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

TL;DR

This paper compares the status of the geodesic principle in Newtonian and relativistic physics, showing that similar theorems establish it as a fundamental result in both frameworks.

Contribution

It demonstrates that the geodesic principle holds as a theorem in both geometrized Newtonian gravitation and General Relativity, highlighting their conceptual similarities.

Findings

The geodesic principle is a theorem in both theories.

Similar interpretations of the theorems in Newtonian and relativistic contexts.

The status of the geodesic principle is comparable in both frameworks.

Abstract

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.