96 lines
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96 lines
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A COMPARISON BETWEEN LORENTZ’S ETHER THEORY
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AND SPECIAL RELATIVITY IN THE LIGHT OF THE
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EXPERIMENTS OF TROUTON AND NOBLE
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by Michael Heinrich Paul Janssen Kandidaats (≈ B.A.) Philosophy, Universiteit van Amsterdam, 1982 Doctoraal (≈ M.S.) Theoretical Physics, Universiteit van Amsterdam, 1988
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Submitted to the Graduate Faculty of Arts and Sciences in partial fulfillment of the requirements for the degree of
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Doctor of Philosophy
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University of Pittsburgh 1995
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Copyright by Michel Janssen 1995
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(committee signature page) iii
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For Suzy
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I was just getting up Hit the road before it’s light Trying to catch an hour on the sun When I saw those thrashers rolling by Looking more than two lanes wide I was feeling like my day had just begun
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—Neil Young
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A COMPARISON BETWEEN LORENTZ’S ETHER THEORY
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AND SPECIAL RELATIVITY IN THE LIGHT OF
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THE EXPERIMENTS OF TROUTON AND NOBLE
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Michel Janssen, PhD
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University of Pittsburgh, 1995
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In Part One of this dissertation, I analyze various accounts of two etherdrift experiments, the Trouton-Noble experiment and an earlier experiment by Trouton. Both aimed at detecting etherdrift with the help of a condenser in a torsion balance. I argue that the difficulties ethertheorists Lorentz and Larmor had in accounting for the negative results of these experiments stem from the fact that they did not (properly) take into account that, if we charge a moving condenser, we not only change its energy, but also its momentum and its mass. I establish two additional results. (1) The Trouton experiment can be seen as a physical realization of a thought experiment used by Einstein to argue for the inertia of energy. (2) Closely following Rohrlich, I develop an alternative to Laue’s canonical relativistic account of the Trouton-Noble experiment to show that the turning couple Trouton and Noble were looking for is a purely kinematical effect in special relativity. I call this effect the Laue effect.
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In Part Two, I use these results to illustrate some general claims about the post-1905 version of Lorentz’s ether theory. I use (1) to illustrate that Lorentz needs to assume more than the contraction of rods and the retardation of clocks to make his ether theory empirically equivalent to special relativity. I use (2) to illustrate that what makes the addition of such assumptions unsatisfactory is not that it would make the theory ad hoc, in the sense that it would compromise its testability, but that it makes Lorentz invariance a symmetry of the dynamics in a classical Newtonian space-time, whereas, in fact, it is a symmetry of the relativistic Minkowski space-time. To provide the necessary context for my claims, I give a detailed account of the conceptual development of Lorentz’s theory from 1895 to 1916. In particular, I analyze the relation between the so-called theorem of corresponding states and what I call the generalized contraction hypothesis. I show that the various versions of Lorentz’s theory have been widely misunderstood in the literature.
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Preface
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This dissertation has been long in the making. I worked on this project—on and off, interrupted by more pressing concerns—for a little over a decade. It seems appropriate to begin this report of my findings with a brief retrospective. This will give the reader an impression of my motivation for pursuing the topics I will discuss, and it will give me an opportunity to thank the many people who helped me in one way or another.
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I first got interested in the role of my countryman H. A. Lorentz in the history of the special theory of relativity back in 1984 when I wrote a text providing a historical introduction to special relativity for Dutch high school students. I used this text as the basis for a class for physics freshmen I taught for three consecutive years at the University of Amsterdam on Lorentz and special relativity. I am grateful to Piet Molenaar and the late Lex van der Meer for the opportunity to teach this class, and my students for their very active participation.
