2063 lines
291 KiB
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2063 lines
291 KiB
Plaintext
47584 cover 27/5/05 1:38 PM Page 1
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Pushing Gravity
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Since Newton’s time many have proposed that gravitation arises from the absorption by material bodies of minute particles or waves filling space. Such absorption would cause bodies to be pushed into each other's shadows. The principal early proponent of this idea was Georges-Louis Le Sage. This book explores:
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• The remarkable three hundred-year saga of Le Sage’s theory • Gravitational shielding and the experiments of Q. Majorana • New and recent Le Sage models
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The reasons for the present resurgence of Le Sage-type models of gravitation are their simplicity and depth - features desirable in any physical theory.Whereas Newton’s theory and (later) Einstein’s relativity were essentially mathematical descriptions of the motions of bodies in gravitation, Le Sage’s theory attempts to arrive at the very cause of gravity.
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- from the Preface by Matthew Edwards
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Edwards (ed.)
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Pushing Gravity
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NEW PERSPECTIVES ON LE SAGE’S THEORY OF GRAVITATION
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Pushing Gravity
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Apeiron
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Edited by Matthew R. Edwards
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Preface
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To many readers of physics, the history of theories of gravitation may be summed up approximately as follows. After a chaotic period featuring vortex ether models and the like, gravity was at last put on a firm scientific footing by Newton. In the following centuries Newton’s theory saw success after success, until a few unexplained anomalies, such as the advance of the perihelion of Mercury, paved the way for Einstein’s General Relativity. The latter theory has remained without serious challenge to the present day. In this grand progression, few will likely have heard of a simple mechanical theory of gravitation, which from Newton’s time has come down through the centuries almost unchanged. Its principal early expression was given by Georges-Louis Le Sage of Geneva in the mid-eighteenth century.
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Le Sage’s theory of gravitation has a unique place in science. For over three centuries it has periodically attracted some of the greatest physicists of the day, including Newton, who expressed interest in Fatio’s earlier version of the theory, and later Kelvin, who attempted to modernize the theory in the late 1800’s. At the same time, the theory has drawn just as many notable critics, including Euler, Maxwell and Poincaré. Despite frequent and spirited obituaries, Le Sage’s theory in various guises has always survived to challenge the prevailing wisdom of the day. Now, at the start of this new century, it appears that the theory may be on the rise again.
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The reasons for the present resurgence of Le Sage-type models of gravitation are their simplicity and depth—features desirable in any physical theory. Whereas Newton’s theory and (later) Einstein’s relativity were essentially mathematical descriptions of the motions of bodies in gravitation, Le Sage’s theory attempts to arrive at the very cause of gravity. The basic idea runs like this. Space is filled with minute particles or waves of some description which strike bodies from all sides. A tiny fraction of the incident waves or particles is absorbed in this process. A single body will not move under this influence, but where two bodies are present each will be progressively urged into the shadow of the other. If any theory of gravity can be said to satisfy Occam’s Razor, it is surely Le Sage’s. Its simplicity and clarity guarantee that it will be conjured up again and again by those who seek to understand gravity’s mechanism, as opposed to merely its rules.
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Other reasons also exist for the recent upsurge of interest. Over the last half century, it has become increasingly common to view space once more as endowed with energy-dense fields, known variously as the zero-point fields, the quantum vacuum and many other names. Since the existence of such fields is the central postulate of Le Sage-type theories, the status of such theories has correspondingly risen. In addition, parallel veins of research in geophysics and cosmology also seem to point to in the direction of Le Sage. As Halton Arp discusses in his foreword, the geophysical link is to the theory of earth expan-
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Pushing Gravity: new perspectives on Le Sage’s theory of gravitation
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i
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edited by Matthew R. Edwards (Montreal: Apeiron 2002)
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ii
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Preface
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sion (as opposed to conventional plate tectonics), while the cosmological link is to alternative cosmologies (rather than the Standard Model).
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The first papers in the book explore the impressive three hundred-year history of Le Sage’s theory. In the opening paper Evans discusses Le Sage’s own contribution and the discouraging reception that Le Sage received from the scientists of his day, such as Euler and Laplace. Le Sage was in fact fighting a trend in the eighteenth century away from mechanical models of gravitation. The setting for his theory was actually much more favourable in the previous century, when another Genevan, Nicolas Fatio de Duillier, burst upon the scene with a very similar theory. Fatio’s role is discussed by van Lunteren in his paper. Newton’s own views on gravitation, which at times were very close to Le Sage’s and Fatio’s, are discussed in the reprinted paper by Aiton. The paper by Edwards discusses the attempt by Kelvin and others to revive Le Sage’s theory in the late 1800’s, when the theory was shown to be compatible with the kinetic theory of gases. This paper also has an overview of some twentieth century developments in the theory.
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The modern wave of Le Sage-type theories is represented in the next group of papers. (While in later centuries it became common for authors to use “Lesage” or “LeSage”, in this book we shall adopt the original spelling.) In these papers there will be seen to be many points of agreement, but also many differences. Some of the models, such as those of Van Flandern, Slabinski and Mingst and Stowe, are corpuscular models in the direct tradition of Le Sage. Others, such as those of Kierein, Edwards and Popescu-Adamut, explore electromagnetic analogues of Le Sage’s theory. Historically, there have been countless names given to the Le Sage corpuscles or waves. In some of the papers the authors have adopted the term ‘graviton’ to refer to these entities.
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The paper by Radzievskii and Kagalnikova provides a good overview of Le Sage’s theory as well as a detailed mathematical description of a modern Le Sage theory. In their model, the gravitational force is propagated by material particles travelling at c. This paper was originally published in 1960 and later translated in a U.S. government technical report, of which the present paper is a slightly corrected version. Dr. Radzievskii, although reported to be ill at this time, nonetheless expressed his strong support for this project.
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In his paper, Van Flandern develops Le Sage’s theory from a modern standpoint and explores its relations to such problems as the existence of gravitational shielding, the advance of the perihelion of Mercury and heating effects. As did Le Sage, he argues that the absence of observed gravitational aberration is explicable with the gravitons having superluminal velocities.
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A potentially major advance in Le Sage-type theories is given in the paper by Slabinski. In the past, these theories have generally supposed that the gravitons incident on bodies are either totally scattered or totally absorbed. In the former case, no gravitational force results, while in the latter an excessive heating of bodies is expected. Slabinski shows that, provided some small fraction
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Preface
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iii
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of the gravitons is absorbed, the scattered gravitons can indeed generate a significant force.
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In his paper, Kierein suggests that the Le Sage medium is in the form of very long wavelength radiation, as had earlier been proposed by Charles Brush. Such radiation penetrates matter easily and, in Kierein’s model, a portion of the radiation traversing bodies is converted to mass through a Compton effect mechanism. The absorption of radiation leads to gravitation, while the mass increase is linked to earth expansion.
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The paper by Edwards proposes that the absorption of gravitons by bodies in a Le Sage mechanism is proportional to the bodies’ velocities as measured in the preferred reference frame defined by the gravitons (essentially the same frame as the cosmic background radiation). Graviton absorption increases the mass and rest energy of the bodies, which therefore lose velocity in the preferred frame. Overall there is conservation of energy (and thus no heating effect) since the rest energy gained by the bodies equals the kinetic energy lost.
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The paper by Toivo Jaakkola is adapted from a longer paper that was originally published posthumously in the memorial issue of Apeiron dedicated to him. It presents Jaakkola’s Le Sage-type model and many observations and conclusions about Le Sage theories in general. The paper by Veselov, reprinted from Geophysical Journal, presents a novel type of Le Sage mechanism, which Veselov links to earth expansion and various astrophysical phenomena.
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In their paper, Mingst and Stowe present a corpuscular Le Sage model. Dynamical aspects of this and other Le Sage models are discussed in the companion paper by Stowe. In her paper, Popescu-Adamut reviews and updates the “electrothermodynamical theory of gravitation” proposed in the 1980’s by her father, Iosif Adamut.
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The next several papers consider the question of gravitational shielding, with special reference to the work of Quirino Majorana. Unlike Le Sage, Majorana proposed that matter itself emits an energy flux of some kind which produces gravitational effects on other bodies. Just as in Le Sage’s theory, however, this flux would be attenuated in passing through other bodies. Majorana performed a famous set of experiments which appeared to demonstrate such a shielding effect. This work is discussed in Martins’ first paper. In his second paper, Martins examines the links between Majorana’s theory and Le Sage’s. Whereas Majorana had thought it possible to distinguish experimentally between his own theory and Le Sage’s, Martins proves that this supposition is false, i.e., that the predictions of both theories in shielding experiments are precisely the same. This finding is in keeping with the notion that the theories of Le Sage and Majorana may actually be two sides of the same coin. In some Le Sage-type theories, the Le Sage flux upon interacting with matter is converted into a secondary flux, which itself does not transmit the gravitational force. Mathematically, such models can be made to resemble Majorana-type models if the primary fluxes are disregarded and the secondary fluxes are modelled as transmitting momentum in the negative sense.
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iv
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Preface
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Majorana’s experiments were never repeated, however, and other confirmation of the existence of gravitational shielding has been very hard to come by. Some of the attempts to find such shielding are reviewed in the paper by Unnikrishnan and Gillies. While evidence for shielding at the present time appears limited, it can only be stated that the question remains open both theoretically and experimentally. For instance, there is the exciting possibility that the Zürich apparatus for measuring G, discussed by these authors, could also be used to directly repeat the experiments of Majorana.
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In their paper von Borzeszkowski and Treder discuss possible nonrelativistic effects in gravitation, such as absorption of gravity, but within the context of relativistic theories of gravitation. One such theory, originally proposed by Riemann, is examined in the following paper by Treder.
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In his paper, Kokus examines the many unusual patterns in earthquakes and other seismic events and discusses the role of alternate theories of gravitation in accounting for them. He argues that many of the patterns can be accounted for in expanding earth or pulsating earth models. Buonomano, in his paper, discusses the possible roles of a Le Sage-type medium in quantum physics. The book concludes with a historical discussion by Hathaway of attempts to manipulate gravitation.
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Collectively, the papers in this book show that the remarkable saga of Le Sage’s theory of gravitation may be entering a new and exciting phase. In the new century, it may even pass that Le Sage’s theory comes into prominence once more. If it does, it would not be entirely surprising. It is, after all, the simplest theory of gravitation.
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Matthew Edwards
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Acknowledgements
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In preparation of this book, I received invaluable assistance from many quarters. Important suggestions on potential contributors and assistance in contacting them came from Craig Fraser, André K.T. Assis, Andreas Kleinert, John Kierein, Tom Van Flandern, Roy Keys, Henry Aujard, Ieronim Mihailă and Victor Kuligin. At the University of Toronto Library, Jeff Heeney, Sophia Kaszuba, Elaine Granatstein, Andrew Sorcik and Roy Pearson provided bibliographic, technical and other assistance. Peter McArthur proofread the many papers and provided valuable technical assistance. I also thank Dennis McCarthy and Robert Villahermosa for their help. The Bibliothèque publique et universitaire, Ville de Genève, and the Library of the Royal Society, London, generously allowed reproduction of figures.
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Throughout the project I benefited immensely from countless discussions with the contributors, especially John Kierein, Tom Van Flandern, James Evans and Roberto de Andrade Martins. Most of all I thank Roy Keys for his assistance throughout the project and my wife Teresa Edwards and daughter Oriane Edwards for their enthusiastic support.
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Foreword
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The Observational Impetus for Le Sage Gravity
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Halton Arp*
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For many years I never questioned the obvious fact that masses attracted each other (inversely as the square of their separation, to complete the mantra). The ‘attraction’ was so blatant that it required no thought. But then observations of galaxies and quasars forced me to accept the fact that extragalactic redshifts were primarily intrinsic and not the result of recessional velocity in an expanding universe.
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How did this lead to my abandoning pulling gravity and investigating pushing gravity? It is interesting how the crumbling of one fundamental assumption can have reverberations throughout the whole underpinning of one’s science. In this case it was the necessity to find a mechanism which would explain intrinsic redshifts that eventually turned out to shake other fundamental assumptions. The search was motivated by a desire to have the discordant observations believed. (Unfortunately, when I asked Feynman about the HoyleNarlikar variable mass theory, he told me “We do not need a new theory because our present one explains everything.”) Nevertheless, the ball had started rolling downhill so to speak and in 1991, with Narlikar’s help, I outlined in Apeiron the way in which particle masses growing with time would account for the array of accumulated extragalactic paradoxes. Later Narlikar and Arp (1993) published in the Astrophysical Journal Narlikar’s original 1977 solution of the basic dynamical equations along with the Apeiron applications to the quasar/galaxy observations.
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We hoped, of course, to gain validation of the new theory by showing that it was a legitimate product of the accepted, one might even say worshipped, general relativistic field equations. All we gained in fact was an audience which totally ignored this new, more rigorous solution. Nevertheless, seeing it in print started the wheels slowly turning in my head.
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The first insight came when I realized that the Friedmann solution of 1922 was based on the assumption that the masses of elementary particles were always and forever constant, m = const. He had made an approximation in a differential equation and then solved it. This is an error in mathematical procedure. What Narlikar had done was solve the equations for m = f(x,t). This is a
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* Max-Planck Institut für Astrophysik, 85741 Garching, Germany
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Pushing Gravity: new perspectives on Le Sage’s theory of gravitation
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1
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edited by Matthew R. Edwards (Montreal: Apeiron 2002)
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2
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Halton Arp
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more general solution, what Tom Phipps calls a covering theory. Then if it is decided from observations that m can be set constant (e.g., locally) the solution can be used for this special case. What the Friedmann and following Big Bang evangelists did was succumb to the typical conceit of humans that the whole of the universe was just like themselves.
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But Narlikar had overwhelmed me with the beauty of the variable mass solution by showing how the local dynamics could be recovered by the simple conformal transformation from t time (universal) to what we called τ time (our galaxy time). The advertisement here was that our solution inherited all the physics triumphs much heralded in general relativity, but also accounted for the non-local phenomena like quasar and extragalactic redshifts. Of course, to date, this still has made no impression on academic science.
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In addition, I eventually realized that an important part of the variable mass solution was that it took place in perfectly flat, Euclidean space. This pointed directly at the revelation that the Riemannian, geometric terms on the left hand side of the famous Gµν = Tµν equation were zero. If Gµν = 0, then the curved space-time had nothing to do with real cosmic physics.
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Two thoughts then presented themselves:
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1) The Gµν terms in the conventional solution usually represent forbiddingly complicated terms. But their existence appears to be required only for the purpose of compensating for the variable m in the Tµν side of the equation, which was assumed constant in the Big Bang solution. These geo-
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metric terms, as is well known, are used to adjust parameters such as H0, q0, etc., when the redshift–apparent magnitude relation is interpreted in an expanding universe. (In the variable mass solution H0 equals only ⅔ the inverse age of our galaxy and is equal to around 50 km/sec/Mpc, with no adjustable parameters.)
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2) If there are no geometric space curvature terms in the variable mass solu-
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tion, and this is a more valid solution, is there ever a legitimate use for these terms? For some time I entertained the idea that near high mass
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concentrations one might need them. But now I see work by Montanus
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and Gill which indicated physics with proper time and local time can reproduce classical relativity tests in flat, Euclidean space. It raises the
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question: Is space-time curvature valid? At this point the elementary
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question that should have been asked long ago by scientists and nonscientists alike is: With any reasonable definition of space, how can one
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“curve” it? (If you have trouble visualizing curved space, try curved
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time!) Curved space-time appears to be, and always to have been, as Tom Phipps casually remarked, an oxymoron!
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In Table 1 appended here is a summary of how conventional relativity
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fails and how the flat space time, local and cosmic time treatment gives common sense results in its place.
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The Observational Impetus for Le Sage Gravity
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3
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Concept
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Variable Mass
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Proper Time
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Relativistic
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Common Sense
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Primary reference frame
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√
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√
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X
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ave. over detection = reference
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flat (Euclidean) space
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√
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√
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X
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space defined as direction
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no singularities (black holes)
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√
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√
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X
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clocks run fast and slow
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no fields (action at a distance)
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√
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√
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X
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causality
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mass ≠ f(v)
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√
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X
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M → ∞ as v → c
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mass = f(t)
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√
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X
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Mach, e.m. speed = c
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no dark matter
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√
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X
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high redshifts not velocity
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no big bang, expansion of space or faster than light inflation
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√ cosmological
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terrestrial
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X historical
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something cannot come from nothing, space cannot expand
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Hoyle Narlikar
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Arp
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Van Flandern Phipps, Gill Selleri,
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Drew Montanus Galeczki
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Einstein Academia
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Media
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Table 1. Some of the most important concepts in modern physics and cosmology are listed in the first column. The next three columns show whether variable mass, proper time, or relativistic physics support or violate these concepts. The last column gives the common sense (operational definition) of the concepts. Finally, at the bottom of the columns are a few of the names associated with the three analytical systems. (From Acta Scientiarum, in press).
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Gravity
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After this long preamble we finally come to the point: If space is not curved by the presence of mass (as per Einstein)—then what causes gravity? We are forced by the solution which explains the redshift dependence on age of matter to look for another cause of gravity. If masses do not move on prefixed tracks in space then there is no hope of having the instaneously acting component of gravity by guiding them with the exchange of some electromagnetic wave travelling with speed c.
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Since the time of the 18th century Genevan physicist, Le Sage, many people have considered what is apparently the only alternative to ‘pulling’ gravity, i.e., ‘pushing gravity’. My attention, however, was called to it belatedly by an article in Tom Van Flandern’s Meta Research Bulletin. The key point for me was that its force behaved “inversely as the square of the separation,” a point which I had not bothered to work out. The force (be with you) is transmitted by a surrounding sea of much faster than light gravitons. Van Flandern (1998) cal-
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4
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Halton Arp
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culates > 2 × 1010 c. So we can have as ‘nearly instantaeneous’ action as we wish and yet not abandon the concept of causality.
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Of course it is interesting to comment on some of the doctrinal problems of the imminently deceased relativity theory. Are inertial and gravitational mass the same? Since the atoms of a feather and of a lead ball are made of the same electrons, protons and neutrons, we will have—to some orders anyway— the same force applied by the absorption from the surrounding sea of gravitons. So the equivalence principle holds. But only if the absorption of gravitons, and subsequent impetus, is proportional to inertial mass.
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My own working hypothesis for gravity now is that gravitons are very low mass particles with a huge de Broglie wavelength compared to photons. Since their wavelength is so long they have much less interaction with the intergalactic medium. So they far exceed the normal velocity of light in ‘vacuum’ (i.e., the vacuum that light in our locality of the universe sees). In other words the photon is transmitted through the average cosmic false vacuum, material vacuum or zero point energy field—to use just a few names given to the old fashioned concept of ‘aether’. But the graviton interacts with much less of this molasses and hence moves much faster. One might speculate that there is a vast amount of matter in the universe which radiates at very long wavelengths.
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Perhaps it is time to wander back to the observations with our new hypothesis in hand. Since the particles of matter in the universe grow as they age and communicate with ever more distant parts of the universe they have to receive information. In the variable mass theory this electromagnetic communication is at the speed of light, c. The gravitons travelling much faster than the speed of light, however, must also carry information. (No one could argue that knowledge of the direction of an adjoining mass is not information). So the old relativistic shibboleth—“information cannot be transmitted faster than the speed of light”—falls by the wayside. Recent experiments with entangled quantum states are also indicating this.
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As the inertial mass of particulate matter grows with time, in order to conserve momentum it must slow its velocity with respect to the primary reference frame. This is an important contribution of the new physics because the observations show that newly created, high redshift quasars are initially ejected as a near zero mass plasma with very high velocities and then grow in mass, drop in redshift and slow in velocity until they eventually form groups of slightly younger companions to the parent galaxy. This is observationally established and can only be explained by the variable mass theory.
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The condensation of low mass plasma into a coherent body in the new theory forms an interesting contrast to condensation of galaxies in the 78-yearold Big Bang theory. Bernard Bligh (2000) has shown thermodynamically that the hot Big Bang cannot cool and condense into galaxies because its expansion is not constrained. As experience would dictate, a hot gas just diffuses. The situation with the near zero mass plasma is different, however, in that the growing mass of its constituent particles slows their velocities, thereby cooling
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The Observational Impetus for Le Sage Gravity
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5
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their temperature. In addition, the growing mass increases the pressure toward condensing into a gravitationally bound body.
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Now that we reference the primary reference frame we are reminded that this is yet another strike against the hallowed relativity theory, which is supposed to have no primary reference frame. But the existence of the microwave background certainly reminds us that an average over the detectable universe certainly represents an obvious, primary reference frame. Moreover, laboratory experiments, including those on the Sagnac effect by Selleri and others, reveal the presence of such a frame.
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The objection by Feynman to pushing gravity, which was brought to my attention by John Kierein, was that objects in orbital motion such as the earth would experience resistance from increased graviton flux in the direction of their motion. The answer, without computation, seems to be that this effect would only come into action at very high orbital speeds because of the very high speed of the gravitons. But, in general, it should be noted that my observational experience sheds doubt on any extragalactic velocities greater than about 300 km/sec. (rotational velocities in galaxies). This would imply that older objects must come very close to rest with respect to—what else but a primary, or universal reference frame.
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Quantization
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An unexpected property of astronomical objects (and therefore an ignored and suppressed subject) is that their properties are quantized. This first appeared when William Tifft showed that the redshifts of galaxies occurred in certain preferred values, e.g., 72, 144, 216, etc. km/sec. Later William Napier demonstrated a periodicity of 37.5 km/sec with great accuracy. The outstandingly important, empirical implication to draw from these by now exceedingly well established observations is that the individual velocities of galaxies must be less than about 20 km/sec; otherwise the sharp quantizations would be blurred. In turn this implied very little motion in a primary reference frame.
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For the quasars, Geoffrey Burbidge noticed soon after the first redshifts began to accumulate that there was a preferred value about resdhift z = 1.95. As more redshifts accumulated it became clear that the whole range of extragalactic redshifts was significantly periodic. K.G. Karlsson showed that they fit the formula
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(1 + zn ) = (1 + z0 ) ×1.23n .
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This was interpreted by Arp in terms of the variable mass theory by hypothesizing that as the electron masses grew with time they increased through permitted mass states which stepped by a factor of 1.23.
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The most astonishing result was then pointed to by Jess Artem, that the same quantization ratio that appeared in quasar redshifts appeared in the orbital parameters of the planets in the solar system. This first manifested itself in the ratio of planetary semi-major axes occurring in some high power of n in 1.23n .
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6
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Halton Arp
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This also appeared to be true of the ratio of planetary and lunar masses and even solar and electron masses.
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Shortly afterward, O. Neto in Brazil, Agnese and Festa in Italy, L. Nottale in France and A. and J. Rubčić in Croatia independently began pointing out similarities to the Bohr atom in the orbital placement of the planets. Different variations of
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Bohr-like radius = n2 or n2 + 1/2n
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fit the planetary semi-major axes extremely well with rather low ‘quantum’ numbers n. Most recently I have learned of a modification to the Titius-Bode law by Walter Murch where the
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planetary radii = 1 + 2n + 2n−1.
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This latter law fits the observed planetary positions exceedingly well for n = −1 to 6 with an average deviation of only 2.4 percent.
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Which of these empirical laws is correct or whether they are all different approximations of a more fundamental law is a mystery at this moment. But it is clear that the properties of the planets are not random and that they are in some way connected to quantum mechanical parameters, both of which are connected to cosmological properties.
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Just to try to tie some of the above results together, in what is obviously an inadequate theory, let us suppose that the planetary system started as some kind of analogue to an atom. In the variable mass theory the matter starts out from zero mass but the basic unit of charge never changes. Therefore the seed planets would be placed according to Bohr atom rules. As time goes on their inertial masses grow, but in steps which are governed by communication with their cosmic environment. Very soon the charge aspect of the planet is overwhelmed by its inertial mass aspect and it is thereafter governed by the currently observed gravitational laws.
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Expanding Earth
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As long ago as 1958, S. Carey reported detailed geological data which implied the earth had been expanding. K.M. Creer (1965) was one of many who showed how accurately the continents fitted together in the past and M. Kokus (1994) calculated how the observed sea floor spreading in the mid Atlantic ridge supported this interpretation. Naturally without an identifiable physical cause most scientists abandoned these empirical conclusions in favour of the theory that there was nothing of significance to explain. It is appropriate to quote Creer, however: “For an adequate explanation we may well have to await a satisfactory theory of the origin and development of the universe.” The variable mass theory is a candidate to fulfill that prophecy.
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But how does Le Sage gravity enter this picture? I would suggest the following trial hypothesis. If much faster than light gravitons are pushing massive bodies toward each other, then they must be transmitting an impulse which could be described as energy. Is it possible that these gravitons are depositing energy or creating mass in the interior of the earth which is causing
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The Observational Impetus for Le Sage Gravity
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7
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energy or creating mass in the interior of the earth which is causing it to expand?
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There are two attractive features of this suggestion. In the Olympia meeting (1993) there were calculations that the mass of the earth had to be increasing. The problem was, however, that the mass had to be increasing too fast. To quote J.K. Davidson (Olympia Meeting, p. 299): “The current expansion rate is very rapid and gives rise to questions like, how is the extra mass being created (it seems to be occurring in the core as there is no evidence at the surface); will the earth ultimately explode and form another asteroid belt or will it become a Jupiter then a sun….” At that meeting I reminded the Geophysics section of the fact that the extragalactic quantization evidence showed that as matter evolved it must jump rapidly from one quantized particle mass value to the next highest. The obvious implication is that this would be a natural explanation for the varying rate of expansion of the earth.
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The second attractive feature of the variable mass theory is that the research of Tom Van Flandern (1993) indicates that planets explode. It has always been clear that where a giant planet should exist between Mars and Jupiter there is instead a belt of rock fragments called the asteroids. But Van Flandern’s careful work on the problem of Mars (which should in all continuity be much larger rather than much smaller than the earth) shows that it has suffered a fragmenting explosion leaving visible effects on one face. So there is evidence that this happens in the solar system. In fact there is visible evidence that it happens in galaxies as well (Arp, 1998, 1999).
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The Current State
|
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The most intriguing problem to me now is to combine the features of the variable mass solution with the features of the pushing gravity models. The Machian communication of the variable mass solution with matter at increasing distances offers a solution for the quantization values as reflecting discrete drops in mean density as we proceed outward in a hierarchical universe (Narlikar and Arp, 2000). But that communication is electromagnetic at the velocity of light. Is it possible to transfer the periodically increasing mass with photons that resonate with the frequency of the electrons and protons in the matter under consideration? Or does this resonance frequency of the electron, for example (Milo Wolff, 1995), just make it possible for the much smaller, much faster than light gravitons to deposit new mass in older material.
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As important as the details are, the observations overall seem now to generally require new matter to continually materialize at various points in the universe. Balance, if necessary, could be obtained from feedback mechanisms between the intergalactic aether and long wavelength radiation from present matter (I presume). The greatest part of the progress independent researchers have made in the past decades, in my opinion, has been to break free of the observationally disproved dogma of curved space time, dark matter, Big Bang, no primary reference frame and no faster than light information.
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8
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Halton Arp
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References
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Apeiron, winter-Spring 1991, pp 18-28. H. Arp, 1998, Seeing Red: Redshifts, Cosmology and Academic Science, Apeiron, Montreal. H. Arp, 1999, ApJ 525, 594. H. Arp, H. Bi, Y. Chu and X. Zhu, 1990, Astron. Astrophys. 239, 33. B. R. Bligh, 2000, “The Big Bang Exploded,” 4 St. James Ave., Hampton Hill, Middlesex, TW12 1HH,
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U.K. K.M. Creer, 1965, Nature 205, 539. M. Kokus, 1994, private communication. J. Narlikar and H. Arp, 2000, “Dynamics of Ejection from Galaxies and the Variable Mass Hypothesis,”
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in preparation. Olympia Meeting, 1993, Frontiers of Fundamental Physics, “Geophysics,” pp 241-335, eds, Barone, M.
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and Selleri, F., (Plenum, New York and London). T. Van Flandern, 1993, Dark matter, Missing Planets and New Comets, North Atlantic Books, Berke-
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ley. T. Van Flandern, 1998, “The Speed of Gravity- What the Experiments Say,” Phys. Lett. A 250, 1. M. Wolff, 1995, “A Wave Structure for the Electron,” Galilean Electrodynamics 6, No. 5, 83.
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Gravity in the Century of Light
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Sources, Construction and Reception of Le Sage’s Theory of Gravitation
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James Evans*
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1. Introduction
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The history of gravitation theories provides excellent opportunities for investigating what “explanation” means, and has meant, in physics. There are two reasons for this. First, the phenomena to be accounted for by a successful theory of (Newtonian) gravity are easily described and understood, which is not the case, for example, with electrodynamics. Second, there were very few additions to these phenomena for two hundred years. The shifting fortunes of gravitation theories in the eighteenth and nineteenth centuries were largely due to causes other than shifts in the empirical evidence. Each generation of physicists, or natural philosophers, sought to place universal gravitation in the context of its own worldview. Often this entailed an effort to reduce gravitation to something more fundamental. What is deemed fundamental has, of course, changed with time. Each generation attacked the problem of universal gravitation with the tools of its day and brought to bear the concepts of its own standard model.1
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The most successful eighteenth-century attempt to provide a mechanical explanation of gravity was that of Georges-Louis Le Sage (1724-1803) of Geneva.2 (Fig. 1.) Like many good Newtonians of the time, Le Sage was an atomist: he wished to explain all the properties of matter in terms of collisions and conglomerations of atoms. But he went further than most, for he believed that even gravity could be explained in this way. Le Sage’s effort reduced gravitation to the eighteenth century’s most austere physical notion, that of mass points, or atoms, in the void.
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Le Sage’s theory is an especially interesting one, for several reasons. First, it serves as the prototype of a dynamical explanation of Newtonian gravity. Second, the theory came quite close to accomplishing its aim. Third, the theory had a long life and attracted comment by the leading physical thinkers of several successive generations. Le Sage’s theory therefore provides an excellent opportunity for the study of the evolution of attitudes toward physical explanation. The effects of national style in science and generational change take on a new clarity.
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* Department of Physics, University of Puget Sound, 1500 North Warner, Tacoma, WA 98416 USA
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Pushing Gravity: new perspectives on Le Sage’s theory of gravitation
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9
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edited by Matthew R. Edwards (Montreal: Apeiron 2002)
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10
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James Evans
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Fig. 1. Georges-Louis Le Sage (1724-1803), in an eighteenth-century engraving. Photo courtesy of Bibliothèque publique et universitaire, Ville de Genève.
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2. Le Sage’s Theory in Bare Outline
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Le Sage imagines that the observable universe is bathed in a sea of ultramundane corpuscles—called ultramundane (ultramondain) because they impinge on us from outside the known universe. These corpuscles have the following properties: minute mass, enormous speed, and complete inelasticity. Now, all apparently solid objects, such as books and planets, are mostly void space. Consequently, gross objects absorb but a minuscule fraction of the ultramundane corpuscles that are incident upon them.
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From these premises Le Sage deduces an attractive force between any two gross objects. Imagine two macroscopic bodies, as in the top portion of Fig. 2. Let us refer to the body on the left as L and the body on the right as R. Ultramundane corpuscles rain on these bodies from both left and right. A small fraction of the corpuscles incident from the left is absorbed by L. Therefore, R stands in the shadow of L: Body R receives fewer corpuscles from the left than it does from the right because of the screening action of L. Consequently, R will be pushed toward the left by the uncompensated corpuscles that are incident from the right. In the same way, L also stands in the shadow of R and experiences an effective force towards the right. The two bodies which appear to pull on one another are actually pushed together. To complete the picture, we must now imagine ultramundane corpuscles incident on the bodies, not just from the left and right, but along all possible trajectories. Le Sage’s theory can be made quantitative, as he certainly intended it to be. With the right auxiliary assumptions it does produce an attraction of two bodies in direct proportion to
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Gravity in the Century of Light
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11
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the product of their masses and in inverse proportion to the square of the distance between them.3
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The goal of this article is to set Le Sage’s theory in historical context. We shall begin by surveying attitudes towards gravity as they developed in the century preceding Le Sage. Then we shall turn to Le Sage’s intellectual development, his construction of his theory, and his efforts to win a hearing for it. Finally, we shall examine the reception of the theory by Le Sage’s contemporaries.
