Abstract
In 1918 the mathematician Hermann Weyl (1885–1955) extended the general theory of relativity that Albert Einstein (1879–1955) had set forth in the years 1915–1916. At one level, Weyl’s theory made it possible to unify the two field phenomena known at this time, namely those described by electromagnetic and gravitational fields. But more was at stake. At the beginning of the paper in which Weyl worked out the mathematical foundations of the theory, he observed that:
According to this theory everything real, that is in the world, is a manifestation of the world metric; the physical concepts are no different from the geometrical ones. The only difference that exists between geometry and physics is, that geometry establishes in general what is contained in the nature of the metrical concepts, whereas it is the task for physics to determine the law and explore its consequences, according to which the real world is characterized among all the geometrically possible four-dimensional metric spaces.
I acknowledge the support of the Alexander von Humboldt-Stiftung and Verbund für Wissenschaftsgeschichte Berlin for writing this paper. It draws upon Sigurdsson, “Hermann Weyl, Mathematics and Physics, 1900–1927” (Ph. D. dissertation, Harvard University, 1991). All translations are mine unless otherwise indicated. I thank William Clark, Lorraine Daston, Joan L. Richards, Tilman Sauer and Silvan S. Schweber for reading and criticizing earlier versions of this paper.
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Notes
Hermann Weyl, “Reine Infinitesimalgeometrie,” in Weyl, Gesammelte Abhandlungen,4 vols. (Berlin: Springer, 1968), Vol. II, pp. 1–28, on p. 2; emph. in orig.
Thomas S. Kuhn, The Structure of Scientific Revolutions (Chicago: University of Chicago Press, 1970 [1st ed. 1962]), on p. 167.
Felix Klein, “The Present State of Mathematics,” in Klein, Gesammelte mathematische Abhandlungen,3 vols. (Berlin: Julius Springer, 1922), Vol. II, pp. 613–615, on p. 615; emph. in orig.
Weyl, “Obituary: David Hilbert (1862–1943),” in Weyl, Ges. Abh. (ref.2), Vol. IV, pp. 121–129, on p. 128.
Weyl, “David Hilbert and His Mathematical Work,” in Weyl, Ges. Abh. (ref. 2), Vol. IV, pp. 130–172, on p. 132.
Weyl, “Zu David Hilberts siebzigstem Geburtstag,” in Weyl, Ges. Abh. (ref. 2), Vol. III, pp. 346–347, on p. 347; emph. in orig.
Richard Courant, interviewed by Thomas S. Kuhn, 9 May 1962, Archive for History of Quantum Physics.
David Hilbert, “Mathematische Probleme,” in Hilbert, Gesammelte Abhandlungen,3 vols. (Berlin: Julius Springer, 1935), Vol. III, pp. 290–329, on p. 295.
Hilbert, “Wesen und Ziele einer Analysis der unendlichvielen unabhängigen Variablen,” in Hilbert, Ges. Abh. (ref. 9), Vol. III, pp. 56–72, on p. 57; emph. in orig.
Hilbert, “Die Grundlagen der Physik (1924),” in Hilbert, Ges. Abh. (ref. 9), Vol. III, pp. 258–289, on p. 258. This paper is a condensed version of Hilbert’s two notes on the foundations of physics of 20 November 1915 and 23 December 1916.
Max Born, “Hilbert und die Physik (1922),” in Born, Ausgewählte Abhandlungen,2 vols. (Göttingen: Vandenhoeck and Ruprecht, 1963), Vol. II, pp. 584–598, on pp. 595–596.
Hilbert, “Die Grundlagen der Physik (1924),” in Hilbert, Ges. Abh. (ref. 9), Vol. III, pp. 258–289, on p. 278.
Albert Einstein to Hermann Weyl, Berlin, 23 November 1916, Nachlass Hermann Weyl HS 91: 536, ETH Library Archives Zürich. Hereafter abbreviated NWeyl.
Weyl, Lecture at the Princeton Bicentennial Conference, December 1946, N Weyl, HS 91a: 18.
Weyl to Einstein, Zürich, 1 March 1918, NWeyl HS 91: 538a.
Weyl, “Gravitation und Elektrizität,” in Weyl, Ges. Abh. (ref. 2), Vol II, pp. 29–42, on p. 30.
Weyl to Einstein, Zürich, 19 May 1918, NWeyl HS 91: 545a.
Fritz London, “Quantenmechanische Deutung der Theorie von Weyl,” Zeitschrift für Physik 42 (1927), pp. 375–389, on p. 377.
Wolfgang Pauli, Theory of Relativity (New York: Dover, 1981 [English transi. 1958]), on p. 202.
Paul Bernays to David Hilbert, Charlottenburg, 25 November 1925, Nachlass David Hilbert 21, Niedersächsische Staats-und Universitätsbibliothek, Göttingen.
Weyl to Robert König, 21 February 1927, quoted in König, “Hermann Weyl,” Bayerische Akademie der Wissenschaften: Jahrbuch (1956), pp. 236–248, on p. 243.
Weyl, “David Hilbert and His Mathematical Work,” in Weyl, Ges. Abh. (ref. 2), Vol. IV, pp. 130–172, on p. 171.
Weyl, “Emmy Noether (1935)” in Weyl, Ges. Abh. (ref. 2), Vol. III, pp. 425–444; Weyl to Carl Seelig, Zürich, 19 May and 26 June 1952, Seelig papers, HS 304: 1062 and 1063, ETH Library Archives Zürich; and Weyl to A. Vibert Douglas, Zürich, 31 October 1953, NWeyl,HS 91: 173.
Weyl to Fanny Minkowski, Princeton [?], 24 March 1947, NWeyl,HS 91: 378. Minkowski’s lecture “Space and Time” is reprinted in H. A. Lorentz et al., The Principle of Relativity (New York: Dover, 1952 [English transi. 1923]), pp. 75–91, on p. 75.
Weyl, “Die Einsteinsche Relativitätstheorie,” in Weyl, Ges. Abh. (ref. 2), Vol. II, pp. 123140, on p. 131; emph. in orig.
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Sigurdsson, S. (1994). Unification, Geometry and Ambivalence: Hilbert, Weyl and the Göttingen Community. In: Gavroglu, K., Christianidis, J., Nicolaidis, E. (eds) Trends in the Historiography of Science. Boston Studies in the Philosophy of Science, vol 151. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3596-4_25
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