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Trying to locate books on the history of special relativity in the library of the institute for theoretical physics at the University of Amsterdam, I discovered they were all charged out to a certain A. J. Kox, who turned out to be a world renowned Lorentz scholar. Kox kindly offered his expertise along with numerous references and photocopies of papers by Lorentz and others, thus initiating me in the field of the history of science. I ended up writing my Master’s thesis in physics under his supervision. My intellectual debt to him is enormous. I sincerely hope he likes what I have to say in the following pages about the man we affectionately refer to as HAL. Practical problems unfortunately prevented him from serving on my doctoral committee, but he continued to offer his much appreciated help via email.
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It was also during my years at the University of Amsterdam that my views on special relativity and my understanding of what makes special relativity a better theory than Lorentz’s empirically equivalent ether theory were shaped decisively in a series of long conversations with Jon Dorling, philosopher of science at the University of Amsterdam. I hope to have added a few arguments to his.
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Sometime in 1986, I hit upon the discrepancy between Larmor’s and Lorentz’s ether theoretic accounts of the Trouton-Noble experiment, the problem that gave my dissertation project its focal point. I was unable to sort out this problem at the time, but my efforts did deepen my understanding of the crucial theorem of corresponding states and the relation between that theorem and what I have come to call the generalized contraction hypothesis. In 1988 and 1989, I was invited to give talks on these results at the University of Utrecht. I
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want to thank Dennis Dieks, Jan Hilgevoord, and Jos Uffink for these invitations and for stimulating discussions.
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In 1988, at a conference in Luminy, I met Arthur Miller, whose 1981 book on special relativity in many ways formed the starting point for my own work. Although I strongly disagree with his interpretation of Lorentz’s work at some points, his book and his papers have been a true inspiration to me, and the conversations I had with him during that conference provided more encouragement that he probably realized.
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At that same conference, I met my thesis advisor, John Norton, who suggested I enroll in the History and Philosophy of Science graduate program at the University of Pittsburgh. My intellectual debt to him is of the same order of magnitude as my intellectual debt to A. J. Kox. In his class on history of special relativity in the spring of 1990 and in an independent study I did with him in the spring of 1992, I returned to the problem of the Trouton-Noble experiment and its ramifications for a comparison between special relativity and Lorentz’s theory. To mention just one of his many contributions, it was John Norton who urged me to carefully look at Laue’s work on the behavior of stressed bodies in motion. The importance of Laue’s analysis for the argument in this thesis can hardly be overstated.
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I could not have solved several technical problems in both the ether theoretic and the relativistic accounts of the Trouton-Noble experiment without the help of Tony Duncan, theoretical physicist at the University of Pittsburgh and one of the best instructors I have ever taken a class with. The dissertation not only benefited from his technical expertise (especially on issues concerning the energy-momentum tensor), but also from the sometimes heated debates we have had over some of the conceptual issues. It seems fitting that, after serving on this committee, Tony Duncan will spend a semester at Columbia University, on the same fellowship that brought Lorentz to New York in the spring of 1906.
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I also want to thank the other members of my committee. I hope John Earman and Wesley Salmon will recognize some of the Pittsburgh approach to philosophy of science in the conceptual analysis in this dissertation. My views on history of science have been strongly influenced by Ted McGuire. I hope he will accept the historical relevance of my analysis. To Gordon Fleming I owe my sensitivity to hyperplane dependence, without which I would not have found the alternative to Laue’s canonical relativistic account of the Trouton-Noble experiment, an alternative that plays an important role in my arguments.
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In this context, I also want to thank David Sandborg for producing the diagram illustrating an argument in which I use these two accounts of the Trouton-Noble experiment.
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In the summer of 1994, I gave a talk at the Max-Planck-Institut für Bildungsforschung in Berlin based on the prospectus for this dissertation. Peter Damerow, Yehuda Elkana,
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Wolfgang Lefèvre, Jürgen Renn, and, especially, John Stachel all offered very interesting suggestions. Rather than a word of thanks, I feel I owe them an apology for not including more of these in the final product. I am looking forward to discuss my latest findings with them when I go back to Berlin this summer.
