Einstein’s popular description is his 1916 book, Relativity: The Special and the General Theory , and his more technical description is his 1922 book, The Meaning of Relativity.
For good explanations of special relativity, see Miller 1981, 2001; Galison; Bernstein 2006; Calder; Feynman 1997; Hoffmann 1983; Kaku; Mermin; Penrose; Sartori; Taylor and Wheeler 1992; Wolfson.
This chapter draws on these books along with the articles by John Stachel; Arthur I. Miller; Robert Rynasiewicz; John D. Norton; John Earman, Clark Glymour, and Robert Rynasiewicz; and Michel Jannsen listed in the bibliography. See also Wertheimer 1959. Arthur I. Miller provides a careful and skeptical look at Max Wertheimer’s attempt to reconstruct Einstein’s development of special relativity as a way to explain Gestalt psychology; see Miller 1984, 189–195.
2. See Janssen 2004 for an overview of the arguments that Einstein’s attempt to extend general relativity to arbitrary and rotating motion was not fully successful and perhaps less necessary than he thought.
3. Galileo Galilei, Dialogue Concerning the Two Chief World Systems (1632), translated by Stillman Drake, 186.
4. Miller 1999, 102.
5. Einstein, “Ether and the Theory of Relativity,” address at the University of Leiden, May 5, 1920.
6. Ibid.; Einstein 1916, chapter 13.
7. Einstein, “Ether and the Theory of Relativity,” address at the University of Leiden, May 5, 1920.
8. Einstein to Dr. H. L. Gordon, May 3, 1949, AEA 58-217.
9. See Alan Lightman’s Einstein’s Dreams for an imaginative and insightful fictional rumination on Einstein’s discovery of special relativity. Lightman captures the flavor of the professional, personal, and scientific thoughts that might have been swirling in Einstein’s mind.
10. Peter Galison, the Harvard science historian, is the most compelling proponent of the influence of Einstein’s technological environment. Arthur I. Miller presents a milder version. Among those who feel that these influences are overstated are John Norton, Tilman Sauer, and Alberto Martinez. See Alberto Martinez, “Material History and Imaginary Clocks,”Physics in Perspective 6 (2004): 224.
11. Einstein 1922c. I rely on a corrected translation of this 1922 lecture that gives a different view of what Einstein said; see bibliography for an explanation.
12. Einstein, 1949b, 49. For other versions, see Wertheimer, 214; Einstein 1956, 10.
13. Miller 1984, 123, has an appendix explaining how the 1895 thought experiment affected Einstein’s thinking. See also Miller 1999, 30–31; Norton 2004, 2006b. In the latter paper, Norton notes, “[This] is untroubling to an ether theorist. Maxwell’s equations do entail quite directly that the observer would find a frozen waveform; and the ether theorist does not expect frozen waveforms in our experience since we do not move at the velocity of light in the ether.”
14. Einstein to Erika Oppenheimer, Sept. 13, 1932, AEA 25-192; Moszkowski, 4.
15. Gerald Holton was the first to emphasize Föppl’s influence on Einstein, citing the memoir by his son-in-law Anton Reiser and the German edition of Philipp Frank’s biography. Holton 1973, 210.
16. Einstein, “Fundamental Ideas and Methods of the Theory of Relativity” (1920), unpublished draft of an article for Nature, CPAE 7: 31. See also Holton 1973, 362–364; Holton 2003.
17. Einstein to Mileva Mari, Aug. 10, 1899.
18. Einstein to Mileva Mari, Sept. 10 and 28, 1899; Einstein 1922c.
19. Einstein to Robert Shankland, Dec. 19, 1952, says that he read Lorentz’s book before 1905. In his 1922 Kyoto lecture (Einstein 1922c) he speaks of being a student in 1899 and says, “Just at that time I had a chance to read Lorentz’s paper of 1895.” Einstein to Michele Besso, Jan. 22?, 1903, says he is beginning “comprehensive, extensive studies in electron theory.” Arthur I. Miller provides a good look at what Einstein had already learned. See Miller 1981, 85–86.
