observations by a returning bomber + + + 12 Foreword +crew could within a few weeks or months affect the fate of cities and the lives of hundreds of aircrew. Not all black boxes were equally effective; some were at best of psychological value, some were a temporary nuisance, and some were not only useless but positively dangerous. In the heat and fog of war any opportunity, however slight, must be exploited, but in retrospect it is clear that clever devices and adroit tactics were usually of limited value. Trivial weaknesses in a system were easy to exploit but equally easy to remedy, and over-sophisticated jamming and warning methods were incompatible with the nightly holocaust over German targets. Subtle countermeasures like ‘Moonshine’ were effective for special operations where surprise could be exploited, and they played an important part in the spoof invasions of the Pas de Calais. But it was straightforward noise jamming and the massive use of ‘Window’ which was most effective in sustained operations. Alfred Price has profited by the lapse of twenty years to put his story of World War II into perspective. He has gone to a lot of trouble to present at each stage both the British and the German story, and he shows how closely developments on one side were matched on the other. There was, for example, the extraordinary similarity in the evolution of British ‘Window’ and German Düppel. Nowadays it is accepted that major technical advances will occur almost simultaneously in a number of countries, even in highly classified military projects. In peacetime the time scale of development is long enough that a year either way in producing a new weapon may not seriously affect the issue, but in war six months can make the difference between victory and defeat; and it was by such narrow margins that the outcome of the Radio War was determined. Both sides entered the war believing that they possessed in radar a unique advantage over the other; and neither foresaw the profound effect that this scientific breakthrough would have on air operations. In 1940 our own radars were in many respects inferior to the Freya and the Würzburg, and we had no bombing and navigation systems to compare with the Knickebein beams and their successors. At the end of the war the Germans were introducing, well ahead of the Allies, a range of guided weapons, including the pilotless aircraft V-1 and the ballistic missile V-2. But the German High Command did not properly appreciate the pace of development or its inevitable + + + Foreword 13 +impact on operations. For two critical years they failed to maintain the momentum of research in radar, and rapidly lost their initial advantage. By the end of the war British and American equipments were far superior both in performance and in range of application; and the German guided weapons came too late to redress the balance. In particular we were quicker to recognise and exploit the intrinsic vulnerability of radar and radio systems, and the initiative in the jamming war lay firmly in our hands. The importance of the electronic environment not only to aircraft and guided weapons but to the whole range of military operations is now well understood; and one of the most important criteria of any radar or radio system is the ability to discriminate against unwanted and irrelevant information. Vulnerability can be theoretically specified, and allowed for. Nevertheless, jamming and deception are always possible, with sufficient effort. Ideally an economic balance should be struck between complexity and vulnerability, so that the cost of nullifying a system is comparable to the cost of establishing it. But this condition can seldom be met in practice, and Alfred Price’s book is a salutary reminder that the impressive panoply of modern weapons is dependent ultimately on the survival, in war, of their guidance and control systems. + + + + + Author’s Acknowledgements +First Edition +In writing Instruments of Darkness I have been greatly helped and encouraged by the many busy men who have unhesitatingly given me their valuable time: to all of them I tender my grateful thanks. Space does not allow me to mention each one by name, but I am particularly indebted to Sir Robert Cockburn, Professor R. V. Jones, Professor D. A. Jackson, Air Marshal Sir Robert Saundby, Air ViceMarshal E. B. Addison, Air Commodore Chisholm, Dr B. G. Dickins and Mr J. B. Supper and, in Germany, the Studiengruppe der Luftwaffe, the Telefunken Company and Herr Hans Ring. I should like to thank Sir Donald MacDougall for allowing me access to Lord Cherwell’s papers and Mr. R. Bruce and Mr. C. Moore for allowing me to examine documents under their control. Also I am indebted to Mr. L. A. Jackets and the staff of the Air Historical Branch for much of the material I have used. I must stress, however, that I alone am responsible for the opinions expressed. My thanks go to Her Majesty’s Stationery Office for permission to quote from The Strategic Air Offensive Against Germany 1939–1945 by Sir Charles Webster and Noble Frankland. I should also like to thank Messrs. Cassell and Co. for allowing me to quote from Winston Churchill’s The Second World War; Messrs. Methuen and Co. for permission to quote from The First and the Last by Adolf Galland; Group Captain J. R. D. Braham for the use of the passage from his autobiography Scramble; and the proprietors of the Daily Mirror for permission to reproduce the Buck Ryan cartoon strip. I should like to record my debt to my wife, who gave valuable support when the going was tough, and my mother, who helped with the German translations. + + + 16 Author’s Acknowledgements +This Edition +In the thirty-seven years since the initial appearance of this book, important additional material has become available. This completely revised edition takes the story up to the time of the Japanese surrender in August 1945, and details the huge US efforts in this area in both the European and the Pacific theatres of operations. I am grateful to the Association of Old Crows, Washington DC, for permission to use material from Volume 1 of The History of US Electronic Warfare, which I wrote to their commission. On a sad note, I must mention that almost all of the men and women I interviewed for this book are no longer alive. Let these pages serve as a memorial to their achievements. + + + ‘The instruments of darkness tell us truths, +Win us with honest trifles, to betray’s +In deepest consequence.’ +Shakespeare, Macbeth + + + + + Prologue +On the evening of 2 August 1939 the giant airship LZ130 Graf Zeppelin lifted off from her base at Frankfurt-am-Main and climbed slowly into the night sky. Leaving the German coast near Cuxhaven, she rumbled out over the North Sea heading for a designated search area off the coast of Great Britain. The LZ130, last of the long line of rigid airships built in Germany, had been designed to fly on the trans-Atlantic passenger service in conjunction with her sister ship, the LZ129 Hindenburg. Before the new airship was completed, however, Hindenburg came to a fiery end. With her died the notion of the airship as a passenger-carrying vehicle. For a time, Graf Zeppelin had no formally assigned role. Then, in the spring of 1939, she was modified for a quite different task. If war came, Luftwaffe intelligence officers would need to know the use potential enemies made of the radio spectrum for communications, navigation and even radar systems. Without such knowledge, and the method of operation and location of these systems, countermeasures would be impossible. Graf Zeppelin’s luxurious passenger compartments now carried a battery of radio receivers and a team of signals experts to operate them. The airship was the world’s first airborne electronic intelligence, or Elint, collector. From April 1939 the Graf Zeppelin flew a series of missions along Germany’s eastern and western frontiers, hunting for radio and other signals of interest emanating from neighbouring countries. On 12 July she ventured over the North Sea, and reached a point about a hundred miles off Middlesborough before turning for home. The mission on 2 August was a more determined attempt to examine the radio spectrum in the skies around Great Britain. For that mission the airship carried a crew of forty-eight, who included a twenty-five-strong team of radio specialists under the command of Dr Ernst Breuning. The airship crossed the North Sea and flew close to the east coast of Scotland, taking care to remain outside territorial waters. She then turned around and flew southeast down the coast to a point abeam Lowestoft, before returning to Germany. + + + While the Zeppelin was within their cover, Britain’s newly erected line of ‘Chain Home’ radars reported her every move. When she passed Aberdeen an RAF Magister training plane took off to get a closer look at the airship, and for a time flew in formation with her. Given the amount of British radar activity over the North Sea, it is surprising that the radio operators aboard the Zeppelin failed to identify British radar signals. Interviewed in 1969, Ernst Breuning told the writer that his team had concentrated their search on the radio spectrum above 100 MHz. That was where early German radars operated, and it seemed reasonable to expect that British radars might do the same. In that part of the spectrum the listeners found none of the expected pulsed radar signals. They did, however, hear transmissions from the new VHF radios being developed in Britain for the RAF. Breuning and his team did make a cursory search in the 20–50 MHz band – which was in fact that part of the spectrum where the early British radars operated. There the listeners found some pulsed signals, but these were discounted. The transmissions sounded just like those picked up during earlier flights, identified as coming from a station in Germany conducting experiments to measure the altitudes of the layers of ionised gas that surround the earth. Missing the British radar signals was an easy enough mistake, given that the German radio operators were learning the rudiments of Elint ‘on the job’ and their receivers had not been designed for this task. Graf Zeppelin’s marathon flight lasted 48 hours and covered a distance of 2,600 miles. It was the longest she would ever make. Less than a month after she returned from her sortie, on 1 September 1939, Germany invaded Poland. Within a couple of days, Great Britain and France entered the conflict in support of their eastern ally. With a major war on its hands, the Luftwaffe saw no further role for the big airship and she was scrapped. Graf Zeppelin’s unsuccessful missions off the coast of Great Britain are of historical interest only, for they achieved little of military value. Yet the notion of searching the radio spectrum for enemy or potential enemy signals, as a prelude to countering them, was an idea whose time had come. The airship’s flights marked the first tentative steps in a completely new form of warfare, one whose significance both sides would quickly learn. +20 Instruments of Darkness + + + Chapter 1 +The Battle of the Beams +‘During the human struggle between the British and German air forces, between pilot and pilot, between AA batteries and aircraft, between ruthless bombing and the fortitude of the British people, another conflict was going on step by step, month by month. This was a secret war, whose battles were lost or won unknown to the public; and only with difficulty is it comprehended, even now, by those outside the small high scientific circles concerned.’ +Winston Churchill, Their Finest Hour +The truth about military intelligence work is that much of its success depends on chance, and much upon tenacity. Little of it is glamorous in the way that readers of espionage thrillers would believe. In the case of a secret device to guide bombers to targets, for example, in time of war it is usually only a matter of time before an aircraft carrying it is shot down and falls in hostile territory. Then, a diligent examination of the wreckage should reveal its existence and survivors, perhaps still shaken after narrow escapes, may be induced to talk under interrogation. Aircrew cannot be expected to memorise detailed lists of radio frequencies, callsigns and the geographical positions of beacons. If that information is to be used in the stress of action, it has to be written down and taken on the sortie. Sooner or later, one of those briefing sheets is bound to be captured. If the system involves radio beams, those investigating it have another clear advantage: such beams cannot be concealed. One has only to look carefully enough and they will be found. Once the transmissions are found, they can be analysed and their purpose deduced. Thus, a handful of intelligence officers can have a bearing on the conflict that is out of all proportion to their numbers. This was why, on the night of 21 June 1940, Flight Lieutenant Harold Bufton came to be patrolling in the darkness over East Anglia in a twin-engined Anson aircraft. In the rear cabin his wireless + + + operator, Corporal Dennis Mackey, carefully searched the ether with his radio receiver. Suddenly Mackey found what he was looking for: a series of Morse dots, sixty to the minute, piercingly clear in his headphones. As the Anson continued on its heading, the dots merged into one steady note. A little later, the steady note broke up, not into ‘dots’ but into Morse ‘dashes’ at the same steady rate of sixty to the minute. Later in the flight, a second radio beam was located. After he landed at his base at Wyton, Bufton reported: +1. There is a narrow beam approximately 400–500 yards wide, passing through a position one mile south of Spalding, having dots to the south and dashes to the north, on a bearing of 104° to 284° True. 2. That the carrier frequency on the night of 21st–22nd June was 31.5 mc/s, modulated at 1,150 c/s and similar to Lorenz in characteristics. 3. That there is a second beam having similar characteristics but with dots to the north and dashes to the south synchronised with the southern beam, apparently passing through a point near Beeston on a bearing lying between 60° and less than 104°. +In terms of the effort involved, the flight of the Anson with the two-man crew was far removed from the Graf Zeppelin’s abortive Elint collection mission off the coast of Great Britain almost a year earlier. Yet in intelligence collection, success is often unrelated to effort involved. The Anson had located a couple of radio beams emanating from Germany, which intersected over the important Rolls-Royce aeroengine factory at Derby. It was a highly significant discovery. +*** +To observe the background of that discovery, we need to look briefly at some scientific developments that had taken place in Germany in the early 1930s. There the Lorenz Company had developed a blindapproach system to help aircraft find airfields in bad weather. The so-called ‘Lorenz System’ used two adjacent radio beams to mark a path extending up to thirty miles from the airfield. In the lefthand beam Morse dots were transmitted, and in the right-hand beam Morse dashes. The signals interlocked, so that where the two beams overlapped a listener heard a steady note. Aircraft navigated +Instruments of Darkness +22 + + + by flying down the steady-note zone until they came to the beams’ transmitter. By the mid-1930s the Lorenz system was in widespread use by civil airlines and some air forces. The Royal Air Force used it, as did the Luftwaffe. In Germany Dr Hans Plendl, a specialist in radiowave propagation, then adapted the Lorenz system to assist aircraft to attack accurately at night or in bad weather. This system became the X-Gerät (‘X-device’) which employed six Lorenz-type beams. Marking the approach to the target were three such beams, one coarse and two fine, all transmitted on different frequencies and all pointing straight at the target. The other three beams crossed the approach beams at three points leading up to the bomb-release point. The X-Gerät radio beams were transmitted on frequencies between 66 and 75 MHz (see map on p. 44). +A bomber using X-Gerät followed the approach beam to the target. When it was 50 km (30 miles) from the bomb-release point, the aircraft flew through the first crossbeam. That served as a warning that it was time to line up accurately in the approach beam. When it was 20 km (12 miles) from the bomb-release point, the aircraft flew through a second crossbeam. As it did so, the navigator pressed a button to start one hand of a special clock, similar to a stopwatch but with two hands that rotated independently. When the bomber was 5 km (3 miles) from the bomb-release point, it passed the third and final crossbeam. When he heard the steady-note signals from +The Battle of the Beams 23 +The Lorenz Beam + + + that beam, the navigator pressed the button on his special clock a second time. The hand which had been moving stopped, and the other hand started rotating to catch it up. The distance from the second crossbeam to the third crossbeam was three times that from the third crossbeam to the bomb-release point (5 km or 3 miles), so the second hand on the clock travelled three times faster than the first. When the hands coincided, a pair of electrical contacts closed and the bombs were released automatically. All in all this was a sophisticated system, considering that it had been produced before World War II. The combination of the clock and the beams provided accurate data on the bomber’s speed over the ground, one of the most important facts to be known for accurate bombing once an aircraft was routed correctly over the target. The Luftwaffe established a special unit to operate with X-Gerät, No. 100 Air Signals Battalion (Luftnachrichten Abteilung 100) based at Köthen near Dessau and equipped with Junkers 52s and Heinkel 111s. Meanwhile Telefunken, a competitor of Lorenz, had produced another blind-bombing system for the Luftwaffe. Called Knickebein (‘Crooked Leg’) this system was much simpler than X-Gerät and it employed only two Lorenz beams. One beam marked the approach to the target, the other crossed the first beam at the bomb-release point. The system was less accurate than the X-Gerät, but it had two major advantages over it. Firstly, the device used the same frequencies – 30, 31.5 and 33.3 MHz – as the Lorenz airfieldapproach receiver fitted as standard in all German twin-engined bombers, so that receiver could pick up the Knickebein signals, and there was no need for the bomber to carry specialised equipment. Secondly, crews trained in the use of the Lorenz airfield-approach receiver could fly the Knickebein beams without further training. Thus Knickebein could be used by the entire Luftwaffe bomber force and not just part of it. The aerial array necessary at the Knickebein ground transmitter was a huge structure, more than 100 feet high and 315 feet wide. The whole thing rested on railway bogies running on a circular track, to allow the beam to be aligned accurately on the distant target. The system’s range depended on the altitude of the receiver aircraft: a bomber at 20,000 feet could receive the signals from a transmitter 270 miles away. The steady-note lane was one-third of +Instruments of Darkness +24 + + + a degree wide, giving a theoretical accuracy of one mile at a distance of 180 miles. By the end of 1939, the Luftwaffe had erected three Knickebein transmitters to cover potential targets in Great Britain and western Europe. One was at Kleve close to the Dutch frontier, a second was at Stollberg in Schleswig-Holstein, and a third was at Lörrach in the southwest corner of Germany. Towards the end of 1939, No. 100 Air Signals Battalion was redesignated Kampfgruppe 100 (KGr 100) and now possessed twentyfive He 111s fitted with X-Gerät. During the campaigns in Norway and France, however, the unit did not use its night precision-attack capability and operated as a normal day-bombing unit. However, soon after the Allied evacuation from Dunkirk in June 1940, Luftwaffe signals personnel began erecting Knickebein and X-Gerät transmitters in Holland and northern France as part of the preparations for attacks on Great Britain. +*** +Until the spring of 1940, the RAF had not considered it likely that German night bombing attacks would prove a serious threat. The general view was that the darkness that hid the bombers from the defences would also hide the targets from the bombers. Dr R. V. Jones, a scientist who a few months earlier had taken up a post at the Directorate of Intelligence at the Air Ministry, had a wide remit. His task was to determine which scientific developments taking place in Germany might affect the air war. He began receiving clues from various sources which suggested that the Luftwaffe possessed, or would soon possess, a radio system to guide bombers to their targets at night or in bad weather. In March 1940, an He 111 bomber crashed in England. In the wreckage, searchers found a scrap of paper which stated: +Navigational aid: radio beacons working on Beacon Plan A. Additionally from 0600 hours Beacon ‘Dunhen’. Light beacon after dark. Radio beacon ‘Knickebein’ from 0600 hours on 315°. +At about the same time, a prisoner admitted under interrogation that Knickebein was ‘something like the X-Gerät’, about which he assumed his captors already knew. He said that a beam was sent from Germany which was so narrow that it could reach London with +The Battle of the Beams 25 + + + divergence of no more than one kilometre (the prisoner had exaggerated the fineness of the beam, though Jones had no way of knowing this). Two months later, the diary of a German airman was found in the wreckage of another He 111. Under 5 March it carried the significant entry: +Two-thirds of the Staffel on leave. In the afternoon we studied Knickebein, collapsible boats, etc. +From these snippets of information Jones deduced that Knickebein – and the X-Gerät which was ‘something like’ it – might be some sort of directional radio beam. The bearing of 315 degrees might point from the northwest coast of Germany to Scapa Flow, an area where Luftwaffe bombers had been active. What seemed unbelievable was the prisoner’s assertion that a radio beam from Germany to London – a minimum distance of 260 miles – could have a divergence of only one kilometre. In fact the prisoner had exaggerated: the beam’s divergence at that distance would have been nearly 11⁄2 miles. By now the Government Code and Cipher School at Bletchley Park was starting to produce a useful stream of decrypts of German radio signals transmitted in high-level Enigma ciphers. One such signal, picked up on 5 June and decrypted four days later, stated: ‘Knickebein at Kleve is confirmed [or established] at point 53° 21' N, 1° W.’ The signal had come from the Chief Signals Officer of Fliegerkorps IV and it seemed that the position, near Retford in Nottinghamshire, might be the location of an illicit radio beacon. A search of the area produced nothing but, significantly, the signal gave the location of a Knickebein. For, apart from being the home of the fourth wife of King Henry VIII, the town of Kleve lay at the part of Germany closest to Great Britain. The next logical step was to examine the radio equipments carried by the He 111 bomber, since this aircraft was linked with each intelligence report on Knickebein. Did it carry any device that could receive beam signals at long range? In October 1939, an He 111 had crash-landed near Edinburgh. At Farnborough, technicians had carefully dissected and analysed each item of the plane’s equipment. At the time they noted that the plane’s Lorenz blind-approach +Instruments of Darkness +26 + + + receiver was far more sensitive than its British counterpart. Might this be the device that picked up the long-range beam signals? At first sight it might seem a simple matter to find out whether the Luftwaffe possessed a long-range radio-beam system. A few flights by aircraft carrying search receivers would settle the matter. But Jones was young and recently appointed and had no such aircraft under his control. Also, he knew he had to play his cards carefully. Jones saw his position as being analogous to that of a watchdog. He had to bark when he saw danger, but if he barked at the first whiff of trouble and none was subsequently revealed, people would learn to disregard his cries. On the other hand if he barked too late, the Luftwaffe could strike unhindered. There could be no mistaking the gravity of the situation, if the Luftwaffe really did possess an accurate method for attacking targets by night at a time when Britain’s air defences were ineffective. There was one man who could secure for Jones the influential backing he needed, and upon whom he could rely for a sympathetic hearing: his tutor at Oxford before the war, Professor Frederick Lindemann. Frederick Lindemann and Winston Churchill had been close friends since 1919, and when Churchill became prime minister in May 1940 the association continued. For all his superlative qualities as a war leader, Churchill had little grasp of scientific matters and he relied heavily on Lindemann to explain these to him. Clearly, if Jones could convince Lindemann of the possible danger of the Luftwaffe radio beams, his battle would be half won. On 12 June Lindemann sent for Jones to discuss another matter. At the end of the conversation, Jones steered the discussion round to Knickebein. Lindemann was unimpressed, however. He said he could not believe that a long-range beam on a frequency of around 30 MHz – the part of the spectrum covered by the Lorenz blindapproach receiver – would bend to follow the curvature of the earth. At that time such signals were thought to travel almost in a straight line, which limited their effective range to about 180 miles if the receiving aircraft was flying at 20,000 feet. That fell far short of the 260-mile range necessary to reach London from the nearest point in Germany. On the day after the unsuccessful encounter, Jones returned to Lindemann’s office carrying an unpublished paper he had discovered. Its author was Thomas Eckersley, scientific advisor to +The Battle of the Beams 27 + + + the Marconi Company and a leading authority on the propagation of radio waves. The paper contained a series of graphs to illustrate the maximum ranges at which radio signals on various frequencies could be received. By taking the extreme end of one of the curves, it looked as if signals on 30 MHz might be picked up by an aircraft flying at 20,000 feet over much of England, provided the transmitter was situated on high ground in Germany. That satisfied Lindemann, who immediately wrote to the Prime Minister: +There seems to be some reason to suppose that the Luftwaffe have some type of radio device with which they hope to find their targets. Whether this is some form of RDF [radar] . . . or some other invention, it is vital to investigate and especially to seek to discover what the wavelength is. If we knew this, we could devise means to mislead them; if they use it to shadow our ships there are various possible answers . . . If they use a sharp beam this can be made ineffective. With your approval I will take this up with the Air Ministry and try to stimulate action. +Before passing the note to Sir Archibald Sinclair, his Secretary of State for Air, Mr Churchill jotted a brief comment at the bottom: ‘This seems most intriguing and I hope you will have it thoroughly examined.’ Now Jones had the big guns firing for him. Sinclair acted promptly and on the following day, 14 June, he placed Air Marshal Sir Philip Joubert in charge of the investigation. On that very day RAF interrogators were questioning another prisoner, who stated that Knickebein was a bombing device involving two intersecting radio beams which could be picked up by the aircraft’s Lorenz receiver. He added that bombers had to fly very high to pick up the beam signals at long ranges. For example, to receive the signals over Scapa Flow the aircraft had to be above 20,000 feet. Jones observed that from Scapa Flow to the nearest point in German-controlled territory – in western Norway – was 260 miles. That was exactly the same distance as from London to the nearest point in Germany. This intelligence was available in time for a meeting Air Marshal Joubert had called for 15 June, attended by Lindemann and Jones. Now there was sufficient evidence to justify bringing more people into the picture, and Joubert summoned a further meeting for the +Instruments of Darkness +28 + + + following afternoon. In addition to Jones the attendees included Air Chief Marshal Sir Hugh Dowding, C-in-C Fighter Command, and Air Commodore Charles Nutting, the RAF Director of Signals. Jones recounted the available evidence, and it was decided to fit special radio receivers to aircraft to hunt for the beams. Three Avro Anson general-purpose aircraft would be made available, and work began immediately to fit them with the necessary radio receivers. Squadron Leader Rowley Scott-Farnie, representing the RAF signals intelligence service at the meeting, opined that the beams would probably be found on a frequency of 30, 31.5 or 33.3 MHz. He said that every Lorenz receiver found in a wrecked Luftwaffe aircraft was tuned to one of those three frequencies. On the following Tuesday, 18 June, fresh evidence arrived in a miscellany of papers salvaged from a German aircraft shot down in France some weeks earlier. On one of them was written: +Long-range radio beacon = VHF 1. Knickebein (near Bredstedt, north-east of Husum) 54° 39' 8° 57' 2. Knickebein (near Kleve) 51° 47' 5" 6° 6' +That served to confirm some of the earlier pieces of information on Knickebein. If those were the locations of two Knickebein transmitters, that would make sense. Those positions were at points in Germany among the closest to England, but they were well separated to give the greatest possible ‘angle of cut’ between a pair of beams. Jones noted that Scapa Flow lay on a bearing of 315 degrees from Bredstedt, which explained the earlier reference. As if more proof were needed, a wrecked Heinkel provided a further clue. The wireless operator’s log had been recovered intact and it included a list of known radio beacons. At the head of the list was a jotted entry: ‘Knickebein Kleve 31.5’. Each of the other beacons was followed by a radio frequency, and the RAF listening service confirmed that the list was correct for the night in question. It was therefore reasonable to assume that the Knickebein at Kleve had on that night been radiating on 31.5 MHz. That fitted in with Scott-Farnie’s prediction. +The Battle of the Beams 29 + + + That evening, 19 June, an Anson took off on the first flight to search for beam transmissions; its receiver developed a fault, however, and the radio operator heard nothing. On the next night, the 20th, another Anson flew a patrol to look for beams but found nothing – the Luftwaffe had stayed at home. Even as that aircraft was airborne, however, an RAF intelligence officer was literally piecing together another clue. A Luftwaffe wireless operator had baled out of his crippled aircraft over England. Soon after landing the airman, more conscientious than many of his compatriots, realised he still had his notebook. He carefully tore it into more than a thousand pieces, but as he attempted to bury them he was captured and the pieces were recovered. The reward of much hard work was a table of data, which confirmed the positions of the Kleve and Bredstedt transmitters and the operating frequency of the former; it also gave the frequency of the latter as 30 MHz. Thus, by the morning of 21 June, R. V. Jones had established the positions and frequencies of two of the Knickebein transmitters. The findings were timely, for that very morning Churchill decided to summon a top-level meeting at No. 10 Downing Street to discuss the latest intelligence on the German radio beams. Among those present were Sir Archibald Sinclair (Air Minister), Lord Beaverbrook (Minister of Aircraft Production), Professor Lindemann, Sir Cyril Newall (Chief of Air Staff), Sir Hugh Dowding and Sir Henry Tizard (Scientific Advisor to the Air Staff). When Jones arrived, the meeting had already started. He arrived to find a discussion in progress on whether aircraft could in fact be guided by long-range radio beams. Both in rank and age, Jones was by far the most junior person present. He sat there waiting to be asked to speak, and after a few minutes the Prime Minister questioned him on a technical point. That was the excuse Jones had been waiting for and he asked ‘Would it help, sir, if I told you the story from the start?’ Churchill said it would, and Jones recounted various pieces of evidence supporting the theory that the Luftwaffe possessed a system of radio beams to direct bombers on to targets. That convinced the meeting that here was a matter worthy of further investigation. The axis of the discussion shifted from ‘Do the German radio beams exist?’ to ‘How can we find out more about them?’ That afternoon Air Commodore Nutting summoned Jones and Eckersley to his office, to discuss the technical details of the beam +Instruments of Darkness +30 + + + transmissions that might be used by Luftwaffe bombers over England. Then Eckersley dropped his bombshell: despite the series of graphs he had previously drawn, he said he could not agree with the widely held explanation of Knickebein. He said he did not believe that radio signals on 30 MHz would bend to follow the curvature of the earth. Jones pressed Eckersley to explain why he had produced the set of graphs upon which he, Jones, had relied so heavily in the Cabinet Room that morning. Eckersley renounced them, saying they applied to a different case when he had tried to stretch his theory. The feelings of Jones can be imagined more readily than described, since he had used Eckersley’s graphs to convince Lindemann that a long-range beam following the curvature of the earth was a possibility. Obviously someone was barking up the wrong tree; Jones could only hope it was not himself. (In fact partial bending to conform with the earth’s curvature does occur with transmissions on 30 MHz, but its extent was not realised in Britain at the time.) While Jones pondered on this unexpected development, the hunt for the beam signals continued. That very night, the patrol by Bufton and Mackey picked up the German beam transmissions over the Midlands, as described at the beginning of this chapter. Appropriately, given the seriousness of the new threat, the RAF code-named the beam system ‘Headache’. It fell to Air Commodore O. G. Lywood to initiate countermeasures. Wing Commander Edward Addison, one of Lywood’s staff officers, latter recalled: +One day he [Lywood] called me in and told me that a young fellow from scientific Intelligence called Jones had produced an extraordinary story of the Luftwaffe using a beam over this country to bomb London. It was known as Knickebein. He said: ‘I can’t tell you how he came by this information, but he has. It looks extremely dangerous. What do you think we ought to do?’ +Addison suggested the formation of a specialised organisation to counter the German beams. Lywood agreed, and placed Addison in charge. Addison’s new unit, No. 80 Wing, was hastily established and set up its headquarters at Garston near Radlett in Hertfordshire. Thing were now moving ahead rapidly, but one further element of the defences was required. There needed to be an organisation +The Battle of the Beams 31 + + + to build the specialised jamming devices to render the German beams unusable. That task fell to Dr Robert Cockburn, a young physicist who had recently joined the Telecommunications Research Establishment (TRE) at Swanage. He and a small team began work to design and build tailor-made jammers to counter Knickebein. The process of building specialised jammers would take time, however, and time was short; an all-out bombing offensive on Great Britain might begin any day. Accordingly, Addison requisitioned several diathermy sets (devices used in hospitals to cauterise wounds) and had these modified into crude spark transmitters to transmit a ‘mush’ of radio noise on the Knickebein frequencies. RAF personnel installed the diathermy jammers in selected police stations, where the duty constable had instructions to switch them on when instructed to do so from No. 80 Wing headquarters. Addison also secured some RAF Lorenz airfield beam-approach transmitters and modified these to radiate a beam similar to that put out by Knickebein. His idea was to produce a fake beam that could be laid across the German beam, in the hope that the German bombers might wander off course without the crews noticing it. Monitoring flights revealed that the deviation produced by the lowpowered device was negligible. Nevertheless, in the interests of getting countermeasures up and running as soon as possible, a few of these systems went into service with No. 80 Wing. An important component of the new wing was the flight of Anson aircraft commanded by Squadron Leader R. Blucke, which now flew patrols each night to determine the directions and crossing points of the German beams. Initially this unit operated under the cover name of the Blind Approach Training and Development Unit (BATDU for short). In September 1940 the unit was renamed the Wireless Intelligence Development Unit (WIDU), but its work continued exactly as before. Soon after the Anson aircraft had first picked up Knickebein signals, the RAF listening service discovered that suitably equipped ground stations could also receive these signals. Several outstations were now set up, which passed information on the beams’ frequencies and of their dot or dash transmissions to No. 80 Wing headquarters where they were plotted out on a special map. Those ground stations alone could not provide an exact picture of the German beam patterns. Yet they provided a useful cue for the Ansons +Instruments of Darkness +32 + + + to get airborne, and greatly narrowed the search area for their crews to hunt for the beams’ steady-note lanes. To underline the increasing potency of the new threat, during August RAF listening posts picked up signals that were traced to two new Knickebein transmitters erected on the north coast of France. One was at Greny near Dieppe, only 120 miles from the centre of London. The other was at Beaumont-Hague near Cherbourg, 150 miles from the capital. While Addison requisitioned equipment for his makeshift jamming organisation to begin operating, there was another commodity he urgently needed: capable personnel. With the highly technical war that was now in the offing, he had no use for other units’ misfits and throw-outs. He needed the best material available. Fortunately, interest in the wing’s well-being extended from the prime minister down, and Addison had free reign to choose people for his unit. A particularly useful source of recruits was the community of peacetime amateur radio enthusiasts. +*** +At the same time as the wing began its improvised countermeasures to Knickebein, it took control of another jamming commitment that had been initiated some months earlier. Luftwaffe aircraft made considerable use of radio beacons set up in friendly territory, to assist navigation. Each German radio beacon transmitted its identification letters in Morse code, then a 50-second tone to allow aircraft radio operators to take bearings on the beacon. At that time in Britain there were fears that German agents might plant radio beacons near targets, to guide in their bombers. To counter the beacons, Post Office engineers had devised a clever device known as the Masking Beacon, or ‘Meacon’. The device comprised a receiver and a transmitter located about 12 miles apart. The receiver was linked to a directional aerial, aligned on the German beacon it was to counter. The receiver picked up the German beacon’s emissions, amplified them and fed them by landline to the ‘Meacon’ transmitter. The transmitter then radiated an exact replica of the German beacon signal, with the same Morse identification letters and 50-second tone, exactly in step with the German signals. But the ‘Meacon’ transmitter was, of course, in a quite different position. +The Battle of the Beams 33 + + + Professor Lindemann explained the operation of the Meacons in a paper he wrote for the Prime Minister early in August. The Luftwaffe, he said, had nearly eighty radio beacons in Germany, Norway and northern France, operating on the medium and long wave bands. Not more than twelve of these beacons were in use at any one time, the remainder being held in reserve. Different groups were used on different days. Lindemann continued: +There are two ways of dealing with such beacons. The first is to jam them, i.e. to make so much disturbance in the ether that their signals cannot be received. If one compares them with lighthouses, it is like turning on the sunlight so that they would become invisible. This method is difficult because they operate on so many different wavelengths that we must produce very strong signals in each band to cover the lot... Further, each lighthouse has its own colour (wavelength) which has to be outmatched, so that the general glare must be produced over the whole spectrum, ranging from 30 metres to 1,800 metres. In order to cover this range eight very powerful stations would be required, but this leads us to another difficulty. If we had eight such stations, the Luftwaffe would soon get to know where they were and could use them as lighthouses to guide them to their targets. It is much easier to fly towards a beacon than to navigate away from it on back bearings. In order to prevent this it would be essential to link our jamming stations in groups of three, making each group of three flash simultaneously. If this is done (though there is no exact optic analogy), the radio receiver cannot tell from whence the beam comes, so these could not be used as homing stations. On the other hand, this would imply the use of 3 x 8, i.e. 24 powerful stations, which would mean that all our home wireless had to be sacrificed for this purpose. By giving up the BBC and all other transmitters, this arrangement could possibly be made in four to six weeks. Even then we should have difficulty if the Luftwaffe chose to use, instead of their normal beacons, the super high-power stations normally used for wireless purposes in France and Holland. This brings us to the second method, called ‘Masking’. For this purpose, we require a number of small stations in England which +Instruments of Darkness +34 + + + pick up and repeat the German signals exactly in phase. If this is done, the wireless operator in the German machine cannot distinguish between the signals from his beacon and the echo signal from our station, and his direction finding is completely set to nought. Since these echo stations are in exact phase with the ground stations it is impossible to home on them, so that they cannot be used as a navigational aid by the enemy as a German station could. They are admittedly slightly more complicated to set up, but we have already six in action and a further nine will be operating within a week. Providing the Luftwaffe do not use more than twelve stations at a time we can mask them completely with these fifteen stations so this method of navigating will be nullified. All masking beacons are being provided as rapidly as possible and it is hoped in a few weeks to be able to cope with any possible German orchestra of beacons. Obviously, if we had eighty, we could deal with them if they turned on all their eighty beacons. On the other hand it is unlikely that they will use too many at a time as it would certainly confuse their own pilots very much. Thirty stations would probably suffice for anything the Luftwaffe are likely to do. +*** +By 18 August 1940, No. 80 Wing had nine ‘Meacon’ stations in operation. Two days later, the strange assortment of hastily erected ‘Headache’ stations – modified diathermy sets and Lorenz transmitters – was ready to begin radiating on the Knickebein frequencies. It was a close-run thing for, on 28 August, a force of 160 bombers delivered the first heavy night attack on a British city, Liverpool. The bombers returned to the port in similar strength on each of the following three nights. The expected night onslaught had opened. On 7 September, the bombers shifted their night attacks to London. From then until 13 November an average of 160 aircraft raided the capital each night, except for one occasion when bad weather prevented operations. This assault coincided with the deployment of the first of the jammers which Robert Cockburn and his team had designed to counter Knickebein. The RAF code-name for the German beam system was ‘Headache’, so the code-name for the antidote system – the jammer – was ‘Aspirin’. The latter +The Battle of the Beams 35 + + + transmitted Morse dashes on the beam frequencies. Those dashes were not synchronised with the beam signals, rather they were superimposed on them. The intention was that when a bomber pilot heard the Morse dashes, he would turn in the required direction. But when he reached what should have been the central steady-note lane he continued to hear dashes and so tended to overshoot. When in the ‘dot zone’, he heard a mixture of dots and dashes which did not resolve themselves into a clear note. The ‘Aspirins’ were prescribed for the more important sites, where they replaced the less efficient modified diathermy sets and Lorenz transmitters. Both of the older types of equipment were then moved to new sites, to increase the area where jamming cover was available. Throughout this period there was discussion as to whether it might be possible to design a countermeasures system to ‘bend’ the German beams, to push the bombers off course without their crews realising it was happening. Technically speaking, such a device was feasible. Such an elegant countermeasure would have taken time to design and build, however, and Addison had to meet a major threat to Britain’s cities; he did not have time to develop subtle approaches to the problem. In the event there was never any deliberate bending of the German beams, though it is widely believed that this was the case. Possibly the story began as a ‘plant’ by British intelligence, to weaken Luftwaffe confidence in Knickebein. As Addison told this writer: +Whenever anything unusual happened, people thought it was us. At the time we worked in such secrecy that when these funny ideas got around we had no means of correcting them – even had we wanted to. On one occasion a German aircraft unloaded its bombs in the castle grounds at Windsor. The next morning, the Comptroller of the King’s Household rang me; he was very cross, and wanted to know why we had bent the beams over Windsor – His Majesty might have been killed. It was the usual case of a lost German getting rid of his bombs – and we got the credit or the blame, depending on where they fell. +Dr Robert Cockburn voiced similar views during an interview with this writer. He commented: +Instruments of Darkness +36 + + + The myth has been established that we bent the beams. In fact we didn’t. I did rig up a system using a receiver at Worth Travers, near Swanage, and a transmitter at Beacon Hill, near Salisbury. I was going to pick up the modulation of the Knickebein, retransmit it, and thus push the beam over. In other words, my transmitter would have produced a beam similar to the German ground station but pointing to where I wanted it to. It was all very nice, but it didn’t happen. By the time the system was ready, the other jamming methods were in full swing and we could not spare the time or the effort to bring out a new system to supplement the old. So the deliberate bending of the German beams, which I had worked out, never happened. +When No. 80 Wing took over the Beacon Hill jamming station the unit used it to transmit unsynchronised Morse dashes, just like the other ‘Aspirins’. In October 1940, Edward Addison was promoted to group captain. No. 80 Wing now comprised twenty officers and 200 men and women, and operated fifteen ‘Aspirin’ sites to jam the Knickebein beams. How effective was this effort? The British ‘official line’, published in several books including the earlier editions of this one, was that the jamming was so effective in disrupting the Knickebein beams that the system fell soon out of use. The truth of the matter is rather different, though the outcome was the same. The Knickebein transmitter at Greny, 120 miles from London, often provided the main beam to the British capital. The BeaumontHague transmitter, 150 miles from the capital, was well placed to provide the necessary crossbeam. If those two transmitters trained their beams on London they could mark out a diamond-shaped patch of sky with sides measuring about 900 yards and 1,600 yards. The threat of over a hundred German night raiders delivering bombs to that degree of accuracy was a fearful prospect, but it never happened. Luftwaffe bomber crewmen who flew over Britain at that time have told the writer that usually they could easily hear the beam signals through the early jamming. Yet, even if it was not fully effective, the presence of the jamming was unsettling to the attackers because it indicated that the defenders were aware of the beams’ +The Battle of the Beams 37 + + + existence and probably knew their location. One Luftwaffe bomber pilot told this writer: +At first we were very excited about Knickebein, a fine new method of navigation and a big help to find our targets. But after we had used it on operations once or twice, we realised that the British were interfering with it. Initially the jamming was weak and it hardly concealed the beam signals at all. But that fact that our enemy obviously knew that the beams existed and that they were pointing towards the target for the night, was very disconcerting. For all we knew, night-fighters might be concentrating all the way along the beam to the target. More and more crews used the Knickebein beams only for range, and kept out of them on the run up to the target. +Instruments of Darkness +38 +Knickebein Beam Stations +The eleven beam stations used during the attacks on Britain are shown. The map also shows attacks made by a Ju 88 pilot with III/KG 1, flying from Roye/Amy. A: raids on Cardiff on the nights of 1 and 3 March 1941, picking up the Beaumont-Hague beam at the coast and flying from there straight to the target. B: Plymouth 21, 28 and 29 April, again using Beaumont-Hague. C: Birmingham 16 May; this time he flew north to pick up the Kleve beam then northwest to find the Stollberg beam and the route to the target. During March and April the bombers often used the same route for repeat attacks. By May it was considered prudent to make a wide detour to avoid the defences in southeast England. + + + Other German aircrew echoed those sentiments, which became progressively stronger as the jamming became more powerful and the night defences became more effective. The primary effect of the jamming had therefore been its effect on the morale of the bomber crews, rather than the disruption it caused to the Knickebein signals. Yet the ‘bottom line’ of the makeshift efforts of No. 80 Wing and Dr Cockburn’s team was that they had successfully neutralised the German beam system. That gave a considerable boost to their prestige both in the RAF and in the corridors of power at Whitehall. It was also a triumph for Dr R. V. Jones and the cause of scientific intelligence; the next time the watchdog started to bark, people would listen. That would soon happen, for the Luftwaffe still had its other beam system. +*** +On 13 August 1940 the Luftwaffe began its large-scale aerial bombardment of targets in Great Britain. On that day the first of the hard-fought daylight battles took place over southern England. After darkness fell, twenty-one He 111 bombers