16. Einstein to Heinrich Zangger, Dec. 6, 1917.
17. “All the really great discoveries in theoretical physics—with a few exceptions that stand out because of their oddity—have been made by men under thirty.” Bernstein 1973, 89, emphasis in the original. Einstein finished his work on general relativity when he was 36, but his initial step, what he called his “happiest thought” about the equivalence of gravity and acceleration, came when he was 28. Max Planck was 42 when, in Dec. 1900, he gave his lecture on the quantum.
18. Einstein to Heinrich Zangger, Aug. 11, 1918; Clive Thompson, “Do Scientists Age Badly?,”Boston Globe , Aug. 17, 2003. John von Neumann, a founder of modern computer science, once claimed that the intellectual powers of mathematicians peaked at the age of 26. One study of a random group of scientists showed that 80 percent did their best work before their early forties.
19. Einstein to Maurice Solovine, Apr. 27, 1906.
20. Aphorism for a friend, Sept. 1, 1930, AEA 36-598.
21. Einstein to Hendrik Lorentz, June 17, 1916; Miller 1984, 55–56.
22. Einstein, “Ether and the Theory of Relativity,” speech at University of Leiden, May 5, 1920, CPAE 7: 38.
23. Einstein to Karl Schwarzschild, Jan. 9, 1916.
24. Einstein, “Ether and the Theory of Relativity,” speech at University of Leiden, May 5, 1920, CPAE 7: 38.
25. Greene 2004, 74.
26. Janssen 2004, 22. Einstein made this clearer in his 1921 Princeton lectures, but also continued to say, “It appears probable that Mach was on the right road in his thought that inertia depends on a mutual action of matter.” Einstein 1922a, chapter 4.
27. Einstein, “Ether and the Theory of Relativity,” speech at University of Leiden, May 5, 1920, CPAE 7: 38.
28. Einstein, “On the Present State of the Problem of Specific Heats,” Nov. 3, 1911, CPAE 3: 26; the quote about “really exist in nature” appears on p. 421 of the English translation of vol. 3.
29. Robinson, 84–85.
30. Holton and Brush, 435.
31. Lightman 2005, 151.
32. Clark 202; George de Hevesy to Ernest Rutherford, Oct. 14, 1913; Einstein 1949b, 47.
33. Einstein, “Emission and Absorption of Radiation in Quantum Theory,” July 17, 1916, CPAE 6: 34; Einstein, “On the Quantum Theory of Radiation,” after Aug. 24, 1916, CPAE 6: 38, and also in Physikalische Zeitschrift 18 (1917). See Overbye, 304–306; Rigden, 141; Pais 1982, 404–412; Fölsing, 391; Clark, 265; Daniel Kleppner, “Rereading Einstein on Radiation,”Physics Today (Feb. 2005): 30. In addition, in 1917 Einstein wrote a paper on the quantization of energy in mechanical theories called “On the Quantum Theorem of Sommerfeld and Epstein.” It shows the problems that the classical quantum theory encountered when applied to mechanical systems we would now call chaotic. It was cited by earlier pioneers of quantum mechanics, but has since been largely forgotten. A good description of it and its importance in the development of quantum mechanics is Douglas Stone, “Einstein’s Unknown Insight and the Problem of Quantizing Chaos,”Physics Today (Aug. 2005).
34. Einstein to Michele Besso, Aug. 11, 1916.
35. I am grateful to Professor Douglas Stone of Yale for help with the wording of this.
36. Einstein to Michele Besso, Aug. 24, 1916.
37. Einstein, “On the Quantum Theory of Radiation,” after Aug. 24, 1916, CPAE 6: 38.
38. Einstein to Max Born, Jan. 27, 1920.
39. Einstein to Max Born, Apr. 29, 1924, AEA 8-176.
40. Niels Bohr, “Discussion with Einstein,” in Schilpp, 205–206; Clark, 202.
41. Einstein to Niels Bohr, May 2, 1920; Einstein to Paul Ehrenfest, May 4, 1920.
42. Niels Bohr to Einstein, Nov. 11, 1922, AEA 8-73.
43. Fölsing, 441.
44. John Wheeler, “Memoir,” in French, 21; C. P. Snow, “Albert Einstein,” in French, 3.
45. Bohr’s quip is often quoted. One source I can find for it, in a less pithy fashion, is from Bohr’s own descriptions of being with Einstein at the 1927 Solvay Conference: “Einstein mockingly asked us whether we could really believe that the providential authorities took recourse to dice-playing (‘. . . ob der liebe Gott würfelt’), to which I replied by pointing at the great caution, already called for by ancient thinkers, in ascribing attributes to Providence in everyday language.” Niels Bohr, “Discussion with Einstein,” in Schilpp, 211. Werner Heisenberg, who was at these discussions, also recounts the quip: “To which Bohr could only answer: ‘But still, it cannot be for us to tell God how he is to run the world.’ ” Heisenberg 1989, 117.