20. This section draws from Gerald Holton, “Einstein, Michelson, and the ‘Crucial’ Experiment,” in Holton 1973, 261–286, and Pais 1982, 115–117. Both assess Einstein’s varying statements. The historical approach has evolved over the years. For example, Einstein’s longtime friend and fellow physicist Philipp Frank wrote in 1957, “Einstein started from the most prominent case in which the old laws of motion and light propagation had failed to yield to the observed facts: the Michelson experiment” (Frank 1957, 134). Gerald Holton, the Harvard historian of science, wrote in a letter to me about this topic (May 30, 2006): “Concerning the Michelson/Morley experiment, until three or four decades ago practically everyone wrote, particularly in textbooks, that there was a straight line between that experiment and Einstein’s special relativity. All this changed of course when it became possible to take a careful look at Einstein’s own documents on the matter ... Even non-historians have long ago given up the idea that there was a crucial connection between that particular experiment and Einstein’s work.”
21. Einstein 1922c; Einstein toast to Albert Michelson, the Athenaeum, Caltech, Jan. 15, 1931, AEA 8-328; Einstein message to Albert Michelson centennial, Case Institute, Dec. 19, 1952, AEA 1-168.
22. Wertheimer, chapter 10; Miller 1984, 190.
23. Robert Shankland interviews and letters, Feb. 4, 1950, Oct. 24, 1952, Dec. 19, 1952. See also Einstein to F. G. Davenport, Feb. 9, 1954: “In my own development, Michelson’s result has not had a considerable influence, I even do not remember if I knew of it at all when I wrote my first paper on the subject. The explanation is that I was, for general reasons, firmly convinced that there does not exist absolute motion.”
24. Miller 1984, 118: “It was unnecessary for Einstein to review every extant ether-drift experiment, because in his view their results were ab initio [from the beginning] a foregone conclusion.” This section draws on Miller’s work and on suggestions he made to an earlier draft.
25. Einstein saw the null results of the ether-drift experiments as support for the relativity principle, not (as is sometimes assumed) support for the postulate that light always moves at a constant velocity. John Stachel, “Einstein and Michelson: The Context of Discovery and Context of Justification,” 1982, in Stachel 2002a.
26. Professor Robert Rynasiewicz of Johns Hopkins is among those who emphasize Einstein’s reliance on inductive methods. Even though Einstein in his later career wrote often that he relied more on deduction than on induction, Rynasiewicz calls this “highly contentious.” He argues instead, “My view of the annus mirabilis is that it is a triumph of what can be secured inductively in the way of fixed points from which to carry on despite the lack of a fundamental theory.” Rynasiewicz e-mail to me, commenting on an earlier draft of this section, June 29, 2006.
27. Miller 1984, 117; Sonnert, 289.
28. Holton 1973, 167.
29. Einstein, “Induction and Deduction in Physics,”Berliner Tageblatt , Dec. 25, 1919, CPAE 7: 28.
30. Einstein to T. McCormack, Dec. 9, 1952, AEA 36-549. McCormack was a Brown University undergraduate who had written Einstein a fan letter.
31. Einstein 1949b, 89.
32. The following analysis draws from Miller 1981 and from the work of John Stachel, John Norton, and Robert Rynasiewicz cited in the bibliography. Miller, Norton, and Rynasiewicz kindly read drafts of my work and suggested corrections.
33. Miller 1981, 311, describes a connection between Einstein’s papers on light quanta and special relativity. In section 8 of his special relativity paper, Einstein discusses light pulses and declares, “It is remarkable that the energy and the frequency of a light complex vary with the state of motion of the observer in accordance with the same law.”
34. Norton 2006a.
35. Einstein to Albert Rippenbein, Aug. 25, 1952, AEA 20-46. See also Einstein to Mario Viscardini, Apr. 28, 1922, AEA 25-301: “I rejected this hypothesis at that time, because it leads to tremendous theoretical difficulties (e.g., the explanation of shadow formation by a screen that moves relative to the light source).”
36. Mermin, 23. This was final
ly proven conclusively by Willem de Sitter’s study of double stars that rotate around each other at great speeds, which was published in 1913. But even before then, scientists had noted that no evidence could be found for the theory that the velocity of light from moving stars, or any other source, varied.
