Testing the quantum nature of spacetime via the decoherence-diffusion trade-off

If one takes the geometric nature of gravity seriously, then it's reasonable to consider the proposition that the spacetime metric should have a classical description.

A classical system can interact with a quantum system in a consistent manner, and recently the most general form of such dynamics was derived. The resulting master equation can then be applied to general relativity interacting with quantum fields. Unlike perturbative quantum gravity, the theory is formally renormalisable, thus gravity retains its geometric description to the shortest distances. The measurement postulate of quantum theory is not needed. I will introduce the formalism with a simple example and discuss what happens at short distances. The requirement that the dynamics be completely positive implies the "decoherence-vs-diffusion trade-off" which can be used to test the nature of spacetime experimentally.