46. Holton and Brush, 447; Pais 1982, 436.
47. Pais 1982, 438. Wolfgang Pauli recalled, “In a discussion at the physics meeting in Innsbruck in the autumn of 1924, Einstein proposed to search for interference and diffraction phenomena with molecular beams.” Pauli, 91.
48. Einstein, “Quantum Theory of Single-Atom Gases,” part 1, 1924, part 2, 1925. This quote occurs in part 2, section 7. The manuscript of this paper was found in Leiden in 2005.
49. I am grateful to Professor Douglas Stone of Yale for helping to craft this section and explaining the fundamental importance of what Einstein did. A theoretical condensed matter physicist, he is writing a book on Einstein’s contributions to quantum mechanics and how far-reaching they really were, despite Einstein’s later rejection of the theory. According to Stone, “99% of the credit for this fundamental discovery called Bose-Einstein condensation is really owed to Einstein. Bose did not even realize that he had counted in a different way.” Regarding the Nobel Prize for achieving Bose-Einstein condensation, see www.nobelprize.org/physics/laureates/2001/public.html.
50. Bernstein 1973, 217; Martin J. Klein, “Einstein and the Wave-Particle Duality,”Natural Philosopher (1963): 26.
51. Max Born, “Einstein’s Statistical Theories,” in Schilpp, 174.
52. Einstein to Erwin Schrödinger, Feb. 28, 1925, AEA 22-2.
53. Don Howard, “Spacetime and Separability,” 1996, AEA Cedex H; Howard 1985; Howard 1990b, 61–64; Howard 1997. The 1997 essay identifies the philosophy of Arthur Schopenhauer as an influence on Einstein’s theories of spatial separability.
54. Bernstein 1996a, 138.
55. More precisely, it is the square of the wave function that is proportional to the probability. Holton and Brush, 452.
56. Einstein to Hedwig Born, Mar. 7, 1926, AEA 8-266; Einstein to Max Born, Dec. 4, 1926, AEA 8-180.
57. aip.org/history/heisenberg/p07.htm; Born 2005, 85.
58. Max Born to Einstein, July 15, 1925, AEA 8-177; Einstein to Hedwig Born, Mar. 7, 1926, AEA 8-178; Einstein to Paul Ehrenfest, Sept. 25, 1925, AEA 10-116.
59. Werner Heisenberg to Einstein, June 10, 1927, AEA 12-174.
60. Heisenberg 1971, 63; Gerald Holton, “Werner Heisenberg and Albert Einstein,”Physics Today (2000), www.aip.org/pt/vol-53/iss-7/p38.html.
61. Frank 1947, 216.
62. Aage Petersen, “The Philosophy of Niels Bohr,” Bulletin of the Atomic Scientists (Sept. 1963): 12.
63. Dugald Murdoch, Niels Bohr’s Philosophy of Physics (Cambridge, England: Cambridge University Press, 1987), 47, citing the Niels Bohr Archives: Scientific Correspondence, 11: 2.
64. Einstein, “To the Royal Society on Newton’s Bicentennial,” Mar. 1927.
65. Einstein to Michele Besso, Apr. 29, 1917; Michele Besso to Einstein, May 5, 1917; Einstein to Michele Besso, May 13, 1917. For a good analysis, see Gerald Holton, “Mach, Einstein, and the Search for Reality,” in Holton 1973, 240.
66. “Belief in an external world independent of the perceiving subject is the basis of all natural science.” Einstein, “Maxwell’s Influence on the Evolution of the Idea of Physical Reality,” 1931, in Einstein 1954, 266.
67. Einstein to Max Born, Jan. 27, 1920.
68. Einstein’s introduction to Rudolf Kayser, Spinoza (New York: Philosophical Library, 1946). Kayser was married to Einstein’s stepdaughter and wrote a semi-authorized memoir of Einstein.
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69. Fölsing, 703–704; Einstein to Fritz Reiche, Aug. 15, 1942, AEA 20-19.
70. Einstein to Max Born, Dec. 4, 1926, AEA 8-180.
CHAPTER FIFTEEN: UNIFIED FIELD THEORIES
1. Einstein, “Ideas and Problems of the Theory of Relativity,” Nobel lecture, July 11, 1923. Available at nobelprize.org/nobel_prizes. This section draws from these papers on Einstein’s unified field quest: van Dongen 2002, courtesy of the author; Tilman Sauer, “Dimensions of Einstein’s Unified Field Theory Program,” forthcoming in the Cambridge Companion to Einstein, courtesy of the author; Norton 2000; Goenner 2004.
