I consider the contrast between Leibniz's relational concept of spacetime and Einstein's special and general theories of relativity. I suggest that there are two interpretations of Leibniz's view, which I call L1 and L2. L1 amounts to saying that there is no real inertial structure to spacetime, whereas in general relativity the inertial structure is dynamical or real in Lande's sense ; i.e., it can be ‘kicked’ and ‘kicks back,’ causing gravitational effects. If there is no real inertial structure to (...) space-time then, as Weyl points out, the concept of the relative motive of several bodies has no more foundation than the concept of absolute motion for a single body. Thus, L1 seems to be untenable. L2 is a more sophisticated view which rejects the geometrical aspect of Newtonian space-time as a container for events, but accepts the existence of a real structure which determines the inertial properties of matter. (shrink)

Spacetime substantivalism leads to a radical form of indeterminism within a very broad class of spacetime theories which include our best spacetime theory, general relativity. Extending an argument from Einstein, we show that spacetime substantivalists are committed to very many more distinct physical states than these theories' equations can determine, even with the most extensive boundary conditions.