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My analysis of Lorentz’s theory provides a new angle on the long standing debate about whether that theory is ad hoc. I am grateful to Adolf Grünbaum, a key player in this debate, for many useful suggestions. I regret that I have not had a chance so far to meet with him to discuss my final conclusions on this matter.
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In the final stages of my project, two fellowships freed me from my teaching duties and allowed me to work full time on my research. I received a pre-doctoral fellowship from the Andrew Mellon Foundation for the academic year 1993–1994, and the John C. Slater Fellowship for the history of 20th century physics from the American Philosophical Society for the academic year 1994–1995. I want to thank both organizations for awarding me these fellowships.
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I also incurred debts of a more personal nature. First of all, I want to thank my fellow graduate students, both in Pittsburgh and in Amsterdam, for providing a very stimulating social and intellectual environment. I want to name just a few: Aristidis Arageorgis, Carl Craver, Ofer Gal, Giel Halberstadt, David Hillman, Cory Juhl, Hans Montanus, Madeline Muntersbjorn (formerly known as Madeline Larson), Keith Parsons, and Laura Ruetsche. To Jonathan Simon I want to apologize for canceling half the Subbuteo season on him.
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I also want to thank my family (pa en ma, Ruud en Denise, Ilse en Bert, Lieke en Stephen, ooms en tantes), and my wonderful in-laws, all forty or so of them, but especially Basil Wilson (for helpful discussion) and my wife’s twin sister Sara (for fostering my love of the theater, for instance, not to mention Glamour Magazine and NBC’s Sisters).
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Finally, I want to thank Suzanne Durkacs, my wife of almost three years. I must have freaked out after each fifty pages I finished, and she got me back on track no less than five times. I am sure the committee will be happy she left it at that. On top of this, she offered her skills as network manager for University Relations, and deserves at least partial credit for the one thing I tend to be a perfectionist about: the layout. For years, I have been walking around with the idea of dedicating my dissertation, if I were to ever write one, to the memory of Evie-Marieke van de Wiel (1960–1987), who taught me some valuable lessons about pursuing your dreams. I am sure Evie would have understood that I want to dedicate my work to Suzy instead, who actually made a dream or two come true.
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TABLE OF CONTENTS
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Preface ........................................................................................................................... vi Introduction ....................................................................................................................1
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Part I: Accounting for the experiments of Trouton and Noble with classical and with relativistic mechanics
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Introduction: Larmor, Lorentz, and Laue on the experiments of Trouton and Noble...............................................................................................10
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Ch. 1: Ether theoretic accounts of the experiments of Trouton and Noble 1.0 Introduction: condensers, contractions, and confusion.........................................17 1.1 Moving condensers and torsion balances.............................................................19 1.1.1 FitzGerald and the Trouton experiment .....................................................19 1.1.2 Larmor on the Trouton experiment............................................................22 1.1.3 The Trouton-Noble experiment ................................................................24 1.2 ‘Corresponding states’ and rest frames; application to the Trouton-Noble experiment ...........................................................................................................30 1.2.1 Electrostatics in moving frames of reference, with and without the contraction hypothesis. ........................................................................30 1.2.2 Application: the turning couple of the Coulomb forces on a moving charged condenser......................................................................33 1.3 Larmor’s 1902 ‘energy’-account of the Trouton-Noble experiment ...................39 1.3.1 Extracting energy from the earth’s motion through the ether, “unless the FitzGerald-Lorentz contraction is a fact”...............................39 1.3.2 The turning couple without the contraction hypothesis..............................45 1.4 Lorentz’s 1904 ‘momentum’-account of the Trouton experiment and the Trouton-Noble experiment.............................................................................47 1.4.1 Lorentz on the experiments of Trouton and Noble ....................................47 1.4.2 Lorentz’s derivation of the expression for the turning couple of the Coulomb forces in the Trouton-Noble experiment...............................56 1.4.3 The electromagnetic energy in a moving condenser according to Lorentz’s theory....................................................................................60