2. Einstein, “The Principles of Research,” a toast in honor of Max Planck, Apr. 26, 1918, CPAE 7: 7.
3. Einstein to Hermann Weyl, Apr. 6, 1918.
4. Einstein to Hermann Weyl, Apr. 8, 1918. In a letter to Heinrich Zangger, May 8, 1918, Einstein called Weyl’s theory “ingenious” but “physically incorrect.” It did, however, later become one of the recognized precursors of Yang-Mills gauge theory.
5. My description of the work of Kaluza and Klein relies on Krauss, 94–104, which is an engaging book on the role extra dimensions have played in explaining the universe.
6. Einstein to Theodor Kaluza, Apr. 21, 1919.
7. Einstein to Niels Bohr, Jan. 10, 1923, AEA 8-74.
8. Einstein to Hermann Weyl, May 26, 1923, AEA 24-83.
9. Einstein, “On the General Theory of Relativity,” Prussian Academy, Feb. 15, 1923.
10. New York Times , Mar. 27, 1923.
11. Pais 1982, 466; Einstein, “On the General Theory of Relativity,” the Prussian Academy, Feb. 15, 1923.
12. Einstein, “Unified Field Theory of Gravity and Electricity,” July 25, 1925; Hoffmann 1972, 225.
13. Steven Weinberg, “Einstein’s Mistakes,”Physics Today (Nov. 2005).
14. Einstein, “On the Unified Theory,” Jan. 30, 1929.
15. Einstein to Michele Besso, Jan. 5, 1929, AEA 7-102.
16. New York Times , Nov. 4, 1928; Vallentin, 160.
17. Clark, 494;London Daily Chronicle , Jan. 26, 1929.
18. “Einstein’s Field Theory,”Time , Feb. 18, 1929. Einstein also appeared on Time’s cover on Apr. 4, 1938, July 1, 1946, and posthumously Feb. 19, 1979, and Dec. 31, 1999. Elsa appeared on the cover Dec. 22, 1930.
19. Fölsing, 605; Clark, 496; Brian 1996, 174.
20. New York Times , Feb. 4, 1929.
21. Einstein to Maja Winteler-Einstein, Oct. 22, 1929, AEA 29-409.
22. Wolfgang Pauli to Einstein, Dec. 19, 1929, AEA 19-163.
23. New York Times , Jan. 23, Oct. 26, 1931; Einstein to Wolfgang Pauli, Jan. 22, 1932, AEA 19-169.
24. Goenner 2004; Elie Cartan, “Absolute Parallelism and the Unified Theory,” Review Metaphysic Morale (1931).
25. For a two-minute home movie of the conference shot by Irving Langmuir, the 1932 Nobel Prize winner in chemistry, see www.maxborn.net/index.php? page=filmnews.
26. Einstein to Hendrik Lorentz, Sept. 13, 1927, AEA 16-613.
27. Pauli, 121.
28. John Archibald Wheeler and Wojciech Zurek, Quantum Theory and Measurement (Princeton: Princeton University Press, 1983), 7.
29. Fölsing, 589; Pais 1982, 445, from Proceedings of the Fifth Solvay Conference.
30. Heisenberg 1989, 116.
31. Niels Bohr, “Discussion with Einstein,” in Schilpp, 211–219, offers a detailed and loving description of the Solvay and other discussions; Otto Stern recollections, in Pais 1982, 445; Fölsing, 589.
32. “Reports and Discussions,” in Solvay Conference of 1927 (Paris: GauthierVillars, 1928), 102. See also Travis Norsen, “Einstein’s Boxes,”American Journal of Physics, vol. 73, Feb. 2005, pp. 164-176.
33. Louis de Broglie, “My Meeting with Einstein,” in French, 15.
34. Einstein, “Speech to Professor Planck,” Max Planck award ceremony, June 28, 1929.
35. Léon Rosenfeld, “Niels Bohr in the Thirties,” in Rozental 1967, 132.
36. Niels Bohr, “Discussion with Einstein,” in Schilpp, 225–229; Pais 1982, 447–448. I am grateful to Murray Gell-Mann and David Derbes for the phrasing of this section.
