Alright, time to discuss some physics again. A while back I outlined the basic dichotomy of quantum gravity. In brief: we have classical general relativity as an excellent description of all observed gravitational phenomena, but when we go to extremely short distances we need to have a good description of quantum gravity. There are two possibilities: either the description of gravitational phenomena by the machinery of general relativity (metric, the principle of equivalence, etc.) holds all the way down to those extremely short distances, or it doesn’t. If it doesn’t, which is my own prejudice, classical general relativity and its variables are never to be quantized, there is no range of energies (or distance scales) which is described by quantum metrics obeying a quantum version of Einstein’s equations.
This situation is similar to the hydrodynamical description of fluid motion: it is a classical effective field theory, which breaks down long before quantum mechanics is needed. We can observe granularity in the fluid on distance scales much larger than those relevant to quantum mechanics. From that perspective, quantizing Einstein’s equations makes as much sense as quantizing the Navier-Stokes equations, which is to say not too much sense.
