Deriving the Geodesic Principle

In the recent philosophy literature, there have been several attempts to use the seminal result by Geroch and Jang (1975) to precisify Harvey Brown’s claim that the geodesic principle can be recovered as a theorem in General Relativity, and then to critique it. We contend that the philosophical debate has unfolded in a curious way: even though Geroch and Jang’s paper contains two distinct approaches to the problem of geodesic motion, the philosophical literature has focused on only one of them. We then argue that the neglected approach offers an alternative—and more physical—set of resources to explain geodesic motion. Motivated by this approach, we prove a new “physical Geroch-Jang theorem”, which provides a scale-relative interpretation of the geodesic principle in General Relativity. We, thereby, make new resources available to re-evaluate Brown’s arguments as well as those of his critics.