attacked the Nuffield factory at Castle Bromwich producing Spitfire fighters, and the nearby Dunlop tyre factory in Birmingham. The unusual feature of this attack was the inordinately high degree of concentration for a night raid – eleven bombs hit the sprawling collection of factory buildings at Castle Bromwich. The aircraft involved belonged to the special beam-flying unit Kampfgruppe 100, and carried the complex X-Gerät beam system. After its impressive start, KGr 100 delivered night attacks on several other small targets. The high degree of bombing accuracy achieved during the initial attack was not repeated often, however, and usually the attacks were not so effective. Halfway through August, the RAF monitoring service picked up unexplained signals on 74 MHz which appeared to originate from a point on the French coast. Jones code-named the new system ‘Ruffian’. By the end of the month the monitors had noted signals on nearby frequencies, and ground direction finders pinpointed their sources to the Calais and Cherbourg areas. The signals differed from those of Knickebein in their frequency and the keying rate, but they were sufficiently similar to identify them as an aid to navigation. During the following month Jones added further items +The Battle of the Beams 39 + + + to his file on ‘Ruffian’ and after his success with Knickebein, his new fears found ready ears. At the end of the third week in September his report, passed via Professor Lindemann, reached the prime minister’s desk: +It appears that the Luftwaffe are making great efforts to improve the accuracy of their night bombing. A number of new beams on a shorter wavelength than before have appeared. . . One Kampfgeschwader, KG 100 consisting of about forty machines [sic – in fact it was a Kampfgruppe, though the unit’s strength was given correctly], has been equipped with special new apparatus to exploit these beams with which apparently accuracies of the order of 20 yards are expected. With the technique they seem to be developing such a result does not seem impossible. We know the exact location of the sources of the beams in question. The parent beam is on the very tip of the Cherbourg peninsula; the crossbeams are in the Calais region. They will probably not reach much beyond London. Apart from attacks on the machines using the beams, our possible lines of defence would be: 1. to try to destroy the specially fitted KG 100 machines which are stationed at Vannes; home station Lüneburg and reserve station at Köthen; 2. to try to destroy the beam stations (a) by bombing, which would be very difficult since they are almost invisible targets (b) by a special [i.e. commando] operation; 3. to employ radio-countermeasures. +Early on in the investigation, RAF intelligence identified the distinctive footprint of the new series of attacks: great accuracy along a line running from Cherbourg, with a somewhat lower accuracy in range. The heaviest bombs used were 550-pounders. From the early summer of 1940 Luftwaffe signals personnel had worked hard to establish landline connections between each of the major bases and airfields in France, and that service’s main communications network in Germany. Starting in eastern France, they gradually worked their way westwards. As each airfield came on line it ceased using wireless for ground-to-ground communications, a move which deprived the cipher crackers at +Instruments of Darkness +40 + + + Bletchley Park of the opportunity to read their traffic. As luck would have it, however, KGr 100’s base at Vannes lay in the extreme west and so was one of the last to be connected to the network. Thus, from the autumn of 1940 until well into 1941, Bletchley Park was able to deliver to Jones’s office a steady stream of decrypted signals on KGr 100’s activities. On occasions the intercepted signals listed the beam frequencies and alignments for a night’s attack. Yet, at that stage of the war, the painstaking task of decryption often took several days. Although the raids were therefore over long before Jones read the signals, the information they contained was invaluable to build up a general picture of how the system worked. He noted that the beams were aligned to within five seconds of arc, which implied a maximum accuracy of the order of twelve feet at a distance of 100 miles from the beam transmitter. From this, Jones estimated accuracy of the new system to be ‘of the order of twenty yards’. In fact his report exaggerated the accuracy of the system by a factor of about six, but even so it represented a potent threat. To counter the X-beams Dr Cockburn and his team hastily modified the transmitter from an Army gunlaying radar to jam the beam frequencies, and code-named the device ‘Bromide’. When the prototype appeared to work satisfactorily, Cockburn’s section began a crash programme to build sufficient ‘Bromides’ to provide cover for potential targets. The immediate plan was to install these jammers at ground stations between Cherbourg – the source of the approach beams – and the Midland towns, Manchester and London. By the end of September KGr 100 had taken part in more than thirty attacks, more than half of which were on London. For the rest of the attacks the unit usually visited targets alone, attempting precision attacks using the beams. Early in October, RAF intelligence noted that KGr 100 had started dropping 1-kg stick-shaped incendiary bombs during some of its attacks. On the face of it that was a strange development; these small weapons scattered over a large area and could not be aimed accurately, which seemed to nullify the major advantage of the X-beam system. There seemed only one reasonable explanation for the change: KGr 100 was practising to lead the rest of the Luftwaffe bomber force to its targets. Apprised of the new information, Lindemann advised Mr Churchill on 24 October: +The Battle of the Beams 41 + + + There is some reason to believe that the method adopted is to send a few KG 100 aircraft fitted with special devices to assist in blind bombing on these expeditions, in order to start fires on the target which any subsequent machines without special apparatus can use. +The note accurately predicted the course the Luftwaffe would adopt a few weeks later. In the meantime, fate played into the hands of British intelligence in one of the more inept episodes of the secret war. Early on the morning of 6 November, a raiding Heinkel bomber suffered a compass failure over England. After tuning their radio compass to the beacon at Saint-Malo in Brittany, the crew turned for home. When the radio compass indicated that the aircraft had passed over the beacon, the aircraft descended but as it broke the cloud the pilot saw he was still over the sea. This had to be the Bay of Biscay, so he reversed his course and headed back to the beacon. By now his fuel was almost exhausted and, when a coastline came into view, he decided to set the bomber down on the beach. The pilot misjudged his approach, however, and in the resultant crash one crewman was killed and two were injured. The survivors scrambled up the shingle beach where, to their great surprise, they were immediately surrounded by soldiers in khaki uniforms. The beacon in which the airmen had misplaced their trust had been covered by a No. 80 Wing ‘Meacon’ transmitter at Templecombe in Somerset. What the crew had thought to be the southwest coast of Brittany, was in fact the beach at West Bay near Bridport. Some soldiers waded out to the wreckage and secured a rope round it, and all would have been well had a Royal Navy vessel not arrived. The ship’s captain pointed out that, since the bomber was in the sea, its salvage was technically a Navy matter. After some wrangling, the Army grudgingly agreed. The sailors took the line aboard their ship and solemnly towed the aircraft out into deeper water, preparatory to lifting it out. Unfortunately, in the course of that operation, the rope snapped and the Heinkel sank to the bottom. Dawn broke to reveal the upper part of the wrecked bomber protruding from the waves, looking rather like a stranded whale. As the tide receded, the plane’s markings gradually came into view; painted on the rear fuselage in characters nearly four feet high were +Instruments of Darkness +42 + + + the identfication markings 6N+BH. And 6N was the unit code for KGr 100. Professor Lindemann was understandably bitter when he learned what had happened. A week later, he wrote to the prime minister: +The KG 100 squadron is the only one known to be fitted with the special apparatus with which the Luftwaffe hope to do accurate night bombing using their very fine beams. As it is important to discover as much as possible about this apparatus and its mode of working, it is a very great pity that inter-Service squabbles resulted in the loss of this machine, which is the first of its kind to come within our grasp. +All was not lost, however. RAF technicians removed the invaluable X-beam receivers from the waterlogged hulk and, looking somewhat the worse for their immersion, they went to Farnborough for examination. Any last doubts regarding the advanced nature of German radio-beam technique were dispelled by the dates on some of the receivers’ inspection-stamps. They went back to 1938. In the second week of November, the Luftwaffe shifted the burden of its attack from London to the Midlands cities. In the first of these attacks KGr 100 was to lead the bomber force to its target, Coventry. On the afternoon of 14 November the Boulogne headquarters of 6th Air Signals Company – the unit which operated the X-beam transmitters – received its orders on beam alignments from KGr 100’s headquarters at Vannes. It relayed these instructions to transmitters Elbe, Oder and Rhein nearby, and to Weser, the ‘approach-beam’ transmitter, on the Cherbourg peninsula. The approach-beam crossed the English coast near Christchurch, ran to the east of Salisbury and Swindon, and passed over Leamington and Coventry. Shortly before the target city the three ‘crossbeams’ intersected it. That night KGr 100 sent thirteen He 111s to mark Coventry. Soon after 1900 hours, the leading aircraft crossed the Thames. Six minutes later it flew through the first of the crossbeams, and moved into the centre of the main approach beam aligned on the city. On that night, only four ‘Bromide’ transmitters were available to counter the X-beams. One of these, at Kenilworth, lay almost directly beneath the bombers’ run in. Yet the jammers caused the raiders little trouble; the system had been conceived in haste at a +The Battle of the Beams 43 + + + time when too little had been known about X-Gerät. Consequently, although the jammers probably emitted on the correct frequency, the radiated note was modulated at 1,500 cycles instead of 2,000 cycles. The difference – between a whistle and a shriek – is just perceptible to the human ear; but the filter circuits in the German receivers were sensitive enough to pick the beam signals out of the jamming with ease. +The leading Heinkel continued on its northerly course undisturbed and at 1906 hours, three miles south of Leamington, it flew through the second crossbeam. The observer started the automatic bomb-release clock and two and a half minutes later, about a mile east of Bagington, the aircraft flew through the third and final crossbeam. The second pointer on the clock began moving rapidly to catch up with the first. Fifty seconds later the two pointers +Instruments of Darkness +44 +Layout of the X-Beams over Coventry, Night of 14 November 1940 + + + overlapped, the pair of electrical contacts closed and the bombs were released. The time was 1920 hours. During the next 45 minutes, the twelve remaining Heinkels from KGr 100 dropped their bombs on the city, starting some fires. By then the first of the main force of bombers had arrived, and in the hours to follow their loads reinforced the destruction already caused. Yet, even without the assistance of KGr 100, it is likely that the main force of bombers would have found the target with little difficulty. It was a bright moonlight night, with clear skies. Feldwebel Günther Unger of Kampfgeschwader 76 (KG 76), piloting a Dornier 17, attacked later that night. He recalled: +While we were still over the Channel on the way in we caught sight of a small pinpoint of white light in front of us, looking rather like a hand torch seen from two hundred yards. My crew and I speculated as to what it might be – some form of beacon to guide British night-fighters, perhaps. As we drew closer to our target the light gradually became larger until suddenly it dawned on us: we were looking at the burning city of Coventry. +One stream of bombers came in over the Wash, another over the Isle of Wight and a third over Brighton. Altogether 449 bombers hit Coventry during the ten hours of the attack. Between them they dropped 56 tons of incendiaries, 394 tons of high-explosive bombs and 127 parachute mines. The city was hit heavily and several factories were forced to cease production, albeit temporarily. Nearly 400 people were killed and a further 800 were seriously injured. The attackers had the rare benefit of a combination of perfectly clear skies, a full moon, a combustible target (there were many old timbered buildings), and weak anti-aircraft defences. Although the X-Gerät beams played a part in the raid’s success, this should not be exaggerated. Crews in the follow-up bomber units, including Günther Unger, have said the night was so bright that they would have found the city even without the assistance of marking by KGr 100. Meanwhile, examination of the captured X-Gerät receiver had revealed the weakness of the ‘Bromide’ jammer, and within a few days of the attack they had all been modified to transmit the correct jamming note. With modified ‘Bromides’ emerging from Cockburn’s workshop at an encouraging rate, it seemed that a much +The Battle of the Beams 45 + + + more effective No. 80 Wing was ready to counter KGr 100’s next major pathfinder marking effort. Birmingham came under attack on the night of 19 November (by thirteen bombers from KGr 100 and 344 aircraft in the followup force), on the 20th (eleven and 105) and the 22nd (nine and 195). Yet that city suffered nothing like the concentrated damage inflicted on its neighbour. Nor, during the months to follow, would any other British city. At the time British intelligence attributed the sudden deterioration in the effectiveness of KGr 100-led attacks to the improvements made to the ‘Bromide’ jammer. With the benefit of hindsight, however, it is possible to offer a quite different explanation for the failure to repeat the destruction inflicted on Coventry. The steady improvement in Britain’s night air defences during the winter of 1940 forced the Luftwaffe to cease large-scale attacks when there was a full moon. Also, during that period, the raiders had to contend with frequent spells of bad weather. So, when Kampfgruppe 100 led attacks on nights when there was little or no moon and poor weather, against targets that were better defended than Coventry and less combustible, it is not surprising that the results were less impressive. Although other cities suffered damage comparable with that suffered by Coventry in relation to their size – notably Liverpool and Plymouth – in their case it was the cumulative effect of several attacks and not just one. Even when X-Gerät worked perfectly, the weak system of target marking usually mitigated against an effective attack. The Luftwaffe was evolving its technique from scratch, and it still had a lot to learn. For one thing, it employed far too few pathfinder aircraft. Sending ten or a dozen bombers mark the target, for a follow-up attack that might last six hours or more, was not enough. Moreover, the 1-kg ‘stick’ incendiary bomb dropped by KGr 100 to start fires had poor ballistics and was a relatively inaccurate weapon. Even if the initial fires were accurately laid, the pathfinder marking rapidly became diluted as bombers in the follow-up force dropped much greater numbers of incendiary bombs with varying degrees of accuracy. Since the bombers all carried more or less the same types of high explosive and incendiary bombs, it was impossible to tell which fires had been started by pathfinders and which by the follow-up bombers. If there was cloud cover, the follow-up bombers often +Instruments of Darkness +46 + + + failed to find their target even if the initial marking had been accurate. In a later chapter we shall observe how the RAF applied the lessons it learned from the Luftwaffe attacks in 1940 and 1941. In the autumn of 1940, No. 80 Wing took control of a special unit to counter the Luftwaffe pathfinder tactics. If the follow-up raiders aimed their bombs at fires on the ground, why not light fires in the countryside for them to bomb? The job of establishing the necessary decoy fires – known as ‘Starfish’ – fell to a section headed by Colonel J. Turner, one-time head of the RAF Works Department. Since the decoys needed to look plausibly like cities under attack, timing was critical. The fires had to be well alight in time to catch the follow-up attackers, and ideally the bombers should need to fly over a decoy to reach the real target. That called for careful control and good communications. The ‘Starfish’ operation was an integral part of No. 80 Wing’s activities, directed from its headquarters. By the end of November twenty-seven decoy sites were ready for action. The first two ‘Starfish’ were ignited on the night of 2 December 1940, just over two weeks after the Coventry attack, during a raid on Bristol. In the course of that action the sites collected sixty-six high-explosive bombs. From then on, the ‘Starfish’ were a regular feature of Britain’s passive defences. If the local fire and civil defence services were able to extinguish the pathfinders’ fires promptly, decoy fires often drew away a large proportion of the bombs intended for city targets. By February 1941, No. 80 Wing had sufficient ‘Bromide’ transmitters to jam all of the approach and crossbeam frequencies. That brought about a significant improvement in jamming effectiveness, and a resultant deterioration in the performance of X-Gerät. Now, when KGr 100 delivered an attack on its own, the unit’s ‘bomb signature’ often showed that a large proportion of its bombs had fallen outside the target area. +*** +In November 1940 the RAF monitoring service noticed more unusual signals on frequencies in the 42–48 MHz band, and R. V. Jones allocated these the code-name ‘Benito’. The new system, called Y-Gerät by the Germans, was another brainchild of Dr Hans Plendl. This employed a single beam made up of 180 directional signals per minute, which was aligned on the target. That was too +The Battle of the Beams 47 + + + fast for human interpretation, and the aircraft carried an electronic analyser to determine its position relative to the beam. To measure the aircraft’s range from the ground station, the ground station transmitted additional signals which the aircraft picked up and re-radiated on a different frequency. The ground station then measured the range using normal radar methods. When the aircraft arrived at the pre-computed bomb-release point, the ground station transmitted the bomb-release signal. Since it used only one ground station, Y-Gerät was more flexible than either of the predecessor systems. It was more accurate than X-Gerät, though it was also a great deal more complex. General Wolfgang Martini, head of the Luftwaffe signals service, later recounted how he tried to explain the operation of Y-Gerät to Hermann Göring. The Reichsmarschall listened for about two hours, then asked a few questions which showed he was none the wiser. Göring, a World War I fighter ace, had little time for such things. He thought wars should be fought by brave men with guns, not like this. He is said to have commented on another occasion, ‘Radio aids contain boxes with coils, and I don’t like boxes with coils.’ It is hard not to feel for him. After a false start in the summer of 1940, Plendl’s new system resumed operations at the end of the year. The Y-Gerät was fitted to the He 111 bombers of III Gruppe of KG 26 (III/KG 26) based at Poix near Amiens, and beam transmitters were situated at Poix, Cherbourg and Cassel in France. When he examined the Y-Gerät signals, Dr Cockburn noted that there were separate transmissions to fix the aircraft’s bearing and range from the ground beacon. To counter the system, therefore, he worked out a separate jamming method for each. At the time it was discovered the new beam system was still at the working-up stage, so Cockburn was under no great pressure to rush his jammers into operation. He even had time to introduce subtlety into his countermeasures. The prototype of Dr Cockburn’s new jammer for Y-Gerät code-named ‘Domino’ – employed a receiver at Highgate and the BBC’s dormant television transmitter at Alexandra Palace north of London. The receiver picked up the ranging signal from the bomber’s transmitter and passed it to Alexandra Palace, where the powerful equipment there returned the ‘echo’ to the German +Instruments of Darkness +48 + + + ground station to produce an erroneous range indication. The first ‘Domino’ went on the air in February 1941, soon followed by another at Beacon Hill near Salisbury. It soon became obvious that the ‘Domino’ transmitters were causing embarrassment to bomber crews relying on the Y-Gerät. On 9 March, the Y-beam signals changed frequency in the middle of an operation in an attempt – unsuccessful – to shrug off the jamming. Two nights later a small force of bombers attacked the Beacon Hill jammer, and one scored a near miss which put the station out of action for a few days. On the following night that jammer was still off the air, when III/KG 26 operated once more. The Alexandra Palace jammer covered the transmitter at Cassel, and none of those crews received the bomb release signal. There was no ‘Domino’ cover for the Beaumont-Hague transmitter, however, and crews using that ground station made accurate attacks. On the next night the Beacon Hill station was back on the air, and full jamming cover returned. Of eighty-nine Y-Gerät sorties flown over England during the first two weeks of March 1941, only eighteen aircraft received the bombrelease instruction. On the night of 3 May 1941, during an attack on Liverpool and Birkenhead, the Y-beam unit lost three Heinkels shot down. In each case the Y-Gerät equipment was removed from the wreckage and sent to Farnborough for examination. This revealed that between each pair of direction signals there was a short gap, which locked the electronic bearing-analyser to the beam. Later Dr Cockburn commented: +Unlocking the Y-beam was a piece of cake: they had fallen into the trap of making things automatic, and when you make things automatic they are more vulnerable. All one had to do was radiate a continuous note on the beam’s frequency. This filled in the gap between the signals, unlocked the beam analyser and sent the whole thing haywire. +Dr Cockburn’s new jammer, code-named ‘Benjamin’, first went on the air on 27 May 1941. By then, however, a major development in the German war strategy had brought about a profound change in the air war over Great Britain. During May 1941 the bulk of the Luftwaffe bomber force moved to bases in eastern Europe, in preparation for the long +The Battle of the Beams 49 + + + planned attack on the Soviet Union. On 21 June the offensive began, and the intensity of the night Blitz suddenly gave way to the boredom of waiting for an enemy who rarely came. An air of almost unreal calm descended on Great Britain, but Group Captain Addison could not rely on the respite lasting for long. If German forces achieved a rapid victory in the east, the Luftwaffe would resume its onslaught on Great Britain. During the summer and autumn of 1941 No. 80 Wing continued its build-up, and replaced the last of the makeshift jammers with purpose-built systems. By September the unit had a strength of some 2,000 men and women of all ranks. It operated eighty-five ground stations scattered throughout the British Isles, and controlled more than 150 ‘Starfish’ decoys. +*** +So ended the first-ever electronic warfare action. Knickebein had surrendered almost without a fight. X-Gerät proved more difficult to jam, but in the time available its capabilities were not exploited sufficiently to provide effective target-marking for Luftwaffe bombers. Y-Gerät played only a minor role, its effectiveness much reduced by jamming, before the bombing campaign ended. We now know that the jamming of Knickebein and X-Gerät was less disruptive than had been thought at the time. Yet, although the initial jamming of Knickebein was insufficiently powerful to conceal the beam signals, it dissuaded Luftwaffe crews from using their beams when flying over England. Although the Luftwaffe reaction to the various countermeasures had been slow in coming, it would unwise to conclude that Luftwaffe technicians could not have modified their radio aids to operate more effectively in the face of the jamming. In fact, before they could do so, the night bombing offensive against Britain had come to a halt. As we shall see, the Luftwaffe could do much better than this. +Instruments of Darkness +50 + + + Chapter 2 +The Instruments +‘I have done my best during the past few years to make our air force the largest and most powerful in the world. The creation of the Greater German Reich has been made possible largely by the strength and constant readiness of the air force. Born of the spirit of the German airmen in the First World War, inspired by its faith in our Führer and Commander-in-Chief – thus stands the German Luftwaffe today, ready to carry out every command of the Führer with lightning speed and undreamed-of might.’ +Order of the Day from Hermann Göring to the Luftwaffe, August 1939 +Radar, like many major inventions in the twentieth century, did not result from a sudden and inspired line of thought pushed to the point of fulfilment by a single inventor. As with many innovations, the basic idea preceded the invention by several decades. Only when each of the major components had been developed, could its realisation become practicable. Again, as with many other inventions, once the background work was complete, development of the device proceeded independently in several nations simultaneously. In the case of radar, by the early 1930s the major components necessary to assemble such a system already existed. These were: a high powered pulsed transmitter; a very sensitive receiver; a device for measuring small time differences very accurately (the cathoderay tube); and a highly directional aerial system. During that decade scientists working independently in Great Britain, the USA, France, Germany, the Netherlands, Japan and the Soviet Union all produced working radars. Each nation claimed the device as its own, and in each the fighting services believed that it offered them a unique advantage. Since they would be the target systems in the next phase of the electronic warfare battle, however, the account that follows will concentrate on radar developments in Germany. +*** + + + When World War II began in September 1939 the German armed forces had two separate types of radar in service and a third was at the advanced testing stage. For early warning against air attack the Gema Company had produced the Freya radar operating on frequencies around 120 MHz, initially with a maximum range of about seventy-five miles. Gema also produced the Seetakt radar operating on 370 MHz, for installation in warships and at shore batteries. This radar provided surface-search and also accurate range information to assist naval gunnery. Late in the 1930s the rival Telefunken Company also entered the field of radar, and its Würzburg equipment was the impressive result. When the war began this equipment was still in the trials stage. The small, highly mobile set operated on what was then the extremely high frequency of 560 MHz, and could plot the position of aircraft to within fine limits at ranges up to twenty-five miles. The Würzburg was the first radar in the world with the precision to allow anti-aircraft gunners to engage targets accurately at night or through cloud. Also at this time, Telefunken had commenced testing a small airborne radar. How well did the German radars compare with their British equivalents at the outbreak of World War II? The Freya, the only German early-warning equipment, had a maximum range of seventyfive miles, its rotating aerial array gave it full 360-degree cover and its wheeled carriage allowed a high degree of mobility. Yet, it could not measure the altitude of approaching aircraft. Its nearest British equivalent, the ‘Chain Home’ operating on the far lower frequencies between 20 and 52 MHz, had a maximum range of 120 miles and could determine the altitude of approaching planes. But the ‘Chain Home’ stations gazed out to sea with a fixed 120-degree angle of look, and for technical reasons the radar could not give reliable plots on aircraft flying over land. Moreover, the four 300-foot high towers – each twice the height of Nelson’s column – supporting each station’s transmitter aerials precluded mobility. It was not in its radar hardware that the RAF had established a lead, but rather in the way in which the information was exploited. Only in Fighter Command could reliable and up-to-date information based on radar plots be passed to fighter pilots by radio. By September 1939 the RAF had nineteen ‘Chain Home’ radars operational, covering the approaches to the east coasts of England +Instruments of Darkness +52 + + + and Scotland. Its system of fighter control had been developed and tested during scores of exercises. The Luftwaffe had made no attempt to perfect such a system of its own before the war. Since it had little to fear from hostile bombers, that service had logically concentrated its energies on offensive developments – like the radio beams. The Seetakt and Würzburg precision radars were the most advanced equipments in the world in their respective categories. When war broke out, the Royal Navy had no equivalent of the Seetakt for its ships nor would it have one for another two years, and the Würzburg was considerably in advance of its nearest British equivalent in both range and plotting accuracy. But Britain had established a lead in the development of radar sets small enough to be carried in aircraft; there were two types on the point of entering service, one for coastal patrol aircraft and one for night-fighters. +*** +In the autumn of 1939 the Luftwaffe had eight Freya stations operating on the chain of islands along the northwest coast of Germany: two on Heligoland, two on Sylt, two on Wangerooge, one on Borkum and one on Norderney. At that time the RAF was prohibited from attacking targets on the German mainland, because this would endanger civilian lives. It therefore sent bombers in probing attacks, to feel out the defences with attacks on German warships in the Heligoland Bight. The first three daylight bombing attacks were inconclusive. Then, on 18 December 1939, twenty-four Wellingtons of Nos. 9, 37 and 149 Squadrons set out from their bases in East Anglia to patrol the Schilling Roads, Wilhelmshaven and the Jade Roads. Two of the Wellingtons turned back early with technical problems, the rest continued with the mission. Just after midday, a Freya radar on the pre-war holiday island of Wangerooge picked up the approaching Wellingtons at a range of seventy miles. The operator reported the formation to the nearby fighter station at Jever and, after a delay, the defending fighters, sixteen Messerschmitt Bf 110s and thirty-four Messerschmitt Bf 109s, took off to engage. By then, having found no warships at sea, the bombers had turned around and were heading for home. It was a clear winter’s day and the fighter pilots could see the RAF formation from several miles away. They quickly caught up with the +The Instruments 53 + + + raiders and, in the heated engagement that followed, bomber after bomber went down. Of the twenty-two bombers involved in the action, only ten regained friendly territory. So the RAF had learned the hard way, as the Luftwaffe was to learn during the Battle of Britain and the US Army Air Force would learn in 1943, that formations of bombers operating over enemy territory by day without fighter escort risked heavy losses. The lesson was clear, and throughout most of the conflict that followed RAF Bomber Command sought to avoid the German defences by delivering attacks under cover of darkness. On 14 May 1940, following the destructive Luftwaffe attack on the city of Rotterdam, Prime Minister Winston Churchill lifted the ban on air attacks on the German mainland. By 4 June, RAF bombers had flown some 1,700 night sorties over Germany at a cost of thirtynine aircraft, most of them lost in accidents. Compared with what Bomber Command would achieve later in the war, those early operations were no more than gestures of defiance. Yet they caused a degree of consternation in Germany. Had not Hermann Göring declared that the Ruhr industrial area would not be exposed to a single bomb from an enemy aircraft? After inspecting the AA gun defences in the Essen area in August 1939, Göring’s imagination had been captivated by the Würzburg radar. Here was a device to enable the gunners to engage enemy planes even through the thickest cloud or at night. It was the success of the early Würzburg trials that had inspired him to make his muchquoted declaration regarding the invulnerability of the Ruhr. Yet the introduction of Würzburg into service took somewhat longer than anticipated, and the first sets did not become operational until the summer of 1940. Lacking radar, the gunners sought out the night raiders using searchlights and largely ineffective sound locators, with poor results. Göring was not at all satisfied by this – while his reputation had suffered, the raiders had not. Since the AA guns alone could not inflict losses sufficient to deter the night raiders, he decided to form a specialised night-fighter force. Up to that time a few intrepid pilots had flown night patrols in single-seat Bf 109 fighters, and on occasions they had shot down raiding bombers. Yet, lacking any formal system of ground control, an interception at night remained a matter of chance. +Instruments of Darkness +54 + + + In July 1940 Göring summoned Oberst Josef Kammhuber to his headquarters, and ordered him to set up a specialist night-fighter unit and a ground-control system to support it. Kammhuber was forty-three when he took on his new appointment. In his previous posts he had demonstrated that he was a methodical worker, displaying great drive tempered by sound judgement. He was to use these qualities to the full in his new post. Kammhuber worked fast. By mid-August 1940 the first specialised night-fighter unit, Nachtjagdgeschwader 1 (NJG 1), had a strength of seventy Bf 110s, seventeen Ju 88s and ten Do 17s. None of these planes carried radar or other specific equipment for their new role, however. Backing these fighters, on the ground, was a regiment of searchlights and a few Freya early-warning radar sets. Kammhuber was promoted to Generalmajor and established his headquarters in a seventeenth-century castle at Zeist near Utrecht. The night-fighter organisation was subordinated to Generaloberst Hubert Weise, responsible for overall command of the air defence of the Reich. During the summer and autumn of 1940, radar-directed nightfighting was in its infancy. Usually fighters were scrambled when early-warning radar stations on the coast reported approaching raiders. After take-off the night-fighters flew to assigned radio beacons, which they orbited until searchlights nearby illuminated an enemy bomber. Then, with his target in sight, the night-fighter pilot closed in for the kill. Known as ‘illuminated night-fighting’ (Helle Nachtjagd), this system achieved some success. The early engagements revealed an important weakness in the system, however. The searchlights were positioned around the bombers’ potential targets, as were the AA guns. There was no effective system of identification, with the result that night-fighters often came under fire from the ground. Quite apart from the loss of men killed or wounded, and in aircraft destroyed or damaged, that made the system manifestly inefficient. The gunners were shooting at fighters, and the fighter pilots had to manoeuvre to avoid the shells, at a time when both should have been engaging enemy bombers. To prevent such ‘friendly fire’ incidents, Kammhuber saw that it was important to designate separate engagement zones for AA guns and night-fighters. He therefore moved his searchlight batteries into +The Instruments 55 + + + the countryside, well clear of the AA gun defences, to form a defensive belt that ran parallel to the coast from Schleswig-Holstein to Liège in Belgium. Raiding aircraft would have to pass through that belt, to reach their targets in Germany. Kammhuber subdivided his searchlight belt into a series of ‘boxes’ about twenty miles wide, each with a radio beacon where a night-fighter would orbit while waiting for the enemy raiders to appear. Having formed his defensive line, Kammhuber set about improving its effectiveness. He saw that any system that relied on searchlights was a slave to the weather. The answer was to use a precision radar on the ground to direct a night-fighter into an attacking position behind an enemy bomber. The Freya was too imprecise for that task, for the ‘blips’ from the night-fighter and the bomber usually merged on the radar screen long before the nightfighter pilot had his quarry in visual range. The Würzburg flakcontrol radar, with its very much higher frequency and superior resolving power, offered a much better prospect. By the end of 1940, production of this radar was getting into its stride and Kammhuber secured a few to direct experimental night interceptions. The initial trials with Würzburg demonstrated the advantages of using radar to direct night-fighters, and Kammhuber requested more sets to equip his defensive line. This now comprised a series of contiguous boxes, forming a barrier which raiding bombers had to cross to reach their targets and again on their return flights. Each night-fighter box was equipped with a Freya and two Würzburg radars, a radio beacon and a ground-control station. The Freya directed one short-range narrow-beam Würzburg to track the nightfighter, while the other tracked the incoming bomber. The Würzburg equipment been designed to direct AA guns and its form of presentation – giving raw range, bearing and elevation information – made it impossible to direct night-fighters from the radar screen. To convert the Würzburg information into a form in which it could be used by the fighter controller, the Luftwaffe developed the so-called ‘Seeburg table’. Located in the headquarters building of each ground-control station, the device looked like a large dais with two flights of steps leading up to a ‘table’ at the centre. The ‘tabletop’ consisted of a horizontal frosted glass screen, bearing an outline map of the area and the Luftwaffe fighter grid. +Instruments of Darkness +56 + + + Directly beneath this glass screen sat two operators for the lightprojectors. Each received telephoned plots on the aircraft he or she was tracking, from the appropriate Würzburg. One operator projected onto the screen above a red light to indicate the bomber’s position, the other projected a blue spot to indicate the fighter’s position. As the coloured spots of light moved across the frosted glass screen, plotters at the top of the ‘dais’ marked the planes’ respective tracks using a coloured wax crayon. The fighter controller stood over the frosted glass screen, passing radio directions to the fighter pilot to bring him into a position to engage the bomber. The ‘Seeburg table’ became a standard item of equipment at each fighter-control station. This method of close controlled night interceptions was code-named Himmelbett. +Initially Kammhuber positioned his Würzburg radars immediately in front of the searchlight belt. That allowed night-fighter pilots to attempt a radar-controlled interception first. If that failed, they could then resort to the tried and tested ‘illuminated night-fighting’ tactics. The radars thus increased the effective ‘depth’ of the searchlight belt, allowing Kammhuber to redeploy searchlights to extend the line from eastern France to the middle of Denmark. +The Instruments 57 +The Seeburg Plotting Table + + + Yet, although the Würzburg radar gave a useful improvement in the effectiveness of the defensive line, it soon became clear that the device’s range performance fell short of what was needed. All too often, Allied bombers emerged from the line and passed out of Würzburg range before the night-fighter could make a successful interception. After prompting from Kammhuber, Telefunken modified the Würzburg to overcome this deficiency. In the spring of 1941, the company produced a variant of the radar with the diameter of the reflector-dish increased from ten feet to twenty-five feet. That narrowed the width of the radar beam, and enabled the equipment to track aircraft up to forty miles away. The new Telefunken radar was called the Giant Würzburg (Würzburg Riese). Apart from its larger reflector and static mounting, electronically it was little different from the smaller version. During the second half of 1941, the first Giant Würzburg radars entered service to replace the standard sets used for night-fighter control. Following a reorganisation of the night air defences early in 1942, it was decided that, with this influx of new electronic equipment, Kammhuber no longer needed the searchlights in his defensive line. At the time he contested the decision, though later he would admit it was for the best. It forced night-fighter crews to trust their ground controllers to guide them to their targets and, when the crews became accustomed to it the system was more effective than ‘illuminated night-fighting’ could ever have been. During the spring of 1942, Kammhuber’s line was strengthened by the introduction of three new radar devices. The formula of using a larger aerial reflector to narrow the radar beam and increase range, which had worked so well in the case of Würzburg, also succeeded with Freya. The result was the Mammut (‘Mammoth’) built by the I. G. Farben company. This was essentially a Freya with a greatly enlarged reflector ninety feet wide and thirty-five feet high – about the size of a tennis court on its side. The structure was fixed on supporting pylons, and determined the azimuth of aircraft by ‘swinging’ the beam electronically through a limited arc of 100 degrees. The enlarged reflector squashed the radar beam into a narrow pencil, which reached out to aircraft up to 185 miles away. Like its smaller predecessor, Mammut could not measure altitude. The second new radar, the Wassermann, built by the Gema company, +Instruments of Darkness +58 + + + gave accurate height, range and bearing readings on aircraft up to 175 miles away. This set employed a reflector 130 feet high and 20 feet wide, mounted on a rotating tower. Wassermann was the finest early-warning radar to be produced by either side during World War II. The Luftwaffe installed Mammut and Wassermann sets along the coast of occupied Europe, to extend the range of its earlywarning cover. Those two new sets were both early-warning systems. The third new radar was of an entirely different character: the Lichtenstein lightweight airborne radar, designed for installation in night-fighters. Another Telefunken product, the Lichtenstein operated on frequencies in the 490 MHz band. It had a maximum range of two miles and a minimum range of about 200 yards. That minimum range figure was an important parameter in a night-fighter radar. While the radar transmitted each high powered pulse, the sensitive receiver had to be ‘switched off’ or it would suffer severe damage. That meant the receiver could not pick up echoes from the nearest targets. That dead distance, between the fighter and the closest target that could be seen on radar, was proportional to the length of the transmitted pulse. In fact, the 200-yard minimum range was low for a first-generation airborne radar. The new airborne radar went into production and the first four night-fighters fitted with Lichtenstein arrived at the operational airfield at Leeuwarden in the Netherlands in February 1942. In ser vice, the shortcomings of the device became clear. The entanglement of aerials and reflectors on the aircraft’s nose increased the drag, impaired handling and reduced the top speed of the Ju 88, for example, by 6 mph. Initially, pilots were unwilling to accept those penalties for the privilege of carrying a radar of uncertain reliability. Paradoxically, the main reason for their conservative attitude was the high quality of the ground control using the Giant Würzburg, which usually placed the fighter within visual range of its target. Hauptmann Ludwig Becker and his crew persevered with the Lichtenstein equipment, however. They found that when the set could be coaxed into working properly – and it had its share of teething troubles – it offered considerable advantages, particularly when engaging the British bombers on moonless nights. As Becker’s score of kills accordingly mounted, other crews began to accept the device. +The Instruments 59 + + + By March 1942, the German defences were destroying an average of four bombers out of every hundred attacking Germany by night. Of these the fighter defences were responsible for about two-thirds, while AA guns accounted for most of the remainder. By now there were four Geschwader of night-fighters with 265 aircraft, of which 140 might be available on any one night. The force continued its expansion. During April it accepted thirty-three Bf 110s, twenty Ju 88s and thirty Do 217s. Telefunken had already manufactured 275 Lichtenstein radars, and production was running at about sixty sets per month. +On the ground-radar side as well, there was a steady strengthening of Kammhuber’s line. To equip the whole of the defensive line as it then stood, he needed 185 Giant Würzburg sets. By the end of March 1942, Telefunken had delivered about half that number, and the rest were following at the rate of about 30 per month. Although the defences were taking a steadily mounting toll of the British night raiders, Kammhuber’s system of fighter control had an obvious Achilles’ heel. For its success it depended on the Lichtenstein, Freya, Mammut, Wassermann and Giant Würzburg radars, and on effective communications between the fighter pilots +Instruments of Darkness +60 +Himmelbett fighter-control stations at the end of 1942 +Interception zone covered by original Himmelbett chain Himmelbett stations +Night-fighter aerodromes +Approximate limit of German early-warning radar cover, against aircraft flying at 10,000 ft + + + and their ground controllers. In some degree, all these systems were vulnerable to interference. In the next chapter we shall observe how the British intelligence service stripped away the veil of secrecy surrounding that organisation. +The Instruments 61 + + + Chapter 3 +Discovery +‘The relief offensive for which Britain’s badly harassed Allies have been begging for such a long time has confined itself to the landing of a few parachutists on the coast of northern France. The parachutists were soon forced to make a glorious retreat across the ocean, without having achieved any useful purpose.’ +German News Broadcast, 28 February 1942 +Throughout 1941 and 1942, RAF Bomber Command was losing a steadily increasing proportion of the planes dispatched against targets in Germany. Yet, until there was detailed knowledge on how the air defences operated, it was impossible to devise appropriate countermeasures. The intelligence sources that had been so useful during the ‘Battle of the Beams’ – the crashed German aircraft, captured aircrew and the analysis of the beams themselves – were now denied, for the RAF bombers were destroyed over enemy territory. Moreover, because the more sensitive items of information concerning the air defence system were usually communicated via landlines, there was little radio traffic on this subject for Bletchley Park to decipher. In consequence, it took many months of hard work to expose the workings of the system Josef Kammhuber had created. In the absence of firm evidence before the war, British scientists had regarded with scepticism the possibility that their German counterparts might also be working on radar, though there was little doubt that they could build such systems once they had the basic idea, since they were known to be advanced in high-frequency radio techniques. In mounting the listening operation with the Graf Zeppelin, the Luftwaffe had concentrated its search for signals on the frequencies used by its radar systems; now British intelligence was taking much the same approach, with a similar lack of success. The first clue that the Germans were working on radar came from the so-called Oslo Report, received via the British Embassy in Oslo in November 1939. Probably sent by a disaffected German scientist, + + + the document mentioned several military technical systems then under development in Germany. There were references to a remotely-controlled glider carrying an explosive warhead, homing torpedoes and remotely-controlled shells. There was a short description of a warning system able to detect aircraft out to a range of 120 km (75 miles) using ‘pulses reflected by the aircraft’. The report added that, during one of the British air attacks on Wilhelmshaven, the stations covering the northwest coast of Germany had detected the RAF bombers at a range of 120 km. That last statement was greeted with some disbelief. The German fighters’ reaction to these attacks seemed very slow, if there had been such a long advance warning (in fact that was due to other weaknesses in the control and reporting system). Certainly, the RAF fighter reaction would have been much faster. +*** +One available source could certainly have confirmed to RAF officers the existence of German radar at this time, had not inter-service secrecy prevented it. In December 1939, the German pocket battleship Graf Spee was scuttled off Montevideo in Uruguay. Five days earlier, the warship had suffered several hits in a battle with Royal Navy cruisers. The German captain had thought his ship could not fight her way back to a friendly port, so to prevent further loss of life he ordered her destruction. The estuary of the River Plate is shallow, however, and when the demolition charges went off the warship sank only about ten feet before she came to rest on the seabed. At first light next morning, a flotilla of sightseeing boats put out from Montevideo to look at the shattered warship. Scores of photographs were taken, to be flashed round the world by news agencies. Most people failed to notice a strange feature on the close-up photographs of the smoking hulk: a structure rather like a bedstead on its side, mounted above the bridge. British naval intelligence sent its own sightseer to Montevideo to look over the warship, radar expert L. Bainbridge Bell. He boarded the wreck and climbed up to the ‘bedstead’ structure – a feat requiring some agility, since the Graf Spee had developed a list. Afterwards, Bainbridge Bell reported that the structure was almost certainly the aerial system for a radar set, probably used for ranging +Discovery 63 + + + the ship’s guns. In this assumption he was correct, this was a Seetakt radar. Armed with that information, naval intelligence officers in London examined other photographs of Graf Spee and observed that the structure was present, though hidden under a canvas cover, on photographs taken as early as 1938. That was a discomforting discovery, for even at the start of 1940 Royal Navy warships had no gun-ranging radars, and no British ship would receive one for well over a year. Bainbridge Bell’s report was pigeonholed in the naval intelligence files, however, and R. V. Jones would not learn of it until 1941. +*** +During the early months of 1940, the RAF scientific intelligence service picked up little information that could be connected with Luftwaffe radar systems. Although we now know that these were technically efficient, they were in limited use at that time. At that stage of the war the German strategy was primarily offensive, and the Luftwaffe therefore concentrated on systems like the navigational beams to aid bombers. Radar, as a purely defensive device at that time, had a lower priority. The British forces, being on the defensive, were compelled to adopt the opposite course. In May 1940, as the RAF night bombing offensive against Germany began, a prisoner mentioned that the German Navy had experimented with a ‘radio echo’ device for measuring the range and bearing of distant objects. He said the Luftwaffe was working on similar systems, though these were not so far advanced. From the description, it seemed that the German system bore unmistakable similarities to the British coastal radar chain. There was much here that agreed with the statements made in the Oslo Report. On 5 July, shortly after the reception of the first Knickebein beam signals by a British aircraft, one of R. V. Jones’s intelligence sources passed him the gist of a secret Luftwaffe report dated a week earlier. This stated that German fighter aircraft had been able to intercept British reconnaissance planes on that day because of information from the ‘Freya Meldung’ – the Freya warning. That seemed to confirm that the Germans had some form of aircraft detection system. On learning of Jones’s interest, the source mentioned that a Freya site was operating at Lannion protected by a battery of light +Instruments of Darkness +64 + + + anti-aircraft guns. Lannion was a small village on the northern coast of Brittany. The report seemed to underline the importance of Freya, for German troops had entered the area only three weeks earlier. There were two obvious ways to follow up: the site should be photographed from the air; also, a listening watch should be maintained for signals that could be traced to the site. Jones also tried a further approach, typical of the methods adopted in the strange craft of military intelligence: he researched the mythological background of the code-name, Freya. Freya was the Nordic goddess of beauty, love and fertility. Her most prized possession was an exquisite necklace called Brisingamen; to acquire this, she had sacrificed her honour and been unfaithful to the husband she loved. Heimdal, watchman of the Nordic gods, guarded Brisingamen. And Heimdal could see a hundred miles in every direction, by day or night. Jones cautiously reported to the Chiefs of Staff: +It is unwise to lay too much stress on this evidence, but these are the only facts that seem to have any relation to our previous knowledge. Actually Heimdal himself would have seemed the best choice for a code-name for RDF [radar] but perhaps it would have been too obvious . . . It is difficult to escape the conclusion therefore that the Freya-Gerät is a form of portable RDF. +This was all good stuff, but it awakened a nagging suspicion in the minds of the War Cabinet. Might the Germans have captured intact a radar set left behind by the British Expeditionary Force in France? How else could the Germans have developed an operational radar system so quickly? On 7 July, Churchill minuted General Ismay, his chief of staff, about the matter: +Ask the Air Ministry whether any RDF [radar] stations fell intact into the hands of the enemy in France. I understand there were two or three. Can I be assured that they were effectively destroyed before the evacuation? +General Ismay made the necessary inquiries, and replied that one radar transmitter had been left behind by the RAF at Boulogne, but this had been thoroughly destroyed. It was doubtful that the Germans could extract useful information from it. One of the Army’s gun-laying radar sets might have been captured in a damaged state, but the others were carefully destroyed. The evacuation ship Crested +Discovery 65 + + + Eagle had been carrying an Army gun-laying radar when she ran ashore near Dunkirk, but a naval party had been put on board to destroy the set. From German sources, we know that their forces had captured a nearly intact British mobile air-warning radar near Boulogne. Far from being impressed with the find, they regarded it as extremely crude and much inferior to the Freya. It was a fair assessment, for at that time the mobile British radars were considerably less effective than their static counterparts. On 14 July, Jones received an intelligence report of a second Freya station in operation, this time at Cap de la Hague on the Cherbourg peninsula. Nine days later, the station played an important part in the operation in which dive-bombers sank the destroyer HMS Delight. At the time, Delight was about twenty miles south of Portland Bill. As she had never been closer than sixty miles from the Freya, and had neither fighter support nor balloons to reveal her position, the action showed that the radar gave cover on lowlevel targets at least as good as that from the latest British equipments. In the second week in August, as the Battle of Britain was about to begin, Jones received the text of a secret Luftwaffe report which stated that Freya was designed to work in conjunction with the fighter defences. Attempts to locate Freya on aerial photographs of the two sites now reported, at Cap de la Hague and at Lannion, met with no success. Photographs were taken from reconnaissance Spitfires flying at 30,000 feet and gave a definition just sufficient to enable the 300foot Knickebein turntables to be picked out. All that could be said for certain was that the Freya had to be smaller than that. In the meantime a radar expert from the TRE, Derek Garrard, set out on a radar hunt on his own account. He filled his car with borrowed receiving equipment, and drove to points along the south coast to look for unusual transmissions. The initiative was rewarded, though his first intercept was not connected with Freya. From a point near Dover he picked up radar transmissions on a frequency of 375 MHz, which could be linked with the shelling of British convoys passing through the Straits of Dover, from gun batteries situated near Calais. In fact, the signals came from a Seetakt radar – the same type as that examined on the Graf Spee many months before. +Instruments of Darkness +66 + + + Garrard’s find caused a commotion among radar experts in Britain; of those prepared to admit the possibility of the Germans having developed radar, few would accept that they had sets superior to those built in Britain. Yet, here was a German radar, working on a frequency so high as to be almost unusable in Britain, directing coastal gun batteries. If the Germans had learned their radar techniques from a British set captured in France, they had applied their new-found knowledge with remarkable despatch. In the autumn of 1940 the introduction of improved reconnaissance cameras brought a great improvement in the quality of RAF aerial photography. The effect on the hunt for the German radar stations was immediate; on 22 November, a high-flying Spitfire returned with photographs of unprecedented clarity showing the village of Auderville near Cap de la Hague. Just to the west of the village were two unexplained circles side by side, each measuring some twenty feet across, looking like a pair of opera glasses laid lenses down. Dr Charles Frank, a physicist who had recently joined Jones’s staff, examined the photographs through a stereoscope and saw that two consecutive frames did not form a perfect stereo pair, as they should have. A shadow associated with one ‘circle’ had changed slightly in the nine seconds between the first exposure and the second. During that time, a thin wide object on top of one circle had rotated through ninety degrees. In each case the shadow was about two millimetres long, but whereas in the first about a tenth of a millimetre wide, the second was two millimetres wide. The difference was hardly greater than the resolving power of the photographs, but it was enough to establish that here was something worth closer examination. The next obvious move would be to lay on a low-level reconnaissance sortie to photograph the ‘opera glasses’ at Auderville. However, with Britain still under imminent threat of invasion, there were demands with a higher priority on the small force of photographic reconnaissance Spitfires. In the interval, Jones received an Ultra decrypt which mentioned another German aircraft detection device called Würzburg. It appeared that one Freya and one – perhaps two – Würzburg sets were earmarked to go to Romania; also, two Würzburg sets were to be sent to Bulgaria. All had been allocated for coastal defence units. Perhaps, Jones reasoned, this represented the minimum +Discovery 67 + + + number of radars necessary to provide continuous cover along the two nations’ coastlines with the Black Sea. If that was so, he calculated that the range of Freya had to be at least fifty-seven miles, and the range of Würzburg to be at least twenty-three miles. At that time Jones did not know that the two radar systems complemented each other, but although his initial premise was wrong the maximum ranges he had postulated for the two systems were remarkably accurate. He now had clues on two distinct types of aircraft-detection apparatus used by the German forces, though neither had yet been clearly seen or heard. Not until 6 February 1941 was a reconnaissance Spitfire available to take a low-level look at the ‘opera glasses’ at Auderville. The first mission was a failure, however. As the Spitfire sped through the area, the circular objects were missed in the gap between two successive frames of the oblique camera. The second low-level sortie, flown by Flying Officer W. Manifould six days later, was more successful. He returned with a magnificent close-up photograph, which showed that each circle was surmounted by a rotatable aerial-array. Unquestionably, this was a radar station (in fact it was a Freya). Even as Manifould’s photographs were being processed, a listening station in southern England identified pulsed signals coming from the direction of Auderville on 120 MHz. Signals on that frequency had been picked up earlier, but the listeners assumed that they came from the new VHF radios fitted to RAF fighters. Only when Derek Garrard examined the signals on a cathode-ray tube was their true significance recognised. Garrard plotted the bearings on their source, and found that these signals originated not only from Auderville, but also from transmitters situated near Dieppe and Calais. Within four hours of each other, Jones received the low-level photographs and the report of the intercepted radar signals, after a hunt that had lasted more than a year. +*** +Within a month of the recognition of the Freya signals, new pulsed signals were picked up on 570 MHz. In the spring of 1941 a special radio-reconnaissance unit, No. 109 Squadron, had begun flying sorties over occupied Europe looking for German radar transmissions. After dark on 8 May one of the unit’s ‘ferret’ +Instruments of Darkness +68 + + + Wellingtons flew a circuitous route taking in the Cherbourg peninsula and Brittany. In the course of the sortie, the plane’s crew obtained rough fixes on nine radar sites. In the months to follow, information on Freya stations came in thick and fast. By the end of October 1941 no fewer than twentyseven of these radars had been located, strung out along the coast between Bordeaux in France and Bodö in Norway. No. 109 Squadron aircraft also brought back scores of fixes on 570 MHz transmitters. Yet the sources of these signals were evidently very small, for they defied all attempts to photograph an example. One spectacular piece of intelligence obtained at this time was a strip of cine film showing a Freya station in operation, with the German crew tracking aircraft targets. Less spectacular, but far more important from the intelligence viewpoint, was the discovery that wireless plots from the Freya units could be overheard in England. When tracking an aircraft, the radar station passed distance-andbearing reports by radio to a central air-defence headquarters. The ‘code’ used to pass the information was relatively simple, and easily broken. For example, on 10 October a listening station in England picked up a Morse transmission which read: +MXF = 114011 = 14E = X =254 = 36 = + +MXF was the radio call-sign of the Freya station; 114011 was the time of the plot in hours, minutes and seconds; 14E was the serial number of the plot. X indicated the number of aircraft present (X meant one, Y meant several and Z meant many); 254 was the bearing from the radar station, and 36 was the range in kilometres British intelligence tapped this source for all it was worth. Reconnaissance aircraft, maintaining an accurate record of their flight path by photographing the ground directly below, flew over German-held territory so that the Freya stations would track them. Listeners in England then recorded the plots on the aircraft’s progress. Afterwards, the bearings and ranges were back-plotted on maps. Several Freya stations were located and identified in this way. Once the various radar stations had been located and identified, the German plotting reports were used to provide up-to-date information on the movements of RAF raiding forces flying over German-held territory and beyond the range of radar stations in Great Britain. +Discovery 69 + + + While this was going on, No. 109 Squadron continued to bring back fixes on the sources of the 570 MHz transmissions. Yet still the device defied all attempts to photograph it. Clearly, it was much smaller than Freya. From agents’ reports, Jones learned that these transmissions were connected with a fire-control device known as the FMG. Towards the end of 1941, news arrived that four FMG sets were operating in the area of Vienna, of all places. Unless Vienna – a city of great beauty but comparatively little military importance – was a radar equipment depot, it seemed reasonable to infer that the FMG device existed in considerable numbers. Another important photographic clue came from the United States, at that time still neutral. The US Embassy in Berlin overlooked the Berlin Zoo district, where a couple of huge concrete flak towers had been built. A photograph arrived on Jones’s desk showing the top of one of the towers; clearly visible was a large dishshaped open-work radar reflector, of a type not seen before. Unfortunately there was nothing nearby to give scale to the object. A few weeks later, a Chinese scientist reported seeing the same device, which he described as paraboloid more than twenty feet in diameter, that could be rotated and elevated. He thought it might be used to direct the anti-aircraft guns. Jones saw that the new radar could not possibly be the 570 MHz radar known to exist in such profusion in German-occupied Europe. Otherwise, its large reflector would have been spotted on aerial photographs long before this. In fact, the Berlin Zoo photograph showed one of the first Giant Würzburg radars to enter service. Still Jones had no picture of the small Würzburg equipment, but the hunt for one was nearing its end. Late in November 1941, Charles Frank was examining a medium-level photograph of the Freya station at Bruneval near Le Havre on the north coast of France. There he saw that a track had been trodden out along the cliff-edge: it ran from the Freya towards a large house, which seemed to serve as a headquarters. Just before it reached the building, the track swung to the right. It ended at a small black object about halfway between the house and the cliff top. Several people had considered it worth their while to tread out a path from the main radar station to the ‘small black object’. Might that object play some part in the working of the Freya? On 3 December Flight Lieutenant Tony Hill, a reconnaissance +Instruments of Darkness +70 + + + pilot, visited the interpretation centre at Medmenham in Buckinghamshire to discuss the photography of German radar sites. Squadron Leader Claude Wavell knew of Charles Frank’s special interest in the Bruneval radar, and mentioned the mysterious black object to Hill. On the following day, on his own initiative, Hill took off in a Spitfire to look at Bruneval. He swept in low over the cliffs, and was past the emplacement before the startled defenders knew what had happened. On his return, Hill discovered that his camera had failed to function properly. It was a cruel blow – but he had seen the device clearly, and was able to say that it looked ‘like an electric bowl-fire and was about ten feet across’. If Hill was right, this might be the elusive source of the 570 MHz transmissions. On the following day, Hill bravely repeated the performance. This time the camera worked perfectly and the photographs he brought back were among the classics of the war. They showed the device exactly as he had described it, like an electric bowl-fire about ten feet across. Although it now seemed highly probable, the evidence was still not conclusive that this was the source of the 570 MHz signals. Until that was certain, countermeasures could not begin. It is difficult to establish who first suggested the idea of pilfering the device at Bruneval. The notion was so obvious – it lay within 200 yards of the coast – that it might have occurred to several people. At all events, by the beginning of January 1942 such an operation was in the detailed planning stage. Clearly a commando raid launched from the sea would be doomed to failure; the device was situated at the top of high cliffs, protected by a sizeable German garrison. Even if the troops could fight their way to the top of the cliffs without suffering serious casualties, it was unlikely they could do so before the defenders had destroyed the radar. The naval commodore in charge of Combined Operations, Lord Louis Mountbatten, suggested that parachute troops should be used instead. On 21 January the Chiefs of Staff agreed to this, and assigned C Company of the 2nd Parachute Battalion to the operation. An operational squadron of Whitley bombers would transport them to the target area, and a force of light naval craft would evacuate the raiders from the nearby beach when the mission was over. Intensive training began for what the men were told would be ‘a special demonstration exercise’ to be watched by the whole +Discovery 71 + + + of the War Cabinet. The venture received the code-name ‘Biting’. Once the device had been captured, the task of dismembering it was to be undertaken by seven men of the Royal Engineers, commanded by Lieutenant D. Vernon. The eighth man in the team was from the RAF: Flight Sergeant C. Cox, a radar mechanic, who was to go along should his specialist knowledge be required. The dismantling party was given a British gun-laying radar – the nearest available equivalent to the expected German system – on which to practise its dismantling skills. Vernon and Cox then received a special briefing on the anticipated layout of the German set. According to the planned time-table, they would have half an hour with the apparatus; in that time they were asked to make sketches and take photographs of the equipment, then dismantle it systematically starting at the aerial and working backwards through the receiver to the presentation gear. The operating frequency could be established beyond doubt by removing the aerial element from the centre of the ‘bowl’, and measuring it. The next target was the receiver and its associated presentation equipment. These would reveal whether any anti-jamming circuitry was built into the set. The transmitter was also wanted, so British scientists could examine German techniques for generating high powered pulses on ultra-high frequencies. Dr Jones also asked that a couple of prisoners be taken, radar operators if possible. These might be persuaded to reveal information on the methods of operating the radar and aircraft reporting. All German signals equipment bore informative labels and inspection-stamps, and useful general intelligence could be obtained from these. Should the various units prove impossible to dislodge, Jones asked that the labels be torn off and brought back. By the fourth week in February Jones had confirmation from other sources that the ‘bowl-fire’ was a radar code-named Würzburg, and that one of these sets was situated near the Freya station at Bruneval. By then all the military preparations for the operation were complete, but now the weather intervened. On the evening of the 24th the weather was unsuitable, as it was on the next two nights. The timing of the raid was critical; the attack had to take place on the night of a full moon, but also when the tide was on the rise so the assault craft would not be left stranded on the beach. The 27th was the last possible date for the operation for a month or more. +Instruments of Darkness +72 + + + That evening the forecast was favourable and the Commander-inChief Portsmouth, Admiral Sir William James, signalled: ‘Carry out operation Biting tonight 27th February.’ The twelve converted Whitley bombers of No. 51 Squadron took off from Thruxton near Andover. On board were 119 paratroops and the RAF flight sergeant, sitting huddled together and trussed up in their uncomfortable parachute harnesses. One soldier later wrote: ‘The mugs of hot tea (well laced with rum) we had drunk before taking off began to scream to be let out. In that restricted space and encumbered as we were there was, alas, no way.’ Shortly after midnight on the morning of the 28th, the first sticks of paratroops leapt from their aircraft. Some ten seconds later the men tumbled on to the carpet of virgin snow some 600 yards to the south of the radar site. They hastily shed their parachute harnesses and cocked their weapons, ready to fight for their lives. But the halfexpected rattle of German small-arms fire did not come. Their arrival had passed unnoticed. The sound of the Whitleys’ engines faded into the night, leaving the men feeling very lonely and vulnerable. As the men assembled into their small groups, their next move was not at all warlike: that tea just had to go. Major John Frost, the force commander, later wrote that this ‘was certainly not good drill, as now was the time when a stick of parachutists was most vulnerable . . . but at least it was a gesture of defiance!’ The assault parties now moved on their assigned targets. One, led by Frost himself and comprising fifty men including the dismantling party, crept towards the radar site and the house nearby. A second party, under Lieutenant Timothy, took up covering positions to screen the force from attack from the landward side. The remainder made off to secure the beach and the escape route. Frost’s men silently surrounded the Würzburg, whose silhouette stood out sharply in the moonlight, and the nearby house. If the house was some kind of headquarters, it might be a centre for resistance. Frost himself stole round to the front door with a small party. Satisfied that all was ready, he gave the signal for battle to begin – a long shrill blast on his whistle. With four men at his heels, Frost burst into the house and began searching each room in turn. It proved something of an anti-climax, the only German present died trying to defend one of the upstairs rooms. Outside, a fierce battle was in progress with almost continuous +Discovery 73 + + + automatic fire punctuated by the bangs from exploding handgrenades. Within minutes, all resistance around the Würzburg had been overcome. But, as that fight ceased, another began. There were about a hundred German troops stationed in the vicinity, and Lieutenant Timothy’s covering force found itself being hotly engaged. In the fight to seize the Würzburg, five of its six operators had been killed. The sixth man made off into the darkness, but in his haste he lost his sense of direction and stumbled over the cliff. Fortunately he managed to grab a projecting rock, and with some difficulty he climbed back to the top. He then found himself being helped over the edge by a British paratrooper. In no position to offer resistance, the man quietly surrendered. With the Würzburg secured, Lieutenant Vernon climbed on top of the operating cabin and examined the aerial with the aid of a hand torch. He then photographed the aerial from each angle – an action no sooner made than regretted, for the light from the flashbulbs attracted bullets from several directions. Vernon then summoned his team and ordered one sapper to saw off the aerial element, while the remainder sought to remove the boxed components in the operating cabin. The aerial came away easily, but the boxes defied all attempts to dislodge them using screwdrivers. This was no time for finesse, for the bullets ricocheting off the cabin’s walls were real enough. The men then brought into play their crowbars, and the equipment gave up the unequal struggle. One by one, the units were ripped from the console. The dismantlers had been at work for barely ten minutes out of the planned thirty, when Major Frost saw three lorries approaching with headlights full on. Almost certainly, these were German reinforcements. If the defenders brought into action weapons heavier than the rifles and machine guns they were already using, the raiding force would be at a severe disadvantage. Frost decided to settle for whatever the dismantling party had already secured, and ordered his force to withdraw to the beach. But now he learned that the shoreline was still in German hands. What had gone wrong? Of the forty men detailed to secure the escape route, half had landed more than two miles from the planned dropping-zone. The senior officer present, Lieutenant E. Charteris, took a quick bearing on the lighthouse at Cap d’Antifer and worked +Instruments of Darkness +74 + + + out his position. He then led his men towards the radar site at a brisk trot, and arrived at the clifftop just as Frost was organising his own force to storm the beach. The combined assault teams rushed the German positions in their path. Now the beach was in British hands and on it lay the wounded, the German prisoners and the items stripped from the Würzburg. Frost told his signallers to call in the naval craft to evacuate the force. It was high time to leave, for on the cliffs on either side of the beach the German forces were becoming increasingly active. After a few minutes, the signallers reported they had had no success in contacting the boats. Frost fired red distress flares, but to no effect. Then, he later wrote, ‘I moved off the beach with my officers to rearrange our defences. It looked as though we were going to be left high and dry, and the thought was hard to bear.’ Just as his troops had begun to take up positions for a final stand, Frost heard a cry: ‘Sir, the boats are coming in!’ He looked back and saw six snub-nosed assault craft sliding to a stop on the beach. With a sigh of relief he ordered his men to embark, while the boats’ crews put down covering fire on the German troops at the top of the cliffs. With the roar of accelerating engines the landing craft backed away from the shore, while the brisk exchange of gunfire continued until the boats were well clear. Safe aboard an assault craft, Major Frost learned the reason for the delay. While he had been signalling, a German destroyer and two patrol boats had passed within a mile of the small British flotilla but noticed nothing. Frost also learned that the pieces of the radar secured by his men were almost exactly what were needed. Mr D. H. Priest, a Telecommunications Research Establishment engineer who had received a temporary commission as a flight lieutenant for the occasion, examined the booty on the boat. Had the coast been clear, he would have landed and climbed to the radar site to look over the Würzburg, but this was not possible. When dawn broke, several Spitfires arrived over the craft and escorted them back to England. The Bruneval operation was successful on almost every count. The raiders had captured most of the radar. Of the three prisoners, one was a radar operator. The paratroops suffered fifteen casualties – two dead, seven wounded and six missing. The dismantling party had done extremely well in the brief time available. The units it brought back included the receiver, the receiver amplifier, the +Discovery 75 + + + modulator – which controlled the timing within the radar – and the transmitter. In addition, there was the sawn-off aerial element. The only unit which Jones had requested and not received was the presentation equipment. If – as had nearly happened – the boxes had proved impossible to tear from their mountings, Jones might have had to make do with the labels alone. So it is interesting to see what could be learned from these. The labels indicated that the manufacturer was Telefunken, a company with factories in the Berlin area. The works numbers were particularly interesting. From previous experience with German serial numbers, Jones had deduced that the number allocated to the first production model of each component was 40,000. The earliest number found on the captured units was 40,144, the latest was 41,093. This suggested that the number of sets of components produced by the date of manufacture of the last item, was 1,093. The earliest inspection date, early November 1940, was stamped on a part of the transmitter; the latest, 19 August 1941, was on the aerial. This did not necessarily mean that 1,093 complete Würzburg sets had been turned out by the latter date, since a proportion of the component units would have served as spares. It was a principle of German design that servicing was facilitated by replacing component units, while the defective ones were returned to a central depot for repair. Assuming that about half the production went into spares, Jones reckoned that around 500 of these radars were available by August 1941, and production was probably running at about 100 sets per month. For him the raid was particularly satisfying, since the intelligence gleaned either confirmed or added to the previous picture. No part of the picture had to be modified or discarded. An important side effect of the raid was that it gave British intelligence added confidence in the accuracy of the information it was receiving. Scientists at the Telecommunications Research Establishment at Swanage made a thorough examination of the Würzburg units. In their view the equipment was considered ‘straightforward and in no respect is it brilliant . . . On the other hand, it must be remembered that the equipment was made in 1940 and designed in 1939 or earlier.’ In 1940, British radar techniques had not been sufficiently advanced to build a set working on 570 MHz with a range of twenty-five miles. While the German radar carried no +Instruments of Darkness +76 + + + specific anti-jamming circuitry, it could be re-tuned over a narrow range of frequencies to overcome electronic jamming. After the Bruneval horse had been ‘rustled’, the German local defence commanders along the French coast made sure that the stable door was well and truly bolted. The remains of the Würzburg were removed, and a new set was installed in the main Freya compound. Within a few weeks, a dense barbed wire entanglement surrounded the compound. Other radar stations followed this lead. Every German radar station near the coast now became conscious of its vulnerability, and surrounded itself with barbed wire. That greatly helped Jones and his staff; there were several sites which were suspected to contain Würzburg sets, but in each case the existing aerial photographs had failed to show them. Now these sites obligingly ringed themselves with barbed wire – which showed up well on aerial photographs – to confirm the suspicions. Not only in Germany were there repercussions of the Bruneval operation. The success of the raid highlighted a golden opportunity for a retaliatory attack on the Telecommunications Research Establishment, hub of British work on radar and situated near Swanage on the south coast of England. In the spring of 1942 the establishment made a rapid move to Malvern College, well clear of the coast. +*** +Two weeks after the Bruneval raid came an event that was to have even greater significance to the development of countermeasures systems in Great Britain. On 11–13 February 1942 the German battlecruisers Scharnhorst and Gneisenau, and a flotilla of smaller ships, had left their temporary base at Brest, run the gauntlet of the defences covering the Straits of Dover, and successfully reached ports in Germany. In doing so they had inflicted a major blow to Britain’s reputation as a naval power. The operation had taken place under the noses of powerful British forces and was a masterpiece of boldness, careful planning and tight security. An important element in the success of the operation was the large scale use of ground jammers. As the warships came within range of the British coastal radars at the eastern end of the Channel, these jammers were switched on simultaneously. Many of the best British radar operators were now serving in the +Discovery 77 + + + Mediterranean theatre, where the heaviest fighting was taking place. Those who replaced them at radars along the south coast of England were less experienced and they reported the clutter on their screens as ‘equipment failure’ or ‘local interference’. As a result commanders did not appreciate the significance of the radar operators’ difficulties until it was too late. This all came out during the far-reaching official inquiry after the event. The escape of the German warships would have significant effects. At the beginning of 1942 several important British radars – those for coast watching, ground-controlled interception, airborne interception, AA gun-control and searchlight-control – all operated on frequencies in the 200 MHz band. A heavy German jamming effort in that part of the spectrum would pay rich dividends if there was a resumption of the night Blitz. Thus, by highlighting that fundamental weakness, the escape of the German warships greatly assisted the British cause. Work began immediately to develop new types of radar that worked in widely different parts of the spectrum. Once those were in place, the Germans would never again have the chance to knock out the radar system with so little effort. +*** +During the spring of 1942, British intelligence gradually improved its picture of the Luftwaffe night air defence system. In March, news arrived of an inland Freya station at Nieuwekerken in Belgium, just to the north of the important night-fighter airfield at Saint-Trond. By this time many coastal Freya stations had been located, but inland stations were thought to be a rarity. A high-flying reconnaissance Spitfire was sent to investigate. The photographs it brought back showed a Freya radar set and a cluster of searchlights, but the latter were grouped round a radar with a large circular open-work bowl – like that photographed in the Berlin Zoo. The proximity to the airfield at Saint-Trond strongly suggested that this was some sort of night-fighter control centre. Shortly afterwards this was confirmed. Then an agent reported a night-fighter control centre at Domburg on the Dutch island of Walcheren. And the subsequent high-level photographic reconnaissance revealed a Freya and two ‘Berlin Zoo’ radars there. A more detailed study of the Nieuwekerken site showed there were two ‘Berlin Zoo’ radars there, also. This called +Instruments of Darkness +78 + + + for a closer look at the new type of radar. On 2 May, a reconnaissance Spitfire ran in fast and low along the Dutch coast and past the Domburg site. Yet again Flight Lieutenant Tony Hill had pulled off a low-level scoop, for he returned with clear photographs of both ‘Berlin Zoo’ type radars. As the Spitfire swept past them, the two radars were pointing in different directions. So Hill’s pictures showed the radar from two quite different angles. Equally important, at one of the sets an operator had been about to climb the ladder to the cabin. He stood watching, helpless, to become a human yardstick when the photographs were analysed. One night two weeks later, a further ploy was adopted to elicit information about the range of this radar. An RAF Beaufighter night-fighter flew towards the Domburg area, closely watched by the British radar station on North Foreland. A German night-fighter rose to intercept, and a long and inconclusive engagement followed. Throughout it, the RAF monitoring service recorded the orders passed to the Luftwaffe pilot. In particular, they noted that he was not permitted to move more than forty miles from the radar station. This was a strong pointer to its maximum range. Soon afterwards, the ‘Berlin Zoo’ radar was identified as the Giant Würzburg. The next major item of intelligence came from a Belgian agent. He had managed to steal from a German headquarters a map showing the deployment of an entire regiment of searchlights. As luck would have it, the map covered the area around Saint-Trond. Marking the station at Nieuwekerken was a lightning flash, as were two more at Zonhoven and Jodoigne, some twenty miles on either side. Might these be fighter-control stations too? And if they were, was twenty miles the standard distance between adjacent sites? Reconnaissance photographs revealed that this was the case. By extrapolating the line, Jones and his staff soon picked out five further night-fighter control stations, strung out at regular intervals along an almost straight line. During the summer of 1942, the clump of flags on the wall map in Jones’s office sprouted shoots to either side of its original starting point in southern Belgium. The great radar hunt was on. Charles Frank christened the defensive belt the ‘Kammhuber Line’, and that appellation caught on in the RAF. Agents were sent to areas previously calculated, to seek out the radar stations. Their catch was good; a paraboloid the size of a +Discovery 79 + + + suburban house could hardly escape being the object of wonder and speculation by the local population. It should be remembered that at this time the ‘man in the street’ had never heard of radar. As a result the descriptive vocabulary of the inhabitants of the Low Countries was seriously strained; ‘inverted umbrella’ and ‘magic mirror’ were typical of the terms used. One Giant Würzburg was talked about so much that it became known as ‘le fameux miroir d’Arsimont’. During their flights over Belgium, Holland and northern France, RAF bombers dropped caged carrier pigeons. The birds’ legs bore labels asking the finder to write in details of any large dish-like structures seen in the area, and then release the pigeons. This method alone assisted in locating three sites previously unknown to Dr Jones. In the next chapter, we shall observe how this information was used to develop the first countermeasures to the Luftwaffe night air defence system. +Instruments of Darkness +80 + + + 81 +The rigid airship LZ-130 Graf Zeppelin, the last of these craft to be built, flew an electronic intelligence gathering mission along the east coasts of England and Scotland in August 1939. +Dr Ernst Breuning (right) led the listening team +aboard the Graf Zeppelin. He described to the author how his team picked up signals from the newly erected British radar chain, but misidentified them as coming from a research station in Germany which was conducting experiments to measure the altitude of the ionised layers surrounding the earth. + + + The huge Knickebein beam-transmitter at Stollberg in Schleswig-Holstein. The aerial array was about 100 feet high, and was supported by railway bogies which ran on a circular track 315 feet in diameter to align the beam on the target. +Heinkel 111 bomber of III/KG 26, the unit which employed the Y-Gerät beam system over Britain in 1940–41. Note the additional aerial for the system, mounted above the fuselage behind the cabin. +Wing Commander Edward Addison commanded No. 80 Wing during the ‘Battle of the Beams’. Later he led No. 100 Group, which provided countermeasures support for bomber operations. + + + 83 +Heinkel 111 of Kampfgruppe 100 on the compass swinging base. Note the two additional aerial masts on the rear fuselage, belonging to the X-Gerät beam attack system. +X-Gerät beam transmitter. Dr R. V. Jones played a major role in uncovering the beam systems used by the Luftwaffe during attacks on Great Britain. + + + 84 +Left: The first photo to reach Britain showing that the Germans had radar in service. The Graf Spee, pictured in December 1939 after she had been scuttled off Montevideo. The aerial array of the Seetakt radar can be seen (circled) above the bridge. +Below: In November 1940 a reconnaissance aircraft took this photo of two unusual tub-shaped structures (circled and inset) at Auderville near Cherbourg. In February 1941 a Spitfire flew a risky low-altitude mission to get this close-up of the ‘tubs’, each of which was found to house a Freya radar. + + + 85 +Messerschmitt Bf 110 night-fighter, with the drag-producing aerial array of the Lichtenstein radar on the nose. +Above: Flight Lieutenant, later Wing Commander, Derek Jackson played a major role in the development of ‘Window’ metal foil strips to jam enemy radars including the Lichtenstein. +Left: Wassermann early +warning radar at Bergen aan Zee in the Netherlands. The surrounding houses give scale to the huge 130-foothigh aerial array. + + + Above: Generalmajor Josef Kammhuber, architect of the Himmelbett system. Left: Close-up of the Würzburg radar. Designed for use by flak and searchlight batteries, this radar was also used for a short time to direct nightfighters into action. +Reconnaissance photograph of the Würzburg at Bruneval, taken three months before the famous raid. +Low-altitude photo of the Giant Würzburg radar on the island of Walcheren, taken in May 1942. + + + Following the Bruneval raid, German radar sites were surrounded with dense barbed-wire entanglements, which made them highly conspicuous on aerial photographs. Below: Himmelbett station with a Freya radar (foreground) for long-range search and two narrow-beam Giant Würzburg radars (left and right) to track the movements of the British bomber and the intercepting night-fighter respectively. + + + H2S indicator in the navigator’s position of a Lancaster bomber. +H2S radar picture of Hamburg (right) compared with a map of the same area. The wide estuary of the River Elbe, pointing at the city from the west, served as a prominent navigation feature on radar. + + + 89 +Aerial of a Korfu ground direction-finding station, which tracked RAF bombers by picking up the radiations from H2S. +Generalfeldmarschall Erhard Milch held frequent conferences to discuss each step in the countermeasures battle as it appeared on the German side. +Oberst Dietrich Schwenke headed the Luftwaffe intelligence section responsible for monitoring technical developments by the Western Allies. + + + 90 +Generalmajor Joseph Schmid (right) took control of Luftwaffe night-fighter operations after General Kammhuber was ousted from that post following the ‘Window’ debacle in July 1943. +Major Hajo Herrmann (centre) seen with Reichsmarschall Herrmann Göring during an inspection of ‘Wild Boar’ night-fighter pilots. Major Herrmann had been instigator of those new tactics. +Ideal ‘Wild Boar’ conditions. Seen from above, a Lancaster bomber silhouetted against a cloud background by searchlights and fires on the ground, photographed over Berlin during the raid on 16 December 1944. + + + 91 +Dr Robert Cockburn led the countermeasures team which designed and put into production many of the British jamming systems. +B-17 Flying Fortress modified as a jamming escort aircraft, before issue to No. 214 Squadron, RAF. The radome under the nose housed the scanner for the H2S radar. +Above right: The 600-pound cylinder of the ‘Jostle’ highpowered VHF communications jammer, mounted on the rear of its special transporting truck. This jammer was fitted to the jamming escort Liberators and Flying Fortresses of No. 100 Group. + + + 92 +From the autumn of 1944 Luftwaffe night-fighters needed to be equipped to avoid RAF intruders, as well as engage bombers. This Ju 88 night-fighter carries the nose-mounted aerial array for the SN-2 radar. The blister on top of the cockpit canopy houses the rotating aerial for the Naxos radar-homing and warning receiver . . . +Note the two upward-firing 20-mm cannon fitted in the fuselage . . . +Also the tail mounted aerial for SN-2 to provide warning of Allied intruders closing in from behind. + + + 93 +Above: The Jagdschloss fighter-control radar was the first German radar to employ the plan position indicator type of display. To avoid electronic jamming, the radar had provision for the operator to select one of four separate operating frequencies. +Left: Effect of ‘Mandrel’ jamming on the screen of a Jagdschloss radar. The screen is north-aligned. The three large ‘spokes’ in the northwest quadrant point to three aircraft jamming as part of a ‘Mandrel’ screen. The caterpillar-shaped return heading south-southeast has the appearance of a bomber stream, though in fact it is ‘Window’ spoof. The scattered returns in the southeast quadrant come from Luftwaffe night-fighters and No. 100 Group Mosquitoes. + + + Above: Formation of B-17 bombers being engaged by a flak battery firing though an overcast. Note the effect probably caused by ‘Carpet’ jamming of the fire-control radars: although the bursts appear to be accurate in line, the shells have detonated at the incorrect range and well below the raiders’ altitude. Left: The APQ-9 ‘Carpet III’ jamming equipment, used in large numbers to counter the German Würzburg and Mannheim flak-control radars. +Right: B-29 bombers pictured at one of the islands on the Marianas group. With assistance from radio-countermeasures, these aircraft made devastating attacks on Japanese cities and industrial targets for minimal losses in the spring and summer of 1945. + + + 95 +Above: The ‘Tuba’ equipment, designed and built at the Radio Research Laboratory at Harvard, was the largest and most powerful jamming system produced during World War II. The man standing at the base of the aerial gives scale to the special directional array developed for the jammer. ‘Tuba’ became operational too late to have any effect, however. + + + 96 +‘Little Boy’, the atomic bomb which devastated the Japanese city of Hiroshima. The aerial elements of two of the four radar airburst fuses can be seen mounted on the side of the weapon. +‘Guardian Angel’ B-29, which served as a jamming escort aircraft to provide cover for bombers attacking Japan. Eight jamming aerials are visible on this view of the aircraft. + + + Chapter 4 +Towards the Offensive +‘If you know the enemy and know yourself you need not fear the result of a hundred battles. If you know yourself but not the enemy, for every victory you will suffer a defeat. If you know neither you will always be beaten.’ +General Sun-Tzu +As German troops advanced deeper into the Soviet Union in the summer of 1941, it became clear in Britain that, after almost a year on the defensive, it was time to seize the initiative in the West. Clearly, an invasion of the continent was out of the question in the foreseeable future. For the time being the only readily available means of striking at the German homeland was through RAF Bomber Command. Prime Minister Churchill assured Russian Premier Josef Stalin that, when the weather improved in the spring of 1942, the RAF would launch a heavy air offensive against Germany and: ‘We are continuing to study other measures for taking some of the weight off you.’ Those ‘other measures’ would not materialise for a long time. At that time, however, Bomber Command was going through a period of soul-searching. The fact that the Luftwaffe had found it necessary to develop radio aids to assist accurate navigation and bombing at night had led to some scepticism concerning the results the British bomber crews might themselves be achieving. After all, they had no such aids. One of the doubters was Air Vice-Marshal Robert Saundby, who took up an appointment as Senior Air Staff Officer at Bomber Command headquarters at the end of 1940. He told his staff that, when a force of bombers claimed to have dropped 300 tons of bombs on a certain target, all they could be certain of was that they had ‘exported 300 tons of bombs in its direction’. Professor Lindemann conducted his own investigation into the results of the RAF bombing, based on the photographs brought back by reconnaissance aircraft. The findings were highly disquieting: of the crews who thought they had hit the target, only one in three + + + had in fact placed their bombs within five miles of it. In the case of targets in the Ruhr industrial area, the figure was as low as one crew in ten. After receiving the report in September 1941, Mr Churchill taxed the Chief of Air Staff with this: +It is an awful thought that perhaps three-quarters of our bombs go astray . . . If we could make it half and half, we should virtually have doubled our bombing power. +As a long-term investment, development began on two radio devices to improve bombing accuracy: Oboe and H2S. These will be described in later chapters. For the moment, the most urgent requirement was for a less ambitious radio aid that would improve basic navigational accuracy at night. Fortunately work on such an aid was well advanced at the Telecommunications Research Establishment and the device, codenamed ‘Gee’, was nearing the service trials stage. The ‘Gee’ (or Grid) system of navigation had been conceived in 1938, and work on the device had begun in earnest in the spring of 1940. ‘Gee’ employed three ground transmitters situated about a hundred miles from each other. These transmitters acted in unison to radiate a train of pulses in a set order. The aircraft carried a special radar receiver, which enabled the navigator to measure the minute time differences between the reception of the various signal pulses. By referring those time differences to a special ‘Gee’ map, the navigator could determine his position to within six miles, while flying up to 400 miles from the furthest transmitter. Closer to the transmitters, the accuracy was even better. In its concept ‘Gee’ was a great improvement over that of Knickebein, its nearest German equivalent. The latter gave an accurate positional fix only at the crossing point for a pair of Lorenz-type beams, whereas ‘Gee’ provided fixes for aircraft anywhere within its area of cover. By the beginning of March 1942, sufficient ‘Gee’ receivers existed to equip about one-third of Bomber Command’s aircraft. The device immediately became popular with crews, who affectionately nicknamed it the ‘Goon box’. The Luftwaffe captured its first ‘Gee’ receiver on 29 March, recovered from the wreckage of a Wellington bomber which came down in the sea off Wilhelmshaven. The device had suffered some salt-water damage, but that water had saved it from complete +Instruments of Darkness +98 + + + destruction. As the crew had abandoned the Wellington, one of them initiated the explosive detonator intended to destroy the box. The system had a built-in delay to give everyone time to get clear, and before it went off the water had smothered the charges. The procedure adopted by Luftwaffe intelligence from this point on was similar to that used by R. V. Jones and his team in Britain. Intelligence officers and radio experts hunted for any further scraps of information relating to the new British system. Oberst Dietrich Schwenke, the intelligence officer in charge of the Luftwaffe section dealing with equipment captured in the West, discussed the find at a high-level conference held in Berlin on 26 May. He said the remains of this equipment had been recognised in several shot-down British aircraft, but in every case except the Wilhelmshaven incident and a second aircraft which had also crashed in the sea, the units had been smashed beyond repair when the demolition charge went off. Schwenke continued: +The British [have developed] a new system which gives the pilot [sic] his position at all times. The equipment for this is the receiver I have just described. Tests have been carried out on it by Telefunken, but the set was unfortunately not received in good condition. Our experts are still not in complete agreement concerning the technical working of the equipment. +Schwenke went on to describe the working principle of ‘Gee’, and the way it was used. He added that the equipment was being installed as standard in the each of the RAF’s principal heavy-bomber types – the Wellington, the Lancaster, the Stirling and the Halifax. He continued: ‘I think it is being used not so much to find pinpoint targets, as to improve dead-reckoning navigation.’ Once a working receiver became available, Schwenke planned to install it in a Luftwaffe aircraft. It would then be possible to establish the accuracy of the system over Germany, using the British transmissions. The transmitters were known to be located in southeastern England, in positions where they could cover the Ruhr industrial district. Schwenke said the possibility of jamming was under investigation, but first it was necessary to find out exactly how the system worked and the frequencies it used. He said the ground transmissions were fairly powerful, but he thought they could be jammed if more powerful jamming transmitters radiated +Towards the Offensive 99 \ No newline at end of file diff --git a/storage/TWTVEKE9/Price - 2017 - Instruments of darkness the history of electronic warfare, 1939-1945.pdf b/storage/TWTVEKE9/Price - 2017 - Instruments of darkness the history of electronic warfare, 1939-1945.pdf new file mode 100644 index 0000000..0d5e581 Binary files /dev/null and b/storage/TWTVEKE9/Price - 2017 - Instruments of darkness the history of electronic warfare, 1939-1945.pdf differ diff --git a/storage/US9ZLYX7/.zotero-ft-cache b/storage/US9ZLYX7/.zotero-ft-cache new file mode 100644 index 0000000..d7257bc --- /dev/null +++ b/storage/US9ZLYX7/.zotero-ft-cache @@ -0,0 +1,2212 @@ +TM'^ Lit *' a^> +*1 p ^j***1'" !•*«. .***». +WHv: +i,MM,»i + + + *•* +:*<**, ** * + + + + + The Illustrated Encyclopedia of +COMBAT +AIRCRAFT +OF +WORLD WAR II + + + + + The Illustrated Encyclopedia or +it +Bill Gunston +feeefe +$ookthfift Qubltcatiot]S +Jfewyork +mtft L +9 + + + A Salamander Book +This edition published 1978 by Bookthrift Inc., 257 Central Park West, +New York, +New York 10024. United States of America +Second impression 1978 +ISBN 89673 000 X +Library of Congress Catalogue No. 77-95252 +© Salamander Books Ltd. 1978 +Salamander House, 27 Old Gloucester Street, +London WC1 N 3AF, United Kingdom. +All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of Salamander Books Ltd. +All correspondence concerning the content of this volume should be addressed to Salamander Books Ltd. +Credits +Editor: Ray Bonds +Designer: Steve Henderson +Color drawings: © Pilot Press Ltd.; +Terry Hadler and County Studios (© Salamander Books Ltd.). +Line drawings and cutaways: © Pilot Press Ltd. +Filmset by SX Composing Ltd., Rayleigh, Essex, England. +Color reproduction by Web Offset Reproductions, 32 Paul +Street, London EC2; Metric Reproductions Ltd., Chelmsford, +Essex and Paramount Litho Company, Basildon, Essex, England. +Two-tone color reproduction by Adtype Ltd 9 Clerkenwell +Road, London EC1, England. +Editors Acknowledgments +This book is not the first to be published on the subject, nor will it be the last. But military aviation enthusiasts will quickly recognize that this volume is unlikely ever to be surpassed for sheer number of facts about and illustrations of combat aircraft of World War II. In order to compile a book of this nature one depends very heavily on the assistance of numerous institutions and individuals all over the world. So many people have helped to produce this volume that, while I thank all of them, there is not the space to mention them all here. In particular, though, I am indebted to Bill Gunston who, apart from displaying his sheer professionalism and depth of knowledge in writing in excess of 1 50,000 words of data and description, also gave many useful "leads" towards tracking down elusive contemporary photographs of World War II aircraft; and to Pilot Press for permitting us to reproduce their magnificent color profile drawings, three-view drawings and cutaways; and to the many manufacturers who, though they could not hope to sell one more of their current production aircraft by supplying photographs of their wartime aeroplanes to a book publisher, nevertheless scoured their archives on our behalf; and to all the museums, institutions and individual aircraft enthusiasts who have similarly strived to supply material for this most colorful volume. I thank them all. +We decided to group the aircraft by country of origin, and present them in alphabetical order of manufacturers' names. Where such a strict order has, for space and technical reasons, threatened to deprive a particular aircraft of its deserved coverage, we "adjusted" the alphabet slightly. In particular, to overcome production problems, we positioned the magnificent Terry Hadler fold-out paintings of the Messerschmitt Bf 109 and Bf 1 1 between the Henschel Hs 1 26 and Hs 1 29, and the Grumman F6F Hellcat and the North American P-51 Mustang between the Martin Marauder and the Martin Baltimore. +Ray Bonds +Printed in Belgium by Henri Proost et Cie, Turnr ut. + + + Contents +Introduction 6 +Australia 8 +Czechoslovakia 8 +France 10 +Germany +Great Britain +18 +76 +Holland 126 j +Italy +Japan Poland +129 | +141 | +172 +Soviet Union 174 +United States +of America 197 +Index 254 +i + + + Introduction +conflict called World War II as simple as that. The : es were drawn in in ghting continuously in J been involved in sporadic a Cninese and the Soviet 930. Forgotten areas such as Abyssinia +ow Somalia had been invaded by Italy id Tripolitania and Cyrenaica had sufProsperous Sweden, on the other =3r became embroiled at all, and it is without aspect to that aeronautically important +nation that its aircraft have been omitted from this volume. For various reasons the aircraft that fought man's biggest and most diverse war have remained sub +jects of lasting interest to each new generation. It +was indeed a war that had everything. In many +places "eyeball" confrontations took place between +fighter pilots who could see each other in the cockpit, and it all hinged on personal skill. In other places +a rather different breed of men stalked the night sky, guided by fickle patterns of brightness on small +cathode-ray tubes, until they could pump cannon +shells into something that was just a little blacker +thanthesky background. Technical development was fantastic, and the pre-war air exercises and even +participation in the Spanish Civil War were soon +irrelevant to new operational circumstances. +At the start the war was one-sided. What most +observers regard as the start of World War II took place 11 minutes ahead of schedule at 04.34 on 1 +September 1939 when "Stukas" dive-bombed the Dirschau bridge over the Vistula. This set the scene. For 27 terrible days Poland was subjected to a rain +of bombs put down with little opposition by everything from Hs 123 biplanes to trimotor Ju 52s. There +was no need for advanced technology, and the +campaign taught the Germans little (and even that +was not heeded). Yet later the scene was to change dramatically. By 1942 the Luftwaffe hardly dared fly +over Britain at all, and when the invasion forces were massing in 1944 the Luftwaffe could not even bring back pictures. By this time the Allies were conquering the Luftwaffe even over the heart of +Germany, but the battle was being fought with new +weapons. Radar pierced cloud and darkness —and +often foolishly served as a beacon on which hostile +fighters could home. New navigation aids guided aircraft to their targets, and back to friendly runways. Powerful warheads no longer fell unguided but could be steered by radio signals or electric signals transmitted through wires right up to the +moment of impact. Cannon, rockets and recoilless guns had transformed air combat, while Germany +had made giant strides with amazing "V-weapons" +which actually did nothing to delay her eventual defeat. In World War II more aircraft of more types were built than at any other time in history. Today, with our inflation on one hand and slashed defence budgets (except in the Soviet Union) on the other, +we find it hard even to comprehend how single +factories could roll out complex four-engined + + + 1 +bombers at the rate of 15 to 20 a day. In Germany in the final months there were a few of the most experienced pilots the world has ever seen, some of +whom had flown more than a thousand combat +missions. There were new fighters by the hundred, +but hardly any suitable petrol. The new jets, with their diesel-oil fuel, usually had some supplies; but Allied air power had often wrecked their airfields and some of the Luftwaffe's jet units finished the war operating from public highways and hiding under the roadside trees. There were countless other facets of this war that +emerge from study of its aircraft. It was the first war +in which air power at last extended everywhere, +even into the middle of the wide North Atlantic. No longer could the U-boat lurk undetected, and the anti-submarine aircraft became so deadly that U-boats had to bristle with flak and try and fight +it out on the . Aircraft learned I heaviest t.mkr, i i take out "heirdom point targets and to pierce reinforced 30 feet thick. For the first time supplies <(m surface forces were flown in, and casualties flown out. Thousands of aircrew became familiar with techniques of electronic warfare, including <.h,iff, decoys, jamming and many other artful dodges that +we are still trying to perfect 35 years later. It would +be foolish to give the impression that they were days to which anyone would gladly return, but they +were certainly great days —and nights- with great aircraft. + + + Commonwealth Boomerang +CA-12 to CA-19 Boomerang +(data for CA-12) +Origin: Commonwealth Aircraft Corporation. Australia. +Type: Single-seat fighter. +Engine: 1 ,200hp Pratt & Whitney R-1830-S3C4G Twin Wasp 14-cylinder +two-row radial. Dimensions: Span 36ft 3in (11m); length 25ft 6in (7-77m); height 1 1 ft 6in +(3 5m). Weights: Empty 5.4501b (2474kg): loaded 7.6001b (3450kg). +Performance: Maximum speed 296mph (474km/h): service ceiling +29.000ft (8845m): range at 1 90mph (304km/h) 930 miles (1 490km). Armament: Normally, two 20mm Hispano cannon and four 303in Browning machine guns in wings. History^ First flight 29 May 1942; first delivery August 1942; final de +liveries, early 1944. User: Australia. +Development: When Australia suddenly found itself in the front line, in December 1941. it had no modern fighters save a few Buffaloes supplied to +the RAF in Singapore. To try to produce a stop-gap quickly the Commonwealth Aircraft Corporation at Fishermen's Bend. Melbourne, decided to +design and build their own. But the design team, under Wing Commander +Above: An echelon of four CA-13 Boomerangs of No 5 Squadron, Royal Australian Air Force. These tough and versatile +aircraft served mainly in the New Guinea campaign. +ia534 +534-III and -IV +Origin: A.S.P.R.L. "Avia". Czechoslovakia. Type: Single-seat fighter. Engine: 760/860hp Avia-built Hispano-Suiza 12 Ydrs 12-cylinder vee liquid-cooled. Dimensions: Span 30ft 1 0in (9 4m); length 26ft 7in (8 1m); height 10ft 2in (3 1m). Weights: Empty 3.2181b (1460kg); loaded 4.364lb (1980kg). Performance: Maximum speed 249mph (400km/h); initial climb 2.953ft (900m)/min; service ceiling 34.770ft (10.600m); range 373 miles (600km). Armament: Four 7 92mm Mk 30 (modified Vickers) machine guns. History: First flight (B 34) late 1931; (B 534) August 1933: final delivery. not known but after 1 938 Users: Czechoslovakia (Army). Germany (Luftwaffe). Slovakia (CB. Insurgent AF). +Development: In 1930 the Avia works at Prague- Letnany. a subsidiary of the great Czech Skoda company, appointed a new chief designer. F. Nowotny. His first design was the B 34 fighter, which in 1 932 was studied with a series of radial and vee engines and eventually gelled as the B 534. Above: Avia 534-IV with tailskid instead of wheel. +LetovS328 +S 328 and 528 +Origin: Vojenska Tovarna na Letadla 'Letov'. Czechoslovakia Type: Two-seat reconnaissance bomber and utility. Engine: (S 328) one 635hp Walter (Bristol licence) Pegasus II M2 ninecylinder radial; (S 528) one 800hp Gnome-Rhone Mistral Major 14Krsd 14cylinder two-row radial Dimensions: Span 44ft 1 Uin (13 7m); length 33ft 11|in (10 35m); (528) 34ft Uin; height 10ft 1 1 in (33m); (528) 11ft 2in. Weights: (328) empty. 3.704lb (1680kg): loaded 5.820lb (2640kg) Performance: Maximum speed 174mph (280km/h); (528) about 205mph (330km/h); initial climb 984ft (300m)/min; service ceiling 23.600ft (7200m); range 435 miles (700km). (328 with overload tank, about 795 miles. 1 280km). Armament: Four 7 92mm Ceska-Zbrojovka Mk 30 machine guns, two +fixed in upper wing and two manually aimed from rear cockpit, with provision for two more Mk 30 fixed in lower wings: underwing bomb load of two 265lb (120kg) or six 1101b (50kg) History: First flight (S 328F) February 1933: (S 528) 1935: final S 328 delivery, after March 1940 Users: Bulgaria. Croatia. Czechoslovakia. Finland. Germany (Luftwaffe). Hungary. Slovakia and Soviet-managed Slovak Insurgent Combined Squadron. +Development: The S 328 saw an amazing amount of active service in various hands, and its similarity to the Swordfish shows what it might have accomplished had it carried a torpedo It was designed by a team led by Alois Smolik. who had been chief designer ever since the Letov company evolved from the Czech Military Air Arsenal in 1 91 8. The basic design was the S 28 of 1929, from which Smolik derived the S 228 supplied to Estonia. In 1933 +Left: This Letov S 328 was one of about 100 assigned to combat duty with the Slovakian Air Force in the Polish campaign and on the Eastern Front against the Soviet Union. It is shown in 1 941 -43 markings, with yellow tactical theatre band. These machines equipped Nos 1 and 3 reconnaissance squadrons and No 2 liaison squadron, chiefly in tracking partisans in the Ukraine. Increasingly the Letovs and crews defected to the Soviet side, and on 29 August 1944 the Slovak Uprising led to a "free combined squadron". + + + the familial Ninth hid +I +194? ' line Figl he [esultn rable and by n +I md ti\ the pn tot ^pe in a further 14 I ahead together and CA 12s were soon fighting in New Guinea. 1 minor changes and 49 CA-19s. as well as a C d square tail Boomerangs did not cai heavies " and undertook close supp iuns +Above: Commonwealth Aircraft CA-13 (CA 12 and 19 simi +Left: A CA-13 Boomerang of RAAF No 5 Sqn (actually the aircraft in the foreground in the formation photograph). +ar). +This was probably the finest fighter of its day. having outstanding speed and manoeuvrability, no vices and the heavy armament of four guns. Originally two were in the lower wing, as in Britain's Gloster Gladiator of two years later Wing vibration when the guns were fired led to all four being put in the fuselage, with a bulge over the belt feed and case boxes In 1935 the type went into large-scale production and at the time of the Munich crisis +in September 1 938 over 300 of the eventual total of 445 had been delivered, so the Czech Army was actually stronger in fighters than the Luftwaffe Many of the aircraft were B 534-llls with enclosed cockpit and -IVs with more powerful 1 2Y engine. A batch of 35. designated Bk 534, were to have had a 20mm cannon firing through the propeller hub; only a few had the +Left: An Avia B 534-IV serving with the Slovakian Air Force on the Eastern Front in late 1941 (probably with the 11th Fighter Squadron). The Slovak tail insignia and yellow tactical theatre band are prominent. Like most Slovakian units, which included some equipped with the Do 17Z-2 bomber, these biplane fighters operated in the Ukraine, mainly on the Kiev sector. +big gun, most having a mere machine gun. with one more on each side. About 350 served with the Luftwaffe in 1 939—41 as trainers and tugs for gliders and targets. Slovak Air Force fighter squadrons 11. 12 and 13 operated on the Russian front from July 1941. but morale was low and many Avias deserted to the Soviet side. Three aircraft survived to fight against the Germans in the Slovak revolt of 1 944. +Above: Three-view of standard Letov S 328. +Finland ordered the S 328F. None were delivered to that customer, but the Czech government ordered the 328 for its own Army Air Force reconnaissance squadrons Though there were small batches of 328N night fighters and 328V twin-float seaplanes, nearly all were reconnaissance bombers They continued to come off the line long after flight testing of the 528. the intended successor, had shown superior performance. Only five 528s were built, but when German troops occupied Bohemia-Moravia in March 1939 more than 445 of the earlier type had been delivered. All were impressed into the Luftwaffe or the new Slovak Air Force, while production at PragueLetnany continued, the final 30 being for the Bulgarian Air Force. More than 200 served in the Polish campaign and. from 1941. on the Russian Front. tracking partisans, night-fighting against Po-2 biplanes and even in closesupport of ground forces Many Slovak Letovs defected and in August 1944 surviving 328s in Czechoslovakia donned Red Stars as part of the Insurgent Combined Squadron which fought bitterly against the occupying German forces. +Left: This Letov S 328 was one of about 270 which were eventually assigned to the Luftwaffe A/B Schulen (pilottraining schools); this example was at the school at Olomouc, in Moravia. In winter 1942-43 many Letovs were withdrawn, with instructors, to serve in newly formed Storkampfstaffeln (night attack units). A few were used by the Bulgarian Air Force to patrol the Black Sea coastline. The Slovak examples that revolted in August 1944 adopted a Red Star or insurgent Slovak insignia. + + + Amiot 143 +143M (B-5) +Origin: Avions Amiot (formerly SECM). Type: F ve-seat reconnaissance bomber. +Engines: Two 900hp Gnome- Rhone 14K Mistral Major 14-cylinder air +cooled radials. +Dimensions: Span 80ft 6in (24-53m); length 59ft 1 1 in (18 25m); height 18ft 7Jm (565m). +Weights: Empty 1 3.448lb (6100kg): loaded 19.5681b (8876kg); maximum +overload 21.3851b (9700kg). Performance: Maximum speed 1 93mph (310km/h) at 13.1 20ft (4000m); +maximum cruising speed 168mph (270km/h); normal range 746 miles (1200km); service ceiling 25.930ft (9000m). Armament: Four 7 5mm MAC 1 934 machine guns; up to 1 ,764lb (800kg) of bombs internally and same weight on external wing racks. History: Prototype flew April 1931; production aircraft flew April 1935: first delivery July 1935. User: France (Armee de I'Air) +Above: Three-view of with dorsal turret furt +Amiot 143M her forward +of later pr and other +oduction series minor changes. +BIOCHMB.152C-1 +MB-150 to 157 (data for 152) +Origin: SNCASO. Type: Single-seat fighter. Engine: 1 .080hp Gnome-Rhone 14N-25 14-cylinder radial. Dimensions Span 34ft 6|in (105m); length 29ft 10in (9 1m): height +13ft Oin (3 95m). Weights: Empty 4.453lb (2020kg); loaded 5.842lb (2650kg). Performance: Maximum speed 323mph (520km/h): climb to 16.400ft (5000m) in 6 minutes; service ceiling 32.800ft (10.000m); range 373 miles (600km). Armament: Two 20mm Hispano 404 cannon (60-round drum) and two +7 5mm MAC 1934 machine guns (500 rounds each): alternatively four +MAC 1934 History: First flight (MB-150) October 1937; (MB-151) 18 August 1938: (MB-152) December 1938: (MB-155) 3 December 1939: (MB-157) March 1942. Users: France (Armee de I'Air. Vichy AF). Greece. Romania. +Development: Like so many French aircraft of the time, the Bloch monoplane fighter story began badly, got into its stride just in time for the capitulation and eventually produced outstanding aircraft which were unable to be used. The prototype 150 was not only ugly but actually failed to fly. the frightened test pilot giving up on 17 July 1936. It was only after redesign with more power and larger wing that the aircraft finally left the ground. Bloch had been absorbed into the new nationalised industry as part of SNCASO and five of the new group's factories were put to work making 25. But the detail design was difficult to make, so the MB-1 51 was produced with the hope that 180 would be made each month from late 1938 Orders were also placed for the slightly more powerful MB-1 52. but by the start of World War II only 85 Blochs had been delivered and not one was fit for use; all lacked gunsights and most lacked propellers! Eventually, after overcoming desperate problems and shortages. 593 were delivered by the capitulation, equipping GC 1/1. 11/1. 1/8. 11/8. 11/9. 11/10. 111/10 and III/9 The Germans impressed 173 surviving Bloch 151 and 152 fighters, passing 20 to Romania The MB-1 55 had a 1 .1 80hp engine and was used by Vichy France. The ultimate model was the superb MB-157. with 1.580hp 14R-4 engine and 441 mph (710km/h) speed, never put into production. By this time the firm's founder had changed his name to Dassault +Left: Bloch 152C-1 of GC 11/1, in +operational service when the Germans +invaded France on 10 May 1940. On +that date only two GC (Groupes de Chasse) were combat-ready despite the fact that well over 300 had been completed except for small but vital items. Total production was 140 MB. 151 and 488 MB. 152. Not especially good performers, they were at least tough. One 152C-1 landed on +15 May 1940 after a fight against 12 Bf 109s; it had 360 bullet holes. +Bloch 174 +174 A3, 175 B3 and T +Origin: SNCASO Type: Three-seat reconnaissance, target marker and light bomber. Engines: Two 1.140hp Gnome-Rhone 14N 14-cylinder radials. Dimensions: Span 58ft 9iin (17 9m); length 40ft 1 ^in (12 23m); height 11ft 7|in (3 59m). Weights: Empty 1 2.346lb (5600kg): maximum 15.7841b (7160kg) Performance: Maximum speed 329mph (529km/h) at 17.060ft (5200m); cruising speed 248mph (400km/h): climb to 26.250ft (8000m) 11min; service ceiling 36.090ft (11.000m): maximum range with 880lb (400kg) bomb load 800 miles (1.450km) +Armament: Two 7 5mm MAC 1934 fixed in wings, three fixed at different angles below and to the rear, and two manually aimed from rear cockpit; internal bay for eight 1101b (50kg) bombs, wing racks for light bombs or flares (175. three 441 lb or equivalent). +History: First flight (170-01) 15 February 1 938; (174-01) 5 January 1939; (first production 174 A3) 5 November 1939; first delivery to combat unit (GR II/33) 19 March 1940 Users: France (Armee de I'Air. Aeronavale. Vichy AF). Germany (Luftwaffe). +Development: Under chief designer Henri Deplante the Bloch 170 was planned as a bomber and army co-operation machine in 1936—37 As a result of indecision by the Armee de I'Air this took three years to evolve into the Bloch 1 74 A3 reconnaissance and target-marking aircraft, with secondary capability as a bomber. By the time production of the 174 stopped in May 1940 a total of 50 had been delivered. The first sortie was flown in March 1940 by the famed Capitaine Antoine de Saint-Exupery. As it had an insignificant bomb load the 1 74 made little impact on the Blitzkrieg - it was only in 1942. in Tunisia, that the survivors were fitted to conduct shallow dive +Left: The excellent 174A3 suffered from its French industrial and political environment and none reached the Armee de I'Air until 19 March 1940. The first operational sortie took place on 29 March. Combat experience was outstanding, and the loss rate was even lower than for the equally fast Douglas DB-7. This example served with Vichy GR II/33 at Tunis El Aouina. +10 + + + Development +17 Ai vere all World War I Lewises, will +gun ai I +i ii position +irtime were GB 34 at Dugny. GB 35 at the Annots fiom GB 22) After leaflet with tl m of the Low Countries on 10 May. and I peradropped 338.626lb (153 t< loss of four aircraft But in a desperate day assault on the Sec) ai only one came back from GB 1/38 and 11/38 These served Vichy France and then the Allies as transports in Tunisia until 1944 +Right: Before World War II the Amiots often flew in loose formation on day exercises; wartime missions were at night. +Above: Bloch 151C-1 with cannon armament (152 similar). +Right, upper: A Bloch 151C-1, outwardly almost identical to the slightly faster 152. Most 151s had four machine guns, but many had two cannon like the majority of the MB. 152 type. Seven MB. 151 fighters were sold to Greece and 30 served with Aeronavale (French Fleet Air Arm) squadrons AC 1 and AC 3. +Right: This line-up of MB. 152 fighters probably formed part +of GC 1/1 or 11/1, which were the first units to become operational. In May-June 1940 the Blochs gained 188 victories at the cost of 86 pilots killed, wounded or taken prisoner. +bombing with bombs of up to 500kg (1.1021b) - but the performance and handling were so outstanding and made such a difference to the casualtyrate among squadrons equipped with the type, that the Bloch 175 was hurriedly planned as a purpose-designed bomber Altogether 25 Bloch 175 B3s were completed before France collapsed, with more than 200 on the production line, and had France been able to resist longer the 175 would have been a potent weapon. A few 174 and 175 aircraft saw service with the Luftwaffe, but most served Vichy France in North Africa and many survived the war. Indeed the torpedo-carrying 175T remained in production for the Aeronavale until 1950 +Above: Three-view of Bloch 1 74A3. +Above: A fully combat-ready Bloch 174A3, probably belonging +to GR II/33 after the French Armistice. Later these aircraft +were painted with the crimson/yellow stripes of the Vichy AF +11 + + + Breguet 690 family +Bre. 690, 691, 693 and 6 5 +Origin: Soc. Louis Breguet. Type: Two-seat light attack bomber. +Engines: Two 640/700hp Hispano-Suiza 14AB10/11 14-cylinder radials (693 two 680/700hp Gnome-Rhone 14M6/7 14-cylinder radials). +Dimensions: Span 50ft 4fin (15 3m); length 33ft 7in (10 22m): height +10ft 3|in (34m). +Weights: Empty 6.834lb (3100kg) (693: 6.636lb. 3010kg); maximum loaded 11.0231b (5000kg) (693: 10.8001b. 4900kg). +Performance: (Very similar for both) maximum speed 300mph (483km/h); time to climb to 13.120ft (4000m) 7 minutes; service ceiling 27.885ft +(8500m): range 840 miles (1350km). Armament: One 20mm Hispano 404 cannon with 60-round drum and two +7 5mm MAC 1934 machine guns (500 rounds each) all fixed firing forward +(pilot could tilt all three 1 5° down for ground strafing); one MAC 1 934 fixed +firing obliquely down at rear (late-model 693 also had two more MAC 1 934 +oblique in nacelles); single MAC 1934 fed by 100-round drums on pivoted +mount in rear cockpit; racks for eight 1101b (50kg) bombs in bomb bay. +History: First flight (Bre. 690) 23 March 1938; (Bre 691) 22 March 1 939: (Bre. 693) 25 October 1 939; (Bre 695) 23 April 1 940. Users: France (Armee de I'Air). Italy (RA). +Development: In 1934 designers in seven countries began work on what +were to become significant members of a new breed of fighter having two engines. These were hoped to be in no way inferior in performance to other, smaller, fighters and to be superior in navigation, long-range escort and ground attack. It was also considered they would be superior if fighting should ever be necessary at night. One of the best designs was Breguet's 690. It was finished in March 1937 but then had to wait almost a year for engines, because Breguet had not joined the newly nationalised French industry and Potez had priority for engines for the 630 family. But once it was able to fly it rivalled even the MS. 406 single-seater, adopted as future Armee de I'Air fighter. With all haste, the Bre 691 light attack version was put into production, all but the first 50 having imported Hamilton propellers because of a shortage of the Ratier type. At aircraft No 78 production switched to the Bre. 693. with more reliable G-R engines of even, smaller diameter. By the capitulation 224 had been delivered, plus 50 Bre 695 +hastily put into production with the American P&W Twin Wasp Junior engine, which was lighter and more powerful but actually harmed flight performance, handling and pilot view. Breguet escadrilles fought valiantly, especially GBA I/54 and II/54. The Luftwaffe took engines from 693s to power Hs 129 and Me 323 aircraft, and some dozens of 693s served Italy in 1942-43. +Right: One of the first of the Breguet 690 family to be delivered was Bre. 691 AB2 No 5, seen in manufacturer's finish prior to being ferried to Orleans-Bricy in October 1939. +Above: Three-view of Breguet 691 A-2. +Above: The various Breguet 690-family models were extremely +similar externally. This unit, possibly GBA I/54, was equipped +with the Bre 693 AB2 in the hectic spring of 1940. +Left: Another Hispano-engined Bre. 691 pictured in operational trim with the 54e escadre, the only one to use this troublesome type. The Hispano engines had the oil cooler and carburettor ducts below and above, respectively. +Right: When the Germans occupied the whole of France in November 1942 they seized many Bre. 693s and transferred them to the Italian Regia Aeronautica. Here they served until the Italian collapse in the autumn of 1943, chiefly as operational trainers. Left: A late-production Bre. 693 +AB2 of GBA II/54, the most +successful Breguet unit which was based at Roye in May 1940 but was later able to evacuate to Toulouse-Francazals. The Breguet 690 family proved extremely agile, tough and effective in operation, and so simple to maintain that combat strength was kept up despite frequent retreats. +12 + + + Dewoitine D 520 +D 520S +Origin: SN( Type: Singh sat fi ihtei Engine: ( Ine 910hp H i 12Y-45 Dimensions: Span +lift 3in (3 4n Weights: I i i. 4.6301b (2100kg); loaded 6 Performance: Maximum speed 329mph (530km/h), initial climb 2 •un. service ceiling 36.090ft (1 1 .000m Armament: One 20mm Hispano-Suiza 404 cannon, with 60 ro +i through the propeller hub. and four 7 5mm MAC 1934 machine guns, each with 500 rounds, in wings. History: First flight (520-01) 2 October 1938. (production. 520-2) 3 December 1939. service delivery 1 February 1940 Users: Bulgaria. France. Italy (RA). Romania +Development: Few people have ever disputed that this neat little fighter was the best produced in France prior to the Armistice, it was certainly the best to reach the squadrons Unlike so many other hopeful types which just +Above: The white arrow and roundel surround show that this D 520S (No 147) was photographed in Vichy service. +Above: Three-view of standard D 520S One +D 521 (Rolls Royce Merlin) was flown before the Armistice. +failed to be ready in time, the D 520 made it Doret did not help when, having made a splendid ' about the retractable landing gear on 27 November 1938 ai prototype out of action. The new fighter was a direct devei ' the 500 series and though it was very small it was hoped 1.300hp - but nothing suitable was available. The first prototype had an open cockpit and the second still had a curved windscreen, tailskid and two drum-fed machine guns, as did the first production machine But the second was up to production standard The Dewoitine plants had vanished into the nationalised SNCA du Midi under the law of 1 936 and these were meant to deliver ten in September 1939 and 30 in October. Actually timing ran about three months late, but with the panic in 1940 industry went mad In May 1940 101 were delivered and by June the output had reached ten per day. a figure seldom exceeded by any aircraft plant in history. GC I/3 was first to go into action, followed in late May by GC II/3. with III/3. III/6 and II/7 following before the capitulation These groups were credited with 147 kills for the loss of 85 fighters and 44 pilots. Subsequently the Vichy government restored the D 520 to production. 740 being built in all In 1942 the Luftwaffe seized 411. passing many to Italy. Romania and Bulgaria But in 1944 GC I/8 was re-formed under Doret and. after painting out the German insignia, went into action against the last German pockets in southern France +Farman F222 +F 221, 222 and 223 series +Origin: SNCA du Centre (until 1936 the Farman company). Type: All. basically, five-seat heavy bombers Engines: (F 221) four 800hp Gnome-Rhone GR14Kbrs 14-cylinder tworow radials; (F 222) four 860hp GR14Kbrs: (F 222/2) four 950hp GR14N 11/15 or Kirs: (F 223) four 1.100hp Hispano-Suiza HS14Aa08/09 vee-12 liquid-cooled; NC 223.3. four 910hp HS12Y29; (NC 223.4) four 1.050hp +HS12Y37 Dimensions: Span (F 221. 222. 222/2) 118ft 1Jin (36m); (F 223. NC 223) 110ft 2|in (33 5m): length (F 221-222/2) 70ft 8ain (21 5m); (F 223. NC 223) 72ft 2in (22m): (NC 223.4) 77ft 1 in (23 5m); height (all) 16ft 9in to 17ft 2iin (5 22m). Weights: Empty (F 222/2) 23.1221b (10.488kg); (NC 223 3) 23.2581b (10.550kg). (NC 223.4) 22.046lb (10.000kg); loaded (F 221) 39.242lb (17.800kg): (F 222/2) 41.2261b (18.700kg); (NC 223 3) 42.3291b (19.200kg); (NC 223.4) 52.9111b (24.000kg) Performance: Maximum speed (F 221) 185mph (300km/h): (F 222/2) 199mph (320km/h); (NC 223 3) 248mph (400km/h) (264mph as unarmed prototype); (NC 223.4) 239mph (385km/h); service ceiling (F 221) 19.700ft (6000m); (F 222/2) 26.250ft (8000m); (NC 223.3 at maximum weight) 24.606ft (7500m); (NC 223 4 at maximum weight) 13.120ft (4000m). range with maximum bomb load (F 221) 745 miles (1200km); F 222/2) 1.240 miles (2000km): (NC 223.3) 1.490 miles (2400km); (NC 223 4) 3.107 miles (5000km) +Below: The third F 222/1, one of the first of the big Farmans to be delivered (to GB 1/15, in 1936). The /I differed in its nose and in having no outer-wing dihedral. +Above: Three-view of standard F 222/2. +Armament: (F 221) three manually aimed 7 5mm MAC 1934 machine guns in nose turret, dorsal and ventral positions; bomb load seldom carried: (F 222/2) same guns as 221; normal bomb load of 5.5101b with maximum +internal capacity of 9,2401b (4190kg); (NC 2233) one MAC 1934 manually +aimed in nose, one 20mm Hispano 404 cannon in SAMM 200 dorsal +turret, one 20mm Hispano 404 in SAMM 109 ventral turret: internal bomb +load of 9.240lb NC 223 4. one manually aimed 7 5mm Darne machine gun in entry door: internal bomb load of 4.4101b (eight 250kg bombs). History: -First flight (F 211) October 1931; (F 221) 1933; (F 222) June 1935: (F 222/2) October 1937; (NC 223) June 1937: (NC 223 3) October 1938: (NC 2234) 15 March 1939 User: France (Armee de I'Air. Aeronavale). +Development: This distinctive family formed the backbone of the Armee de I'Air heavy bomber force from 1935 until the collapse in 1940 It began with the F 210 of 1930. which set the pattern in having an angular box-like body, high-mounted wing and four engines slung on braced struts from the wing and fuselage in push/pull double nacelles By way of the 220 came the 221. which served mainly as a 20-seat troop transport. The 222 introduced retractable landing gear, and the 36 F. 222/2 bombers of GBI/15 and 11/15 served tirelessly in the dark months of 1940. often flying bombing missions by night over Germany and even Italy and as transports in North Africa until late 1944. The NC. 223.3. developed after nationalization, was a complete redesign and the most powerful and capable night bomber of 1938—40. The 223 4. a transatlantic mailplane. served with the Aeronavale as a heavy bomber, and in an epic 1 3hr 30min flight on 7—8 June 1 940 one bombed Berlin +13 + + + Morane-Saulnier M.S.406 +M.S.405, M.S.406C-1 +by SNCAO at +Dornier-Werke. +-cooled. (8-1 6m); height +Origin: Aeroplanes Morane-Saulnier; also assembled +St Nazaire-Bouguenais; variant built under licence by +Switzerland. Type: Single-seat fighter. +Engine: One 860hp Hispano-Suiza 12Y-31 vee-12 liquid +Dimensions: Span 34ft 9|in (1060m); length 26ft 9^in +9ft 3|in (2-83m). +Weights: (406) empty 4.1891b (1900kg); loaded 5.364-5.445lb; maximum +loaded 6.000lb (2722kg). +Performance: Maximum speed 302mph (485km/h); initial climb 2.789ft +(850m)/min; service ceiling 30,840ft (9400m); range (without external +tanks) 497 miles (800km). +Armament: One 20mm Hispano-Suiza HS-9 or 404 cannon with drum +of 60 rounds, and two 75mm MAC 1934 in wings each with 300 rounds. +History: First flight (405) 8 August 1935; (production 405) 3 February +Above: Three-view of the standard M.S.406C-1 . The unusual +ventral radio aerial mast is shown retracted. +Right: Cutaway of a typical M.S.406C-1. All the 1,081 fighters of this type completed prior to the Armistice were essentially +identical, and little different +in engineering from the biplanes that preceded them. + + + Utara +Development +continued on page 16 +Above: An M.S.406C-1 with the coolant radiator wound down to the fullest extent. In the air the radiator was progressively cranked up into the fuselage to try to reduce aircraft drag, but the long ventral radio aerial was extended. +Cannon muzzle Propeller spinner +Chauviere 351 M two-pitch propeller Cannon barret Oil filler cap Oil tank Oil cooler 8 Coolant intake 9 Louvres Exhaust ports Hispano-Suiza 12Y-31 12cylinder vee engine +Mam engine support bearer 1 3 Supercharger 14 Fireproof bulkhead (with cannon cut-out) 15 Hispano-Suiza S7 cannon of 20-rnm calibre Cannon ammunition drum (60 rounds capacity) "Plymax" stressed wing skinning 18 Starboard navigation light 1 9 Starboard aileron 20 Ring-and-bead auxiliary sight +"7 +21 Fuselage fuel tank (90 2 +mp gal/410 litres capacity) 22 Main upper longeron elage frame 24 Control column 25 Port instrument console 26 Main instrument console 27 Unarmoured windscreen 28 Reflector gunsight (OPL 31 +) +mounting 29 Sliding cockpit canopy 30 Pilot's seat 31 Seat support frame 32 Provision for oxygen stowage 33 Control runs 34 Transmitter/receiver (Radiondustrie 537) 35 Canop\ tt 36 Crash support bar 37 Aft cockpit glazing 38 Aerial mast 39 "Plymax"' decking 40 Dorsal fabric (over wooden stringers) 41 Elektron formers 42 Main aft fuselage framework (Dural tubing) 43 Cross bracing 44 Fuselage/fin attachment frame 45 Tailskid bracing 46 Rear fuselage frame 47 Fin attachment point 48 Fin construction 49 Fin spar (Duralumin) 50 Balance 51 Rudder framework +52 Rudder post 53 Rudder hinge RudeTab cable Tailplane strut Elevator construction 58 Elevator balance 59 Tailplane structure 60 Ta 61 Ventral fabnc 62 Hinged ventral aenal 63 Wing root fairing 64 Flap construction 65 Port aileron 66 vVingtip constr^ . 67 Port navigation light 68 Wing ribs 69 Forward (main) wing spar 70 Aft wing spar 71 Rear spar/fuselage attachment point 72 Front spar/fuse age attachment points (two) 73 Starboard mainwheel 74 Retractable radiator 75 Radiator retraction links 76 Undercarriage well inner shell +77 Port 7.5-mm MAC 1934 machine gun 78 Ammunition drum (300 round capacity) Pitot tube Mainwheel leg Port mainwheel (lowpressure tyre shown at ground angle) Mainwheel leg fairing Head-on view of canted +mainwheel when ur +79 80 81 +82 83 +15 + + + An unusual feature was the fact that, except for the fabric-covered rear +fuselage, most of the covering was Plymax (light alloy bonded to plywood). +The M.S. 406 was the 405 production version incorporating all the re +quested modifications. The production was shared out among the national +ised groups (Morane retaining only a small part of the work), with production +lines at Bouguenais and Puteaux. By the time of the collapse in June 1940 no fewer than 1 .081 had been completed, despite a desperate shortage of +engines. In May 1940 the 406 equipped 19 of the 26 French combat-ready fighter groups. One who flew them said they were "free from vices, but too slow to catch German aircraft and too badly armed to shoot them down Poorly protected, our own losses were high" The Vichy government fitted 32gal drop tanks to Moranes sent to Syria to fight the RAF. Many were used by Finland, fitted with skis and often with Soviet M-105P engines of higher power (the so-called LaGG-Morane). +•>;r +Above: Comrades in arms, and neither adequate to face the Luftwaffe: an M.S.406C-1 escadrille visited by a Fairey Battle light bomber of the British Advanced Air Striking Force. +Left: M.S. 406C-1 of 1e Escadrille, GC I/2. based at Nimes in the spring of 1940. +Below: New Moranes straight from Bouguennais +are prepared for service at an Armee de I'Air unit in the autumn of 1939. The M.S. 406 was as numerous as the Bf 109 in spring 1940. +,f A A t + + + France +Potez 63 series +630. 631. 633, 637 and 63 11 +Origin : Avi< ins Henri I Type: ti> «> oil ) i ind i > i> l r , 633) eal lighl attai k bomb I t army co operation rei onnaissance. Engines: (t>^0) two 725hp Hisi 14AB ndi row radials all othei version! I IM ol iami I Dimensions: Span 52fl 6in (16m) length I6fl Mn (11 07m); (63-11 36ft lin (I Im) height l If! 9Jin ( i 6m) Weights: Empty (630. 631. 633) typically 5.730lb (2600kg) (I 6.390lb (2900kg). (6311) 6.9121b (3205kg) maximum loaded (631) 8.235lb (3735kg). (633. 637) 9.285lb (4210kg). (63 11) 9.98/lh (45 I0I |) Performance: Maximum speed (630. 631. 633) 273mph (440km h) (637) 267mph (430km/h). (63 11) 264mph (425km h> initial climb (typical) 1 .800ft (550m)/min: service ceiling (630. 631 ) 32.800ft (10.000m). +(others, typical) 26.250ft (8000m) +Armament: See text +History: Fust flight (Potez 63) 25 April 1936. (production 630) February 1938. (prototype 63-11) December 1938 Users: Prance. Germany (Luftwaffe). Greece. Romania. Switzerland +Development: Winner of a 1934 competition for a C3 (three-seat fighter) for the Armee de I'Air. the Potez 63 was a clean twin-finned machine powered by two of the new Hispano slim radials It soon branched into a host of sub-variants, including many for foreign customers. The first 80 production aircraft were 630s. but they were soon grounded due to severe engine failure after only a few hours The 631. however, was more successful and 208 were delivered (121 in May 1940 alone), equipping five fighter squadrons, two Aeronavale squadrons and many other units and shooting down 29 German aircraft (12 by the navy squadrons) in the Battle for +Above: Three-view of Potez 633, the unsuccessful attack bomber version which was widely exported but used as a combat aircraft by the Armee de I'Air on only one mission +France. Most had two (some only one) 20mm Hispano 9 or 404 +one or two 7 5mm MAC in the rear cockpit and. from February 194 +MAC faired under the outer wings. The 633 had only two machine guns, one forward-firing and the other in the rear cockpit, and the profusion of export variants had several different kinds of gun Maximum bomb load was 1.3231b (600kg). including 8801b (400kg) internal Many 633s had a busy war. Greek examples fighting with the Allies and Romanian examples fighting the Russians The 637 was used in numbers in May 1940 but was only a stop-gap for the 63 1 1. with glazed nose and humped rear canopy, which was used in large numbers by the Luftwaffe. Vichy French. Free French and others Over 900 were built, bringing the total for the 63 family to more than 1 .300 +Left : Potez 63 11 No 831 . shown as it was in 1943 when operating alongside other Allied air units in Tunisia. Large numbers of similar aircraft had fought against the RAF in several theatres, and more than 270 served with the Luftwaffe as advanced trainers and light utility transports. In 1942 many Vichy 631 1s were bartered with the Romanians for petrol. +SNCASE LeO 451 +LeO 45, 451 B4 and derivatives +Origin: Soc Liore et Olivier, Argenteuil. in 1937 nationalized as part of SNCASE. production see text. Type: Medium bomber, later transport Engines: Two 1.140hp Gnome-Rhone 14N 48/49 14-cylinder radials Dimensions: Span 73ft lOfin (22 52m). length 56ft 4m (17 17m); height 14ft 9^in (4 50m). Weights: Empty 17.2251b (7813kg). normal loaded 25.1331b (11.400kg); max 26.455lb (12.000kg) Performance: Maximum speed 307mph (495km/h). service ceiling 29.530ft (9000m); range with 1.1021b (500kg) bomb load 1.430 miles (2300km) +Armament: One 20mm Hispano-Suiza 404 cannon in SAMM retractable +dorsal turret. 7 5mm MAC 1934 in retractable ventral turret and MAC 1934 fixed in nose firing ahead; internal bay for up to 4.4101b (2000kg) of bombs. +Above: Three-view of LeO 451 B4 with armament retracted. +Above: The Hispano is prominent on this LeO 451 of the Vichy Air Force (GB I/25, based at Tunis El Aouina) in mid-1942. +History: First flight 16 January 1937; service delivery 16 August 1939; final delivery 1 943 Users: France (Armee de I'Air. Vichy French and post-war AF). Germany (Luftwaffe). Italy (RA and CB). UK (RAF) and US (AAF). +Development: Beyond doubt the best bomber developed in France in the final years before the war. the LeO 45 was also available in substantial numbers Despite chaotic conditions caused by nationalization of the airframe industry and widespread sabotage, production at Paris (Clichy and Levallois) and assembly at Villacoublay got into its stride by the spring of 1939 To provide the stipulated catwalk past the bomb bay small secondary bays were added in the inner wing and the main bay made even narrower than the slim fuselage Production was dispersed to take in factories around Lyons, a second assembly-line at Amberieu (Ain) and a third line at Marignane (Marseilles), and the evacuated Villacoublay plant was hastily moved to an underground works at Cravant near Auxerre in May 1 940 The 451 B4 had been in action from the first day of war. and by May 1940 some 472 equipped eight Armee de I Air groups Missions could not have been more impossible, negating all the type's brilliant qualities. 47 being lost in the first 288 sorties (though on one mission the dorsal gunner destroyed two Bf 110s). Several sub-types served the Vichy forces and Luftwaffe, one Gruppe switching from Stalingrad to equip with the LeO 451 T. Italy, the RAF and USAAF used the aircraft chiefly as a utility transport. +17 + + + Arado Ar 96 +Ar 96A-1, Ar 96B-2 and Ar 396 +Origin : jzeugwerke; production almost entirely assigned to Ago a and Letov in Czechoslovakia Type and multi-role tactical. +Engine: Jhp Argus As IOC inverted vee-8 aircooled; (B) 465hp As 410A-1 inverted vee-12 aircooled. +Dimensions: Span 36ft 1 in (11 00m). length (A) 27ft 1 in. (B) 29ft 1Hin 3m); height 8ft 6^in (2 60m) +Weights: Empty (A) 11871b. (B) 2.8541b (1295kg); maximum (A) 3.476lb +(1577kg). (B) 3.747lb (1695kg). Performance: Maximum speed (A. B) 205mph (330km/h); range (A) 560 miles (900km). (B) 615 miles (990km) +Armament: iA) none; (B) invariably one 7 92mm MG 17 above engine +on right, sometimes 7 92mm MG 15 in rear cockpit and/or other guns in wing bulges and/or light bombs. History: First flight 1938. (B) January 1940. final delivery (C.2B) 1948 Users: Czechoslovakia (post-war). France (S.10). Germany, plus most other Axis air forces. +Development: Designed by Walter Blume. the Ar 96 was a typical Arado product, with distinctive tail and clean stressed -skin structure It proved an ideal advanced trainer, and the Ar 96A entered Luftwaffe service in 1939 In 1 940 much larger orders were placed for the 96B with more fuel and a larger engine, and this remained by far the most important advanced trainer of the Axis. The two-blade Argus propeller had a distinctive pitchcontrol windmill on the spinner, and there were five chief B sub-types of which a few could be used for gunnery and bombing training. The 96B towed light gliders, and even served in tactical roles on the Eastern front with various augmented armament Total production by December 1 944 was 11.546. and Letov built the C 2B version until 1948. The planned Ar 296 was developed into the 396. an all-wood replacement with 580hp As 41 +1 +Crude but effective, this was assigned to the French SI PA works, which after the liberation made large numbers as the S.11. followed by the metal S 1 2 +Right: The Ar 96B series was built in greater numbers than any other trainer in history except the American T-6 family, just topping the Vultee BT-13 Valiant family (11.537). The aircraft illustrated, probably Ar 96B-2 pilot trainers, do not bear the badge of an A/B Schule but by 1942 these were often omitted. All wartime Luftwaffe pilots knew the 96. +Arado Ar 196 +Ar 196A-1 to A-5 (data for A-3) +Origin: Arado Flugzeugwerke GmbH. Type: Two-seat maritime reconnaissance seaplane. +Engine: 960hp BMW 132K nine-cylinder radial. Dimensions: Span 40ft 8in (12 4m); length 36ft 1 in (11m); height 14ft 4Jin (4-4m). Weights: Empty 6.580lb (2990kg); loaded 8.223lb (3730kg). Performance: Maximum speed 193mph (310km/h) at 13.120ft (4000m); initial climb 980ft (300m)/min; service ceiling 23.000ft (7020m); range 670 miles (1070km) at 1 58mph (253km/h) +Armament: Two MG FF 20mm cannon in wings outboard of propeller +disc, one MG 17 7-92mm in top decking and twin MG 17 on pivoted mounting aimed by observer Rack under each wing for 1101b (50kg) bomb. History: First flight (196V1) May 1938; first operational service 1 August 1939 Users: Bulgaria. Germany (Luftwaffe. Kriegsmarine). Romania +Development: One of the very few float seaplanes to be used in World War II outside the Pacific area, the Ar 196 was designed as a replacement +Above: Built in small numbers in 1941, the Ar 196A-4 served on catapults of Kriegsmarine warships and preceded the A-3. +Below: By far the most numerous Ar 196 variant was the A-3, two of which are seen here flying on coastal patrol with 2/SAGr 128. This was formed in July 1943 at Brest and later moved to the south French coast where it ceased to exist. +^feu, +9 1i + + + he He 60 biplane on the catapults of all the German Navy's capital ships Its duties were thus primarily reconnaissance and shadowing of surface vessels, but in comparison with such Allied types as the Curtiss Seagull and Fairey Seafox it had a much higher performance and eventually was given +formidable armament Four prototypes, powered by the 880hp BMW 1 32Dc +engine (derived in Germany from the Pratt & Whitney Hornet), were flown in 1938. two with twin floats and the others with a large central float The following year. 26 Ar 196A-1s were built, entering service in August aboard the battle cruisers Gneisenau and Schamhorst. and at shore bases on the North Sea In 1940 the Ar 196A-3 entered service, and this type made up the bulk of the 401 aircraft built Though quite outclassed by the best fighters, the A-3 was a versatile multi-role aircraft which actually spent most of the war operating on sea patrols from coastal bases, mainly on the Bay of Biscay and islands in the Mediterranean. Batches were built by Vichy- France at Saint Nazaire and, in a slightly modified A-5 form, by Fokker at Amsterdam in 1943-44. About 50 served with co-belligerent Balkan air forces in the Adriatic and Black Sea. The type was never developed as an effective anti-submarine search and strike machine, despite its obvious potential Above: Three-view of a typical Ar 196A-3. +Left: This Ar 196A-3. seen with 1101b SC50 bombs on its wing racks, served with 1 Bordfliegergruppe 196 in the Lofoten Islands in 1943. These seaplanes were scattered throughout the entire shoreline of Europe in 1942-44. +L2#X41 +Left: A rare bird, one of the 20 Ar 196A-1s delivered in 1939 Most went to 1 / and 5/ Bordfliegerstaffeln 196 for embarkation, but this one served with 10 (See)/LG2 at Travemunde. +19 + + + AradoAr 234 Blitz +Ar 234B-1 and B-2 Blitz +Origin: Arado Flugzeugwerke GmbH. Type: Single-seat reconnaissance bomber. +Engines: Two 1.9801b (900kg) thrust Junkers Jumo 004B axial turbojets. Dimensions: Span 46ft 3^in (14 2m); length 41ft 5£in (1265m); height 14ft Uin (43m). +Weights: Empty 11.4641b (5200kg); loaded 18.5411b (8410kg); maximum with rocket takeoff boost 21 .71 5lb (9850kg). Performance: Maximum speed (clean) 461 mph (742km/h); service ceiling 32.800ft (10.000m); range (clean) 1.013 miles (1630km). (with 3.300lb bomb load) 684 miles (1100km). +Armament: Two fixed MG 151 20mm cannon in rear fuselage, firing to rear and sighted by periscope; various combinations of bombs slung under fuselage and/or engines to maximum of 3.300lb (1500kg). History: First flight (Ar 234V1) 15 June 1943. (Ar 234V9 with landing gear) March 1944. (Ar 234B-0 pre-production) 8 June 1944; operational delivery September 1944. User: Germany (Luftwaffe) +Development: As the first jet reconnaissance bomber, the Ar 234 Blitz (meaning Lightning) spearheaded Germany's remarkably bold introduction of high-performance turbojet aircraft in 1944 Its design was begun under Walter Blume in 1941. after long studies in 1940 of an official specification for a jet-propelled reconnaissance aircraft with a range of 1.340 miles The design was neat and simple, with two of the new axial engines slung under a high wing, and the single occupant in a pressurised cockpit forming the entire nose. But to achieve the required fuel capacity no wheels were fitted When it flew on 1 5 June 1 943 the first 234 took off from a three-wheel trolley and landed on retractable skids. After extensive trials with eight prototypes the ninth flew with conventional landing gear, leading through 20 pre-production models to the operational 234B-1. with ejection seat, autopilot and drop tanks under the engines. Main production centred on the 234B-2. made in many sub-variants, most of them able to carry a heavy bomb load. Service over the British Isles with the B-1 began in September 1944, followed by a growing force of B-2s which supported the Battle of the Bulge in the winter 1 944-45. In March 1 945 B-2s of III/KG76 repeatedly attacked the vital Remagen bridge across the Rhine with 2.205lb (1 ,000kg) bombs, causing its collapse Though handicapped by fuel shortage these unmterceptable aircraft played a significant role on all European fronts in the closing months of the war. 210 being handed over excluding the many prototypes and later versions with four engines and an uncompleted example with a crescent-shaped wing. +Above: Ar 234 V1 (first prototype) with skid landing gear. +Above: Take-off by the Ar 234 V9 (ninth prototype), first of the B-series with conventional landing gear. Other advanced features included pressure cabin, ejection seat and computer. +Blohm und Voss Bv 138 +Bv 138A-1, B-1 and C-1 (data for C-1 +) +Origin: Hamburger Flugzeugbau GmbH Type: Six-crew reconnaissance flying boat. Engines: Three 880hp Junkers Jumo 205D diesels with 12 opposed pistons in six cylinders. Dimensions: Span 88ft 7in (27m); length 65ft 1 Jin (19 85m); height 19ft 4iin (5 9m) Weights: Empty 24.250lb (11.000kg); loaded 31.9671b (14.500kg); (rocket assist) 36.337lb (16.480kg). Performance: Maximum speed 171 mph (275km/h); climb to 10.000ft (3050m) in 24mm; service ceiling 16.400ft (5000m). maximum range 2.500 miles (4023km). Armament: 20mm MG 1 51 cannon in front and rear turrets; 1 3mm MG 1 31 in cockpit behind centre engine; four 331 lb (1 50kg) depth charges or other stores under inner right wing. History: First flight (Ha 138V-1) 15 July 1937; first delivery (A-1) January 1940; (C-1) 1941. User: Germany (Luftwaffe). +Below: The definitive version was the Bv 138C, and examples served in many parts of Europe. This C-1 was operated by 3.