37. Einstein to Paul Ehrenfest, Apr. 25, June 20, 1912. By taking this approach, Einstein was continuing to lay the foundation for a quandary about quantum theory that would bedevil him for the rest of his life. In his light quanta paper, he had praised the wave theory of light while at the same time proposing that light could also be regarded as particles. An emission theory of light could have fit nicely with that approach. But both facts and intuition made him abandon that approach to relativity, just at the same moment he was finishing his light quanta paper. “To me, it is virtually inconceivable that he would have put forward two papers in the same year which depended upon hypothetical views of Nature that he felt were in contradiction with each other,” says physicist Sir Roger Penrose. “Instead, he must have felt (correctly, as it turned out) that ‘deep down’ there was no real contradiction between the accuracy—indeed ‘truth’—of Maxwell’s wave theory and the alternative ‘quantum’ particle view that he put forward in the quantum paper. One is reminded of Isaac Newton’s struggles with basically the same problem—some 300 years earlier—in which he proposed a curious hybrid of a wave and particle viewpoint in order to explain conflicting aspects of the behavior of light.” Roger Penrose, foreword to Einstein’s Miraculous Year (Princeton: Princeton University Press, 2005), xi. See also Miller 1981, 311.
38. Einstein, “On the Electrodynamics of Moving Bodies,” June 30, 1905, CPAE 2: 23, second paragraph. Einstein originally used V for the constant velocity of light, but seven years later began using the term now in common use, c.
39. In section 2 of the paper, he defines the light postulate more carefully: “Every light ray moves in the ‘rest’ coordinate system with a fixed velocity V, independently of whether this ray of light is emitted by a body at rest or in motion.” In other words, the postulate says that the speed of light is the same no matter how fast the light source is moving. Many writers, when defining the light postulate, confuse this with the stronger assertion that light always moves in any inertial frame at the same velocity no matter how fast the light source or the observer is moving toward or away from each other. That statement is also true, but it comes only by combining the relativity principle with the light postulate.
40. Einstein 1922c. In his popular 1916 book Relativity: The Special and General Theory, Einstein explains this in chapter 7, “The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity.”
41. Einstein 1916, chapter 7.
42. Einstein 1922c; Reiser, 68.
43. Einstein 1916, chapter 9.
44. Einstein 1922c; Heisenberg 1958, 114.
45. Sir Isaac Newton, Philosophiae Naturalis Principia Mathematica (1689), books 1 and 2; Einstein, “The Methods of Theoretical Physics,” Herbert Spencer lecture, Oxford, June 10, 1933, in Einstein 1954, 273.
46. Fölsing, 174–175.
47. Poincaré went on to reference himself, saying that he had discussed this idea in an article called “The Measurement of Time.” Arthur I. Miller notes that Einstein’s friend Maurice Solovine may have read this paper, in French, and discussed it with Einstein. Einstein would later cite it, and his analysis of the synchronizations of clocks reflects some of Poincaré’s thinking. Miller 2001, 201–202.
48. Fölsing, 155: “He was observed gesticulating to friends and colleagues as he pointed to one of Bern’s bell towers and then to one in the neighboring village of Muri.” Galison, 253, picks up this tale. Both cite as their source Max Flück iger, Einstein in Bern (Bern: Paul Haupt, 1974), 95. In fact, Flückiger merely quotes a colleague saying that Einstein referred to these clocks as a hypothetical example. See Alberto Martinez, “Material History and Imaginary Clocks,” Physics in Perspective 6 (2004): 229. Martinez does concede, however, that it is indeed interesting that there was a steeple clock in Muri not synchronized with the clocks in Bern and that Einstein referred to this in explaining the theory to friends.
49. Galison, 222, 248, 253; Dyson. Galison’s thesis is based on his original research into the patent applications.
50. Norton 2006a, 3, 43: “Another oversimplification pays too much attention to the one part of Einstein’s paper that especially fascinates us now: his ingenious use of light signals and clocks to mount his conceptual analysis of simultaneity. This approach gives far too much importance to notions that entered briefly only at the end of years of investigation . . . They are not necessary to special relativity or to the relativity of simultaneity.” See also Alberto Martinez, “Material History and Imaginary Clocks,”Physics in Perspective 6 (2004): 224–240; Alberto Martinez, “Railways and the Roots of Relativity,”Physics World ,Nov. 2003; Norton 2004. For a good assessment, which gives more credit to Galison’s research and insights, see Dyson. Also see Miller 2001.
