Erich Kretschmann

Erich Kretschmann (1887-1973) was a German mathematician and Gymnasium (school) teacher.

He obtained his "D.Phil." at Berlin University in 1914 with his dissertation entitled "Eine Theorie der Schwerkraft im Rahmen der ursprünglichen Einsteinschen Relativitätstheorie".His advisors were Max Planck and Heinrich Rubens.

In his 1915 papers, he introduced the Kretschmann scalar. In his 1915 papers he also introduced, though not in name, the point coincidence argument in relativity. Similar ideas appeared in Einstein's writings on general relativity. Historians Don Howard and John Norton suggest that Einstein may have failed to adequately acknowledge Kretschmann's contribution. Kretschmann's use of the argument was more topological while Einstein's use involved physical measurements.

Kretschmann is most famous for his 1917 claim that Einstein's use of the principle of covariance in General Relativity is vacuous. Kretschmann claimed that the demand that a theory be put in generally covariant form does not limit or restrict the range of acceptable theories, but is simply a challenge to the mathematician's ingenuity. According to Kretschmann, any theory can be put in generally covariant form. Einstein responded that even if general covariance is not a purely formal limitation on acceptable theories, it plays "an important heuristic role" in the formulation of General Relativity.

Einstein wrote concerning Kretschmann's objection:"Although it is true that every empirical law can be put in a generally covariant form, yet the principle of relativity possesses a great heuristic power....Of two theoretical systems, both of which agree with experience, the one is to be preferred which, from the point of view of the absolute differential calculus is the simpler and more transparent. Let one express Newtonian mechanics four-dimensionally in the form of generally covariant equations and one will surely be convinced that the principle of relativity excludes this theory from the practical, though not the theoretical, viewpoint." (1918, p. 242)

Einstein suggested that Newtonian theory would be impossibly complex if put in covariant form, although since Einstein made that claim it has been formulated in covariant form by several physicists, including Elie Cartan in 1923 and Friedrichs in 1927. Misner, Thorne, and Wheeler, in their textbook "Gravitation" (1973) Ch. 12 present the covariant version of Newton.

In a letter of 1925 Arnold Sommerfeld wrote favorably of Kretschmann's work in relativity and the statistics of atoms, but said that he needed to get a different teaching position (get away from Königsberg) in order to be able to do more research.

The issue of whether covariance is a real restriction and if so in what sense appears in various contributions to the philosophical debate concerning Einstein's "hole argument." This argument initially had led Einstein in 1913 for a time to reject generally covariant theories, because a region of space/time without forces would undermine determinism or unique extension of trajectories. He later concluded that space/time points without gravity would not be individuated.

It has been claimed also that Kretschmann discovered that the conformal geometry of General Relativity corresponds to the light cone structure, a point rediscovered by and extensively exploited by Hermann Weyl, and since then developed by Jürgen Ehlers and collaborators.

Kretschmann's prose is so convoluted and obscure that reception and appreciation of his work was generally delayed. James Anderson, in the mid-1960s made Kretschmann's work more well-known, though he used it as an object of criticism with respect to Kretschmann's claims concerning the symmetry groups of special and general relativity.

Kretschmann published half a dozen less noted papers during the 1920s and early 1930s, the last in 1934, though he continued to live in Germany for decades. Whether the Nazi seizure of power had anything to do with his ceasing to publish should be investigated.

ee also

*Hole argument

External links

* [http://www.lrz-muenchen.de/~Sommerfeld/PersDat/02425.html Kretschmann in A. Sommerfeld's correspondence]
* [http://genealogy.math.ndsu.nodak.edu/html/id.phtml?id=52000 E.K.'s thesis cited at Mathematics Genealogy Project]

* [http://philsci-archive.pitt.edu/archive/00002123/ "Einstein’s First Systematic Exposition of General Relativity", by M. Janssen, on philsci-archive.pitt.edu]

[http://www.pitt.edu/~jdnorton/papers/decades.pdf Norton, John D., "General Covariance and the Foundations of General Relativity: Eight Decades of Dispute," Rep. Progr. Theor. Phys., vol. 56, 1993, 751-856.]