(F)/SAGr 125, based at Constanza. Romania, on patrol over the Black Sea. +Above The Bv 138 MS minesweeper with degaussing ring. +Right: Somewhere on the bitter Arctic convoy route this Bv 138C of SAGr 130 has made rendezvous with a +U-boat — possibly to take on fuel oil +for its diesels. +20 + + + Below : The Ar 234 was the only jet bomber to be operational m +World War II. and though it did not affect the c mice of tinwar its pinpricks were usually unstoppable. This B 2/P Blit/ served with 9/KG 76 operating from Achmer in February 194b +It is seen with 1.102 lb (SC500) bombs hung under the micelles. but the fuselage rack could carry a 3.086 pounder. +Below: In 1943 development began on a more powerful four engined Ar 234C +series. Some had twinned nacelles. +Development: Originally designated Ha 138. reflecting the fact that the aircraft subsidiary of the Blohm und Voss shipyard is (even today) Hamburger Flugzeugbau. the 138 was designed by Richard Vogt and took a long time to reach its final form Major changes had to be made to the hull, wing, tail and tail booms, though none of the alterations were due to the unusual layout The first 25 Bv 1 38A-1 boats were intended to be ocean reconnaissance platforms, but were not a success and ended up as transports in the Norwegian campaign and thereafter They were underpowered with three +600hp Jumo 205 C diesel engines, the fuel oil being carried inside the tubular main spar of the wing. In late 1940 the Bv 138B-1 entered service with 880hp Jumo 205D engines, further modified tad and a 20mm turret at each end of the hull After building 21. production was switched to the +final Bv 138CM. of which 227 were delivered in 1 941 —43 This had im +proved propellers, added a dorsal MG 131 and was greatly improved in equipment Throughout 1942-45 the 1 38C gave good front-line service in the Arctic, the Baltic, the North Atlantic and Mediterranean. +21 + + + BlohmundVoss +Bv222Wiking +Bv 222 prototypes, 222A and 222C +Origin: Hamburger Flugzeugbau GmbH. Type: Strategic transport flying boat (see text) +Engines: (Most) six 1 .OOOhp Bramo (BMW) Fafnir 323R nine-cylinder +radials. (V7 and 222C) six 980hp Junkers Jumo 207C six-cylinder (12 +piston) diesels. Dimensions: Span 150ft 1 1 in (4600m); length 121ft 4|in (37 00m): +height 35ft 9in (109m). Weights: Empty (A) about 64.000lb (29.000kg). (C) 67.5721b (30.650kg); +maximum (all) 108.0301b (49.000kg). +Performance: Maximum speed (all) 242mph (390km/h) without arma +ment. 183mph (295km/h) with; maximum cruise at height 214mph +(345km/h). (armed) 1 56mph (252km/h); maximum range at 1 52mph (245km/h) 3.790 miles (6100km); endurance 28hr. +Armament: Varied greatly from single 7 92mm MG 81 to five/six power +turrets; (C) 13mm MG 131 manually aimed in bow. 20mm MG 151 in one or two dorsal turrets and two wing turrets (upper surface behind outer +nacelles) plus various MG 131 or MG 81 from side windows History: First flight 7 September 1940; first service mission 10 July 1941. User: Germany (Luftwaffe). +Development: Deutsche Luft Hansa ordered three of the large Bv 222 boats in 1937 for use on the North and South Atlantic. The prototype (222V- 1) was civil, but after initial flight trials was modified into a freight transport for the Luftwaffe. There followed nine further aircraft, no two alike, V9 also being the first of four production 222C-0 transports with Jumo engines and improved armament, as well as FuG 200 Hohentwiel radar and FuG 216 rear warning. Only 13 were flown, and decision to drop the diesels led to a switch to the Fafnir. used in the majority of the prototypes. +Right: The last of the radial-engined A-series was the V8, seen here on the slipway with all engines running. It served only a few weeks with LTS See 222 before being shot down. +s=fi^s-w-" +*t +* +1 +-- ,-J +:^ +Above: Three-view of Bv 222C (V9); inset, right wing of V7. +from No 20. which with 14-19 were almost complete From 1941 the Wikings shuttled from northern Norway to Africa bringing urgent stores. Despite their rmproving equipment, nearly all were shot down or destroyed at their moorings, but four survived to VE-day. one being scuttled by its crew and the others being flown to Britain and the USA for trials. The Wiking posed many development problems, and always seemed underpowered, but its basic qualities were good From it derived the even bigger Bv 238. described at the end of the German section +Dornier Do 17 +Do 17E, F, K and P +Origin: Dornier-Werke GmbH. Type: Three-seat medium bomber (17F. reconnaissance). +Engines: Two 750hp BMW VI 7 3 12-cylinder vee liquid-cooled; (17P) +two 1. OOOhp BMW 132N nine-cylinder radials Dimensions: Span 59ft Oiin (18m); length (17E. F) 53ft 3Jin (1625m) (17P) 52ft 9|in (16 1m); height (17E. F) 14ft 2in (4-3m); (17P) 14ft 1 1 in (4 57m). Weights: Empty (17E. F) 9.9211b (4500kg); (17P) 10.1401b (4600kg); loaded (17E) 15.5201b (7050kg); (17F) 15.4301b (7000kg). (17P) 16.8871b (7660kg). Performance: Maximum speed (V7E. F) 220mph (355km/h): (17P) 249mph (400km/h); service ceiling (17E) 16.730ft (5100m); (17F) 1 9.685ft (6000m). (1 7P) 20. 340ft (6200m); typical range (1 7E) 620 miles (1000km); (17F) 994 miles (1600km); (17P) 745 miles (1200km) +Armament: (17E) one 7 92mm MG 15 manually aimed from rear ventral hatch and one manually aimed to rear from dorsal position, with internal +bomb load of 1.6501b (750kg); (17P) three MG 15s. one (normally fixed to fire ahead) in right windscreen, one in ventral hatch and one in dorsal position, with internal bomb load of 2.205lb (1000kg). History: First flight (single-fin V1 prototype) autumn 1934. (Do 17E) 7 November 1936: (Do 17F) 10 November 1936: (Do 17P) late 1937 Users: Germany (Luftwaffe). Jugoslavia. Soviet Union (2 aircraft only). +Development: Popularly dubbed "the flying pencil" in both Germany and Britain, the Do 17 was not planned as a bomber and secretly tested as a civil transport; its history was the other way round. Deutsche Luft Hansa decided its slender body left much too little room for the six passengers, but the Reichsluftfahrtministerium eventually decided the Do 17 was worth developing as a bomber. Numerous prototypes were built with different noses and engines and eventually the Do 1 7E-1 and the F-1 reconnaissance machine went into large-scale, and widely subcontracted, production for the embryo Luftwaffe. As early as March 1 937 both were in combat service, with +Above: Three-view of the first major Luftwaffe versions, the Do 17F-1 (reconnaissance) and (bottom) Do 17E-1 bomber. +one Staffel of 17Fs being in Spain with the Legion Kondor (there to prove virtually immune to interception by the Republican forces). In the spring of 1937 a Do 1 7M prototype with powerful DB 600 engines walked away from all the fighter aircraft at the International Military Aircraft Competition at Zurich. This caused a great sensation and the first nation to buy the new bomber was Jugoslavia, receiving 20 from Germany plus a construction licence. The Jugoslav Do 17Kb-1 had a very early nose profile (the same, in fact, as the Zurich demonstrator) and Gnome-Rhone 14N radial engines They had a 20mm Hispano cannon and three 7 92mm Brownings. About 70 were on strength when the Germans invaded Jugoslavia in April 1941. two escaping to Greece with cargoes of gold bullion. The several hundred E and F models formed the biggest portion of the Luftwaffe bomber and reconnaissance force up to 1 939. but by the end of that year had been relegated to operational training. The later Do 1 7M-1 (Bramo Fafnir radials of 1 .OOOhp) and Do 17P succeeded the E and F in production during 1937 and saw combat during World War II. They were the final types to retain the slender "flying pencil" shape and hemispherical nose-cap. +Left: A BMW-radialengined Do 1 7P-1 reconnaissance model, serving with 4(F)/14 "Munchausen" +Staffel. In 1939 this was with Luftf lotte IV in Austria, Silesia and Czechoslovakia. +22 + + + DFS 230 +DFS230A-1. B-1, C-1, F-1 +Origin: Deu ,; ititul I +ind i 'iii' i +Type: Dimensions: iih (A B height Weights: I mpl B-1 .'090 (B-1 L630II !100kg) Performance: Normal towing .peed 1 30mph (21 Okm, +1 +180mph ( 2 9 1 ^ +History: First flighl 'iH- 1937; service delivery (A-0) 1938. (A I) User: Germany, and possibly other Axis countries +Development: Apparently no serious thought had been givei ise of gliders in war until Ernst Udet. later head of the Luftwaffe te< hnii al procurement department, visited DFS in 1933 He later placed an order I military transport glider, the DFS 230. which was flown with conspicuous success by Hanna Reitsch in 1937. After demonstrations before senior officers the DFS 230 became the basis around which the new technique of glider-borne assault was developed. On 10 May 1940 it was put into effect with total success by 45 gliders, towed by Ju 52s to carefully planned pinpoint operations on bridges and forts in the Low Countries. The classic assault was on Fort Eben Emael. in Belgium, on the Albert Canal. The vast modern fortress was knocked out and held by 72 men who arrived silently within the outer walls at dawn. They held until the German Army arrived more than 24hr later, suffering total casualties of six men killed and 20 wounded In Crete large forces of DFS 230 and other gliders suffered heavily, but took the island. Hundreds of 230s were used in North Africa and Italy, with progressively less effect, but went out in a blaze of glory when Otto Skorzeny's handpicked force stormed the mountain-top hotel where Mussolini was being held under armed guard and flew him out in a Storch. Most 230s were of the B-1 type with braking parachute: the C-1 had three solid fuel rockets in the nose to stop it in 30 metres, and the F-1 was an enlarged model seating 15 Nearly all were delivered before 1941. output being 1.022 +Above: Three view of .i typical DFS 230A 1 (wheels juttisoimd; +Below: An operational DFS 230A 1 on tow, possibly (luring a +combat mission. The tug was almost always the Ju 52/3m. and +much research was done with close-coupled Starschlepp tows, used later in the war to tow heavy fuel tanks, bombs and even Fi 103 flying bombs. +——1 + +Above: In September 1939 the Do 17P-1 reconnaissance aircraft equipped 22 staffeln, but few were left a year later. +Below: Seen in the 1937 camouflage livery, this Do 17E-1 bomber had the benefit of combat experience in Spain. +23 + + + + Dornier Do 17Z and 215 +Do 17Z-1 and -2 and Do 215A-1, B-1 and B-5 +Origin: Dornier-Werke GmbH. Type: Four-seat medium bomber and reconnaissance. +Engines: (Do 17Z-2) two 1 .OOOhp Bramo Fafnir 323P nine-cylinder +radials: (Do 215B-1) two 1.075hp Daimler-Benz DB 601 A 12-cylinder +inverted-vee liquid-cooled. +Dimensions: (Both) span 59ft O^in (18m); length 51ft 9Jin (15 79m): +height 14ft 1 Hin (4 56m). +Weights: Empty (Do 17Z-2) 11.4841b (5210kg): (Do 215B-1) 12.7301b +(5775kg): loaded (both) 19.8411b (9000kg). +Performance: Maximum speed (Do 17Z-2) 263mph (425km/h): (Do +21 5B-1 ) 280mph (450km/h): service ceiling (Do 1 7Z-2) 26.740ft (81 50m); +(Do 215B-1) 31.170ft (9500m): range with half bomb load (Do 17Z-2) 721 miles (1160km); (Do 215B-1) 932 miles (1500km). +Armament: Normally six 7 92mm Rheinmetall MG 15 machine guns, one +fixed in nose, remainder on manually aimed mounts in front windscreen, two +beam windows, and above and below at rear; internal bomb load up to 22051b (1000kg). +History: First flight (Do 1 7S prototype) early 1938: (Do 17Z-2) early 1939; (Do 215V1 prototype) late 1938; first delivery (Do 17Z-1) January +1939. (Do 215A-1) December 1939; termination of production (Do 1 7Z series) July 1940. (Do 215 series) January 1941 User: Germany (Luftwaffe) +Development: Whereas the slenderness of the first families of Do 1 +7 +bombers had earned them the nickname of "Flying Pencil", the Do 17S +introduced a completely new front end with much deeper cabin and extensive window area all round. Such a change had been obvious from the inadequate defensive armament of the earlier models, revealed in the +Spanish Civil War. and the penalty of increased weight and drag was to +Above: Three-view of the Do 17Z-2. +some degree countered by a search for more powerful engines. The S prototype had DB 600 liquid-cooled engines, as did the Do 17U five-seat pathfinder, of which 12 were delivered to the nine Bomber Groups already using earlier Do 17s. The Do 1 7Z. powered by the Bramo radial engine, was at first underpowered and full bomb load had to await the more powerful Fafnir 323P of the 17Z-2 Between late 1939 and the summer of 1940 about 535 Do 1 7Z series bomber and reconnaissance machines were delivered and. though they suffered high attrition over Britain, they did much effective work and were the most popular and reliable of all Luftwaffe bombers of the early Blitzkrieg period The Do 215 was the Do 1 7Z renumbered as an export version, with the more powerful DB 601 engine. The Do 215A-1 for Sweden became the Do 215B-0 and B-1 for the Luftwaffe and altogether 101 were put into service for bomber and reconnaissance roles: 12 were converted as Do 215B-5 night intruders, with a "solid" nose carrying two cannon and four machine guns, and operated by night over Britain before transfer to Sicily in October 1941. +Left. The Z-2 bombers of MI/KG 2 saw intense action in all campaigns up to 1941 +. +Below: Another Do 17Z-2 of KG 2 seen over the blue Aegean with an almost defenceless Greece ahead, in April 1941. Later, things got tougher. +24 + + + lany +Dornier Do 18 +Do 18D. G, H. N +Origin : i lorniei Werke < imbl i Type: D G reconnaissance md lii i in n le 1 +1 trainei N n i Engines: (D) tandem push/pull lunkers lumo !05< dii I h rated al 600hp (G H N) 'OOhp lumo !05D Dimensions: Span 77ft 9in (23 'm) length 63fl !in (19 !5nr0 heighl +i ii 'ini (5 45m) +Weights: (G I) empty 12.9001b (5850k 1 1 maximum !2.046lb i 1 0.000 kg) Performance: (G-1) Maximum speed at sea level 162mph (260km h) typical cruise I06mph (170km/h); range 2.175 miles (3500km) +Armament: (D-1 ) typically one 7 92mm MG 15 manually aimed from bo and rear cockpits, with underwing racks for 1,1021b (500kg) load of +weapons or stores on each side; (G-1) 13mm MG 131 in bow cockpit, +20mm MG 151 in power dorsal turret, same wing capacity: (H, N) none. History: First flight (civil) 15 March 1935: (D) early 1938: final delivery. late 1939 User: Germany (Luftwaffe. DLH) +Development: 1 he Do 1 8. a pleasant and relatively harmless machine, was the first Luftwaffe type shot down by British aircraft in World War II: a flight of Skuas from Ark Royal caught three of the boats shadowing British warships on 26 September 1939 (and it is a fair reflection on the +~T~ Above. The Do 18G 1 was the most +important sub type of Do 18 +Skua's capabilities as a I 100 were deli-. armed G version Nearly all were < Baltic/Atlantic areas The N used to appeal painted n\ red crosses, though post-war evidence sometimes were engaged in Flint (eli +Below: One of the earlier variants was the Do 18D-1. one of +which is seen on North Sea patrol (possibly with KuFIGr 106) +Dornier Do 24 +Do 24T +Origin: Dornier-Werke GmbH; production by Weser. Aviolanda and Potez-CAMS (SNCAN). post-war. CASA. Spain Type: Reconnaissance flying boat (typical crew. six). Engines: Three 1 .000hp Bramo Fafnir 323R-2 nine-cylinder radials Dimensions: Span 88ft 7in (27m); length 72ft 2in (22m): height 17ft 10in (5 45m) Weights: Empty 29.700lb (13.500kg); loaded 40,565lb (18.400kg). Performance: Maximum speed 211mph (340km/h); service ceiling 19.360ft (5900m). maximum range 2.950 miles (4750km) +Armament: One 7 92mm MG 15 machine gun in bow turret, one MG 15 +in tail turret and one 20mm MG 151/20 or 30mm MK 103 cannon in dorsal turret behind wing; underwing racks for 12 1101b (50kg) bombs or other stores. History: First flight (Do 24V3) 3 July 1937. service delivery (Do 24K) November 1937. withdrawal from service (Spain) 1967 Users: Germany. Netherlands. Spain, Sweden; post-war, France +Below: The main Luftwaffe type was the Do 24T-1, this example being one of the 170 supplied from the Netherlands in 1941 -44. +Above: The Dutch (Cycloneengined) Do 24K-2 of 1937. +Development: This excellent trimotor flying boat was one of the very few aircraft of the Nazi period to be designed for a foreign government The customer was the Netherlands and by 1940 a total of 11 had been built by Weserflugzeugbau and flown out to the Dutch East Indies naval air service (MLD) In addition. 26 more had been supplied by the Dutch de Schelde and Aviolanda companies, under a government-purchased licence After the invasion of the Low Countries production was continued in Holland for the Luftwaffe, with the French Potez-CAMS factory at Sartrouville also assigned to Do 24 production in 1941 Production for the Luftwaffe amounted to 170 in Holland and 48 in France and the type was met all round the European coasts One force-landed in Sweden in 1944. was impressed into RSAF service as the Tp 24 and not surrendered to the USSR +until 1951 After VE-day the CAMS factory continued in production, making a further 20 aircraft to augment ex-Luftwaffe machines for a force of more than 60 in Aeronavale service until 1 955 The remaining aircraft were sold to Spain to augment an original force of 12 purchased from Germany in 1944 Designated HR-5. the Do 24T-3 in Spain and the Spanish Mediterranean and Atlantic islands was the last type of large military flying boat operating in Europe. Since 1969 Dornier has been seeking markets for the proposed Do 24/72 development, powered by three 1 ,800hp Lycoming turboprops +25 +__ + + + DornierDo217 +Do 217E-2, K-2, M-1, J-2/N-2, P-1 +Origin: Don : GmbH. +Type: (E. K M) four-seat bomber: (J. N) three-seat night fighter; (P) four +seat high-altitude reconnaissance. +Engines- (E-2 J-2) two 1 ,580hp BMW 801 A or 801 M 18-cylinder two +row radials: (K-2) two 1 ,700hp BMW 801 D; (M-1. N-2) two 1.750hp +Daimler-Benz DB 603A 12-cylinder inverted-vee liquid-cooled: (P-1) two +1.860hp DB 603B supercharged by DB 605T in the fuselage. +Dornier Do 217K-1 +cutaway drawing key: 1 Starboaid rudder tab 2 Rudder controls 3 Rudder mass balance (lead insert) 4 Starboard tailfin 5 Leading-edge slot 6 Tailplane/tailfin attachment 7 Elevator 8 Elevator mass balance 9 Fixed tab 10 Tr 11 Tailplane construction 1 2 Elevator controls 1 3 Rear navigation light +14 Four aft-firing 7 9-mm MG 81 machine guns (Rustsaiz [field conversion set] 1 9) --!" munition boxes 16 Tailplane trim control 17 Fuel emergency jettison 18 Mudguard 19 Tailwheel 20 Taifwheel doors 21 Tailwheel retraction mechanism 22 Tailplane carry-through 23 Fuselage skinning 24 Master compass 25 Dipole antenna +26 Anti-collision beacon 27 Elevator mass balance 28 Port tailfin 29 Leading-edge slot +30 Bomb bay division +31 Bomb bay hinge line +32 Bomb bay rear bulkhead +entry/inspection hatch • +Dimensions: Span 62ft 4in (19m): (K-2) 81ft 4iin (24 8m); (P-1) 80ft 4in (24-4m): length 56ft 9^in (173m); (E-2 with early dive brakes) 60ft 10iin (18 5m); (K-2 and M-1) 55ft 9in (17m); (J and N) 58ft 9in +(179); (P) 58ft 1 1 in (17 95m); height 16ft 5in (5m) (all versions same +within 2in). Weights: Empty (E-2) 19.5221b (8850kg); (M-1) 19.985 (9000kg); (K-2. J andN) all about 21 .000lb (9450kg): (P) about 23.000lb (10.350kg); loaded (E-2) 33.070lb (15.000kg); (K-2. M-1) 36.8171b (16.570kg); (J and N) 30.203lb (13.590kg): (P) 35.200lb (15.840kg) +Performance: Maximum speed (E-2) 320mph (515km/h): (K-2) 333mph +(533km/h); (M-1) 348mph (557km/h): (J and N) about 311mph (498km/h); (P)488mph (781 km/h): service ceiling (E-2) 24.610ft (7500m): (K-2) 29.530ft (9000m); (M-1) 24.140ft (7358m); (J and N) 27.560ft +(8400m): (P) 53.000ft (16.154m); range with full bomb load, about 1.300 miles (2100km) for all versions. +Armament: (E-2) one fixed 15mm MG 151/15 in nose, one 13mm +MG 131 in dorsal turret, one MG 131 manually aimed at lower rear, and +three 7-92mm MG 1 5 manually aimed in nose and beam windows: maximum bomb load 88181b (4000kg). including 33071b (1500kg) external: (K-2) +52 53 +54 +33 Spherical oxygen cylinders +34 Starboard mainwheel 35 Mudguard 36 Mainwheel doors 37 Mainwheel retraction mechanism 38 Mainwheel well 39 FuG 25 (A-A recognition) 40 FuG101 radio altimeter 41 Outer section split flaps 42 Starboard aileron 43 Aileron tab 44 Control lines 45 Rear spar 46 Braced wing ribs 47 Intermediate ribs 48 EGS 101 antenna 49 Starboard navigation light 50 Front spar 51 Leading-edge hot-ait de-icing Hot-air duct Balloon-cable cutter in leading-edge Starboard outer fuel tank (35 Imp gal/1 601 capacity) 55 Starboard oil tank (51 7 Imp gal/2351 capacity) 56 Flame-damping exhaust pipes 57 Sliding-ring cooling air exit 58 BMW801D14-cylinder two-row radial engine 59 Annular oil cooler +60 VDM Three-blade metal propeller of 12 79ft (3 90m) diameter 61 Cooling fan 62 Cowling sliding nose-ring 63 Propeller boss 64 Starboard inner fuel tank (1 75 Imp gal/7951 capacity) 65 Fuselage main fuel tank (231 Imp gal/10501 capacity) 66 Wing spar carry-through +67 Bomb bay top hinge line +68 Load-bearing beam +69 Bomb shackle +70 Bomb bay centre hinge line +71 Typical bomb load: two +2.205-lb(1000-kg) SC +1 000 bombs +Forward bomb doors +1 3-mm MG 1 31 machine gun in ventral position (1.000 rounds) +72 73 +74 Ammunition ejection chute 75 Ventral gunner's station 76 Armoured bulkhead 77 Cartridge collector box 78 Batteries (two 24-Volt) 79 Radio equipment 80 Dorsal gunner's seat support 81 Cabin hot-air 82 Dorsal gunner's station 83 Armoured turret ring 84 Aerial mast 85 Gun safety guard 86 Starboard beam-mounted +7 9-mm MG 81 machine gun (750 rounds) +87 1 3-mm MG 131 machine +gun (500 rounds) 88 Electrically-operated dorsal turret 89 Revi gunsight 90 Angled side windows 91 Jettisonable decking 92 Bomb-aimer's folding seat 93 Navigator's table 94 Pilot's contoured seat 95 Rear-view gunsight 96 Upper instrument panel 97 Nose glazing 98 Control horns 99 Engine controls +100 One 1 3-mm MG 131 in strengthened nose glazing (alternatively twin 7-9-mm +MG81Z) +101 Balloon-cable cutter in nose horizontal frame +102 Cartridge ejection chute 103 Ammunition feed 104 Lotfe 7D bombsight +105 Bomb aimer's flat panel 106 Control column counterweight 107 Nose armour 108 Ventral gunner's quilt 109 Ammunition box (nose +MG 131) +110 Cartridge collector box +11 +1 +Entry hatch 112 Entry hatch (open) 1 1 3 Entry ladder 114 Port mainwheel doors 115 Mudguard 116 Port mainwheel 117 Mainwheel leg cross struts 118 Port engine cowling 119 Landing light (swivelling) 120 Control linkage 1 21 Pitot head 122 Port navigation light 123 Port aileron 1 24 Aileron trim tab +Above: The sixth pre-production Do 217E-0 +was used by BMW for engine development. +26 + + + Above: The Do 217K-1 with new cockpit but original wing +History +Users: +Development +B +I +continued on page 28 +27 + + + different in detail design. Much of Domier's efforts in 1 938-40 were devoted +to finding more powerful engines and improving the flying qualities, and +when the BMW 801 radial was available the 217 really got into its stride +and carried a heavier bomb load than any other Luftwaffe bomber of the +time. Early E models, used from late 1 940. had no dorsal turret and featured a very long extension of the rear fuselage which opened into an unusual dive brake. This was soon abandoned, but the 217 blossomed out into a prolific +family which soon included the 21 7J night fighter, often produced by +converting E-type bombers, and the N which was likewise produced by converting the liquid-cooled M. Several series carried large air-to-surface missiles steered by radio command from a special crew station in the bomber. Long-span K-2s of lll/KG 100 scored many successes with their +formidable missiles in the Mediterranean, their biggest bag being the Italian capital ship Roma as she steamed to the Allies after Italy's capitulation The pressurised high-altitude P series had fantastic performance that would have put them out of reach of any Allied fighters had they been put into service in time. From 1943. Dormer devoted more effort to the technically difficult Do 317. which never went into service +Below: This Do 217. Werk-Nr 4572, was the first of the K-2 family. Major structural stiffening allowed the span to be increased to about 81ft 4^in, enabling the aircraft to lift additional fuel and two of the Fritz X guided missiles which weighed 3,454lb each. +Dornier Do 335 Pfeil +Do 335A-1 and A-6 +Origin: Dornier-Werke GmbH. Type: (A-1) single-seat fighter. (A-6) two-seat night fighter. Engines: Two 1 ,900hp Daimler-Benz DB 603G 12-cylinder mverted-vee liquid-cooled, in push/pull arrangement. Dimensions: Span 45ft 4in (13 8m); length 45ft 6in (13 87m); height 16ft 4in (4m) Weights: Empty (A-1) 16.3141b (7400kg); (A-6) 16.9751b (7700kg); maximum loaded (both) 25.8001b (11.700kg). Performance: Maximum speed (A-1) 413mph (665km/h) sustained; 477mph (765km/h) emergency boost (A-6 about 40mph slower in each case); initial climb (A-1) 4.600ft (1400m)/min; service ceiling (A-1) 37.400ft (11.410m); (A-6) 33.400ft (10.190m); maximum range (both) 1 .280 miles (2050km) clean, up to 2.330 miles (3750km) with drop tank Armament: Typical A-1. one 30mm MK 103 cannon firing through front +propeller hub and two 15mm MG 151/15 above nose, underwing racks for light stores and centreline rack for 1 .1 001b (500kg) bomb. A-6 did not carry +bomb and usually had 15mm guns replaced by 20mm MG 151 /20s. History: First flight (Do 335V1) autumn 1943. (production A-1) late November 1944 User: Germany (Luftwaffe) +Development : Dornier took out a patent in 1 937 for an aircraft powered by two engines, one behind the other, in the fuselage, driving tractor and pusher propellers In 1939—40 Schempp-Hirth built the Go 9 research aircraft to test the concept of a rear propeller driven by an extension shaft and in 1941 work began on the Do 231 fighter-bomber. This was replaced by the Do 335 and by first flight Dornier had orders for 14 prototypes, ten preproduction A-Os. 11 production A-1s and three dual-control trainer A-10 and A-1 2 with stepped tandem cockpits. At high speed the 335 was prone to unpleasant porpoising and snaking, but production continued on the A-1. the A-4 reconnaissance batch and the A-6 with FuG 220 radar operated by a rear-seat observer. Though heavy, the 335 was strong and very fast and was notable in having the first production type of ejection seat (for obvious reasons). By VE-day about 90 aircraft had been rolled out. more than 60 flown and about 20 delivered to combat units. Work was also well advanced on a number of versions of the Do 335B heavy fighter, +with added 30mm MK 108 cannon in the wings (some having two-stage engines and long-span wings), the Do 435 with various very powerful engines, and the twinned Do 635 with two Do 335 fuselages linked by a new parallel centre-section. The 635. which was being designed and produced by Junkers as the 8-635. would have weighed 72.0001b as a reconnaissance aircraft, and flown 4.050 miles cruising at 398mph. Pfeil means "arrow ". +Right: The only Pfeil in existence is this completely rebuilt +exhibit. It was originally the second Do 335A-0. flying in late +May 1944. In 1945 it was taken to the USA, languished at the Smithsonian's Silver Hill store, and 25 years later was returned +to Germany and restored by Dornier at Oberpfaffenhofen. +Above: Three-view of the Do 335A-6 two-seat night fighter with (inset) the long-span wing of B-8. +Below: The Do 335 V9, completed to full production standard +and tested at Rechlin in May 1944. +28 + + + Germany +Right A Do 21 7E 2/R19 of 9 KG 2 based at Gilze Rijen for missions against England in 1941 43 +Right: A Do 217E-5 of 6/KG 100 based +at Istres, near Marseilles. This was one of the first aircraft to use the Hs 293 radio-guided missile in action. +Above: An earlier picture of the second A-0, the same machine +as seen on the opposite page. It was used by EKdo 335. +Below: The Do 335 V3, like the second prototype, differed in many respects from the V1 flown in October 1943. +29 + + + Fieseler Fi 156 Storch +Fi 156A, C, D, E, Fi 256 +Origin: Gerhard Fieseler Werke GmbH. Kassel; production almost entirely orane-Saulnier. Puteaux. and Benes-Mraz. Czechoslovakia. Type: STOL multi-role, see text. Engine: (Almost all) 240hp Argus As 10C inverted-vee-8 aircooled; certain sub-types used other As 10 models of 260 or 270hp Dimensions: Span 46ft 9in (14 25m); length 32ft 5|in (9 90m); height +9ft 1 0in (300m). +Weights: (Typical C) empty 2.0501b (930kg); maximum 2.9101b (1320kg) +Performance: Maximum speed 109mph (175km/h): minimum speed 32mph (51km/h): ground run (takeoff) 213ft (65m). (landing) 61ft (20m); range (max payload) 236 miles (380km). (max fuel) 600 miles (966km) at 60mph (97km/h). History: First flight May 1936: service delivery, about May 1937. final delivery (France) 1949. Users: Bulgaria. Croatia. Finland. France (1944 onwards). Germany. Hungary. Italy. Romania. Slovakia. Switzerland; captured specimens by most Allied air forces. +Development: Though only about 2.700 Storch (Stork) were built for the Axis. 2.549 of them during the war. it was used on every European front and for a vast range of duties. It beat two aeroplanes and a helicopter in a 1935 RLM competition for a STOL army co-op. casevac and liaison +Above: Fi 156C-1, with in-flight landing-gear position dotted. +*4feS +l +Focke-Wulf Fw44 +Fw 44A, B and C Stieglitz (Goldfinch) +Origin: Focke-Wulf Flugzeugbau. Bremen, licence-built in Argentina. Austria. Brazil. Bulgaria and Sweden Type: Primary trainer (also civil sporting aircraft) Engine: (Fw 44A and C) 1 50hp Siemens Sh 14A seven-cylinder radial Dimensions: Span 29ft 6im (9 00m): length 23ft 11 Jin (7 30m): height 8ft 10iin (2 70m) Weights: Fw 44C empty 1.1581b (525kg); loaded (aerobatic) 1.6981b (770kg). (normal) 1.9181b (870kg). Performance: Maximum speed 1 1 5mph (185km/h); range 419 miles (675km). History: First flight September 1932; final delivery after 1938 Users: Argentina. Austria. Bolivia. Brazil. Bulgaria. Chile. China. Colombia. Czechoslovakia. Finland. Germany (Luftwaffe and Luftdienst). Hungary. Romania. Sweden and Turkey. +Development: Designed under Kurt Tank in 1931 as the A44 (from the former Albatross-werke). the Fw 44 was the first really big success by Focke-Wulf and many thousands were made over a period of about a decade. At least 300 were exported prior to World War II. some of these being of the Fw 44B type with 1 20hp Argus As 8 inverted four-in-line engine. Of mixed construction, this trim tandem-seat biplane was delightful to fly and fully aerobatic. The cockpits had small fold-down side doors, bucket seats for a seat-type parachute and a folding rear seat for access to a baggage locker where a blind-flying hood could be clipped In winter many Luftwaffe Stieglitz operated on skis This popular machine equipped +Above: Three-view of typical Fw 44C with wheeled landing gear. +at least ten of the regular Flugzeugfuhrerschulen (FFS. pilot schools) and the officer candidate school at Furstenfeldbruck. Munich +Below: The Fw 44 was one of the mass-produced aircraft of +the Luftwaffe, but unlike the Ar 66 and Go 145 it was not used as a tactical attacker by night. A curious feature of nearly all Focke-Wulfe aircraft of 1930-38 was the tail, with high tailplane ahead of the fin (and often with small auxiliary fins). + + + © +Above: A Fieseler Fi 156C-3/ Trop operating in the North African theatre. Many were assigned as hacks to Luftwaffe units. +Left: One of the first production Fi 156C-1 Storch STOL aircraft making a tail-high full-flap landing (note full upelevator). The Storch was large enough to fly many kinds of battlefield mission, and its only significant shortcoming was slow cruising speed (never more than 93mph). Feldmarschall +Kesselring eventually switched to the faster Fw 189. +5F* K T +indard Si also the usual model formations, and it could large cabin There was only two seats The side wim so that a small lower row < important series were the D sub Morane-Saulmer developed the wide fiv fui miles (3300kmi Armament: See text +History: Fust flighl (prototype) about October 1936. service del (I ISA 0) July 193/. final delivery about July 1944. Users: Bulgaria. Finland. Germany. Norway. Sweden. UK (RAF) +Development: A wholly outstanding machine in all respects, the 1 1 5 was tough, beautiful to fly at speeds down to 75 knots, and carried a substantial load at relatively high speeds. In 1938 the prototype was specially streamlined to set class records, and the first Luftwaffe operational version, the A 1 +. +Above: A Weser built He 115B of 1939. one of the earliest versions for service use. Survivors were later re equipped. +was sold to Norway and Sweden with small ch carried one LTF 5 or 6b torped' other stores, and the nose and real gun. By 1939 long-range B models were in production, whi the new 2.028lb (920kg) magnetic mine in add ! 02lb (50 bomb load at a cruising speed of some 1 50mph The B-2 hac thened for ice or snow In April 1940 the Norwegian aircraft wer< in fierce combat and made many bombing missions on Germar the four survivors set out for Scotland. One of these was fitted with wing machine guns and used by the RAF on secret agent-dropping between Malta and North Africa. Another Norse escapee was used in Finland In 1940 production centred on the C series, with many variants and often an +MG 151 cannon in the nose The single D had 1.600hp BMW 801 engines. and after being out of production 18 months a further 141 E -models were built in 1944 to bring the total past the 400 mark Like the earlier versions the E-series were used for armed reconnaissance, minelaying. utility transport and casevac and even shallow dive bombing and torpedo bombing. +Left: Three-view of He 115B-1 ; later a nose cannon was added. +Heinkel He 177 Greif +He 177A-0 to A-5, He 277 and He 274 +Origin: Ernst Heinkel AG: also built by Arado Flugzeugwerke Type: He 177. six-seat heavy bomber and missile carrier. Engines: Two 2.950hp Daimler-Benz DB 610A-1/B-1, each comprising two inverted-vee-1 2 liquid-cooled engines geared to one propeller. Dimensions: Span 103ft 1|in (31 -44m); length 72ft 2in (22m). height 21ft (6 4m) Weights: Empty 37.038lb (16.800kg). loaded (A-5) 68.343lb (31.000kg) Performance: Maximum speed (at 41.0001b. 18.615kg) 295mph (472 km/h), initial climb 853ft (260m)/min; service ceiling 26.500ft (7080m): range with FX or Hs 293 missiles (no bombs) about 3.107 miles (5000km) +Armament: (A-5/R2) one 7 92mm MG 81J manually aimed in nose, one +20mm MG 1 51 manually aimed at front of ventral gondola, one or two 1 3mm +MG 131 in forward dorsal turret, one MG 131 in rear dorsal turret, one MG +1 51 manually aimed in tail and two MG 81 or one MG 1 31 manually aimed at rear of gondola: maximum internal bomb load 13.2001b (6000kg). seldom carried; external load, two Hs 293 guided missiles. FX 1400 guided bombs, mines or torpedoes (more if internal bay blanked off and racks added below it) History: First flight (He 177V-1) 19 November 1939. (pre-production He 177A-0) November 1941: service delivery (A-1) March 1942. (A-5) February 1943. first flight (He 277V-1) December 1943: (He 274. alias AAS 01 A) December 1945 User: Germany (Luftwaffe) +Above: The He177A-1/R1. the first major production version in 1942. +Development: The Heinkel 1 77. Germany's biggest bomber programme in World War II, is remembered as possibly the most troublesome and unsatisfactory aircraft in military history, and it was only through dogged courage and persistence that large numbers were put into service. Much of the fault lay in the stupid 1938 requirement that the proposed heavy bomber and anti-ship aircraft should be capable of dive bombing. Certainly the wish to reduce drag by using coupled pairs of engines was mistaken, because no engines in bomber history have caught fire so often in normal cruising flight Six of the eight prototypes crashed and many of the 35 preproduction A-Os (built mainly by Arado) were written off in take-off swings or in-flight fires. Arado built 1 30 A-1 s. followed by 1 70 Hemkel-built A-3s and 826 A-5s with repositioned engines and longer fuselages. About 700 +served on the Eastern Front, many having 50mm and 75mm guns for tankbusting; a few nervously bombed Britain in 400mph shallow dives, without any proper aiming of their bombs. So bothersome were these beasts that Goering forbade Heinkel to pester him any more with plans to use four separate engines, but Heinkel secretly flew the He 277. with four 1.750hp DB 603A. at Vienna, as the first of a major programme The almost completely redesigned He 274 was a high-altitude bomber developed at the Farman factory at Suresnes. with four 1.850hp engines, a 145ft wing and twin fins After the liberation it was readied for flight and flown at OrleansBricy. +Left: Main operational model was the A-5. of which 826 were built. This A-5/R2 has external racks for Fritz-X and Hs 293 guided missiles under its wings and on the centreline. +41 + + + Heinkel He 162 Salamander +He162A-2 +Origin: Ernst Heinkel AG: first batch Vienna-Schwechat. production totally dispersed with underground assembly at Nordhausen (Mittelwerke). Bernberg (Junkers) and Rostock (Heinkel) Type: Single-seat interceptor. +Engine: One 1.7601b (800kg) thrust BMW 003E-1 or E-2 Orkan single +shaft turbojet. Dimensions: Span 23ft 7|in (7 2m); length 29ft 8iin (9m); height 6ft 6^in +(2-6m). Weights: Empty 4.796lb (2180kg); loaded 5.940lb (2695kg). +Performance: Maximum speed 490mph (784km/h) at sea level. 522mph (835km/h) at 19.700ft (6000m): initial climb 4.200ft (1280m)/min: service ceiling 39.500ft (12.040m): range at full throttle 434 miles (695km) +at altitude. +Armament: Early versions, two 30mm Rheinmetall MK 108 cannon with +50 rounds each; later production, two 20mm Mauser MG 1 51/20 with 1 20 rounds each History: First flight 6 December 1944: first delivery January 1945 User: Germany (Luftwaffe). +Above: Three-view of the mass-produced He 162A-2 Salamander. +Right: An He 162A-2 of l/JG 1 at Parchim for pilot conversion in March 1945. +Above: At one of the Heinkel plants an unpainted 162A-2 sits +with canopy shattered in May 1945. +Development: Popularly called "Volksjager" (People's Fighter), this incredible aircraft left behind so many conflicting impressions it is hard to believe the whole programme was started and finished in little more than six months To appreciate the almost impossible nature of the programme. Germany was being pounded to rubble by fleets of Allied bombers that darkened the sky. and the aircraft industry and the Luftwaffe's fuel supplies were inexorably running down Experienced aircrew had nearly all been killed, materials were in critically short supply and time had to be measured not in months but in days. So on 8 September 1944 the RLM issued a specification calling for a 750km/h jet fighter to be regarded as a piece of consumer goods and to be ready by 1 January 1945. Huge numbers of workers were organised to build it even before it was designed and Hitler Youth were hastily trained in primary gliders before being strapped into the new jet. Heinkel. which had built the world's first turbojet aircraft (He 178. flown 27 August 1939) and the first jet fighter (He 280 twin-jet. flown on its jet engines 2 April 1941) won a hasty competition with a tiny wooden machine with its engine perched on top and blasting between twin fins. Drawings were ready on 30 October 1 944. The prototype flew in 37 days and plans were made for production to rise rapidly to 4.000 per month Despite extreme difficulties. 300 of various sub-types had been completed by VE-day. with 800 more on the assembly lines. I/JG1 was operational at Leek, though without fuel. Despite many bad characteristics the 162 was a fighter of a futuristic kind, created in quantity far quicker than modern aircraft are even drawn on paper +Right : This He 1 62A-2 belonged to 2/JG 1 at Leek, where conditions were completely chaotic. +Right: A third He 162A-2. this time assigned to 3/JG-1 at Leek, a Gruppe that never converted to jets. +Right: Another He 162A-2 from 3/JG 1 at Leek. As they burned diesel oil the jets did have at least some fuel. +42 + + + He219Uhu +He 219A-0 to A-7, B and C series +Origin : I rnsl I leinkel +Type Engines: l lsual n I +: Ohp Daimlei I +liquid coi Dimensions: 60f1 Bin (18! +s) 50ft I I jin (15-! I +Weights: (A Performance limb +1.804ft (550m)/min. service 1 1 ,660ft (12. /00m) range I 243 mile, (2000km) Armament: \ aried. see text History: ( irsl flight (219V-1) 15 November 1942; service delivery (pi types) May 19 i n 219A 1) November 1943 User: Germany (Luftwaffe) +Development: I mst Heinkel was the pioneer of gas-turbine jet an flying the He 178 on 27 August 1939 and the He 280 twin-jet fighter as a glider on 22 September 1940 and with its engines on 2 April 1941 (before the purely experimental Gloster E 28/39) But Heinkel was unable to build the extremely promising He 280 in quantity, which was fortunate for the Allies He had no spare capacity for the He 219 either, which had excited little official interest when submitted as the P. 1060 project in August 1940 as a high-speed fighter, bomber and torpedo carrier It was only when RAF night attacks began to hurt, at the end of 1 941 . that he was asked to produce the 21 9 as a night fighter (Uhu meaning Owl). The He 219V-1. with 1.750hp +DB 603AS and two MG 151/20 cannon, plus an MG 131 in the rear cockpit, was fast and extremely manoeuvrable and the test pilots at Rechlin were thrilled by it. Successive prototypes had much heavier armament and radar and 100 were ordered from five factories in Germany. Poland and Austria The order was soon trebled and Luftwaffe enthusiasm was such that even the early prototypes were sent to Venlo. Holland, to form a special trials unit The first six night sorties resulted in the claimed destruction of 20 RAF bombers, six of them the previously almost immune Mosquitoes 1 More than 15 different versions of the 219 then appeared, immediately proving +outstandingly formidable The A-2/R1 had 603As. two MG 151/20 in the +wing roots and two or four in a belly tray and two 30mm MK 108 firing upward at 65° in a Schrage Musik (Jazz Music) installation for destroying bombers by formating below them. The A-7/R1 had MK 108s in the wing +roots and two of these big guns and two MG 151/20 in the tray, plus the Schrage Musik with 100 rounds per gun (the most lethal of all). Some versions had three seats, long-span wing and DB 603L turbocharged engines, or Jumo 213s or even the 2.500hp Jumo 222 with six banks of four cylinders. The B and C families would have been enlarged multi-role versions with rear turrets. Total A-type production was only 268. the officials at one time ignoring Luftwaffe enthusiasm by ordering production to be stopped +! +Above: The proposed He 219C-2 Jagdbomber with Jumo 222 engines. +I o. +I1 > +%Y" +I +/ +. +o +__. +Above: Three view of He 219A 5/R1 . lower side view, the +lengthened A-5/R4 with MG 131 in the rear cockpit for defence +The He 219A-7/R4 had exceptional high-altitude equipment and performance, plus ejection seats, but armament was reduced to +four MG 151/20, all firing ahead. This was relatively light. +Above: The proposed He 219C-1 four-seat night fighter. +Above: An He 219A-5/R2 just after capture of its airfield by the Allies. Splendid to fly, the 219 was a formidable machine. +Below: Another He 219A-5, this time fitted with not only SN-2 radar but also the older Lichtenstein C-1 in the centre. +43 + + + HenscheIHsl23 +Hs123A-1 +Origin: Henschel Flugzeugwerke AG Type: Single-seat dive bomber and close-support. +Engine: One 880hp BMW 132 Dc nine-cylinder radial. +Dimensions: Span 34ft 5iin (10 5m); length 27ft 4in (8 3m) height +10ft 6Jin (3 2m). Weights: Empty 3.3161b (1504kg); loaded 4.888lb (2217kg). +Performance: Maximum speed 214mph (345km/h); initial climb 2.950ft (900m)/min; service ceiling 29.530 ft (9000m); range 530 miles (850km) +Armament: Two 7 92mm Rheinmetall MG 17 machine guns ahead of pilot; underwing racks for four 1101b (50kg) bombs, or clusters of anti +personnel bombs or two 20mm MG FF cannon. History: First flight, spring 1 935 (public display given 8 May); first delivery (Spain) December 1936; final delivery. October 1938 User: Germany (Luftwaffe). +Development: Though representing a class of aircraft generally considered obsolete by the start of World War II. this trim little biplane was kept +Above : Three-view of the Hs 1 23A-1 . +hard at work until 1 942. achieving results which in retrospect seem almost unbelievable. The prototype needed extensive modification to produce the A-1 production version, which was tested in the Spanish Civil War Contrary to the staff-college theories then adhered to by the newly formed Luftwaffe, the Henschels were able to give close support to ground troops of a most real and immediate kind, strafing and bombing with great accuracy despite the lack of any radio link or even an established system of operation. Eventually the Luftwaffe realised that the concept of a close-support aircraft was valid, and a few Henschels were allowed to operate in this role, but all the effort and money was put into the Ju 87. and the Hs 1 23 was phased out of production before World War II Yet in the Polish campaign these aircraft proved unbelievably useful, having the ability to make pinpoint attacks with guns and bombs and. by virtue of careful setting of the propeller speed, to make a demoralising noise Moreover, it established an extraordinary reputation for returning to base even after direct hits by AA shells As a result, though the whole force was incessantly threatened with disbandment or replacement by later types, the Hs 123 close-support unit II (Schlacht)/ LG2 was sent intact to the Balkans in April 1941 and thence to the USSR Here the old biplanes fought around the clock, proving far better adapted to the conditions than more modern types and continuing in front-line operations until, by the end of 1944. there were no more left. +Left: An Hs 123A-1 in front-line service, possibly with Schlacht LG 2, in the campaign in France or the Balkans. By 1942 hardly any of the Henschels still wore their spats. +Henschel Hs 126 +Ms 126A and B +Origin: Henschel Flugzeugwerke AG. Schonefeld. Type: Army co-operation, later multi-role tactical. Engine: One nine-cylinder radial. (A-O) 830hp Bramo Fafnir 323A, (A-1) +880hp BMW 132 Dc. (B) 900hp BMW Bramo Fafnir 323A-2 or Q-2 Dimensions: Span 47ft 6jin (14 50m); length 35ft 7|in (10 85m); height 12ft 3|in (3 75m). Weights: Empty (B-1) 4.480lb (2032kg); maximum 7.209lb (3270kg) Performance: Maximum speed 221 mph (355km/h); service ceiling 27.070ft (8250m); maximum range at sea level 360 miles (580km) +Armament: One synchronized 7 92mm MG 17 and one manually aimed +7 92mm MG 1 5; light bombs or 1 101b (50kg) bomb or extra tank. History: First flight August 1936; service delivery (A-0) June 1937; final delivery January 1941. Users: Bulgaria. Croatia. Greece. Germany. Spain. +Development: Developed in early 1936 from the disappointing Hs 122. the parasol-winged Hs 126 was a thoroughly sound machine very like the British Lysander in character though more conventional. The crew of two sat below and behind the wing in a capacious tandem cockpit, the pilot's portion being enclosed. Typical photographic, radio and light bombing equipment was carried, and the aircraft proved to have excellent STOL +Above: Three-view of the Hs 126A (B-series, almost identical). By about 1941 nearly all the spats had been removed. +capability and ability to absorb much punishment. Altogether about 802 were delivered, maintaining the Aufklarungsstaffeln (recce squadrons) at a front-line strength of around 280 aircraft By June 1941 virtually all were on the Eastern Front or in the Balkans or North Africa. A few survived until 1944—45 in operations against partisans in the Balkans, but most had been replaced by the Fw 189 and used for towing gliders The 200-odd combat veterans served in Nachtschlacht (night ground attack) wings, often using a variety of armament schemes. (See page 61 for Henschel Hs 129) +Left: This Hs126A-1 was serving with 2.