Einstein (124 page)
Authors: Walter Isaacson
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
Entwurf
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
H
. When it is properly generalized, it permits an arbitrary
H
. From this it was demonstrated that covariance with respect to ‘adapted’ coordinate systems was a flop.”
66
. Norton 2000, 152.
67
. There is a subtle divergence of opinion among the group of general relativity historians about the extent of his purported shift from the physical to the mathematical strategy in Oct.–Nov. 1915. John Norton has argued that Einstein’s “new tactic was to reverse his decision of 1913” and go back to a mathematical strategy, emphasizing a tensor analysis that would produce general covariance (Norton 2000, 151). Likewise, Jeroen van Dongen says the shift in tactics was clear: “Einstein immediately got hold of the way out of the
Entwurf
’s quagmire: he returned to the mathematical requirement of general covariance that he had abandoned in the Zurich notebook” (van Dongen, 25). Both scholars produce quotes from Einstein’s later years in which he claims that the big lesson he learned was to trust a mathematical strategy. On the other side, Jürgen Renn and Michel Janssen say that Norton and van Dongen (and the older Einstein in his hazy memory) make too much of this shift. Physical considerations still played a major role in finding the final theory in Nov. 1915. “In our reconstruction, however, Einstein found his way back to the generally-covariant field equations by making one important adjustment to the
Entwurf
theory, a theory born almost entirely out of physical considerations . . . That mathematical considerations pointed in the same direction undoubtedly inspired confidence that this was the right direction, but guiding him along this path were physical not mathematical considerations” (Janssen and Renn, 13; the quote I use in the text is on p. 10). Also, Janssen 2004, 35: “Whatever he believed, said, or wrote about it later on, Einstein only discovered the mathematical high road to the Einstein field equations after he had already found these equations at the end of a poorly paved road through physics.”
68
. Einstein to Arnold Sommerfeld, Nov. 28, 1915.
69
. Einstein, “On the General Theory of Relativity,” Nov. 4, 1915, CPAE 6: 21.
70
. Einstein to Michele Besso, Nov. 17, 1915; Einstein to Arnold Sommerfeld, Nov. 28, 1915.
71
. Einstein to Hans Albert Einstein, Nov. 4, 1915.
72
. Einstein to David Hilbert, Nov. 7, 1915.
73
. Overbye, 290.
74
. Einstein, “On the General Theory of Relativity (Addendum),” Nov. 11, 1915, CPAE 6: 22; Renn and Sauer 2006, 276; Pais 1982, 252.
75
. Einstein to David Hilbert, Nov. 12, 1915.
76
. Einstein to Hans Albert Einstein, Nov. 15, 1915; Einstein to Mileva Mari, Nov. 15, 1915; Einstein to Heinrich Zangger, Nov. 15, 1915 (released in 2006 and printed in supplement to vol. 10).
77
. Einstein to David Hilbert, Nov. 15, 1915.
78
. Einstein, “Explanation of the Perihelion Motion of Mercury from the General Theory of Relativity,” Nov. 18, 1915, CPAE 6: 24.
79
. Pais 1982, 253; Einstein to Paul Ehrenfest, Jan. 17, 1916; Einstein to Arnold Sommerfeld, Dec. 9, 1915.
80
. Einstein to David Hilbert, Nov. 18, 1915.
81
. David Hilbert to Einstein, Nov. 19, 1915.
82
. The equation has been expressed in many ways. The one I use follows the formulation Einstein used in his 1921 Princeton lectures. The entire left-hand side of the equation can be expressed more compactly as what is now known as the Einstein tensor: G
μν
.
.
83
. Overbye, 293; Aczel 1999, 117; archive.ncsa.uiuc.edu/Cyberia/NumRel/Ein steinEquations.html#intro. A variation of Wheeler’s quote is on p. 5 of the book he coauthored with Charles Misner and Kip Thorne,
Gravitation
.
84
. Greene 2004, 74.
85
. Einstein, “The Foundations of the General Theory of Relativity,”
Annalen der Physik
(Mar. 20, 1916), CPAE 6: 30.
86
. Einstein to Heinrich Zangger, Nov. 26, 1915; Einstein to Michele Besso, Nov. 30, 1915.