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3. Explaining Gravity: From Descartes to Huygens and Newton
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In Paris, on several consecutive Wednesdays of the year 1669, the newly established Royal Academy of Sciences held a debate on the cause of weight.4 Gilles Personne de Roberval read the first memoir on the subject on August 7.
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Fig. 2. Pairs of macroscopic bodies traversed by currents of ultramundane corpuscles. From Le Sage’s Essai de chymie méchanique. Photo courtesy of the Library of the Royal Society, London.
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12
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James Evans
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Roberval divided physical thinkers into three schools: (1) some hold that weight resides in a heavy body; (2) others make it common and reciprocal between the heavy body and the body towards which it gravitates; (3) yet others make it an effect of a third body, which pushes the heavy body. All attempts at establishing a mechanism naturally belong to the third school of thought. As Roberval pointed out, the thinkers of this school all have recourse to a subtle body which moves with extreme rapidity, which insinuates itself among the particles of larger bodies, and thus produces the effects of weight and levity. Roberval pointed out the following difference between the thinkers of the third school and those of the other two camps. Those who ascribe weight to the very nature of the heavy body, or to the common nature of two bodies, make weight the cause of motion; but those of the third school want motion to be the cause of weight. Roberval also remarked that all three opinions were the products of pure thought and had nothing solid to support them. But the first two schools had this advantage, that once postulating the quality, they explained everything without effort. But the third school, after postulating its subtle fluid, still had a good deal of work to do. For his own part, Roberval suspected that men might lack the special sense required to know anything of this subject, in the same way that the blind cannot know anything of light or colors.
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The next Wednesday, Nicolas Frenicle asserted that one must admit the reality of attraction. He pointed out analogies between weight and the attraction of a magnet for iron, of amber for dry things, and of drops of mercury for one another. But one week later, Jacques Buot objected to those who spoke of a virtue or desire for union between the particles of a body. No one, he said, had ever conceived the cause of such desires or affections in inanimate things. He then turned to the vortex theory of Descartes.
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In his Principles of Philosophy (1644) Descartes had imposed upon natural philosophy stringent new rules of explanation.5 Descartes banished the occult qualities of the medieval scholastics, such as sympathy, affinity and attraction (characteristic of Roberval’s first two schools of thought), and insisted that all natural phenomena be explained by the impact of contiguous bodies upon one another. This way of thinking about nature came to be called “mechanical philosophy.” According to Descartes, the planets are carried around the Sun by a vortex (tourbillon) of celestial fluid. The weight of a body at the surface of the Earth is also due to a vortex of celestial fluid. This subtle fluid, seeking to recede from the center of its vortex, impels the ordinary terrestrial matter towards the center. In one of his published letters, Descartes even described a demonstration to illustrate his theory of weight. Fill a round vessel with fine lead shot. Among this shot place some pieces of wood, lighter and larger than the shot. If you then turn the vessel rapidly, “you will find that this small shot will drive all these pieces of wood … toward the center of the vessel, just as the subtle matter drives the terrestrial bodies.”6 Descartes realized that in his explanations of celestial and terrestrial phenomena he had granted himself considerable freedom to invent invisible mechanisms. To forestall his critics, he
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claimed that he offered these mechanisms only as hypotheses. Moreover, even if these hypotheses happened to be false, they could still be valuable. A false hypothesis that successfully accounts for the phenomena could be as useful as the truth itself.7 Nevertheless, Jacques Buot, in his discourse of August 21, 1669, accepted Descartes’ explanation of weight as fully established.
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Christiaan Huygens read his own paper on August 28. Huygens’ contribution was an important one, for he was the first to suggest a mechanism for gravity that was supported by calculation. He brought to bear his own new theorem on circular motion in order to estimate the speed of the matter in the ethereal vortex. In this he raised the argument over the cause of weight to a new level—a fact not immediately appreciated by his contemporaries. He raised the level of discourse in another way, by his avoidance of circularity of thought in his explanation and his criticism of Descartes for just such a failing. Huygens pointed out that while Descartes’ demonstration experiment certainly works, it works only because the lead and wood have different densities. That is, Descartes had to assume inherent differences in weight—which were supposed to be a product of the explanation, not a part of the premise. Although Huygens stressed that his theory of weight was different from that of Descartes, it nevertheless was certainly in the Cartesian tradition. In 1690, Huygens published his Discourse on the Cause of Weight, in which he presented his theory of gravity, reworked and expanded, but unchanged in its essence.8
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In this debate at the Paris Academy, which occurred nearly two decades before the publication of Newton’s Principia, we can already see the shape of the larger and more vociferous debate that followed the enunciation of the law of universal gravitation. Newton chose his title carefully and meant it as a rebuke to Descartes: these were not vague and sloppy “principles of philosophy” but rather Mathematical Principles of Natural Philosophy. In the preface to the first (1687) edition Newton asserted that the whole burden of philosophy is “to discover the forces of nature from the phenomena of motions and then to demonstrate the other phenomena from these forces.”9 To the second edition of 1713 he added the celebrated General Scholium, in which he feigned no hypotheses about the cause of gravity: “For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy.”10 In renouncing metaphysical and occult qualities, Newton was only endorsing what Descartes had begun. But in attacking physical or mechanical hypotheses, he was attacking Descartes himself and the whole school of Cartesian mechanical philosophy.
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It was possible for Newton to make a point of renouncing mechanical hypotheses because the plan of his Principia did more or less correspond to the burden of natural philosophy: induction of the inverse-square law of gravitational attraction from the phenomena, and deduction of new phenomena from the force law. But Newton’s rejection of hypotheses in the General Scholium was also partly a rhetorical device, introduced to answer the critics of the first
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James Evans
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edition of the Principia who complained that he had not given the cause of gravity, and that he had even reintroduced the occult forces of the medieval scholastics.
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Newton himself was certainly not the positivist that later generations made of him. In his youth he was steeped in the vortices of Descartes and he abandoned them only after a struggle. While composing the Principia, Newton still thought the vortices at least to be worth refuting as a mechanical cause of gravity. At the end of Book II he took pains to show they could not be made consistent with Kepler’s laws of planetary motion. But even then Newton did not cease speculating about the cause of gravity. In his Opticks he was inclined to attribute the effects of gravity to the same ethereal medium as was responsible for the refraction of light. Newton held that this ether was most rare inside bodies and that it increased in density with distance from the surface of a body. Thus, the ethereal medium was far denser in the outer parts of the solar system than in the vicinity of the Sun. According to Newton, if the elastic force of this medium is sufficiently great, “it may suffice to impel bodies from the denser parts of the medium towards the rarer, with all that power which we call gravity.”11
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The intellectual heritage of Newton was therefore ambiguous. The Newton of the Principia had renounced mechanical hypotheses as vain speculation and had asserted that it was enough to be able to calculate the effects of gravity. The Newton of the Opticks, confronted by a host of new optical phenomena, was far more speculative: so little was known about the nature of light that one had to seek explanations below the surface of the visible phenomena. In the development of eighteenth-century epistemology, it was the Newton of the Principia who weighed most heavily. This is clear, for example, in the article “Hypothesis” published in the Encyclopédie of Diderot and d’Alembert.12 The article takes a sensible middle ground, saying that there are two excesses to avoid in the matter of hypotheses—either to put too much faith in them, as did Descartes, or to proscribe them entirely. According to the Encyclopédie, Newton and especially his disciples fell into this contrary error. “Disgusted with the suppositions and errors with which they found the philosophical books filled, they protested against hypotheses, they tried to render them suspect and ridiculous, calling them the poison of reason and the plague of philosophy.” The Encyclopédie points out, accurately, that Newton himself used hypotheses (what else is the principle of universal gravitation?). But the key point is that Newton was believed to have been unalterably opposed to the use of hypotheses in natural philosophy. As the eighteenth century progressed, there was a decided shift toward the positivistic position. This did not happen all at once. But by the time Le Sage began to promote his mechanical theory of gravity, principled agnosticism about the cause of gravity was well on its way to becoming the majority position among the first rank of physicists. As we shall see, this attitude had major consequences for the reception of Le Sage’s theory.13
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Gravity in the Century of Light
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15
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4. Sources and Development of Le Sage’s Theory
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Georges-Louis Le Sage was educated at a private grammar school and then at the Collège de Genève. But his education was greatly supplemented at home through the efforts of his father, who stressed languages and—after a fashion— the sciences. The father, also called Georges-Louis Le Sage, was a teacher of philosophy, a writer of books, a man of strong opinions, skeptical of pretentious learning, rankled by the power of privilege in Genevan political affairs. His influence over his son’s development was considerable for both good and ill. On the one hand, he read works in Latin and in English with his son and drove him to study hard. But he was strong-willed and overbearing and Le Sage never fully escaped from his domination until his father’s death. A strong sense of the father’s personality can be had from his Hazarded Thoughts on Education, Grammar, Rhetoric and Poetics, in which his philosophy of education is expressed in a series of caustic aphorisms:
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There is a great deal of charlatanry in the notebooks from which the professors crib to their pupils. Sometimes these are only disguised copies of books already published, unknown to the pupils; and often these notebooks fall into contempt, as soon as they are published.
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Systems that fix one’s ideas favor the laziness of masters and disciples, and are contrary to the search for truth.
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The fruits that one draws from algebra are not of a sufficiently general usage to make this science enter into the ordinary course of studies.
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In the renovation of philosophy, the great aid that Galileo, Kepler, Descartes and others had drawn from geometry in order to improve physics made many people believe that the study of geometry rendered the mind exact and capable of reasoning well on everything. But the oddities that one has seen certain mathematicians produce on matters that do not have quantity as the object clearly make one see the opposite. There are no people more distracted, and less capable of applying themselves to the affairs of civil life, than the poets and the geometers.
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Physics is necessary to Great Lords so that they may protect themselves against two sorts of people to whom they are continually exposed: empirics and chemists.14
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Le Sage père also wrote a textbook of physics, the first to be published at Geneva.15 However, he reassured his readers that he would spare them any mathematics. Le Sage’s physics textbook therefore consists of a series of short sections surveying subjects of traditional interest. Although a reader of Le Sage’s textbook would not have learned up-to-date physics—let alone the mathematical methods of physics—the book is interesting in its CartesiNewtonian stance. Thus, Le Sage père prefers to explain weight in terms of vortices. But on the controversial issue of the shape of the Earth, he favors Newton’s spheroid flattened at its poles. This is all the more remarkable because Le Sage’s textbook of physics was published in 1732, before the famous expedition to Lapland by the French Academy of Sciences decisively settled the question of the Earth’s shape. It seems that the hand of Descartes weighed less heavily in francophone Geneva than in France.
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16
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James Evans
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Nevertheless, the physics textbook of Le Sage père was, in its essence, a collection of facts and pronouncements. Apparently, his conversation was of the same nature. He liked to express his decisions in proverbs or maxims, which he used as unanswerable arguments to shut off discussion. The father, in short, had no sympathy for protracted lines of reasoning or for anything systematic in education. System was what the young Georges-Louis craved. When they read English together, the son would ask his father for the meanings of the roots of words that they encountered. This information the father refused to give, on the grounds that the root changed its meaning in composition. And when the young Georges-Louis set up his little scientific experiments, he found that his apparatus was not respected by the household. Nevertheless, the father helped to stimulate Georges-Louis’ interest in natural philosophy by pointing out curious phenomena to him and by his oracular remarks upon them.
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The boy began to read Lucretius, in Latin, with his father at the age of thirteen and was profoundly affected by the ancient atomist. The Greek school of atomic physical theory was founded in the fifth century B.C. by Leucippus and Democritus; but, apart from a few quotations by later writers, nothing of their work survives. The most important Greek atomist is Epicurus (341-270 B.C.), who elaborated the atomic theory of Democritus and who also introduced a major ethical component into his philosophy, even going so far as to make physics subservient to ethics. Lucretius (c. 99-55 B.C.) was the author of De rerum natura (On the Nature of Things), a verse exposition of the philosophy of Epicurus, with considerable emphasis on his physical doctrines. The Latin poem was popular in the Enlightenment for its exaltation of scientific rationalism and its denunciation of traditional religion as the principal source of mankind’s fear of death and of the gods. That Le Sage’s father was fond of Lucretius is clear from the frequent citations of the Roman poet in his textbook of physics.
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Not only the rationalism of Lucretius but also the atomic doctrine itself appealed to the boy’s imagination. Lucretius was bold in inferring facts about the invisible world of the very small from the phenomena of everyday life. Atoms are invisible, but so are many other things whose effects show them to be corporeal, such as wind. That invisibly small bodies do in fact exist is clear from the phenomenon of scent, from the evaporation of water, and from the wearing away of the right hands of metal statues, over the years, as passers-by grasp them for good luck. That void exists is clear as well, or else bodies could not be penetrated, nor would it be possible for things to move. The porosity of objects and the existence of atoms of different sizes is clear from the fact that light can penetrate horn, but water cannot. How else can this be explained but by supposing that the atoms of light are smaller than those of water?16
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Arguments of just this sort had currency in eighteenth-century mechanical philosophy. In principle, Descartes himself was not an atomist, for he believed neither in void spaces nor in the existence of irreducibly small, fundamental constituents of matter. Nevertheless, in many of his explanations of phenomena
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Gravity in the Century of Light
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17
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Descartes had recourse to mechanisms involving invisible particles. And some of Descartes’ contemporaries developed mechanical philosophies that were forthrightly corpuscularian, Pierre Gassendi being a notable example. The ancient atomic philosophy of Lucretius resonated strongly in many eighteenthcentury minds.
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Already at the age of thirteen Le Sage began to wonder about gravity. When he asked his father why the Earth doesn’t fall, his father replied, “It is fixed by its own weight,” and added that he ought to find it even more amazing to see other objects fall. In his teens, Le Sage enrolled at the Academy of Geneva, where he learned some mathematics under Cramer and some physics under Calandrini.17 While at the academy he achieved celebrity by refuting a supposed quadrature of the circle. Near the end of his academic studies he met Jean-André Deluc in the mathematics classes. They became good friends and maintained a constant correspondence. Deluc recorded a conversation that occurred about this time: Le Sage pointed out that a horse which appears to pull a cart is actually pushing against the breast-piece of the harness.
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After Le Sage left the Academy, his father pressed him to choose a vocation. What attracted Georges-Louis above all else were philosophy and physics. His mother and father, who disagreed about all else, were united in opposition. To them, the situation of a man of letters was the least desirable of all. This situation, to which the father felt himself reduced and to which the son certainly would be reduced, amounted to living on the proceeds of a few private lessons. The son would have to choose a real career. Georges-Louis hesitated between theology and medicine and eventually decided on the latter. His father sent him to study at Basle. He spent a year at the university, without great benefit. But while there, he happened to hear Daniel Bernoulli, in an inaugural lecture, discuss the possible existence of certain magnitudes so enormous or so small that they revolt the imagination. At a later stage of his development, Le Sage was to draw on the corpuscular theory of gases in the 10th chapter of Bernoulli’s Hydrodynamics.18
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After his year in Basle, Le Sage went to Paris to continue his medical studies. At his father’s insistence, he refrained from studying higher mathematics. But in Paris the deficiencies of his education in physics and mathematics began to dawn on him. In a letter to his father, after listing several very well known books of physics that he had never read, he added that the situation was still worse when it came to mathematics. Here he entered into great detail in order to disabuse his father, who still flattered himself that he had taught the boy quite enough to battle with the savants of Paris. Some of the things he did not know, Georges-Louis wrote, were for these savants only the A, B, C of mathematics. However, he won friends and respect by demonstrating the falsity of a supposed perpetual motion machine.
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Quite by accident, he came across a copy of La Caille’s Elementary Lessons in Astronomy, which he found at a friend’s house, on the mantle of a fireplace. After reading through some of the articles, he read the conclusion, where
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18
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James Evans
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La Caille set down the obligation of the physicist: to explain all of astronomy in terms of mechanics. This grand idea echoed in his mind for weeks. And whenever he thought about it, he saw as a means of explanation only his atoms.
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As at Basle, Le Sage supplemented his allowance by tutoring. When he abruptly lost his position with a wealthy family, he found time to take up his old meditations on the cause of gravity. Then, on January 15, 1747, at 11:30 in the evening, he wrote to his father:
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||
Eureka, Eureka. Never have I had so much satisfaction as at this moment, when I have just explained rigorously, by the simple laws of rectilinear motion, those of universal gravitation, which decreases in the same proportion as the squares of the distances increase. I had already four years ago a new idea on the mechanism of the universe: only two things impeded me—the explanation of the repulsion that one observes in the particles of certain elements and the law of the square of the distances. Now I found the first of these things the day before yesterday, and the second only a moment ago. The whole almost without seeking it and even in spite of myself.19
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He finished his letter with a dream: “perhaps this will win me the prize proposed by the Academy of Paris on the theory of Jupiter and Saturn.”
|
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His father’s response was to cut short his stay in Paris, although he had not yet finished his medical studies. When Le Sage returned to Geneva, his father pressed him to begin a medical practice, in spite of Georges-Louis’ protests that he did not know anything about medicine. The father precipitated matters by inserting in a paper printed at Geneva a notice that read: G.-L. Le Sage, young physician of Geneva, offers his service to the public. Now this advertisement caused a scandal, for it flouted Genevan law. Le Sage’s mother was a native of Geneva, but his father was not. (He had emigrated from France as a Protestant refugee from religious persecution.) Consequently, although Le Sage himself had been born in Geneva to a mother born in Geneva, he was not of bourgeois status. As a member of a lower legal class (the class of natifs), he was forbidden by law to practice the professions, including medicine. Although this law had been in temporary abeyance, his father’s advertisement outraged the authorities, who restored it to its former force and handed down a formal prohibition against Le Sage’s practice of the profession of medicine. This shock opened the eyes of his father, who finally gave up trying to direct him.
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This run-in with the magistrates was also a contributing cause in the composition of a political pamphlet by Le Sage’s father. A pamphlet titled The Spirit of the Laws and consisting of 103 aphorisms appeared in Geneva in 1752. Though anonymous, and clearly borrowing its title from the famous book of Montesquieu, the pamphlet was soon traced to Georges-Louis Le Sage père. The Small Council (the executive governing body of Geneva) found that the pamphlet contained “dangerous maxims against Religion and the Government” and decreed that the pamphlet should be suppressed and all copies of it withdrawn. In truth, there was little of religious import in the pamphlet, except a plea for religious tolerance, in emulation of the English, and an expression of
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preference for natural religion. The truly seditious part of the pamphlet was its attack on aristocracy and hereditary privilege: “Every perpetual privilege which is not useful to the Generality is an injustice. Such were the privileges of the patricians among the Romans…. If all men are born equal, a privilege which is an exception to the law is contrary to natural law.”20
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If young Georges-Louis were really to pursue a career in medicine, one hope yet remained: to get hold of enough money to purchase bourgeois status. To Georges-Louis there seemed but one way to do it: win the prize for 1748 offered by the Paris Academy for a treatment of the theory of irregularities in the motions of Jupiter and Saturn. Le Sage sent in a hastily composed piece, called Essai sur l’origine des forces mortes (Essay on the origin of dead forces), which bore the epigraph “plus ultra.” Le Sage ignored the prize topic and instead outlined his theory of gravity. But it was all for naught, since his contribution arrived too late and was refused by the Academy’s secretary, Fouchy. A memoir by Euler was crowned—a memoir that actually treated the prize question and that brought to bear the whole power of contemporary mathematical methods. No better demonstration could be wished of Le Sage’s isolation from the real concerns and methods of mid-eighteenth-century mathematical physics.
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Four years later, the Academy of Sciences announced a second prize competition on the same subject. Le Sage, still full of hope, reworked and sent once more to the Academy his Essai sur l’origine des forces mortes. This time it bore as brave epigraph two lines from Lucretius:
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Debent nimirum praecellere mobilitate Et multo citius ferri quam lumina solis.
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Most certainly they must be of exceeding swiftness and must be carried far more quickly than the light of the Sun.
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Lucretius, De rerum natura II, 161-162 (trans. Rouse).
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As before, Le Sage’s goal was the explanation of gravity itself and he ignored the prize question except in its most general connection with his own topic. After a long delay, he learned the inevitable—Euler had won again21—and Le Sage finally renounced all hope of a career in medicine.
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When the chair of mathematics came empty at the Academy of Geneva, Le Sage aspired to fill it. In those days, however, candidates for academic positions at Geneva were required to participate in a public competition. Le Sage, afflicted with a debilitating timidity, withdrew from the competition. Throughout his life, he made ends meet by living with the utmost frugality and by giving private lessons in mathematics. Georges-Louis Le Sage settled into the life from which his father had most wished to preserve him, that of an impoverished man of letters.
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Around this time, Le Sage learned he had been anticipated in his principal idea, the explanation of attraction by rectilinear impact. It was his former professor, Gabriel Cramer, who told him about Fatio. Nicolas Fatio de Duillier
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20
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James Evans
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(1664-1753) was born at Basle, but his family settled near Geneva and obtained bourgeois status in 1678. By the age of seventeen Fatio had invented a new method for measuring the distance between the Earth and the Sun and had offered an explanation of the ring of Saturn. He became well known for his development of J.D. Cassini’s explanation of the zodiacal light. After living in Paris and in Holland, in 1688 he settled in England and was named a member of the Royal Society. By 1689 he had become a close friend of Isaac Newton. The exact nature of their relationship has been the subject of controversy— some holding that they were lovers, others that Newton may only have been Fatio’s “alchemical father.” In any case, their four-year-long relationship was intense and its rupture played a role in Newton’s mental breakdown of 1693. After that, Fatio turned to millennialism and prophecy and became closely involved with the Camisard refugees from France. He collaborated in the printing and distribution of a book of the prophecies of Elie Marion, a book that was attacked as both blasphemous and seditious. This led in 1707 to Fatio’s trial and condemnation to the pillory. In December of that year he was exposed for one hour on two successive days at Charing Cross and at the Royal Exchange, with a notice attached to his hat: “Nicolas Fatio convicted for abetting and favouring Elias Marion, in the wicked and counterfeit prophecies, and causing them to be published, to terrify the queen’s people.” After his release, he wandered as a missionary across Europe, as far as Asia Minor, eventually resettling in England in 1712. However, Fatio did not completely abandon his scientific interests, for he published some minor works on navigation and other subjects late in his life.22
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Fatio had in 1690 presented to the Royal Society of London a corpuscular theory of gravity remarkably like that of Le Sage.23 However, Fatio had not worked out the consequences of his hypotheses in detail, and in any case he had never published his treatise.24 Late in his life, Fatio returned to this subject. In 1729 he composed a Latin poem on the cause of weight, in the style of Lucretius, which he submitted to a scientific competition of the Paris Academy of Sciences. When this failed, he conceived the hope of dedicating this poem to the Royal Society of London.
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Since neither of Fatio’s works on the cause of weight were published— neither the French-language treatise of 1690 nor the Latin poem of 1729—one may well ask how Le Sage’s teacher, Gabriel Cramer, learned of Fatio’s theory. Apparently, the connection was as follows. Fatio’s elder brother had, around 1700, made a copy of Fatio’s treatise on the cause of weight. When the brother died in 1720, this copy passed to his nephew and heir, Jean-Ferdinand Calandrini of Geneva. Another member of the Calandrini family, Jean-Louis Calandrini (1703-1758), was Cramer’s fellow teacher at the Academy of Geneva. Cramer became sufficiently interested in Fatio’s theory to use it as a source of theses for his students.25 Indeed, in 1731 Cramer’s student Jalabert defended at Geneva thirty-seven physico-mathematical theses concerning weight.26
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Gravity in the Century of Light
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21
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The academic custom of defense of theses descended from the disputations of the medieval universities. In the eighteenth century these affairs served two different purposes. Some disputations were only for exercise (“exercitationis causa”). Others were doctoral disputations (“disputatio inauguralis” or “pro gradu”), held to establish the fitness of the student for the doctorate. In either case, the list of theses, or positions, to be defended was published and the defense itself was a public event in which the student was examined orally. Rarely were these lists of theses intended to be original contributions to learning. Customs varied from place to place and evolved with time. In the seventeenth century, the theses were generally written by the professor under whose presidency the theses were defended, even though in the published document the student might be identified as “author.” Not surprisingly, the theses of a disputation often paralleled the contents of a professor’s course, perhaps with the addition of a few original theses at the end, contributed by the student with the professor’s approval. Sometimes a professor held a series of disputations (each at a different date and with a different student) on a common subject, and after conclusion of the series published the whole thing as a textbook. As the eighteenth century wore on, there was a shift toward the writing of the theses by the student.27
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In Cramer’s examination of Jalabert on weight, it appears that the majority of the 37 theses were composed by Cramer himself and that they reflected the contents of a course Jalabert had taken from him. Most of the 37 theses concerned theories elaborated by Copernicus, Kepler, Descartes, Malebranche, Newton and others. But the final few theses bore on the theory of Fatio, without, however, mentioning him by name. It seems that for Jalabert himself, the ultimate cause of weight was theological.
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After learning of Fatio, Le Sage scrupulously gave him credit in all his writings and often mentioned Cramer and Jalabert as well. Moreover, Le Sage went to great trouble to collect some of Fatio’s papers, which Pierre Prévost deposited in the library at Geneva after Le Sage’s death. There they still remain. Le Sage even began to gather materials to assist him in writing a life of Fatio, which he never completed.28 Le Sage’s interest in preserving Fatio’s memory was no doubt strengthened by the fact that Fatio had connections to Geneva. But when Le Sage learned of a dissertation by a German physician named Redeker29 with similar ideas about weight, he took care also to mention this predecessor.
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These, then, were Le Sage’s principal influences: Le Sage père, Lucretius, Daniel Bernoulli, La Caille, Fatio, and, of course, Newton. The haphazard nature of his preparation reflects not only his isolation, but also his mental disorganization, which was a fundamental aspect of his personality. Le Sage wrote much but published little. Indeed, he was almost incapable of finishing a treatise. He strove to meet every imaginable objection. Worse, his memory failed him and he found himself rewriting fragments of a composition that he had begun, laid aside, then utterly forgotten. He jotted his thoughts down on the backs
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22
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of playing cards, which he kept in separate envelopes and boxes labeled with thematic titles. There still exist in the archives of the University of Geneva some 35,000 of Le Sage’s annotated playing cards, many of them indecipherable.30 Among his writings was a collection of jottings headed “on the immiscibility of my thoughts with those of others.”
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5. Gravitation and Generation
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Shortly after his return to Geneva, Le Sage became a friend of Charles Bonnet (1720-1793), who provided him encouragement and moral support. Like Le Sage, Bonnet was educated at the Academy of Geneva. But because he was several years older than Le Sage, they do not appear to have become close until later. Bonnet’s first scientific work was in entomology. He produced a sensation in the early 1740s with his discovery that the aphid reproduces parthenogenetically (i.e., “by virgin birth”). After Abraham Trembley’s discovery of animal regeneration in the polyp, or fresh-water hydra, Bonnet demonstrated that fresh-water worms also could regenerate when cut into pieces. The polyp posed a difficulty in classification: was it plant or animal? On the one hand it reproduced by budding and could regenerate itself from cuttings, which seemed plant-like. On the other hand, it was capable of motion and obviously fed by ingestion. But for Bonnet the most vexing problem posed by the polyp was metaphysical: if both halves of a cut polyp could become intact animals, what did this say about the existence of animal soul?31
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A childhood illness had left Bonnet practically deaf. And in 1745 he became nearly blind. He led a sedentary existence, scarcely leaving his wife’s estate at Genthod, except for short visits to Geneva. In his later work, Bonnet turned increasingly to theory, partly because of his own metaphysical predisposition, but partly because the loss of his sight left him unable to pursue the experimental and observational approach that had characterized his early work. In his Considerations on Organized Bodies,32 Bonnet took a highly speculative and hypothetical approach to explaining the mysteries of generation and development. A number of reviewers of this book complained that it was full of conjectures.
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Bonnet’s most widely read work was his Contemplation of Nature. This was not a technical report of his researches, but rather a popular meditation on the Great Chain of Being, which links the Creator to all His creatures. The inanimate and the animate form a scale of insensibly small steps, from rocks and crystals to plants to simple organisms to sensate and intelligent animals. The polyp naturally serves as the link between plant and animal. In the preface to Contemplation of Nature, Bonnet responds to the attacks on his earlier work on generation and to the complaints that he hypothesized too freely. “What author,” he asks, “has distinguished more carefully than I the facts from their consequences, immediate or mediate?” The accusation that he had muddied the distinction between the facts and his own conjectures clearly vexed him—he
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Gravity in the Century of Light
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23
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“who had so often protested against the abuse of conjectures and of hypotheses.”
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Bonnet mentions two great enigmas that physicists and natural historians have so far been unable to penetrate: the cause of weight and the mystery of generation. And here he inserts a sympathetic reference to Le Sage’s attempt to find the true cause of gravity, without, however, mentioning Le Sage by name:
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The great NEWTON abstained from seeking the cause of weight. An estimable physicist [Le Sage] modestly tries to explain it; he has recourse to an ingenious hypothesis, which happily satisfies the phenomena, & which he nevertheless gives only for what it is. Our zealous writers immediately put him on trial, condemn him without understanding him, praise to the point of breathlessness the reserve of NEWTON, which they understand no better, and finish by declaiming against the Spirit of System.33
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According to Bonnet, the Naturalist or the Physicist ought to confront his critics with these words: “I beg the true physicists to tell me if I have so far reasoned correctly, if I have violated the facts, if I have contradicted my principles.” Bonnet ends by pleading: “To banish entirely from physics the art of conjecture would be to reduce us to pure observation; and what use would these observations be to us, if we were not to draw from them the least consequence?”
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In Charles Bonnet, then, Le Sage found a kindred spirit—a fellow Genevan who felt one had to take risks to infer the order of nature behind the facts of observation, and who felt that he had been unfairly criticized for doing so, that he had been lumped together with vain and careless systematizers. Le Sage and Bonnet maintained a lively correspondence. Their conversations and letters were full of corpuscles. Bonnet took to signing his own letters Anaxagoras and to addressing Le Sage sometimes as Leucippus, but more often as Democritus. Le Sage spoke continually of writing a great History of Weight, which would treat the whole history of attempts to explain gravity, from antiquity to the eighteenth century, culminating in Le Sage’s own final explanation. Bonnet urged him to leave off revising and to publish. Bonnet pleaded with Le Sage to ignore the ancient adage of Horace, that one should correct a work for nine years before publishing: it was enough to correct it for nine months.34
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6. Winning a Hearing
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The first published sketch of Le Sage’s theory had appeared in the popular miscellany Mercure de France in May, 1756. In the February issue, an anonymous academician of Dijon had published an article that ascribed gravity to the action of light. The author did not sign his piece, preferring not to attach his name to the theory until he could develop it more fully. In his response, Le Sage agreed with the academician on the necessity of attributing gravity to a rectilinear impulsion (as opposed to the circular or vortical impulsion that characterized the theories of Descartes and Huygens). But he gently criticized
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24
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the academician for not having done his literature search, and for failing to cite earlier theories of the same sort, most notably that of Jean Bernoulli. Le Sage then thoroughly refuted Bernoulli’s theory. At the close of the piece, Le Sage explained how the academician might improve a gravitation theory based on rectilinear impulsion and, in so doing, briefly outlined his own theory of gravity, while giving most of the credit to Fatio.35
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In 1758 the Academy of Rouen held a prize competition on the following subject: “To determine the affinities that exist between mixed principles, as begun by Geoffroy36; and to find a physico-mechanical system for these affinities.” The point of the competition was to explain chemical affinity. But Le Sage, like many of his time, believed that one explanation would be found to underlie both the laws of chemistry and the law of universal gravitation—a point of view that persisted well into the nineteenth century. Accordingly, Le Sage’s Essay on Mechanical Chemistry, 37 submitted for the competition, is an attempt to account for chemical affinity by the same mechanism that explains universal gravitation.
