Walter Isaacson - Einstein - His Life and Universe

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field equations—and how Einstein kept feeling that the

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did indeed comply with Mach’s principle—see Einstein to Michele Besso, ca. Mar. 10, 1914.

27

. Einstein to Ernst Mach, June 25, 1913; Misner, Thorne, and Wheeler, 544.

28

. Einstein to Hendrik Lorentz, Aug. 14, 1913. But two days later, he writes Lorentz again to say that he has resigned himself to the belief that covariance is impossible: “Only now, after this ugly dark spot seems to have been eliminated, does the theory give me pleasure.” Einstein to Hendrik Lorentz, Aug. 16, 1913.

29

. The hole argument basically said that a generally covariant gravitational theory would be indeterministic. Generally covariant field equations could not determine the metric field uniquely. A full specification of the metric field outside of some small region that was devoid of matter, known as “the hole,” would not be able to fix the metric field within that region. See Stachel 1989b; Norton 2005b; Janssen 2004.

30

. Einstein to Ludwig Hopf, Nov. 2, 1913. See also Einstein to Paul Ehrenfest, Nov. 7, 1913: “It can be proved that

generally covariant

equations that determine

the field completely from the matter tensor cannot exist at all. Can there be anything more beautiful than this, that the necessary specialization follows from the conservation laws? Thus, the conservation laws determine the surfaces that, from among all the surfaces, are to be privileged as coordinate surfaces. We can designate these privileged surfaces as planes, since we are left with linear substitutions as the only ones that are justified.” Einstein’s clearest explanation of the hole argument is “On the Foundations of the Generalized Theory of Relativity and the Theory of Gravitation,” Jan. 1914, CPAE 4: 25.

31

. When Einstein appeared at the annual convocation of German-speaking scientists in Sept. 1913, the rival gravitation theorist Gustav Mie rose to launch a “lively” attack on him and subsequently published a violent polemic that displayed a vitriol far beyond anything explained by scientific disagreements. Einstein also engaged in a bitter debate with Max Abraham, whose own gravitational theory Einstein had attacked with great relish throughout 1912. Report on the Vienna conference, Sept. 23, 1913, CPAE 4: 17.

32

. Einstein to Heinrich Zangger, ca. Jan. 20, 1914.

33

. Einstein to Heinrich Zangger, Mar. 10, 1914. Jürgen Renn has pointed out that the 1913–1915 period of defending and refining the

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, even though it did not save that theory, did help Einstein to better understand the difficulties that seemed to bedevil the tensors he had explored in the mathematical strategy. “Practically all of the technical problems Einstein had encountered in the Zurich notebook with candidates derived from the Riemann tensor were actually resolved in this period in the course of his examination of problems associated with the

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theory.” Renn 2005b, 16.

34

. Einstein to Erwin Freundlich, Jan. 8, 1912, mid-Aug. 1913; Einstein to George Hale, Oct. 14, 1913; George Hale to Einstein, Nov. 8, 1913.

35

. Clark, 207.

36

. Einstein to Erwin Freundlich, Dec. 7, 1913.

37

. Einstein to Erwin Freundlich, Jan. 20, 1914.

38

. Fölsing, 356–357.

39

. Einstein to Paul Ehrenfest, Aug. 19, 1914.

40

. Ibid.

41

. Einstein to Paolo Straneo, Jan. 7, 1915.

42

. For a good description from which this is drawn, see Levenson, especially 60–65.

43

. Elon, 277, 303–304.

44

. Fölsing, 344.

45

. Einstein to Hans Albert Einstein, Jan. 25, 1915.

46

. Nathan and Norden, 4; Elon, 326. Also translated as the “Manifesto to the Civilized World.”

47

. Einstein to Georg Nicolai, Feb. 20, 1915. The full text is in CPAE 6: 8, and Nathan and Norden, 5. Clark, 228, makes the case that some of the writing was Einstein’s. See also Wolf William Zuelzer,

The Nicolai Case

(Detroit: Wayne State University Press, 1982); Overbye, 273; Levenson, 63; Fölsing, 346–347; Elon, 328.

48

. Nathan and Norden, 9; Overbye, 275–276; Fölsing, 349; Clark, 238.

