Erich Kretschmann (1887-1973) was a German mathematician and Gymnasium (school) teacher. 1887 (MDCCCLXXXVII) is a common year starting on Saturday (click on link for calendar) of the Gregorian calendar or a common year starting on Monday of the Julian calendar. ... 1973 (MCMLXXIII) was a common year starting on Monday. ... Leonhard Euler is considered by many people to be one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is mathematics. ... A gymnasium (pronounced /gim-/ as opposed to /jim-/) is a type of school of secondary education in parts of Europe. ... A teachers room in a Japanese middle school, 2005. ...

He obtained his Dr. 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. Alternative meaning: Humboldt State University, located in Arcata, California German Humboldt-Universität zu Berlin) is the successor to Berlins oldest university, the Friedrich Wilhelm University (Friedrich-Wilhelms-Universität), founded in 1810 by the liberal Prussian educational reformer and linguist Wilhelm von Humboldt whose university model has strongly... 1914 (MCMXIV) was a common year starting on Thursday. ... Max Planck Max Karl Ernst Ludwig Planck (April 23, 1858 – October 4, 1947) was one of the most important German physicists of the late 19th and early 20th century; he is considered to be the founder of quantum theory. ...

In his 1915 papers, he introduced the Kretschmann scalar. 1915 (MCMXV) was a common year starting on Friday (see link for calendar). ... In the theory of Lorentzian manifolds, particularly in the context of applications to general relativity, the Kretschmann scalar is a quadratic scalar invariant. ...

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. He 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.

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)

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.

Kretschmann also 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.

External links

• Kretschmann in A. Sommerfeld's correspondence
• E.K.'s thesis cited at Mathematics Genealogy Project
• "Einstein’s First Systematic Exposition of General Relativity", by M. Janssen, on philsci-archive.pitt.edu

Selected 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 Annalen der Physik is one of the best-known and oldest (it was founded in 1799) physics journals worldwide. ... Annalen der Physik is one of the best-known and oldest (it was founded in 1799) physics journals worldwide. ...

Einstein, Albert, 1918 "Principielles zure allgemainen Relativitaetstheorie," Annalen der Physik, vol. 55.