(H)/31 (Pz) from a base in Greece in April 1 941 . Like more than half the 126 strength, this machine was assigned to a Panzer corps, whose emblem it wears. +Increasingly, the Fw 189 took over the front-line reconnaissance missions while the parasol-winged 126 was relegated to supply dropping, harrying partisans and general utility communications. +44 + + + I .-tl II. ' .J., I +the H-, 1/ J look.nl Ilka +thil ..,, II-. \J !A .-I +7/SK. 168 l 'I +111,11111 Ij.r.H'l .il I ui m mifiildlii uck, near +Muim h in Oi .lobar 1937 +Right: A startling contrast is provided by this Hs 123A-1, built long before the war but pictured in 1 943 in round-theclock work with 4 (Schlacht)/G2 on the Eastern Front. Apart from the absence of spats the aircraft has a new head fairing and +much new equipment. +Left: This Hs126B-1 is illustrated in winter camouflage whilst serving on the Don front with 3(H)/21 in January 1943. +Below: This frame from a Luftwaffe cine film shows an Hs 126B-1 serving with an Aufklarungsstaffel (recce squadron) during the assault on Greece in April 1941. It is flying over Athens. + + + Messerschmitt Bf 109 +Bf 109B, C, D, E, F, G, H and K series, +S-99and 199, Ha-1109and -1112 +Origin: Bayensche Flugzeugwerke. later (1938) renamed Messerschmitt +AG: very widely subcontracted throughout German-controlled territory and built under licence by Dornier-Werke. Switzerland, and Hispano-Aviacion. Spain (post-war. Avia. Czechoslovakia). Type: Single-seat fighter (many, fighter bomber). +Engine: (B. C) one 635hp Junkers Jumo 210D inverted-vee-1 2 liquid +cooled (D) LOOOhp Daimler-Benz DB 600Aa. same layout: (E) 1.100hp +DB 601 A. 1.200hp DB 601 N or 1 ,300hp DB 601 E: (F) DB 601 E: (G) +1 475hp DB 605A-1. or other sub-type up to DB 605D rated 1 ,800hp with +MW50 boost: (H-1) DB 601 E: (K) usually 1.550hp DB 605ASCM/DCM +rated 2.000hp with MW50 boost: (S-199) 1 .350hp Jumo 21 1 F: (HA-1109) +1.300hp Hispano-Suiza 1 2Z-89 upright vee-12 or (M1L) 1.400hp R-R Merlin 500-45. Dimensions: Span (A to E) 32ft 4iin (9 87m): (others) 32ft 6iin (9 92m): +length (B. C) 27ft 1 1 in: (D. E. typical) 28ft 4m (8 64m). (F) 29ft Oiin: (G) 29ft 8in (9 04m): (K) 29ft 4in: (HA-1 109-M1 L) 29ft 1 1 in: height (E) 7ft 5im (2 28m): (others) 8ft 6in (2 59m). Weights: Empty (B-1) 3.483lb: (E) 4.1891b (1900kg) to 4.4211b: (F) around 4.3301b. (G) 5.8801b (2667kg) to 6.1801b (2800kg): (K. typical) 6.0001b: maximum loaded (B-1) 4.850lb: (E) 5.523lb (2505kg) to 5.875lb (2665kg): (F-3) 6.054lb: (G) usually 7.496lb (3400kg): (K) usually 7.439lb (3375kg). Performance: Maximum speed (B-1) 292mph: (D) 323mph: (E) 348-354 +mph (560-570km/h): (F-3) 390mph: (G) 353 to 428mph (569-690km/h). (K-4) 452mph (729km/h): initial climb (B-1) 2.200ft/min; (E) 3.100 to 3.280ft (1000m)/min: (G) 2.700 to 4.000ft/min: (K-4) 4.823ft (1470m)/ mm: service ceiling (B-1) 26.575ft; (E) 34.450ft (10.500m) to 36.090ft (11.000m): (F. G) around 38.000ft (11.600m): (K-4) 41.000ft (12.500m): range on internal fuel (all) 365-460 miles (typically. 700km). +Armament: (B) three 7 92mm Rheinmetall-Borsig MG 17 machine guns +above engine and firing through propeller hub: (C) four MG 17. two above engine and two in wings, with fifth through propeller hub in C-2; (early +E-1 ) four MG 1 7. plus four 50kg or one 250kg (551 lb) bomb: (later E-1 and +most other E) two MG 17 above engine, each with 1.000 rounds (or two +MG 17 with 500 rounds, plus 20mm MG FF firing through propeller hub) +and two MG FF in wings, each with 60-round drum; (F-1) two MG 17 and +Above: Abandoned high-altitude variant, the Bf 109H of 1944 +Below: The original prototype, with British Kestrel engine. +one MG FF; (F-2) two 1 5mm MG 1 51 and one MG FF: (F-4) two MG 1 51 +. +one MG FF and one 20mm MG 151 in fairing under each wing; (G-1) +two MG 17 or 13mm MG 131 over engine and one MG 151; (G-6) one +30mm MK 108. two MG 1 31 above engine and two MG 1 51 under wings; +(K-4) twoMG 151 above engine and one MK 108 or 103: (K-6) two MG 131 +above engine, one MK 103 or 108 and two MK 108 under wings: (S-199) +two MG 1 31 above engine and two MG 1 51 under wings: ( HA- 1 1 09 series) +two wing machine guns or 20mm Hispano 404 Many German G and K carried two 210mm rocket tubes under wings or various bomb loads History: First flight (Bf 109 V-1) early September 1935 (date is unrecorded): (production B-1) May 1937: (Bf 109E) January 1939: (Bf 109F prototype) July 1940; replacement in production by Bf 109G. May 1942 Users: Bulgaria. Croatia. Finland. Germany (Luftwaffe). Hungary. Italy (ARSI). Japan. Jugoslavia. Romania. Slovakia. Slovak (CB Insurgent). Soviet Union (1940). Spain, Switzerland; (post-war) Czechoslovakia. Israel continued on page 49> +Above: Taken from a German propaganda film of 1941, this photograph depicts a pair of Bf 109E-4/Trop fighters of l/JG 27 flying over the Cyrenaican (Libyan) desert, soon after the entry of the Afrika Korps. Finish is 78 Light Blue, 79 Sand Yellow and 80 Olive Green, with the white tail band denoting the Mediterranean theatre of operations. +Above: One of the last Bf 109E sub-types, this is an E-7, seen with a large dust filter on the engine air inlet. It was operating on the Leningrad front in 1942 with JG 5. +46 + + + ^nt lfe . +Above: The same l/JG 27 aircraft as seen at far left. This view from above flatters the camouflage capabilities of the 79/80 colour scheme against the North African terrain. +47 + + + Above: Bf 109G-2s of II (left) and lll/JG 54 "Grunherz" (Green Heart) geschwader operating on the northern sector of the Eastern Front (probably at Silverskaya) in the summer of 1942. Relative merits of the Luftwaffe and Soviet fighters continue to be hotly debated. +Right: The Bf 109G-14/U4 introduced a wooden tail, previous improvements being the clearview "Galland" hood and (five years late, and often incomplete) geared tabs on ailerons and/ or elevators. +Me sserschmitt Bf 109G-14/U4 +cutaway drawing key: +1 Starboard navigation light 2 Starboard wmgtip 3 Fixed trim tab 4 Starboard Frise-type aileron 5 Flush-riveted stressed wingskinning 6 Handley Page leading-edge automatic slat 7 Slat control linkage 8 Slat equalizer rod 9 Aileron control linkage 10 Fabric-covered flap 11 Wheel fairing 12 Ammunition-feed fairing (both sides of fuselage) +13 Rheinmetall Borsig 13mm +MG 131 14 Engine accessories 15 Starboard gun trough +16 Daimler-Benz DB 605AM twelve-cylinder inverted-vee liquid-cooied engine +1" Detachable cowling panel 18 Oil filler access +•9 Oil tank 20 Propeller pitch-change mechanism +21 VDM electrically-operated constant-speed propeller 22 Spinner 2 3 Engine-mounted cannon muzzle 24 Blast tube 25 Propeller hub 25 Spinner back plate 27 Auxiliary cooling intakes 23 Coolant header lank 29 Anti-vibration rubber engine-mounting pads 30 Elektron forged engine bearer 31 Engine bearer support strut 56 attachment 57 32 Plug leads 3 3 Exhaust manifold fairing strip 34 ejector exhausts 58 +J5 Cowling fasteners 36 Oil cooler 59 +3^ Oif cooler intake 60 38 Starboard mainwheel 61 39 Oil cooler outlet flap 82 +4C Wing root fillet 53 41 Wing-fuselage fairing +42 Firewall/bulkhead +^3 Supercharger air intake 65 +44 Supercharger 66 +4 5 20mm magazine +4r 1 3mm ammunition feed 67 47 Engine bearer upper attachment -3 48 Ammunition feed fairing +40 MG 131 breeches o9 +52 Instrument panel 70 +51 20mm Mauser MG 151/20 7 1 +cannon breech ~2 5 2 Heel rests 53 Rudder pedals "3 54 Undercarriage emergency retraction cables 55 Fuselage frame 1A +48 +Wing/fuselage fairing Undercarriage emergency retraction handwheel (outboard) Tail trim handwheel (inboard) Seat harness Throttle lever Control column Cockpit ventilation inlet Revi 16B reflector gunsight (folding) Armoured windshield frame Anti-glare gunsight screen +90mm armourglass windscreen Galland'-type clear-vision hinged canopy Framed armourglass head/ +back panel Canopy contoured frame +Canopy hinges (starboard) Canopy release catch Pilot's bucket-type seat +(8mm back armour) Underfloor contoured fuel tank (88 gal/400 litres of 87 octane B4) Fuselage frame +Circular access panel Tail trimming cable conduit Wireless leads +MW 50 (methanol water) tank (25 gal/114 litres capacity) Handhold Fuselage decking Aerial mast D/F loop Oxygen cylinders (three) +93 94 95 96 97 98 99 100 101 102 103 +104 105 106 107 +andFuG 25a IFF) Main fuel filler cap Fuselage top keel (connector -stringer) Aerial lead-in Fuselage skin plating sections U' stringers Fuselage frames (monocoque construction) Tail trimming cables Fin root fairing Starboard fixed tailplane Elevator balance Starboard elevator Geared elevator tab All-wooden fin construction 125 Aerial attachment 126 Rudder upper hinge bracket 127 Rudder post Fabric-covered wooden rudder structure Geared rudder tab Rear navigation light Port elevator Elevator geared tab +128 129 130 131 132 133 +Tailplane structure Rudder actuating linkage Elevator control horn Elevator connecting rod Elevator control quadrant Tailwheel leg cuff Castoring non- retractable tailwheel Lengthened tailwheel leg^ Access panel Tailwheel shock-strut Lifting point Rudder cable Elevator cables First-aid pack Air bottles Fuselage access panel Bottom keel (connector stringer) Ventral IFF aerial Master compass Elevator control linkage Wing root fillet Camber-changing flap Ducted coolant radiator Wing stringers Wing rear pick-up point Spar/fuselage upper pin joint (horizontal) + + + Development +I +bh to apprecial +in in hi :1 +I38). Early vi +i +hi end if August 1 939 941 it was b +is alsi +i luring thi firsl eai rid War II tl +iub types were called o1 ti ihtei igainsl hid ppo the S| itl h it greatlv outnumber! i +;i2i mi and cheap production, high a good power of manoeuvre Neai 09 Es were i +three 20mm cannon, with range and striking powei grea eight mi,' < .iiibre guns. Drawbacks were the swing on take-off or landing, extremely poor lateral conl needs, +and the fact that in combat the slats on the wings often opened in +hums while this prevented a stall, it snatched at the ailerons and thre pilot off his aim After 1942 the dominant version was the 109G ("Gu +which made up over 70 per cent of the total received by the Luftwaffe +Though formidably armed and equipped, the vast swarms of "Gustavs" +continued on pagn SO +Above: Maj Walter Oesau's Bf 109E (7/JG 51. Jan. '40). +Left: Obit H-J Marseille's 109F (3/JG 27. score at 101). +Below: 109F of Hpm Assi Kahn (lll/JG 2. score 31, later 108). +1 34 Spar/fuselage lower pin join* 1 35 Flaps equalizer rod 1 36 Ruestsatz R3 auxiliary fuel tank ventral rack 137 Undercarriage electrical interlock 1 38 Wing horizontal pin forward pick-up 139 Undercarriage retraction jack mechanism 140 Undercarriage pivot/bevel 141 Auxiliary fuel tank (Ruestsatz R3) of 66 gal (300 litres) capa I 142 Mainwheel leg • a 143 Mainwheel oleo leg 144 Brake lines 1 45 Mainwheel fa 146 Port mainwheel 147 Leading-edge 148 Port mainwheel well 1 49 Wing spar 150 Flap actuating linkage 151 Fabric-covered control surfaces 1 52 Slotted flap structure 153 Leading-edge slat actuating 174 mechanism 175 +154 155 +156 157 158 159 +161 162 163 164 165 +166 167 168 +171 172 !73 +Slat equalizer rod Handley Page automatic leading-edge slat Wing stringers Spar flange decrease Wing ribs Flush-riveted stressed wing-skinning Metal-framed Fnse-type aileron Fixed trim tab Wingtip construction Port navigation light Angled pitot head Ruestsatz R6 optional underwing cannon gondola 1 4-point plug connection Electrical junction box Cannon rear mounting bracket +20mm Mauser MG ' +cannon Cannon front mou' I bracket Ammunition feed chute Ammunition magaz r Underwing panel Gondola fairing Cannon barrel + + + Messerschmitt Bf 109 +continued +Top: Bf 109F-4/B carrying SC 500 (1.1021b) bomb. This particular machine was that of Staffelkapitan Liesendahl of 10 (Jabo)/JG 2, based at Caen in June 1942. +Above: Bf 109F-4/Trop with 66-gallon drop tank. This aircraft belonged to ll/JG 27. based at Sanyet in September 1942. It is finished in the standard "Colour No 79 Sand-yellow" specified for upper surfaces of tropical aircraft. The tropical filter is prominent. +Below: Typical of the Luftwaffe's chief (and almost sole) type of front-line single-engined fighter during the Battle +of France is the Bf 109E flown by Major Erich Mix, CO of lll/JG 2 in May 1940. It forms an instructive counterpart to the aircraft of 10/JG 2 of 1942 pictured at top left. +o +-1 1 "1 +Vo^^^c^>l bum OMnen +rtuhler isl im Noub«rf«l eingebouf +N + + + Top: Bf 109F-2 Trop of III JG 27, based at Qasaba in the autumn of 1942. It was just at this time that Hans-Joachim Marseille, staffelkapitan of III JG 27 and top scoring pilot in the west, was killed after destroying 158 Allied aircraft. +Above: One of the pre-war 109s was this Bf 109D-1 of ll/JGr 102, based at Bernburg in the winter 1938-39. Sides and upper surfaces look uniform dark green, but in fact Luftwaffe records show that all authorised colour schemes had very slightly contrasting shades, such as 70 blackgreen and 71 dark green. +51 + + + Top: Bf 109F-5 of l(F)/122 based in Sardinia in 1943. This was a tactical reconnaissance aircraft, with vertical camera in the rear fuselage (and the engine-mounted cannon removed). Performance was not always high enough to escape interception, especially by two-stageMerlin Spitfires. +Above: This Bf 109E of lll/JG 52, based at Hopstadten in August 1940, has an unusual colour scheme with crisscrosses of 71 dark green sprayed on 02 grey. Underside is regulation 65 light blue. +52 + + + 53 + + + Messerschmitt Bf 110 + + + Below: A typical Luftwaffe night fighter of the late war +period was this Bf 110G 4 of 7/NJG 4 based at many airfields in northwest Germany and at St Trond and Venlo in the Netherlands. Finished in 76 Light Blue all over, the upper surfaces were then given a sprayed mottle of 75 Grey-Violet. +55 + + + Below: A day-flying DB 605-powered version, a Bf 110G-2 of 5/ZG 76. based at Grossenhain in winter 1943-44. In happier days in 1939-41, ZG 76 had been the original Haifisch unit, with prominent shark mouths on its aircraft noses. +Below: Bf 110C-4/B, one of the earlier DB 601 -powered models. +It is shown flying with SKG 1 (fast bomber geschwader 1 ) on the Eastern Front, with that theatre's yellow tactical band. +SKG 1 retained the wasp motif it had used when it was ZG 1, +the original zerstorer geschwader nicknamed Wespen (Wasp). + + + Germany +continued on page 58 +57 + + + Messerschmitt Bf 110 ^^ +Bf 1 10B series to H series (data for Bf 110C-4/B) +Origin: Bayensche Flugzeugwerke. after 1938 Messerschmitt AG; widely dispersed manufacture. Type: Two-seat day and night fighter (also used on occasion for ground attack and reconnaissance). Engines: Two 1.100hp Daimler-Benz DB 601 A; (later C-4s) 1 ,200hp DB 601 N 12-cylinder inverted-vee liquid-cooled; (G. H) two 1.475hp DB 605B. same layout Dimensions: Span 53ft 4|in (16 25m); length 39ft 8iin (12 1m); height 11ft 6in (3 5m). Weights: Empty 9.920lb (4500kg): loaded 15.4301b (7000kg). Performance: Maximum speed 349mph (562km/h) at 22.966ft (7000m): climb to 18.045ft (5500m). 8 minutes: service ceiling 32.800ft (10.000m). range 528 miles (850km) at 304mph (490km/h) at 16.400ft (5000m). +Armament: Two 20mm Oerlikon MG FF cannon and four Rheinmetall +7 92mm MG 17 machine guns fixed firing forward in nose, one 7 92mm +MG 15 manually aimed machine gun in rear cockpit: C-4/B also fitted with racks under centre section for four 5511b (250kg) bombs. (G-4 night continued on page 60> +Above: Bf 110D of 8 ZG 26 climbing out of rugged territory in Sicily in 1942 to rendezvous with a bomber force for Malta. +Messerschmitt Bf 110G-4b +cutaway drawing key: 1 Trie Hirschgeweih (Stag s Antlers) array for the FuG +220b Lichtenstein SN 2 radar 2 Single-pole type antenna for the FuG 212 Lichtenstein C-1 radar 3 Camera gun 4 Cannon muzzles 5 Cannon ports 6 Blast tubes 7 Starboard mainwheel 8 Armour plate (10-mm) +9 Twin 30-mm Rheinmetall +Borsig MK 108 (Rus' Field Conversion Set 3) with 1 35 rpg +. 18 +R3 +10 Armoured bulkhead +1 +1 +Supercharger intake 12 Position of nacelle +mounted instruments on day fighter model +1 3 Exhaust flame damper 14 Auxiliary tank +15 Three-blade VDM airscrew 16 Leading-edge automatic slat 17 Pilot tube 18 FuG 227/1 Flensburg homing aerial fined to some aircraft by forward maintenance units (to home on Monica tailwarning radar emissions) 1 9 Stressed wing skinning +20 Starboard aileron 35 Aerial mast 53 Elevator tab 75 Wmgtip +21 Trim tab 36 Upward-firing cannon 54 Centre section fairing 76 Flensburg aerial (see 18> +22 Slotted flap muzzles 55 Rear navigation light 77 Port navigation light +23 Hinged canopy roof 37 Two 30-mm MK 108 56 Port elevator 78 Leading-edge automatic +24 Armoured glass windscreen cannon in schrage Musik 57 Port tailfin slat +(60-mm) (oblique music) installation 58 Rudder 79 Wing ribs +25 Instrument panel firing obliquely upward 59 Hinged tab 80 Mainspar +26 Cockpit floor armour (optional installation 60 Tailwheel 81 Underwing auxiliary fuel +(4-mm) supplied as an Umrust- 61 Fuselage frames tank (66 lmpgal/300-l +27 Twin 20- mm Mauser MG Bausatz/Factory 62 Control lines capacity) +1 51 cannon with 300 Conversion Set) 63 Dipole tuner 82 Landing light +rounds (port) and 350 38 Ammunition drums 64 Batteries 83 Undercarriage door +rounds (starboard) 39 Aft cockpit bulkhead 65 Transformer 84 Mainwheel well +28 Pilot's seat 40 FuG 10P HF R/T set 66 Sloned flap 85 Supercharger intake +29 Control column 41 FuBI 2F airfield blind 67 Fuel tank of 57 3 Imp gal 86 Undercarriage pivot point +30 Pilot's back and head approach receiver (260 51) capacity 87 Mainwheel leg +armour (8-mm) 42 Handhold 68 Oil tank of 7 7 Imp gal 88 Mainwheel 31 Cannon magazine - Oxygen bottles (351) capacity 89 Oil cooler 32 Centre section carry- 44 Aerials 69 Ventral antenna 90 Oil cooler intake +through 45 Master compass 70 Coolant radiator 91 VDM airscrew 33 Radar operator's swivel seat 46 Starboard tailfin 71 Radiator intake 34 D/F loop 47 Rudder balance 72 Hinged intake fairing +48 Rudder 73 Aileron tab ^ ^ +V^M 49 Tab 74 Aileron construction +50 51 +Starboard elevator Starboard tailplane +^^SSs^/^****""**- t^~ +^*Ss*sSs^ ^^"Sn»^ 52 Variable- incidence tailplane +I +58 + + + 92 Pitch-change mechanism +93 Armoured ring (b mm) 94 Coolant tank 95 t KhaitSl flame damper 90 Anti vibration engine mounting pad +Daimler Ben/ DB 605B 1 1 2 cylinder inverted Vee enqine (rated at 1 .4 /bhp tor take off and 1 3bbhp at 18.700ft/b/00m) Gorged engine bearer I uel tank (8? b Imp gal/ 3/b I capacity) , +100 f uselage/matnspar attachment point 101 Kiselaye/foiward auxiliary spar attachment point 102 Watfenwanne 151Z. a ventral tray housing a pax +of 20 mm MG 1 bl cannon (optional) +Above: Bf 110C 4 of IM/ZG 76 creates its own sandstorm in the Western Desert in the winter 1941 42. Like the Bf 110 opposite it has yet to receive Sand Yellow livery and the white bands denoting the Mediterranean tactical theatre +Below: From 1942 onward night fighting was by far the most important task of the Bf 110. The G-4b/R3 was one of the purpose-designed NJG models with upward-firing cannon. + + + fighter) two 30mm MK 108 and two 20mm MG 151 firing forward, and +two MG 151 in Schrage Musik installation firing obliquely upwards (some +times two 7 92mm MG 81 in rear cockpit). History: First flight (Bf 110V1 prototype) 12 May 1936; (pre-production Bf 110C-0) February 1939; operational service with Bf 110C-1. April 1939; final run-down of production (Bf 110H-2 and H-4) February 1945. User: Germany (Luftwaffe). +Development: As in five other countries at about the same time, the Reichsluftfahrtministerium decided in 1934 to issue a requirement for a new kind of fighter having two engines and exceptional range. Called a Zerstorer (destroyer), it was to be as capable as small single-seaters of fighting other aircraft, possibly making up in firepower for any lack in manoeuvrability. Its dominant quality was to be range, to escort bombers on raids penetrating deep into enemy heartlands. Powered by two of the new DB 600 engines, the prototype reached 316mph. considered an excellent speed, but it was heavy on the controls and unimpressive in power of manoeuvre. Too late to be tested in the Spanish Civil War. the production Bf 110B-1. which was the first to carry the two cannon, was itself supplanted by the C-series with the later DB 601 engine with direct fuel injection and greater power at all heights. By the start of World War II the Luftwaffe had 195 Bf 1 10C fighters, and in the Polish campaign these were impressive, operating mainly in the close-support role but demolishing any aerial opposition they encountered- It was the same story in the Blitzkrieg war through the Low Countries and France, when 350 of the big twins were used. Only when faced with RAF Fighter Command in the Battle of Britain did the Bf 110 suddenly prove a disaster. It was simply no match for the Spitfire or even the Hurricane, and soon the Bf 109 was having to escort the escort fighters! But production of DB 605-powered versions, packed with radar and night-fighting equipment, was actually trebled in 1943 and sustained in 1944. these G and H models playing a major part in the night battles over the Reich in 1 943—45. +Above: An unidentified trio of what appear to be Bf 110Ds reveal little beyond the staffel colour of yellow seen on the tips of the spinners. They are probably from 9'ZG 26 newly assigned to the North African theatre. +Below: Bf 110G-2 of 12/NJG 3 (Stavanger, 1945); no radar. +Below : A fine photo of two Bf 110D-1sof ZG26, soon after the Luftwaffe first went to Africa in 1941. Sand Yellow all over, with white theatre band. + + + Henschel Hs 129 +Hs 129A and B series +Origin: Hi Type: Single ipport and g +Engines: I +two n iw i idi il +Dimensions: Span It M +lOfl Sin I i "mil Weights: (Typi. il B-1) empty 8.940lb (406" ,.,| m (51 I Ok n Performance: (1 pii il B I) maximum pi h (408km hi +limb l --saOft (425m)/min; service ceiling 29.530ft (9000n +miles (880kmi Armament: See text +History: Firs! flight (Hs 129V-1) early 1939; service delivery (129AO) early 1941 Firsl Might (129B) October 1941; service delivery (129B) kite 1942. Users: Germany (Luftwaffe). Hungary. Romania +Development: Though there were numerous types of specialised close support and ground attack aircraft in World War I, this category was virtually +ignored until the Spanish Civil War showed, again, that it is one of the most +"H p r +Above: A Henschel Hs 129B-2/R2 of Schlachtgeschwader 9 on +the Eastern Front, spring 1943 but still in winter colours. +Below: Another Hs 129B-2, in this case of 4 (Pz)/Sch.G 1, +from the same period, with 70/71 oversprayed with white blobs. +Above: Three view of Hs 129B 1/R4 with bomb kit +itant of all In 1938 the RLM issued a spe' the whole purpose of the Luftwaffe Blitzkrieg-type battles - to back up thi bomber Henschel's Dipl-lng F Nicholaus dev what resembling the twin-engined fighters of the pe< armour and less-powerful engines (two 495hp Argus As 41 0A 1 inverted-vee-1 2s) The solo pilot sat in the extreme nose behind a v. 3in thick, with armour surrounding the cockpit The triangu fuselage housed self-sealing tanks, guns in the sloping sides and a ham: +for a bomb underneath Test pilots at Rechlin damned the A-0 pre-prod>. batch as grossly underpowered, but these aircraft were used on the Eastern Front by the Romanian Air Force The redesigned B-series used the vast +numbers of French 1 4M engines that were available and in production by +the Vichy government for the Me 323. Altogether 841 B-series were built, and used with considerable effect on the Eastern Front but with less success +in North Africa The B-1/R1 had two 7 92mm MG 17 and two 20mm MG +151/20. plus two 1101b or 48 fragmentation bombs The R2 had a 30mm +MK 101 clipped underneath and was the first aircraft ever to use a 30mm +gun in action. The R3 had a ventral box of four MG 1 7. The R4 carried up to 5511b of bombs. The R5 had a camera for vertical photography. The B-2 +series changed the inbuilt MG 17s for MG 131s and other subtypes had +many kinds of armament including the 37mm BK 37 and 75mm BK 7 5 with muzzle about eight feet ahead of the nose The most novel armament, used against Russian armour with results that were often devastating, was a +battery of six smooth-bore 75mm tubes firing recoilless shells down and to the rear with automatic triggering as the aircraft flew over metal objects. +Below: A highly cleaned-up and somewhat +falsified Hs 129B (sub-type obscured by changes ncluding removal of the large pilot sight) in American charge long after World War II. Only two Hs 129s are thought to exist today. +61 + + + Junkers Ju 52/3m +Ju 52/3m in many versions; +data for 3mg5e to 3mg14e +Origin: Junkers Flugzeug und Motorenwerke AG: also built in France on German account by a SNCASO/Breguet/Amiot group; built under licence by CASA. Spain. Type: Passenger and freight transport (also bomber, reconnaissance. mine countermeasures. cas-evac and glider tug). +Engines: Three (one in Ju 52) of following types: 600hp BMW Hornet. +725hp BMW 132A. 830hp BMW 132T (standard on nearly all wartime +versions). 925hp Bristol or PZL Pegasus. 750hp ENMASA Beta E-9C or +710hp Wright Cyclone (all nine-cylinder radials) or Jumo 5 diesel. Jumo +206 or BMW VI in-lines Dimensions: Span 95ft 1 1 iin (29 25m); length 62ft (18 9m): height +(landplane) 14ft 9in (4 5m). Weights: Empty 12.3461b (5600kg): loaded 24.3171b (11.030kg). Performance: Maximum speed 1 90mph (305km/h); initial climb 689ft (210m)/min; service ceiling 18.045ft (5500m): range 808 miles (1300km) Armament: Usually none: in combat zones it was usual to mount one +13mm MG 131 manually aimed from open dorsal cockpit and two 7 92mm +MG 1 5s manually aimed from beam windows. +History: First flight (Ju 52) 13 October 1930; (Ju 52/3m) May 1932. (Ju 52/3mg3e bomber) October 1934; final delivery (AAC 1 ) August 1947. (CASA 352-L) 1952 Users: Argentina. Colombia. Ecuador. France. Germany (Luftwaffe. Kriegsmarine. Lufthansa). Hungary, Peru. Portugal. Slovakia. Spam. Sweden. +Development: One of the great aircraft of history, the Ju 52/3m was briefly preceded by the single-engined Ju 52 which had no military history Most early Ju 52/3m versions were 1 5/1 7-passenger airliners which sold all over the world and also made up 75 per cent of the giant fleet of Lufthansa (reducing that airline's forced landings per million kilometres from 7 to only +Above: Three-view of typical pre-war civil Ju 52/3m. +15). In 1935 the 3mg3e bomber, with manually aimed MG 1 5s in a dorsal cockpit and ventral dustbin and bomb load of 3.307lb (1500kg) equipped the first bomber squadrons of the Luftwaffe. By 1 936 about half the 450 built had been supplied to the Legion Kondor in Spain and to the Nationalist air force, but nearly all were equipped as troop transports, freighters and casualty-evacuation ambulances These were the roles of most military versions, which were by far the most common transports on every front on which Nazi Germany fought It is typical of the Nazi regime that, despite a wealth of later and more capable aircraft, the old 'Auntie Ju" or "Iron Annie" was kept in full production throughout the war Good STOL performance, with patented "double wing" flaps, robust construction, interchangeable wheel/ski/float landing gear and great reliability were the Ju 52s attributes Total German output was 4.845 Many were built in France where 400 were completed as AAC 1s in 1947 The final 170 were built in Spain as CASA 352-Ls for the Spanish Air Force, which used them as T 2B multirole transports until 1975. +Above: A typical early-wartime model, probably a Ju 52/3mg5e, +which served with ll/KGz.b.V 1 in southern Greece in May 1941. +Below: A Ju 52/3mg7e pictured crossing the Mediterranean in 1942. Rommel's Afrika Korps increasingly relied upon the "Tante Ju" (Auntie Ju), which suffered high attrition. +S^foZSJ +; :< + + + Junkers Ju 86 +Ju 86D. E, G, K, P and R +Origin : Junki and built Type: (I) I G and +Engines: (D) 600h| +800 Di 880hp BMW 132 ni I | two 905hp Bristol Mercury XIX nine cylindei I lumo 207A 1 or 207B 3/V tu led oppoDimensions: Span 73ft 1 0. i (P) 84t 12m) length (typical) 58ft 8}in (17 9m). (G) 56ft bin (P. R) 54) bin (4 7m) Weights: Empty (E-1) 11.4641b (5200kg). (R-1) 14.7711b (6700kg). loaded (El) 18.0801b (8200kg). (R-1) 25.420lb (11.530kg) Performance: Maximum speed (E-1) 202mph (325km/h). (R-1) 261 mph (420km/h). initial climb (E) 918ft (280m)/mm, service ceiling (I 1) 22.310ft (6800m). (R-1) 42.650ft (13.000m). range (E) 746 miles (1200m). (R-1) 980 miles (1577km) +Armament: (D. E. G. K) three 7 92mm MG 15 manually aimed from nose, dorsal and retractable ventral positions, internal bomb load of four 551 lb +(250kg) or 16 1 101b (50kg) bombs: (P) single 7 92mm fixed MG 1 7. same bomb load. (R) usually none. History: First flight (Ju 86V 1 ) 4 November 1 934; (V-5 bomber prototype) January 1936: (production D-1) late 1936. (P-series prototype) February 1940. Users: Bolivia. Chile. Germany (Luftwaffe. Lufthansa). Hungary. Portugal. South Africa. Spain. Sweden. +Development: Planned like the He 1 1 1 as both a civil airliner and a bomber, the Ju 86 was in 1 934 one of the most advanced aircraft in Europe. The design team under Dipl-lng Zindel finally abandoned corrugated skin and created a smooth and efficient machine with prominent double-wing flaps and outward-retracting main gears. The diesel-engined D-1 was quickly put into Luftwaffe service to replace the Do 23 and Ju 52 as the standard heavy bomber, but in Spain the various- D-versions proved +Above: Three view of the ultimate extreme-altitude Ju 86. the Ju 86R-1 Their chief accomplishment was to trigger the development of numerous Allied high-altitude fighters. +vulnerable eve r +BMW radial, were faster and th< engined Ks. of which 40 were built by Ju- • 1936) and 16 by Saab (last delivery 3 January 1941) Many D ai bombers were used against Poland, but that was their swan 1939 Junkers was working on a high altitude version wit! engines and a pressure cabin and this emerged as the PI bomb' bomber/reconnaissance which was operational over the Soviet i gathering pictures before the German invasion of June 1941 The R had a span increased even beyond that of the P and frequently operated over southern England in 1941-2 until - with extreme difficulty - solitary Spitfires managed to reach their altitude and effect an interception Total military Ju 86 production was between 810 and 1.000 Junkers schemed many developed versions, some having four or six engines +Below: One of the colourful Ju 86K-2 bombers of the Hungarian 3. /I Bombazo Oszataly, based at Tapolca in 1938 Few were left when the Axis attacked the Soviet Union in 1941. +Below: The Ju 86G-1 was the only sub-type still in combat service with the Luftwaffe at the start of the Polish campaign in 1939. + + + Junkers Ju 87 +Ju 87A, B and D series +Origin: Junkers Flugzeug und Motorenwerke AG: also built by Weser Flugzeugbau and SNCASO. France. Type: Two-seat dive bomber and ground attack. continued on page 66 +V +Below: The cutaway drawing shows the Ju 87D-3. one of the more powerful and aerodynamically improved D-series that made up more than three-quarters of all production. The bombs shown, with Dienartstab fuzes, are among a great diversity of weapons and equipment that could be carried. + + + Below Though the (utility of using unfunny bombs against tanks was recogmsetf on the fourth il.iy of the Germ. in InvMlOII of the Soviet Union, it was not until 1943 tlmt ,i better .in-.wer became available This Ju 87G 1 was probably serving with +10 (P/) SG 2 on the Eastern Front In October 1943 +67 Ad +hand grip ie and head arn69 Sliding ca(shown pan open) 70 Rmg-and bead gunsights +Mauser MG +81Z machine gun on +GSL-K 81 mount 72 Canopy track fairing 73 Peil G IV 0/F equipment 74 Circular plexiglass access panel Back-to-back L-section stringers (fuselage horizontal break) First-aid stowage 77 Z-section fuselage frames 78 Radio aerial 79 Faired elevator mass balance 80 Starboard elevator +117 Ba +Spinner Pitch change mechanism housing Blade hub +Junkers VS 1 1 constantspeed propeller Anti-vibration engine mounting attachments 6 Oil filler point and marker 7 Auxiliary oil tank (5 9 Imp gal /26 81 capacity) +8 Junkers Jumo 211 J-1 12cylinder inverted-vee liquid cooled engine 9 Magnesium alloy forged engine mount 10 Coolant (Glysantin-water) header tank +1 +1 +Ejector exhaust stubs 1 2 Fuel injection unit housing 13 Induction air cooler 1 4 Armoured radiator +15 Inertia starter cranking point 16 Ball joint bulkhead fixing (lower) 17 Tubular steel mount support strut 18 Ventral armour (8mm) 19 Main oil tank (9 9 Imp gal (451 cac 20 Oil filling point 21 Transverse support frame 22 Rudder pedals 23 Control column 24 Heating point 25 Auxiliary air intake 26 Ball joint bulkhead fixing (upper) 27 Bulkhead 28 Oil tank (6 8 Imp gal/311 capacity) 29 Oil filler point and marker Intava 100) 30 Fuel filler cap 31 Self-sealing starboard outer fuel tank (33 Imp gal/1 501 capacity) 32 Underwing bombs with Dienartstab percussion rods 33 Pitot head 34 Spherical oxygen bottles 35 Wing skinning 36 Starboard navigation light 37 Aileron mass balance 38 Double wing' aileron and flap (starboard outer) 39 Aileron hinge +48 49 50 51 52 53 +54 55 +56 57 +58 +59 60 61 62 +63 +64 65 66 +Corrugated wing rib station Reinforced armoured windscreen Reflector sight Padded crash bar Signal flare tube Braced fuselage mainframe Front spar/fuselage attachment point Pilots seat (reinfor:r +4-mm side and 8-mm rear armour) Inter-cockpit bulkhead Sliding canopy handgrip External side armour Pilot's back armour (8mm) Headrest Aft-sliding cockpit canopy (shown part open) Radio mast cut-out Anti -crash hoop (magnesium casting) Radio mast Radio equipment (FuGe 16) compartment Additional (internal) side armour Canopy track Handhold/footrests Braced fuselage mainframe Rear spar/fuselage attachment point Radio-operator/gunner's seat (folding) Floor armour (5mm) +Armoured bulkhead (8mm) Ammunition magazine racks +88 89 90 91 +81 Tailplane structure 82 Tailplane brace/spar attachment point 83 Tailplane bracing strut 84 Fuselage skinning 85 Control runs 86 Tailfin attachment fairing 87 Tailfin structure Rudder horn balance Rudder Rudder trim tab controls Rudder trim tab 92 Rudder control linkage 93 Rudder post 94 Rear navigation light 95 Elevator tab 96 Port elevator 97 Faired elevate ~ balance 98 Tailplane front spar 99 Control pulley circular access panels 1 00 Rudder lower hinge fairing 1 01 Tailplane bracing strut 102 Emergency tailskid 103 Tailwheel 104 Tailwheel leg 105 Jacking point 106 Fuselage stringers 107 Master compass 1 08 Crew entry step (port and starboard) 1 09 Entry step support (with control run cut-outs) 110 Wing root fairing 111 Non-slip walkway (aft section external metal strakes) +1 19 Inboard flap si 120 Flap hinge +121 Rhemmetall-Borsig MG 17 machine gun of 7 92 ' cahbre (port and starboard) 122 Ammunition tank (1.000 rounds c = . of rib 123 Port outer sel? tank (33 Imp gal/1 501 cap* 1 24 Corrugated wing rib +125 ETC bomb rack support bar +126 ETC bomb rack unde fairing 127 Port outboard flap 1 28 Port aileron 1 29 Aileron mass balance 1 30 Rear spar 131 Wing nb 132 Port navigatic 1 33 Front spar 1 34 Wing leading edge +135 Underwing bomb lo = 110-lb/50-kg bombs) on multi-purpose carrier +1 36 Bomb shackles 137 Dienartstab percussion rod attachments 138 ETC 50/VIII fairing 1 39 Air brake (extended) 1 40 Air brake activating anism 141 Air brake (retracted) 142 Landing lamp 1 43 Wheel spat 144 Fork/spat attachment 145 Port mainwheel 146 Brake reservoir filler point 1 47 Cantilever fork 1 48 Leather shroud 149 Oleo-pneumatic shock absorber 1 50 Mainwheel leg 1 51 Siren fairing +1 52 Barrel of MG 1 7 machine +gun +153 Wnd-dnven siren 1 54 Starboard whe +1 55 PVC ventral bomb rack +156 Bomb cradle 1 57 Starboard wheel fork 1 58 Starboard mainwheel +1 59 Bomb release trapese +160 551-lb(250-kg) bomb with Dienartstab attachment +Above: This Ju 87R is seen in Norway in April 1940. Then a new model, it carried extra fuel plus underwing tanks. 65 + + + Engine: (Ju 87B-1) one 1.100hp Junkers Jumo 211Da 12-cylinder mverted-vee liquid-cooled; (Ju 87D-1. D-5) 1.300hp Jumo 211J. Dimensions: Span (Ju 87B-1. D-1) 45ft 3^in (13 8m): (D-5) 50ft OJin (1 5 25m); length 36ft 5in (11 -1m); height 1 2ft 9in (3 9m) Weights: Empty (B-1. D-1) about 6.080lb (2750kg). loaded (B-1) 9.3711b (4250kg); (D-1) 12.6001b (5720kg); (D-5) 14.5001b (6585kg). Performance: Maximum speed (B-1) 242mph (390km/h): (D-1) 255mph (408km/h); (D-5) 250mph (402km/h); service ceiling (B-1) 26.250ft (8000m); (D-1. D-5) 24.000ft (7320m); range with maximum bomb load (B-1) 373 miles (600km): (D-1. D-5) 620 miles (1000km) +Armament: (Ju 87B-1) two 7 92mm Rheinmetall MG 17 machine guns +in wings, one 7 92mm MG 15 manually aimed in rear cockpit, one 1.1021b (500kg) bomb on centreline and four 1101b (50kg) on wing racks; (D-1. +D-5) two MG 17 in wings, twin 7 92mm MG 81 machine guns manually aimed in rear cockpit, one bomb of 3.968lb (1800kg) on centreline; (D-7) +two 20mm MG 151/20 cannon in wings; (Ju 87G-1) two 37mm BK (Flak +18. or Flak 36) cannon in underwing pods; (D-4) two underwing WB81 +weapon containers each housing six MG 81 guns. History: First flight (Ju 87V1 ) late 1935: (pre-production Ju 87A-0) November 1 936; (Ju 87B-1 ) August 1 938: (Ju 87D-1 ) 1 940; termination of production 1944. Users: Bulgaria. Croatia. Germany (Luftwaffe). Hungary. Italy. Romania. +Slovakia. +Development: Until at least 1942 the Ju 87 'Stuka" enjoyed a reputation that struck terror into those on the ground beneath it First flown with a British R-R Kestrel engine and twin fins in 1935. it entered production in 1 937 as the Ju 87A with large trousered landing gear and full equipment for dive bombing, including a heavy bomb crutch that swung the missile well clear of the fuselage before release. The spatted Ju 87B was the first aircraft in production with the Jumo 211 engine, almost twice as powerful as the Jumo 210 of the Ju 87A. and it had an automatic device (almost an autopilot) to ensure proper pull-out from the steep dive, as well as red lines at 60°. 75° and 80° painted on the pilot's side window Experience in Spain had shown that pilots could black-out and lose control in the pull-out. Later a whole formation of Ju 87Bs in Spain was late pulling out over misty ground +Above: The Ju 87G-1 anti-tank aircraft with two 37mm guns. +Above: Ju 87D-3 with two two-seat passenger pods, intended to be released and parachuted. +and many hit the ground In Poland and the Low Countries the Ju 87 was terribly effective and it repeated its success in Greece. Crete and parts of the Russian front. But in the Battle of Britain its casualty rate was such that it was soon withdrawn, thereafter to attack ships and troops in areas where the Axis still enjoyed some air superiority In 1942-45 its main work was close support on the Eastern front, attacking armour with big guns (Ju 87G-1 ) and even being used as a transport and glider tug. Total production, all by Junkers, is believed to have been 5.709 +Left: A Ju 87B-2/Trop serving with MI/StG 1 in Libya in 1941. The equipment of StG 1 had mostly been in action in Poland and the Low Countries. France and England since the start of the war. +Below: Flanked by a 1,1021b SC500 bomb, this Ju 87B "Stuka" s seen parked on a Greek airfield during the continuation of the Blitzkrieg campaign through the Balkans into north Africa. This was the last campaign in which the Ju 87 demolished its targets and encountered little opposition. + + + Junkers Ju 88 +Many versions: data for Ju 88A-4, C-6. G-7, S-1 +Origin: ( izeug und M i di imong \A +I +i +ii +t ii i +ii +i +Type: Military lin i ifi de igned as dive I bi imbing. close sum" irt. night fi and as pid itle missile. Crew tv. Engines: (A 4) two 1 ,340hp Junkers Jumo 211 J 1? cylindei iled (C-6) same as A 4. (G /) two 1 .880hp Junki +1 .' cylinder inverted-vee liquid cooled: (S-1) two l./OOhp BMW 801 G 18 cylinder two row radials. Dimensions: Span 65ft 1 0^in (20 13m) (early versions 59ft 10 ; 'i ,im (14 4m) (G 7. 54ft liin): height 15ft 1 1 in (4 85m). (C-6) 16ft 7iin (5m) Weights: Empty (A-4) 17.6371b (8000kg): (C-6b) 19.0901b (8660kg). (G-7b) 20.0621b (9100kg). (S-1) 18.3001b (8300kg). maximum loaded (A-4) 30.8651b (14.000kg): (C-6b) 27.500lb (12.485kg): (G-7b) 32.350lb (14.690kg). (S-1) 23.1001b (10.490kg) Performance: Maximum speed (A-4) 269mph (433km/h): (C-6b) 300mph (480km/h). (G-7b) (no drop tank or flame-dampers) 402mph (643km/h). (S-1) 373mph (600km/h): initial climb (A-4) 1.312ft (400m)/ mm. (C-6b) about 985ft (300m)/mm. (G-7b) 1.640ft (500m)/mm: (S-1) 1.804ft (550m)/min. service ceiling (A-4) 26.900ft (8200m): (C-6b) 32.480ft (9900m): (G-7b) 28.870ft (8800m): (S-1) 36.090ft (11.000m): range (A-4) 1.112 miles (1790km): (C-6b) 1.243 miles (2000km). (G-7b) 1.430 miles (2300km): (S-1) 1.243 miles (2000km) +Armament: (A-4) two 7.92mm MG 81 (or one MG 81 and one 13mm +MG 1 31 ) firing forward, twin MG 81 or one MG 1 31 upper rear, one or two +MG 81 at rear of ventral gondola and (later aircraft) two MG 81 at front of +gondola. (C-6b) three 20mm MG FF and three MG 17 in nose and two +20mm MG 151/20 firing obliquely upward in Schrage Musik installation. +(G-7b) four MG 151/20 (200 rounds each) firing forward from ventral +fairing, two MG 151/20 in Schrage Musik installation (200 rounds each) +and defensive MG 131 (500 rounds) swivelling in rear roof: (S-1) one +MG 131 (500 rounds) swivelling in rear roof: bomb loads (A-4) 1.1001b (500kg) internal and four external racks rated at 2.2001b (1000kg) (inners) and 1.1001b (500kg) (outers) to maximum total bomb load of 6.6141b (3000kg): (C-6b and G-7b. nil). (S-1) up to 4 410lh ( 7000kg ) on external racks +1 +OfQ +.! +Above: Three-view of the first loiwj sp.in version, the A 4 +Above: Three-view of the Ju 88G-7a night fighter, with side elevations of G-7b (centre. FuG 218 Neptun) and -7c (FuG 240). +History: Fust flight (Ju 88V1) 21 December 1936. (first Ju 88A-1) 7 September 1939: (first fighter. Ju 88C-0) July 1939: (Ju 88C-6) mid-1942, (first G-series) early 1944: (S series) late 1943: final deliveries, only as factories were overrun by Allies. Users: Bulgaria (briefly). Finland. Germany (Luftwaffe). Hungary. Romania continued on page 68* +Left: Ju 88A-4 of l/KG 54 "Totenkopf" (Death's Head) at Gerbini. April 1942; colours 78/79/80. +Below: Yet another A-4, this time belonging to one of the most famous units. I/KG 51 "Edelweiss". It was photographed on the Eastern Front in the summer of 1941, in 70/71/65 trim. +.-- V +" +' ? %» + + + Development: Probably no other aircraft in history has been developed in +so many quite different forms for so many purposes - except, perhaps, for +the Mosquito Flown long before World War II as a civil prototype, after a +rapid design process led by two temporarily hired Americans well-versed +in modern stressed-skin construction, the first 88s were transformed into the +heavier, slower and more capacious A-1 bombers which were just entering +service as World War II began. The formidable bomb load and generally good +performance were offset by inadequate defensive armament, and in the A-4 +the span was increased, the bomb load and gun power substantially aug +mented and a basis laid for diverse further development. Though it would be +fair to describe practically all the subsequent versions as a hodge-podge of +lash-ups. the Ju 88 was structurally excellent, combined large internal fuel +capacity with great load-carrying capability, and yet was never so degraded +in performance as to become seriously vulnerable as were the Dornier and +Heinkel bombers. Indeed, with the BMW radial and the Jumo 213 engines +the later versions were almost as fast as the best contemporary fighters at all +altitudes and could be aerobatted violently into the bargain. A basic design +feature was that all the crew were huddled together, to improve combat +morale; but in the Battle of Britain it was found this merely made it difficult +to add proper defensive armament and in the later Ju 1 88 a much larger +crew compartment was provided. Another distinctive feature was the large +single struts of the main landing gear, sprung with stacks of chamfered rings +of springy steel, and arranged to turn the big. soft-field wheels through 90° +to lie flat in the rear of the nacelles. In 1940 to 1943 about 2.000 Ju 88 +bombers were built each year, nearly all A-5 or A-4 versions. After splitting +off completely new branches which led to the Ju 188 and 388, bomber +development was directed to the streamlined S series of much higher +performance, it having become accepted that the traditional Luftwaffe +species of bomber was doomed if intercepted, no matter how many extra +guns and crew it might carry. Indeed even the bomb and fuel loads were cut +in most S sub-types, though the S-2 had fuel in the original bomb bay and +large bulged bomb stowage (which defeated the objective of reducing drag). +Final bomber versions included the P series of big-gun anti-armour and +close-support machines, the Nbwe with flame-throwers and recoilless +rocket projectors, and a large family of Mistel composite-aircraft combinations, in which the Ju 88 lower portion was a pilotless missile steered by the +fighter originally mounted on top. Altogether bomber, reconnaissance and related 88s totalled 10.774. while frantic construction of night fighter versions in 1944-45 brought the total to at least 14.980. The Ju 88 night fighters (especially the properly designed G-series) were extremely formidable, bristling with radar and weapons and being responsible for destroying more Allied night bombers than all other fighters combined. +Above: One of the first Ju 88 combat missions sta a long-span A-5 model, with yellow-staffel spinne SC 250 bombs hung externally. +Below: One of countless Ju 88 lash-ups was the P +heavy-gun platform with 75mm PaK 40 with large +rts engines +: +rs and two +1 anti-tank muzzle brake. +19 +17 + + + Above: One of the outstanding Ju 88 night fighters +the G-7a with Jumo 213 engines. Lichtenstein SN-2 FuG 220 radar and devastating armament. +Above: Another propaganda film shot of an early raid by a Ju 88A-5. Though still troublesome in 1939-40, the Ju 88 was the best German offensive aircraft. +Junkers Ju 88G-1 cutaway drawing key: 1 Starboard navigation light 2 Wingtip profile 3 FuG 227 Flensburg homing receiver aerial 4 Starboard aileron 5 Aileron control lines 6 Starboard flap 7 Flap-fairing strip 8 Wing ribs 9 Starboard outer fuel tank (91 gal/414 10 Fuel filler cap 11 Leading-edge structure 12 Annular exhaust slot 13 Cylinder head fairings +1 +4 +Adiustable nacelle nose ring 15 Twelve-blade cooling fan 16 Propeller boss 17 Three blade variable-pitch VS 1 1 1 propeller 18 Leading-edge radar array 19 Lichtenstein SN 2 radar array 20 SN-2 radar 21 Bulkhead +22 Gyro compass 23 Instrument panel 24 Armoured-glass windscreen sections 25 Folding seat 26 Control column 27 Rudder pedal/brake cylinder 28 Control lines 29 Pilot's seal +30 Sliding window section 31 Headrest 32 Jettisonable canopy roof section 33 Gun restraint 34 Radio operator/gunner's seat +35 13mm MG 131 gun +36 Radio equipment 37 Ammunition box (500 rounds) 38 Lichtenstein SN-2 indicator box 39 FuG 227 Flensburg indicator box +40 Control linkage 41 Bulkhead 42 Armoured gun mounting 43 Aerial post/traverse check 44 Fuel filler cap 45 Whip aerial 46 Forward fuselage fuel tank (105 gal/480 litres) 47 Fuselage horizontal construction joint 48 Bulkhead 49 Fuel filler cap 50 Aft fuselage fuel tank (230 gal/1.046 litres) 51 Access hatch 52 Bulkhead 53 Control linkage access plate 54 Fuselage stringers 55 Upper longeron 56 Maintenance walkway 57 Control linkage 58 Fuselage horizontal construction joint +Left: This cutaway reveals most of the salient features of the Ju 88G-1, the first of the purpose-designed night fighter versions with new Ju 188-type tail and completely revised armament. No other night fighter in wide use in +World War II carried so many effective sensors; but the RAF played into the enemy's hands by emitting streams of signals. +Port outer fuel tank location (91 gal/414 litres) Ventral gun pack (offset to port) Ball and socket fuselage/ wing attachment points Port inner fuel tank location (93 4 gal/425 litres) Ammunition boxes (200 rpg) +Four Mauser MG 151 +20mm cannon Mainwheel leg retraction yoke Leg pivot member Mainwheel door actuating jack Mainwheel door (rear section) Mainwheel door (front section) Leg support strut Port mainwheel Mainwheel leg Annular exhaust slot Exhaust stubs (internal) +BMW 801 D engine (part +deleted to show gun pack) Annular oil tank Cannon muzzles (5 deg downward angle) Twelve-blade cooling fan (3 17 times propeller speed) Propeller mechanism Three-blade variable-pitch VS 1 1 1 propeller +FuG 16ZY aerial Starboard mainwheel +59 Z'-section fuselage frames 60 Dinghy stowage 61 Fuel vent pipe 62 Master compass 63 Spherical oxygen bottles 64 Accumulator 65 Tailplane centre-section carry-through 66 Starboard tailplane 67 Elevator balance 68 Aerial 69 Starboard elevator Elevator tab Fin front spar/fuselage attachment Fin structure Rudder actuator 74 Rudder post 75 Rudder mass balance 76 Rudder upper hinge 77 Rudder tab (upper section) 78 Inspection/maintenance handhold +70 71 +72 73 +79 Rudder structure 114 80 Fin rear spar/fuselage attachment 81 Rudder tab (lower section) 115 82 Rear navigation light +83 Elevator tab 116 84 Port elevator +85 Elevator balance 117 86 Elevator tab actuator +87 Heated leading-edge 118 88 Tailbumper/fuel vent outlet +89 Tailwheel doors 119 90 Tailwheel retraction +mechanism 120 91 Shock-absorber leg 92 Mudgard 121 +93 Tailwheel 122 94 Access hatch +95 Fixed antenna 123 96 D/F loop +97 Lower longeron 124 98 Nacelle/flap fairing +99 Port flap 125 +100 Wing centre/outer section 126 +attachment point 127 +101 Aileron controls 128 102 Aileron tab (port only) 129 +103 Aileron hinges 130 104 Rear spar 105 Port aileron 131 106 Port navigation light 132 107 FuG 101 a radio altimeter +aerial 133 108 Wing structure +109 Leading-edge radar array 134 +110 Front spar 135 1 1 1 Pitot head 1 12 Landing lamp 136 113 Mainwheel well rear 137 bulkhead +69 + + + Junkers Ju 188 +Ju 188A, D and E series, +and Ju 388, J, K and L +Origin: Junkers Flugzeug und Motorenwerke AG: with subcontract manufacture of parts by various French companies Type: Five-seat bomber (D-2. reconnaissance). +Engines: (Ju 188A) two 1.776hp Junkers Jumo 21 3A 12-cylinder inverted-vee liquid-cooled; (Ju 188D) same as A; (Ju 188E) two 1.700hp +BMW 801 G-2 18-cylinder two-row radials. Dimensions: Span 72ft 2in (22m); length 49ft 1 in (14 96m); height 16ft +1 in (4 9m) Weights: Empty (188E-1) 21.8251b (9900kg); loaded (188A and D) 33,730lb (15.300kg); (188E-1) 31.9671b (14.500kg) Performance: Maximum speed (188A) 325mph (420km/h) at 20.500ft +(6250m); (188D) 350mph (560km/h) at 27.000ft (8235m); (188E) 31 5mph (494km/h) at 19.685ft (6000m); service ceiling (188A) 33.000ft (10.060m); (188D) 36.090ft (11.000m); (188E) 31.170ft (9500m); range with 3.300lb (1500kg) bomb load (188Aand E) 1.550 miles (2480km) +Armament: (A. D-1 and E-1) one 20mm MG 1 51/20 cannon in nose, one +MG 151/20 in dorsal turret, one 13mm MG 131 manually aimed at rear +dorsal position and one MG 1 31 or twin 7 92mm MG 81 manually aimed at rear ventral position; 6.6141b (3000kg) bombs internally or two 2.2001b (1000kg) torpedoes under inner wings History: First flight (Ju 88B-0) early 1940; (Ju 88V27) September 1941; +(Ju 1 88V1 ) December 1 941 ; (Ju 1 88E-1 ) March 1 942: (Ju 388L) May 1 944 User: Germany (Luftwaffe). +Development: In 1939 Junkers had the Jumo 213 engine in advanced development and. to go with it. the aircraft side of the company prepared an +-J_ +Above: Three-view of the Ju 188E-1 bomber, one of the +versions with the BMW 801 G-2 radial engine +Below: Almost gaudy in 72/73 green shades oversprayed with 65 Light Blue, this Ju 188D-2 was operated by 1 (F)/124 at Kirkenes, northern Norway, in 1944. +Junkers Ju 290 +Ju 290A-1 to A-8 and B-1 , B-2 and C +Origin: Junkers Flugzeug und Motorenwerke; design and development at Prague- Letnany. prototypes at Dessau and production at Bernberg Type: Long-range transport and reconnaissance bomber +Engines: Four BMW 801 14-cylinder radials. (A) usually 1 .700hp 801 D. (B) 1.970hp 801 E. Dimensions: Span 137ft 9Jin (42 00m); length 92ft 1 in to 97ft 9in (A-5. 