49

. Einstein to Romain Rolland, Sept. 15, 1915; CPAE 8a: 118 (German edition), footnote 2; Romain Rolland diary, cited in Nathan and Norden, 16; Fölsing, 366.

50

. Einstein to Paul Hertz, before Oct. 8, 1915; Paul Hertz to Einstein, Oct. 8, 1915; Einstein to Paul Hertz, Oct. 9, 1915.

51

. Einstein, “My Opinion on the War,” Oct. 23–Nov. 11, 1915, CPAE 6: 20.

52

. Einstein to Heinrich Zangger, after Dec. 27, 1914, CPAE 8: 41a, in supplement to vol. 10.

53

. Hans Albert Einstein to Einstein, two postcards, before Apr. 4, 1915, part of the family correspondence trust that was under seal until 2006. CPAE 8: 69a, 8: 69b, in supplement to vol. 10.

54

. Einstein to Hans Albert Einstein, ca. Apr. 4, 1915.

55

. Einstein to Heinrich Zangger, July 16, 1915.

56

. Einstein to Elsa Einstein, Sept. 11, 1915; Einstein to Heinrich Zangger, Oct. 15, 1915; Einstein to Hans Albert Einstein, Nov. 4, 1915. For Einstein’s complaint that he was barely able to see his boys during the Sept. 1916 visit, see Einstein to Mileva Mari

, Apr. 1, 1916: “I hope that this time you will not again withhold the boys almost entirely from me.”

57

. Einstein to Heinrich Zangger, Oct. 15, 1915; Michele Besso to Einstein, ca. Oct. 30, 1915.

58

. Once again, I have drawn on the works of Jürgen Renn, Tilman Sauer, John Stachel, Michel Janssen, and John D. Norton.

59

. Horst Kant, “Albert Einstein and the Kaiser Wilhelm Institute for Physics in Berlin,” in Renn 2005d, 168–170.

60

. Wolf-Dieter Mechler, “Einstein’s Residences in Berlin,” in Renn 2005d, 268.

61

. Janssen 2004, 29.

62

. Einstein to Heinrich Zangger, July 7, ca. July 24, 1915; Einstein to Arnold Sommerfeld, July 15, 1915.

63

. Specifically, the issue was whether the

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field equations were invariant under the non-autonomous transformation to rotating coordinates in the case of the Minkowski metric in its standard diagonal form. Janssen 2004, 29.

64

. Michele Besso memo to Einstein, Aug. 28, 1913; Janssen 2002; Norton 2000, 149; Einstein to Erwin Freundlich, Sept. 30, 1915.

65

. Einstein to Hendrik Lorentz, Oct. 12, 1915. Einstein describes his October 1915 breakthroughs in a subsequent letter to Lorentz and another one to Arnold Sommerfeld. Einstein to Hendrik Lorentz, Jan. 1, 1916: “Trying times awaited me last fall as the inaccuracy of the older gravitational field equations gradually dawned on me. I had already discovered earlier that Mercury’s perihelion motion had come out too small. In addition, I found that the equations were not covariant for substitutions corresponding to a uniform rotation of the new reference system. Finally, I found that the consideration I made last year on the determination of Lagrange’s

H

function for the gravitational field was thoroughly illusory, in that it could easily be modified such that no restricting conditions had to be attached to

H

, thus making it possible to choose

it completely freely. In this way I came to the conviction that introducing adapted systems was on the wrong track and that a more broad-reaching covariance, preferably a

general

covariance, must be required. Now general covariance has been achieved, whereby nothing is changed in the subsequent specialization of the frame of reference ...I had considered the current equations in essence already three years ago together with Grossmann, who had brought my attention to the Riemann tensor.” Einstein to Arnold Sommerfeld, Nov. 28, 1915: “In the last month I had one of the most stimulating and exhausting times of my life, and indeed also one of the most successful. For I realized that my existing gravitational field equations were untenable! The following indications led to this: 1) I proved that the gravitational field on a uniformly rotating system does not satisfy the field equations. 2) The motion of Mercury’s perihelion came to 18” rather than 45” per century. 3) The covariance considerations in my paper of last year do not yield the Hamiltonian function