On the status of the geodesic principle in Newtonian and relativistic physics

A theorem due to Bob Geroch and Pong Soo Jang ["Motion of a Body in General Relativity." Journal of Mathematical Physics 16, ] provides a sense in which the geodesic principle has the status of a theorem in General Relativity. I have recently shown that a similar theorem holds in the context of geometrized Newtonian gravitation [Weatherall, J. O. "The Motion of a Body in Newtonian Theories." Journal of Mathematical Physics 52, ]. 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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DOI 10.1016/j.shpsb.2011.09.004
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Dennis Lehmkuhl (2014). Why Einstein Did Not Believe That General Relativity Geometrizes Gravity. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 46 (2):316-326.
Adán Sus (2014). On the Explanation of Inertia. Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 45 (2):293-315.

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