PeterDonis said:
Do you have a reference for any actual theories along these lines?
Logunov, A.A. (1990). The relativistic theory of gravitation. Theor Math Phys 85(1)
Logunov, A.A. (2002). The Theory of Gravity. arxiv:gr-qc/0210005
Schmelzer, I. (2012). A Generalization of the Lorentz Ether to Gravity with General-Relativistic Limit. Advances in Applied Clifford Algebras 22(1), 203-242, resp. arxiv:gr-qc/0205035.
Schmelzer has considered your problem with superpositions of different spacetimes to, in (unpublished, but may be interesting in this context)
Schmelzer, I. (2009). The background as a quantum observable: Einstein's hole argument in a quasiclassical context, arXiv:0909.1408.
PeterDonis said:
This is not giving up the spacetime interpretation; it's just saying spacetime geometry is not a quantum degree of freedom and can't participate in quantum dynamics.
It gives up the spacetime interpretation of the gravitational field. This allows the gravitational field to be handled like other matter fields and to become a quantum degree of freedom. Then, indeed, space and time can't participate in quantum dynamics, but classical space and time don't participate in dynamics anyway.
PeterDonis said:
This is an additional, separate restriction on the spacetime geometry: basically in such a model the spacetime geometry would be flat Minkowski spacetime, but this geometry would be unobservable because gravitational fields would distort the measurements so it looked like the spacetime geometry was curved. This is, of course, just the "spin-2 field on flat spacetime" interpretation of GR, and it has been known for decades that it is mathematically equivalent to the usual curved spacetime interpretation (except possibly for issues of global topology, which I don't think we need to go into for this discussion).
Correct. I don't like to refer to the field-theoretic interpretation of GR because I have no good reference which clarifies the conceptual questions (like what destroys covariance, the status of the gauge condition). Whatever, it can be quantized (as an effective theory) without problems, see
Donoghue, J.F. (1994). General relativity as an effective field theory: The leading quantum corrections. Phys Rev D 50(6), 3874-3888
Instead, to quantize GR in the spacetime interpretation leads to topological foam and similar ...
PeterDonis said:
The issue I see for using a model like this with the Transactional Interpretation would be that, as it currently stands, the TI expects to use the actual, physical light cones--the ones that we actually measure--but in the kind of model you're describing, it wouldn't, it would have to use the unobservable light cones of the background Minkowski spacetime. For example, in an experiment with entangled photons, where we have a superposition of different gravitational fields due to, say, a quantum event making a heavy ball go left or right, the actual events where the photons are emitted and detected would be the ones determined by the actual, observable light cones of whichever curved spacetime (aka flat spacetime with gravitational field) corresponded to the measured outcome of where the ball went, whereas the TI would be using different events for the "transaction", the ones corresponding to the background (unobservable) flat spacetime. But that contradicts the whole reason for using the TI in the first place, that the "transaction" occurs between the actual emission and detection events.
Both theories allow to solve this problem, because they both have also some causality condition which requires that the actual light cones are inside the background Minkowski light cone (RTG) resp. inside absolute future (Schmelzer). So, once the Bell violation experiment requires, in TI, some "transaction" inside the observable lightcone, the corresponding "transaction" would be possible in the background structure too.