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The Principle of Relativity

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The Principle of Relativity Eötvös Loránd Tudományegyetem Bölcsészettudományi Kar Doktori Disszertáció Gömöri Márton The Principle of Relativity An Empiricist Analysis (A relativitás elve – empirista elemzés) Filozófiatudományi Doktori Iskola Vezetője: Boros Gábor, DSc, egyetemi tanár Logika és Tudományfilozófia Program Vezetője: E. Szabó László, DSc, egyetemi tanár A bizottság tagjai: A bizottség elnöke: Bodnár István, egyetemi tanár, CSc, egyetemi tanár Felkért bírálók: Andréka Hajnal, DSc, professzor Szabó Gábor, PhD, tudományos főmunkatárs A bizottság titkára: Ambrus Gergely, PhD, egyetemi docens A bizottság további tagjai: Máté András, CSc, egyetemi docens Mekis Péter, PhD, adjunktus Székely Gergely, PhD, tudományos munkatárs Témavezető: E. Szabó László, DSc, egyetemi tanár Budapest, 2015 Contents 1 Introduction5 2 What Exactly Does the Principle of Relativity Say? 11 2.1 Einstein 1905............................... 11 2.2 The Electromagnetic Field of a Static versus Uniformly Moving Charge 30 2.3 Conceptual Components of the Relativity Principle.......... 35 2.4 The Formal Statement of the Relativity Principle........... 41 2.5 Covariance................................. 47 2.6 Initial and Boundary Conditions..................... 52 2.7 An Essential Conceptual Component: “Moving Body”........ 60 3 Operational Understanding of the Covariance of Electrodynamics 68 3.1 A Logical Problem with Postulating Relativity............. 68 3.2 Lorentzian Pedagogy........................... 77 3.3 The Case of Electrodynamics...................... 78 3.4 Operational Definitions of Electrodynamic Quantities in K ...... 80 3.5 Empirical Facts of Electrodynamics................... 86 3.6 Operational Definitions of Electrodynamic Quantities in K0 ...... 89 3.7 Observations of the Moving Observer.................. 93 3.8 Are the Transformation Rules Derived from Covariance True?.... 99 4 Does the Principle of Relativity Hold in Electrodynamics? 101 4.1 The Problem of M ............................ 101 4.2 Motion and Persistence.......................... 102 4.3 The Case of a General Electrodynamic System............. 107 4.4 Ontology of Classical Electrodynamics................. 113 Appendix I 116 Appendix II 118 2 CONTENTS 3 References 120 I have for long thought that if I had the opportunity to teach this subject, I would emphasize the continuity with earlier ideas. Usually it is the discontinuity which is stressed, the radical break with more primitive notions of space and time. Often the result is to destroy completely the confidence of the student in perfectly sound and useful concepts already acquired. (From J. S. Bell: “How to teach special relativity”, Bell 1987, p. 67.) Chapter 1 Introduction 1. Here is Galileo’s lively description of the special principle of relativity as appear- ing in the famous passages of the Dialogue: Shut yourself up with some friend in the main cabin below decks on some large ship, and have with you there some flies, butterflies, and other small flying animals. Have a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it. With the ship standing still, observe carefully how the little animals fly with equal speed to all sides of the cabin. The fish swim indifferently in all directions; the drops fall into the vessel beneath; and, in throwing something to your friend, you need throw it no more strongly in one direction than another, the distances being equal; jumping with your feet together, you pass equal spaces in every direction. When you have observed all these things carefully (though doubtless when the ship is standing still everything must happen in this way), have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still. In jumping, you will pass on the floor the same spaces as before, nor will you make larger jumps toward the stern than toward the prow even though the ship is moving quite rapidly, despite the fact that during the time that you are in the air the floor under you will be going in a direction opposite to your jump. In throwing something to your companion, you will need no more force to get it to him whether he is in the direction of the bow or the stern, with yourself situated opposite. The droplets will fall as before into the vessel beneath without dropping toward the stern, although while the 5 CHAPTER 1. INTRODUCTION 6 drops are in the air the ship runs many spans. The fish in their water will swim toward the front of their bowl with no more effort than toward the back, and will go with equal ease to bait placed anywhere around the edges of the bowl. Finally the butterflies and flies will continue their flights indifferently toward every side, nor will it ever happen that they are concentrated toward the stern, as if