That the gravitational field, alone among all fields, should be classical, while all others are quantum, sounds arbitrary. But it’s very hard to show experimentally that gravity is quantized (look for papers on detecting a graviton!). So one can get away with supposing that maybe the world works like this.
There are also logical/technical difficulties with the idea. Coupling classical gravity to quantum fields has been done by theorists for a long time—e.g. Hawking made use of this—but only as an approximation. If you have a superposition of field states that should imply different geometries, how can you not have a superposition of geometries? The stochastic dynamics are meant to deal with this—a definite geometry is always being selected, albeit randomly.
At the bottom of the first page, the author points out that a construction like this may even have value as an approximation to fully quantum gravity. I add that in terms of a multiverse framework like e.g. Jim Hartle’s, it may even describe the internal dynamics of an individual history, for some physical regimes. The apparent stochasticity would be the manifestation within an individual history, of the phase-space distancing among the many histories, required for mutual decoherence.
That the gravitational field, alone among all fields, should be classical, while all others are quantum, sounds arbitrary. But it’s very hard to show experimentally that gravity is quantized (look for papers on detecting a graviton!). So one can get away with supposing that maybe the world works like this.
There are also logical/technical difficulties with the idea. Coupling classical gravity to quantum fields has been done by theorists for a long time—e.g. Hawking made use of this—but only as an approximation. If you have a superposition of field states that should imply different geometries, how can you not have a superposition of geometries? The stochastic dynamics are meant to deal with this—a definite geometry is always being selected, albeit randomly.
At the bottom of the first page, the author points out that a construction like this may even have value as an approximation to fully quantum gravity. I add that in terms of a multiverse framework like e.g. Jim Hartle’s, it may even describe the internal dynamics of an individual history, for some physical regimes. The apparent stochasticity would be the manifestation within an individual history, of the phase-space distancing among the many histories, required for mutual decoherence.