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In the introduction to this work, Le Sage remarks that chemists are not comfortable with algebra and that he will therefore explain his theory in ordinary language, relegating a few calculations to the back of the work. The basic phenomenon to be explained is attraction. According to Le Sage, attraction is called gravitation if the bodies are separated from one another and cohesion if they are in contact. Thus gravity, cohesion and chemical affinity are all aspects of a single more general phenomenon. Le Sage attempts to lead his readers inexorably through a sequence of arguments that develop all the features of his theory of attraction:
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● Whenever we have discovered the true cause of some change in state of a body, we have found that it is due to impulsion. For example, the rise of a column of water in a pump is due to the pressure of the air. Thus it is reasonable to suppose that the approach of two attracting bodies toward one another is actually due to the impulsion of some sort of invisible matter. This argument takes its strength from the following axiom: “similar effects come from similar causes.” Or, if we prefer, we may regard it as a proof by analogy, which, according to Le Sage, is the strongest kind of proof in physical reasoning.
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● Because the matter that produces the attractions of bodies does not offer sensible resistance to their motion, its parts must give free passage to them. Thus, the invisible matter must be fluid.
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● This fluid must travel faster than the bodies it causes to accelerate. Because the acceleration of a falling body does not cease even when the body is moving rapidly, the speed of the fluid must be very great. In remarks added to the Mechanical Chemistry after the period of the competition, Le Sage used an argument from planetary motion to show that the speed of the fluid must be at least 1013 times the speed of light. And here he again quoted those lines from Lucretius: “Most certainly they must be
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Gravity in the Century of Light
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of exceeding swiftness/ and must be carried far more quickly than the light of the Sun.” ● Since all bodies fall toward the center of the Earth, the fluid must be able to move through a single space simultaneously in all directions. Thus the parts of the fluid must be isolated from one another. This fluid therefore consists of discrete corpuscles, which do not interfere with one another in the least. ● Curvilinear motion is forced. Once the generator of the force is removed, curvilinear motions immediately become rectilinear. Since the corpuscles of the fluid do not interfere with one another, but move with complete freedom, their paths must be rectilinear. And here Le Sage could not resist inserting a remark about the wrong-headedness of the old doctrine of vortices. ● The weights of objects do not sensibly decrease under roofs. Thus, the corpuscles must be very small, or subtle, and roofs must be porous. Indeed, the pores of bodies must be a very great proportion of the bodies themselves, so that the corpuscles have nearly free passage through the bodies. For the gravitation of celestial bodies is very nearly in proportion to the quantity of their matter, and this could not be the case if the outer layers of a body absorbed a sensible fraction of the incident corpuscles.
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Thus Le Sage has led us inexorably to “corpuscles, isolated, very subtle, which move in straight lines, in a great number of different directions, and which encounter very porous bodies. Voilà, therefore, the only possible material cause of attraction.”
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Le Sage believes that the final cause of the corpuscles that produce the effects of gravity is an incorporeal being, who launched them into motion at the moment of creation. In view of the enormous speed of the corpuscles, those that reach the Earth today must have traveled an immense distance since the beginning of the world. Those that will reach us tomorrow will have traveled an even more immense distance. Since these corpuscles come to us from outside the known universe, they are called ultramundane.
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Le Sage deduces the inverse-square law simply by the following verbal argument. Imagine a physical point, that is, a small spherical region of space, traversed by currents of ultramundane corpuscles traveling in all directions. The number of corpuscles that cross a unit of area on the surface of this small sphere will be spread out over a correspondingly larger area on the surface of a larger surrounding sphere, in such fashion that the number crossing through a unit area will fall off as the inverse square of the distance. And this is exactly analogous to the law of the decrease of the intensity of light.
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After developing the general principles of attraction in the course of his discussion of gravitation, Le Sage turns to cohesion. The basic phenomenon to be explained is the fact that two bodies made of the same substance attract more strongly than two bodies made of different substances. Thus two drops of oil, or two drops of water, will attract each other and unite, which is not the
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Fig. 3. Pierre Prévost (1751-1839), Le Sage’s pupil and disciple. Oil portrait by F. Langlois after a drawing by Mme. Munier-Romilly. Photo courtesy of Bibliothèque publique et universitaire, Ville de Genève. It was Prévost who read Le Sage’s Newtonian Lucretius before the Academy of Berlin and who published some of Le Sage’s works after Le Sage’s death.
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case for a drop of oil and a drop of water. Moreover, even when we consider the attraction of like for like, different substances manifest this attraction with different forces. For example, two drops of oil attract one another with greater force than two drops of water of the same size. In his Mechanical Chemistry Le Sage accounts for chemical affinity by introducing ultramundane corpuscles of various sizes, as well as pores of various sizes in ordinary bodies, as shown in Fig. 2. Attraction is strongest for bodies that have similar pores. This represents an obvious generalization of his theory of gravity.
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The Essay on Mechanical Chemistry was the first complete exposition of Le Sage’s theory of gravity. The essay was crowned by the Academy of Rouen for its treatment of the second (theoretical) part of the prize question. In 1761, Le Sage had copies of the essay printed, but it never was published in any regular way. Le Sage hoped that it would eventually form a part of a collection of related essays that might be published as a book. This never happened, so Le Sage contented himself with giving copies of Mechanical Chemistry, from
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Gravity in the Century of Light
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27
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time to time, to those he hoped would be interested, usually with a handwritten title page placed over the printed treatise. There is a copy of Mechanical Chemistry in the library of the Royal Society of London that was sent by Le Sage in 1774. The printed treatise is accompanied not only by the handwritten title page but also by an elaborate hand-written synopsis, which doubles as a table of contents. Apparently, Le Sage realized that his argument in Mechanical Chemistry was too long for most readers. The handwritten synopsis is a useful and concise addition.
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As mentioned above, Le Sage won the prize for the second, or theoretical, part of the competition on the nature of affinity sponsored by the Academy of Rouen. The first, or experimental, part of the competition was won by JeanPhilippe de Limbourg, a physician of Liège, who had his own treatise printed in 1761.38 At the end of his book, Limbourg included a general account of the ideas in Le Sage’s Mechanical Chemistry. This was the first published discussion of Le Sage’s theoretical views by another writer. About thirteen years later, a chemist and apothecary named Demachy discussed both of these treatises on affinity. But Demachy did not have a copy of Le Sage’s Mechanical Chemistry, and based his account of Le Sage’s theory on the synopsis that had been given by Limbourg.39 Le Sage complained bitterly of the short shrift he had been given by Limbourg, as well as of the inaccuracies in Demachy’s account, based as it was on the imperfect summary by Limbourg.40 Here we see foreshadowed the fate of Le Sage’s system. It was, throughout its life—and this includes the period of its nineteenth- and twentieth-century revivals—more often talked about than read in the original. But a large part of the responsibility for this rests with Le Sage himself for his failure to publish.
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The Essay on Mechanical Chemistry is burdened with much that is irrelevant to gravitation. A more succinct exposition of the theory is Le Sage’s Newtonian Lucretius, which in 1782 was read by his pupil and disciple, Pierre Prévost, before the Royal Academy of Berlin, where Prévost was resident as a member.41 (See Fig. 3.) Le Sage seeks to combine the principles of atomism (hence Lucretius) with those of Newton. The paper is organized around a fanciful conceit: Le Sage describes how the ancient atomists of the Lucretian school might have hit upon the law of Newtonian gravitation if they had only followed Le Sage’s train of thought. This mode of exposition could hardly have helped Le Sage win adherents. Nevertheless, Newtonian Lucretius was the chief published form of the theory available to Le Sage’s contemporaries. It bore as epigraph a quotation from Fontenelle’s elegy of Cassini:
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In every matter, the first systems are too limited, too narrow, too timid. And it seems that truth itself is the reward only of a certain boldness of reason.
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The most systematic account of Le Sage’s theory is his Mechanical Physics,42 which was pieced together from his notes and drafts by Pierre Prévost after Le Sage’s death. However, the Mechanical Physics was not published until 1818, it does not seem to have been widely read, and it had little effect on the debate over Le Sage’s theory of gravitation.
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7. Reception of the Theory: Attitudes toward Explanation in Physics
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Le Sage’s most effective manner of promoting his system was not by publication, but rather by private letter. He argued for the ultramundane corpuscles in a lively correspondence that included most of the scientific luminaries of his day. For this reason, Le Sage’s voluminous correspondence is an excellent resource for the study of eighteenth-century attitudes toward hypotheses in physics. In 1774, Le Sage sent a copy of his Mechanical Chemistry to Matthew Maty, secretary of the Royal Society of London. Le Sage also sent to Maty a long letter43 in which he recounted the frustrations he had experienced in trying to win a hearing for his theory. Le Sage gives a perceptive and often touching account of the reactions he had provoked and of the objections he had attempted to answer. He writes that when he tried to lead certain enlightened persons to accept his mechanism, he “sensed on their part an extreme repugnance quite independent of its more or less perfect accord with the phenomena.”
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Some correspondents insisted on an analogy. That is, Le Sage was asked to point to another physical phenomenon in which similar principles were at work. “And, not having found in my mechanism a perfect analogy with any known mechanism, except only a considerable analogy with light, I despaired of ever being able to convince those people.”
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Some of those to whom Le Sage tried to communicate his theory “found it easier to pass judgement on hypothesis [itself] than to examine my distinction between solid hypotheses and those which are not. And one continued to spout at me gravely with the most trivial commonplaces against hypotheses taken in a very vague sense.”
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Other critics wished Le Sage to prove that gravity “is not an essential quality of matter, nor ... the immediate effect of divine will.” To satisfy the scruples of these people, he had to “go back to metaphysics,” which he “had abandoned a very long time ago.”
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Others maintained that even if he had established the reality of his system, he “still would have satisfied only a vain curiosity, which is no longer in fashion in this century, in which one devotes oneself only to useful knowledge.” To answer these people, Le Sage felt compelled to examine the advantage that physics and metaphysics would draw from his making known the nature and cause of gravity.
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It is indeed possible to find most of these responses in letters from the leading philosophers of the day to Le Sage. Leonhard Euler is a good example of those who asked for analogies and then remained unimpressed by what Le Sage could produce. When people complained to Le Sage that they could neither visualize nor accept the currents of ultramundane particles traversing every small volume of space simultaneously in hundreds of thousands of different directions, he tried to soothe them by offering an analogy to light. Particles of light stream constantly in all directions, without disturbing one another in the least. Euler was not assuaged. He wrote bluntly:
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Gravity in the Century of Light
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Without engaging myself in an examination of whether such an infinity of currents in all directions would be possible, or could continue for a single instant without disturbing itself, I remark only that the proof drawn from the movement of light has no weight with me, since I am convinced that light is not at all hurled from luminous bodies, but that it is propagated from them in the same manner as sound from sonorous bodies, without anything really escaping from bright bodies.44
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In a debate by correspondence that stretched over several years, Euler had begun by agreeing with Le Sage on the importance of banishing from physics attraction and cohesion, along with the ancient occult qualities. He congratulated Le Sage for his efforts, but held out for waves in an ethereal fluid as the probable mechanism of gravity. Le Sage made Euler admit that the properties of the light-carrying ether were incapable of explaining gravity too. But then Euler fell back on a second ether, much more subtle and elastic, for the explanation of gravity. Finally, he could no longer contain his disgust:
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And so you will excuse me, Monsieur, if I still feel a very great repugnance for your ultramundane corpuscles; and I would always rather admit my ignorance of the cause of gravity than to have recourse to hypotheses so strange.45
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For metaphysical objections to Le Sage’s theory, we can find no richer source than the letters of Roger Boscovich to Le Sage. Boscovich granted that in his Mechanical Chemistry Le Sage had succeeded where Descartes, Huygens and Bulfinger had all failed: he had explained how gravity could be produced by the impulsion of a material substance that still produced no sensible resistance to motion.46 But Boscovich withheld approval. This most radical of atomists found Le Sage’s system “unnatural” and branded it an arbitrary hypothesis. Moreover, Boscovich objected that each ultramundane corpuscle served a function only during the very short time that it was in the act of colliding with a heavy object, and that this was a minuscule fraction of the corpuscle’s duration. But Boscovich’s strongest aversion to the theory was due to the extraordinary number of ultramundane corpuscles required. Since heavy bodies stopped but a tiny fraction of the corpuscles incident upon them, the great majority of corpuscles were superfluous, for they never collided with any heavy object. This implied an extravagant wastefulness on the part of the Creator. In vain did Le Sage respond that one could suppress all the superfluous corpuscles once one admitted perfect foresight on the part of the Creator: He need only have created those corpuscles that had the right initial conditions of velocity and position actually to encounter some heavy object in the course of their travels.
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If we can discern any pattern in the objections of Le Sage’s correspondents it is this. Many of the older mathematicians and philosophers—people who had been born between 1700, say, and 1720—were willing to debate the physical mechanism responsible for gravitation. They were still mopping up after the great battle that had banished occult qualities from physics. Gravitation had to be reducible to mechanics: this was an article of their faith. However,
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most people who took this point of view already subscribed to some other mechanical system and were therefore unlikely to be converted to Le Sage’s views. So we have seen in the cases of Euler and Boscovich.
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The most sympathetic of Le Sage’s correspondents of this generation was Daniel Bernoulli, who was pleased to see Le Sage drawing on his corpuscular theory of gases. And, like many of his contemporaries, Bernoulli was sympathetic to the effort to reduce gravity to mechanics. But, while heaping general praise upon Le Sage, Bernoulli withheld approval of his system.47 Bernoulli considered his own corpuscular theory of gases to be unproved, “a pure hypothesis, and even a rather gratuitous hypothesis.”48 And so he could hardly agree with Le Sage that the existence of ultramundane corpuscles had been proved beyond a reasonable doubt.
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Younger people—those born in the 1730s and 1740s—were accustomed to using gravitational attraction as a demonstrated fact without troubling themselves over its causes. They had become convinced of the fruitlessness of pursuing mechanical hypotheses that always were more or less arbitrary and that were not susceptible of proof. The battle that had expunged occult qualities from physics belonged to the remote past. These younger physicists simply had little interest in the underlying cause of gravitation and little confidence that the cause could be discovered. This attitude is often called Laplacian, but we find it already present in people who reached maturity well before Laplace.
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A good example is provided by the response of the French astronomer, Jean-Sylvain Bailly. After receiving a lengthy letter in which Le Sage explained his system, Bailly replied in friendly form and praised Le Sage for the profundity of his subject and his reasoning. And yet, we encounter a note of irony in his praise and an unanswerable rebuff in his confession of faith:
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I do not flatter myself, Monsieur, to delve as you do into the principles of Nature; I have, at most, the strength to follow you. But I have followed you with pleasure; and, not being strong enough to make you objections, I limit myself to making you my profession of faith. I am a Newtonian: I am even led to believe that gravity is a property of matter....49
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Bailly complacently indicated a willingness to accept an ethereal fluid that reduced gravitation to impulsion, “provided that this fluid explains everything and without effort.” But, clearly, a man ready to accept gravity as an inherent property of matter was going to have a low tolerance for effort in any sort of mechanical explanation.
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8. Laplace’s Response and Implications for Celestial Mechanics
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Pierre-Simon Laplace (1749-1827) was the foremost mathematical physicist of his generation. He is best known for his Celestial Mechanics, which appeared in five volumes between 1799 and 1825 and which put this science on a new and more systematic foundation. Although Laplace never gave Le Sage’s theory serious consideration, he was influenced by it to explore two effects that
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would represent departures from the Newtonian theory: a finite speed of
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propagation of gravity and a resistive force experienced by the planets in their
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orbits. Le Sage’s friend and compatriot, Jean-André Deluc, was in Paris in
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1781, where he was on friendly terms with Laplace and tried to interest him in
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Le Sage’s theory. Laplace declined to be draw in, but did admit to an interest in
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exploring the resistive force implicit in Le Sage’s sea of corpuscles:
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Before pronouncing on this subject, I have taken the course of waiting until M. Sage has published his ideas; and then I propose to pursue certain analytical researches that they have suggested to me. As for the particular subject of the secular equations of the motion of the planets, it has appeared to me that the smallness of that of the Earth would imply in the gravific fluid a speed incomparably greater than that of light, and all the more considerable as the Sun and the Earth leave a freer passage to this fluid, which conforms to the result of M. Sage. This prodigious speed, the immense space that each fluid molecule traverses in only a century, without our knowing where it comes from or where it goes or the cause that has put it into motion—all that is quite capable of terrifying our weak imagination; but in the end, if one absolutely wants a mechanical cause of weight, it appears to me difficult to imagine one which explains it more happily than the hypothesis of M. Sage….50
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Indeed, it is not difficult to show that Le Sage’s hypothesis leads to an ef-
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fective attractive force Fatt that conforms to Newton’s law of gravitation. If M1 and M2 are the masses of two infinitesimal bodies, the force that one exerts upon the other is
|
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Fatt
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=
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kM1M 2 r2
|
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||
,
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where r is the distance between the bodies and k is a constant that depends
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upon properties of the sea of ultramundane corpuscles. It turns out that k, the
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constant of universal gravitation, is given by
|
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k
|
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=
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nm 4π
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v2
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f
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||
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2
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,
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where m is the mass of a single ultramundane corpuscle, n is the number of
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corpuscles per unit volume of space, v is the speed of the corpuscles (assumed
|
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||
for simplicity to be the same for all) and f is a (presumably universal) constant
|
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with dimensions of area/mass. f is the cross-sectional area for collision pre-
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sented to the corpuscles by a macroscopic object of unit mass. (Here it must be
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emphasized that Le Sage himself never published such formulas.)
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As we have seen, in Le Sage’s system, apparently solid objects must be
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made mostly of empty space. In his Mechanical Physics, Le Sage speculated
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that the atoms of ordinary matter are like “cages”—that is, they take up lots of
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space, but are mostly empty. In this way, ordinary objects block only a tiny
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fraction of the ultramundane corpuscles that are incident upon them. Other-
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wise, as Le Sage himself points out, merchants could change the weights of
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their stuff by arranging it in wide, thin layers (in which case it would weigh
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more) or in tall piles (in which case it would weigh less). More significantly for
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James Evans
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precision measurement, the gravitational attraction of the Moon toward the
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Earth would be diminished during a lunar eclipse because of the interposition of the Earth between the Sun and the Moon, a phenomenon that has never been noticed by the astronomers. Thus, in order to have a theory consistent with the phenomena, f must be so small that even planet-sized objects absorb a negligi-
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ble fraction of the corpuscles incident upon them. The constant of universal gravitation k can be made to agree with the facts no matter how small we make f, provided that we suitably increase n or v.
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There is an unwanted side effect in Le Sage’s system, to which Laplace
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refers. Planets traveling through the sea of corpuscles will be slightly retarded.
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This is the effect to which Laplace refers under the rubric of secular equations.
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A body of mass M1 moving through the sea of ultramundane corpuscles will experience a resistive force Fres that is proportional to the speed u of the body:
|
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Fres
|
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=
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4 3
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||
M1
|
||
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||
fnmvu
|
||
|
||
.
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The resistive force is directed oppositely to the body’s velocity u. (Again, Le Sage himself did not publish such a formula.) Since no resistance of this kind had been detected, it was necessary to insist that the resistive force suf-
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|
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fered by a planet be much smaller than the attractive force exerted by the Sun
|
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|
||
on the planet. Thus, if we let M1 denote the mass of a planet and M2 that of the Sun, we require
|
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Fres Fatt << 1.
|
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Upon substitution of the expressions for the forces, we obtain
|
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|
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u r2 << 1. v fM 2
|
||
M2, u and r (the mass of the Sun, the speed of the planet and the radius of the planet’s orbit) are not adjustable. Thus we are led to the conclusion that the speed v of the corpuscles must be very large. Moreover, since we need f to be
|
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|
||
very small, we are forced to make v even greater. This is what Laplace meant
|
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|
||
when he said that the smallness of the secular equation of the Earth “would imply in the gravific fluid a speed incomparably greater than that of light, and all the more considerable as the Sun and the Earth leave a freer passage to this
|
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|
||
fluid.” The prodigious velocity required for Le Sage’s corpuscles appears, more than many other features of the theory, to have repelled Laplace.
|
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Some years later, after the publication of Laplace’s Exposition of the System of the World, Le Sage wrote to express his disappointment that Laplace
|
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|
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had not discussed his mechanical theory of gravity. Laplace’s reply drew a clear boundary between his generation’s way of doing physics and the old mechanical philosophy espoused by Le Sage:
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||
If I have not spoken in my work of your explanation of the principal of universal weight, it is because I wanted to avoid everything that might appear to be based upon a system. Among philosophers, some conceive of the action of bodies upon one another only by means of impulsion and, to them, action
|
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33
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at a distance seems impossible. Your ingenious manner of explaining universal gravitation, in proportion to the masses and in reciprocal proportion to the square of the distances, should satisfy these philosophers and bring them to admit this great law of nature, which they would reject despite the observations and all the calculations of the geometers, if it were well demonstrated to them that it could result from impulsion.
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Other philosophers, on the contrary, admit their ignorance on the nature of matter, of space, of force and of extension, and trouble themselves little about first causes, seeing in attraction only a general phenomenon which, being subjectable to a rigorous calculation, gives the complete explanation of all the celestial phenomena and the means of perfecting the tables and the theory of the motion of the stars. It is uniquely under this point of view that I have envisaged attraction in my work.
|
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Perhaps I have not had enough consideration for the first philosophers of whom I have just spoken, in not presenting to them your manner, as simple as ingenious, of bringing the principle of weight back to the laws of impulsion; but this is a thing that you have done in a manner leaving nothing to be desired in this regard. However, I propose to calculate in my Treatise on Celestial Mechanics the deteriorations that must result from your hypotheses in the long run in the mean motions and the orbits of the planets and the satellites.51
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Laplace did, indeed, include calculations in the fifth volume of his Celestial Mechanics which grappled with some of the consequences of Le Sage’s theory. But even here Laplace did not see fit to mention Le Sage by name.52
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9. Le Sage’s Legacy
|
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Modern historians of science often do not know what to do with Le Sage. Many regard Le Sage’s system as bizarre or even worse. One writer has characterized it as “imprecise, qualitative and even retrogressive.”53 But Le Sage’s contemporaries did not deny that his system accomplished its aim, i.e., that its premises did, indeed, result in Newtonian gravitation. And, contrary to the impression given by some recent writing, Le Sage was a good Newtonian and he fought hard in one of the last rear-guard actions of the anti-Newtonians.
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In 1773 Le Sage unmasked as frauds two purported experiments reported in the Journal des Beaux-Arts & des Sciences by a mysterious Jean Coultaud and a certain Mercier. These writers claimed to have performed pendulum experiments on mountains in the Alps, near villages that they named, in which a pendulum was found to swing more rapidly at the summit of a mountain than near the mountain’s base. These results led Coultaud and Mercier to the conclusion that the weights of objects increase with their distance from the center of the Earth, in accordance with some versions of Cartesian vortex theory. This claim was rebutted by leading Newtonians, including d’Alembert and Lalande, who attributed the anomalous results to localized density variations. Le Sage went a long step farther. He began an investigation, making use of his network of correspondents, friends and relatives. Le Sage proved that the experiments had never taken place and that “Coultaud” and “Mercier” were fictitious per-
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34
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James Evans
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sons. Le Sage scored a victory for Newtonian gravitation in one of the strangest controversies of the day.54 This detective work helped win him election as a foreign member of the Royal Society of London. He had already been named a correspondant of the Paris Academy of Sciences. Thus, it is clear that his contemporaries regarded him as a legitimate member of the international community of physicists, even though very few of them endorsed his system.
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||
The views of some modern writers that Le Sage was an apostate antiNewtonian, and that his system was only qualitative, derive partly from Le Sage’s failure to clothe his exposition in adequate mathematical dress, and partly from the peculiarities of his character and his manner of exposition, which made him seem strange in his own day and which make him appear even more so today. Equally important, Le Sage’s theory and Le Sage’s methods of argument were in conflict with the prevailing anti-hypothetical epistemology of his day, as we have seen by examining his scientific correspondence. Most of Le Sage’s converts were people who knew him personally and who had some connection with Geneva. Examples include Deluc, Prévost and the English experimental scientist and radical politician, Charles Stanhope, whose son was a pupil of Le Sage’s at Geneva. Horace-Bénédict de Saussure, although not exactly a convert, did discuss Le Sage’s theory in his physics courses at the Academy of Geneva.
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||
In spite of the defects and obscurity of Le Sage’s publications, he succeeded in making his theory widely known through correspondence. The international scientific connections of Geneva helped to a great extent. Moreover, Geneva was an important destination and stopping point for well-heeled travelers of all sorts, including those with interests in the sciences.55 It is likely that most savants who passed through Geneva over a period of two generations heard something of Le Sage’s theory. By 1770 his theory was well enough known in France to be the subject of a disputation at Lyon. There a student named Sigorgne defended some theses under the presidency of Professor P.-F. Champion combating the opinions of Le Sage on attraction.56 This was not what Le Sage would have wished, of course, but at least it meant that his theory was being noticed.
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Le Sage’s friends did their part to popularize his ideas. As we have seen, Prévost was responsible for the publication of Newtonian Lucretius in the French-language memoirs of the Berlin Academy. Deluc harangued Laplace about the system in a series of letters. And, of course, Prévost saw Le Sage’s posthumous Mechanical Physics through the press in 1818. Moreover, both Deluc and Prévost mentioned Le Sage’s system in some of their own published works. In his Researches on the Modifications of the Atomosphere (1772), Deluc made a number of sympathetic references to Le Sage and his theory.57 More significantly, Prévost in his On the Origin of Magnetic Forces (1788), gave a brief but coherent overview of Le Sage’s theory, made a case for its importance, and pleaded with his readers to suspend judgment until Le Sage had a chance to publish his own proofs of the theory.58
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Both Deluc’s and Prévost’s books received translations into German.59 Indeed, it was largely from the German translation of Prévost’s book that the philosopher F.W.J. von Schelling learned of Le Sage’s theory. In Germany, the mechanical physics of Le Sage was usually seen as a rather repellant competitor to the dynamical view of nature proposed by Kant and most famously developed by Schelling under the rubric Naturphilosophie. For Schelling, Le Sage’s theory was simply anathema. Thus Schelling devotes long parts of his Ideas for a Philosophy of Nature to an attack on Le Sage’s view of the world. Schelling mocks Le Sage for merely showing “that the fall of bodies can be very intelligibly explained by reference to things that we know nothing whatever about.” Moreover, Schelling criticizes Le Sage’s whole approach to knowledge with this complaint: “The mechanical physics begins with postulates, then erects possibilities upon these postulates, and finally purports to have constructed a system that is beyond all doubt.”60 This was not quite fair to Le Sage, who believed that he had carefully applied the method of exclusion to eliminate all other possible explanations of gravity. Only a few German writers of the older generation, who deplored the excesses of both Romanticism and metaphysics, tended to be sympathetic to Le Sage. This was the case with the physicist Georg Christoph Lichtenberg, who was attracted to Le Sage’s theory.61 In the Germany of Naturphilosophie Lichetenberg was, of course, a lonely exception. Nevertheless, the prominence of Schelling’s attack on Le Sage’s theory at least guaranteed that it would not be forgotten.
|
||
In Britain, Le Sage’s views were helped by the relocation of Jean-André Deluc. For in 1773 Deluc moved to England, where, the following year, he took the official position of Reader to Queen Charlotte, the wife of George III. As a scientist of reputation and a fellow of the Royal Society, he had many opportunites to enlighten his English friends on the cause of gravity. In Britain, as well as in France and Germany, Le Sage’s theory became a part of the common knowledge of physical thinkers. If his works were rarely read, his ideas nevertheless remained in circulation. Le Sage’s theory even enjoyed a brief revival in the Victorian period because of the enthusiasm of William Thomson, Lord Kelvin.62
|
||
As we have seen, Le Sage’s theory of the ultramundane corpuscles failed to affect mainstream thinking about gravity. However, Le Sage’s ideas about discrete gases (of which the ultramundane corpuscles are a special case) did have a remarkable influence in the development of one branch of physics—the theory of thermal equilibrium, especially in the case of phenomena involving radiant heat. Around 1790, Marc-Auguste Pictet of the Academy of Geneva discovered an astonishing fact: radiant cold could be reflected and focused by mirrors in the same way as radiant heat. In his experiment, Pictet used a pair of concave tin mirrors facing one another across a distance of 10 feet. A sensitive air thermometer was placed at the focus of one mirror. When a flask of snow was placed in the focus of the second mirror, the thermometer immediately descended. This experiment posed quite a puzzle. Some thinkers were used to re-
|
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36
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James Evans
|
||
|
||
garding cold as a mere negative, a privation of heat. Under this view it was difficult to see how cold could be radiated and reflected. Nearly everyone regarded thermal equilibrium as a static situation. Two objects in thermal equilibrium were like two springs in contact, each under the same tension. Pierre Prévost explained the paradoxical experiment by introducing the idea of dynamic equilibrium. According to Prévost, two objects in thermal equilibrium constantly emit and absorb particles of heat in a balanced, mutual exchange. Prévost took this idea, as he tells us himself, directly from Le Sage, and used it to explain Pictet’s experiment in complete detail.63 Pictet’s experiment on the radiation and reflection of cold was the immediate stimulus for the researches of Benjamin Thompson, Count Rumford, into a whole host of thermal phenomena.
|
||
|
||
Acknowledgement
|
||
I am grateful to Christiane Vilain, Frans van Lunteren and Rienk Vermij for insights into eighteenth-century academic customs, to Roger Hahn for alerting me to a letter of Laplace, to Theodore Feldman for information about Le Sage’s relations with Jean-André Deluc, and to Alfred Nordmann for communications about Lichtenberg’s interest in Le Sage. The University of Puget Sound generously provided research support that made it possible to consult rare publications. Thanks are also due to the efficient and helpful staffs of the Bibliothèque Publique et Universitaire de Genève and the Library of the Royal Society (London) for providing microfilm copies of manuscripts.
|
||
|
||
Notes
|
||
1 “The standard model” is, of course, a term of late twentieth-century particle physics. John Heilbron has applied this term in a useful way to the set of widely accepted physical tenets of the late eighteenth century. J.L. Heilbron, Weighing Imponderables and Other Quantitative Science around 1800. Historical Studies in the Physical and Biological Sciences, Supplement to Vol. 24, Part 1 (1993). See especially pp. 5-33. For a discussion of gravitation theory as the embodiment of a worldview, see F.H. van Lunteren, “Gravitation and Nineteenth-Century Worldviews,” in P.B. Scheurer and G. Debrock, eds., Newton’s Scientific and Philosophical Legacy (Dordrecht: Kluwer, 1988). For more detail, see the same author’s doctoral dissertation, Framing Hypotheses: Conceptions of Gravity in the 18th and 19th Centuries (Rijksuniversiteit Utrecht, 1991).
|
||
2 For Le Sage the best biographical source, on which all later accounts depend, is the book by Le Sage’s pupil and disciple, Pierre Prévost, Notice de la vie et des écrits de George-Louis Le Sage de Genève (Genève: J. J. Paschoud, 1805). Useful brief notices are found in the following works. Jacques Trembley, ed., Les savants genevois dans l’Europe intellectuelle du XVIIe au milieu du XIX siècle (Genève: Editions du Journal de Genève, no date but c. 1987), pp. 117-119, 413. Frank A. Kafker and Serena L. Kafker, The Encyclopedists as individuals: a biographical dictionary of the authors of the Encyclopédie. Studies on Voltaire and the Eighteenth Century 257 (Oxford: Voltaire Foundation, 1988), pp. 223-226. By far the most important source of unpublished manuscripts is the large collection of Le Sage papers at the Bibliothèque Publique et Universitaire de Genève (cited below as BPU).
