Comment by nathan_compton

Well, I'm have a little guilty bias towards spacetime non-substantivalism and I've always been interested in getting back to physics in this area. I've particularly found the Shape Dynamics program to be at least somewhat interesting and while I have a sort of ok grasp of the language and mathematics of GR translating that to the SD world has been a persistent challenge. If I had time I'd try to figure that out.

Briefly, one usually formulates the theory of gravity in terms of a a 4d spacetime with curvature but you can also formulate it as a theory of curved 3d shapes if you allow the lagrangian to carry more structure. This is often performed in GR, in fact, by decomposing the metric into a "spatial" and "temporal" part but shape dynamics kind of runs with this idea in an attempt to formulate a totally relational version of the theory of gravity.

Shape Dynamics apparently produces a reasonable theory of gravity which agrees with GR in many situations but forbids, I believe, closed timelike curves, and may be more amenable to quantization since it re-separates space and time.

Anyway, it all seems very beyond me, maybe even if I had the time, which I do not.