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

A theorem due to Geroch and Jang (1975) 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 (Newton–Cartan theory) (Weatherall, J.O., 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.

► Explores the status of inertial motion in geometrized Newtonian gravitation and GR.
► Argues that in both theories, the geodesic principle has the status of a theorem.
► Concludes that if GR explains inertial motion, so does Newtonian gravitation.