|
||
3 For other discussions of Le Sage’s theory see the following. Samuel Aronson, “The Gravitational Theory of Georges-Louis Le Sage,” The Natural Philosopher 3 (1964) 51-74. William B. Taylor, “Kinetic Theories of Gravitation,” Annual Report of the Board of Regents of the Smithsonian Institution for the Year 1876 (Washington: Government Printing Office, 1877), 205-282, on pp. 217-221. However, Taylor mistakenly brushes aside Le Sage’s theory as not meeting its goals. The survey by S. Tolver Preston, “Comparative Review of some Dynamical Theories of Gravitation,” Philosophical Magazine, 5th Series, 39 (1895) 145-159, is still useful, although Preston’s evaluations of the
|
||
|
||
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merits of the various theories can safely be ignored. These sources provide citations of many nineteenth-century discussions of Le Sage’s theory, including the attempted revival of the theory by William Thomson, Lord Kelvin, and the subsequent criticism by Maxwell. For this episode the key sources are William Thomson, “On the Ultramundane Corpuscles of Lesage,” Philosophical Magazine, 4th Series, 45 (1873), 321-345 and J.C. Maxwell, “Atom,” Encyclopædia Britannica (1875 and later editions), reprinted in W. D. Niven, ed., The Scientific Papers of James Clerk Maxwell, 2 vols. (Cambridge: Cambridge U. P., 1890), Vol. 2, 445-484. 4 An account of the debate, with texts of the communications, is available in Oeuvres complètes de Christiaan Huygens publiées par la Société Hollandaise des Sciences, Vol. 19 (La Haye: Martinus Nijhoff, 1937), pp. 628-645. 5 René Descartes, Les principes de la philosophie, in Oeuvres de Descartes, ed. by Charles Adam and Paul Tannery, Vol. IX-2 (Paris: J. Vrin, 1978). The Principles of Philosophy was written in Latin and was published in 1644 under the title Principa philosophiae. The first publication of the French translation was in 1647. 6 Descartes to Mersenne, 16 octobre 1639, in Oeuvres de Descartes, Vol. II, pp. 593-594. This letter was first published by Clerselier in 1659, in the second volume of his edition of Lettres de Mr Descartes. 7 Descartes, Principes de la philosophie, Part 3, Paragraph 44, in Oeuvres de Descartes (Ref. 5), Vol. IX-2, p. 123. 8 Christiaan Huygens, Discours de la cause de la pesanteur (Leiden: Pierre vander Aa, 1690), reprinted in Oeuvres complètes de Christiaan Huygens, Vol. 21 (1944). 9 Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy, trans. by I. Bernard Cohen and Anne Whitman (Berkeley: University of California Press, 1990), p. 382. Newton restated the same position near the end of Query 28 of the Opticks. 10 Newton, Principia, trans. Cohen and Whitman, p. 943. 11 Isaac Newton, Opticks, based on the fourth edition of 1730 (New York: Dover, 1952). Query 21, pp. 350-351. In Newton’s view, then, gravity is a sort of hydrostatic force, and not a dynamical one as in the theory of Huygens. The first edition of Opticks appeared in 1704. Later editions differed largely in the expansion of the Queries. Query 21 first appeared in the second English edition of 1717. 12 “Hypothèse,” Encyclopédie, ou dictionnaire raisonné des sciences, des arts et des métiers, Vol. 8 (Paris: 1765), pp. 417-418. This article was written by the abbé Jean-Baptiste de La Chapelle, one of the principal contributors on mathematics. 13 For a philosophical perspective on Le Sage’s confrontation with the anti-hypothetical epistemology of his day, see: Larry Laudan, “George-Louis LeSage: A Case Study in the Interaction of Physics and Philosophy,” in Akten des II. Internationalen Leibniz-Kongresses Hanover, 17-22 Juli 1972, vol. 2 (Wiesbaden: F. Steiner, 1974), pp. 241-252. Larry Laudan, “The medium and its message: a study of some philosophical controversies about ether,” in G.N. Cantor and M.J.S. Hodge, eds., Conceptions of Ether (Cambridge: Cambridge U.P., 1981). 14 Georges-Louis Le Sage (père), Pensées hazardées sur les études, la grammaire, la rhetorique, et la poëtique (La Haye: Jean Van Duren, 1729), pp. 59, 74, 101, 100, 104. The dates of Le Sage père are 1684-1759. For useful remarks on the place of Le Sage père and fils in Genevan scientific culture, see Burghard Weiss, “Zur Newton-Rezeption der Genfer Aufklärung,” Philosophia Naturalis 23 (1986) 424-437. 15 Georges-Louis Le Sage (père), Cours abrégé de physique, suivant les derniers observations des Académies Royales de Paris & de Londres (Genève: Frabri & Barrillot, 1732). 16 Lucretius, De rerum natura, ed. and trans. by W.H.D. Rouse, revised by M.F. Smith, 2nd ed., Loeb Classical Library (Cambridge: Harvard U. P. ; London: William Heinemann, 1975), Book 1, lines 265-357; Book 2, lines 381-397. 17 The mathematician Gabriel Cramer (1704-1752) is best known for “Cramer’s rule” and other work on determinants. Jean-Louis Calandrini (1703-1758) helped edit a Latin edition of Newton’s Principia, published at Geneva, 1739-1742, to which he added several chapters of commentary. He claimed to have discovered, six years before Clairaut, Newton’s error in the treatment of the motion of the lunar apogee. A valuable account of the cultural matrix of Genevan science, including a discussion of education under Cramer and Calandrini, is given by Virginia P. Dawson, Nature’s Enigma: The Problem of the Polyp in the Letters of Bonnet, Trembley and Réaumur, Memoirs of the American Philosophical Society 174 (Philadelphia: 1987), pp. 51-83.
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18 Daniel Bernoulli, Hydrodynamica, sive de viribus et motibus fluidorum commentarii (Strasbourg: Johann Reinhold Dulsecker, 1738). Hydrodyanmics by Daniel Bernoulli and Hydraulics by Johann Bernoulli, trans. by Thomas Carmody and Helmut Kobus (New York: Dover, 1968).
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19 Prévost, Notice de la vie (Ref. 2), pp. 50-51. 20 André Gür, “Un précédent à la condamnation du Contrat social: l’affaire Georges-Louis Le Sage
|
||
(1752),” Bulletin de la Société d’Histoire et d’Archéologie de Genève 14 (1968) 77-94. 21 Euler’s piece that won the prize awarded for 1752 was called “Recherches sur les irrégularités du
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mouvement de Jupiter et de Saturne” and was published in Recueil des pièces qui ont remporté les prix de l’Académie Royale des Sciences, Vol. 7 (Paris: Panckoucke, 1769). Euler’s piece that won the prize for 1748 was called “Recherches sur les inégalités du mouvement de Saturne et de Jupiter.” It was printed in 1749. It is found bound at the end of some, but not all, copies of Vol. 6 of the Recueil (1752). 22 The most complete biographical study is Charles Andrew Domson, Nicolas Fatio de Duiller and the Prophets of London: An Essay in the Historical Interaction of Natural Philosophy and Millennial Belief in the Age of Newton (Ph. D. dissertation, Yale University, 1972). Domson argues that Fatio’s religious fanaticism, which is usually described as a tragic falling away from Newtonianism, was actually a consequence of the influence of Newton himself. 23 For more on Fatio’s theory and Newton’s view of it, see the article by Frans van Lunteren in this volume. For the text of Fatio’s treatise (never published in his lifetime), see Bernard Gagnebin, “De la cause de la pesanteur: Mémoire de Nicolas Fatio de Duiller présenté à la Royal Society le 26 février 1690,” Notes and Records of the Royal Society of London 6 (May, 1949) 105-160. 24 It must also be said that Fatio’s explanation is difficult to follow, since he postulates several orders of particles in nature, with varying degrees of elasticity and hardness. On the one hand, he insists that either the corpuscles responsible for the effects of weight or the bodies that they impinge upon must be like perfect springs. On the other hand, he insists that there must be inelasticity somewhere, in order to produce a loss of motion in the corpuscles. See Gagnebin, “De la cause de la pesanteur” (Ref. 23), pp. 128-129. Inelasticity is, indeed, the key idea. For if the interactions are perfectly elastic, they will not produce an effective attractive force between two macroscopic bodies. Air molecules are a concrete realization of a sea of elastic corpuscles: obviously, ordinary objects immersed in the atmosphere are not pressed together. 25 This trajectory was constructed by Horst Zehe, Die Gravitationstheorie des Nicolas Fatio de Duiller (Hildesheim: Gerstenberg Verlag, 1980), p. 279. 26 Gabriel Cramer, Theses Physico-Mathematicae de Gravitate, …, quas Deo dante, sub Praesidio D.D. Gabrielis Cramer, tueri conabitur Johannes Jallabert, Author (Genevae: 1731). For a brief discussion of this document of 27 pages, see Zehe, Die Gravitationstheorie des Nicolas Fatio (Ref. 25), pp. 279-280. Cramer’s student, Jean Jalabert (1712-1768), was ordained a minister and became a theologian. But in 1737 he took the chair of experimental physics at Geneva and is best known for his work on electricity. 27 For these remarks about academic customs I am indebted to a manuscript by Rienk Vermij, provisionally titled The Reception of Copernicanism in the Dutch Republic 1575-1750 and soon to be published by Edita, the publishing department of the Royal Dutch Academy of Arts and Sciences. 28 Le Sage’s materials for a biographical notice of Fatio are preserved in Geneva, BPU, Ms. 2043. 29 [Franz Albert Redeker], Franc. Alb. Redekeri…De causa gravitatis meditatio (Lemgoviae: ex off. Meyeriana, 1736). 30 Le Sage’s playing cards have been but little studied. Many of the envelopes into which Le Sage organized them were labeled with categories of his own psychological self-examination. For a fascinating psychological portrait of Le Sage based on some of these cards, see Bernard Gagnebin, “Un maniaque de l’introspection rélévé par 35,000 cartes à jouer: Georges-Louis Le Sage,” in Mélanges d’histoire du livre et des bibliothèques offerts à monsieur Frantz Calot (Paris: d’Argences, 1960), pp. 145-157. 31 A good brief account of these experiments and their consequences for eighteenth-century metaphysics and physiology is given by Thomas L. Hankins, Science and the Enlightenment (Cambridge: Cambridge U. P., 1985), pp. 130-145. 32 Charles Bonnet, Considérations sur les corps organisés, où l’on traite de leur origine, de leur développement, de leur réproduction…. (Amsterdam: Marc-Michel Rey, 1762). 33 Charles Bonnet, Contemplation de la nature, 2nd ed., 2 vols. (Amsterdam: Marc-Michel Rey, 1769), Vol. 1, p. vi. The first edition was published in 1764.
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Gravity in the Century of Light
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39
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34 Bonnet to Le Sage, 20 juillet 1766, quoted in Prévost, Notice (Ref. 2), pp. 331-332. Bonnet to Le Sage, 12 novembre 1773, quoted in Prévost, Notice, p. 342.
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35 [Le Sage], “Letter à un académicien de Dijon, dont il a paru dans le Mercure de Février un Systême du monde, où l’on explique, par l’impulsion d’un fluide, les phénomenes que M. le Chevalier Newton a expliqués par l’attraction,” Mercure de France, May 1756, 153-171.
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36 The essential problem of chemical affinity is that a certain substance may combine easily with some substances but not with others. Suppose there are two substances A and B in combination. And suppose that A has a stronger affinity with a free substance C. If the combination AB is placed in proximity with C, then C will combine with A, leaving B free. Etienne-François Geoffroy (1672-1731) was the first to systemize such chemical knowledge in a table of affinities. Etienne-François Geoffroy, “Table des différens rapports observés entres différens substances,” Mémoires de l’Académie Royale des Sciences for 1718 (published in 1719), 202-212.
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37 Essai de chymie méchanique (privately printed; no place; no date). Le Sage wrote this piece for the prize competition of the Academy of Rouen in 1758. After it was crowned, Le Sage had it printed in 1761. The printed version was substantially revised from the version originally submitted to the academy.
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38 Jean-Philippe de Limbourg, Dissertation de Jean-Philippe de Limbourg, docteur en medecine, sur les affinités chymiques, qui a remporté le prix de physique de l’an 1758, quant à la partie chymique, au jugement de l’Académie Royale des Sciences, Belles-Lettres & Arts, de Rouen (Liège: F. J. Desoer, 1761). Limbourg’s summary of Le Sage’s theory is found on pp. 70-87.
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39 Jacques-François Demachy, Recueil de dissertations physico-chymiques présentées à différentes académies par M. de Machy, des Académies de Berlin & de Rouen, & celle des curieux de la nature, Démonstrateur de Chymie au Jardin des Apothicaires, & Maître Apothicaire de Paris (Amsterdam and Paris: Monory, 1774).
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40 “Lettre écrite à l’auteur de ce recueil par M. Lesage de Genève,” Observations sur la Physique 2 (1774) 244-246.
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41 Le Sage, “Lucrèce Newtonien,” Nouveaux Mémoires de l’Académie Royale des Sciences et BellesLettres, Année 1782 (Berlin, 1784) 404-427. Reprinted in Pierre Prévost, Notice de la vie et des écrits de George-Louis Le Sage de Genève (Genève: J.J. Paschoud, 1805). English translation in S.P. Langley, “The Le Sage Theory of Gravitation,” Annual Report of the Board of Regents of the Smithsonian Institution for the Year Ending June 30, 1898 (Washington: Government Printing Office, 1899) pp. 139-160.
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42 Le Sage, Physique mécanique, in Pierre Prévost, Deux traités de physique mécanique, publiés par Pierre Prévost, comme simple éditeur du premier et comme auteur du second (Genève: J.J. Paschoud, 1818).
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43 Le Sage to Maty, 18 avril 1774. Royal Society; Letters & Papers VI, 199. 44 Euler to Le Sage, 16 avril 1763. Quoted in Prévost, Notice (Ref. 2), 382-386. 45 Euler to Le Sage, 18 septembre 1765. Quoted in Prévost, Notice (Ref. 2), 389-390. 46 Boscovich to Le Sage, 13 juillet 1771. Quoted in Prévost, Notice (Ref. 2), 354-360. 47 Daniel Bernoulli to Le Sage, 28 mars 1761. Geneva, BPU, Ms. Suppl. 512, f. 70. 48 Daniel Bernoulli to Le Sage, 15 avril 1767. Geneva, BPU, Ms. Suppl. 512, f. 72. 49 Bailly to Le Sage, 1 avril 1778. Quoted in Prévost, Notice (Ref. 2), 299-301. 50 Laplace to J.-A. Deluc [octobre, 1781]. In the Le Sage papers, Geneva, BPU; Ms. Suppl. 513, f. 260. 51 Laplace to Le Sage, 17 germinal an V (= 6 April 1797). Geneva, BPU, Ms. Suppl. 513. 52 Pierre-Simon Laplace, Traité de mécanique céleste, vol. 5 (Paris: Bachelier, An VII-1825. Reprinted,
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Bruxelles: Culture et Civilisation, 1967). On the possibility of a diminution of the attraction by the interposition of other bodies, see Book XVI, Ch. 4, pp. 403-407. 53 J.L. Heilbron, Electricity in the 17th and 18th Centuries (Berkeley: U. of California Press, 1976), p. 76. J.B. Gough, too, has suggested that Le Sage’s system achieved only an approximation to Newton’s law of universal gravitation: see Gough, article “Le Sage,” in C.C. Gillispie, ed., Dictionary of Scientific Biography (New York: Scribner, 1970-1980). 54 James Evans, “Fraud and Illusion in the Anti-Newtonian Rear Guard: The Coultaud-Mercier Affair and Bertier’s Experiments, 1767-1777,” Isis 87 (1996) 74-107. In this paper, I have suggested that the fraudulent papers by “Coultaud” and “Mercier” were actually written by Hyacinthe-Sigismonde Gerdil (1718-1802), theologian, Cartesian philosopher, later a cardinal of the Catholic church, and, in the last years of his life, a candidate for the papacy. For a defense of Gerdil and another possibil-
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40
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James Evans
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ity, see Massimo Germano, Scienza impura nel seculo dei lumi (Torino: Levrotto & Bella, 1998), as well as an exchange of letters in Isis 90 (1999) 95-96. 55 For a list of foreign scientists who spent some time in Geneva between 1791 and 1822, see René Sigrist, Les origines de la Société de Physique et d’Histoire Naturelle (1790-1822), Mémoires de la Société de Physique et d’Histoire Naturelle de Genève, Vol. 45, Fasc. 1 (1990), pp. 209-212. For a sociological study of networks linking the Genevans with one another, as well as with foreign scientists, see Cléopâtre Montadon, Le développement de la science à Genève aux XVIIIe et XIXe siècles (Vevey: Editions Delta, 1975). 56 Papiers relatifs aux thèses soutenues à Lyon le 12 juin 1770. Geneva, BPU, Ms. 2048. 57 Jean-André Deluc, Recherches sur les modifications de l’atmosphère (Genève: 1772), Vol. I, pp. 166167, 229; Vol. II, pp. 368-369, 435-438. Deluc’s title page bears a quotation from Lucretius: “There are also a number of things for which it is not enough to name one cause….” (De rerum natura, VI, 703-704). That is, when we cannot be sure of the cause of some phenomenon, we should try to consider all the possible causes. 58 Pierre Prévost, De l’Origine des forces magnétiques (Genève: Barde, Manget et Cie, 1788), pp. 3339. 59 Jean-Andre De Luc, Untersuchungen über die Atmosphäre und die zu Abmessung ihrer Veränderungen dienlichen Werkzeuge, trans. by Joh. Sam. Traugott Gehler (Leipzig: Müller, 1776-1778). Pierre Prévost, Vom Ursprunge der magnetischen Kräfte, trans. by David Ludewig Bourguet (Halle: Waisenhaus, 1794). 60 Friedrich Wilhelm Joseph von Schelling, Ideas for a Philosophy of Nature, trans. of ed. of 1803 by Errol E. Harris and Peter Heath (Cambridge: Cambridge U. P., 1988), pp. 168 and 161. See also Reinhard Lauth, “Die Genese von Schellings Konzeption einer rein aprioristischen Physik und Metaphysik aus der Auseinandersetzung mit Le Sages spekulativer Mechanik,” Kant-Studien 75 (1988) 75-93. 61 See Paul Hahn, Georg Christoph Lichtenberg und die exakten Wissenschaften. Materialien zu seiner Biographie (Göttingen: Vandenhoeck & Ruprecht, 1927) and Armin Hermann, “Das wissenschaftliche Weltbild Lichtenbergs,” in Helmut Heissenbüttel, ed., Aufklärung über Lichtenberg (Göttingen: Vandenhoeck & Ruprecht 1974), pp. 44-59. 62 For this episode, see the article by Matthew Edwards in this volume. 63 For an account of this paradoxical experiment and Prévost’s explanation of it, see James Evans and Brian Popp, “Pictet’s experiment: The apparent radiation and reflection of cold,” American Journal of Physics 53 (1985) 737-753. For more detail on Rumford’s use of the experiment, see Hasok Chang, “Rumford and the Reflection of Radiant Cold: Historical Reflections and Metaphysical Reflexes,” Physics in Perspective (in press). A broader study of Genevan physics in the spirit of Le Sage and Prévost is given by Burghard Weiss, Zwischen Physikotheologie und Positivismus: Pierre Prévost (1751-1839) und die korpuskularkinetische Physik der Genfer Schule (Frankfurt am Main: Verlag Peter Lang, 1988).
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Nicolas Fatio de Duillier on the Mechanical Cause of Universal Gravitation
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Frans van Lunteren*
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Attempts to explain Newton’s universal attraction of material bodies date back to the early reception of Newton’s Principia (1687). In a sense, Newton himself had opened the door to the causal issue. For in the Principia Newton repeatedly stressed that he did not conceive of attraction in a physical sense, that is as an immediate action of one body upon another. ‘Attraction’ was to be understood as merely a shorthand expression for the tendency of material bodies to approach one another, whatever the cause of this tendency. It might, as far as Newton was concerned, arise from ‘the action of the aether or of the air, or of any medium whatever’.†
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But Newton’s disclaimers carried little weight. It would be hard for any reader to believe that the author was really open to the notion of bodies being driven to one another by a material fluid. For one, Newton rejected all dense fluids as being incompatible with the unhindered motion of planets and other bodies. His theory of planetary motion required a space that contained little, if any matter. How could an extremely tenuous fluid exert the immense power needed to move the massive planets towards the sun? Moreover, if Newton really believed that bodies were ‘pushed’ or ‘impelled’ rather than ‘attracted’, why use the controversial word ‘attraction’? Finally, what kind of fluid or mechanism would be able to account for the mutual endeavour of objects as small as the least particles of matter in accordance with a precise mathematical relationship?‡
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Yet some readers did not take mechanical explanation and universal attraction to be incompatible conceptions. The first conspicuous attempt to elucidate the physical cause of Newtonian gravity was made in 1690 by a gifted young Swiss mathematician and natural philosopher named Nicolas Fatio de Duillier. His current repute hinges less on his scientific advancements than on his choice of friends. For some years he was an intimate of Isaac Newton, or rather the intimate of Newton. The nature of their relationship and its sudden ending have been the subject of much speculation among historians.§
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* Institute for the History and Foundations of Science, Department of Physics and Astronomy, Utrecht University, Utrecht, The Netherlands
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† F. van Lunteren, Framing hypotheses: Conceptions of gravity in the 18th and 19th centuries (unpublished dissertation: Utrecht, 1991) 22-23; I.B. Cohen (ed.), Isaac Newton’s Philosophiae naturalis principia mathematica (Cambridge, 1972) 298.
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‡ Van Lunteren, Framing hypotheses, 23-24, 28-29, 44, 46, 50-51, 60. § F. Manuel, A portrait of Isaac Newton (Cambridge, Mass., 1968) 191-212; R. Westfall, Never at rest: a biography of Isaac Newton (Cambridge, 1980) 493-497, 516-517, 528-533, 538-539.
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Pushing Gravity: new perspectives on Le Sage’s theory of gravitation
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41
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edited by Matthew R. Edwards (Montreal: Apeiron 2002)
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42
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Frans van Lunteren
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In 1699, some years after the breach, Fatio caused a scandal by hinting publicly that Leibniz had stolen the invention of the calculus from Newton. This step triggered a series of events that eventually would bring Leibniz and his supporter Johann Bernoulli into a bitter priority conflict with Newton and his British allies, above all John Keill.* Another seven years later Fatio joined the French Camisards. The leaders of this radical Huguenot sect from the Cevennes had been exiled from France. They roamed the streets of London, prophesying the imminent millennium, holding seances and speaking in tongues. The local authorities, concerned about the public display of religious zeal, brought Fatio and his co-religionists to trial. Their sentence involved public humiliation: they were to stand on the scaffold with a paper denoting their offences.†
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Although Fatio had swiftly managed to make a reputation for himself as a mathematician, his theory of gravity failed to gain approval. His contemporaries either ignored or dismissed his causal explanation. After Fatio’s death his compatriot Georges-Louis Le Sage rescued it from complete oblivion. The latter, having developed similar views on the cause of gravity, honoured Fatio as his prime precursor. This, however, was to be only the first of a series of resurrections of the theory.‡ Few theories have met with so much resistance or even scorn and yet have shown such resilience. This fact in itself justifies an account of its first inception.
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The story, moreover, is not without interest even setting aside the later fate of the theory. For Fatio’s theory emerged from close interactions with the two most renowned mathematicians and natural philosophers of his time: Isaac Newton and Christiaan Huygens. As we will see, Fatio’s theory of gravitation was to a large extent the outcome of earlier attempts to reconcile Newton’s theory of gravity with that of Huygens. Unfortunately, his synthesis seems to have convinced neither of his mentors. Yet, unlike Huygens, Newton may well have been mildly sympathetic to Fatio’s ideas on gravitation, at least for some time. But it is hard to tell whether such appreciation concerned the theory itself or its author. For his judgement changed radically after the rift.
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This then is the story of the genesis of Fatio’s theory and its reception by his contemporaries. The first part of this essay contains a brief sketch of Fatio’s life, with special emphasis on his connections to Huygens and Newton. Subsequently, we will discuss some pre-Newtonian explanations of terrestrial gravity, including those of Fatio and Huygens. His conversion to Newton’s theory resulted in an attempt to combine Newtonian mathematical attraction with Huygens’ physical mechanism. Flawed as this attempt may have been, it con-
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* For a full account of the priority dispute, see A.R. Hall, Philosophers at war: the quarrel between Newton and Leibniz (Cambridge, 1980).
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† H. Zehe, Die Gravitationstheorie des Nicolas Fatio de Duillier (Hildesheim, 1980) 43-47. ‡ For Le Sage’s theory, see the article by James Evans in this volume. Later attempts to revive the theory are discussed in the article by Matthew Edwards .
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Fatio on the Cause of Universal Gravitation
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43
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tained the seeds of his subsequent theory of gravitation. The last part discusses the reception of Fatio’s theory.*
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Seeking patronage
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Nicolas Fatio de Duillier was born in Basel in 1664. The son of a wealthy Swiss landowner, he first received private tuition at home and afterwards continued his studies at the Académie in Geneva. His main mentor at the Genevan academy was the philosopher Jean-Robert Chouet. Chouet had broken the scholastic tradition at the academy, until then a centre of Calvinist scholarship, by introducing such novelties as Cartesian philosophy and demonstration experiments. It was probably through his influence that Fatio renounced an ecclesiastic career, disregarding the explicit wish of his father, and instead focussed on mathematics and natural philosophy.†
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Interrupting his theological studies at the age of eighteen, Fatio moved to France to assist Domenico Cassini, the famous head of the Royal Observatory. He stayed in Paris for a year and a half. The death of Colbert, the academy’s main patron, probably prompted him to return to his home town. Back in Geneva he applied his astronomical skills in a series of geodetic measurements. The proximate aim of the work, which he undertook in collaboration with his brother, was the design of a new map of the lake of Geneva and its surroundings. The ultimate goal was to gain scientific recognition abroad and perhaps even membership in the Parisian academy.
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Fatio also studied the zodiacal light, a phenomenon discovered by Cassini at the time that Fatio was in Paris. His observations resulted in an ingenious theory, which he communicated to Cassini and other acquaintances. Although Cassini presented these letters to the French academy, their effect was not what Fatio had hoped for. The members were irritated by Fatio’s circumspection in securing his priority. For Fatio had already sent a manuscript containing his theory to a Parisian journal, while postponing publication until his observations provided greater clarity.‡
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With his chances in Catholic France dwindling, Fatio placed his hopes in protestant Europe. Having heard of a French plot against the Prince of Orange, he travelled to Holland in the spring of 1686 to inform the Prince of the pending dangers. The Dutch authorities handsomely rewarded Fatio by promising him a mathematical professorship in The Hague on behalf of the state. The latter would involve a yearly stipend of twelve hundred florins. While waiting for this prospect to materialise, Fatio entered into a close cooperation with Christiaan Huygens, Europe’s leading mathematician. It was probably Huygens who had testified to Fatio’s mathematical competence.§
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* This paper is largely based upon Zehe’s aforementioned study. † B. Gagnebin, ‘De la cause de la pesanteur: Mémoire de Nicolas Fatio de Duillier’, Notes and Records of the Royal Society of London 6 (1949) 106-107; C.A. Domson, Nicolas Fatio de Duillier and the prophets of London (New York, 1981) 4-11; Zehe, Die Gravitationstheorie, 2-3. ‡ Ibid., 4-15. § Ibid., 15-19.
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44
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Frans van Lunteren
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At the time Huygens was working on two specific topics, the first being his theory of gravity and the second his method of determining the tangent to certain mathematical curves. As in Paris, Fatio adapted to the interests of his new mentor, while trying to move ahead. His own solution to the tangent problem, worked out in collaboration with Huygens, made a strong impression on the latter and cemented their relationship. In a similar vein the ambitious Fatio would eventually develop his own theory of gravity, taking that of Huygens as a starting point.
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When in the spring of 1687 the Dutch authorities still failed to deliver, Fatio decided to spend the summer in England. In London he was quick to associate himself with the leading members of the Royal Society, among them Robert Boyle. While visiting the meetings of the Society, he was informed of a forthcoming work by the Cambridge mathematician Isaac Newton that would revolutionise natural philosophy. In June Fatio was proposed for membership of the Royal Society. The final decision on his admittance, however, was not taken before the end of the year. The delay forced Fatio to extend his stay in Britain. Only in the spring of 1688 was he formally admitted as a member of the Society.
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In the following months he lectured the Society on various subjects, including Huygens’ theory of gravity. His new prominence did not, however, procure him a salaried position. But in the spring of 1689 Fatio saw his chances multiply. The Glorious Revolution had placed the Prince of Orange on the British throne, and Fatio soon moved in courtly circles. More than once he was offered a position as secretary to one of King William’s diplomats. Yet he declined these offers, as they did not match his ambitions. The only patron he was willing to serve was his close friend John Hampden, the son of the king’s chancellor. But unfortunately Hampden fell out of favour with the court, thereby diminishing Fatio’s prospects.*
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Fatio and Newton
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When in the late spring of 1689 Huygens paid his first visit to England, Fatio escorted his friend about the capital. He was also present at the Royal Society meeting where Huygens and Newton met for the first time. It probably also served as the occasion for Fatio’s introduction to Newton. The encounter had a strong impact on both men. Before long Fatio openly expressed his veneration of Newton, ‘the most honourable man I know, and the ablest mathematician who has ever lived’. Newton’s letters to Fatio show that the affection was mutual and in Newton’s case exceptionally strong. The scrutiny of Newton’s Principia convinced Fatio of the failure of all theories based upon Cartesian vortices, including Huygens’ theory of gravity.†
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In March 1690 Fatio presented his own theory of gravity to the Royal Society. Two days later Newton came over to London and spent a month in the
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* Ibid., 19-25. † Westfall, Never at rest, 493-495
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Fatio on the Cause of Universal Gravitation
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45
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company of Fatio. Fatio took care to obtain Newton’s signature at the bottom of the paper that he had presented, as well as that of Halley. Together Fatio and Newton studied Huygens’ recently published Traité de la Lumière, which also contained Huygens’ views of gravity as well as some brief comments on Newton’s theory.*
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Later that spring, having accepted a position as a private tutor, Fatio accompanied his pupil on a trip to the Netherlands. Here he repeatedly visited Huygens, with whom he discussed his own theory of gravity as well as his mathematical innovations. After the death of the young man entrusted in his care Fatio returned to England in September 1691.† Upon his return, Fatio and Newton immediately resumed contact. Fatio ignored his brother’s advice to compose a book on his theory of gravity and instead started work on a new edition of Newton’s Principia in which he meant to include his own theory. By adding extensive comments to Newton’s forbidding mathematics, he hoped to make the work more accessible. But the task proved to be more demanding than he had expected and in fact it never materialised.‡
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As the correspondence between Newton and Fatio makes clear, Fatio came to share Newton’s interests in alchemy and biblical prophecies. It has been suggested that it was Newton who set Fatio on the course leading to his religious extravaganza.§ In early 1693 Newton invited Fatio to come over to Cambridge and take the chambers adjacent to his own. He even offered him an allowance. At the time Fatio was considering a voyage to Geneva to settle his affairs after the death of his mother. Although he was strongly tempted by Newton’s offer, he did not move to Cambridge. Fatio and Newton met in London in the summer of 1693, but their relationship seems to have come to a sudden end later that year. In September of the following year Fatio admitted to Huygens that he had not heard of Newton for seven months. Whatever its cause, the rupture between both men was never fully healed.**
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Meanwhile Fatio had declined offers for professorships in Amsterdam and Wolfenbüttel, the latter coming from Leibniz. As he explained, he lacked the required ‘knowledge, health, and diligence’.†† Instead Fatio once again accepted a private tutorship in early 1694, spending most of the following years in Oxford. Only in January 1698, during a trip to Holland, did he part company with his young protégé. In June Fatio returned to London, where he spent the following year. Here he resumed his mathematical studies, solving a problem set by Johann Bernoulli four years earlier.‡‡ The problem in question was that of the brachistochrone, or the curve of quickest descent.
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* Gagnebin, ‘De la cause de la pesanteur’, 115-116; Westfall, Never at rest, 496. † Zehe, Die Gravitationstheorie, 25-27. ‡ Ibid., 27, 30-32. § Domson, Nicolas Fatio de Duillier, 37, 42-43, 48-52, 55-66. ** Westfall, Never at rest, 531-533, 538-539. †† Domson, Nicolas Fatio de Duillier, 41; Zehe, Die Gravitationstheorie, 34. ‡‡ Ibid., 35.