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Ch. 2: Relativistic accounts of the experiments of Trouton and Noble 2.0 Introduction: the ‘Laue effect’ and how to define it away....................................63 2.0.1 The fate of the experiments of Trouton and Noble in the history of the special theory of relativity....................................................63 2.0.2 The kinematical nature of the turning couples in the Trouton-Noble experiment ........................................................................65 2.0.3 Outline of chapter two ...............................................................................68 2.1 The energy-momentum tensor; the transformation of four-momentum of ‘complete static systems’ ................................................................................72 2.1.1 The energy-momentum tensor...................................................................72 2.1.2 Laue’s notion of a ‘complete static system’..............................................74 2.1.3 A general theorem: the four-momentum of a system transforms as a four-vector if and only if the system is closed ....................................76 2.1.4 Laue’s proof of the claim that the energy and momentum of a complete static system transform as a four-vector......................................81
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2.2 The 4/3-puzzle of the Lorentz-Poincaré electron and the Laue effect: the Laue definition of four-momentum versus the Rohrlich definition.................86 2.2.1 The relation between the Trouton-Noble experiment and the Lorentz-Poincaré electron..............................................................86 2.2.2 A brief history of the 4/3-puzzle of the Lorentz-Poincaré electron.............86 2.2.3 The Rohrlich and Laue definitions of the four-momentum of spatially extended systems ....................................................................88 2.2.4 Applying Rohrlich’s insights to the Trouton-Noble experiment................92 2.2.5 The Rohrlich and Laue definitions of the angular momentum of spatially extended systems ....................................................................92
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2.3 Two ‘four-momentum’-accounts of the Trouton-Noble experiment based on the Laue and Rohrlich definitions of four-momentum ........................100 2.3.1 Laue on the Trouton-Noble experiment as an example of a complete static system (1911)...............................................................100 2.3.2 Comparing the Laue picture of what happens in a moving condenser to the Rohrlich picture .............................................................................100 2.3.3 Derivation of expressions for the matrix of the Lorentz transformation to a conveniently chosen rest frame and for the electromagnetic and non-electromagnetic energy-momentum tensors in that frame.................103 2.3.4 The division of the total momentum into electromagnetic and non-electromagnetic momentum in the Laue and in the Rohrlich picture......................................................................................................108 2.3.5 A closer look at the difference between the Laue and the Rohrlich picture of what happens in a moving condenser: the argument for the kinematical nature of the Laue effect..................................................113
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2.4 A ‘forces’-account of the Trouton-Noble experiment; the role of the relativity of simultaneity ..............................................................120 2.4.1 Laue’s attempt to give a more intuitive account of the Trouton-Noble experiment ......................................................................120 2.4.2 A stream-lined version of Laue’s 1912 ‘forces’-account of the Trouton-Noble experiment ......................................................................121 2.4.3 Forces, energy, and the relativity of simultaneity: Einstein on situations similar to those in the Trouton-Noble experiment....................127 2.4.4 Toward a more intuitive understanding of the kinematical nature of the Laue effect.....................................................................................130
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2.5 The experiments of Trouton and Noble and two well-known thought experiments in special relativity.............................................................135 2.5.1 The Lewis-Tolman bent lever and the Trouton-Noble experiment ...........135 2.5.2 The mass-energy equivalence and the Trouton experiment......................139
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Part II: Reassessing Lorentz’s theory for the electrodynamics of moving bodies
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Introduction: Manifesto on how to do history of special relativity .....................146
