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New light on the Einstein-Hilbert priority question

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Notes

  1. Leo Corry, Jürgen Renn and John Stachel, “Belated Decision in the Hilbert-Einstein Priority Dispute,”Science 278 1270–1273 (1997).

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  2. See John Stachel, “The Genesis of General Relativity,” in H. Nelkowskiet al, eds.,Einstein Symposion Berlin, Lecture Notes in Physics 100 (Berlin/Heidelberg/ New York: Springer-Verlag, 1980), pp. 428–442; “Einstein and the Rigidly Rotating Disc,” in A. Held ed.General Relativity and Gravitation One Hundred Years After the Birth of Albert Einstein (New York: Plenum, 1980), pp. 1–15, reprinted in D. Howard and J. Stachel, eds.,Einstein and the History of General Relativity/ Einstein Studies, vol. 1 (Boston/Basel/Stuttgart: BirkhÄuser, 1989), pp. 48–62; “How Einstein discovered general relativity: a historical tale with some contemporary morals,” in M. A. H. MacCallum, ed.,General Relativity and Gravitation/ Proceedings of the 11th International Conference on General Relativity and Gravitation (Cambridge: Cambridge University Press, 1987), pp. 200–208; “Einstein's Search for General Covariance, 1912–1915,” in D. Howard and J. Stachel, edsEinstein and the History of General Relativity/Einstein Studies, vol. 1 (Boston/ Basel/Stuttgart: BirkhÄuser, 1989), pp. 63–100.

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  3. Albert Einstein, “über das RelativitÄtsprinzip und die aus demselben gezogenen Folgerungen,”Jahrbuch der RadioaktivitÄt und Elektronik 4, 411–462 (1907); reprinted in John Stachel et al., eds.The Collected Papers of Albert Einstein, vol. 2,The Swiss Years: Writings 1900–1909, (Princeton University Press, 1989), pp. 433–488. At that time he still referred to the principle, rather than the theory, of relativity, when referring to what was later called special relativity.

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  4. 4 See ref. in note 3, pp. 476–484.

  5. See Albert Einstein, “Lichtgeschwindigkeit und Statik des Gravitationsfeldes,”Annalen der Physik 38, 355–369 (1912), p. 365.

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  6. 6 Some physicists looking for a relativistic theory of gravitation continued to adhere to the special-relativistic principle (Gunnar Nordström and Gustav Mie); one physicist abandoned the relativity principle entirely in his search for a field theory of gravitation (Max Abraham).

  7. See ref. in note 5, and Albert Einstein, “Zur Theory des statischen Gravitations-feldes,”Annalen der Physik 38, 443–458 (1912); both papers are reprinted in Martin J. Kleinet al, eds,The Collected Papers of Albert Einstein, vol. 4,The Swiss Years: Writings 1912–1914, (Princeton University Press, 1995), pp. 130–144,147–162.

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  8. 8 See second reference in note 7, p. 458.

  9. 9 The consideration of stationary gravitational fields, and in particular the gravita tional field on a rotating disc, also played a role in convincing Einstein of the need to go beyond flat space to solve the gravitational problem. See John Stachel, “Einstein and the Rigidly Rotating Disc,” reference in note 2.

  10. See Albert Einstein and Marcel Grossmann,Entwurf einer verallgemeinerten RelativitÄtstheorie und einer Theorie der Gravitation, (Leipzig/Berlin, B.G. Teubner, 1913). Part I, “Physikalische Teil,” was written by Einstein, Part II, “Mathematischer Teil,” by Grossmann. The paper is reproduced in Martin J. Kleinet al, eds,The Collected Papers of Albert Einstein, vol. 4,The Swiss Years: Writings 1912 1914, (Princeton University Press, 1995), pp. 303–339.

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  11. 11 See John Stachel, “Einstein's Search for General Covariance, 1912–1915,” reference in note 2.

  12. For more detailed discussions, see John Stachel, “The Meaning of General Covariance: The Hole Story,” in John Earman et al., eds.,Philosophical Problems of the Internal and External World/Essays on the Philosophy of Adolf Grünbaum (Konstanz: UniversitÄtsverlag/Pittsburgh: University of Pittsburgh Press, 1993), pp 129–160; and “Einstein's Search for General Covariance, 1912–1915,” reference in note 2.

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  13. 13 By speaking of diffeomorphisms instead of coordinate transformations, I am modernizing the argument, but am not being unfaithful to the essence of Einstein's argument.

  14. Einstein to Arnold Sommerfeld, 15 July 1915, in Robert Schulmannet al., eds.The Collected Papers of Albert Einstein, vol. 8,The Berlin Years: Correspondence, 1914–1918 Part A: 1914–1917, (Princeton University Press, 1998), Doc. 96, p. 147.