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46
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Frans van Lunteren
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Within a few months following Bernoulli’s public challenge, the problem had been solved by Europe’s foremost mathematicians, being, apart from Johann himself and his brother Jakob, L’Hôpital, Leibniz and Newton. In response to the various solutions, Leibniz had remarked that he had correctly predicted the names of those capable of tackling the problem. Fatio, who had not bothered with mathematics for years, was deeply hurt by the implicit suggestion of impotence. In 1699 Fatio published a small mathematical tract, in which he expounded his own solution to the Bernoulli-problem as well as those to other mathematical questions. He boasted that the invention of his own version of the calculus had been independent of Leibniz’ publications. He added that Newton’s letters and manuscripts proved Newton to be the first inventor. He also insinuated that Leibniz, notwithstanding his own priority claims, had actually ‘borrowed’ some vital insights from Newton.*
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The accusation may have helped to at least partly restore the relationship with Newton. Three years later, again tutoring in London after a two-year stay in Geneva, Fatio was mentioned by Gregory as being among those to whom Newton had promised to publish his own mathematical methods as well as his work on optics. In 1704 Gregory noted that Newton was trying watches with jewel bearings made by Fatio, and in 1706 Gregory mentioned a manuscript by Fatio on comets that he had seen. Fatio repeatedly visited the meetings of the Royal Society, now under Newton’s presidency. Apparently, he was still active in scientific circles.†
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But in the course of 1706 Fatio sealed his scientific fate. That year he joined the Cévenol prophets, becoming a secretary to Elie Marion, one of the leaders of the movement. Fatio did not restrict himself to keeping records of miracles and divine messages. He even seems to have made a public attempt to raise a man from the dead. His punishment did not serve to sober him. In 1710 he left London to accompany Marion on a missionary tour through Europe, bringing them as far as Constantinople. By the time he returned to London his reputation as a mathematician and philosopher had been effectively ruined.‡
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Subsequent attempts to renew contacts with the Royal Society did not meet with success. In spite of some new papers on mathematics, astronomy and technological innovations, Fatio failed to regain scientific respectability. He died in May 1753, ninety years old, and little more than a curiosity.
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Mechanical explanations of terrestrial gravity
|
||
For a better understanding of the nature and genesis of Fatio’s theory of gravity, we must first consider pre-Newtonian accounts of the cause of terrestrial gravity. In the course of the seventeenth century philosophers came to reject
|
||
* Hall, Philosophers at war, 104-109, 118-121; Zehe, Die Gravitationstheorie, 35-40. † Manuel, A portrait of Isaac Newton, 205-206; D. Gjertsen, The Newton handbook (London & New York, 1986) 198; Westfall, Never at rest, 654. ‡ Domson, Nicolas Fatio de Duillier, 83-92; Zehe, Die Gravitationstheorie, 43-46; For Newton’s mixed attitude towards the Camisards, see M. Jacob, ‘Newton and the French Prophets’, History of science 16 (1978) 134-142, and Westfall, Never at rest, 654-655.
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Fatio on the Cause of Universal Gravitation
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47
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the traditional view of gravity as a natural tendency of solid and fluid bodies to move downwards. The mechanical philosophy did not tolerate the attribution of such quasi-active properties to material objects. As the followers of Gassendi and Descartes stressed time and again, inanimate matter is unable to initiate motion. Therefore the cause of gravity must consist in an external agent that pushes heavy bodies downward. Apparently the particles of this material, though insensible agent impinge upon heavy bodies, thereby transferring part of their motion to the grosser particles of the falling body.*
|
||
Most seventeenth-century mechanical accounts of gravity fit in either of two broad categories, the one reaching back to Descartes, the other to Gassendi. In both cases we are confronted with a circulation of subtle matter. In Descartes’ cosmology contiguous whirlpools of insensible, subtle matter fill the universe. Solar vortices carry planets around suns; planetary vortices move moons around planets. The planetary vortices allow for a natural explanation of gravity. For according to Descartes, a terrestrial body owes its gravity to the downward pressure of subtle matter circulating in the terrestrial vortex.
|
||
In a certain sense, bodies at the surface of the earth are light rather than heavy, due to the spinning of the earth. If the space surrounding the earth had been empty, all terrestrial parts not firmly attached to one another would fly off towards the heavens. But as the subtle matter encompassing the earth moves with a speed exceeding that of terrestrial bodies, it has a stronger centrifugal tendency. In Descartes’ stuffed world, the only way it can recede from the centre is by pushing slower bodies downwards. The resultant force upon terrestrial bodies, known as their weight, depends upon the proportion of their pores, penetrated by subtle matter, to their solid parts.†
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||
The second type of gravitational mechanism consists in an upward and downward stream of subtle matter. In this scenario, the main task is to account for the fact that the downward stream has a stronger effect upon terrestrial bodies than its upward moving counterpart. One may assume that the descending particles move with greater speed, or that they are coarser than the ascending particles. The latter solution was of course based upon the analogy with rain or hail. Newton’s earliest views on gravity belong to this category, as did those of Fatio.‡
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Both kinds of explanation suffer from serious drawbacks. Two flaws mark the Cartesian theory. Firstly, a unidirectional terrestrial vortex would impel heavy objects towards the terrestrial axis rather than towards the centre of the earth. Secondly, one would expect the rapidly rotating torrents of subtle matter to drag the falling body along the tangent. This would seem to preclude a perfectly vertical fall. As we will see, Huygens’ vortical theory of gravity was based upon the awareness of these shortcomings.§
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|
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* Van Lunteren, Framing hypotheses, 6-9. † Ibid., 9; R. Descartes, Principia Philosophiae [1644], in Descartes, Œuvres (13 vols., Paris, 1964742) IX, 210-215. ‡ Van Lunteren, Framing hypotheses, 18-19, 39-40. § Ibid., 17.
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48
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Frans van Lunteren
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But the notion of a gravitational hail also has its problems. We have already noticed the asymmetry between the upward and downward currents. But even more problematic is the cause of this circulatory motion. Whence the downward motion of the gravitational particles? It is no use to explain the gravity of terrestrial bodies by appealing to the gravity of the subtle fluid. Yet, few philosophers were discouraged by such difficulties. They either ignored these problems or they invented ingenious ad hoc explanations.
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Fatio and Huygens on terrestrial gravity
|
||
In a manuscript composed in 1685, Fatio expounded his thoughts on the nature of gravity. He spoke of a ‘fierce current of exceptionally subtle matter’, that flows from all possible directions towards the centre of the earth, pushing all bodies downward. The larger their surface and their quantity of matter, the greater the impact of the current. According to Fatio, the speed of the current far exceeds that of falling bodies. This assumption was required by Galileo’s law of falling bodies, which makes the increment of speed independent of the momentary speed of a falling object.
|
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When the subtle matter reaches the centre of the earth, the central fire attenuates it. Its parts are broken down into smaller pieces. Thus energised and rarefied the subtle matter flows outward. In its attenuated form it lacks its former power to move terrestrial bodies. Elsewhere Fatio suggested that this outward motion of particles, caused by the central fire, effects the sucking down of grosser particles, filling the vacated places of the former. Although fully aware of the hypothetical nature of his theory of gravity, Fatio did point to what he saw as empirical support. Experiments with the airpump by Boyle and Huygens suggested that under certain circumstances the height of a mercury column in a glass tube could far exceed the customary value, attributed to the pressure of the air.*
|
||
Within two years Fatio learnt of another explanation of gravity. In early 1687 Fatio was copying some of Huygens’ manuscripts. In his notebook he commented on those pieces that were of special interest to him. In February he expressed his appreciation for Huygens’ theory of gravity. Huygens had presented this theory to the French Academy in 1669, but until then postponed publication. Huygens assumed that the spherical space, which included the earth and its atmosphere, contained a fluid ‘diversely agitated in all directions with much rapidity’. As other matter surrounded this space, the fluid was unable to leave the sphere. As a result its particles described large circles around the centre of the earth in all possible directions.
|
||
Huygens countered the objection that these motions would oppose each other with the argument that the extreme smallness and the large mobility of the particles could account for the preservation of the multidirectional agitation, as in the case of boiling water. Heavy bodies plunged into this fluid would
|
||
|
||
* H. Zehe, Die Gravitationstheorie, 88-95.
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Fatio on the Cause of Universal Gravitation
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49
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not acquire any sensible horizontal motion, due to the rapid succession of the impulses. He agreed then with the essential point of the Cartesian theory, namely that the centripetal tendency of heavy bodies is due to the exceeding centrifugal tendency of the particles of the celestial matter.*
|
||
By patching up Descartes’ theory of gravity, Huygens lost the simplicity and the unity of the Cartesian conception. For the multidirectional vortex was in Huygens’ view surrounded by a unidirectional vortex, responsible for the motion of the moon. He also left intact the Cartesian solar vortex. Such multiplication of vortices did not put Fatio off. He even suggested an extension of Huygens’ multidirectional vortex so as to be superimposed upon the Cartesian vortices, even in the case of the solar vortex. In his view the concerted action of both vortices would account for the fact that all planets circulate more or less in the same plane and in the same direction.
|
||
Yet, in his notes Fatio did not restain his doubts about all vortical explanations of gravity. As he made clear he failed to see how the centrifugal tendency of the fluid would suffice to push bodies downward, whereas the direct, horizontal collisions of the fluid particles did not exert the least sensible pressure upon those bodies. In his earlier theory, these collisions had played the central role in the gravitational mechanism. His enthusiasm for Huygens’ theory may have been genuine; it was certainly not unqualified.†
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Reconciling Newton and Huygens
|
||
In July 1688 Fatio was requested to present Huygens’ theory of gravity to the members of the Royal Society. They were probably eager to know how the views of Europe’s leading natural philosopher related to Newton’s recently published conceptions. In the mean time Fatio had read the Principia. His initial reservations with regard to Newton’s principle of attraction had given way to unqualified acceptance. Such acceptance was facilitated by the fact that, unlike others, Fatio saw no insuperable discrepancy between Newtonian attraction and mechanical explanation. For in his lecture at the Royal Society, Fatio attempted to combine Newton’s attraction with what he regarded as a modified form of Huygens’ theory.
|
||
In the first part of his lecture Fatio expounded Huygens’ original theory of gravity. He now dismissed the notion that bodies were pressed downwards by partly intercepting a vertical current of particles as absurd. For it would be impossible to account for such a current; and neither was it clear what would happen to these particles when they reached the centre of the earth. Therefore the only natural explanation of terrestrial gravity would involve circular motions around the centre of the earth. What followed were the details of Huygens’ theory.‡
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|
||
* Ibid., 71-83; Van Lunteren, Framing hypotheses, 17-18; Œuvres Complètes de Christiaan Huygens, 23 vols. (The Hague, 188-1950) vol. XIX, 628-639.
|
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† H. Zehe, Die Gravitationstheorie, 96-100. ‡ Ibid., 102-113.
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50
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Frans van Lunteren
|
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|
||
In the second part of the lecture he suggested a modification of the theory which would enable it to account for the Newtonian attraction between all material bodies. To this end he transferred the centrifugal tendency of the subtle matter from the neighbourhood of celestial bodies to that of solid material particles. He gave two different accounts of this tendency. The first anticipated his ultimate theory of gravity. Consider an infinite number of extremely small particles flying in all possible directions through empty space. Assume moreover that these particles take up only a marginal part of space. According to Fatio the presence of much larger solid spherical particles will change the motion of the subtle particles in such a way as to make them flee these solid bodies. For all particles moving away from a solid body will keep on doing so, whereas those particles approaching the solid body will face an imminent change of motion because of its presence. After the collision they will likewise flee the solid body.*
|
||
This account will strike the modern reader as seriously flawed. For by intercepting a particle the solid body will indeed augment the number of particles moving away from the body at that side, but it will also diminish the number of particles moving away at the opposite side of the body. Moreover, a centrifugal motion of particles moving rectilinearly through empty space is something very different from a centrifugal tendency in a rotating fluid, where such centrifugal motion is prohibited. Fatio may well have been aware of the weaknesses in his first account for he immediately suggested a ‘better’ explanation of the centrifugal tendency, being in fact the one proposed by Huygens and now transferred to the microscopic realm.
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According to Fatio, the resulting centrifugal tendency would produce a dilution of the subtle matter (which he now considered to be elastic) in the neighbourhood of solid bodies. The density of subtle matter in the space between two neighbouring bodies would thereby be diminished. As a consequence, these bodies would suffer a stronger pressure on the external sides and therefore tend to approach one another. As a result all material bodies, consisting of these gross, spherical particles, would tend to approach one another in accordance with Newton’s theory.†
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||
But the latter theory also had its problems. Here the difficulty is to account for the multidirectional circular motions of the subtle particles. If space were indeed almost empty, as Fatio now believed, then why would these particles move in curved trajectories? As we will see, before long Fatio would relinquish the second explanation in favour of a modified version of the first.
|
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|
||
Huygens’ objections
|
||
Meanwhile Huygens had worked out his own compromise. His attitude towards Newton’s theory was ambivalent. He accepted Newton’s claim that an inverse square centripetal force, rather than a Cartesian vortex produced plane-
|
||
* Ibid., 114-117. † Ibid., 117-121.
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Fatio on the Cause of Universal Gravitation
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51
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tary motion. But he dismissed Newton’s mutual attraction of all material bodies in the universe. In his view, such an attraction was both unwarranted and redundant. Instead, he extended his explanation of terrestrial gravity to the solar realm. It only remained to investigate the cause of the inverse-square diminution of the centripetal force with increasing distance from the sun, ‘a new and remarkable property of gravity’.*
|
||
He clarified his objections in his Discours sur la cause de la pesanteur, published in 1690 as an appendix to his Traité de la lumière:
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||
That is something I would not be able to admit because I believe that I see clearly that the cause of such an attraction is not explainable by any of the principles of mechanics, or of the rules of motion. Nor am I convinced of the necessity of the mutual attraction of whole bodies, since I have shown that, even if there were no earth, bodies would not cease to tend towards a centre by that which we call gravity.†
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||
A point that troubled Huygens was the inference, implicit in Newton’s analysis, that the unhindered motion of the planets and comets required that the celestial spaces contained little if any matter, the very point that was conceded by Fatio. This conclusion seemed to shut the door to Huygens’ explanation of gravity and, above all, his doctrine of light. For in Huygens view, expounded in the Traité, light consisted in pulses transmitted by contiguous particles of the ubiquitous subtle matter. As Huygens argued, the subtlety of this matter does not imply that its parts are separated by large distances. Instead he suggested that the particles ‘touch each other, but that their tissue is rare and interspersed with a great number of small void spaces.’‡ Being an atomist Huygens did not have any serious objections to the void.
|
||
Huygens ended his discussion of Newton’s theory with a repetition of his mechanistic creed: ‘It would be different, of course, if one would suppose that gravity is a quality inherent in corporeal matter. But that is something which I do not believe that M. Newton would admit because such a hypothesis would move us far away from Mathematical or Mechanical Principles.’ In truth Huygens, like other continental philosophers, was sceptical with regard to Newton’s adherence to mechanical principles. As he confided to Leibniz in 1690, he was not satisfied by Newton’s theory of the tides, or by all the other theories that Newton built on his ‘Principle of Attraction, which to me seems absurd.’§
|
||
Unlike Fatio, then, Huygens was both unwilling and unable to follow Newton all the way. He did not believe in the possibility of a mechanical explanation of Newton’s attraction, and Newton’s evacuation of space conflicted with his cherished theories of light and gravity, both of which required mutual contact between contiguous particles. Neither did he see any need for Newton’s attraction, because his own mechanical account of a celestial centripetal force sufficed to explain all relevant phenomena. As we will see similar considera-
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|
||
* Van Lunteren, Framing hypotheses, 44; Œuvres Complètes de Christiaan Huygens, XXI, 472. † Ibid., 471. ‡ Ibid., 473. § Œuvres Complètes de Christiaan Huygens, IX, 538.
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52
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Frans van Lunteren
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tions precluded him from accepting Fatio’s new theory of gravity, first disclosed in a letter to Huygens in 1690.
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Fatio’s theory of universal gravitation
|
||
In the summer of 1689 Fatio had discussed his views on gravity with Huygens, who at the time was visiting London. While reading Huygens’ Discours in early 1690, Fatio realised that he had failed to convince Huygens of the validity of his approach. He may have entertained a hope that Huygens would comment favourably on his ideas in his new book. Huygens’ failure to do so triggered some new considerations from Fatio’s side. Commenting on Huygens’ book in a series of letters, Fatio re-entered the subject of gravity, eventually disclosing his new ideas. As he emphasised, he had finally cleared his theory of all possible objections. He suggested that Huygens’ reserve was due to the same difficulty that had bothered him for some time.*
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Part of the theory may seem familiar. He resumed the supposition of very subtle particles, speeding rectilinearly through empty space in all possible directions. To this hypothesis, he added the crucial assumption that these particles would lose a small part of their motion whenever they collided with gross material bodies. He claimed that these assumptions would result in Newton’s gravitational action in accordance with an inverse-square law.
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||
The argument ran more or less as follows. Consider only those particles that will collide at a certain point on the surface of an impenetrable solid sphere. As they move in converging currents, the force of these currents will be inversely as the square of the distance. After the collision these same particles will move away from this point in diverging currents, again with a force inversely as the square of the distance. Due to the loss of motion, however, the latter force will be somewhat smaller than the former. At large distances the dimensions of the sphere become negligible and the net result will be a centripetal force, inversely as the square of the distance. Adding to this the assumption that material bodies are extremely porous, Fatio could also account for the mass dependency of gravitation and the lack of gravitational screening by interposed material bodies.†
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||
Now comes the aforementioned difficulty. Fatio originally believed that his assumption of a loss of motion would imply an increasing accumulation of subtle matter in the neighbourhood of gross material bodies. But he finally came to realise that the extent of condensation would be finite, and that it would be established almost immediately without any further increase. Moreover, as he later realised, it could be reduced to any desired amount if one increased the velocity of the gravific particles.‡
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||
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* Fatio to Huygens, March 6, 1690 in: Œuvres Complètes de Christiaan Huygens, IX, 384; Zehe, Die Gravitationstheorie, 130.
|
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† Œuvres Complètes de Christiaan Huygens, IX, 384-386; Zehe, Die Gravitationstheorie, 134-138. ‡ Œuvres Complètes de Christiaan Huygens, IX, 387; Zehe, Die Gravitationstheorie, 140-142, 147, 154.
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Fatio on the Cause of Universal Gravitation
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53
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In March 1690 Fatio read a copy of his letter to Huygens at a meeting of the Royal Society. He asked Edmond Halley, at that time secretary to the Society, to sign each page of the paper. Some weeks later he also received Newton’s signature. In the manuscript that bears these signs Fatio had added a few considerations to the content of the letter. He argued explicitly for an infinitesimally small density of the subtle matter. The gravitational force being proportional to both the velocity squared and the density, one could diminish the density to an arbitrary extent, by introducing a compensating increase in the velocity. For most practical purposes, Fatio’s gravitational fluid was indistinguishable from empty space.*
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||
In a later supplement to the theory Fatio calculated the resistance experienced by a spherical body moving through his gravific fluid. His result was a resistance that was proportional to both the velocities of the particles and their density. Given the fact that the force exerted by the particles was proportional to the density and the square of the velocity, one could easily arrive at an arbitrarily small resistance for any given force by decreasing the density and increasing the velocity.†
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The contemporary reception of Fatio’s theory
|
||
The few philosophers with first-hand knowledge of the theory were hardly impressed by Fatio’s exercise. Hooke, who had attended the Royal Society meeting, noted his reaction in his diary: ‘Facio [Fatio] read his own hyp[othesis] of Gravity, not sufficient.’ The following week he condescendingly referred to Fatio as the ‘Perpet[ual] Motion man’.‡ Halley was later said to ‘laugh at Mr Fatios manner of explaining gravitation.’§ Fatio likewise failed to convince Huygens. In a letter written in reply to Fatio’s exposition, Huygens heaped up a number of objections. In Huygens’ view, either the subtle matter would have to be annihilated at the central body, or no central force would arise. For the receding current would equal the approaching current. Moreover, without the annihilation, he could not see why the subtle matter would converge on the central body.
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||
Fatio replied that he did not assume all subtle matter to converge on the central sphere. As the particles moved in all possible directions only a very small part would actually move towards the sphere. For his explanation of gravity, however, it sufficed to take only those particles into consideration. As far as the other objection was concerned, Fatio argued that an arbitrarily small loss of motion at each collision could produce the same force as the total annihilation of any given velocity. For the central force varied as the difference of the squares of the initial and the final velocities. For a fixed difference and an
|
||
* Gagnebin, ‘De la cause de la pesanteur’, 115-116, 129-134. † Zehe, Die Gravitationstheorie, 249-250. ‡ R. Hooke quoted in G.E. Christianson, In the presence of the Creator: Isaac Newton & his times (New York & London, 1984) 345. § D. Gregory quoted in I. Newton, The Correspondence (Cambridge, 1959-1977) 7 vols., vol. III, 191.
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54
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Frans van Lunteren
|
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|
||
increasing initial velocity, the final speed would approach the initial speed indefinitely. He also stressed that an arbitrary small amount of subtle matter, if sufficiently split up and agitated, could produce all the required attractive forces in the solar system.*
|
||
As is clear from the marginal notes that Huygens added to Fatio’s letter, he was not impressed by Fatio’s rebuttal. Still he did not take up the subject again in his correspondence. They probably discussed the matter when Fatio visited Huygens in the Netherlands. Whatever the nature of these discussions, they left Fatio with the impression that he had convinced Huygens of the soundness of his theory. As Huygens’ subsequent letters to L’Hôpital and Leibniz prove, the belief was erroneous. Huygens held on to his conviction that Fatio’s theory implied an accumulation of matter at the attracting body.†
|
||
The inappropriateness of some of Huygens’ criticisms leads one to suspect an utter lack of interest. He completely misrepresented the theory by comparing it to the theory of gravity of Varignon. The latter had explained terrestrial gravity by an elastic fluid surrounding the earth. The motion of an object at a certain distance from the earth was determined by the length of the columns of subtle matter below and above the object, both exerting a pressure on the object proportional to the length of the column. Near the surface the upper column, being much longer, exerted a far greater pressure, thereby pushing bodies downward. There is hardly any resemblance with Fatio’s theory.‡
|
||
Fatio’s unusual assumptions probably sufficed to make the theory unpalatable to Huygens and other followers of the mechanical creed. The vacuity of space around and within material bodies, the extreme velocities that Fatio granted to his subtle particles, all this contradicted mechanical common sense, and even worse, the physical theories cherished by all these natural philosophers. Leibniz, another correspondent of Fatio, noted disapprovingly that Fatio regarded his doctrine of empty space not as a hypothesis, but as an indisputable truth. To Leibniz, as to most Cartesians, empty space was anathema.§
|
||
The sole exception to this general dismissal may well have been Isaac Newton. In a private memorandum, written at a much later date, Fatio boasted of Newton’s consent:
|
||
Sir Isaac Newton’s Testimony is of the greatest weight of any. It is contained in some additions written by himself at the End of his own printed Copy of the first edition of the Principles, while he was preparing for a second Edition. And he gave me leave to transcribe that testimony. There he did not scruple to say “That there is but one possible Mechanical cause of Gravity, to wit that which I had found out…”**
|
||
|
||
* Huygens to Fatio, March 21, 1690 & Fatio to Huygens April 21, 1690, in: Œuvres Complètes de Christiaan Huygens, IX, 391-393, 407-412.
|
||
† Ibid., 412, Œuvres Complètes de Christiaan Huygens, vol. X, 354, 613. ‡ Van Lunteren, Framing hypotheses, 19-20, 42-43. § Zehe, Die Gravitationstheorie, 174. ** Newton, The Correspondence, III, 69-70.
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Fatio on the Cause of Universal Gravitation
|
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55
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Newton on Fatio’s theory
|
||
|
||
When Fatio returned to England in 1692, he still had not published his theory of gravity. In fact he had lost the manuscript. In time, however, he managed to retrieve it. Meanwhile he had put his hopes on Newton. A new and enlarged edition of the Principia would be the ideal vehicle for the disclosure of his causal explanation.
|
||
Newton began his revision of the Principia immediately after its publication. He entered the alterations in several copies of the book, allowing some of his intimates to see and even transcribe them. Fatio actually transmitted a list of Newton’s emendations directly to Huygens, who passed them on to Leibniz. In turn, Fatio also scrutinized the work for author’s and printer’s errors, jotting down his own improvements.*
|
||
In December 1691 Fatio informed Huygens of his intentions to prepare a new edition and see it through the press. He planned to add extensive commentaries to make the work more accessible. He expected the task to take him two or three years. News of the new edition spread rapidly. Both Huygens and Leibniz considered Fatio to be well qualified for the job.† At the time Fatio was writing to Huygens, the mathematician David Gregory, another young intimate of Newton, testified to Fatio’s plans of including his own theory in the intended second edition:
|
||
Mr Fatio designs a new edition of Mr Newtons book in folio wherin among a great many notes and elucidations, in the preface he will explain gravity acting as Mr Newton shews it doth, from the rectilinear motion of particles the aggregate of which is but a given quantity of matter dispersed in a given space. He says that he hath satisfied Mr Newton, Mr Hugens & Mr Hally in it.‡
|
||
Although Fatio may well have misjudged the opinions of Halley and Huygens, solid evidence supports his claim of Newton’s favourable attitude. A draft addition in Newton’s hand to his discussion of the vacuity of the celestial spaces in Book III of the Principia praises both theory and its author.
|
||
They are mistaken therefore who join the least particles of bodies together in a compact mass like grains of sand or a heap of stones. If any particles were pressed together so densely, the gravitating cause would act less towards the interior ones than towards the exterior ones and thus gravity would cease to be proportional to the [quantity of] matter. Other textures of the particles must be devised by which their interstices are rendered more ample. And these are the necessary conditions of an Hypothesis by which gravity is to be explained mechanically. The unique hypothesis by which gravity can be explained is however of this kind, and was first devised by the most ingenious geometer Mr. N. Fatio. And a vacuum is required for its operation since the more tenuous particles must be borne in all directions by motions which are
|
||
|
||
* I.B. Cohen, Introduction to Newton’s ‘Principia’ (Cambridge, 1971) 162, 177-179. † Ibid., 177-179. ‡ Ibid., 180
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56
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Frans van Lunteren
|
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|
||
rectilinear and very rapid and uniformly continued and these particles must experience no resistance unless they impinge upon denser particles.*
|
||
However, as Fatio knew well enough, Newton entertained doubts about a mechanical cause of gravitation. As Fatio later admitted, ‘he would often seem to incline to think that Gravity had its Foundation only in the arbitrary Will of God.’† Indeed, Newton seems to have planned the incorporation in his Principia of extensive references to ancient sources, supportive of the view that God, being omnipresent, activated the entire cosmos. As Gregory recorded in a memorandum:
|
||
The plain truth is that he believes God to be omnipresent in the literal sense […] But if this way of proposing this his notion be too bold, he thinks of doing it thus. What cause did the Ancients assign of Gravity[?] He believes that they reckoned God the cause of it, nothing else, that is no body being the cause, since every body is heavy.‡
|
||
And at some unknown date Gregory added to his note on Fatio’s claim of Newton’s and Halley’s consent: ‘Mr. Newton and Mr. Hally laugh at Mr Fatios manner of explaining gravitation’.§ Perhaps Newton changed his mind with regard to the merits of Fatio’s theory. It is not unlikely that the proposed tribute to Fatio stemmed primarily from the strong affection that Newton felt for his young protege. After the break-up, Newton never mentioned Fatio’s theory again. In the second edition of the Principia, appearing as late as 1713, he incidentally dismissed all mechanical theories of gravity.
|
||
[Gravity] must proceed from a cause that penetrates to the very centres of the sun and the planets, without suffering the least diminution of its force; that operates not according to the quantity of the surfaces of the particles upon which it acts (as mechanical causes used to do), but according to the quantity of the solid matter which they contain.**
|
||
Let us compare this argument with his previous comments on Fatio’s theory. At that time he saw no difficulty in combining the empirically determined proportionality of gravity to mass with a mechanical explanation, as long as one accepted the extreme rarity of solid matter within ponderable bodies. In fact, Newton still adhered to this conception of matter. By now however he extended his requirements of a mechanical explanation from the penetration of bodies to that of the ultimate solid parts of matter. This was of course a condition that no mechanical theory could meet, Fatio’s theory being no exception.
|
||
But the proportionality of gravitation and mass does not strictly imply the latter condition. As long as the ultimate particles of matter, or atoms, all share the same ratio of surface area to volume Newton’s objection loses its force. Now, it may have been that Newton’s dismissal was merely rhetorical and only
|
||
|
||
* Newton in A.R. Hall & M. Boas Hall (ed.) The unpublished scientific papers of Isaac Newton (Cambridge, 1962) 315.
|
||
† Newton, The Correspondence, III, 70. ‡ W.G. Hiscock, David Gregory, Isaac Newton and their circle: Extracts from David Gregory’s Memoranda 1677-1708 (Oxford, 1937) 29-30. § Newton, The Correspondence, III, 191. ** I. Newton, Mathematical principles of natural philosophy (Berkeley, 1962) 546.
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|
||
Fatio on the Cause of Universal Gravitation
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57
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|
||
reflected his unwillingness to consider mechanical causes. On the other hand the objection may have stemmed from a solid, but unprovable conviction that the ultimate particles of matter differ in size or figure, an assumption that would render his argument valid.
|
||
And even when in 1717 Newton did suggest a material cause of gravitation in the third edition of his Opticks, his fluid did not resemble that of Fatio in any respect. For its activity did not derive from the rapid motions of the particles, but rather from the repulsive forces between the static particles.* It seems therefore safe to conclude that whatever Newton’s original views of Fatio’s theory, he eventually became as sceptical as other contemporaries.
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|
||
The further development of the theory
|
||
The lukewarm reactions to his work did not undermine Fatio’s faith in his theory of gravity. In his view the theory was as indubitable and as well established as Newton’s law of gravitation, to which it formed a natural supplement. He regarded Newton’s work as essentially incomplete without his own physical account of Newton’s mathematical principle of gravitation.
|
||
In the further course of his life Fatio returned to his theory at several occasions. In 1696 he composed a manuscript in quarto entitled ‘On the cause of gravity’ during his stay in Oxford as a tutor of a young nobleman. In the 40page manuscript he refined and expanded his theory, without changing anything in its physical assumptions. The additions were concerned with the structure of atoms required by the proportionality of gravity and mass and the free passage of light through glass and crystal in each and every direction; with the pressure exerted by the gravific particles on a solid plane; and above all with the concept of infinity as applied to the velocity and rarity of the fluid.†
|
||
In 1700, while staying in Geneva, Fatio entered a correspondence with Jacob Bernoulli. The latter probably considered any enemy of his brother a likely ally. When Fatio’s theory cropped up in the correspondence, Jacob, intrigued by the hints that Fatio had dropped, begged Fatio for a full account: ‘I am dying of impatience to see your theory of gravity’. Eventually Fatio did send a detailed account. From the following correspondence it is clear that the theory caused Bernoulli severe difficulties. Finally, Bernoulli praised the essay as providing solid proof of Fatio’s talents and never addressed the subject again. After Fatio’s return to England the correspondence seems to have come to an end.‡
|
||
In 1706 Fatio added some new paragraphs to his manuscript. His subsequent flirtation with religious heterodoxy did not put a stop to his natural philosophical ambitions. After his missionary wanderings through Europe ending in 1712, he resumed his mathematical and philosophical studies. In 1716 he left London to settle in Maddersfield. His research now focussed on alchemy, the
|
||
* I. Newton, Opticks (New York, 1952) Queries 17-24. † Gagnebin, ‘De la cause de la pesanteur’, 119; Zehe, Die Gravitationstheorie, 34-35. ‡ Ibid., 177-180.
