On the Status of the Geodesic Principle in Newtonian and Relativistic Physics

Details On the Status of the Geodesic Principle in Newtonian and Relativistic Physics On the Status of the Geodesic Principle in Newtonian and Relativistic Physics

2011-06-12

arxiv.org/abs/1106.2332v1

Physics

History and Philosophy of Physics

16 pages

Scientific paper

A theorem due to Bob Geroch and Pong Soo Jang ["Motion of a Body in General Relativity." Journal of Mathematical Physics 16(1), (1975)] provides a sense in which the geodesic principle has the status of a theorem in General Relativity (GR). I have recently shown that a similar theorem holds in the context of geometrized Newtonian gravitation (Newton-Cartan theory) [Weatherall, J. O. "The Motion of a Body in Newtonian Theories." Journal of Mathematical Physics 52(3), (2011)]. Here I compare the interpretations of these two theorems. I argue that despite some apparent differences between the theorems, the status of the geodesic principle in geometrized Newtonian gravitation is, mutatis mutandis, strikingly similar to the relativistic case.

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