93ft 11iin. 28 64m): height 22ft 4Jin (6 83m) Weights: Empty, not known (published figures cannot be correct); maximum (A-5) 99.1411b (44.970kg). (A-7) 101.4131b (45.400kg). (B-2) 111.3321b (50.500kg) Performance: Maximum speed (all. without missiles) about 273mph (440km/h); maximum range (typical) 3.700 miles (5950km). (B-2) 4.970 miles (8000km) +Armament: See text +History: First flight (rebuilt Ju 90V5) early 1939. (production 290A-0) October 1 942: programme termination October 1 944. User: Germany (Luftwaffe). +Development: In 1936 Junkers considered the possibility of turning the Ju 89 strategic bomber into the Ju 90 airliner With the death of Gen Wever the Ju 89 was cancelled and the Ju 90 became the pride of Deutsche Lufthansa. By 1937 the civil Ju 90S (Schwer = heavy) was in final design, +with the powerful BMW 139 engine. By 1939 this had flown, with a new +wing and BMW 801 engines, and via a string of development prototypes led to the Ju 290A-0 and A-1 transports first used at Stalingrad The A-2 was +an Atlantic patrol machine, with typical armament of five 20mm MG 1 51 +(including two power turrets) and six 13mm MG 131 There were many other versions, and the A-7 introduced a bulbous glazed nose: armament of +the A-8 series was ten MG 151 and one (or three) MG 131, the most powerful carried by any bomber of World War II The B carried more fuel and pressurized crew compartments, and like some A versions had radar and could launch Hs 293 and other air/surface missiles. In 1944 three A-5 made round trips to Manchuria +Right: Taken at the Junkers plant at Bernburg, the centre for Ju 290 development, this shows the first production A-7 +(Werk-Nr 0186) being readied for flight in May 1944. The A-7 +was the most advanced sub-type to reach production status; even so the initial batch of 25 was not completed. +Above: One of the later sub-types was the Ju 290A-7, one of which is illustrated at the foot of the page. +Above: The Ju 90 V4, a development aircraft of 1937 (pre-290). +70 + + + 18 with a largei 81 tn imlined i rew i ant pointed wings and la |i tail After protracted developi +i/ent into production as the lu 1 881 I fitted with BMW 801 b the i" iwerful lurrv i till not read , rhe plani al > +I +i i and ' few radai i quipped turretle is I I i mce I +i +i bel hi mid 1943 finally getting into production with the A l m Leipzig fi h id iu buill the tl pad exhau nighl i iperatii ins and the A I torpedo bombei rhe D as a I aircraft and the Ju 188S i i familv i ii high ipeed i various duties capable oi up to I35mph (696km h) Numi me with a ren ti tiled twin M(i I 11 tail turret led even faster ami highei flying Ju 188 family ol nighl fighters | I) n ;ance (L) and bomber aircraft (K) Altogether about 1.100 Ju 188 i about 120 388s were delivered vhile al the wai s end the mm h I irgi i and markedly differenl Iu .'88 had been shelved and the ! +i much enlarged foul engined 388. had been built at Toulouse All these aircraft and the even greater number of stillborn protects, were evidence "i the im rea ingl^ urgent need to make up for the absence of properly conceived new designs by wringing the utmost development out of the obsolescent types with which the I utM.ifte had started the war. Above: Capable of carrying two advanced LT 1b or LT F5b torpedoes, and Hohentwiel radar, the Ju 188E-2 was one of the best anti-shipping aircraft of World War II. +Above: The Ju 188A-2, a four-seat bomber with Jumo 213 engines boosted to 2,240hp each. Above: Ju 188D-2 (shown in colour opposite). +Above: The Ju 188C, with hydraulic tail barbette (abandoned). Above: Ju 188G-0 with wooden bomb pannier and manned turret. +Above: A rare air-to-air shot of the first Ju 290A-5 to be delivered to FAGr 5 ocean-reconnaissance geschwader in 1943. +Above, from the top: Ju 290A-2, the first ocean patrol type; Ju 290A-8 with ten cannon; and the Ju 290B-1 heavy bomber. +Below: This picture of the first Ju 290A-3 (also used by 1/FAGr 5) shows the impressive size of these aircraft. +71 +__. + + + Messerschmitt Me 163 Komet +Me163B-1 +Origin: Messerschmitt AG Type Single-seat interceptor. +Engine: One 3.750lb (1700kg) thrust Walter HWK 509A-2 bi-propellant rocket burning concentrated hydrogen peroxide (T-stoff) and hydrazine/ methanol (C'-stoff) Dimensions: Span 30ft 7in (9 3m); length 18ft 8in (5 69m); height 9ft Oin (274m) Weights: Empty 4.1911b (1905kg); loaded 9.042lb (4110kg). Performance: Maximum speed 596mph (960km/h) at 32.800ft (1 0.000m); initial climb 16.400ft (5000m)/mm: service ceiling 54.000ft (16.500m); range depended greatly on flight profile but under 100km (62 miles): endurance 2imin from top of climb or eight min total. +Armament: Two 30mm MK 108 cannon in wing roots, each with 60 rounds. History: First flight (Me 1 63V1 ) spring 1941 as glider. August 1941 under power; (Me 163B) August 1943; first operational unit (I/JG400) May 1944. User: Germany (Luftwaffe) +Development: Of all aircraft engaged in World War II the Me 163 Komet (Comet) was the most radical and. indeed, futuristic. The concept of the short-endurance local-defence interceptor powered by a rocket engine was certainly valid and might have been more of a thorn in the Allies' side +Below: The prototype Me 163A V1 (first prototype), which +languished 18 months as a glider before its rocket was fitted. +Above: Me 163B-1a showing takeoff trolley and landing skid +than it was. Even the dramatically unconventional form of the Me 1 63. with no horizontal tail and an incredibly short fuselage, did not lead to great difficulty; in fact, the production fighter was widely held to have the best and safest characteristics of any aircraft in the Luftwaffe. But the swift strides into uncharted technology were bold in the extreme. It was partly to save weight and drag that the tailless configuration was adopted, and partly because the moving spirit behind the project was at first Dr Alex Lippisch. +Below: Purging the propellant pipes, with C-stoff generating steam clouds. On the ground the Komet was extremely dangerous ! +Messerschmitt Me 210 +and 410 Hornisse +Me 21 0A, B and C series. +Me 41 0A and B series +Origin: Messerschmitt AG. Type: Two-seat tactical aircraft for fighter, attack and reconnaissance duties with specialised variants. Engines: (Me 210. usual for production versions) two 1.395hp DaimlerBenz DB 601 F inverted-vee-12 liquid-cooled; (Me 41 0A series, usual for production versions) two 1.750hp DB 603A of same layout. (Me 41 0B series) two 1 ,900hp DB 603G Dimensions: Span (210) 53ft 7Jin. later 53ft 7|in (16-4m): (410) 53ft 7|in: length (without 50mm gun. radar or other long fitment) (210) 40ft 3in (12 22m); (410) 40ft 10in or 40ft 1 1 iin (12 45m); height (both) 14ft OJin (4 3m) Weights: Empty (21 0A) about 12.0001b (5440kg); (410A-1) 13.5601b (6150kg); maximum loaded (210A-1) 17.8571b (8100kg); (410A-1) 23.483lb (10.650kg). Performance: Maximum speed (both, clean) 385mph (620km/h): initial climb (both) 2.133ft (650m)/min; service ceiling (210A-1) 22.967ft (7000m); (410A-1) 32.800ft (10.000m); range with full bomb load (210A-1) 1.491 miles (2400km): (410A-1) 1.447 miles (2330km). Armament: Varied, but basic aircraft invariably defended by two remotelycontrolled powered barbettes on sides of fuselage each housing one 13mm +MG 1 31 and. if bomber version, provided with internal weapon bay housing two 1.1021b (500kg) bombs: external racks on nearly all (210 and 410) for two 1.1021b stores (exceptionally, two 2.2041b). Normal fixed forward +firing armament of two 20mm MG 151/20 and two 7 92mm MG 17. +Me 410 versions had many kinds of bomber-destroyer armament, as described in the text. History: First flight (Me 210V-1) 2 September 1939; (pre-production 210A-0) April 1941; final delivery (210) April 1942: first flight (310) 11 September 1943: (410V-1) probably December 1942 User: Germany (Luftwaffe). +Development: Planned in 1937 as a valuable and more versatile successor to the Bf 1 10 twin-engined escort fighter, the Me 210 was little more than a flop and made hardly any contribution to the German war effort. After severe flight instability and landing-gear problems some progress was made in 1941 towards producing an acceptable machine which could be put into +Above: Three-view of Me 210A-2 (upper side view, A-0). +Right: This Messerschmitt Me 410A-3 Hornisse was captured by +the RAF at Trapani in Sicily in 1943. Previously operated by 2.(F)/122, it was one of the specialized photo-reconnaissance variants with a deepened forward fuselage without an internal weapons bay to allow the installation of two Rb 20/30, 50/30 or 75/30 cameras. +Below: Another A-3 showing the deep fuselage. Previous +photo-reconnaissance versions of the Me 410 Hornisse had been mere lash-ups, with the cameras inadequately installed in the bomb bay and giving extremely poor results. +I +72 + + + i .-it An m.) I63B la Komd "t II J'< 400 +OpCI .il.il il Bl .null-, in .-.ii ly 1 B46 I In- Mi- Hi I in-i-ilml nulnn-iivii -. +| +mi i.i I +ground I. ii ililiu-. .mil unly nin« .111 in-ill-, wore ever equipped foi 11 +Right: An Me 163B 1a of TrainingStaffel (Erganzungsstaffel)/JG 400 at Udetfeld in the winter 1944-45 This was a more usual colour scheme +Below: The Me 263 (Junkers Ju 248) +was planned as a much better successor to the Komet. but it never got into service. +who liked tailless designs Choice of two rocket propellents that reacted violently when they came into contact solved the problem of ignition in the combustion chamber but added an extremely large element of danger Moreover, the 163 had no landing gear, taking off from a jettisoned trolley and landing on a sprung skid, and the landing impact often sloshed residual propellants together causing a violent explosion Many aircraft were lost this way. and the. original test pilot, glider champion Heini Dittmar, was badly injured when the skid failed to extend Nevertheless by 1944 these bat-like specks were swooping on US bomber formations with devastating effect. Numerous improved versions were flying at VE day. but only 370 Komets had seen service and these had suffered high attrition through accidents. +Above: Three-view of Me 410A-1 Hornisse (Hornet). +production against the order for 1.000 placed "off the drawing board" in June 1939 Accidents were nevertheless frequent and manufacture was terminated at the 352nd aircraft This major blow to the Luftwaffe and the company, which was reflected in an official demand for Willi Messerschmitt's resignation from the board, was partly salvaged by a further redesign and change to the DB 603 engine. The Me 310 was a highaltitude fighter-bomber with 58ft 9in wing and pressure cabin, but this was abandoned in favour of a less radical change designated 410 As with the 210. the reconnaissance 410s usually had cameras in the bomb bay and no +MG 17s. while some attack or destroyer versions had four forward-firing +MG 1 51 cannon, or two MG 1 51 and a 50mm BK 5 gun with 21 rounds The +Me 410A-2/U-2 was an important night fighter with SN-2 Lichtenstein +radar and two MG 151 and two 30mm MK 108 Many of the 1.121 Me 410s +carried Rustsatz external packs housing two more MG 151. MK 108 or +MK 1 03. and occasionally experienced pilots fitted as many as eight MG 1 51 +all firing ahead. The 210mm rocket tube was a common fitment by 1944. some aircraft having a rotating pack of six tubes in the bomb bay. +73 +j +. + + + Messerschmitt Me 262 +Me 262A-1a Schwalbe, Me 262A-2 +Sturmvogel, Me262B-1a +Origin: Messerschmitt AG Type: (A-1a) single-seat fighter. (A-2a) single-seat bomber. (262B-1a) two-seat night fighter. Engines: Two 1.9801b (900kg) thrust Junkers Jumo 004B single-shaft axial turbojets. Dimensions: Span 40ft 11Jin (12 5m). length 34ft 9Jin (10-6m). (262B1a. excluding radar aerials) 38ft 9in (11 8m); height 12ft 7in (38m). Weights: Empty (A-1a. A-2a) 8.820lb (4000kg); (B-1a) 9.700lb (4400kg); loaded (A-1a. A-2a) 15.5001b (7045kg); (B-1a) 14.1101b (6400kg) Performance: Maximum speed (A-1a) 540mph (870km/h); (A-2a. laden) 470mph (755km/h): (B-1a) 497mph (800km/h); initial climb (all) about 3.940ft (1200m)/min; service ceiling 37.565ft (11.500m); range on +internal fuel, at altitude, about 650 miles (1050km). +Armament: (A-1a) four 30mm MK 108 cannon in nose, two with 100 +rounds each, two with 80: (A-1a/U1) two 30mm MK 103. two MK 108 and +two 20mm MG 151/20: (A-1b) as A-1a plus 24 spin-stabilised R4/M 50mm +rockets. (B-1a) as A-1a: (B-2a) as A-1a plus two inclined MK 108 behind cockpit in Schrage Musik installation: (D) SG 500 Jagdfaust with 12 +rifled mortar barrels inclined in nose; (E) 50mm MK 114 gun or 48 R4/M rockets, bomb load of two 1.1001b (500kg) bombs carried by A-2a. History: First flight (262V1 on Jumo 210 piston engine) 4 April 1941; (262V3on two Jumo 004-0 turbojets) 18 July 1942; (Me 262A-1a) 7 June 1944: first delivery (A-0 to Rechlin) May 1944: first experimental combat unit (EK 262) 30 June 1944; first regular squadron (8/ZG26) September 1944 User: Germany (Luftwaffe). +Development: In the Me 262 the German aircraft industry created a potentially war-winning aircraft which could have restored to the Luftwaffe command of the skies over Germany. Compared with Allied fighter's of its day. including the RAF Meteor I. which entered service a little earlier, it was much faster and packed a much heavier punch Radar-equipped night fighter versions and sub-types designed to stand off from large bomber formations and blast them out of the sky were also developments against which the Allies had no answer Yet for years the programme was held back by official disinterest, and by the personal insistence of Hitler that the worldbeating jet should be used only as a bomber! It was in the autumn of 1938 that Messerschmitt was asked to study the design of a jet fighter, and the resulting Me 262 was remarkably unerring First flown on a piston engine in the nose, it then flew on its twin turbojets and finally, in July 1943. the fifth development aircraft flew with a nosewheel. Despite numerous snags. production aircraft were being delivered in July 1944 and the rate of production was many times that of the British Meteor. On the other hand the +Above: Three-view of the Me 262B-1a night fighter; lower side view, the longer B-2a specially designed for this role. +Above: Starting the Jumo 004B engines of an A-1a of the +Kommando Nowotny in late October 1944 (probably at Achmer). +The Me 262 was potentially the greatest fighter of the war. +German axial engines were unreliable and casualties due to engine failure, +fires or break-up were heavy. The MK 108 gun was also prone to jam. and the landing gear to collapse. Yet the 262 was a beautiful machine to handle and. while Allied jets either never reached squadrons or never engaged enemy aircraft, the 100 or so Me 262s that flew on operations and had fuel available destroyed far more than 100 Allied bombers and fighters. Even more remarkable, by VE-day total deliveries of this formidable aircraft reached 1.433 +Messerschmitt Me 321 +and 323 Gigant +Me 321A and B, Me 323D and E +Origin: Messerschmitt AG Type: (321) heavy cargo glider. (323) heavy cargo transport Engines: C321) none; (323 production variants) six 1.140hp GnomeRhone 14N 48/49 14-cylinder two-row radials Dimensions: Span 180ft 5£in (55m): length 92ft 4^in (28 15m); height (321B-1) 33ft 3iin (10 15m): (323) 31ft 6in (96m). Weights: Empty (321 B-1) 27.432lb (12.400kg); (323D-6) 60.260lb (27.330kg); (323E-1) 61.7001b (28.010kg); maximum loaded (321 B-1) 75.8521b (34,400kg); (323D-6) 94.8151b (43.000kg): (323E-1) 99.208lb (45.000kg). Performance: Maximum speed (321 on tow) 99mph (160km/h); (323D series) 1 77mph (285km/h); initial climb (321 towed by three Bf 1 1 0) 492ft (1 50m)/min: (323D series) 710ft (21 6m)/min; service ceiling (323D) about 1 3.1 00ft (4000m); range with "normal" payload (presumably not maximum) 684 miles (1100km). Armament: See text +History: First flight (321V-1) 7 March 1941; service delivery (321) about June 1941; final delivery (321) April 1942; first flight (323V-1) some reports claim April 1941 but others, much more plausible, state "autumn 1941"; service delivery (323D-1) May 1942: final delivery March 1944 User: Germany (Luftwaffe). +Development: Following the dramatic vindication of the previously untried Blitzkrieg concept of airborne forces in May 1940 the Reichsluftfahrtministerium (RLM) asked Junkers and Heinkel to design huge transport gliders far bigger than the little DFS 230 used in the invasion of the +Benelux countries. Junkers' Ju 322 Mammut was an expensive failure, but +Right: Man-handling an artillery piece, probably a 75mm +Pak.40 anti-tank gun. up into the hold of an Me 323D-1. +74 +Above: Two-view of the Me 323D-1, the most numerous version. + + + Below: An Me 262A 1 ,i U3 serving with the I iiih.it/koinniiindo iw .nun -uli|i--. in the toiw.nd t u-.t'l.icje +Below: An Me 262A 2a Sturmvogel bomber serving with l/KG 51 in early 1945 at Hopsten. +Below: One of the first A-2a Sturmvogels, an A-2a/U1 with special sight and only two guns, serving with EKdo Schenk in November 1944. +the Me 321 Gigant went into production, despite the fact it was extremely tiring to fly on account of the very high control forces needed. Made chiefly of welded steel tube, with plywood or fabric covering, it carried the large payload of 48.500lb (22 tonnes), or a company of infantry The 321 A-1 had a single pilot but most of the 1 75 built were 321 B-1 with a pair of crew who served as navigator and radio operator and manned two twin 7 92mm +MG 15 machine guns in beam windows. Usual towing scheme was three Bf 110 in formation, but the specially built He 111Z was preferable and many units used various arrangements of take-off boost rockets Dipl-lng Degel then studied the powered 321 C and D and eventually these became the 323V-1 with four engines (complete nacelles already in production at SNCASO for the Bloch 175) and 323V-2 with six. The six-engined Gigant +went into production, the D-1 having three-blade metal propellers and the +D-2 two-blade wooden, each having five MG 15 in the nose and mounts +for six MG 34 infantry m.g. in beam windows Most later had five 13mm +MG 1 31 added, but this did not stop Beaufighters shooting 14 into the sea as they ferried petrol to Rommel Final versions in the run of 210 were the +E-series with 1.340hp Jumo 21 1 F. the E-1 having an MG 151 20mm turret above each centre-engine nacelle, and the 323G with 1.320hp Gnome-Rhone 1 4R +Below: Takeoff of an Me 321 A-1 Gigant under the lusty pull of a Heinkel He 111Z five-engined tug. The Z could handle the monster glider without the latter needing a. to. rockets. +75 +^\ + + + Airspeed AS. 51 Horsa +Horsa I and II +Origin: Airspeed (1934) Ltd (from January 1944 Airspeed Ltd). Type: Assault glider. Engine: None. Dimensions: Span 88ft Oin (26 84m). length 67ft Oin (20 43m); height +19ft 6in (5 9m). Weights: Empty 7.500lb (3402kg); loaded 15.2501b (6917kg) Performance: Typical towing speed 127mph (204km/h); gliding speed 100mph (161km/h). History: Prototype (DG597) flew 12 September 1941; first delivery (DP279) May 1942. +Users: Portugal. Turkey. UK (RAF). US (AAF) +Development: Germany's success with airborne assault in the Low Countries in May 1940 was so self-evident that the British decided to emulate and. if possible, improve on it. Urgent work went ahead with a number of types of training, troop-carrying and cargo glider and of these by far the most important was the Airspeed AS. 51 Horsa. designed to specification X. 26/40 as a multirole assault aircraft It was the biggest glider that could reasonably be towed by available twin-engined tugs. At first training proceeded with Whitley V tugs, with Horsas camouflaged above and painted below with the diagonal black/yellow stripes first seen on target-towing aircraft. By 1943. the usual tug was the Albemarle and the operational gliders had black sides and undersurfaces. Very large orders were placed, not only with Airspeed at Christchurch but also with the Harris Lebus furniture firm. Austin Motor Co and Tata Industries of India. The Indian contract was cancelled but in Britain 3.655 Horsas were built and most saw action. In flight the Horsa creaked loudly and smelled of the wood from which it was made. The Mk I had towing brackets on the wings, necessitating a bifurcated +Above: Horsa I with landing gear in position. +rope. The Mk II had a single socket under the nose for a rope which by 1 944 was often springy nylon. The rear fuselage could be jettisoned, and there was a large door on the left side; the whole nose of the Mk II could also swing open. With its huge flaps lowered by compressed air and air brakes above and below the wings, the Horsa could almost stand on its nose and swoop quietly into small fields, carrying up to 25 troops Halifaxes towed two on a special mission to Norway in November 1942 The same type of tug was used in the invasion of Sicily Hundreds of Horsas took nearly a quarter of the air-supplied loads in the Normandy invasion and. in March 1945. 440 carried the 6th Airborne Division across the Rhine Many also served with the US Army. +Left: DP726 was one of a batch of 100 Horsa I gliders built by the Austin Motor Company, It is depicted in normal training configuration, but on an operational mission was designed to jettison the entire main landing gears and alight on a large sprung ash skid under the centre fuselage. +Airspeed Oxford +AS. 10 (Oxford I, II) and AS. 46 (III, V) +Origin: Airspeed (1934) Ltd. Portsmouth, also made at Christchurch and by de Havilland. Percival and Standard Motors Type: Advanced trainer; see text. Engines: (I) two 355hp Armstrong Siddeley Cheetah IX seven-cylinder radial; (II) 375hp Cheetah X: (III) 425hp Cheetah XV; (IV) 300hp DH Gipsy Queen IV in-line: (V) 450hp Pratt & Whitney R-985-AN6 Wasp Junior nine-cylinder radial Dimensions: Span 53ft 4in (1625m); length 34ft 6in (10 52m); height 11ft 1 in (3 38m). Weights: Empty, equipped (II) 5.3801b (2440kg). (V) 5.6701b (2575kg); maximum (II) 7.6001b (3450kg). (V) 8.0001b (3629kg). Performance (without turret); Maximum speed (I. II) 188mph (301km/h). (V) 202mph (325km/h); initial climb (II) 1.480ft (450m)/min. (V) 2.000ft +Above: Oxford II nav/radio trainer (but retaining bomb bay). +(610m)/min; service ceiling (typical) 20.000ft (6100m); range (typical) 550 miles (885km). +Armament: See text. +History: First flight 19 June 1937; service delivery November 1937; final delivery 14 July 1945. Users (WWII): Australia. Canada. Egypt. France. New Zealand. Portugal. S Rhodesia. Turkey. UK (RAF. RN). USA (AAF). +Development: The "Ox-box " has never been one of the famed aircraft of history, yet its contribution to World War II was immense. Throughout the Commonwealth it was the chief vehicle in which were trained the scores of thousands of aircrew for the RAF and many other Allied air forces, and the number built (8.751 ) made it one of the major production programmes of all time. Built of wood, it was a trim machine which demanded precision of its pilots, and would never tolerate a sloppy landing. Early examples had an +AW dorsal turret, and in 1940 a few carried additional guns Nearly all had provision for bombing training, and other roles included training in navigation, photography, radio and twin-engine pilot conversion. Many hundreds served in communications, ambulance. AA co-operation and radio/radar calibration. The IV was an engine test-bed The III and V had constant-speed propellers and higher performance +Left: AS515 was an Oxford I with turret. It is shown in use at an air-gunnery school in Canada. +76 + + + Armstrong Whit worth A.W. 38 Whitley +Whitley I to VIII (data for V) +Origin Sir W. G +Type : I ive ;eat h< ibei +Engines: l"wo 1 ,145hp Roll R Dimensions: ipai 6m) length 70h 6in i ! +i 5m) heighl I mi Dm (4 5 'm) +Weights: I mpt\ l +1 +' 3 SOIb i I 5001b I 15 I96( |) +Performance: M i'imitm ;peed 222mph peed iboul 185mph (297km/h) initial climb 800ft (244m mil e ceiling from 1 7. 600-21. 000ft (5400-640i mg th maxim (756km). range with 3.000lb (1361kg) bombs 1.650 miles (265* Armament: One 303 in Vickers K ii irrel I" m 303 in Brow in tail turret; up to 7.0001b (3175kg) bombs in cells in fuselage and n w ings. +Above: Typical Whitley V with landing gear extended +Left: This Whitley V served in the early part of the war with 102 Sqn. It took part in many leaflet raids, minelaying sorties and early missions to bomb targets in Germany and northern Italy. +History: lust flight (prototype) 17 March 1936: first delivery (Mk I) January 1937; first flight (Mk V) December 1938; first delivery (Mk V) August 1939: production termination June 1943. User: UK (RAF. BOAC). +Development: Designed to Specification B.3/34. this heavy bomber was at least an all-metal monoplane with retractable landing gear, but the original Mk I was still primitive. Its thick wing, which in the first batch had no dihedral, was set at a marked positive incidence, so that at normal cruising speeds the long slab-sided Whitley flew in a characteristic nosedown attitude. Powered by 795hp Armstrong Siddeley Tiger IX radials, the Mk I was soon replaced by the Mk II, and then by the III with the 920hp Tiger VIII In 1938 production switched to the greatly improved Mk IV, with Merlin engines and a power-driven rear turret mounting four machine guns. The Mk IVA had a more powerful Merlin, and this was retained in the +Mk V which was 1 Sin longer and had straight-edged fins. AWA made 1 .466 Whitley Vs. the last in June 1943. and also delivered 146 longer-range GR.VIII patrol aircraft with ASV radar for Coastal Command. Whitleys bore the brunt of long leaflet raids, starting on the first night of the war. On 19 March 1940 Whitleys dropped the first bombs to fall on Germany since 1918. and during the next two years these tough and capable aircraft made missions as far as Turin and Pilsen. often in terrible conditions, highlighting deficiencies in navigation and equipment the hard way. Coastal's first U-boat kill was U-206. sunk by a Whitley VII in November 1941 . From 1942 the Whitley served mainly as a trainer for paratroops, as a glider tug and with 100 Group as a carrier of experimental or special-purpose radars and countermeasures. Total production was 1.737. +Below: Ground and aircrew investigate a last minute engine snag before the day air test that always preceded a mission. + + + Armstrong Whitworth A.W.41 Albemarle +Albemarle I to VI +Origin: A. W Hawks^ Type: Four-crew special transport and glider tug. Engines: .o 1.590hp Bristol Hercules XI 14-cylinder sleeve-valve +radials Dimensions: Span 77ft Oin (23 47m); length 59ft 1 1 in (18 25m); +height 15ft 7in (4-75m) Weights: Empty (GT.VI) 22.600lb (10.260kg); maximum 36.500lb (16.570kg) Performance: Maximum speed 265mph (426km/h); initial climb 980ft (299m)/min; service ceiling 18.000ft (5490m); typical range 1.350 miles (2160km) Armament: None except in Mk 1/1 (Boulton Paul dorsal turret with four 303m Brownings and powered ventral turret with two 303in Brownings) and ST. I (manual dorsal installation with various guns). History: First flight 20 March 1940; (production aircraft) December 1941; final delivery December 1944. User: Soviet Union. UK (RAF). +Development: After Bristol had proposed the Type 155 bomber with a nosewheel landing gear (which at that time had not been used in Britain except experimentally) the Air Ministry issued Specification B. 18/38 which was notable for its insistence on minimal use of light alloys, which were likely to be in short supply in event of war. Instead the design was to be made mainly of steel and wood, even though this would increase weight. Bristol dropped the 1 55. and the specification was met by the AW.41 . first flown on 20 March 1940 Production was entirely subcontracted to firms outside the aircraft industry, and parts were brought to a plant at Gloucester for which Hawker Siddeley formed a company called A. W. Hawksley Ltd. Thus, not only did the Albemarle conserve strategic materials (with very small penalty, as it turned out) but it had no parent factory or design organization. Delivery began in October 1941. but only 32 were completed as bombers and these were converted as transports. Altogether 600 were delivered by the end of 1944. in many versions grouped into two main families: ST. or Special Transport, used all over Europe and North Africa: and GT. Glider Tug. used in Sicily. Normandy and at Arnhem Glider towing needed high power at low airspeeds, and the Hercules overheated and poured oil smoke, but the Albemarle was otherwise pleasant to f +Above: An Albemarle, probably an ST. II. on takeoff with Horsa I at the Heavy Glider Conversion Unit, Brize Norton. +Above: The original Albemarle I Series I before conversion. +Avro 652M Anson +652A Anson I and later marks to +T.22, USAAF AT-20 +Origin: A V Roe Ltd. Chadderton. Bracebridge Heath. Newton Heath and Yeadon; in Canada by Federal Aircraft Type: Originally reconnaissance bomber, later crew trainer and multirole Engines: (I. X) two 355hp Armstrong Siddeley IX seven-cylinder radial; (II. Ill) 330hp Jacobs L-6MB (R-915) of same layout; (IV) 450hp Wright R-975-E3 Whirlwind: (V. VI) 450hp Pratt & Whitney R-985-AN14B Wasp Junior; (XI. XII) 420hp Cheetah XIX or XV Dimensions: Span 56ft 6in (17 22m): length (nearly all) 42ft 3in (12 88 m); height 1 3ft 1 in (3 99m). Weights: Empty, equipped (I) 5.375lb (2438kg). (V) 6.693lb (3036kg). (XII) 6.5101b (2953kg); maximum (I) 8.0001b (3629kg). (V) 9.4601b (4291kg). (XII) 9.900lb (4491kg). Performance (no turret): Maximum speed (I) 188mph (303km/h). (V) 190mph (306km/h). (XII) 175mph (282km/h); typical cruise 1 50mph (241km/h); typical range 700 miles (1127km) Armament: See text +History: First flight 24 March 1935: service delivery 6 March 1936: final delivery May 1952 +Below: Though the vast majority of Ansons were trainers, +utility transports and hacks, this original Mk I is seen in +1942 still with 217 Sqn Coastal Command after six years. +1 T\ \ +Users (WW2): Australia. Canada. Egypt. France. Greece. Netherlands. UK (RAF. RN. ATA. BOAC). US (AAF). +Iran, Ireland. +Development: The abiding memory of "Faithful Annie" is of the most docile and reliable machine in the whole war Yet when it was first delivered to 48 Sqn RAF Coastal Command it was very much a "hot ship" It was a monoplane, and it had retractable landing gear (laboriously cranked up and down by hand), and despite a large dorsal turret it was almost the fastest thing in the service One attacked a U-boat only two days after the start of the war. and in June 1 940 a close vie of three survived attacks by nine Bf 109Es. shooting down at least two of the German fighters despite having only a single drum-fed Lewis in each turret Later many Mk I trainers +had twin belt-fed Brownings in a Bristol turret, and virtually all Mk Is carried at leas; provision for bombing training Altogether 6.704 Mk I were built, and thousands were used for general communications or converted into Mk X transports with smooth engine cowls and strong freight floors DH Canada fitted some with American engines to produce the III and IV Federal built 2.882 Ansons from 1941. most being Mk II (USAAF AT-20) but later batches being the V and VI with fuselages of Vidal moulded ply instead of steel tube and fabric. The XI and XII at last introduced hydraulic landing gear (on the Canadian machines from the start) and a much roomier fuselage, as well as constant-speed propellers and many other changes. These evolved into the modern stressed-skin C 19 and T.20. 21 and 22 for the post-war RAF. Total production was 1 1 .020 +Above: Anson X with astro-dome (often absent). + + + Avro679 Manchester +679 Manchester I and IA +Origin: v Type Hea Engines: I no Rolls -R. +but ii +Dimensions: Sp [m) Weights: I mpty 31.2001b (14 ied above 50.000lb (22.I Performance: M i> mum speed (i ig (42.000lb) 19.500ft (5852m 1.200 miles (1930km) Armament: Eighl 303in Browning in power tui iose (2) upper (2) and tail (4) internal fuselage bay accommodating bomb load up to 10.3501b (4695kg) History: First flight 25 July 1939; service delivery November 1940. withdrawal from production November 1941 User: UK (RAF) +Development: Rolls-Royce's decision in 1935 to produce a very powerful engine by fitting two sets of Peregrine cylinder-blocks to one crankcase (the lower pair being inverted, to give an X arrangement) prompted the Air Ministry to issue specification P. 13/36 for a twin-engined heavy bomber of unprecedented capability Handley Page changed to four Merlins (see Halifax) but Avro produced the Manchester with the Vulture engine. In most respects it was the best of all the new heavy bombers, but the engine was grossly down on power, and had to be derated further because of extreme unreliability. Originally the Manchester had two fins: in the production Mk I a fixed central fin was added, and the bulk of the 209 delivered had two larger fins (no central fin) and were designated IA So hopeless was the engine situation that the plans to build Manchesters at Armstrong Whitworth and Fairey were cancelled, and MetropolitanVickers stopped at No 32 Avro went on until the vastly superior Lancaster could take over, the first batches of Lancasters having Manchester fuselages with a row of small windows along each side +Above: L7516. "S-Sugar" of 207 Sqn. the first unit to receive +the Manchester in November 1940 This aircraft was a Mk IA +Below: Mk IA with two enlarged fins on increased-span tailplane +Avro 683 Lancaster +683 Lancaster I to MR. 7 (data for I) +Origin: A V Roe Ltd: also Armstrong Whitworth. Austin Motors. Metropolitan -Vickers and Vickers-Armstrongs. UK. and Victory Aircraft. Canada Type: Seven-seat heavy bomber Engines: Four 1 ,460hp Rolls-Royce or Packard Merlin 20 or 22 (Mk II only: four 1,650hp Bristol Hercules VI. 14 cylinder two-row. sleeve-valve radials) Dimensions: Span 102ft Oin (31 1m): length 69ft 4in (21 1m). height 19ft 7in (5 97m) Weights: Empty 36.900lb (16.705kg); loaded 68.000lb (30.800kg). overload with 22.000lb bomb 70.000lb (31.750kg) +Performance: Maximum speed 287mph (462km/h) at 11.500ft (3500m). cruising speed 210mph (338km/h): climb at. maximum weight to 20.000ft (6095m) 41 minutes; service ceiling 24.500ft (7467m): range with 14.0001b (6350kg) bombs 1.660 miles (2675km) Armament: Nose and dorsal turrets (Mk II also ventral) with two 303in Brownings (some, including Mk VII. had Martin dorsal turret with two 5in). tail turret with four 303 in Brownings. 33ft Oin (10 06m) bomb bay carrying normal load of 14.0001b (6350kg) or 22.0001b (9979kg) bomb with modification History: First flight 9 January 1941; service delivery (for test and training) September 1 941 ; last delivery from new 2 February 1 946. continued on page 80 +Below: An inspiring sight to anyone who remembers those great +days — the final assembly line at A. V. Roe's Woodford plant in +1943 (Mk Is with serials in the batch JA672-JB748). + + + Users: Australia. Canada. New Zealand. Poland. UK (RAF. BOAC) +Development: Undoubtedly one of the major influences on World War II. and one of the greatest aircraft of history, the "Lane" came about because of the failure of its predecessor In September 1936 the Air Staff issued specification P 1 3/36 for a twin-engined bomber of exceptional size and capability to be powered by two of the very powerful engines then under development: the Rolls-Royce Vulture 24-cylinder X engine was preferred. Handley +Page switched to four Merlins with the Halifax, but A V. Roe adhered to the big-twin formula and the first Type 679 Manchester flew on 25 July 1939 Altogether 209 Manchesters were delivered by November 1941, but the type was plagued by the poor performance and unreliability of its engine. +Though it equipped eight Bomber Command squadrons, and parts of two others plus a flight in Coastal Command, the Manchester was withdrawn from service in June 1942 and survivors were scrapped. Nevertheless the basic Manchester was clearly outstandingly good, and in 1940 the decision was taken to build a longer-span version with four Merlin engines. The first Lancaster (BT 308) flew as the Manchester III at the beginning of 1941. So outstanding was its performance that it went into immediate large-scale production, and Manchesters already on the line from L7527 onwards were completed as Lancasters (distinguished from later aircraft by their row of rectangular windows in the rear fuselage) Deliveries began in early 1942 to 44 Sqn at Waddington. and on 17 April 1942 a mixed force of 44 and 97 Sqns made a rather foolhardy daylight raid +against the MAN plant at Augsburg, whereupon the new bomber's existence +was revealed. continued on page 82 +Above: Late-war Lanes letting go thousand-pounders over a +cloud-covered target in daylight, common from spring 1944. +Below: Cutaway drawing of a Lancaster III, similar to a Mk I +except for Packard nameplates and US accessories on the engines. Usual night load was a 4,000-pounder plus incendiaries. +Avro Lancaster III +cutaway drawing key: +1 Two 303in Browning machine guns 2 Frazer- Nash power-operated nose turret 3 Nose blister 4 Bomb-aimer's (optically flat) panel 5 Bomb-aimer's control panel 6 Side windows +7 External air temperature thermometer 8 Pitot head 9 Bomb-aimer's chest support 10 Fire extinguisher 11 Parachute emergency exit 12 F 24 camera 13 Glycol tank and step 14 Ventilator fairing 15 Bomb-door forward actuating jacks 16 Bomb-bay forward bulkhead 17 Control linkage 18 Rudder pedals 19 Instrument panel 20 Windscreen de-icer sprays 21 Windscreen 22 Dimmer switches 23 Flight-engineer's folding seat 24 Flight-engineer's control panel 25 Pilot's seat 26 Flight-deck floor level 27 Elevator and rudder control rods (underfloor) 28 Trim-tab control cables 29 Main floor/bomb- bay support longeron 30 Fire extinguisher 31 Communications radio and (if fitted) electronic jammers 32 Navigator's seat 33 Canopy vision blister 34 Pilot's head armour 35 Emergency escape hatch 36 D/F loop 37 Aerial mast support 38 Electrical services panel 39 Navigator's window 40 Navigator s desk 41 Aircraft and radio compass receiver 42 Wireless-operator's desk 43 Wireless-operator's seat 44 Wireless-operator's window 45 Front spar carry-through/ fuselage frame 46 Astrodome 47 Inboard section wing ribs 48 Spar join 49 Aerial mast 50 Starboard inner engine nacelle 51 Spinner 52 Three-blade de Havilland constant-speed propellers 53 Oil-cooler intake 54 Oil-cooler radiator 55 Carburettor air intake 56 Radiator shutter 57 Engine bearer frame 58 Exhaust flame-damper shroud +80 +59 Packard-built Rolls-Royce Merlin 28 liquid-cooled engine 60 Nacelle/wing fairing 61 Fuel tank bearer ribs 62 Intermediate ribs 63 Leading-edge structure 64 Wing stringers 65 Wingtip skinning 66 Starboard navigation light 67 Starboard formation light 68 Aileron hinge fairings 69 Wing rear spar 70 Starboard aileron 71 Aileron balance tab + + + Above: Lancaster B.I R5868 S Sugar" of 467 Sqn. Waddmgton Mistakenly thought to be the top scoring "heavy", she was not scrapped (as was the true record holder. B III ED888. 140 plus trips with 103 and 576 Sqns at Elsham Wolds) and sheepishly +proclaims her No 2 status in the RAF Museum to this day Yellow-outlined code-letters, and the individual aircraft letter repeated on the fin. were extremely unusual; but at +east the aircraft in the museum is the genuine R5868 1 +72 Balance-tab conlrol rod 73 Aileron trim-tab 74 HF aerial 75 Split trailing-edge flap (outboard section) 76 Emergency (ditching) exit 77 Crash axe stowage 78 Fire extinguisher 79 Hydraulic reservoir 80 Signal/flare pistol stowage 81 Parachute stowage box/spar step 82 Rear spar carry-through 83 Bunk backrest 84 Rear spar fuselage frame 85 Emergency packs 86 Roof light +87 Dinghy manual release cable (dinghy stowage in starboard wing-root) Mid-gunner's parachute stowage Tail turret ammunition box 90 Ammunition feed track 91 Emergency (ditching) exit 92 Flame floats stowage 93 Sea markers stowage 94 Roof light 95 Dorsal turret fairing 96 Frazer- Nash power-operated dorsal turret +97 Two 303in Browning machine-guns 98 Turret mounting ring 99 Turret mechanism 100 Ammunition track cover plate 1 01 Turret step bracket 102 Header tank 103 Oxygen cylinder 104 Fire extinguisher +105 DR compass housing 106 Handrail 107 Crew entry door (starboard) 108 Parachute stowage +109 First-aid pack 110 Starboard tailplane 111 Rudder control lever 112 Starboard fin 113 Rudder balance weights 114 Starboard rudder 1 1 5 Rudder datum hinge 116 Rudder-tab actuating rod 117 Rudder tab 118 Starboard elevator 1 1 9 Elevator balance tab 120 Roof light 1 21 Tail main frame 1 22 Parachute stowage 123 Fire extinguisher 124 Tail-turret entry door 125 Frazer- Nash poweroperated tail turret 126 Four 303m Browning machine guns 127 Cartridge-case ejection chutes 128 Rear navigation light and Monica tail-warning radar 129 Elevator trim-tab 1 30 Fin construction 131 Rudder balance weights 132 Port rudder frame +149 Bomb-bay aft bulkhead 150 Bomb- bay doors 151 Bomb-door aft actuating jacks 1 52 Reserve ammunition boxes 153 Main floor support structure 1 54 Flap-operating hydraulic lack 155 Flap-operating tube 156 Flap toggle links 1 57 Flap-tube connecting imk 158 Rear spar 159 Split trailing-edge flap (inboard) 160 Split trailing-edge flap (outboard) 161 Aileron control lever 162 Aileron trim-tab control linkage 163 Aileron trim tab 164 Aileron balance-tab control rod 165 Aileron balance tab 1 66 Aileron hinge fairings 167 Port aileron 168 Port wingtip 1 69 Port formation light +1 70 Port navigation light 171 Retractable landing lights (port wing only) 1 72 Cartridge-operated cable cutters 1 73 Fuel vent pipe 1 74 Aileron control rod 175 Port outer (No 3) fuel tank (114 gal) 1 76 Outboard engine support frame/rear spar pick-up 1 77 Fuel booster pump 178 Fire extinguisher 179 Engine sub-frame 180 Filler cap 181 Outboard engine oil tank 182 Firewall/bulkhead 183 Carburettor air intake 184 Outboard engine support frame 185 Port mainwheel 1 86 Undercarriage oleo struts 187 Flame-damper shroud 188 Outboard engine support frame/main spar pick-up +189 Undercarriage retraction jacks 190 Oleo strut attachme r ' 191 Undercarriage suppon beam (light-alloy casting) 192 Centre-section outeundercarriage support 193 Location of po" mediate (No 2) fuel tank (383 gal) 194 Mainwheel well 1 95 Emergency retraction air valve 196 Retraction cylinder attachment 197 Port inner (No 1) fuel tank (580 gal) 198 Oxygen-bottle stowage 199 Rest bunk Main spar Hinged inboard leadingedge -eater installation Air intake 204 Inboard engine support frame Inboard engine o Carburettor intake a r guard Port inner nacelle 208 Flame-dampers 209 Detachable co. +210 Bomb shackles 211 Bomb-bay dc +212 8.000 1b bomb +200 201 +201 203 +205 206 +207 +11 + + + From then until the end of World War II Lancasters made 1 56.000 sorties in Europe and dropped 608.612 long tons of bombs. Total production, including 430 in Canada by Victory Aircraft, was 7.377. Of these 3.425 +were Mk I and 3.039 the Mk III with US Packard-built engines. A batch of 300 was built as Mk lis with the more powerful Bristol Hercules radial, +some with bulged bomb bays and a ventral turret The Mk I (Special) was +equipped to carry the 1 2.000lb (5443kg) light-case bomb and the 1 2.000lb and 22.000lb (9979kg) Earthquake bombs, the H 2 S radar blister under the +rear fuselage being removed. The Mk I (FE) was equipped for Far East operations with Tiger Force. The aircraft of 617 (Dambusters) Sqn were +equipped to spin and release the Wallis skipping drum bomb. The Mk VI had high-altitude Merlins and four-blade propellers and with turrets removed served 635 Sqn and 100 Grp as a countermeasure and radar spoof carrier. Other marks served as photo-reconnaissance and maritime reconnaissance and air/sea rescue aircraft, the last MR. 7 leaving RAF front-line service in February 1954. Lancasters took part in every major night attack on Germany. They soon showed their superiority by dropping 132 long tons of bombs for each aircraft lost, compared with 56 (later 86) for the Halifax and 41 for the Stirling. They carried a heavier load of bigger bombs than any other aircraft in the European theatre. The 1 2.000lb AP bomb was used to sink the Tirpitz. and the 22.000lb weapon finally shook down the stubborn viaduct at Bielefeld in March 1945. Around Caen. Lancasters were used en masse in the battlefield close-support role, and they finished the war dropping supplies to starving Europeans and ferrying home former prisoners of war. +I +Above: Incendiaries cascade from one of the highly secret Bis +of No 101 Sqn, from Ludford Magna, with Airborne Cigar electronic jamming equipment (note the two tall dorsal masts). +Left: Three-view of a typical Mk I or Mk III Lancaster. +Below: Colour photography was rare in Britain in World War II. This splendid picture was taken from beside the pilot of a Lane of 50 Sqn at Swinderby (Press visit, 28 August 1942). + + + Blackburn Skua and Roc +Skua II. Roc I +Origin +Type Engine: 905hp Bi Dimensions: S| +Weights npty (S) 5.4901b (2490kg) (R) I sib (3732kg). (R) 8.8001b | Performance: peed (S) 225mph (362km/h). (R) 196mph (315km/h). service ceiling 20.200ft (6157m). range (1 (1287km) Armament S) four 303m Browning fixed in wings, one 303in Lewis or Vickers K in rear cockpit. 500lb (227kg) bomb on hinged arms under fuselage, light bombs under wings. (R) four 303m Browning in power dorsal turret, light bombs under wings. +History +U-..M +Development +I +by 1941 tl +i6 built to O 30/3! withdrawn A fe\A +Above: Skua II showing four wing guns and upturned tips. +Right: Pre-war picture of a Skua making a practice bombing dive, with patented Zapp flaps fully depressed to limit speed. +Below: Though pleasant to fly, one wonders how the Roc, a 196mph fighter, could have been considered for combat duty. +[ +i +83 + + + Boulton Paul P. 82 Defiant +Defiant I and II (data for I) +Origin: Boulton Pau .Volverhampton. Type: Two-seat fighter. Engine: I. 1 .030hp Rolls-Royce Merlin III vee-12 liquid-cooled: II. 1.260hp Merlin 20. Dimensions: Span 39ft 4in (12m): length 35ft 4in (1075m); height +•1). +Weights 6.0001b (2722kg): loaded 8.3501b (3787kg). Performance: ' 'aximum speed 303mph (488km/h): initial climb 1.900ft (579m)/min; service ceiling 30.500ft (9300m); range, probably about 500 miles (805km). Armament: Hydraulically operated dorsal gun turret with four 0-303in Browning machine guns, each with 600 rounds. History: First flight (prototype) 11 August 1937; (production Mk I) 30 July 1939; first delivery December 1939. User: UK (RAF). +Development: 3. 1933 military staffs were intensely studying the enclosed gun turret, manually worked or power-driven, either to defend a bomber or to arm a fighter. A primitive form was seen on the Hawker Demon in 1 936. while in France the Multiplace de Combat class of aircraft were huge fighters with turrets alLover. The Defiant was a bold attempt to combine the performance of the new monoplanes with a powered enclosed turret carrying four 0-303in Brownings, each with 600 rounds. The gunner, behind the pilot, had a control column moved left/right for rotation, fc for depression and elevation and with a safety/firing button on top. The Defiant itself was a clean and pleasant aircraft, but rather degraded in performance by carrying a crew of two and the heavy turret. No 264 Sqn went into action on 12 May 1940 in desperate fights over the Low Countries. On the 1 3th six escorted Battle bombers, and only one returned, it seemed the +Right: Defiant II of 125 Sqn on night operations in 1941-42 but lacking radar. Note fold-down radio masts. +Below: Fighter Command's 264 Sqn was the first recipient of the Defiant, and this photograph was taken during the working-up period in early 1940. In fact the concept of the sluggish two-seat fighter was faulty, and production of 1,060 (continued until February 1943) was a disgraceful error. +Defiant was a failure against the Bf 109E. But seven days later remnants of 264 shot down "17 Messerschmitts without loss" and later on the same day destroyed eleven Ju 87s and 88s. Once the enemy were familiar with the Defiant it had had its day by daylight, but it did well in 1 940—41 as a night fighter and was later fitted with radar. Most of the 1 .064 built served as night fighters, target tugs and in air/sea rescue in Britain, the Middle East and Far East. Defiants carried the Mandrel jamming system to confuse German defences. +Above: Defiant I (II similar) with turret fairings raised + + + Bristol Type 156 Beaufighter +Beaufighter I to TF.X (data mainly Mk X) +Origin: Bri iti il *\en iplane i +i +i ilti m and Wi Dep irtmenl ol ^in raft Products isti ilia Type: rwo-seat torped fightei (othei marl night I |l +. +Engines: I wo I ' 'Ohp I Iri :ti il Hen ules XVII M radials [Mi II) I 250hp R R Merlin XX (i thai m irks) difl I I lei (one of! i had R R Griffons and Wrighl i iR !600 i i +i .1 +Dimensions: Span 5 'fl lOin 1 1 6 In ngth 41f1 B 2 6m) (II, 42ft 9in) height 15ft 1 Oin (4 8'l Weights: Empty 15.6001b (7100kg) (I, II. 13.8001b. VI. XI. 14.9001b); loaded 25.4001b (11.530kg) (most other marks 21.000li> 95 !5kg) Performance: Maximum speed 312mph (502km/h) (fightei marks 330mph, 528km h) initial (limb 1.850ft (564m) min service 26.500ft (8077m) (fighters. 30.000ft. 9144m) range 1 .540 mile I 1478km) Armament: Four 20mm Hispano cannon fixed in underside of Forward Fuselage (initially hand loaded with 60-round drums, later with belt feed), and one 303m Vickers K aimed by observer (fighters, also six 0-303in Brownings, two fixed in outer left wing and four in right. One 1.6051b (728kg) torpedo on centreline or 2.1271b (954kg) and wing racks for eight rocket projectiles or two 1 ,0001b (454kg) bombs. History: First flight (Type 1 56 prototype) 1 7 July 1 939; (production Mk I) May 1940; service delivery 27 July 1940. first flight (Mk 21, Australia) 26 May 1944; last delivery from new (UK) September 1945. (Australia) October 1945 Users: Australia. Canada. New Zealand. South Africa. UK (RAF). US (AAF). other countries post-war. +Development: During the critical years 1935-39 the most ql in the RAF's armoury was the lack of any long armed fighter and any fighter capable of effecti +Right: Seventh "Beau" +built, a Mk IF of 25 Sqn at North Weald (before radar fitted). +Below: Typical Mk VIF, without AI.VIII radar.(probably) in Tunisia in 1942-43 +(amilii +I +I +! +is to bi +latei A +ai lov peed hid did I continued on paau 86 +I + + + Early models barely exceeded 300mph with low-power Hercules and. in +the absence of Griffon engines. 450 were fitted with Merlins, but these were +less powerful and accentuated instability Speed was soon judged less im +portant when the need for night fighters to beat the Blitz became urgent. +Equipped with Al Mk IV radar the early deliveries to 25 and 29 Sqns were a +major reason for the Luftwaffe giving up the Blitz on Britain Eventually the +"Beau" served on all fronts, having thimble-nose Al Mk VII in 1942. tor +pedoes in 1943. rockets in 1944 and a spate of special installations in 1945 +A total of 5,564 were built in England and 364 in Australia, the last fighter and +torpedo versions serving with Coastal Command, the Far East Air Force and +the RAAF until 1960, To the Luftwaffe it was a feared opponent even 500 +miles out in the Atlantic, to the Japanese it was "Whispering death", so named because of the quietness of the sleeve-valve engines It was sheer luck the "Beau" could be produced in time. +' +Bristol Beaufighter I cutaway drawing key: +1 Starboard navigation light (forward) and formationkeeping light (rear) 2 Wing structure 3 Aileron adjustable tab 4 Starboard aileron +5 Four Browning 303in machineguns 6 Machine gun ports 7 Starboard outer fuel tank (87 gal/395 litres) 8 Split trailing-edge flaps. Iraulically actuated 9 Fixed trailing edge 10 Flapoperatingjack 11 Starboard nacelle tail I 12 Oil lank (1 7 gal/77 litres) +13 Starboard inner fuel ank (188gal/855 litres) 14 Cabin air duct 15 Hinged leading-edge for access 16 Engine bulkhead 17 Engine bearers 18 Auxiliary intake 19 Supercharger air intake 20 Cooling gills 21 Bristol Heroules III i nder sleeve-valve engine. 