Uniform motion and relationalism

An old objection to relationalism about space--an objection going back to the Leibniz-Clarke correspondence--is that it seems possible for all things to move together at the same speed in the same direction. But since the relations between things don't change when they all move together, on a relationalist view of space it seems impossible to make sense of global uniform motion.

Here's a solution to the objection: The motion of an object x can be characterized by saying that x at t₂ is at a non-zero spatial distance from x at t₁. This allows one to characterize absolute motion in a relationalist account of space, which has typically been held impossible.

The above story works most neatly if we have eternalism and temporal parts: then x moves provided that it has temporal parts at a spatial distance from each other. But we can also do this with eternalism without temporal parts, provided that we index distance relations to two times. Whether a presentist who is a relationalist about space can make use of the solution depends on how well the presentist can solve the problem of cross-time relations.

I don't personally like this story, because I would prefer a relationalism based on spacetime relations rather than spatial ones.