I've heard my entire life that QM and GR are incompatible, but I don't exactly understand how. There are other questions about that general question, e.g. A list of inconveniences between quantum mechanics and (general) relativity?
But just to ask a more specific question: Is it possible to define spacetime according to einstein's field equations, and then just define a wave function for a set of particles on that curved spacetime, as you would in relativistic QM? I.e. don't try to "quantize gravity" or anything. Just define QM on a curved spacetime background.
Does this work? If not, where does it fail? If it doesn't work for quantum fields, does it at least work for a fixed set of quantum particles?
Is the issue that the curvature has to evolve over time, which makes it hard to solve?
If it's hard to solve, can we at least run numerical simulations (in principle, ignore computational intractability).
Or is it even fundamentally unclear how to mathematize this?
