Bell’s theorem tells us that there is no local hidden variable theory which reproduces the statistics of quantum theory. Fine. One way to think about moving onward given Bell’s theorem is to given to look for nonlocal hidden variable theories which reproduce quantum theory. But now there is something strange that happens. If you have nonlocal hidden variables, i.e. quantities describing the state of the universe but which are jointly accessible by two spacelike seperated observers, what is the difference between this and assuming that your notion of spacelike separation is not correct. Suppose you come up with a nonlocal theory. What prevents anyone from reinterpreting your nonlocal theory as a totally local theory in which spacelike separation is defined different? Well there is, as far as I can tell, exactly one difference: in quantum theory we cannot use entangled particles to communicate between spacelike separated observors. But this difference doesn’t disallow interpretting a nonlocal hidden variable theory as simply spacelike separation being defined differently, it just tells us the spacelike sepearation of entangled particles must force a nonsignaling constraint (and reproduce quantum theory!) So why don’t we spend more time thinking about where the structure of our spacetime manifold comes from?
O brave new quantum world!