87
. Thorne, 119.
88
. For an analysis of Hilbert’s contribution, see Sauer 1999, 529–575; Sauer 2005, 577–590. Papers describing Hilbert’s revisions include Corry, Renn, and Stachel; Sauer 2005. For a flavor of the controversy, see also John Earman and Clark Glymour, “Einstein and Hilbert:Two Months in the History of General Relativity,”
Archive for History of Exact Sciences
(1978): 291; A. A. Logunov, M. A. Mestvirishvili, and V. A. Petrov, “How Were the Hilbert-Einstein Equations Discovered?,”
Uspekhi Fizicheskikh Nauk
174, no. 6 (June 2004): 663–678; Christopher Jon Bjerknes,
Albert Einstein:The Incorrigible Plagiarist
, available at home.comcast.net/~xtxinc/AEIPBook.htm; John Stachel, “Anti-Einstein Sentiment Surfaces Again,”
Physics World
, Apr. 2003, physicsweb.org/articles/review/16/4/2/1; Christopher Jon Bjerknes, “The Author of
Albert Einstein: The Incorrigible Plagiarist
Responds to John Stachel’s Personal Attack,” home.comcast.net/~xtxinc/Response.htm; Friedwardt Winterberg, “On ‘Belated Decision in the Hilbert-Einstein Priority Dispute,’ ”
Zeitschrift
fuer Naturforschung A
, (Oct. 2004): 715–719, www.physics.unr.edu/faculty/winterberg/Hilbert-Einstein.pdf; David Rowe, “Einstein Meets Hilbert: At the Crossroads of Physics and Mathematics,”
Physics in Perspective
3, no. 4 (Nov. 2001): 379.
89
. Reid, 142. Although this comment is cited in other secondary sources as well, Tilman Sauer of the Einstein Papers Project, who is writing a book on Hilbert, says he has never found a primary source for it.
90
. Einstein to David Hilbert, Dec. 20, 1915.
91
. Einstein to Arnold Sommerfeld, Dec. 9, 1915; Einstein to Heinrich Zangger, Nov. 26, 1915.
92
. It is a contentious question as to whether general relativity actually succeeds in making all forms of motion and all frames of reference equivalent. It can certainly be said that two observers in nonuniform relative motion can each legitimately view himself as “at rest” and the other as affected by a gravitational field. That does not necessarily mean (as Einstein sometimes seemed to believe and at other times not) that two observers in nonuniform relative motion are always physically equivalent, especially when it comes to rotation. See, for example, Norton 1995b, 223–245; Janssen 2004, 8–12; Don Howard,“Point Coincidences and Pointer Coincidences,” in Goenner et al. 1999, 463; Robert Rynasiewicz, “Kretschmann’s Analysis of Covariance and Relativity Principles,” in Goenner et al. 1999, 431; Dennis Diek, “Another Look at General Covariance and the Equivalence of Reference Frames,”
Studies in the History and Philosophy of Modern Physics
37 (Mar. 2006): 174.
93
. Fölsing, 374; Clark, 252.
94
. Einstein to Michele Besso, Dec. 10, 1915.
CHAPTER TEN: DIVORCE
1
. Michele Besso to Einstein, Nov. 29, 1915; Einstein to Michele Besso, Nov. 30, 1915; Neffe, 192.
2
. Hans Albert Einstein to Einstein, before Nov. 30, 1915; Einstein to Hans Albert Einstein, Nov. 30, 1915.
3
. Michele Besso to Einstein, Nov. 30, 1915. See also Einstein to Heinrich Zangger, Dec. 4, 1915: “The boy’s soul is being systematically poisoned to make sure that he doesn’t trust me.”
4
. Einstein to Mileva Mari
5
. Einstein to Hans Albert Einstein, Dec. 23 and 25, 1915. Einstein wrote a similar postcard to Hans Albert on Dec. 18, 1915. Einstein to Hans Albert Einstein, Mar. 11, 1916.
6
. Einstein to Heinrich Zangger, Nov. 26, 1915; Einstein to Michele Besso, Jan. 3, 1916.
7
. Overbye, 300.
8
. Einstein to Mileva Mari