37. Einstein, “Maxwell’s Influence on the Evolution of the Idea of Physical Reality,” 1931, in Einstein 1954, 266.
38. Einstein, “Reply to Criticisms” (1949), in Schilpp, 669.
39. A fuller discussion of Einstein’s realism is in chapter 20 of this book. For contrasting views on this issue, see Gerald Holton, “Mach, Einstein, and the Search for Reality,” in Holton 1973, 219, 245 (he argues that there is a very clear change in Einstein’s philosophy: “For a scientist to change his philosophical beliefs so fundamentally is rare”); Fine, 123 (he argues that “Einstein underwent a philosophical conversion, turning away from his positivist youth and becoming deeply committed to realism”); Howard 2004 (which argues, “Einstein was never an ardent ‘Machian’ positivist, and he was never a scientific realist”). This section also draws on van Dongen 2002 (he argues, “Broadly speaking, one can say that Einstein moved from Mach’s empiricism, earlier in his career, to a strong realist position later on”). See also Anton Zeilinger, “Einstein and Absolute Reality,” in Brockman, 121–131.
40. Einstein, “On the Method of Theoretical Physics,” the Herbert Spencer lecture, Oxford, June 10, 1933, in Einstein 1954, 270.
41. Einstein 1949b, 89.
42. Einstein, “Principles of Theoretical Physics,” inaugural address to the Prussian Academy, 1914, in Einstein 1954, 221.
43. Einstein to Hermann Weyl, May 26, 1923, AEA 24-83.
44. John Barrow, “Einstein as Icon,”Nature , Jan. 20, 2005, 219. See also Norton 2000.
45. Einstein, “On the Method of Theoretical Physics,” the Herbert Spencer lecture, Oxford, June 10, 1933, in Einstein 1954, 274.
46. Steven Weinberg, “Einstein’s Mistakes,”Physics Today (Nov. 2005): “Since Einstein’s time, we have learned to distrust this sort of aesthetic criterion. Our experience in elementary-particle physics has taught us that any term in the field equations of physics that is allowed by fundamental principles is likely to be there in the equations.”
47. Einstein, “Latest Developments of the Theory of Relativity,” May 23, 1931, the third of three Rhodes Lectures at Oxford, this one coming on the day he was awarded his honorary doctorate there. Reprinted in the Oxford University Gazette, June 3, 1931.
48. Einstein, “On the Method of Theoretical Physics,” Oxford, June 10, 1933, in Einstein 1954, 270.
49. Marcia Bartusiak, “Beyond the Big Bang,”National Geographic (May 2005). Elsa’s quip is widely reported but never fully sourced. See Clark, 526.
50. Associated Press, Dec. 30, 1930.
51. Einstein to Michele Besso, Mar. 1, 1931, AEA 7-125.
52. Greene 2004, 279: “That would certainly have ranked among the greatest discoveries—it may have been the greatest discovery—of all time.” See also Edward W. Kolb, “The Greatest Discovery Einstein Didn’t Make,” in Brock-man, 201.
53. Einstein,“On the Cosmological Problem of the General Theory of Relativity,” Prussian Academy, 1931; “Einstein Drops Idea of ‘Closed’ Universe,”New York Times , Feb. 5, 1931.
54. Einstein 1916, appendix IV (first appears in the 1931 edition).
55. Gamow 1970, 149.
56. Steven Weinberg, “The Cosmological Constant Problem,” in Morris Loeb Lectures in Physics (Cambridge, Mass.: Harvard University Press 1988); Steven Weinberg, “Einstein’s Mistakes,”Physics Today (Nov. 2005); Aczel 1999, 167; Krauss 117; Greene 2004, 275–278; Dennis Overbye, “A Famous Einstein ‘Fudge’ Returns to Haunt Cosmology,”New York Times , May 26, 1998; Jeremy Bernstein, “Einstein’s Blunder,” in Bernstein 2001, 86–89.
57. Lawrence Krauss of Case Western Reserve and Michael Turner of the University of Chicago have argued that an explanation of the universe requires use of a cosmological term that is different from the one Einstein added into his field equations and then discarded. Their version arises
from quantum mechanics, not general relativity, and is based on the premise that even “empty” space does not necessarily possess zero energy. See Krauss and Turner, “A Cosmic Conundrum,”Scientific American (Sept. 2004).
58. “Einstein’s Cosmological Constant Predicts Dark Energy,”Universe Today , Nov. 22, 2005. This particular headline was based on a research project known as the Supernova Legacy Survey (SNLS). According to a press release from Caltech, SNLS “aims to discover and examine 700 distant supernovae to map out the history of the expansion of the universe. The survey confirms earlier discoveries that the expansion of the universe proceeded more slowly in the past and is speeding up today. However, the crucial step forward is the discovery that Einstein’s 1917 explanation of a constant energy term for empty space fits the new supernova data very well.”