Munich Center for Mathematical Philosophy (MCMP)

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Talk: Dennis Lehmkuhl (Bonn)

Location: Ludwigstr. 31, ground floor, Room 021.

29.01.2020 16:00  – 18:00 


The Einstein-Weyl correspondence and a generalisation of the Geroch-Jang Theorem to Weylian spacetimes


Abstract: In 1918, Hermann Weyl and Albert Einstein exchanged almost two dozen letters. In the majority of them, they focus on comparing general relativity (GR) with Weyl's unified field theory. The latter is based on a generalisation of pseudo-Riemannian geometry that we now call Weyl geometry. One of the most interesting aspects of this correspondence is the discussion of the motion of test particles in GR as compared to their motion in Weyl's theory. Einstein argued that uncharged test particles must move on the geodesics of Weyl geometry, whereas Weyl argued that the way test particles move in a field theory ought to be derived rather than assumed. Indeed, Weyl gave such a derivation during the course of the correspondence, a version of which he later repurposed as one of the first 'geodesic theorems' for GR. In 1975, Geroch and Jang provided a new type of proof for such a geodesic theorem. I will argue that the Geroch-Jang theorem can be generalised to at least integrable Weyl geometry if the latter is decoupled from the project of a unified field theory, thus providing a geodesic theorem for a much larger class of spacetime theories. I shall conclude by discussing the extent to which the new theorem sheds light on the positions advocated by Einstein and Weyl in their correspondence of 1918.