  15. For a discussion of Hilbert's work during this period, see Leo Corry, “From Mie's Electromagnetic Theory of Matter to Hilbert's Unified Foundation of Physics,”Studies in History and Philosophy of Modern Physics 30B, 159–183 (1999); Tilman Sauer, “The Relativity of Discovery: Hilbert's First Note on the Foundations of Physics,”Archive for History of Exact Sciences 53, 529-575 (1999); and Jürgen Renn and John Stachel, “Hilbert's Foundations of Physics: From a Theory of Everything to a Constituent of General Relativity,” (Berlin, Max-Planck-Institut für Wissenschaftsgeschichte Preprint 118, 1999).

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  16. For discussions of the reasons for his abandonment of the Einstein-Grossman equations and his return to general covariance, see John Stachel, “Einstein's Search for General Covariance,” reference in note 2; John Norton, “How Einstein Found His Field Equations, 1912–1915,”Historical Studies in the Physical Sciences 14, 253-316 (1984); Michel Janssen, “Rotation as the Nemesis of Einstein's Entwurf Theory,” in Hubert Goenneret al. (eds),The Expanding Worlds of General Relativity, Einstein Studies, vol. 7, (Boston/Basel/Berlin, BirkÄuser 1999), pp. 127–157.

  17. Albert Einstein, “Zur allgemeinen RelativitÄtstheorie,”Königlich Preu\ischenAkademie der Wissenschaften (Berlin),Sitzungberichte, 778–786 (1915), “Zur allgemeinen RelativitÄtstheorie (Nachtrag),ibid., 799-801 (1915).

  18. Albert Einstein, “ErklÄrung der Perihelbewegung des Merkur aus der allgemeinen RelativitÄtstheorie,”Königlich Preu\ischen Akademie der Wissenschaften (Berlin),Sitzungberichte, 831–839(1915).

  19. Albert Einstein, “Die Fieldgleichungen der Gravitation,”Königlich Preu\ischen Akademie der Wissenschaften (Berlin)Sitzungsberichte, 844–847 (1915). The papers cited in notes 17, 18 and this note are reprinted in Martin J. Klein et al, eds.The Collected Papers of Albert Einstein, vol. 6,The Berlin Years: Writings 1914–1917 (Princeton University Press, 1996), pp. 215–223, 226–228, 234–242, and 245–248.

  20. Albrecht Fölsing,Albert Einstein: a biography (Viking, New York, 1997), pp. 375–376. The translation has been slightly modified and is taken from ref. 1.

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  21. David Hilbert, “Die Grundagen der Physik (Erste Mitteilung),”Nachrichten von der Königl. Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-physikalische Klasse, 395–407(1915).

  22. The proofs are in the Handschriftenabteilung of the Staats- und UniversitÄtsbibliothek Göttingen, Cod. Ms. D. Hilbert 634.

  23. Albert Einstein to David Hilbert, 18 November 1915, in Robert Schulmannet al, eds.The Collected Papers of Albert Einstein, vol. 8,The Berlin Years: Correspondence, 1914–1918 Part A: 1914–1917, (Princeton University Press, 1998), Doc. 148, pp. 201–202.

  24. Albert Einstein, “Research Notes on a Generalized Theory of Relativity,” in Martin J. Kleinet al., eds.The Collected Papers of Albert Einstein, vol. 4,The Swiss Years: Writings 1912–1914, (Princeton University Press, 1995), pp. 201–269 for a transcription, pp. 630–682 for a facsimile. For a brief review of its significance, see Jürgen Renn and Tilman Sauer,” Einsteins Züricher Notizbuch,”Physikalische BlÄtter 52, 865–872 (1996).

  25. Reference in note 23.

  26. See the reference in note 15.

  27. Albert Einstein to Heinrich Zangger, 26 November 1915, in Robert Schulmannet al., eds.The Collected Papers of Albert Einstein, vol. 8,The Berlin Years: Correspondence, 1914–1918 Part A: 1914–1917, (Princeton University Press, 1998), Doc. 152, pp. 204–205; citation from p. 205.

  28. References in notes 17, 18 and 19.

  29. David Hilbert, “Die Grundlagen der Physik (Zweite Mitteilung),”Nachrichten von der Königl. Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-physikalische Klasse, 53–76 (1917).

  30. It was reprinted, with extensive changes, inMathematische Annalen 92, 1 (1924).

  31. It was not impossible to do this in theGöttinger Nachrichten. Related papers by Klein and Noether, for example, carry such revised datelines (see the paper by Renn and Stachel cited in note 15).

  32. Albert Einstein to David Hilbert, 20 December 1915 in Robert Schulmannet al., eds.The Collected Papers of Albert Einstein, vol. 8,The Berlin Years: Correspondence, 1914–1918 Part A: 1914–1917, (Princeton University Press, 1998), Doc. 167, pp. 222.

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Stachel, J. New light on the Einstein-Hilbert priority question. J Astrophys Astron 20, 91–101 (1999). https://doi.org/10.1007/BF02702345

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