Geometry and Motion in General Relativity

Abstract

A classic problem in general relativity, long studied by both physicists and philosophers of physics, concerns whether the geodesic principle may be derived from other principles of the theory, or must be posited independently. In a recent paper [Geroch & Weatherall, "The Motion of Small Bodies in Space-Time", Comm. Math. Phys. (forthcoming)], Bob Geroch and I have introduced a new approach to this problem, based on a notion we call "tracking". In the present paper, I situate the main results of that paper with respect to two other, related approaches, and then make some preliminary remarks on the interpretational significance of the new approach. My main suggestion is that "tracking" provides the resources for eliminating "point particles"-a problematic notion in general relativity-from the geodesic principle altogether. This link is sometimes called the geodesic principle; it is analogous to Newton's first law of motion. Because of its centrality to the interpretation of spacetime geometry in

The general-relativistic case for super-substantivalism

“…the derivation of matter dynamics from GR's constraints on spacetime (see e.g. Weatherall, 2017Weatherall, , 2019, explanations involving symmetries (for instance, in the context of conservation laws, see Lange, 2007Lange, , 2009, gravitational waves, gravitational collapse, energy extraction processes of black holes, etc. On the geometric interpretation of GR, spacetime structure genuinely and ultimately explains (some) aspects of the behaviour of matter.…”