tired out from keeping up with the course of the ship, from which they will have been separated during long intervals by keeping themselves in the air. And if smoke is made by burning some incense, it will be seen going up in the form of a little cloud, remaining still and moving no more toward one side than the other. The cause of all these correspondences of effects is the fact that the ship’s motion is common to all the things contained in it, and to the air also. That is why I said you should be below decks; for if this took place above in the open air, which would not follow the course of the ship, more or less noticeable differences would be seen in some of the effects noted. (Galilei 1953, pp. 186–187) Compare Galileo’s description with a sample from the huge variety of formulations of the principle available in the literature: ... the laws of physical phenomena should be the same, whether for an observer fixed, or for an observer carried along in a uniform movement of translation. (Poincaré 1956, p. 167) If a system of coordinates K is chosen so that, in relation to it, physical laws hold good in their simplest form, the same laws hold good in relation to any other system of coordinates K0 moving in uniform translation relatively to K. (Einstein 1916, p. 111) ... it is impossible to measure or detect the unaccelerated translatory motion of a system through free space or through any ether-like medium. (Tolman 1949, p. 12) ... all physical phenomena should have the same course of development in all system of inertia, and observers installed in different systems of inertia should thus as a result of their experiments arrive at the establishment of the same laws of nature. (Møller 1955, p. 4) ... the laws of Physics take the same mathematical form in all inertial frames (Sardesai 2004, p. 1) The same laws of nature are true for all inertial observers. (Madarász 2002, p. 84) CHAPTER 1. INTRODUCTION 7 The uniform translatory motion of any system can not be detected by an observer traveling with the system and making observations on it alone. (Comstock 1909, p. 767) The laws of nature and the results of all experiments performed in a given frame of reference are independent of the translational motion of the system as a whole. More precisely, there exists a ... set of equivalent Euclidean reference frames ... in which all physical phenomena occur in an identical manner. (Jackson 1999, p. 517) If we express some law of physics using the quantities of one inertial frame of reference, the resulting statement of the law will be exactly the same in any other inertial frame of reference. ... we write down exactly the same sentence to express the law in each inertial frame. (Norton 2013) ... all inertial frames are equivalent for the performance of all physical experiments (Rindler 2006, p. 12) ... the laws of physics are invariant under a change of inertial coordinate system (Ibid., p. 40) The outcome of any physical experiment is the same when performed with identical initial conditions relative to any inertial coordinate system. (Ibid.) ... all the laws of nature are identical in all inertial systems of reference. In other words, the equations expressing the laws of nature are invariant with respect to transformations of coordinates and time from one inertial system to another. This means that the equation describing any law of nature, when written in terms of coordinates and time in different inertial reference systems, has one and the same form. (Landau and Lifshitz 1980, p. 1) ... the phenomena in a given reference system are, in principle, inde- pendent of the translational motion of the system as a whole. To put it more precisely: there exists a triply infinite set of reference systems moving rectilinearly and uniformly relativity to one another, in which the phenomena occur in an identical manner. (Pauli 1958, p. 4) The postulate of relativity implies that a uniform motion of the center of mass of the universe relativity to a closed system will be without influence on the phenomena in such a system. (Ibid., p. 5) CHAPTER 1. INTRODUCTION 8 ... experience teaches us that ... all laws of physical nature which have been formulated with reference to a definite coordinate system are valid, in precisely the same form, when referred to another co-ordinate system which is in uniform rectilinear motion with respect to the first. ... All physical events take place in any system in just the same way, whether the system is at rest or whether it is moving uniformly and rectilinearly. (Schlick 1920, p. 10) ... laws must be Lorentz covariant. Lorentz covariance became syn- onymous with satisfaction of the principle of relativity. (Norton 1993, p. 796) The laws of physics don’t change, even for objects moving in inertial (constant speed) frames of reference.
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