51. Einstein interview, Bucky, 28; Einstein 1956, 12.
52. Moszkowski, 227.
53. Overbye, 135.
54. Miller 1984, 109, 114. Miller 1981, chapter 3, explains the influence of Faraday’s experiments with rotating magnets on Einstein’s special theory.
55. Einstein, “On the Electrodynamics of Moving Bodies,” Annalen der Physik 17 (Sept. 26, 1905). There are many available editions. For a web version, see www.fourmilab.ch/etexts/einstein/specrel/www/. Useful annotated versions include Stachel 1998; Stephen Hawking, ed., Selections from the Principle of Relativity (Philadelphia: Running Press, 2002); Richard Muller, ed., Centennial Edition of The Theory of Relativity (San Francisco: Arion Press, 2005).
56. Einstein, unused addendum to 1916 book Relativity, CPAE 6: 44a.
57. Einstein 1916.
58. Bernstein 2006, 71.
59. This example is lucidly described in Miller 1999, 82–83; Panek, 31–32.
60. James Hartle, lecture at the Aspen Center for Physics, June 29, 2005; British National Measurement Laboratory, report on time dilation experiments, spring 2005, www.npl.co.uk/publications/metromnia/issue18/.
61. Einstein to Maurice Solovine, undated, in Solovine, 33, 35.
62. Krauss, 35–47.
63. Seelig 1956a, 28. For a full mathematical description of the special theory, see Taylor and Wheeler 1992.
64. Pais, 1982, 151, citing Hermann Minkowski, “Space and Time,” lecture at the University of Cologne, Sept. 21, 1908.
65. Clark, 159–60.
66. Thorne, 79. This is also explained well in Miller 2001, 200: “Neither Lorentz, Poincaré, nor any other physicist was willing to grant Lorentz’s local time any physical reality . . . Only Einstein was willing to go beyond appearances.” See also Miller 2001, 240: “Einstein inferred a meaning Poincaré did not. His thought experiment enabled him to interpret the mathematical formalism as a new theory of space and time, whereas for Poincaré it was a generalized version of Lorentz’s electron theory.” Miller has also explored this topic in “Scientific Creativity: A Comparative Study of Henri Poincaré and Albert Einstein,” Creativity Research Journal 5 (1992): 385.
67. Arthur Miller e-mail to the author, Aug. 1, 2005.
68. Hoffmann 1972, 78. Prince Louis de Broglie, the quantum theorist who theorized that particles could behave as waves, said of Poincaré in 1954, “Yet Poincaré did not take the decisive step; he left to Einstein the glory of grasping all the consequences of the principle of relativity.” See Schilpp, 112; Galison, 304.
69. Dyson.
70. Miller 1981, 162.
71. Holton 1973, 178; Pais 1982, 166; Galison, 304; Miller 1981. All four authors have done important work on Poincaré and the credit he deserves, from which some of this section is drawn. I am grateful to Prof. Miller for a copy of his paper “Why Did Poincaré Not Formulate Special Relativity in 1905?” and for helping to edit this section.
72. Miller
1984, 37–38; Henri Poincaré lecture, May 4, 1912, University of London, cited in Miller 1984, 37; Pais 1982, 21, 163–168. Pais writes: “In all his life, Poincaré never understood the basis of special relativity . . . It is apparent that Poincaré either never understood or else never accepted the Theory of Relativity.” See also Galison, 242 and passim.
73. Einstein to Mileva Mari, Mar. 27, 1901.
74. Michelmore, 45.
75. Overbye, 139; Highfield and Carter, 114; Einstein and Mileva Mari to Conrad Habicht, July 20, 1905.
76. Overbye, 140; Trbuhovic-Gjuric, 92–93; Zackheim, 62.
77. The issue of whether Mari’s name was in any way ever on a manuscript of the special theory is a knotted one, but it turns out that the single source for such reports, a late Russian physicist, never actually said precisely that, and there is no other evidence at all to support the contention. For an explanation, see John Stachel’s appendix to the introduction of Einstein’s Miraculous Year, centennial reissue edition (Princeton: Princeton University Press, 2005), lv.
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