Geometry and Motion in General Relativity

TL;DR

This paper discusses a new approach called 'tracking' in general relativity that aims to derive the geodesic principle without relying on problematic point particles, offering a fresh perspective on motion in space-time.

Contribution

The paper introduces 'tracking' as a novel method to derive the geodesic principle, potentially eliminating the need for point particles in general relativity.

Findings

'Tracking' provides a new framework for understanding geodesic motion.

It helps eliminate the concept of point particles from the theory.

The approach offers interpretational insights into space-time motion.

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.