[http://www.pitt.edu/~jdnorton/papers/labyrinth-HGR3.pdf Don Howard and John D. Norton, "Out of the Labyrinth? Einstein, Hertz, and the Gõttingen Response to the Hole Argument," in John Earman, Janssen, and John Norton, eds., "The Attraction of Gravitation: New Studies in the History of General Relativity" Boston: Birkhãuser,1993, 30-62.]

Major works by Erich Kretschmann

* Kretschmann, Erich. 1915. "Über die prinzipielle Bestimmbarkeit der berechtigten Bezugssysteme beliebiger Relativitätstheorien (I), (II)". Annalen der Physik 48: 907–942, 943–982.

* ———. 1917. "Über den physikalischen Sinn der Relativitätspostulate. A. Einsteins neue und seine ursprüngliche Relativitätstheorie". Annalen der Physik 53: 575–614.

Einstein's Response to Kretschmann:

Einstein, Albert, 1918 "Principielles zur allgemainen Relativitãtstheorie," Annalen der Physik, vol. 55.

Commentary:

Robert Rynasiewicz, "Kretshmann's Analysis of Covariance and Relativity Principles," in "The Expanding Worlds of General Relativity" ed. Hubert Goeener, et al, Boston: Birkhãuser, 1999, 431-462.

Other and Later Works of Kretschmann:

Beitrag zur Kritik der Blochschen Theorie der Elektrizitätsleitung. Z. f. Physik 87, 518-534(1934)

Über die Resonanzbedingung und über die Beschleunigung der Elektronen in derBlochschen Theorie der Elektrizitätsleistung. Z. f. Physik 88, 792-799. (1934)

Beitrag zur Theorie des elektrischen Widerstandes und der Supraleitfähigkeitder Metalle. Annalen d. Physik (5) 13, 564-598. 1932

Atom und Welle. Schriften Königsberg 6, 216-231. 1929

Eine Bemerkung zu Herrn A. Sommerfelds Arbeit: ``Zur Elektronentheorie derMetalle auf Grund der Fermischen Statistik". Z. f. Physik 48, 739-744.(1928)

Die Supraleitfähigkeit nach Schrödingers Wellengleichung und FermisStatistik. Annalen d. Physik (4) 86, 914-928.(1928)

Theorie der Dauerströme in Supraleitern. Annalen d. Physik (4) 80, 109-136. Berichtigung. Annalen d. Physik (4) 80,532. (1926)

Über die Ableitung der Helmholtzschen Wirbelsätze in der Lorentz-Einsteinschen Relativitätstheorie. Schriften Königsberg 1, 179-191.(1925)

Zur Theorie der Supraleitfähigkeit und der gewöhnlichen elektrischenLeitfähigkeit der Metalle. Schriften Königsberg 1, 193-204. (1925)

Das Maxwell-Boltzmannsche Geschwindigkeits- und Energieverteilungsgesetz inder Relativitätstheorie. Phys. Zs. 25, 162-165. 192

Das statische Einkörperproblem in der Einstein'schen Theorie. Antwort anHrn. A. Gullstrand. Ark. för Mat., Astron, och Fys. 17, Nr. 25, 4 S. 1923

Eine Bemerkung zu Hrn. A. Gullstrands Abhandlung: ``Allgemeine Lösung desstatischen Einkörperproblems in der Einsteinschen Gravitationstheorie".Ark. för Mat., Astron. och Fys. 17, Nr. 2, 4 S. (1922)

Der Liouvillesche Satz und die Relativitätstheorie. Physik. Zs. 21, 484-487.192

Eine Theorie der Schwerkraft im Rahmen der ursprünglichen {itEinstein}schen Relativitätstheorie. Berlin, 113 1914