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||
|
||
58
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Frans van Lunteren
|
||
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cabbala and theological speculations. In 1728 he wrote an obituary for Isaac Newton. Subsequent attempts to regain his repute in learned circles met with little success. In the same year 1728 he competed for the prize set by the Paris academy for a physical explanation of celestial gravitation. Fatio’s submission, a Latin poem in the style of Lucretius, was passed over by the judges. Instead they awarded a theory based upon Cartesian vortices. An adaptation of the poem, sent to the Royal Society in 1730, met with a similar fate. Attempts to procure a readership for his theory through subscription likewise failed.*
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||
Meanwhile, a copy of Fatio’s manuscripts had come into the hands of the Genevan professor Gabriel Cramer. In 1731 Cramer published a dissertation consisting of 37 theses on gravity, to be defended by his student Jallabert. Of the 37 theses the last eight contained a summary of Fatio’s theory, without however mentioning his name. It was also Cramer who in 1749 drew Le Sage’s attention to Fatio’s theory.†
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||
The final occasion for Fatio to return to his theory of gravity was in 1742. Again he polished his earlier arguments without adding anything meaningful. If he was still pondering the publication of the intended ‘Treatise on the cause of gravity’, such plans were soon thwarted by a stroke causing paralysis. Fatio’s magnum opus never materialised. When Fatio died in 1753 his theory seemed to have disappeared with its author. Yet by this time Le Sage was already working on its revival.‡
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Conclusion
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Fatio’s ideas on the cause of gravity fell on barren soil. In the course of time philosophers were more and more divided along partisan lines. Those who kept insisting upon mechanical explanations filled the universe with matter in vortical motion; those who swore by the void invoked ‘active principles’. Fatio’s theory of gravity appealed to neither group. In the eighteenth century those who accepted Newton’s universal gravitation took it for an irreducible principle, the cause of which was unfathomable. If pressed they would either hint at an inherent, although not essential property bestowed upon matter by God at the creation, or at a direct and continuous manifestation of God’s will. Even the French and Germans eventually came to adopt such views.§
|
||
It seems unlikely then that a published version of Fatio’s theory would have made much of a difference. Perhaps philosophers would have been somewhat more careful in dismissing all mechanical accounts of universal gravitation. Three arguments pervaded among the public dismissals of all mechanical explanations of gravity. A fluid offering no resistance to the motion of bodies cannot exert a sensible power upon these bodies; gravity, being proportional to mass, must pervade the inner substance of bodies; the force does not
|
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||
* Ibid., 47-48. † Ibid., 279-280. ‡ Ibid., 49-50. § Van Lunteren, Framing hypotheses, 84-90.
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Fatio on the Cause of Universal Gravitation
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59
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depend upon the velocity of the attracted bodies. As we have seen Fatio’s theory was not vulnerable to any of these objections.*
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Yet it seems likely that such objections should be seen as a symptom, rather than the cause of the dissatisfaction with mechanical theories. The former preference for mechanical explanation was now seen to rest upon prejudice. Given the fact that we know nothing of the essence of matter, it was said, how can we decide that attraction (in a physical sense) is less conceivable than impulse. In the words of Maupertuis, pleading the Newtonian cause in the Paris Academy in 1732: ‘Is it more difficult for God to make two remote bodies tend or move towards one another, than to wait, in order to move it, until a body has been encountered by another?’†
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||
Given our state of ignorance, philosophers added, it seemed best to heed Newton’s ‘Hypotheses non fingo’. For without any empirical clues it would be useless to speculate on the cause of gravitation. This profound insight found its most plastic expression in Voltaire’s writings:
|
||
Those philosophers who create systems with regard to the secret construction of the universe are like our travellers who go to Constantinople, and talk about the serail: they have only seen its outside, and yet pretend to know what the sultan does with his favourites.‡
|
||
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||
* Ibid., 71, 86-87, 90. † P.L.M. de Maupertuis, Œuvres (Lyon, 1756) I, 93-94. ‡ Voltaire, Elémens de Philosophie de Newton (Neuchatel, 1773) 390-391.
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Newton’s Aether-Stream Hypothesis and the Inverse Square Law of Gravitation*
|
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|
||
E.J. Aiton, M.Sc., Ph.D.†
|
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[…] When he was writing the Principia, Newton was anxious to convince Hal-
|
||
ley that he had learnt nothing from Hooke. In a letter to Halley dated 20 June 1686, Newton claimed that the inverse square law for the attraction was implied in his unpublished essay, ‘An Hypothesis explaining the Properties of Light discoursed of in my severall Papers’,‡ communicated to Oldenburg in 1675 and registered in the Royal Society.
|
||
In this document, Newton developed the hypothesis of a universal aether, explaining not only the properties of light but also the action of various forces, such as the electric, magnetic and gravitational forces. The aether causing gravity was not identical with the optical aether but something thinly diffused through it, of a tenacious and elastic nature. Just as vapours condense on solid surfaces, Newton supposed, the earth condenses so much of the gravitational aether, or ‘spirit’ as he termed it,§ as to cause it to descend from above with great velocity:
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||
‘In which descent it may beare downe with it the bodyes it pervades with force proportionall to the superficies of all their parts it acts upon; nature makeing a circulation by the slow ascent of as much matter out of the bowells of the Earth in an aereall forme which for a time constitutes the Atmosphere, but being continually boyed up by the new Air… riseing underneath, at length… vanishes againe into the aethereall Spaces,…and is attenuated into its first principle’.**
|
||
In his letter of 20 June 1686 Newton suggested to Halley that if he considered the nature of the hypothesis, he would find
|
||
‘the gravity decreases upward and can be no other from the superficies of the Planet than reciprocally duplicate of the distance from the center, but downwards that proportion does not hold’.††
|
||
Newton also remarked that he had never extended the inverse square proportion inside the earth, and had suspected that it did not hold exactly down to the surface until he had demonstrated this the previous year‡‡, whereas Hooke, to whom he referred obliquely as a bungler, erred in extending the inverse square proportion down to the centre. Hooke did not in fact extend the inverse square
|
||
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||
* This is an abridged version of an article originally published in Annals of Science, 25, 255-260 (1969). Permission to reprint it was given by Taylor & Francis (http://www.tandf.co.uk/journals).
|
||
† Didsbury College of Education, Manchester. ‡ Correspondence, vol. i, pp. 362-386. § Ibid., p. 365. ** Ibid., p. 366. †† Correspondence, vol. ii, p. 440. ‡‡ Ibid., p. 435.
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Pushing Gravity: new perspectives on Le Sage’s theory of gravitation
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61
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edited by Matthew R. Edwards (Montreal: Apeiron 2002)
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62
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E.J. Aiton
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law to the centre of the earth; moreover, in one of his letters to Newton,* he remarked that in discussing such a possibility he was only considering a hypothetical case that he did not believe to be true. Newton also referred Halley to Sir Christopher Wren; for he was almost confident that Wren knew the inverse square law two years before the date of Hooke’s letter, and the absence of a statement of the law in Hooke’s Cometa (1678) showed that of the three, Hooke was the last to know it.†
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Commenting on the hypothesis in a further letter to Halley, Newton explained how the inverse square law followed. In the hypothesis, Newton wrote, he had supposed
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||
‘…that the descending spirit acts upon bodies here on the superficies of the earth with force proportional to the superficies of their parts, which cannot be unless the diminution of its velocity in acting upon the first parts of any body it meets will be recompensed by the increase of its density arising from that retardation. Whether this be true is not material. It suffices that ‘twas the Hypothesis. Now if this spirit descend from above with uniform velocity, its density and consequently its force will be reciprocally proportionall to the square of its distance from the center. But if it descend with accelerated motion, its density will every where diminish as much as its velocity increases, and so its force (according to the Hypothesis) will be the same as before, that is still reciprocally as the square of its distance from the center’.‡
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Although the increase in density of the gravitational aether on entering bodies was needed to explain the dependence of weight on mass, the optical aether was supposed to be less dense in the interior of bodies than in free space. Newton evidently soon recognized the inconsistency of supposing such different properties for the two aethers; for in a letter to Boyle, four years later, he replaced the aether-stream explanation of gravity by another depending on a supposed increase in size of the particles with distance from the centre of the earth, both inside the earth and in free space. As the larger particles were less apt to be lodged in the pores of bodies, these endeavoured to make way for the smaller particles below, thus displacing the body downwards.§ In the second English edition of the Opticks (1717) Newton suggested yet another explanation: he supposed the density of the aether to increase with distance from the earth, the elastic force of the aether impelling bodies towards the less dense parts.**
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None of these speculations amounts to an explanation of universal gravitation. The nearest approach is to be found in the elastic-aether hypothesis of the Opticks, in which the heavenly bodies, supposed, like the earth, to be centres of low aether density, were impelled towards one another by the expansive force of the aether. This symmetry was not explicitly extended to terrestrial bodies; these bodies were impelled towards the earth, but evidently the earth
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|
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* Ibid., p. 309. † Ibid., p. 435. ‡ Ibid., p. 447. § Ibid., p. 295. ** Newton, Opticks, Dover Publications, 1952, Query 21.
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Newton’s Aether-Stream Hypothesis
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63
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was not similarly impelled in the opposite direction, neither were terrestrial bodies impelled towards one another. It is true that the density of the optical aether was less in the interior of bodies than outside, but the density gradient extended only a short distance.
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Newton’s first explicit statement of the principle of universal gravitation was given in the Principia,* but the principle was implied in the calculation of the attraction of a sphere, achieved, as Newton remarked in a letter to Halley,† in 1685. The idea of universal gravitation had indeed already been conceived by Descartes, who erroneously attributed it to Roberval.‡ An explanation of universal gravitation, evidently acceptable to Newton,§ was presented to the Royal Society in 1690 by Nicolas Fatio de Duillier.** As conceived by Fatio, the aether consisted of rapidly moving particles so widely scattered that their straight paths were rarely impeded by mutual collisions.†† Gravity was caused by the inelastic collisions of the aether particles with gross bodies, not only the earth and heavenly bodies but also ‘les Atomes qui les composent’. Two opposite streams were envisaged, one towards the body, the other away from the body, the latter consisting of particles rebounding with reduced speed or emerging, again with reduced speed, after traversing the interior of the body.‡‡ Huygens objected that the inward stream would not form unless the aether condensed in the body, and this he regarded as impossible.§§
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In the correspondence with Halley, Newton’s argument rested exclusively on the aether-stream hypothesis. A constant inward stream of S particles per unit time, moving with speed υ, at a distance r from the centre would have a density ρ = S/(4π r2υ). In his commentary, Newton explains that, if the aether stream descends with accelerated motion, the density decreases everywhere as much as the velocity increases, so that the force in free space would be the same as if the velocity were constant. This implies that Newton supposed the force to be proportional to the density and the velocity: that is, in the notation already introduced, to S/(4π r2), which is independent of the velocity of the aether stream. Also Newton explains that, in meeting bodies near the surface of the earth, the loss of momentum of the individual particles is compensated by
|
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* Principia, Book III, prop. 7. † Correspondence, vol. ii, p. 435. ‡ See E. J. Aiton, ‘The Cartesian Theory of Gravity’, Ann. Sci., 1959, 15, 30. § See A. R. Hall and M. B. Hall, Unpublished Scientific Papers of Isaac Newton, London, 1962, p. 313. ** B. Gagnebin, ‘De la cause de la pesanteur: mémoire de Nicolas Fatio de Duillier’, Notes and Records of the Royal Society of London, 1949, 6, 105-160. Two years earlier, Fatio had read a memoir to the Royal Society on Huygens’s theory of gravity, but he seems to have rapidly assimilated Newton’s ideas. On Huygens’s theory, see E. J. Aiton, loc. cit., pp. 34 ff. †† The aether of Newton’s Opticks is of the kind envisaged by Fatio rather than the continuous fluid of Newton’s own aether-stream hypothesis. See Query 28. ‡‡ Gagnebin, loc. cit., p. 127. §§ Huygens, Œuvres complètes de Christiaan Huygens, La Haye, 1888-1950, vol. ix, pp. 391-393. Moreover, the loss of speed of the aether in the inelastic collisions and the consequent running down of the system was unacceptable to Huygens. Thus he remarked that, even if the two streams did form, their effects would cancel.
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E.J. Aiton
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an increase in density of the aether stream, so that the force is constant throughout the body. Thus the force of the aether stream is not diminished by meeting bodies; ρv is constant both in free space and in the interior of bodies. The inverse square law would indeed hold to the centre of the earth if the compensating increase in density were not checked. Evidently Newton did not consider an explanation of how the departure from the inverse square law inside the earth followed from his hypothesis to be necessary, confident that Halley would recognize the obvious implication that the increase in density was offset to some extent by the removal of particles from the aether stream owing to condensation.*
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The force with which bodies were impelled by the aether stream was similar to the resistance of a fluid to the motion of solid bodies through it, discussed in Book II of the Principia, and was proportional to the momentum communicated.† The principal difference was that the aether penetrated the body so that the force was proportional to the volume, whereas in the case of fluids such as air and water, the resistance was proportional to the surface on which the fluid impinged. In the Principia, Newton considers the cases of resistance proportional to the velocity and to the square of the velocity. Although experiments had shown that the second case corresponded to reality, Newton evidently intended Halley to believe that, in 1675 he supposed the resistance to be proportional to the velocity.
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An evaluation of Newton’s claims in the letters to Halley may now be attempted. Although, as Newton admitted, the hypothesis was ‘one of my guesses which I did not rely on’,‡ his argument rested on the premise that, in its implications, the hypothesis reliably reflected his exact scientific views. As interpreted by Newton himself, the aether-stream hypotheses implies the inverse square law in free space, whether the velocity of the aether-stream is constant or accelerated, and moreover implies a departure from this law in the interior of the earth owing to the reduction of the aether stream by condensation. Granting his premise, Newton could therefore claim the aetherstream hypothesis as evidence that in 1675 he believed the inverse square law to hold in free space, but did not assume its validity to the centre of the earth. Nevertheless his assertion that Hooke failed to recognize this limitation of the inverse square law was untrue, as was clear from one of Hooke’s letters in his possession.§ […]
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* In a letter to the author, dated 17 January 1969, Professor L. Rosenfeld accepts this interpretation in place of that given in his article, ‘Newton and the law of gravitation’, Archive for History of Exact Sciences, 1965, 2, 365. Professor Rosenfeld has also made a reappraisal of Newton’s aether hypotheses in a new article, ‘Newton’s views on aether and gravitation’, which he has kindly allowed the author to read in typescript.
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† Principia, Book II, Scholium, Section 1. ‡ Correspondence, vol. ii, p. 440. § Ibid., p. 309.
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Le Sage’s Theory of Gravity: the Revival by Kelvin and Some Later Developments
|
||
Matthew R. Edwards*
|
||
An account is given of the attempts by Kelvin and later authors to revive Le Sage’s theory of gravity. Predictions of Le Sage’s theory in relation to shielding and eclipse experiments, as well as some possible links to relativity and cosmology, are briefly discussed.
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Introduction
|
||
One of the oldest mechanical theories of gravity of which we have knowledge is that of Georges-Louis Le Sage, proposed in the mid-eighteenth century.† Le Sage’s theory reached its zenith of popularity in the late nineteenth century, when it was shown by Kelvin to be compatible with the then newly discovered kinetic theory of gases. It stood alone among the mechanical theories of gravity of the day in its ability to reproduce Newton’s law exactly. By the turn of the century, however, the theory had been thoroughly discredited, most notably by Maxwell, and today is generally considered of historical interest only. Feynman, for example, refers to the theory as a sort of primitive stepping stone in the early evolution of physics (Feynman et al., 1963).
|
||
In this article, I briefly examine some of the later attempts to revive Le Sage’s theory, beginning with its expression by Kelvin. An underlying focus is to discern whether the reasons for its dismissal by the physicists of the day were entirely valid. Our discussion of recent Le Sage-type models will be brief, as many of them appear elsewhere in this book.
|
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Early History of Le Sage’s Theory
|
||
Details of the early history of Le Sage’s theory may be found in Le Sage’s own paper, “Lucrèce Newtonien” (Le Sage, 1784), Kelvin’s paper (Kelvin, 1873) and numerous later accounts (Taylor, 1877; Darwin, 1905; Aronson, 1964; Roseveare, 1982; Van Lunteren, 1991; see also the articles by Van Lunteren and Evans in this volume). The following account is drawn primarily from Aronson (1964).
|
||
Le Sage proposed that gravity is caused by the continuous bombardment of ordinary matter by “ultramundane corpuscles” originating from the depths of
|
||
|
||
* Gerstein Science Information Centre, University of Toronto, Toronto, Ontario, Canada, M5S 3K3. E-mail: matt.edwards@utoronto.ca
|
||
† Many years earlier Nicolas Fatio de Duillier proposed a similar theory, in which Newton expressed a sympathetic interest for some time. Fatio’s contribution is discussed in the paper by Van Lunteren in this book.
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Matthew R. Edwards
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space. So small were these corpuscles and so porous the structure of ordinary matter that the vast majority of particles, like the neutrinos of modern physics, passed unhindered through even massive bodies such as the Earth. Le Sage proposed separately that the corpuscles were miniscule relative to their separation; that their motions were rectilinear; that they rarely if ever interacted; that their motions could be regarded as equally dense streams moving in all directions; and that their velocities were extremely high. The latter postulate allowed the frictional resistance of the corpuscular sea to bodies in motion through it to be kept insensibly small relative to the attractive force. In order that the gravitational force be proportional to the mass of a body, rather than its cross-sectional area, Le Sage postulated moreover that the basic units of ordinary matter were highly porous to the corpuscles. In some of his writings he referred to them as cage-like structures, in which the diameters of the “bars” were small relative to the dimensions of the “cages”. An isolated body in this medium would be shelled uniformly from all directions and would thus experience no net force upon it. In a system of two or more bodies, however, the mutual shading of corpuscles would result in an apparent force of attraction between the two bodies.
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A critical aspect of the model, which was recognized by Le Sage and would later lead to grave difficulties, related to the nature of the collisions between the corpuscles and the units of ordinary matter. The collisions could not be entirely elastic, for in this case the shading effect would be exactly nullified by corpuscles rebounding from the shading mass to strike the shaded one. Instead, Le Sage proposed that the particles were either carried away at reduced velocities or else stuck to the bars of the cage-like units of matter.
|
||
With these postulates, Le Sage was able to show that his mechanism could reproduce Newton’s law of gravitation. The following argument is taken from Preston (1877). Let A and B be two masses separated by a distance R. Consider the force which B by virtue of its shading effect exerts on A. The particles impinging on A may be viewed as originating from a spherical surface with radius R centred about A. The number of particles ordinarily striking A, if B were absent, is proportional to the cross-sectional area of A and hence, by the assumption of A’s cage-like structure, to its mass. With B present, however, a fraction of particles is intercepted which varies directly with the cross-sectional area of B, and hence B’s mass, and indirectly with the surface area of the sphere, which is proportional to R2. The attractive force is thus proportional to the product of the masses over the square of the separation. Similarly, A exerts an equal and opposite force on B.
|
||
Due to their ad hoc and somewhat unusual formulation, Le Sage’s ideas were not well-received during his day (see Evans, this volume). Le Sage, however, was completely undeterred by his critics and spent the greater part of his life developing epistemological arguments to defend his theory. According to Laudan (1981), it is Le Sage’s efforts to advance the “method of hypothesis”,
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Le Sage’s Theory of Gravity: the Revival by Kelvin
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which is today taken for granted, that were his major contribution, not the theory itself.
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The Revival by Kelvin
|
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After Le Sage, the theory fell into a historical pattern typical for this theory, which can be characterized as general oblivion punctuated by isolated introductions of variant forms. Since long intervals frequently lapsed between these renewals, the latter have very often lacked historical context. This pattern persists to the present day. The many and complex threads of Le Sage’s successor theories in the eighteenth and nineteenth centuries are discussed in fine detail by Van Lunteren (1991).
|
||
An exception to this general pattern of neglect was a surge of interest in the 1870’s, when Kelvin updated the work by demonstrating a close analogy with the kinetic theory of gases (Kelvin, 1873).* All of the various postulates introduced by Le Sage concerning the gravitational corpuscles (rectilinear motion, rare interactions, etc.) could be collected under the single notion that they behaved as a gas. Kelvin thus stated that:
|
||
… inasmuch as the law of the inverse square of the distance, for every distance, however great, would be a perfectly obvious consequence of (Le Sage’s) assumptions, were the gravific corpuscles infinitely small and therefore incapable of coming into collision with one another, it may be extended to as great distances as we please, by giving small enough dimensions to the corpuscles relatively to the mean distance of each from its nearest neighbour. The law of masses may be extended to as great masses as those for which observation proves it (for example, the mass of Jupiter), by making the diameters of the bars of the supposed cage-atoms constituting heavy bodies, small enough. Thus, for example, there is nothing to prevent us from supposing that not more than one straight line of a million drawn at random towards Jupiter and continued through it, should touch one of the bars. Lastly, as Le Sage proves, the resistance of his gravific fluid to the motion of one of the planets through it, is proportional to the product of the velocity of the planet into the average velocity of the gravific corpuscles; and hence, by making the velocities of the corpuscles great enough, and giving them suitably small masses, they may produce the actual forces of gravitation, and not more than the amount of resistance which observation allows us to suppose that the planets experience.
|
||
In this single passage, Kelvin at the same time touches on three potentially problematic aspects of Le Sage’s theory. The range of the gravitational force would be proportional to the mean free path of the Le Sage corpuscles, which in turn would be governed by their diameters and numerical densities. While Kelvin states here merely that this range could be placed beyond observational limits if the corpuscles were imagined sufficiently small, Preston subsequently seized upon this aspect of the theory as one of its major attractions.
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* According to Brush (1976), it was in fact the theories of Le Sage and Hartley which paved the way conceptually for the kinetic theory.
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Preston recognized that a finite range of the gravitation was crucial to the notion of a gravitationally stable universe.
|
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In the same passage, Kelvin also notes that the potentially observable deviations from Newton’s law due to ‘self-shading’ of corpuscles in large planets, for example, can be minimized by extending their porosity to as great proportions as necessary, by imagining that the cage bars of Le Sage’s atoms were sufficiently small. This aspect of Le Sage’s model was also appreciated by others, such as Maxwell (1875) and Poincaré (1918), who incorporated it in their calculations. Kelvin also adopts Le Sage’s explanation for the imperceptible resistance experienced by bodies in motion through the corpuscular medium. The velocities of the corpuscles can be imagined so great that the ratio of a body’s velocity to the average corpuscular velocity can be effectively reduced to zero, thereby eliminating the calculated resistive force (see also Darwin, 1905). I shall argue below that this approach, though seemingly innocuous, may actually have retarded the development of the theory.
|
||
Kelvin’s major contribution to the debate lay in the thorny problem of the nature of collisions between Le Sage corpuscles and ordinary bodies. Whereas Le Sage had argued that these collisions must be wholly or partially inelastic, to avoid the aforementioned difficulty of rebounding corpuscles, Kelvin suggested that elastic collisions might be feasible if, following Clausius’ notion of vibrational and rotational energies in gas molecules, the translational energies of Le Sage corpuscles after collision were given over to these other modes. In this way, the total energy of the system would be conserved. Le Sage’s theory had been criticized for requiring an endless expenditure of energy from the outside. Moreover, the translational energies of the corpuscles could be restored in later collisions between corpuscles, as Clausius had shown that the translational component of kinetic energy in a gas remains in a constant ratio to the total kinetic energy. There would thus be no need for a ‘gravitational death’ of the Universe owing to the progressive loss of translational kinetic energy of corpuscles.*
|
||
At this point, the historical picture becomes more complicated. Maxwell’s evaluation of the Kelvin-Le Sage theory was to become, according to Aronson, a turning point ultimately leading to the overthrow of the theory. Maxwell’s critique appeared in the Ninth Edition of the Encyclopaedia Britannica under the title ‘Atom’ in 1875. After presenting a lucid account of the revised theory and noting its potential promise, Maxwell condemned it on thermodynamic grounds, stating that the temperature of bodies must tend to approach that at which the average kinetic energy of a molecule of the body would be equal to the average kinetic energy of an ultramundane corpuscle. Maxwell assumed that the latter quantity was much greater than the former and thus concluded
|
||
|
||
* Kelvin and Aronson both cite Le Sage as also predicting a gravitational collapse of the Universe for these same reasons. But for Le Sage, a finite duration of the Universe was dictated by other factors specific to his own model (James Evans, personal communication).
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Le Sage’s Theory of Gravity: the Revival by Kelvin
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that ordinary matter should be incinerated within seconds under the Le Sage bombardment. He next gave the following proof to support this assessment:
|
||
Now, suppose a plane surface to exist which stops all the corpuscles. The pressure on this plane will be p = NMu2 where M is the mass of corpuscle, N the number in unit of volume, and u its velocity normal to the plane. Now, we know that the very greatest pressure existing in the universe must be much less than the pressure p, which would be exerted against a body which stops all the corpuscles. We are also tolerably certain that N, the number of corpuscles which are at anyone time within one unit of volume, is small compared with the value of N for the molecules of ordinary bodies. Hence, Mu2 must be enormous compared with the corresponding quantity for ordinary bodies, and it follows that the impact of the corpuscles would raise all bodies to an enormous temperature.
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As noted by Preston (1877), the questionable assumption with Maxwell’s argument is that the value of N for corpuscles is much smaller than N for ordinary bodies. Preston argued that, on the contrary, the value of N for corpuscles might be made as large as desired if the value for M was correspondingly smaller. In this way, the Le Sage pressure could be maintained despite the low kinetic energies of the individual corpuscles. What Maxwell thought of this rebuttal may not be known; he died just two years after Preston’s paper appeared, in 1879. Some authors, however, such as Aronson, apparently believe that Maxwell had the last word on the subject.
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||
An unusual development came with the abandonment of Kelvin’s theory by Kelvin himself. Here it should be emphasized that Kelvin had great ambitions for the theory. For him, the Le Sage theory complemented his dynamical scheme based on vortex atoms which was intended to account for all physical phenomena. When for various reasons he was forced to abandon his dynamical scheme in favour of an elastic-solid ether, Le Sage’s theory was apparently dropped as well. By 1881, his assessment of the Le Sage theory was gloomy:
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||
Le Sage’s theory might easily give an explanation of gravity and of its relation to inertia of masses, on the vortex theory, were it not for the essential aeolotropy of crystals, and the seemingly perfect isotropy of gravity. No finger-post pointing towards a way that can possibly lead to a surmounting of this difficulty, or a turning of its flank, has been discovered, or imagined as discoverable (Kelvin, 1881).
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A postscript to the Kelvin-Le Sage theory was issued by G. H. Darwin (1905), who drew an analogy between Le Sage’s mechanism and the newly appreciated phenomenon, discovered by Poynting, whereby two radiating spheres would repulse one another.* In his paper, Darwin calculated the gravitational force between two bodies at extremely close range to determine if geometrical effects would lead to a deviation from Newton’s law. He concluded that only in the instance of perfectly inelastic collisions, or in the case that Kelvin’s compensatory mechanism were operating and all translational ki-
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* A possible indication of the decline of the Kelvin-Le Sage model by 1905 is evident in Darwin’s statement in his paper that his calculations were mostly done years earlier, and that it was only Poynting’s work which now prompted him to publish.
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netic energy was given up by corpuscles after collision with bodies, would Newton’s law stand up.
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From this brief summary, it is apparent that several closely interconnected problems frustrated the development of Le Sage’s theory, problems which have also plagued Le Sage-type models ever since. These relate to the thermodynamic question and the likelihood of a frictional drag and gravitational aberration effect. The complications introduced by these problems are illustrated in the analysis of Poincaré (1918), who concluded that the Le Sage corpuscles must travel with such high velocities, some 1024 times c, that the Earth would be incinerated in seconds. Like other critics of the Le Sage theory, Poincaré failed to address the modifications introduced by Kelvin and Preston.
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At the same time, there are other disquieting features of Kelvin’s revised theory. If, as Darwin calculated, all the translational kinetic energy had to be converted to other modes after collisions, then a steady accrual of Le Sage corpuscles in the vicinity of masses would surely result. Secondly, the solution adopted by both Le Sage and Kelvin to the resistance problem—the invocation of arbitrarily high corpuscular velocities—effectively divorces the theory from both Special and General Relativity, in which the quantity c is pervasive. It would seem more satisfactory if the Le Sage corpuscles possessed this average speed. Kelvin’s modification thus appeared to sequester the gravitational force from the other forces. The Le Sage corpuscles operated within a sphere of their own, such that Kelvin’s grand scheme of integrating the forces of nature could not be realized.
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The combined influence of the many negative assessments, perhaps in conjunction with a general shift away from mechanical ether theories, appear to have led to a progressive loss of interest in the Le Sage-Kelvin theory. Still, Le Sage’s theory was not without its supporters even up to the turn of the century and beyond. The status of Le Sage’s theory at this time was summarized by Van Lunteren (1991, p. 276):
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In spite of the blows which Maxwell dealt the theory of Le Sage, the debate surrounding this model continued until after the turn of the century. Most contributions to the debate were critical, but the very fact that so many prominent physicists took pains to criticize the theory in itself attests to its prominence. Le Sage’s theory was certainly the most conspicuous explanation of gravitation. For many critics the theory embodied the very notion of a dynamical theory of gravitation. Refuting the theory was sometimes regarded to constitute a proof of the inexplicability of gravitation. It was also most reminiscent of the crude materialism of the ancient atomists.
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Le Sage’s Theory in the Twentieth Century
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In the twentieth century Le Sage’s theory was more or less entirely eclipsed by Einstein’s General Relativity. Just as in the previous centuries, isolated efforts to improve the theory have nonetheless been made. Several of these attempts are discussed or reprinted elsewhere in this volume and, for this reason, will not be examined at length here. In some cases these theories have had only a
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very limited exposure. If there is a common thread amongst the twentieth century theories, it is that the main obstacles that faced Kelvin in his day are still in need of resolution today.
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Soon after the revival by Kelvin, many authors, including Lorentz (1900) and Brush (1911), attempted to substitute electromagnetic waves for Le Sage’s corpuscles. Many of the most recent efforts have continued in this vein. The earliest such theory was due to Lorentz (1900). Assuming that space is filled with radiation of a very high frequency, Lorentz showed that an attractive force between charged particles (which might be taken to model the elementary subunits of matter) would indeed arise, but only if the incident energy were entirely absorbed. This situation thus merely reinforced the previous difficulties noted above in Le Sage’s own theory and served to discourage further research along this line. In essence, this same problem has continually thwarted all subsequent Le Sage-type models.
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One possible difficulty of electromagnetic Le Sage models is connected to the problem of gravitational aberration. As pointed out initially by Laplace and later by many others, it would appear that the gravitational force would need to be propagated at a velocity >> c to avoid introducing forces into astrophysics that are known not to exist (see also Van Flandern, this volume). At the same time, other authors (e.g., Poincaré, 1906 (cited in Roseveare, 1982); Jaakkola, 1996) had expressed the view that within the Galaxy and Solar System such forces may be compensated for by others and that aberration effects in these settings may thus not arise.
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The Theory of Majorana
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In an unusual development, Le Sage’s theory in this century became intertwined with an alternative theory of gravitation, also involving shading effects, proposed by Q. Majorana (1920). The history of Majorana’s theory is detailed in two papers in this volume by Martins and will only be briefly discussed here. Majorana took as a starting assumption that a material screen set between two other bodies would diminish the force of attraction between the latter due to gravitational absorption by the screen. This state of affairs might be most readily envisioned if the gravitational force was caused by “a kind of energical flux, continually emanating from ponderable matter”. The situation might then be analogous to the absorption of light in passage through a semi-transparent medium. His view thus differed sharply from Le Sage’s, in that matter itself, rather than the remote regions of space, are the source of the gravitational fluxes. A complication of Majorana’s theory was that bodies must be continually losing energy as a result of the gravitational emission. In a famous set of experiments Majorana found evidence for gravitational shielding of the same magnitude as would be consistent with astrophysical data. Majorana was aware of Le Sage’s theory and in one set of experiments tried to distinguish which of the theories was correct, his own or Le Sage’s. As shown by Martins (this vol-
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ume), however, a clear distinction between Le Sage and Majorana using shielding experiments may be impossible even in principle.
