It is unclear to me (1) what precisely diffeomorphism means and (2) what happens when all matter is removed from the spacetime. Sean Carrol says that: "the theory is free of "prior geometry" and there is no prefered coordinate system for spacetime." http://arxiv.org/pdf/gr-qc/9712019v1.pdf page 138 Including this I imagine that removal of all matter means, that even space-time does not remain if all matter is removed. I also understood isham similarly “However, the use of a fixed causal structure is an anathema to most general relativists and therefore, even if this approach to quantum gravity had worked (which it did not), there would still have been a strong compunction to reconstruct the theory in a way that does not employ any such background.” http://arxiv.org/pdf/gr-qc/9310031v1.pdf But, some physicists claim that spacetime of Minkowski remains after all matter is removed. Besides, Carroll says also that "In SR or Newtonian physics, meanwhile, the existence of a preffered set of coordinates saves us from such ambiguities." How it is with this?