3. Einstein, Letter to the Royal Society on Newton’s bicentennial, Mar. 1927.
4. Einstein 1949b, 19.
5. For the influence of Faraday’s induction theories on Einstein, see Miller 1981, chapter 3.
6. Einstein and Infeld, 244; Overbye, 40; Bernstein 1996a, 49.
7. Einstein to Conrad Habicht, May 18 or 25, 1905.
8. Sent on Mar. 17, 1905, and published in Annalen der Physik 17 (1905). I want to thank Yale professor Douglas Stone for help with this section.
9. Max Born, obituary for Max Planck, Royal Society of London, 1948.
10. John Heilbron, The Dilemmas of an Upright Man (Berkeley: University of California Press, 1986). Lucid explanations of Einstein’s quantum paper, from which this section is drawn, include Gribbin and Gribbin; Bernstein 1996a, 2006; Overbye, 118–121; Stachel 1998; Rigden; A. Douglas Stone, “Genius and Genius2: Planck, Einstein and the Birth of Quantum Theory,” Aspen Center for Physics, unpublished lecture, July 20, 2005.
11. Planck’s approach was probably a bit more complex and involved assuming a group of oscillators and positing a total energy that is an integer multiple of a quantum unit. Bernstein 2006, 157–161.
12. Max Planck, speech to the Berlin Physical Society, Dec. 14, 1900. See Light-man 2005, 3.
13. Einstein 1949b, 46. Miller 1984, 112; Miller 1999, 50; Rynasiewicz and Renn, 5.
14. Einstein, “On the General Molecular Theory of Heat,” Mar. 27, 1904.
15. Einstein to Conrad Habicht, Apr. 15, 1904. Jeremy Bernstein discussed the connections between the 1904 and 1905 papers in an e-mail, July 29, 2005.
16. Einstein, “On a Heuristic Point of View Concerning the Production and Transformation of Light,” Mar. 17, 1905.
17. “We are startled, wondering what happened to the waves of light of the 19th century theory and marveling at how Einstein could see the signature of atomic discreteness in the bland formulae of thermodynamics,” says the science historian John D. Norton. “Einstein takes what looks like a dreary fragment of the thermodynamics of heat radiation, an empirically based expression for the entropy of a volume of high-frequency heat radiation. In a few deft inferences he converts this expression into a simple, probabilistic formula whose unavoidable interpretation is that the energy of radiation is spatially localized in finitely many, independent points.” Norton 2006c, 73. See also Lightman 2005, 48.
18. Einstein’s paper in 1906 noted clearly that Planck had not grasped the full implications of the quantum theory. Apparently, Besso encouraged Einstein not to make this criticism of Planck too explicit. As Besso wrote much later, “In helping you edit your publications on the quanta, I deprived you of a part of your glory, but, on the other hand, I made a friend for you in Planck.” Michele Besso to Einstein, Jan. 17, 1928. See Rynasiewicz and Renn, 29; Bernstein 1991, 155.
19. Holton and Brush, 395.
20. Gilbert Lewis coined the name “photon” in 1926. Einstein in 1905 discovered a quantum of light. Only later, in 1916, did he discuss the quantum’s momentum and its zero rest mass. Jeremy Bernstein has noted that one of the most interesting discoveries Einstein did not make in 1905 was the photon. Jeremy Bernstein, letter to the editor, Physics Today , May 2006.
21. Gribbin and Gribbin, 81.
22. Max Planck to Einstein, July 6, 1907.
23. Max Planck and three others to the Prussian Academy, June 12, 1913, CPAE 5: 445.
24. Max Planck, Scientific Autobiography (New York: Philosophical Library, 1949), 44; Max Born, “Einstein’s Statistical Theories,” in Schilpp, 163.
25. Quoted in Gerald Holton, “Millikan’s Struggle with Theory,”Europhysics News 31 (2000): 3.
26. Einstein to Michele Besso, Dec. 12, 1951, AEA 7-401.
27. Completed Apr. 30, 1905, submitted to the University of Zurich on July 20, 1905, submitted to Annalen der Physik in revised form on Aug. 19, 1905, and published by Annalen der Physik Jan. 1906. See Norton 2006c and www.pitt.edu/~jdnorton/Goodies/Einstein_stat_1905/.
28. Jos Uffink, “Insuperable Difficulties: Einstein’s Statistical Road to Molecular Physics,”Studies in the History and Philosophy of Modern Physics 37 (2006): 37, 60.
29. bulldog.u-net.com/avogadro/avoga.html.
30. Rigden, 48–52; Bernstein 1996a, 88; Gribbin and Gribbin, 49–54; Pais 1982, 88.
31. Hoffmann 1972, 55; Seelig 1956b, 72; Pais 1982, 88–89.
32. Brownian motion introduction, CPAE 2 (German), p. 206; Rigden, 63.
33. Einstein, “On the Motion of Small Particles Suspended in Liquids at Rest Required by the Molecular-Kinetic Theory of Heat,” submitted to the Annalen der Physik on May 11, 1905.
34. Einstein 1949b, 47.
35. The root mean square average is asymptotic to ff2n/?. Good analyses of the relationship of random walks to Einstein’s Brownian motion are in Gribbin and Gribbin, 61; Bernstein 2006, 117. I am grateful to George Stranahan of the Aspen Center for Physics for his help on the mathematics behind this relationship.
36. Einstein, “On the Theory of Brownian Motion,” 1906, CPAE 2: 32 (in which he notes Seidentopf ’s results); Gribbin and Gribbin, 63; Clark, 89; Max Born, “Einstein’s Statistical Theories,” in Schilpp, 166.
CHAPTER SIX: SPECIAL RELATIVITY
1. Contemporary historical research on Einstein’s special theory begins with Gerald Holton’s essay, “On the Origins of the Special Theory of Relativity” (1960), reprinted in Holton 1973, 165. Holton remains a guiding light in this field. Most of his earlier essays are incorporated in his books Thematic Origins of Scientific Thought: Kepler to Einstein (1973), Einstein, History and Other Passions (2000), and The Scientific Imagination, Cambridge, Mass.: Harvard University Press, 1998.
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 exp
lanation.
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 finally 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.
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