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The phenomenon uncovered by Majorana initially attracted considerable interest, especially from A. A. Michelson. Upon publication of an article by the astronomer H. N. Russell (1921), however, Michelson apparently lost interest and Majorana’s work was largely neglected by physicists. Russell first demonstrated that, in order that large deviations from Kepler’s laws not occur under Majorana’s theory, the inertial masses of bodies must remain at all times proportional to the gravitational masses. Russell then went on, however, to show that even granted this proportionality, a major problem arose in the case of the tides, the solar tides in particular being some 370 times greater on the side of the Earth facing away from the Sun compared to the side facing the Sun. This criticism was subsequently attacked by Radzievskii and Kagalnikova (1960, reprinted here) and Shneiderov (1961b). The details of Russell’s analysis are complex and were never fully accepted by Majorana, who felt that the whole question of tidal forces and measurements needed closer examination. Russell’s paper is discussed further below in connection with General Relativity.
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Since the time of Majorana’s experiments, a number of laboratory investigations have been conducted in an effort to duplicate Majorana’s findings (for a review, see Gillies, 1997; see also Unnikrishnan and Gillies, this volume). While these studies have failed to detect an effect of the same magnitude as Majorana’s, it should be noted that none have employed Majorana’s beam balance technique of quick, successive measurements where the shielding mass was first present, then absent. The latter-day studies have instead often relied on highly sensitive torsion balances featuring many electrical components. The suitability of torsion balances for detecting extremely tiny deviations from the norm was discussed by Speake and Quinn (1988). The major difficulty with such balances, in their view, is that such small weights must be used, due to the inherent weakness of the fibre, that nongravitational noise, chiefly of seismic or thermal origin, may mask the miniscule deviations sought.
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An experimental apparatus which may be suitable for replicating Majorana’s work is the Zürich apparatus for measuring G (see Unnikrishnan and Gillies, 2000, and references therein). The Zürich experiment involves the deployment of large shielding masses in a manner highly reminiscent of Majorana’s experiments. While data from the Zürich experiment do not at the moment appear to support Majorana (Unnikrishnan and Gillies, 2000, but see also Dedov et al., 1999), a direct replication of Majorana’s experiments in an effort to decide this important issue would be highly desirable.
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Recently, support for the theories of Majorana and Le Sage has come from a different direction. A puzzling aspect of gravitation has long been the inability of researchers to precisely determine the value of the gravitational constant, G. This difficulty continues to motivate efforts in this area, such as
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the aforementioned Zürich experiment. In a detailed study, however, Dedov et al. (1999) consider the effects of the Earth’s screening action in such experiments according to the theories of Le Sage and Majorana. The authors conclude that the Earth’s screening effect, which would have a different mathematical form depending on the specific experiment, does account for the observed variations in the measured value of G.
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A few decades ago there was an upsurge of interest in Majorana’s work due to speculation that gravitational shielding might be associated with the socalled “fifth force” (Fischbach et al., 1988). More recently, renewed interest has followed experiments involving rotating semiconductors hinting at some type of gravitational absorption (for discussions of the latter, see the papers by Unnikrishnan and Gillies and Hathaway in this volume).
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Eclipse Experiments
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Observational evidence for gravitational absorption has also been sought during solar and lunar eclipses, with findings both for and against being reported (for reviews, see Gillies, 1997, Martins, 1999 and Borzeszkowski and Treder, this volume). In these studies, however, it is not entirely clear what the predicted effects should be for Le Sage’s theory. In the case of a gravimeter passing through totality during a solar eclipse, for example, we would need to compute separately the attenuation effects for four bodies—the Earth, the Sun, the Moon and the gravimeter. In practice, such computations are extremely difficult and a comprehensive treatment under Le Sage’s theory has yet to be done.
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On the other hand, it would appear that a Le Sage-type mechanism could possibly account, at least qualitatively, for the gravitational effects reported during a recent total solar eclipse in China (Wang et al., 2000; but see also Unnikrishnan et al., 2001; Unnikrishnan and Gillies, this volume). Using a spring-mass gravimeter during the solar eclipse of March 9, 1997, Wang et al. observed a decrease in surface gravity of 7 µgal at two times, one immediately before the onset of the eclipse and one just after the eclipse. At the height of the eclipse, however, there was no effect.
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||
At first glance this result appears to be the opposite of what one might expect under Le Sage’s theory. From the standpoint of the Earth, in Le Sage’s theory, the Moon and Sun immediately before and after the eclipse screen off a greater quantity of the total background flux of Le Sage particles (or waves) than during the eclipse. This is because the flux passing through the Moon during the eclipse has already been attenuated while passing through the Sun. The two shadows ‘cancel’ each other partly at this time leading to an increased flux hitting the Earth compared to the situation immediately before and after the eclipse. We might thus expect an increase in the surface gravity of the Earth during the eclipse according to Le Sage’s theory.
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During a total eclipse, however, it is important to note that only a small region of the Earth, along the path of totality, is encompassed at any one time in the eclipse cone of shadow. It is only in this region that there is an increased
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flux of Le Sage particles or waves from the direction of the Moon. This allows for a very different interpretation of the gravimeter readings (this interpretation was suggested by Roberto de Andrade Martins, personal communication). Consider the situation just before the gravimeter passes into the cone of shadow. At this time the Earth under the shadow experiences a repulsive force from the direction of the Sun-Moon system. A small acceleration is imparted to the Earth, which is recorded as a slight decrease in surface gravity by the nearby gravimeter not yet under the shadow. As the shadow passes directly over the study site, both the gravimeter and the column of Earth beneath it are now exposed to the same increased flux and pushing force. There is thus no change in the relative acceleration between the Earth and the gravimeter and no anomaly at this time. As the cone of shadow passes to the other side of the study site, the Le Sage flux on that side increases and the gravimeter again records the slight acceleration of the Earth. This could account for the curious ‘before-and-after’ effect in the Chinese study. In eclipses where the study site does not experience totality, it would be expected under this mechanism that just one peak would be observed, corresponding to the period when the region of totality passes closest to the study site. In this respect, a single-peak decrease of 10-12 µgal was reported by Mishra and Rao (1997) for a solar eclipse in India in 1995. In this instance the study site only experienced 80 per cent totality.
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Recent Le Sage-Type Theories
|
||
Despite the general emphasis on Majorana’s rather than Le Sage’s theory, the latter has cropped up in new forms several times in the last half-century. A partial listing of these newer theories would include the works of Radzievskii and Kagalnikova (1960), Shneiderov (1943, 1961a), Buonomano and Engel (1976), Adamut (1976, 1982), Veselov (1981), Jaakkola (1996) and Van Flandern (1999). As many of these theories are discussed more fully elsewhere in this book, and in some cases reprinted, the present brief discussion will be limited to Shneiderov.
|
||
In a very ambitious model, Shneiderov (1943, 1961a) argued that Le Sage did not take into account the progressive character of the absorption of a ray of gravitons as it passed through a body. He named his own theory, which corrected this supposed deficiency, the “exponential theory” of gravity. Shneiderov’s approach is similar in some respects to that of Radzievskii and Kagalnikova (1960), but contains a few assumptions which are not well explained. Shneiderov was most interested in exploring the geological consequences of his theory and attempted to link his work to the internal heating of planets and to Earth expansion (see Kokus, this volume). At the end of his 1961 article the editor of the Italian journal indicated his enthusiasm for Shneiderov’s theory by issuing a call for papers for a conference devoted to it. Whether or not such a conference ever came to pass I have been unable to discern.
|
||
In a separate paper, in which he attacked Russell’s criticism of Majorana’s theory, Shneiderov (1961b) proposed an experiment to test the validity of
|
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Majorana’s and his own theory. It is unclear whether any such experiment has ever been attempted. The details of the proposed experiment were as follows:
|
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An accurate balance is put into a vacuum casing. A light, evacuated, and hermetically sealed spherical shell is suspended from one arm of the balance. Suspended in the spherical shell, at its center is a light receptacle with 50 g of liquid mercury in it. A counterweight is put on the scale of the other arm to balance the instrument. The mercury is evaporated to fill the shell uniformly. The weight of the shell filled with 50 g of mercury vapor should be greater than when the mercury is in the liquid state, and the arm of the balance supporting the sphere should, therefore, go down if the exponential theory of gravitation were correct.
|
||
Shneiderov calculated that the ratio of the mass of mercury in the vapour state to its mass in the liquid state would be 1 + 5.143 × 10−11. A possible complication in Shneiderov’s experiment is the unknown effects of the change of phase from liquid to vapour.
|
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Shneiderov also attempted to account for the electrostatic force between charges in his model (Shneiderov, 1961a). Unlike bulk matter, which was mostly porous to radions (his term for Le Sage’s particles), electrons in his scheme intercepted the entire incident flux of radions. To Shneiderov, this accounted for the enormously greater strength of the electrostatic force over gravity. In a similar vein, Jones (1987) and more recently Byers (1995) have given arguments supporting Le Sage-type shielding as the source of the strong force binding nucleons. These notions are consistent with an electromagnetic unification of all the forces and particles of nature, an occasional theme in Le Sagetype theories.
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|
||
Le Sage Gravity and General Relativity
|
||
Some possible links between Le Sage gravity and GR are also evident. Near a large body, such as the Sun, an object necessarily experiences a reduced Le Sage pressure from the direction of the body. If the ‘Le Sage frame’ were defined as one in which the velocities and numerical densities of Le Sage corpuscles or waves are the same in all directions, then it is apparent that such a frame in the vicinity of the Sun would be ‘falling’ towards it. This suggests a Le Sage formulation of GR, in which changing Le Sage pressures near masses provide the physical basis for the mathematically derived expressions related to the ‘curvature of space’. In this respect, it should be noted that Einstein considered a gravitational ether, which would differ fundamentally from the electromagnetic ethers of Fresnel and Lorentz, to be necessary to account for the inertia and acceleration of bodies (see Kostro, 2001).
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Given the close connections between the theories of Le Sage and Majorana (see Martins, this volume), some comments by Russell on Majorana’s theory may also be relevant in this light. As noted above, Russell published an article highly critical of Majorana’s theory. Russell did not express unease with Majorana’s experimental findings, however, and in the same article made the following interesting suggestion:
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But what then becomes of Professor Majorana’s long and careful series of experiments? If their result is accepted, it seems necessary to interpret it as showing that the mass of one body (his suspended sphere of lead) was diminished by the presence of another large mass (the surrounding mercury); that the effect was a true change in mass (since inertial mass and gravitational mass are the only kinds of mass we know of); and that it depended on the proximity of the larger mass, and not upon any screening action upon the earth’s gravitation. Strange as this notion may seem, it is not inherently absurd. Indeed, if the phenomena of gravitation and inertia may be accounted for by assuming that the four-dimensional “world” possesses certain nonEuclidean properties, or “curvature”, both in the presence of matter and remote from it, it is not very surprising if the curvature induced by one mass of matter should be modified to some degree by the superposition of the curvature due to another, so that the effects were not exactly additive.
|
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Clearly, the tiny effect found by Majorana was viewed by Russell as a possible manifestation of the then newly proposed theory of General Relativity.
|
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Le Sage gravity, in view of Russell’s interpretation above, could shed light on one of the unsolved problems of GR. In the Newtonian model, the total energy Et of a gravitating pair of masses, such as the Moon and the Earth, can be expressed as
|
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||
Et = Ek + E p ,
|
||
|
||
(1)
|
||
|
||
where Ek is the kinetic energy of the two bodies and Ep is the potential energy. Ep tends to increase with increasing separation, while Ek tends to decrease. But as energy is associated with mass in GR, a difficulty arises since Ep cannot be tied to a specific point in the system (Bondi, 1991). The concept of shielded or
|
||
|
||
‘hidden’ mass may prove useful in this context. Rather than regarding the two
|
||
|
||
masses as separate, independent units, as in Newtonian theory, they may be
|
||
|
||
treated as a single mass, which may be dispersed in space to a greater or lesser
|
||
|
||
degree. The expression for the total mass of the system, Mt, may be given as
|
||
|
||
M t = M ap + M s ,
|
||
|
||
(2)
|
||
|
||
where Map is the apparent mass of the bodies, in the sense of Majorana, and Ms is the shielded or hidden mass. The apparent mass of the two bodies will be
|
||
seen to vary in precisely the same way as the potential energy, increasing to a
|
||
maximum at infinite separation. Conversely, Ms will tend to increase as the two bodies approach each other. Thus, the motion from a lower to a higher orbit
|
||
can be viewed as the creation of ‘new’ mass, as shielded portions of the bodies
|
||
become exposed to Le Sage corpuscles.
|
||
Such an interpretation of mass could have implications for cosmology. As
|
||
noted above, under either the Le Sage or Majorana theories, celestial objects
|
||
like the Sun have Map reduced relative to the situation that they were finely distributed throughout space. As Majorana showed, for very large bodies, in
|
||
which the attenuation of the gravitational flux might approach 100 per cent, Map becomes proportional to the cross-sectional area, and thus to R2. In such cases the core regions of the bodies receive no corpuscles at all from the exter-
|
||
nal surroundings. The core of a body in this case would not be held in place by
|
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its own self-gravitation, but by the gravitational pressure of the outer shell. Map of the core would fall to zero. Outside the domain of gravity, and perhaps the other forces as well, the core region would exist as a kind of reservoir of unrefined matter and energy.
|
||
The hidden reservoirs of degraded matter might then give rise to unusual physical and cosmological phenomena. Large ‘black hole’-type objects, for example, might remain stable until an external event, such as a stellar collision, disrupts the equilibrium of forces. Ruptures of the shell might then lead to jetting of core material into the surrounding space, which in turn could give rise to new hydrogen atoms and subsequently new stars and galaxies. Such a sequence might correspond in a general sense to the theory of formation of quasars outlined by Arp (1998, see also this volume). In this way equilibrium might be attainable between the processes of hydrogen consumption (in stars) and hydrogen renewal (in quasar formation) in a static Universe.
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References
|
||
Adamut, I.A., 1976. “Analyse de l’action gravitationelle du rayonnement électromagnétique sur un système de corps. Une théorie électrothermodynamique de la gravitation”, Nuovo Cimento B 32, 477-511.
|
||
Adamut, I.A., 1982. “The screen effect of the earth in the TETG. Theory of a screening experiment of a sample body at the equator using the earth as a screen”, Nuovo Cimento C 5, 189-208.
|
||
Aronson, S., 1964. “The gravitational theory of Georges-Louis Le Sage”, The Natural Philosopher, 3, 51.
|
||
Arp, H.C., 1998. Seeing Red:Redshifts Cosmology and Academic Science, Apeiron, Montreal.
|
||
Bondi, H, 1991. “Gravitation”, Curr. Sci. 63, 11-20.
|
||
Brush, C.F., 1911. “A kinetic theory of gravitation”, Nature, 86, 130-132. The same article also appeared in Science, 33, 381-386.
|
||
Brush, S.G., 1976. “The kind of motion we call heat”, Studies in Statistical Mechanics, Vol. 6, NorthHolland Publishing Co., Amsterdam, pt. 1, pp. 21-22, 48.
|
||
Buonomano, V. and Engel, E., 1976. “Some speculations on a causal unification of relativity, gravitation, and quantum mechanics”, Int. J. Theor. Phys. 15, 231-246.
|
||
Byers, S.V., 1995. “Gravity, inertia and radiation” (website article, http://home.netcom.com/~sbyers11/).
|
||
Darwin, G.H., 1905. “The analogy between Lesage’s theory of gravitation and the repulsion of light”, Proc. Roy. Soc. 76, 387-410.
|
||
Dedov, V.P., et al., 1999. “Gravitational screening effect in experiments to determine G”, Meas. Tech. 42, 930-941.
|
||
Feynman, R.P., et al., 1963. The Feynman Lectures on Physics, Vol. 1, Addison-Wesley Publishing Co., Menlo Park, Ca., Sections 7-7.
|
||
Fischbach, E. et al., 1988. “Possibility of shielding the fifth force”, Phys. Rev. Lett. 60, 74.
|
||
Gillies, G.T., 1997. “The Newtonian gravitational constant: recent measurements and related studies”, Rep. Prog. Phys. 60, 151-225.
|
||
Jaakkola, T., 1996. “Action-at-a-distance and local action in gravitation: discussion and possible solution of the dilemma”, Apeiron 3, 61-75. Reprinted in this book.
|
||
Jones, W.R., 1987. “How the ether replaces relativity”, in Progress in Space-Time Physics 1987 (J.P. Wesley, ed.), Benjamin Wesley, Blumberg, Germany, pp. 66-82.
|
||
Kelvin, see Thomson, W.
|
||
Kostro, L., 2001. Einstein and the Ether, Apeiron, Montreal.
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||
Laudan, L., 1981. Science and Hypothesis, Reidel, Dordrecht, pp. 118-123.
|
||
Le Sage, G.-L., 1784 (for the year 1782), “Lucrèce Newtonien”, Memoires de l’Academie Royale des Sciences et Belles Lettres de Berlin, 1-28.
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Lorentz, H.A., 1900. Proc. Acad. Amsterdam, ii, 559. A brief treatment in English appears in Lectures on theoretical physics, Vol. 1(1927), MacMillan and Co., Ltd., 151-155 (an edited volume of translations of a lecture series by Lorentz).
|
||
Majorana, Q., (1920). “On gravitation. Theoretical and experimental researches”, Phil. Mag. [ser. 6] 39, 488-504.
|
||
Martins, de Andrade, R., 1999. “The search for gravitational absorption in the early 20th century”, in: The Expanding Worlds of General Relativity (Einstein Studies, vol. 7) (eds., Goemmer, H., Renn, J., and Ritter, J.), Birkhäuser, Boston, pp. 3-44.
|
||
Maxwell, J.C., 1875. “Atom”, Encyclopedia Britannica, Ninth Ed., pp. 38-47.
|
||
Mishra, D.C. and Vyaghreswara Rao, M.B.S., 1997. “Temporal variation in gravity field during solar eclipse on 24 October 1995”, Curr. Sci. 72, 782-783.
|
||
Poincaré, H., 1906. “Sur le dynamique de l’électron”, Rend. Circ. mat Palermo 21, 494-550.
|
||
Poincaré, H., 1918. Science and method, Flammarion, Paris. An English translation was published as Foundation of Science, Science Press, New York, 1929.
|
||
Preston, S.T., 1877. “On some dynamical conditions applicable to Le Sage’s theory of gravitation”, Phil. Mag., fifth ser., vol. 4., 206-213 (pt. 1) and 364-375 (pt. 2).
|
||
Radzievskii, V.V. and Kagalnikova, I.I., 1960. “The nature of gravitation”, Vsesoyuz. Astronom.Geodezich. Obsch. Byull., 26 (33), 3-14. A rough English translation appeared in a U.S. government technical report: FTD TT64 323; TT 64 11801 (1964), Foreign Tech. Div., Air Force Systems Command, Wright-Patterson AFB, Ohio (reprinted here).
|
||
Roseveare, N.T., 1982. Mercury’s Perihelion from Le Verrier to Einstein, Oxford University Press, Oxford.
|
||
Russell, H.N., 1921. “On Majorana’s theory of gravitation”, Astrophys. J. 54, 334-346.
|
||
Shneiderov, A.J., 1943. “The exponential law of gravitation and its effects on seismological and tectonic phenomena: a preliminary exposition”, Trans. Amer. Geophys. Union, 61-88.
|
||
Shneiderov, A.J., 1961a. “On the internal temperature of the earth”, Bollettino di Geofisica Teorica ed Applicata 3, 137-159.
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||
Shneiderov, A.J., 1961b. “On a criticism of Majorana’s theory of gravitation”, Bollettino di Geofisica Teorica ed Applicata 3, 77-79.
|
||
Speake, C.C. and Quinn, T.J., 1988. “Detectors of laboratory gravitation experiments and a new method of measuring G”, in Gravitational Measurements, Fundamental Metrology and Constants, (eds. V. De Sabbata and V.N. Melnikov), Kluwer, Dordrecht, pp. 443-57.
|
||
Taylor, W.B., 1877. “Kinetic theories of gravitation”, Annual Report of the Board of Regents of the Smithsonian Society, 205-282.
|
||
Thomson, W. (Lord Kelvin), 1873. “On the ultramundane corpuscles of Le Sage”, Phil. Mag., 4th ser., 45, 321-332.
|
||
Thomson, W. (Lord Kelvin), 1881. Roy. Inst. Gr. Brit. Proc. 9, 520-521.
|
||
Unnikrishnan, C.S. and G. T. Gillies, 2000. “New limits on the gravitational Majorana screening from the Zürich G experiment”, Phys. Rev. D 61, 101101(R).
|
||
Unnikrishnan, C.S., Mohapatra, A.K. and Gillies, G.T., 2001. Phys. Rev. D 63, 062002. Van Flandern, T., 1999. Dark Matter, Missing Planets and New Comets, 2nd ed., North Atlantic Books,
|
||
Berkeley, Chapters 2-4. Van Lunteren, F.H., 1991. Framing Hypotheses: Conceptions of Gravity in the 18th and 19th Centuries,
|
||
PhD thesis (Rijksuniversiteit Utrecht).
|
||
Veselov, K.E., 1981. “Chance coincidences or natural phenomena”, Geophys. J. 3, 410-425. Reprinted in this book
|
||
Wang, Q.-S. et al., 2000. “Precise measurement of gravity variations during a total solar eclipse”, Phys. Rev. D 62, 041101(R).
|
||
|
||
The Nature of Gravitation*
|
||
V.V. Radzievskii† and I.I. Kagalnikova
|
||
|
||
Introduction
|
||
The discovery of the law of universal gravitation did not immediately attract the attention of researchers to the question of the physical nature of gravitation. Not until the middle of the 18th century did M.V. Lomonosov [1] and several years later, Le Sage [2,3], make the first attempts to interpret the phenomenon of gravitation on the basis of the hypothesis of ‘attraction’ of one body to another by means of ‘ultracosmic’ corpuscles.
|
||
The hypothesis of Lomonosov and Le Sage, thanks to its great simplicity and physical clarity, quickly attracted the general attention of naturalists and during the next 150 years served as a theme for violent polemics. It gave rise to an enormous number of publications, among which the most interesting are the works of Laplace [4], Secchi [5], Leray [6], W. Thomson [7], Schramm [8], Tait [9], Isenkrahe [10], Preston [11, 12], Jarolimek [13], Vaschy [14], Rysanek [15], Lorentz [16], D. Thomson‡ (cited in [17]), Darwin (18), H. Poincaré [19, 20], Majorana [21-25], and Sulaiman [26,27].
|
||
In the course of these polemics, numerous authors proposed various modifications to the theory of Lomonosov and Le Sage. However, careful examination of each of these invariably led to conclusions which were incompatible with one or another concept of classical physics. For this reason, and also as a result of the successful elaboration of the general theory of relativity, interest in the Lomonosov–Le Sage hypothesis declined sharply at the beginning of the 20th century and evidently it would have been doomed to complete oblivion if, in 1919-1922, the Italian scientist Majorana had not published the results of his highly interesting experiments. In a series of extremely carefully prepared experiments, Majorana discovered the phenomenon of gravitational absorption by massive screens placed between interacting bodies, a phenomenon which is easily interpreted within the framework of classical concepts of the mechanism of gravitation, but theretofore did not have an explanation from the point of view of the general theory of relativity.
|
||
The famous experimenter, Michelson [28], became interested in the experiments of Majorana. However, his intention to duplicate these experiments faded, evidently as a result of the critical article by Russell [29], in
|
||
|
||
* This paper is a corrected version of U.S. government technical report FTD-TT-64-323/1 + 2 + 4 [AD-601762]. The original article in Russian appeared in: Bull. Vsesoyuz. Astronomo-Geod. Obschestva, No. 26 (33), pp. 3-14, 1960. Reprinted with permission of V.V. Radzievskii.
|
||
† Present address: Nizhnii Novgorod Pedagological University, Nizhnii Novgorod, Russia. ‡ Editor’s note: The D. Thomson mentioned in this paper possibly refers to W. Thomson
|
||
|
||
Pushing Gravity: new perspectives on Le Sage’s theory of gravitation
|
||
|
||
79
|
||
|
||
edited by Matthew R. Edwards (Montreal: Apeiron 2002)
|
||
|
||
80
|
||
|
||
V.V. Radzievskii and I.I. Kagalnikova
|
||
|
||
which it was shown that if Majorana’s gravitational absorption really did exist, then the intensity of ocean tides on two diametrically opposite points on the earth would differ almost 400 fold. On the basis of Russell’s calculation, Majorana’s experimental results were taken to be groundless in spite of the fact that the experimental and technical aspect did not arouse any concrete objections.
|
||
In acquainting ourselves with the whole complex of pre-relativity ideas about the nature of gravitation, we were compelled to think of the possibility of a synthesis of the numerous classical hypotheses, such that each of the inherent, isolated, internal contradictions or disagreements with experimental data might be successfully explained. The exposition of this ‘synthesis’, i.e., a unified and modernized classical hypothesis of gravitation created primarily from the work of the authors cited above and supplemented only to a minimum degree by our own deliberations, is the main problem of this work. The other motive which has impelled us to write this article is that we have discovered the above mentioned objections of Russell against Majorana’s experimental results to be untenable: from the point of view of the classical gravitation hypothesis no differential effect in the ocean tides need be observed. Therefore we must again emphasize that Majorana’s experimental results deserve the closest attention and study. It seems to us that duplication of Majorana’s experiments and organization of a series of other experiments which shed light on the existence of gravitational absorption are some of the most urgent problems of contemporary physics. Positive results of detailed experiments could introduce substantial corrections into even the general theory of relativity concerning the question of gravitational absorption, which within the framework of this theory still remains a blank spot.
|
||
Evidently a strict interpretation of the Majorana phenomenon is possible only from the position of a quantum-relativistic theory of gravitation. However, insofar as this theory is still only being conceived, it seems appropriate, as a first approximation, to examine an interpretation of this problem on the basis of the ‘synthetic hypothesis’ presented below, especially as the latter includes the known attempts at a theory of quantum gravitation. We shall begin with a short exposition of the history of the question.
|
||
|
||
1. Discussion of the Lomonosov-Le Sage hypothesis
|
||
According to the Lomonosov-Le Sage hypothesis, outer space is filled with ‘ultracosmic’ particles which move with tremendous speed and can almost freely penetrate matter. The latter only slightly impedes the momentum of the particles in proportion to the magnitude of the penetrating momentum, the density of the matter, and the path length of the particle within the body.
|
||
Thanks to spatial isotropy in the distribution and motion of the ultracosmic particles, the cumulative momentum which is absorbed by an isolated body is equal to zero and the body experiences only a state of compression. In the presence of two bodies (A and B) the stream of particles from body B, imping-
|
||
|
||
The Nature of Gravitation
|
||
|
||
81
|
||
|
||
ing on body A, is attenuated by absorption within body B. Therefore, the surplus of the flux striking body A from the outer side drives the latter toward body B.
|
||
In connection with the Lomonosov-Le Sage hypothesis, the question of the mechanism of momentum absorption immediately arises. Generally speaking, the following variants are possible:
|
||
|
||
1. The overwhelming majority of particles pass through matter without loss of momentum, and an insignificant part are either completely absorbed by the matter or undergo elastic reflection (Schramm [8]). Evidently, in the first case, constant ‘scooping’ of ultracosmic particles by matter must take place, leading to a secular decrease in the gravitation constant. In addition, as can easily be shown, an inadmissible rapid increment of the body’s mass in this case must occur if the speed of the ultracosmic particles is close to that of light. In the second case, as Vaschy [14] showed, the reflected particles must compensate for the anisotropy in the motion of the particles which was created by the interacting bodies. In other words, the driving of the bodies in this case would be completely compensated for by the repulsion of the reflected particles and no gravitation would result.
|
||
2. All particles passing through matter experience something like friction, as a result of which they lose part of their momentum owing to a decrease in speed (Le Sage [2, 3], Leray [6], Darwin [18], and others). Evidently in this case there would also be a gradual weakening of the gravitational interaction of the bodies (Isenkrahe [10]).
|
||
|
||
A way out from the described difficulty was made possible by the proposal of Thomasin (cited in [19, 17]), D. Thomson (cited in [17]), Lorentz [16], Brush [30], Klutz [31], Poincaré [19, 20], and others for a new modification of the Lomonosov-Le Sage hypothesis, according to which the ultracosmic particles are replaced by extremely hard and penetrating electromagnetic wave radiation. If in this case we assume that matter is capable of absorbing only primary radiation and radiated secondary radiation, which still possesses great penetrating power, then the Vaschy effect (repulsion of secondary radiation) may be eliminated.*
|
||
The next question which arises in connection with the LomonosovLe Sage hypothesis concerns the fate of the energy which is absorbed by the body along with the momentum of the gravitational field. As Maxwell [32] and Poincaré [19, 20] have shown, if we attribute to gravity a speed not less than the speed of light, then in order to ensure the gravitational force observed in nature it is necessary to accept that momentum is absorbed which is equal to an amount of energy that can transform all material into vapor in one second.
|
||
|
||
* However, in order that a secular decrease in the gravitation constant does not occur it is necessary to suppose that the quanta of secondary radiation, after being radiated, decompose to primary radiation and, as a consequence, at some distance, depending on the duration of their lives, the gravitational interaction between bodies approaches zero.
|
||
|
||
82
|
||
|
||
V.V. Radzievskii and I.I. Kagalnikova
|
||
|
||
However, these ideas lose their force when the ideas of Thomasin, D. Thomson, and Lorentz are considered, according to which the absorbed energy is not transformed into heat, but is reradiated as secondary radiation according to laws which are distinct from the laws of thermal radiation.
|
||
There was still one group of very ticklish questions connected with the astronomical consequences of the Lomonosov-Le Sage hypothesis. As Laplace had shown [4], the propagation of gravitation with a finite speed must cause gravitational aberration, giving rise to so many significant disturbances in the motion of heavenly bodies that it would be possible to avoid them only if the propagation velocity of gravitation exceeded the velocity of light by at least several million times.
|
||
Poincaré [20] directed attention to the fact that the motion of even an isolated body must experience very significant braking as a result first of the Doppler effect (head-on gravitons become harder and consequently have more momentum than ones which are being overtaken) and second, the mass being absorbed sets the body in motion and a part of the body’s own motion is communicated to the mass. In order for this braking not to be detected by observation, it is necessary to assume that the speed of gravitational radiation exceeds the speed of light by 18 orders. This idea of Poincaré is considered to be one of the strongest arguments against the Lomonosov-Le Sage hypothesis.
|
||
Not long ago a modification to the Lomonosov-Le Sage hypothesis was suggested by the Indian academician Sulaiman [26, 27].
|
||
According to this hypothesis, an isolated body A radiates gravitons in all possible directions isotropically, experiencing a resultant force equal to zero. The presence of a second body B slows the process of graviton radiation by body A more strongly, the smaller the distance between the bodies. Therefore the quantity of gravitons being radiated from the side of the body A facing body B will be less than from the opposite side. This gives rise to a resultant force which is different from zero and tends to bring body A and body B together.
|
||
Further, Sulaiman postulated invariability of the graviton momentum with respect to a certain absolute frame of reference. Here the moving body must experience not braking, but rather acceleration coinciding with the direction of speed which compensates the braking influence of the medium.
|
||
Sulaiman’s hypothesis is very interesting. Unfortunately, it does not examine the question of decreasing mass of the radiating bodies or the question of the fate of the radiated gravitons.
|
||
As can easily be shown by elementary calculation, so that the impulse being radiated by the body can secure the observed force of interaction between them, it is necessary that they lose their mass with an unacceptably great speed. It is completely clear that no combination of longitudinal and transverse masses can save the thesis. There is a well-defined relationship between the relativistic expressions of the momentum and the energy [33], and it is impos-
|
||
|
||
The Nature of Gravitation
|
||
|
||
83
|
||
|
||
sible to imagine that a body radiating energy E (i.e., mass E/c2) could with this momentum radiate more than E/c.
|
||
If we suppose that the radiation of the mass is compensated by the reverse process of graviton absorption, then we return to a more elementary variant of the Lomonosov-Le Sage hypothesis. Graviton absorption and the screening effect which is inescapably linked with it guarantee a gravitational attraction force without the additional concept of anisotropic graviton radiation by one body in the presence of another.
|
||
|
||
2. Majorana’s experiment, Russell’s criticism
|
||
|
||
Majorana did not insist in his investigations on a concrete physical interpretation of the law of gravitation. He simply started from the supposition that if there is a material screen between two interacting material points A and B, the force of their attraction is weakened by gravitational absorption of this screen [21, 22, 25]. As in the Lomonosov-Le Sage hypothesis, Majorana took attenuation of the gravitational flux to be proportional to the value of the stream itself, the true density of the substance being penetrated by it, and the path length through the substance. The proportionality factor h in this relationship is known as the absorption coefficient. It is evident that with the above indicated supposition the relationship of the gravitational flux value to the path length must be expressed by an exponential law.
