If you look at Schroedinger’s equation for one particle, it’s easy to generalize it so that the particle is in curved spacetime. The problem is when you get entanglement involved. Normally, for n particles, you do Schroedinger’s equation in R^3n, and each triplet corresponds to the coordinates of one particle. You could generalize that to M^n where M is an arbitrary manifold, but that means you’d have to use that manifold for every universe.
You could try running Einstein’s field equations on the 3n+1-dimensional configuration space (+1 being time, not an extra space dimension) and running Schroedinger’s equation on that. I don’t know if that would work. If it does, you didn’t get MWI without quantum gravity. You discovered quantum gravity.
If you look at Schroedinger’s equation for one particle, it’s easy to generalize it so that the particle is in curved spacetime. The problem is when you get entanglement involved. Normally, for n particles, you do Schroedinger’s equation in R^3n, and each triplet corresponds to the coordinates of one particle. You could generalize that to M^n where M is an arbitrary manifold, but that means you’d have to use that manifold for every universe.
You could try running Einstein’s field equations on the 3n+1-dimensional configuration space (+1 being time, not an extra space dimension) and running Schroedinger’s equation on that. I don’t know if that would work. If it does, you didn’t get MWI without quantum gravity. You discovered quantum gravity.