One need to address the conceptual problems related to combining quantum mechanics and general relativity. They are as follows:
- The Problem of time: Physics is used to make predictions. Knowing the past, physics helps predict the future. Without time the subject of physics is thoroughly weakened. In classical gravity time-evolution is clearly present. The Wheeler-Dewitt equation, which is the fundamental equation for quantum gravity, appears to contain time evolution internally, and we need a way to extract time evolution from it in a quantum general relativistic context.
- Since general relativity is a description of the macroscopic universe, quantum general relativity requires addressing the quantum reduction problem. So developing a theory of quantum gravity requires including quantum reduction theory. Usually the difficulty maintaining superposition closely relates to the mass of the quantum system. Higher the mass of the object, more difficult it is to maintain superposition of macroscopic states. More the mass of the object, stronger the gravitational field. And so the gravitational field associated may need to be linked to appearance of decoherence. For example, Roger Penrose has already promoting an idea of gravitational quantum reduction. A systematic theory for quantum reduction using gravity is not yet available and it needs to be developed.
- Quantum States are not covariant objects, and they depend on the space-time foliation. Quantum reduction depends on foliation. We need a way to objectively describe the quantum reductive evolution and the issue of foliation on the manifold on which the process depends, locally or globally.
- Because of non-perturbative nature of quantum gravity one may need to approach it like lattice gauge theory. This leads to discretizing space-time and fields. Also quantum reduction leads to randomness. These leads to problems in recovering back the continuum physics. So we need way to recover back continuum classical physics addressing the issues of smoothness and determinism.
Let us look at some of the proposals to tackle this problem by clicking here: Proposals.