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Ch. 3: Setting the record straight on the theorem of corresponding states 3.0 Introduction: common misconceptions about the theorem of corresponding states and the contraction hypothesis .................................................................157 3.1 The first order theorem of corresponding states (1895).......................................xx 3.1.1 What is the theorem of corresponding states? ...........................................xx 3.1.2 How the Lorentz invariance of the source free Maxwell equations to first order in v/c and the general nature of patterns of light and darkness account for the negative result of almost any conceivable first order ether drift experiment in optics..................................................xx 3.1.3 How the Fresnel dragging coefficient and the classical formulae for aberration and Doppler effect drop out of Lorentz’s first order theorem of corresponding states................................................................xx 3.2 The original contraction hypothesis (1892/1895).................................................xx 3.2.1 The Michelson-Morley experiment, the Lorentz-FitzGerald contraction, and electrostatics in moving frames of reference........................................xx 3.2.2 How the Lorentz-FitzGerald contraction accounts for the negative result of the Michelson-Morley experiment...............................................xx 3.2.3 The problem of the empirical testability of the contraction hypothesis.......xx 3.2.4 Variations on the Michelson-Morley experiment (Kennedy-Thorndike, Liénard)..................................................................xx 3.2.5 A “corresponding states”-like treatment of electrostatics in moving frames of reference....................................................................................xx 3.2.6 Lorentz’s plausibility argument for the Lorentz-FitzGerald contraction ....xx
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3.3 The exact theorem of corresponding states and the “generalized contraction hypothesis” (1899/1904)..................................................................xx 3.3.1 The generalization of the theorem of corresponding states ........................xx 3.3.2 A simplified treatment of electrostatics in moving frames..........................xx 3.3.3 How the Lorentz invariance of the source free Maxwell equations, the hypothesis that corresponding states physically transform into one another, and the general nature of patterns of light and darkness can account for the negative result of almost any conceivable optical ether drift experiment.................................................................................xx 3.3.4 The status of the generalized contraction hypothesis for Lorentz...............xx 3.3.5 How the relativistic formulae for aberration and Doppler effect drop out of Lorentz’s exact theorem of corresponding states and the generalized contraction hypothesis.......................................................xx 3.3.6 The generalized contraction hypothesis and the velocity dependence of mass......................................................................................................xx
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3.4 Lorentz’s electron model (1904)..........................................................................xx 3.4.1 The dilemma posed by the electron models of Lorentz, Abraham, Bucherer and Langevin: the electromagnetic view of nature or the principle of relativity ............................................................................xx 3.4.2 The electromagnetic mass of spherical charge distributions subject to the Lorentz-FitzGerald contraction ........................................................xx 3.4.3 Abraham, Poincaré, Bucherer, Langevin, and the ambiguity in the expression for the longitudinal mass of Lorentz’s electron .......................xx 3.4.4 Choosing between the electromagnetic view of nature and the principle relativity: Planck, Lorentz, and Sommerfeld...............................................xx
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3.5 Lorentz’s interpretation of the Lorentz transformation formulae after 1905: from mathematical auxiliaries to effective coordinates and fields .........................xx 3.5.1 The state of Lorentz’s theory in 1905........................................................xx 3.5.2 Grünbaum’s “doubly amended theory” as a model for Lorentz’s mature theory.............................................................................................xx 3.5.3 The problem of non-static charge distributions..........................................xx 3.5.4 Lorentz taking to heart a lesson from Einstein (after ignoring a similar lesson from Poincaré)....................................................................xx 3.5.5 The reciprocity of the Lorentz transformation............................................xx 3.5.6 The transformation of charge and current density and the solution of the problem of non-static charge distributions ...................xx 3.5.7 Lorentz’s arguments for preferring his own theory over Einstein’s ..........xx