|
||
Let us imagine a material point which is interacting with an extended body. Since any element of this body’s mass will be attracted to the material point with a force attenuated by screening of that part of the body which is situated between the element and the material point, on the whole the heavy mass of this body will diminish in comparison with its true or inert mass.
|
||
In his work [21], Majorana introduced a formula for the relationship between the heavy (apparent) mass Mα and the inert (true) mass Mυ of a spherical body of radius R and a constant true density δυ
|
||
|
||
Mα
|
||
|
||
= ψMυ
|
||
|
||
=
|
||
|
||
3 1 4 u
|
||
|
||
−
|
||
|
||
1 2u3
|
||
|
||
+
|
||
|
||
e−2u
|
||
|
||
|
||
|
||
1 u2
|
||
|
||
+
|
||
|
||
1 2u3
|
||
|
||
|
||
|
||
M
|
||
|
||
υ
|
||
|
||
,
|
||
|
||
(1)
|
||
|
||
where u = hδυ R.
|
||
|
||
Expanding (1) into a series, it is easy to see that when u → 0, Mα → Mυ and when u → ∞, Mα → πR2/h. From this
|
||
|
||
h
|
||
|
||
≤
|
||
|
||
π R2 Mα
|
||
|
||
.
|
||
|
||
(2)
|
||
|
||
Applying the result of (2) in the case of the sun, which is a body with the most reliably determined apparent weight, Majorana obtained
|
||
|
||
h ≤ 7.65 ⋅10−12 CGS.
|
||
|
||
(3)
|
||
|
||
To experimentally determine the absorption coefficient h it is theoretically sufficient to weigh some “material point” without a screen and then determine the weight of this “material screen” after placing it in the center of a hollow
|
||
|
||
84
|
||
|
||
V.V. Radzievskii and I.I. Kagalnikova
|
||
|
||
sphere. If in the first case we obtain a value m, then in the second case we will register a decreased value as a result of gravitational absorption by the walls of the hollow sphere
|
||
|
||
mα = me−hδl ≅ m (1 − hδ l ) ,
|
||
|
||
(4)
|
||
|
||
where δ is the density of the material from which the screening sphere is made,
|
||
|
||
and l is the thickness of its walls. Designating ε as the weight decrease m − mα, we easily find that
|
||
|
||
h
|
||
|
||
=
|
||
|
||
ε mδ
|
||
|
||
l
|
||
|
||
⋅
|
||
|
||
(5)
|
||
|
||
To determine the absorption coefficient value by formula (5), Majorana
|
||
|
||
began, in 1919, a series of carefully arranged experiments, weighing a lead
|
||
|
||
sphere (with a mass of 1,274 gm) before and after screening with a layer of
|
||
|
||
mercury or lead (a decimeter thick).
|
||
|
||
After scrupulous consideration of all the corrections it turned out that, as a
|
||
|
||
result of screening, the weight of the sphere had decreased in the first series of experiments by 9.8 × 10−7 gm, which, according to (5), yields h = 6.7 × 10−12. In the second series of experiments, h = 2.8 × 10−12 was obtained.
|
||
|
||
As already mentioned, in 1921 Russell came out with a critical article de-
|
||
|
||
voted to Majorana’s work.
|
||
|
||
Assuming that the interaction force between two finite bodies is expressed
|
||
|
||
by the formula
|
||
|
||
F
|
||
|
||
=
|
||
|
||
Gm1ψ1m2ψ2 r2
|
||
|
||
,
|
||
|
||
(6)
|
||
|
||
where, in accordance with expression (1)
|
||
|
||
ψ
|
||
|
||
=
|
||
|
||
3 1 4 u
|
||
|
||
−
|
||
|
||
1 2u3
|
||
|
||
+
|
||
|
||
e−2u
|
||
|
||
|
||
|
||
1 u
|
||
|
||
+
|
||
|
||
1 2u3
|
||
|
||
|
||
|
||
,
|
||
|
||
and assuming at first that the decrease in weight as a result of self-screening occurs while leaving the inert masses unchanged, Russell obtained on the basis of (6) the third law of Kepler in the form
|
||
|
||
a13 a23
|
||
|
||
=
|
||
|
||
T12 T22
|
||
|
||
|
||
|
||
ψ1 ψ2
|
||
|
||
|
||
|
||
.
|
||
|
||
(7)
|
||
|
||
The value of ψ, calculated by Russell with the absorption coefficient h = 6.7 × 10−12 found by Majorana for several bodies of the solar system, is
|
||
|
||
equal to:
|
||
|
||
Sun:
|
||
|
||
0.33
|
||
|
||
Mars:
|
||
|
||
0.993
|
||
|
||
Jupiter:
|
||
|
||
0.951
|
||
|
||
Moon:
|
||
|
||
0.997
|
||
|
||
Saturn:
|
||
|
||
0.978
|
||
|
||
Eros:
|
||
|
||
1.000
|
||
|
||
Earth:
|
||
|
||
0.981
|
||
|
||
From this it follows that the true density of the sun is not 1.41, but 4.23 g/cm2.
|
||
|
||
Using the above tabulated values of ψ and Kepler’s law, Russell showed
|
||
|
||
convincingly that the corresponding imbalance between the heavy and inert
|
||
|
||
The Nature of Gravitation
|
||
|
||
85
|
||
|
||
masses of the planets would lead to unacceptably great deflections of their motions. In order that the deflection might remain unnoticed, it would be necessary for the absorption coefficient h to be 104 times less than the value found by Majorana. From this Russell came to the undoubtedly true conclusion that if as a result of self-screening the weight decrease found by Majorana did occur, then there would have to be a simultaneous decrease in their inert masses.
|
||
Russell made this conclusion the basis of the second part of his article, which was devoted mainly to investigation of the question of the influence of gravitational absorption on the intensity of lunar and solar tides. Following Majorana’s ideas, Russell suggested that a decrease in attraction and necessarily also a decrease in the inert mass of each cubic centimeter of water in relation to the sun or moon would occur only if they were below the horizon. If this is admitted, then sharp anomalies in the tides must be observed, viz., the tides on the side of the earth where the attracting body is located must be less intense (2 times for lunar tides and 370 times for solar tides) than on the opposite side of the earth. In conclusion Russell contended that his calculations demonstrated the absence of any substantial gravitational absorption and that consequently Majorana’s results are in need of some other interpretation. Russell himself, however, did not come to any conclusions in this regard.
|
||
While acknowledging the ideas presented in the first part of Russell’s work to be unquestionably right, we must first of all state that the selfscreening effect and the weight decrease associated with it cannot be seen as a phenomenon which is contradictory to the relativistic principle of equivalence: any change in a heavy mass must be accompanied by a corresponding change in the inert mass of the body. But is it possible to agree with the results of the second part of Russell’s article, according to which gravitational absorption on the scale discovered by Majorana is contradicted by the observation data of lunar and solar tides? Let us remember that Russell came to this conclusion starting from the freshly formed Majorana hypothesis of gravitational absorption only under the condition that the attracting bodies are on different sides of the screen. Meanwhile, application of the Lomonosov-Le Sage hypothesis, which painted a physical picture of gravitational absorption, leads, as we will show in the following section, to conclusions which are completely compatible with Majorana’s experimental results and with the concepts set forth in the first part of Russell’s article, but at the same time, all of the conclusions about tide anomalies lack any kind of basis. Skipping ahead somewhat let us say in short that according to the Lomonosov-Le Sage hypothesis, the weakening of attraction between two bodies must occur when a screen intersects the straight line joining them, regardless of whether there are gravitational bodies on various sides or on one side of this screen.
|
||
|
||
86
|
||
|
||
V.V. Radzievskii and I.I. Kagalnikova
|
||
|
||
3. The ‘Synthetic’ Hypothesis
|
||
|
||
Let us suppose that outer space is filled with an isotropic uniform gravitational field which we can liken to an electromagnetic field of extremely high frequency. Let us designate ρ as the material density of the field, keeping in mind with this concept the value of the inert mass contained in a unit volume of space. Evidently the density of that part of the field which is moving in a chosen direction within the solid angle dω is ρ(dω/4π). Under these conditions a mass of
|
||
|
||
dµ
|
||
|
||
=
|
||
|
||
dSρ
|
||
|
||
dω 4π
|
||
|
||
c
|
||
|
||
,
|
||
|
||
(8)
|
||
|
||
carrying a momentum
|
||
|
||
dp
|
||
|
||
=
|
||
|
||
dSρ
|
||
|
||
dω 4π
|
||
|
||
c2
|
||
|
||
(9)
|
||
|
||
will pass through any area element dS in its normal direction within the solid angle dω in unit time.
|
||
The mass flux (8) will fill an elementary cone, one cross section of which
|
||
|
||
serves as the area element dS. At any distance from this area element, let us draw two planes parallel to it which cut off an elementary frustrum of height dl, and let us imagine that the frustrum is filled with material of density δ. It is evident that the portion of the flux (8) absorbed by this material will be
|
||
|
||
d (dµ) = dµ hδ dl
|
||
|
||
(10)
|
||
|
||
or
|
||
|
||
d
|
||
|
||
(
|
||
|
||
dµ)
|
||
|
||
=
|
||
|
||
hρc
|
||
|
||
dω 4π
|
||
|
||
dm
|
||
|
||
,
|
||
|
||
(11)
|
||
|
||
where dm = δ dS dl is the mass of the elementary frustrum.
|
||
|
||
Let us imagine a ‘material point’ of mass m in the form of a spherical
|
||
|
||
body of density δ and of sufficiently small dimensions so that it is possible to
|
||
|
||
neglect the progressive character of the absorption within it and to consider that
|
||
|
||
the absorption proceeds in conformity with formula (11). Let us divide the sec-
|
||
|
||
tion of this spherical body into a number of area elements and construct on
|
||
|
||
each of them an elementary cone with an apex angle dω. Applying formula
|
||
|
||
(11) to these cones, and integrating with respect to the whole mass of the mate-
|
||
|
||
rial point, we obtain
|
||
|
||
∆
|
||
|
||
( dµ
|
||
|
||
)
|
||
|
||
=
|
||
|
||
hρc
|
||
|
||
dω 4π
|
||
|
||
m
|
||
|
||
.
|
||
|
||
(12)
|
||
|
||
Formula (12) determines the value of the absorbed portion of the field mass
|
||
|
||
which has passed in unit time through a cone with an apex angle dω, which is
|
||
|
||
circumscribed around a sufficiently small spherical body of mass m.
|
||
|
||
To obtain the total rate of increment in the mass of the point, it is neces-
|
||
|
||
sary to take into consideration absorption of the field impinging on it from all
|
||
|
||
possible directions, which is equivalent to integration (12) over the whole solid
|
||
|
||
angle ω. This gives
|
||
|
||
The Nature of Gravitation
|
||
|
||
87
|
||
|
||
Figure 1. Diagram for calculation of mass absorption of the flux of a material field.
|
||
|
||
dm dt
|
||
|
||
=
|
||
|
||
hρcm
|
||
|
||
.
|
||
|
||
(12′)
|
||
|
||
Returning to formula (10), imagine that the field flux inside the cone cir-
|
||
|
||
cumscribed around material point m penetrates the material throughout the finite section of the path AB = l (Fig. 1).
|
||
Integrating (10) from B to A, we obtain an expression which determines
|
||
|
||
the total absorption within the cone AB when δ = const
|
||
|
||
(dµ)1 = dµe−h δ l .
|
||
|
||
(13)
|
||
|
||
Let dµ be the mass of the field striking cone AB from side B, and (dµ)1 be the mass of the field exiting this cone and impinging on body m. The decrease in
|
||
|
||
the mass of the flux because of absorption in AB is equivalent to the decrease
|
||
|
||
in its density up to the value
|
||
|
||
ρ1 = ρe−h δ l .
|
||
|
||
(14)
|
||
|
||
Thus from the left a flux of density ρ [its absorbed portion is expressed by for-
|
||
mula (12)] strikes material point m, and from the right, a flux of density ρ1. The portion which is absorbed will be
|
||
|
||
∆ (dµ)1
|
||
|
||
=
|
||
|
||
hρce−h
|
||
|
||
δ
|
||
|
||
l
|
||
|
||
dω 4π
|
||
|
||
m
|
||
|
||
.
|
||
|
||
(15)
|
||
|
||
Calculating (15) and (12) and multiplying the result by c, we obtain a vector
|
||
|
||
sum of the momentum absorbed by point m in unit time equal to the value of the force dF, from which point m is ‘attracted’ to cone AB.
|
||
|
||
( ) dF
|
||
|
||
=
|
||
|
||
hρc2
|
||
|
||
dω 4π
|
||
|
||
1 − e−h δ
|
||
|
||
l
|
||
|
||
.
|
||
|
||
(16)
|
||
|
||
It would not be hard to show that with such a force cone AB is ‘attracted’ to point m.
|
||
|
||
Setting l = dl in (16) we obtain the attraction force of point m to a cone of elementary length
|
||
|
||
d
|
||
|
||
(dF )
|
||
|
||
=
|
||
|
||
h2 ρc2
|
||
|
||
dω 4π
|
||
|
||
mδ
|
||
|
||
dl
|
||
|
||
.
|
||
|
||
(17)
|
||
|
||
88
|
||
|
||
V.V. Radzievskii and I.I. Kagalnikova
|
||
|
||
As can be seen, force (17) at the assigned values of δ, dω, and dl depends neither on the distance between point m and the attracting elementary frustrum,
|
||
|
||
nor on the mass of the latter. This result corresponds completely to the data of
|
||
|
||
Newton’s theory of gravity and is explained by the fact that the mass of the
|
||
|
||
frustrum being examined is directly proportional to the square of its distance
|
||
|
||
from point m.
|
||
|
||
Differentiating (16) with respect to l, we obtain the value of the attraction
|
||
|
||
force of point m to element C of cone AB, which also does not depend on the
|
||
|
||
position of this element
|
||
|
||
d
|
||
|
||
( dF
|
||
|
||
)
|
||
|
||
=
|
||
|
||
h2 ρc2
|
||
|
||
dω 4π
|
||
|
||
me−h
|
||
|
||
δ
|
||
|
||
lδ dl
|
||
|
||
.
|
||
|
||
(18)
|
||
|
||
Comparison of (18) and (17) shows, however, that element C attracts point m
|
||
|
||
with a weakened force and the degree of its weakness depends on the general
|
||
|
||
thickness l of the screening material, regardless of whether point m and ele-
|
||
|
||
ment C are on different sides or on the same side of the screen. The latter result
|
||
|
||
is mathematical evidence of the groundlessness (within the framework of the
|
||
|
||
Lomonosov-Le Sage hypothesis) of the critical ideas in the second part of Rus-
|
||
|
||
sell’s article.
|
||
|
||
Let us now determine the total attraction force of material point m to a
|
||
|
||
spherical homogeneous body of mass M. Multiplying the right side of (16) by cosψ for this purpose and taking into account that l = 2 R2 − r2sin2ψ and
|
||
dω = 2π sinψ dψ, we easily find that
|
||
|
||
arcsin R
|
||
|
||
∫ ( ) F
|
||
|
||
=
|
||
|
||
hρc2m 2
|
||
|
||
r
|
||
1 − e−2hδ R2 −r2sin2ψ
|
||
0
|
||
|
||
cos ψ
|
||
|
||
sinψ
|
||
|
||
dψ
|
||
|
||
=
|
||
|
||
h2 ρc2 4π
|
||
|
||
mψM r2
|
||
|
||
,
|
||
|
||
(19)
|
||
|
||
where
|
||
|
||
ψ
|
||
|
||
=
|
||
|
||
3 1 4 u
|
||
|
||
−
|
||
|
||
1 2u3
|
||
|
||
+
|
||
|
||
e−2u
|
||
|
||
|
||
|
||
1 u2
|
||
|
||
+
|
||
|
||
1 2u3
|
||
|
||
|
||
|
||
,
|
||
|
||
(20)
|
||
|
||
in which µ = hδ R.
|
||
|
||
As has already been noted above, ψ ≅ 1 whence follows that the value
|
||
|
||
G
|
||
|
||
=
|
||
|
||
h2 ρc2 4π
|
||
|
||
(21)
|
||
|
||
plays the role of a gravitational constant. The value ψ which depends on pro-
|
||
|
||
gressive gravitational absorption within the body M must be considered to be
|
||
|
||
the weight decrease coefficient of the latter.
|
||
|
||
In correspondence with the later experiments of Majorana, let us suppose
|
||
|
||
that the coefficient of gravitational absorption is
|
||
|
||
h = 2.8 ⋅10−12 .
|
||
|
||
(22)
|
||
|
||
Then on the basis of (21) we easily find that
|
||
|
||
ρ = 1.2 ⋅10−4 g cm−3 .
|
||
|
||
(23)
|
||
|
||
The Nature of Gravitation
|
||
|
||
89
|
||
|
||
Such a relatively high material density for outer space cannot meet objections, since the material of the gravitational field can almost freely penetrate any substance and is noticeable only in the form of the phenomenon of gravitational interaction of bodies. Now let us see how this business fares with the Doppler and aberration effects. It is quite evident that if the material behaves like a ‘black body’, i.e., if it absorbs gravitational waves of any frequency equally well, then the Doppler effect will cause inadmissibly intense braking of even an isolated body moving in a system, relative to which the total momentum of the gravitational field is equal to zero. Therefore, we are forced to admit that matter absorbs gravitational waves only within a definite range of frequencies ∆ν which is much greater than the Doppler frequency shift caused by motion, and at the same time substantially overlaps that region of the field spectrum adjacent to ∆ν, whose intensity may be considered to be more or less constant. It is easy to see that under these conditions, a moving body will not experience braking, just as a selectively absorbing atom moving in an isotropic field with a frequency spectrum having a surplus overlapping the whole absorption spectrum of the atom, does not exhibit the Poynting-Robertson effect.
|
||
Actually, in system Σ which accompanies the atom, the observer will detect from all sides absorption of photons of the same frequency corresponding to the properties of the atom. From the point of view of this observer, the resulting momentum borne by the photons which are absorbed by the atom will be equal on the average to zero. The mass of photons being absorbed in system Σ is not set in motion and therefore does not derive any momentum from the atom. On the other hand an observer in system S relative to which the field is isotropic will detect that the moving atom is overtaken by harder photons and is met by softer photons. In other words it will seem to him that the atom absorbs a resulting momentum which differs from zero and is moving in the direction of the motion of the atom and compensates the loss of momentum, which is connected with the transmission of its absorbed mass of photons.
|
||
In this manner the observer in system S will also fail to observe either braking or acceleration of the atom’s motion.
|
||
As concerns the effect of aberration, according to the apt remark of Robertson [34], which is completely applicable to a gravitational field, consideration of this phenomenon is the worst method of observing the Doppler effect. Actually, an isolated body such as the sun is a sink for the gravitational field being absorbed and a source for one not being absorbed. Since we are interested only in the form, we may say that in the presence of a body, something analogous to distortion of the gravitational field occurs; at each point of the field there arises a non-zero resulting momentum directed towards the center of the sink. Evidently such a momentum may collide with any other body in a direction towards this center. The very fact of motion, as follows from the aforementioned considerations, cannot cause the appearance of a transversal force component.
|
||
|
||
90
|
||
|
||
V.V. Radzievskii and I.I. Kagalnikova
|
||
|
||
Thus it is possible to see that the modernized Lomonosov-Le Sage hypothesis presented here is not in conflict with a single one of the empirical facts which up to now have been discussed in connection with this hypothesis. At the same time, of course, it is impossible to guarantee that a more detailed analysis of the problem will not subsequently lead to discovery of such conflicts.
|
||
The Lomonosov-Le Sage hypothesis not only makes it possible to easily interpret the Majorana phenomenon, but also in clarifying the essence of gravity opens up perspectives for further investigations of the internal structure of matter and for a study of the possibility of controlling gravitational forces, and consequently the energy of the gravitational field. To illustrate the power of the energy, it suffices to recall that in the Majorana experiments the weight of the lead sphere, when introduced into the hollow sphere of mercury, decreased by 10−6 gm, which is equivalent to the liberation of twenty million calories of gravitational energy.
|
||
Most recently the authors have become aware of the experiments of the French engineer Allais who discovered the phenomenon of gravitational absorption by observations of the swinging of a pendulum during the total solar eclipse on June 30, 1954. In connection with this we feel compelled to mention that towards the end of the 19th century, the Russian engineer I.O. Yarkovskiy [35] was busying himself with systematic observations of the changes in the force of gravity, which resulted in the discovery of diurnal variations and a sharp change in the force of gravity during the total solar eclipse on August 7, 1887.
|
||
|
||
References
|
||
1. M.V. Lomonosov. Polnoye sobraniye sochineniy, Vol. 1. Izd. AN SSSR. 2. G.-L. Le Sage. Nouv. Mém. de l’Acad. de Berlin, 1782. 3. Deux traités de physique mécanique, publiés par Pierre Prévost. Genève–Paris, 1818. 4. Laplace. Oeuvres, v. IV. 5. A. Secchi. L’unita delle forze fisiche, 1864. 6. Leray. Comptes rendus, 69, 615, 1869. 7. W. Thomson. Proc. Roy. Soc. Edinburgh 7, 577, 1872. 8. H. Schramm. Die allgemeine Bewegung der Materie als Grundursache der Erscheinungen. Wien,
|
||
1872. 9. P.G. Tait. Vorlesungen über einige neuere Fortschritte der Physik. Braunschweig, 1877. 10. G. Isenkrahe. Das Rätsel der Schwerkraft. Kritik der bisherigen Lösungen des Gravitationsprob-
|
||
lems. Braunschweig, 1879. 11. T. Preston. Philosophical Magazine, 4, 200, 364, 1877; 15, 391, 1881. 12. T. Preston. Sitzungsber. Akad. Wiss., Wien, 87, 795, 1883. 13. A. Jarolimek. Wien. Ber., 88, 897, 1883. 14. M. Vaschy. Journ. de phys., (2), 5, 165, 1886. 15. Rysanek. Rep. de phys., 24, 90, 1887. 16. H.A. Lorentz. Mém. de l’Acad. des Sci. d’Amsterdam, 25, 1900. 17. Z.A. Tseytlin. Fiziko-khimicheskaya mekhanika kosmicheskikh tel i system. M.–L., 1937. 18. G.H. Darwin. Proc. Roy. Soc. London, 76, 1905. 19. H. Poincaré. Sci. et méthode. Paris, 1918. 20. H. Poincaré. Bull. Astronomique, 17, 121, 181, 1953.
|
||
|
||
The Nature of Gravitation
|
||
|
||
91
|
||
|
||
21. Q. Majorana. Atti Reale Accad. Lincei, 28, 2 sem., 165, 221, 313, 416, 480, 1919. 22. Q. Majorana. Atti Reale Accad. Lincei, 29, 1 sem., 23, 90, 163, 235, 1920; Philos. Mag., 39, 488,
|
||
1920. 23. Q. Majorana. Atti Reale Accad. Lincei, 30, 75, 289, 350, 442, 1921. 24. Q. Majorana. Atti Reale Accad. Lincei, 31, 41, 81, 141, 221, 343, 1922. 25. Q. Majorana. Journ. phys. et radium, 1, 314, 1930. 26. S.M. Sulaiman. Proc. Acad. Sci. India, 4, 1, 1934; 4, 217, 1935. 27. S.M. Sulaiman. Proc. Acad. Sci. Unit. Prov., 5, 123, p. 2, 1935. 28. A.A. Michelson. Atti della Soc. per il progresso della scienza, Congresso di Trieste, settembre,
|
||
1921. 29. H.N. Russell. Astrophys. Journ., 54, 334, 1921. 30. C.F. Brush. Proc. Amer. Phys. Soc., 68, 1, 55, 1929. 31. H. Klutz. Techn. Engng. News, 35, No. 1, 1953. 32. J.C. Maxwell. Encyclopedia Britannica, 9 ed., v. 3, 46, 1875. 33. (English translation erroneous for this reference) 34. H. Robertson. Monthly Notices of Roy. Astron. Soc., 97, 423, 1937. 35. I.O. Yarkovskiy. Vsemirnoye tyagateniye, kak sledstviye obrazovaniya vesomoy materii. Moskva,
|
||
1889.
|
||
|
||
Gravity
|
||
Tom Van Flandern*
|
||
All known properties of gravity can now be modeled in a deterministic way starting with a unit, or “quantum,” of gravity called the “graviton.” The key to a successful and complete model is recognizing the need for two different media operating at vastly different scales. One of these, the contiguous “light-carrying medium” (elysium), provides the relativistic properties usually attributed to “space-time curvature,” but through the vehicle of refraction instead of curvature. The other medium is that of the discrete, super-minute, strongly fasterthan-light, force-carrying agents we here call gravitons. These latter provide all the Newtonian properties of gravity. This complete model also implies several new properties of gravity not yet recognized by current physics. However, a brief survey of observational data suggests no conflict with, and indeed some support for, the existence of these new properties.
|
||
|
||
Introduction
|
||
As Isaac Newton remarked so eloquently in the 17th century, the logical mind, competent in philosophical matters, finds it inconceivable that one object might act on another across a gulf of space without some intermediaries passing between the objects to convey the action. The alternative would require some form of magic, an effect without a cause. As such, it would violate the causality principle, one of the fundamental Principles of Physics. These principles have a higher status than the so-called “laws of physics,” such as Newton’s Universal Law of Gravitation. Such laws may change as knowledge increases. By contrast, the Principles of Physics are deductions about nature so closely related to pure logic that a definite observed violation of one of them would bring into question the very nature of the reality we live in (objective, external vs. dream-like or virtual). [1]
|
||
Of course, nothing about nature requires that the individual agents conveying an action be observably large or otherwise suitable for detection by any human-built apparatus. At one time, single air molecules (the conveyors of common sound waves) were unknown to science, although bulk sound was easily detectable. Likewise, the photon, or unit of light, was once unknown, although humankind was able to perceive bulk light long before forming cogent ideas about its true nature.
|
||
When we consider the forces of nature, the same principles undoubtedly apply. Newton explicitly made no hypothesis about the fundamental nature of gravity, leaving open the question of the agents that convey it (usually called “gravitons”). When Newtonian gravity was replaced by Einstein’s general relativity (GR), two possible interpretations of the nature of gravity came with it:
|
||
|
||
* Meta Research, P.O. Box 15186, Chevy Chase, MD 20825-5186
|
||
|
||
Pushing Gravity: new perspectives on Le Sage’s theory of gravitation
|
||
|
||
93
|
||
|
||
edited by Matthew R. Edwards (Montreal: Apeiron 2002)
|
||
|
||
94
|
||
|
||
Tom Van Flandern
|
||
|
||
the field and the geometric. In recent
|
||
|
||
years, the latter has tended to become
|
||
|
||
dominant in the thinking of mathemati-
|
||
|
||
cal relativists. In the geometric inter-
|
||
|
||
pretation of gravity, a source mass
|
||
|
||
curves the “space-time” around it, caus-
|
||
|
||
ing bodies to follow that curvature in
|
||
|
||
preference to following straight lines
|
||
|
||
through space. This is often described
|
||
|
||
by using the “rubber sheet” analogy, as
|
||
|
||
shown in Figure 1.
|
||
|
||
However, it is not widely appreci-
|
||
|
||
Figure 1. Rubber sheet analogy for gravity. Source mass M makes dent in “space-time” sheet, causing target body
|
||
|
||
ated that this is a purely mathematical model, lacking a physical mechanism to initiate motion. For example, if a
|
||
|
||
at P to roll “downhill” toward M.
|
||
|
||
“space-time manifold” (like the rubber
|
||
|
||
sheet) exists near a source mass, why
|
||
|
||
would a small particle placed at rest in that manifold (on the rubber sheet) be-
|
||
|
||
gin to move toward the source mass? Indeed, why would curvature of the
|
||
|
||
manifold (rubber sheet) even have a sense of “down” unless some force such as
|
||
|
||
gravity already existed? Logically, the small particle at rest on a curved mani-
|
||
|
||
fold would have no reason to end its rest unless a force acted on it. However
|
||
|
||
successful this geometric interpretation may be as a mathematical model, it
|
||
|
||
lacks physics and a causal mechanism.
|
||
|
||
GR also recognizes a field interpretation of its equations. “Fields” are not
|
||
|
||
well defined in regard to their basic structure. Yet they clearly represent a type
|
||
|
||
of agent passing between source and target, able to convey an action. As such,
|
||
|
||
the field interpretation has no intrinsic conflict with the causality principle of
|
||
|
||
the sort that dooms the geometric interpretation. However, all existing experi-
|
||
|
||
mental evidence requires the action of fields to be conveyed much faster than
|
||
|
||
lightspeed. [2]
|
||
|
||
This situation is ironic because the reason why the geometric interpreta-
|
||
|
||
tion gained ascendancy over the field interpretation is that the implied faster-
|
||
|
||
than-light (ftl) action of fields appeared to allow causality violations. A corol-
|
||
|
||
lary of special relativity (SR) is that anything propagating ftl would be moving
|
||
|
||
backwards in time, thereby creating the possibility of altering the past and
|
||
|
||
causing a logical paradox. For example, an action in the present, propagated
|
||
|
||
into the past, might create a condition that prevented the action from coming
|
||
|
||
into existence in the present, thereby eliminating the action propagating into
|
||
|
||
the past, which restores the original situation, etc., in an endless loop of causal-
|
||
|
||
ity contradiction. The causality principle excludes effects before causes be-
|
||
|
||
cause of just such logical paradoxes.
|
||
|
||
Yet the field interpretation of GR requires ftl propagation. So if SR were a
|
||
|
||
correct model of reality, the field interpretation would violate the causality
|
||
|
||
Gravity
|
||
|
||
95
|
||
|
||
Figure 2. A: Force applied to exterior of body is resisted by each internal constituent. B: If a force is applied to every constituent, it does not matter how many there are.
|
||
principle, which is why it fell from popularity. However, it has only recently been appreciated that SR may be a valid mathematical theory in agreement with most experimental evidence, yet still be an invalid theory of physics. This is because an infinite number of theories that are mathematically equivalent to SR exist. [3] One of these, Lorentzian Relativity (LR), has been shown to be in full accord with all eleven independent experiments that test SR in the lightspeed or sub-lightspeed domains, yet does not forbid ftl propagation in forward time, as SR does. [4] If LR (for example) were a better physical theory than SR, then ftl propagations in forward time are allowed, and the field interpretation of GR would not imply any causality violations after all.
|
||
Our task here then is to follow this line of inquiry—the field of interpretation of GR combined with LR—and combine it with the logical need for agents to convey an action, to develop a model of gravity that is complete in its fundamentals, right down to the nature and properties of the unit of gravity, the hypothetical graviton.
|
||
How gravitons can give Newtonian properties of gravity
|
||
Gravity has properties unlike most other forces of nature. For example, its effect on a body is apparently completely independent of the mass of the affected body. As a result, heavy and light bodies fall in a gravitational field with equal acceleration. This is contrary to our intuitions based on experience with other types of forces. We have come to expect that a heavy body will resist acceleration more than a light one. But gravity does not behave that way. It is as if gravity was oblivious to the law of inertia.
|
||
However, on closer inspection, this property is not so surprising after all. Our intuitions are based on experience with mechanical, electric, magnetic, radiation, and other forces, most of which act directly on only part of a body; for example, only on its surface, or only on its charged particles. That action then creates pressure waves that pass through the entire body, forcing other parts of the body not acted on by the force to respond also. Hence, we see the origin of the property of “inertia,” or resistance to motion—the effect of an active force is diluted as each affected part of a body contacts its unaffected neighbors and requires them to change their state of motion also. See Figure 2A. In general, the greater the mass of the body, the greater will be the ratio of the number of molecules unaffected directly by the force to the number directly affected; for example, the ratio of interior molecules to surface molecules. This increased ratio requires the effect of the force to be diluted over more molecules, creating the appearance of a greater resistance to motion.
|
||
|