On the Status of the "Geodesic Law" in General Relativity

Harvey Brown believes it is crucially important that the "geodesic principle" in general relativity is an immediate consequence of Einstein's equation and, for this reason, has a different status within the theory than other basic principles regarding, for example, the behavior of light rays and clocks, and the speed with which energy can propagate. He takes the geodesic principle to be an essential element of general relativity itself, while the latter are better seen as contingent facts about the particular matter fields we happen to encounter. The situation seems much less clear and clean to me. There certainly is a sense in which the geodesic principle can be recovered as a theorem in general relativity. But one needs more than Einstein's equation to drive the theorems in question. Other assumptions are needed. One needs to put more in if one is to get the geodesic principle out. My goal in this note is to make this claim precise, i.e., that other assumptions are needed