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Ch. 4: Comparing Lorentz’s understanding of Lorentz invariance to Einstein’s 4.0 Introduction: putting the pieces together ..............................................................xx 4.1 What price empirical equivalence of Lorentz’s theory to special relativity?..........xx 4.1.1 How to make Lorentz’s theory empirically equivalent to special relativity in the context of experiments that involve more than the observation of patterns of light and darkness.............................................xx 4.1.2 Example 1: the Trouton experiment and the inertia of energy....................xx 4.2 Why Einstein’s interpretation of Lorentz invariance is preferable to Lorentz’s?..xx 4.2.1 How kinematical effects in special relativity come out as dynamical effects in Lorentz’s theory: a ‘common cause’-type argument for Minkowski space-time...............................................................................xx 4.2.2 Example 2: the Trouton-Noble experiment and the Laue effect .................xx 4.3 Why Lorentz failed to appreciate Einstein’s new kinematics? .............................xx 4.3.1 Theories of principle versus constructive theories......................................xx 4.3.2 Example 3: the transformation of charge density.......................................xx 4.3.3 Example 4: the transformation of mass......................................................xx
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Bibliography ....................................................................................................................xx
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LIST OF FIGURES
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Figure 1.1 Moving charged condenser. Figure 1.2 Trouton’s experimental design to detect an impulseupon charging
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or discharging a moving condenser (seen from above). Figure 1.3 On the left: condenser moving “flatwise” (Trouton), “transversal”
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(Larmor), θ = π/2. On the right: condenser moving “edgewise” (Trouton), “longitudinal” (Larmor), θ = 0. Figure 1.4 Work done upon rotating a moving condenser. Figure 1.5 Trouton and Noble’s experimental design to detect a turning couple on a charged moving condenser (seen from above). Figure 1.6 Forces on a moving static charge distribution. Figure 1.7 Moving condenser (with the Lorentz-FitzGerald contraction). Figure 1.8 Moving condenser (without the Lorentz-FitzGerald contraction). Figure 1.9 Forces on a charged moving condenser (with the Lorentz-FitzGerald contraction). Figure 1.10 Forces on charged moving condenser (without the Lorentz-FitzGerald contraction). Figure 1.11 Electromagnetic momentum G of the field of a moving condenser. Figure 2.1 The hypersurfaces Σ1 and Σ2. Figure 2.2 The hyperplane Σ(nµ,τ). Figure 2.3 Relation between integrals over Σ1 and Σ2 for static systems. Figure 2.4 Two different conventions for choosing spacelike hyperplanes in the definition of four-momentum Pµ(t) for spatially extended systems in an arbitrary xµ-frame. Figure 2.5 The hyperplanes ΣL (Laue) and ΣR (Rohrlich). Figure 2.6 Condenser in the xµ-frame in which it is moving (solid lines) and in the x′µ-frame in which it is at rest (shaded lines). Figure 2.7 Electromagnetic and non-electromagnetic contributions to the total momentum in a charged moving condenser according to Laue. Figure 2.8 The worldlines of selected points of the condenser Figure 2.9 Forces in a charged condenser at rest. Figure 2.10 Forces in a charged moving condenser. Figure 2.11 Condenser plates suspended on wires that are cut simultaneously
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in the condenser’s rest frame. Figure 2.12 Condenser plates suspended on wires that are cut at different times
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in a frame in which the condenser is moving. Figure 2.13 The Lewis-Tolman bent lever. Figure 2.14 A thought experiment by Einstein to establish the equivalence of
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mass and energy. Figure 2.15 Balancing the box in Einstein’s thought experiment on a wedge. Figure 2.16 The Trouton experiment revisited.
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Figure 3.1 Diagram to illustrate Lorentz’s first order theorem of corresponding states.
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Figure 3.2 The classical Doppler and aberration effects. Figure 3.3 Light traveling back and forth in the arm of a moving interferometer. Figure 3.4 Interferometer arm at rest in the ether (left); and contracted are
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moving through the ether (right). Figure 3.5 Crude static model of the molecular structure of an arm of a
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Michelson interferometer; on the left: at rest in the ether (“system C”); on the right: moving through the ether (“system B”). Figure 3.6 Moving interferometer and its corresponding state (without the Lorentz-FitzGerald contraction). Figure 3.7 Moving interferometer and its corresponding state (with the LorentzFitzGerald contraction). Figure 3.8 Aberration and Doppler effect in Lorentz’s exact theory of 1899 and 1904. Figure 3.9 The transformation of charge density. Figure 4.1 The Laue effect in a variant on the Trouton-Noble experiment. Figure 4.2 The conservation of total momentum in a rotating moving condenser.
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