1 .650 hp 22 De Havilland Hydron propeller +23 Sp +24 Lockheed oleo-pneumatic shock-absorber 25 Starboard mainwheel. Dunlop brakes +26 Forward identification lamp ,e cap 27 Rudder pedals 28 Control column 29 Cannon ports 30 Seat adjusting 31 Pilot's seat 32 Instrument panel 33 Clear vision panel +34 Flat bullet-proof windscreen 35 Fixed canopy (sidewayshinged on later aircraft) 36 Spar carry-through step 37 Nose/centre section attachment 38 Fuselage/centre section attachment 39 Pilot's entry/emergency escape hatchway 40 Underfloor cannon blast tubes 41 Fuselage/centre section attachment 42 Centre section attachment longeron reinforcement 43 Cabin air duct 44 Cannon heating duct 45 Rear spar carry-through 46 Bulkhead cut-out (observer access to front hatch) 47 Bulkhead +48 Hydraulic header tank 49 Aerial mast +50 Monocoque fuselage construction 51 Starboard cannon (two +Hispano 20mm) 52 Floor level 53 Steps 54 Observer's swivel sea f mall , for ward 55 Radio controls and intercom 56 Observer's cupola 57 Hinged panel 58 Aerial 59 Oxygen bottles 60 Vertical control cable shaft 61 Sheet metal bulkhead 62 Control cables 63 Tailplane structure 64 Elevator 65 Elevator balance tab 66 Fin (extended forwards in dorsal fin on later aircraft) 67 Rudder balance 68 Rudder framework 69 Tail lights: formationkeeping (upper) and navigation (lower) +70 Rudder 71 Ruddertrimtab 72 Elevator trim tab 73 Elevator balance tab 74 Elevator structure +75 Port tailplane (12deg dihedral on later aircraft) 76 Rudder hinge (lower) 77 Tailwheel retraction mechanism 78 Retracting tailwheel 79 Tailwheel bay 80 Tail-unit lointnng 81 Control cables +Below: Tough defender of +Malta, this Mk IF has under +wing bomb racks. Red-doped fabric covers the muzzles of the guns. + + + Below Cutaway of the otiyuml Mk I Beaufiyhter as delivm *;d +to Fighter Command In July 1940 without radai and with drum +fed cannon (the first 50 aircraft did not have the six wing +machine guns installed when first delivered). 66 +58 +64 +r* +ri +", +'50 *> +'51 +1 +f/ +52 +54 +*£ +107 +'05 +118 +56 +89 +59 +57 +:.' +J~; 85 +86 +90 +9\ +.93 +^? +104 103 +Right: One of the first batch of TF.X (built at Weston), of 455 Sqn Later batches had a large dorsal fin += 60 i +82 +83 +94 +61 +80 +"95S +~^ +M +79 +Z +r +97 +78 +82 Pd jbes 83 F +85 L 86 E' ' +88 Port cannon breeches and +magazine drum 89 D +90 V. ooard flap 91 Flap operating +attac 1 93 Tw mac • 94 Wing above outboard flap 95 Rear spar ron control rod and • age +98 +;96c^c^ +*9® +99 +'31 +'02 '00 +98 +100 I +103 ' son +104 >. 105 ' 106 f107 ' 108 Er 109 • age +110 C +11 +1 +Super 112 Eng 113 Cowling nos^ +114*. I speed +116 Port mam wheel 7 Retractio118 Undercarriage door +H +NE237 +.. + + + Bristol Type 152 Beaufort +Beaufort I to VIII +Origin: Bristol Aeroplane Company; also made by Department of Aircraft Production. Fishermen's Bend. Australia. Type: Four-seat torpedo bomber. Engines: Two 1.130hp Bristol Taurus VI 14-cylinder sleeve-valve radials +(most other marks, two 1.200hp Pratt & Whitney Twin Wasp). Dimensions: Span 57ft 1 0in (17 63m): length 44ft 2in (1346m); height 14ft 3in (434m). Weights: Empty 13.1071b (5945kg); loaded 21.2301b (9629kg). Performance: Maximum speed 260mph (418km/h) clean. 225mph (362km/h) with torpedo; service ceiling 16.500ft (5030m); range 1.600 miles (2575km). Armament: Various, but typically two 303in Vickers K in dorsal turret and one fixed forward-firing in left wing, plus one 303in Browning in remotecontrol chin blister. Alternatively four 0303in Brownings in wing, two Brownings manually aimed from beam windows and (Mk II) twin Brownings +in dorsal turret (final 140 Australian Mk VIII. two 50in Brownings in dorsal turret). One 18in torpedo semi-external to left of centreline or bomb load of 2.000lb (907kg). +Above: Three-view of Beaufort I Series II with trailing edge extensions and rearward-firing barbette under the nose. +Below: Australian-built Beaufort VIM with Twin Wasp engines and increased-area fin. All served in the southwest Pacific. +Right: Beauforts in torpedo practice with 217 Sqn, Coastal Command (in 1940, before the grey/white colour scheme was introduced). +Below: A Beaufort II, with Twin Wasp engines, snug in one of the blast pens built at Luqa from Malta's bombed buildings. The unit is probably 86 Sqn, which replaced 217 in Malta when the original squadron flew to Burma. +History: First flight 15 October 1938; first delivery October 1939; first flight of Australian aircraft (Mk V) August 1941; last delivery (Australia) August 1944 Users: Australia. Turkey. UK +Development: Derived from the Blenheim, the torpedo-carrying Beaufort was inevitably heavier because the Air Staff demanded a crew of four Performance on Mercury engines was inadequate and. after studying an installation of the sleeve-valve Perseus, the choice fell on the Taurus, an extremely neat two-row engine only 46in in diameter. A clever installation was schemed for this but it overheated and various engine troubles held the programme back in the early days, but 22 and 42 Sqns of Coastal Command were fully operational by August 1 940 As well as laying hundreds of mines they bombed the battlecruiser Scharnhorst. torpedoed the Gneisenau and sank numerous smaller ships. In 1939 plans were laid for Beaufort production in Australia and. because of the difficulty of supplying engines from Britain, the Australian Mks V-VIII had Twin Wasp engines, most of them made in Australia. A large batch of British Beauforts (Mk II) had this engine, but a Merlin-Beaufort was abandoned and from No 165 the Mk II reverted to later models of Taurus The total built was 2.080. including 700 built in Australia for duty in the Southwest Pacific Australian models had a bigger fin and progressed through four series with different equipment, ending with transport and trainer versions. The finest RAAF missions were against Japanese fleets at Normanby Island, in the Timor Sea and around New Guinea and the Solomons +Below: One of the first Mk I Beauforts to be delivered to 42 Sqn in early 1940. It has an early dorsal turret and under-nose gun but lacks the trailing edge extension-plates. +88 + + + JtMLO + + + Bristol Type 142 Blenheim +Types 142 M, 149 and 160 Blenheim/Bisley/ +Bolingbroke (data for Blenheim IVL) +Origin: Bristol Aeroplane Company: also made by A. V. Roe. Rootes Securities and Canadian Vickers Ltd. Type: Three-seat light bomber (IF. IVF. fighter versions). Engines: Two 920hp Bristol Mercury XV (I. Bolingbroke I. II. 840hp Mercury VIM; Bolingbroke IV series. 750—920hp Twin Wasp Junior. Cyclone or Mercury XX: Blenheim V. 950hp Mercury XXX). Dimensions: Span 56ft 4in (17T7m) (V. 56ft 1 in); length 42ft 9in (13m) (I. 39ft 9in; Bolingbroke III. 46ft 3in: V. 43ft 1 1 in); height 12ft 10in (3 91m) (Bolingbroke III. 18ft). Weights: Empty 9.790lb (4441 kg) (I. Bolingbroke III. 8.700lb: V. 1 1 .OOOIb); loaded 1 4.400lb (6531 kg) (1. 1 2.250lb; Bolingbrokes 1 3.400lb; V. 1 7.000lb) Performance: Maximum speed 266mph (428km/h). (I) 285mph; (early IV) 295mph; (Bolingbrokes and V) 245-260mph; initial climb 1.500ft (457m)/min (others similar); service ceiling 31.500ft (9600m) (others similar except Bolingbroke III. 26.000ft); range 1.950 miles (3138km); (I) 1.125 miles; (Bolingbrokes) 1 .800 miles; (V) 1 .600 miles. Armament: One 303in Vickers K in nose, two 303in Brownings in FN. 54 chin turret and two 303in Brownings in dorsal turret; (I) single fixed Browning and single Vickers K in dorsal turret; (IF. IVF) four fixed Brownings under fuselage: bomb load 1.0001b (454kg) internal (nonstandard aircraft had underwing 5001b racks). History: First flight (Type 142) 12 April 1935; (142M Blenheim I) 25 June 1936; service delivery November 1936: termination of production (VD) June 1943; withdrawal from service (Finland) 1956 Users: Canada. Finland. France. Greece. Jugoslavia. Lithuania. Portugal. Romania. Turkey. UK (RAF). +Development: It was the newspaper magnate Lord Rothermere who asked the Bristol company to build him a fast executive aircraft to carry a +Above: Almost certainly taken at Northolt shortly after the +start of World War II, this line-up of 604 (County of Middlesex) +Sqn shows the Mk IF fighter. Soon this acquired the world's first airborne radar and operated mainly by night. +Below: A standard Blenheim I bomber of 60 Sqn. at Lahore, India. By 1940, the year relevant to this colour scheme, many Blenheims were being shipped out of England or withdrawn from operations. +Below: A trio of Blenheim IV bombers of 1 39 Sqn. On 3 September 1939 one of these was the first Allied +aircraft to cross +the German +frontier in World War II. Before long, however, the Blenheim was found to be extremely vulnerable to modern fighters. +I +rffl + + + 1 +'mph iih +I +luantitie to a built, many of whicl I wei Al Mk I +1 +in ii . pei il ii fightei radar in thi intense fi ireign mteiest and ma lugoslavia tiiuania. Romania and Gre<>> ead o1 'in piiii Hie nose was then lengthens type was named Bolingbroke. a name retained for al! the vai i i i the Bolingbroke Mk III being a 1 revised asymmetric nose was adopted for prod the speedy Mk IV, which later acquired a fighter gun pack (IVF) or a manu.il i chin gun (IVL). finally having a two-gun chin turret. Made by Bristol. Avro and Rootes. like the Mk I. the IV was the main combat version with the RAF. 3,297 being delivered and making many daylight missions in many theatres. The heavily armed and armoured two-seat Bisley attack aircraft did not go into production, but the three-seat equivalent did, as the Blenheim Mk V Heavy and underpowered, the 902 VDs served in North Africa and the Far East. +\ +,1 +Above: Mk IV as originally delivered without under-nose gun. +Below: The "long-nosed" Blenheim IV, seen here in 1941, provided a proper station in the nose for the navigator/bomb +aimer. It carried more fuel than the Mk I, and needed more power, ship off Bordeaux. +Above: In the first two years of World War II British and other Allied aircraft were less effective against ships than such Luftwaffe aircraft as the Ju 87 and Ju 88. This Blenheim IV of 107 Sqn was photographed in June 1940 over a burning British + + + De Havilland 82A Tiger Moth +D.H.82 and 82A Tiger Moth I and II. PT-24 +Origin : The de Havilland Aircraft Co. Hatfield: most UK production by Morris +Motors. Cowley, and overseas production by DH Australia. DH Canada and DH New Zealand, with 200 assembled in Bombay. Type: Primary trainer. +Engine: (I) 1 20hp DH Gipsy III inverted four-in-line. (II) 1 30hp Gipsy +Major I. Dimensions: Span 29ft 4in (8 94m); length (landplane) 23ft 1 1 in (7 29m). height (landplane) 8ft 9iin (2 68m). +Weights: Empty 1 .100-1 ,200lb (525kg); maximum (most) 1.8251b +(828kg). Performance (landplane); Maximum speed 109mph (175km/h); service ceiling 13.600ft (4150m); range 300 miles (482km) History: First flight 26 October 1931; final delivery March 1945 +Users: (Wartime) Australia. Canada. Egypt. Iran. Iraq. New Zealand. Portugal. +S Africa. S Rhodesia. UK (RAF. RN). Uruguay. USA (USAAF). +Development: The original Moth of 1925 was developed into the Gipsy Moth and Genet Moth, both used as standard RAF elementary trainer and liaison aircraft, and then into the Tiger Moth with airframe of a different shape ideally suited for military training with seat-type parachute. Fully aerobatic. the Tiger was used for all ab initio pilot training and in a few cases (eg. m Iraq) carried armament. Total production amounted to 1 .61 1 pre-war. 795 wartime at Hatfield. 3.210 by Morris. 1.520 in Canada. 1.085 in Australia and 344 in New Zealand. A few had floats, and many Canadian Tigers had heated enclosed cockpits and skis (USAAF designation PT-24). +Nearly all Tigers were of the more powerful Mk II type, and in 1940 antispin strakes were added ahead of the tailplane roots. For a few weeks in 1 940 +@ +Above: Tiger Moth II (early series) with fuselage bomb rack. +a considerable number were flown by EFTS instructors on armed coastal patrol around Britain. Tigers continued in service in many air forces into the 1950s. +DE HAVILLAND QUEEN BEE (DH.82B) +First flown in 1935. this radio-controlled target was derived from the Tiger Moth by fitting a new all-wood fuselage with only the front cockpit A few were seaplanes, and by 1944 Hatfield had built 320 and Scottish Aviation 60 for the RAF and Fleet Air Arm for use as targets for AA gunnery and in research programmes +Left: This Tiger Moth II is typical of the early wartime aircraft, without extended tailplane-root strakes. In 1940 there was fear of German gas attack, and British service aircraft had a square or triangle of special paint, usually ahead of the fin (but sometimes on the fin itself) which changed colour in presence of gas. +Below: This later Mk II, with tailplane-root strakes, is +being used for practice bombing in the post-1942 era — in the author's experience, most unusual. EM836, built by Morris Motors at Cowley, is fitted with a blind-flying hood over the rear cockpit and has a training-yellow side stripe. +92 + + + De Havilland 98 Mosquito +D H 98 Mosquito I to 43 +Origin +Type Engines 1.63! XVI) /10hp Mi ihp Merlin 25. (Mnits had corresponding Merlins mad' Dimensions: Span (except Mk XV) 54 ft ; ion) 40fi 6m (1234m). (boi fighters .ind Mks 34-38) typically 41ft 9in. (Mk 3 l » on) 1 5ft 3-,in (4 66m) Weights: Empty (Mks ll-VI) about 14.1001b. (Mks VIII-30) 15.2001b: (beyond Mk 30) about 1 5.900-1 6.8001b. ma> (Mks II and III) around 17.5001b: (Mks IV and VI) about 22.5001b. (later fighters) about 20.5001b (but HF XV only 1 7.3951b). (Mks IX. XVI narks beyond 30) typically 25.0001b (1 1 .340^ Performance: Maximum speed, from 300mph ( 370mph (595km/h) for early night fighters. 380mph (612kr II. IV and VI. 410mph (660km/h) for IX. XVI and 30. and 425mph for 34 and 35. service ceiling, from 30.000ft (9144m) for low-rated naval versions to 34.500ft (10.520m) for most marks, to around 40.000ft (12.190m) for high-blown versions, with Mk XV reaching 44.000ft (13.410m): combat range, typically 1.860 miles (2990km). with naval TFs down at 1.260 miles and PR. 34 up to 3.500 miles +Armament: See text History: See text Users: Australia. Belgium. Canada. China, Czechoslovakia. France. Jugoslavia. New Zealand. Norway. Soviet Union. Turkey. UK (RAF. RN. BOAC). US (AAF). continued on page 95 +Right: An FB.VI. the most numerous single mark, attacking a ship in 1944. Cannon were used to help sight the eight rockets, which appear to have hit ideally below the waterline. +Below: A B.IV of 139 Sqn (the second user) at Marham, 1942. +DZ4B4 +Below: Almost certainly taken at Swanton Morley in early 1942, this scene shows +quartets of 500-pounders then all the "Mossie" could +carry — going aboard a 105 +Sqn B.IV. +41 + + + De Havilland Mosquito B. Mk +cutaway drawing key 48 +49 1 Starboard navigation light 50 +2 Detachable w- 51 3 Starboard formation light 4 Resin lamp 52 +5 Wing structure 53 +6 Starboard aileron 54 7 Aileron trim tab 55 B Aileron control linkage 56 9 Flap outer section 10 Flap jack inspection/access 57 panel 58 +-ooard outer fuel tanks. 59 +24 Imp gals (1091) outboard/34 Imp gals 60 (155 1) inboard 61 1 2 Starboard inner fuel tanks 62 +65i Imp gals (2981) 63 +outboard/78 Imp gals 64 (355 1) inboard 65 +13 Nacelle fairing 66 +1 4 Oil and coolant radiators 67 +(gun heating inboard) 68 +15 Exhaust flame damping 69 +shroud 70 +16 Starboard nacelle 71 +17 Coolant pipe fairing 72 1 8 Propeller constant speed unit 73 19 Propeller hub 74 20 Spinner 75 +21 Three-blade de Havilland ". hydromatic propeller 77 22 Navigation headlamp 78 23 Air thermometer 79 24 Bomb-aimer's windscreen 80 g jet 81 +25 Bomb-aimer's healed 82 (optically fat) window 83 26 Bombsight 84 27 Starboard mair . 85 +28 Bomb selector switch panel 86 29 Bomb-ai- - :ablet 87 30 Elbow rest 31 Nose compartment side 88 wine 32 Fireman's axe 89 33 Camera leads St 90 34 Oxygen bayonet socket 91 35 Bomb-aimer's kneeling 92 cushion 36 Fire-extinguisher (hand- 93 held) 94 37 Very cartridge stowage 95 (twelve) 96 38 Parachute stowage -ment panel 97 40 D'S' 41 Windscreen de-icif- 98 42 Folding navigation table (starboard wall) 99 43 Windscreen panels 100 44 Control c : - ever 101 45 Throttle quadrant 46 Compass +94 +IV 47 Elevator and aileron control linkage Rudder pedal assembly Elevator trim handwheel Wingroot radiator intake Oil and coolant radiators (cabin heating inboard) Intercomm equipment bay Pilot's seat harness Aft-vision canopy blister Pilot's armoured headrest Crast- e erge exit section Signal pistol discharge port T +1 1 54 transmitter Forward spar wing attachment Bulkhea: +HT power unit Dinghy stowage Hydraulic reservoir ~ast Bulkhead No 3 g fluid reservoir +T R9F transmitter/receiver +Bulkhead No 4 Fuselage longerons Flare chute Bulkhead No 5 Fuselage sandwich skinning +Spiral graining Rudder control linkage J No 6 Fin attachment strt dure Starboard tailplane Elevator balance Starboard elevator Aerial attachment Pitot head R jdder balance Rudder upper hinge Rudder structure Rudder trim tab Rudder trim tab control linkage Elevator internal mass balance Tail cone Rear navigation light Elevator trim tab Elevator trim tab control linkage - . ator Tailplane structure tor linkage Tailplane spar support frame eel retraction mechanism "immy (chined) tailwheel -el leg j No 7 Rudder internal mass bale 102 Control cables +Top of page: Mosquito II night fighter of 23 Sqn, based at Luqa, Malta, in 1942. No. 23 was a pioneer NF squadron. +103 Ventral j amps (green/amber) 104 Fuselage lower longeron 1 05 Aft camera mounting boxes 106 F24car-e = 107 Camera heating cable stowage 108 Aft entry: access door I 09 Oxygen bottles (port and starboard) 110 Bomb winch 1 Rear spar attachment 112 Centre-section fuel tanks (two). 68 Imp gals +(309 I) each 113 Double wing uppe +: +(interleaved stringers) I I 4 Forward spar 115 Coolant header tank 1 1 6 Spinner + + + Development l"hi de Havilli +I +rhe first | +1 2 in January 1940 to 30 ii 25 November 19'!i +PR I Unarmed photo reconnaissance, witl of prototype to 54ft 2in but still will +F II +windscreen, extended nacelles (as in all sul th flaps divided into inner and outer segments) and an ^Omm Hispano cannon with 300 rounds each under the floor and four 303m Brownings with 2,000 rounds each in the nose First flew 15 May 1941; subsequently fitted with Al Mk IV or V radar or 1 iht T.lll Dual-control trainer, first flown January 1942 but produced n after the war (last delivery 1949) B IV Unarmed bomber, carrying four 500lb (227kg) bombs internally. first delivered to 105 Sqn at Swanton Morley November 1941. making first operational sortie (Cologne, the morning after the first 1.000-bomber night attack) on 31 May 1942 Some later fitted with bulged bomb bays for 4.000lb (1814kg) bomb. FB VI Fighter-bomber and intruder, by day or night: same guns as F.ll but two 250lb (1 13kg) bombs in rear bay and two more (later two 5001b) on wing racks; alternatively. 50 or 100 gal drop tanks, mines, depth charges or eight 601b rockets Some fitted with Al radar. Total production 2.584. more than any other mark. B VII Canadian-built Mk IV. used in North America only. PR VIII Reconnaissance conversion of B.IV with high-blown Merlin 61 Mk IX Important advance in bomber (BIX) and reconnaissance (PR. IX) versions; high-blown two-stage engines, bulged bomb bay for 4.000lb bomb or extra fuel, much increased weight, paddle-blade propellers and new avionics (Rebecca. Boozer. Oboe or H 2 S Mk VI). +NF.XII Conversion of F.ll fitted with new thimble nose containing Al Mk VIM centimetric radar in place of Brownings. NF.Xlll Similar to Mk XII but built as new. with thimble or bull nose and same wing as Mk VI for drop tanks or other stores: flew August 1943 +Facing page, lower: One of the first batch of Mk IV bomber +Mosquitoes. Though slower than prototypes of later fighters, they were the fastest aircraft in service in 1941. +Mk r +Nl XVII r. +Nf- XIX Ml +B XX Cai till B IV +all built NF 30 Ni' - i with tv +PR 32 Extended-si 113/114 Mk 33 First Royal Navy Sea M< oleo main legs (in place of rubber ii driving four-blade propellers, arrester hook, four 20mm < various bomb/rocket loads). American ASH radar ai PR. 34 Strategic reconnaissance version, with 113/114 e bulged belly for 1.269 gal fuel (200gal drop tanks) and pres'. B 35 Equivalent bomber version, with PR and target-tug offshoi NF 36 Postwar fighter, with 113/114 engines and Al Mk X TF.37 Naval torpedo-fighter, basically Mk 33 with AI/ASV Mk XIII NF 38 Final fighter, mainly exported. Al Mk IX. forward cockpit TT 39 Complete rebuild by General Aircraft as specialised target tug FB 40 Australian-built Mk VI. with PR. 40 as conversions PR 41 Australian-built derivative of PR. IX and Mk 40 T.43 Australian trainer; all Australian production had Packard engines. +Left: Cutaway drawing of a +typical Mk IV, the original bomber version that entered squadron service in November 1941, within a year of first flight. +Subsequently the bomb load was doubled. +Above: Three-view of Mosquito IV bomber. +149 117 Rolls-Royce Merlin XXI liquid-cooled 1 2-cylinder Vee engine 118 Exhaust (fishtail) stubs 119 Spark plug-cooling intake 120 Engine bearer assembly 121 Coolant pipes 122 Carburettor air intake +(snow/debris guard mesh) 123 Fuel pump cooling intake 124 Flame-resistant insert panel 125 Engine accessories +126 Engine controls/coolant pipes 127 Fuselage bomb-bay racks +128 Aft bulkhead bomb door jacks 129 Flap jack and crank 130 Undercarriage strut/rear spar attachment +U0 +131 +132 133 134 +Port outer fuel tanks. 24 Imp gals (109 I) outboard/34 Imp gals (155 I) inboard Port wing flaps Nacelle aft fairing Aileron trim tab +135 Port aileron 1 36 Aileron control linkage 137 Resin lamp 138 Port formation light 1 39 Port (detachable) wingtip 140 Port navigation light 141 Wing outboard stiffeners 142 Wing ribs 143 Landing lamp (underwmg port and starboard) Undercarriage struts Cross-bracing Undercarriage retraction jack Oil tank 148 Radius rod cross-member 149 Undercarriage doors 1 50 Mudguard +144 145 146 +151 Wheel guards 152 Undercarriage oleo leg fairing 153 Shock pads 1 54 Port mainwheel tyre 155 Axle +156 Optional weapon loads inc +157 Small bomb containers two 450 lb (204 kg) (illustrated) or four 390 lb (177 kg) +158 Four 250 lb (114 kg) GP bombs 159 Four 500 lb (227 kg) +short-tailed GP or MC bombs, or +1 60 Two 500 lb ( 227 kg) GP +bombs + + + FaireyAlbacore +Albacore +I +Origin: Fairey Aviation Co. Hayes and Hamble. Type: Carrier torpedo bomber Engine: 1 ,065hp Bristol Taurus II 14-cylinder sleeve-valve radial or 1 ,130hp +Taurus XII. Dimensions: Span 50ft Oin (15 24m): length 39ft 9iin (12 13m); height +15ft 3in (4 65m). Weights: Empty 7.250lb (3289kg); maximum 10.6001b (4808kg). Performance: Maximum speed 1 61 mph (259km/h); service ceiling 20.700ft (6309m); range 930 miles (1497km). Armament: Two 303in Vickers K manually aimed from rear cockpit. sometimes 0-303in Browning in lower right wing; 1.6101b (730kg) torpedo or up to 2.0001b (907kg) bombs. History: First flight 12 December 1938: service delivery December 1939; combat service March 1940; final delivery May 1943 User: Canada (RCAF). UK (RN). +Development: Planned as a successor to the Swordfish. the Albacore was designed to specification S. 41/36. Though still a biplane, with wings braced with wire and covered with fabric, it had an all-metal monocoque fuselage and heated enclosed cabin. Pilot view was superb, and the 'Applecore" was in fact very pleasant to fly. Fairey built 803. and though this was only a quarter of the number of Swordfish built (which stayed in production at Blackburn to the end of the war) the Albacore saw intense +Above: Albacore I with multiple underwing stores racks. +Right: BF759, an Albacore I (the only mark, though there were many detail differences). It is apparently carrying mines on the wing racks, and the flaps are down. +action from the Arctic to Malaya. The first major torpedo attack was at Cape Matapan in March 1941; by 1942 there were 15 FAA squadrons, several of them shore-based in North Africa. Missions included target marking with flares, close support of troops with bombs, minelaying of European harbours and sinking flak-bristling E-boats from mast height But it never became famous +Fairey Barracuda +Type 100 Barracuda I, II, III and V +Origin: The Fairey Aviation Company; also built by Blackburn Aircraft. Boulton Paul Aircraft and Westland Aircraft Type: Three-seat (Mk V. two-seat) naval torpedo/dive bomber. Engine: (I) one 1 ,260hp Rolls-Royce Merlin 30 vee-12 liquid-cooled; (II and III) one 1 ,640hp Merlin 32; (V) one 2.020hp R-R Griffon 37 Dimensions: Span (l-lll) 49ft 2in (15m): (V) 53ft Oin (16 15m); length (l-lll) 39ft 9in (12 12m); (V) 41ft 1 in (125m); height (l-lll) 15ft 1 in (4-6m). (V) 13ft 2in (4m) Weights: Empty (I) 8.700lb (3946kg); (II. Ill) 9.407lb (4267kg); (V) 9.800lb (4445kg); loaded (I) 13.5001b (6125kg); (II, III) 14.1001b (6395kg); (V) 16.4001b (7450kg). Performance: Maximum speed (I) 235mph; (II) 228mph (367km/h); (III) 239mph; (V) 264mph (422km/h); initial climb (l-lll) 950ft (290m)/ min; (V) 2.000ft (610m)/min: service ceiling (I) 18.400ft; (II) 16.600ft (5060m): (III) 20.000ft (6096m); (V) 24.000ft: range with full weapon load. (I. II) 524 miles (845km). (Ill) 686 miles (1104km); (V) 600 miles. Armament: (l-lll) two 303in Vickers K manually aimed in rear cockpit: (V) one fixed 50in Browning in wing, no rear guns; one 18in torpedo (1.610 or 1.6201b) or bomb load up to 2.0001b (907kg) under fuselage and wings (including mines or depth charges). History: First flight 7 December 1940; production Mk I. 18 May 1942; service delivery. 10 January 1943; first Mk V (converted II) 16 November 1944: final delivery January 1946 User: UK (RN). +Development: The Barracuda was designed to Specification S. 24/37 to replace the Albacore. which in turn had been designed to replace the venerable Swordfish. The Albacore was withdrawn from production in 1943. after 800 had been built, while manufacture of Swordfish continued. The Barracuda, however, was in a different class and might have played a greater part in World War II had it not been so severely delayed. The first delay, from 1938—40. was due to abandonment of the proposed Rolls-Royce Exe engine, and the low-rated Merlin was only marginally powerful enough +Above: Three-view of Barracuda II, without ASV radar. +as a substitute Pressure of other programmes held back production two further years, but in May 1 943 No 827 Sqn. Fleet Air Arm. was fully equipped and in April 1 944 Victorious and Furious sent 42 aircraft to Kaafjord. Norway, to score 15 direct hits on the Tirpitz (for the loss of only two aircraft) in steep dive-bombing with armour-piercing bombs Later the same month Barracudas were in heavy actions in the Dutch East Indies, and others were equipped to para-drop secret agents (from underwing nacelles) to occupied Europe. The II had more power and four-blade propeller, later receiving ASV. UN radar, while the III had ASV10 in an under-fuselage radome. Wartime output of "Barras" was: Fairey 1.131. Blackburn 700. Boulton Paul 692 and Westland 18 (mostly lis). In 1945 production began on the much more powerful Mk V. later called TF 5. with redesigned structure and accommodation Radar was housed in a left-wing pod. and later Mk Vs had a tall pointed tail and other changes, but only 30 were built and used mainly for training +Below: A Barracuda II of a late batch fitted with ASV. UN radar. Though curious in layout, and underpowered, the "Barra" proved effective in numerous difficult roles. \ No newline at end of file diff --git a/storage/US9ZLYX7/Gunston - The illustrated encyclopedia of combat aircraft of World War II.pdf b/storage/US9ZLYX7/Gunston - The illustrated encyclopedia of combat aircraft of World War II.pdf new file mode 100644 index 0000000..b059e40 Binary files /dev/null and b/storage/US9ZLYX7/Gunston - The illustrated encyclopedia of combat aircraft of World War II.pdf differ diff --git a/storage/XLPB7F9L/Miles-Board - The Radio War waged by the Royal Air Force against Germany, 1940 - 1945.pdf b/storage/XLPB7F9L/Miles-Board - The Radio War waged by the Royal Air Force against Germany, 1940 - 1945.pdf index 23a3887..c4edda1 100644 Binary files a/storage/XLPB7F9L/Miles-Board - The Radio War waged by the Royal Air Force against Germany, 1940 - 1945.pdf and b/storage/XLPB7F9L/Miles-Board - The Radio War waged by the Royal Air Force against Germany, 1940 - 1945.pdf differ diff --git a/storage/YX2EADGE/Wang and Hatch - 2002 - Conducting a Crucial Experiment of the Constancy o.pdf b/storage/YX2EADGE/Wang and Hatch - 2002 - Conducting a Crucial Experiment of the Constancy o.pdf index c6b125b..33801dd 100644 Binary files a/storage/YX2EADGE/Wang and Hatch - 2002 - Conducting a Crucial Experiment of the Constancy o.pdf and b/storage/YX2EADGE/Wang and Hatch - 2002 - Conducting a Crucial Experiment of the Constancy o.pdf differ diff --git a/storage/Z9HGCEPA/2000-Re-examine the Two Principles of Spe-Wang.pdf b/storage/Z9HGCEPA/2000-Re-examine the Two Principles of Spe-Wang.pdf index 44df3c8..3aaef97 100644 Binary files a/storage/Z9HGCEPA/2000-Re-examine the Two Principles of Spe-Wang.pdf and b/storage/Z9HGCEPA/2000-Re-examine the Two Principles of Spe-Wang.pdf differ diff --git a/styles/apa.csl b/styles/apa.csl index 573f4ca..1c63c9d 100644 --- a/styles/apa.csl +++ b/styles/apa.csl @@ -14,7 +14,7 @@ - 2024-08-24T16:16:51+00:00 + 2024-08-27T18:44:31+00:00 This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 License @@ -832,7 +832,7 @@ - + diff --git a/translators/Emerald Insight.js b/translators/Emerald Insight.js index a2deaeb..a4f41ba 100644 --- a/translators/Emerald Insight.js +++ b/translators/Emerald Insight.js @@ -1,15 +1,15 @@ { "translatorID": "a14301dc-be1c-4f34-bcaa-1b53b08ce80d", + "translatorType": 4, "label": "Emerald Insight", "creator": "Sebastian Karcher", "target": "^https?://www\\.emerald\\.com/insight/(publication/|content/|search\\?)", "minVersion": "3.0", - "maxVersion": "", + "maxVersion": null, "priority": 100, "inRepository": true, - "translatorType": 4, "browserSupport": "gcsibv", - "lastUpdated": "2019-12-25 15:35:07" + "lastUpdated": "2024-08-29 15:40:00" } /* @@ -35,13 +35,11 @@ ***** END LICENSE BLOCK ***** */ -// attr()/text() v2 -// eslint-disable-next-line -function attr(docOrElem,selector,attr,index){var elem=index?docOrElem.querySelectorAll(selector).item(index):docOrElem.querySelector(selector);return elem?elem.getAttribute(attr):null;}function text(docOrElem,selector,index){var elem=index?docOrElem.querySelectorAll(selector).item(index):docOrElem.querySelector(selector);return elem?elem.textContent:null;} +let doiRe = /\/(10\.[^#?/]+\/[^#?/]+)\//; function detectWeb(doc, url) { // ensure that we only detect where scrape will (most likely) work - if (url.includes('/content/doi/') && (url.search(/\/(10\.[^#?/]+\/[^#?/]+)\//) != -1 || url.includes("/full"))) { + if (url.includes('/content/doi/') && doiRe.test(url)) { if (attr(doc, 'meta[name="dc.Type"]', 'content') == "book-part") { return "bookSection"; } @@ -78,36 +76,47 @@ function getSearchResults(doc, url, checkOnly) { } -function doWeb(doc, url) { +async function doWeb(doc, url) { if (detectWeb(doc, url) == "multiple") { - Zotero.selectItems(getSearchResults(doc, url, false), function (items) { - if (!items) { - return; - } - var articles = []; - for (var i in items) { - articles.push(i); - } - ZU.processDocuments(articles, scrape); - }); + let items = await Zotero.selectItems(getSearchResults(doc, url, false)); + if (!items) return; + for (let url of Object.keys(items)) { + // requestDocument() doesn't yet set doc.cookie, so pass the parent doc's cookie + await scrape(await requestDocument(url), url, doc.cookie); + } } else { - scrape(doc, url); + await scrape(doc, url); } } - -function scrape(doc, url) { - var DOI = url.match(/\/(10\.[^#?/]+\/[^#?/]+)\//); - var risURL; - if (DOI) { - risURL = "/insight/content/doi/" + DOI[1] + "/full/ris"; +async function scrape(doc, url, cookieFallback) { + let response; + let DOI = url.match(doiRe)[1]; + let cookie = doc.cookie || cookieFallback; + let xsrfTokenMatch = cookie && cookie.match(/XSRF-TOKEN=([^;]+)/); + if (xsrfTokenMatch) { + let xsrfToken = xsrfTokenMatch[1]; + Z.debug('Using new API. XSRF token:'); + Z.debug(xsrfToken); + + let risURL = "/insight/api/citations/format/ris?_xsrf=" + xsrfToken; // Already URL-encoded + let body = JSON.stringify({ dois: [DOI] }); + response = await requestText(risURL, { + method: 'POST', + headers: { + 'Content-Type': 'application/json', + 'X-XSRF-TOKEN': decodeURIComponent(xsrfToken) + }, + body + }); } else { - Z.debug("can't find DOI, trying alternative approach for risURL"); - risURL = url.replace(/\/full.*/, "/full/ris"); + Z.debug('Using old API'); + + let risURL = "/insight/content/doi/" + DOI + "/full/ris"; + response = await requestText(risURL); } - // Z.debug(risURL); var pdfURL; // make this works on PDF pages @@ -118,66 +127,63 @@ function scrape(doc, url) { pdfURL = attr(doc, 'a.intent_pdf_link', 'href'); } - // Z.debug("pdfURL: " + pdfURL); - ZU.doGet(risURL, function (response) { - // they number authors in their RIS... - response = response.replace(/A\d+\s+-/g, "AU -"); + // they number authors in their RIS... + response = response.replace(/^A\d+\s+-/gm, "AU -"); - var abstract = doc.getElementById('abstract'); - var translator = Zotero.loadTranslator("import"); - var tags = doc.querySelectorAll('li .intent_text'); - translator.setTranslator("32d59d2d-b65a-4da4-b0a3-bdd3cfb979e7"); - translator.setString(response); - translator.setHandler("itemDone", function (obj, item) { - if (pdfURL) { - item.attachments.push({ - url: pdfURL, - title: "Full Text PDF", - mimeType: "application/pdf" + var abstract = doc.getElementById('abstract'); + var translator = Zotero.loadTranslator("import"); + var tags = doc.querySelectorAll('li .intent_text'); + translator.setTranslator("32d59d2d-b65a-4da4-b0a3-bdd3cfb979e7"); + translator.setString(response); + translator.setHandler("itemDone", function (obj, item) { + if (pdfURL) { + item.attachments.push({ + url: pdfURL, + title: "Full Text PDF", + mimeType: "application/pdf" + }); + } + else { + item.attachments.push({ + title: "Snapshot", + document: doc + }); + } + + for (let tag of tags) { + item.tags.push(tag.textContent); + } + + var authorsNodes = doc.querySelectorAll("div > a.contrib-search"); + if (authorsNodes.length > 0) { + // prefer the authors information from the website as it contains the last and first name separately + // where the RIS data does not separate them correctly (it uses a space instead of comma) + // but the editors are only part of the RIS data + var authors = []; + for (let author of authorsNodes) { + authors.push({ + firstName: text(author, "span.given-names"), + lastName: text(author, "span.surname"), + creatorType: "author" }); } - else { - item.attachments.push({ - title: "Snapshot", - document: doc - }); - } - - for (let tag of tags) { - item.tags.push(tag.textContent); - } - - var authorsNodes = doc.querySelectorAll("div > a.contrib-search"); - if (authorsNodes.length > 0) { - // prefer the authors information from the website as it contains the last and first name separately - // where the RIS data does not separate them correctly (it uses a space instead of comma) - // but the editors are only part of the RIS data - var authors = []; - for (let author of authorsNodes) { - authors.push({ - firstName: text(author, "span.given-names"), - lastName: text(author, "span.surname"), - creatorType: "author" - }); - } - var otherContributors = item.creators.filter(creator => creator.creatorType !== "author"); - item.creators = otherContributors.length !== 0 ? authors.concat(separateNames(otherContributors)) : authors; - } - else { - Z.debug("No tags available for authors"); - item.creators = separateNames(item.creators); - } + var otherContributors = item.creators.filter(creator => creator.creatorType !== "author"); + item.creators = otherContributors.length !== 0 ? authors.concat(separateNames(otherContributors)) : authors; + } + else { + Z.debug("No tags available for authors"); + item.creators = separateNames(item.creators); + } - if (item.date) { - item.date = ZU.strToISO(item.date); - } - if (abstract) { - item.abstractNote = ZU.trimInternal(abstract.textContent).replace(/^Abstract\s*/, ""); - } - item.complete(); - }); - translator.translate(); + if (item.date) { + item.date = ZU.strToISO(item.date); + } + if (abstract) { + item.abstractNote = ZU.trimInternal(abstract.textContent).replace(/^Abstract\s*/, ""); + } + item.complete(); }); + await translator.translate(); } function separateNames(creators) { @@ -283,18 +289,18 @@ var testCases = [ "creators": [ { "lastName": "Menk", - "creatorType": "author", - "firstName": "K. Bryan" + "firstName": "K. Bryan", + "creatorType": "author" }, { "lastName": "Malone", - "creatorType": "author", - "firstName": "Stephanie" + "firstName": "Stephanie", + "creatorType": "author" } ], "date": "2015-01-01", "ISBN": "9781784415877 9781784415884", - "abstractNote": "Originality/value This technique creates opportunities for students to have unique assignments encouraging student to student teaching and can be applied to assignments in any accounting course (undergraduate and graduate). This testing method has been used in Intermediate I and II, Individual Taxation, and Corporate Taxation.", + "abstractNote": "Purpose The subject area of the assignment is accounting education and testing techniques. Methodology/approach This paper details an effective method to create individualized assignments and testing materials. Using a spreadsheet (Microsoft Excel), the creation of the unique assignments and answer keys can be semi-automated to reduce the grading difficulties of unique assignments. Findings Because students are using a unique data set for each assignment, the students are able to more effectively engage in student to student teaching. This process of unique assignments allows students to collaborate without fear that a single student would provide the answers. As tax laws (e.g., credit and deduction phase-outs, tax rates, and dependents) change depending on the level of income and other factors, an individualized test is ideal in a taxation course. Practical implications The unique assignments allow instructors to create markedly different scenarios for each student. Using this testing method requires that the student thoroughly understands the conceptual processes as the questions cannot be predicted. A list of supplementary materials is included, covering sample questions, conversion to codes, and sample assignment questions. Originality/value This technique creates opportunities for students to have unique assignments encouraging student to student teaching and can be applied to assignments in any accounting course (undergraduate and graduate). This testing method has been used in Intermediate I and II, Individual Taxation, and Corporate Taxation.", "bookTitle": "Advances in Accounting Education: Teaching and Curriculum Innovations", "extra": "DOI: 10.1108/S1085-462220150000016007", "libraryCatalog": "Emerald Insight", @@ -306,7 +312,8 @@ var testCases = [ "volume": "16", "attachments": [ { - "title": "Snapshot" + "title": "Snapshot", + "mimeType": "text/html" } ], "tags": [ @@ -339,24 +346,24 @@ var testCases = [ "title": "The influence of context upon consumer sensory evaluation of chicken‐meat quality", "creators": [ { + "firstName": "Orla", "lastName": "Kennedy", - "creatorType": "author", - "firstName": "Orla" + "creatorType": "author" }, { + "firstName": "Barbara", "lastName": "Stewart‐Knox", - "creatorType": "author", - "firstName": "Barbara" + "creatorType": "author" }, { + "firstName": "Peter", "lastName": "Mitchell", - "creatorType": "author", - "firstName": "Peter" + "creatorType": "author" }, { + "firstName": "David", "lastName": "Thurnham", - "creatorType": "author", - "firstName": "David" + "creatorType": "author" } ], "date": "2004-01-01", @@ -371,8 +378,8 @@ var testCases = [ "volume": "106", "attachments": [ { - "title": "Full Text PDF", - "mimeType": "application/pdf" + "title": "Snapshot", + "mimeType": "text/html" } ], "tags": [ @@ -401,33 +408,33 @@ var testCases = [ "creators": [ { "lastName": "Kutz-Flamenbaum", - "creatorType": "author", - "firstName": "Rachel V." + "firstName": "Rachel V.", + "creatorType": "author" }, { "lastName": "Staggenborg", - "creatorType": "author", - "firstName": "Suzanne" + "firstName": "Suzanne", + "creatorType": "author" }, { "lastName": "Duncan", - "creatorType": "author", - "firstName": "Brittany J." + "firstName": "Brittany J.", + "creatorType": "author" }, { "lastName": "Earl", - "creatorType": "editor", - "firstName": "Jennifer" + "firstName": "Jennifer", + "creatorType": "editor" }, { - "lastName": "A. Rohlinger", - "creatorType": "editor", - "firstName": "Deana" + "lastName": "Rohlinger", + "firstName": "Deana A.", + "creatorType": "editor" } ], "date": "2012-01-01", "ISBN": "9781780528816 9781780528809", - "abstractNote": "Research implications – We argue that events such as the G-20 meetings provide protesters with opportunities to gain temporary “standing” with the media. During such times, activists can use tactics and frames to alter the balance of power in relations with the media and the state and to attract positive media coverage, particularly when activists develop strategies that are not exclusively focused on the media. We argue that a combination of political opportunities and activist media strategies enabled protest organizers to position themselves as central figures in the G-20 news story and leverage that position to build media interest, develop relationships with reporters, and influence newspaper coverage.", + "abstractNote": "Purpose – Movements typically have great difficulty using the mass media to spread their messages to the public, given the media's greater power to impose their frames on movement activities and goals. In this paper, we look at the impact of the political context and media strategies of protesters against the 2009 G-20 meetings in Pittsburgh on media coverage of the protests.Methodology – We employ field observations, interviews with activists and reporters, and a content analysis of print coverage of the demonstrations by the two local daily newspapers, the Pittsburgh Post-Gazette and the Pittsburgh Tribune-Review.Findings – We find that protesters were relatively successful in influencing how they were portrayed in local newspaper stories and in developing a sympathetic image of their groups’ members. Specifically, we find that activist frames were present in newspaper coverage and activists were quoted as frequently as city officials.Research implications – We argue that events such as the G-20 meetings provide protesters with opportunities to gain temporary “standing” with the media. During such times, activists can use tactics and frames to alter the balance of power in relations with the media and the state and to attract positive media coverage, particularly when activists develop strategies that are not exclusively focused on the media. We argue that a combination of political opportunities and activist media strategies enabled protest organizers to position themselves as central figures in the G-20 news story and leverage that position to build media interest, develop relationships with reporters, and influence newspaper coverage.", "bookTitle": "Media, Movements, and Political Change", "extra": "DOI: 10.1108/S0163-786X(2012)0000033008", "libraryCatalog": "Emerald Insight", @@ -438,7 +445,8 @@ var testCases = [ "volume": "33", "attachments": [ { - "title": "Snapshot" + "title": "Snapshot", + "mimeType": "text/html" } ], "tags": [ @@ -475,29 +483,29 @@ var testCases = [ "title": "Tourism research in Spain: The contribution of geography (1960–1995)", "creators": [ { + "firstName": "Salvador", "lastName": "Antón i Clavé", - "creatorType": "author", - "firstName": "Salvador" + "creatorType": "author" }, { + "firstName": "Francisco", "lastName": "López Palomeque", - "creatorType": "author", - "firstName": "Francisco" + "creatorType": "author" }, { + "firstName": "Manuel J.", "lastName": "Marchena Gómez", - "creatorType": "author", - "firstName": "Manuel J." + "creatorType": "author" }, { + "firstName": "Sevilla", "lastName": "Vera Rebollo", - "creatorType": "author", - "firstName": "Sevilla" + "creatorType": "author" }, { + "firstName": "J.", "lastName": "Fernando Vera Rebollo", - "creatorType": "author", - "firstName": "J." + "creatorType": "author" } ], "date": "1996-01-01", @@ -513,8 +521,8 @@ var testCases = [ "volume": "51", "attachments": [ { - "title": "Full Text PDF", - "mimeType": "application/pdf" + "title": "Snapshot", + "mimeType": "text/html" } ], "tags": [ @@ -547,6 +555,72 @@ var testCases = [ "seeAlso": [] } ] + }, + { + "type": "web", + "url": "https://www.emerald.com/insight/content/doi/10.1108/JACPR-02-2022-0685/full/html", + "items": [ + { + "itemType": "journalArticle", + "title": "A multi-level, time-series network analysis of the impact of youth peacebuilding on quality peace", + "creators": [ + { + "firstName": "Laura K.", + "lastName": "Taylor", + "creatorType": "author" + }, + { + "firstName": "Celia", + "lastName": "Bähr", + "creatorType": "author" + } + ], + "date": "2023-01-01", + "DOI": "10.1108/JACPR-02-2022-0685", + "ISSN": "1759-6599", + "abstractNote": "Purpose Over 60% of armed conflicts re-occur; the seed of future conflict is sown even as a peace agreement is signed. The cyclical nature of war calls for a focus on youth who can disrupt this pattern over time. Addressing this concern, the developmental peace-building model calls for a dynamic, multi-level and longitudinal approach. Using an innovative statistical approach, this study aims to investigate the associations among four youth peace-building dimensions and quality peace. Design/methodology/approach Multi-level time-series network analysis of a data set containing 193 countries and spanning the years between 2011 and 2020 was performed. This statistical approach allows for complex modelling that can reveal new patterns of how different youth peace-building dimensions (i.e. education, engagement, information, inclusion), identified through rapid evidence assessment, promote quality peace over time. Such a methodology not only assesses between-country differences but also within-country change. Findings While the within-country contemporaneous network shows positive links for education, the temporal network shows significant lagged effects for all four dimensions on quality peace. The between-country network indicates significant direct effects of education and information, on average, and indirect effects of inclusion and engagement, on quality peace. Originality/value This approach demonstrates a novel application of multi-level time-series network analysis to explore the dynamic development of quality peace, capturing both stability and change. The analysis illustrates how youth peace-building dimensions impact quality peace in the macro-system globally. This investigation of quality peace thus illustrates that the science of peace does not necessitate violent conflict.", + "issue": "2", + "libraryCatalog": "Emerald Insight", + "pages": "109-123", + "publicationTitle": "Journal of Aggression, Conflict and Peace Research", + "url": "https://doi.org/10.1108/JACPR-02-2022-0685", + "volume": "15", + "attachments": [ + { + "title": "Full Text PDF", + "mimeType": "application/pdf" + } + ], + "tags": [ + { + "tag": "Developmental peace-building model" + }, + { + "tag": "Education" + }, + { + "tag": "Engagement" + }, + { + "tag": "Inclusion" + }, + { + "tag": "Information" + }, + { + "tag": "Quality peace" + }, + { + "tag": "Time-series network analysis" + }, + { + "tag": "Youth peacebuilding" + } + ], + "notes": [], + "seeAlso": [] + } + ] } ] /** END TEST CASES **/ diff --git a/translators/Queensland State Archives.js b/translators/Queensland State Archives.js index 7f0bdc6..9014b42 100644 --- a/translators/Queensland State Archives.js +++ b/translators/Queensland State Archives.js @@ -9,7 +9,7 @@ "priority": 100, "inRepository": true, "browserSupport": "gcsibv", - "lastUpdated": "2024-08-21 19:45:00" + "lastUpdated": "2024-09-03 15:30:00" } /* @@ -88,7 +88,10 @@ async function scrape(url) { let item = new Zotero.Item("manuscript"); item.title = data.title; if ("record_type" in data.subject_terms) { - item.type = data.subject_terms.record_type.join("; "); + let recordTypes = data.subject_terms.record_type.map( + term => term.term + ); + item.type = recordTypes.join("; "); } item.archive = "Queensland State Archives"; item.archiveLocation = data.qsa_id_prefixed; @@ -115,8 +118,7 @@ async function scrape(url) { }); } // Add digital representation - if (data.digital_representations.length > 0) { - let image = data.digital_representations[0]; + for (let image of data.digital_representations) { let imageID = image.qsa_id_prefixed; let mimeType, imageTitle; if (image.file_type == "JPEG") { @@ -127,12 +129,12 @@ async function scrape(url) { mimeType = "application/pdf"; imageTitle = "PDF " + imageID; } - item.attachments = [{ + item.attachments.push({ title: imageTitle, url: "https://www.archivessearch.qld.gov.au/api/download_file/" + imageID, mimeType: mimeType, snapshot: true - }]; + }); } item.complete(); } @@ -240,7 +242,62 @@ var testCases = [ { "type": "web", "url": "https://www.archivessearch.qld.gov.au/search?f[]=keywords&has_digital=false&op[]=AND&open=false&q[]=wragge&sort=relevance&type[]=archival_object", + "defer": true, "items": "multiple" + }, + { + "type": "web", + "url": "https://www.archivessearch.qld.gov.au/items/ITM276520", + "items": [ + { + "itemType": "manuscript", + "title": "Criminal files - Supreme Court, Northern District, Townsville", + "creators": [ + { + "lastName": "A267, Supreme Court, Northern District, Townsville", + "creatorType": "contributor", + "fieldMode": 1 + } + ], + "archive": "Queensland State Archives", + "archiveLocation": "ITM276520", + "extra": "Issued: 1875/1876\nArchive Collection: S7833, Criminal Files - Supreme Court, Northern District, Townsville", + "libraryCatalog": "Queensland State Archives", + "manuscriptType": "Depositions and indictments", + "rights": "Copyright State of Queensland", + "url": "https://www.archivessearch.qld.gov.au/items/ITM276520", + "attachments": [ + { + "title": "PDF DR87978", + "mimeType": "application/pdf", + "snapshot": true + }, + { + "title": "PDF DR87979", + "mimeType": "application/pdf", + "snapshot": true + }, + { + "title": "PDF DR87980", + "mimeType": "application/pdf", + "snapshot": true + }, + { + "title": "PDF DR87981", + "mimeType": "application/pdf", + "snapshot": true + }, + { + "title": "PDF DR87982", + "mimeType": "application/pdf", + "snapshot": true + } + ], + "tags": [], + "notes": [], + "seeAlso": [] + } + ] } ] /** END TEST CASES **/ diff --git a/zotero.sqlite b/zotero.sqlite index eb06748..2377ceb 100644 Binary files a/zotero.sqlite and b/zotero.sqlite differ diff --git a/zotero.sqlite-journal b/zotero.sqlite-journal index 09070c1..728b516 100644 Binary files a/zotero.sqlite-journal and b/zotero.sqlite-journal differ diff --git a/zotero.sqlite.1.bak b/zotero.sqlite.1.bak index 5d7a916..618de75 100644 Binary files a/zotero.sqlite.1.bak and b/zotero.sqlite.1.bak differ diff --git a/zotero.sqlite.bak b/zotero.sqlite.bak index cf1057f..bf8d062 100644 Binary files a/zotero.sqlite.bak and b/zotero.sqlite.bak differ