It is not my favorite, but an approach which should at least be easy to understand is the “zigzag in time” interpretation, which says that spacelike correlations are due to microscopic time loops. Physics is local, but there are inflection points where forward-in-time causality turns into backwards-in-time causality, and the actual causal web of the universe therefore involves nonlocal-looking regularities. On this view, quantum mechanics is the statistical mechanics of a physics with causal chains running forward and backward in time, and such a physics becomes possible with general relativity.
The first part of this idea—causes operating in both directions of time—is almost as old as quantum mechanics. It’s in the Wheeler-Feynman absorber theory, the transactional interpretation of John Cramer, Yakir Aharonov’s time-symmetric quantum mechanics, and the work of Huw Price, among others; but I prefer the relatively obscure work of Mark Hadley, because he gives it the clearest foundation: the “inflection” in which the time direction of a causal chain reverses, as arising from a non-time-orientable patch in the space-time 4-manifold.
If the microscopic topology of space-time admits such regions, then not only is its evolution in time non-deterministic, but it will be non-deterministic in a complexly correlated way: causal loops in the far future topology constrain what happens on a spacelike hypersurface in the present, in a way that looks highly nonlocal. One manifestation of this would be nonlocally correlated perturbations to the passage of a particle or a wave through space, perturbations correlated not just with each other but also with distant distributions of matter; thus, the effects seen in the double-slit experiment, and all the other standard quantum phenomena.
If this approach worked, it would be very elegant, because it would turn out that quantum mechanics is a microscopic side effect of general relativity. It would require the matter fields to exhibit microscopic violations of the energy conditions which normally prevent wormholes and time machines, but this is not impossible, there are many simple models in which the energy conditions are violated. The challenge would be to show (1) a combination of fields which exhibits those violations and reduces to the standard model (2) that the rules of quantum probability actually do follow from the existence of microscopic time loops. Hadley has an argument that the nondistributive logic of quantum propositions also characterizes the nonlocal constraints arising from time loops, and that this in turn implies the rest of the quantum formalism (e.g. the use of Hilbert space and noncommutative operators for observables); but I believe he needs to actually exhibit some simple solutions to general relativity containing time loops, and show how to obtain the Schrodinger equation from the application of probability theory to such a class of simple solutions, before his argument can be taken seriously.
If this approach worked, it would be very elegant, because it would turn out that quantum mechanics is a microscopic side effect of general relativity. It would require the matter fields to exhibit microscopic violations of the energy conditions which normally prevent wormholes and time machines, but this is not impossible, there are many simple models in which the energy conditions are violated.
Energy conditions (well, the topological censorship, really) in classical GR prevent only traversable wormholes, and only in 3+1 dimensions. Non-simply connected spacetimes are otherwise allowed in a covariant formulation of GR, though they do not arise in an initial value problem with a simply connected spacelike initial surface.
Additionally, changing one’s past is absolutely incompatible with GR, as there is a unique metric tensor associated with each spacetime point, not two or more different ones, one for each go through a closed timelike curve. The only way time travel can happen in GR is by unwrapping these time loops into some universal cover. And there is a heavy price to pay for that, but that discussion is straying too far afield, so feel free to PM me if you want to talk further.
Okay. So how would your favored interpretation handle that sort of subjectivity?
It is not my favorite, but an approach which should at least be easy to understand is the “zigzag in time” interpretation, which says that spacelike correlations are due to microscopic time loops. Physics is local, but there are inflection points where forward-in-time causality turns into backwards-in-time causality, and the actual causal web of the universe therefore involves nonlocal-looking regularities. On this view, quantum mechanics is the statistical mechanics of a physics with causal chains running forward and backward in time, and such a physics becomes possible with general relativity.
The first part of this idea—causes operating in both directions of time—is almost as old as quantum mechanics. It’s in the Wheeler-Feynman absorber theory, the transactional interpretation of John Cramer, Yakir Aharonov’s time-symmetric quantum mechanics, and the work of Huw Price, among others; but I prefer the relatively obscure work of Mark Hadley, because he gives it the clearest foundation: the “inflection” in which the time direction of a causal chain reverses, as arising from a non-time-orientable patch in the space-time 4-manifold.
If the microscopic topology of space-time admits such regions, then not only is its evolution in time non-deterministic, but it will be non-deterministic in a complexly correlated way: causal loops in the far future topology constrain what happens on a spacelike hypersurface in the present, in a way that looks highly nonlocal. One manifestation of this would be nonlocally correlated perturbations to the passage of a particle or a wave through space, perturbations correlated not just with each other but also with distant distributions of matter; thus, the effects seen in the double-slit experiment, and all the other standard quantum phenomena.
If this approach worked, it would be very elegant, because it would turn out that quantum mechanics is a microscopic side effect of general relativity. It would require the matter fields to exhibit microscopic violations of the energy conditions which normally prevent wormholes and time machines, but this is not impossible, there are many simple models in which the energy conditions are violated. The challenge would be to show (1) a combination of fields which exhibits those violations and reduces to the standard model (2) that the rules of quantum probability actually do follow from the existence of microscopic time loops. Hadley has an argument that the nondistributive logic of quantum propositions also characterizes the nonlocal constraints arising from time loops, and that this in turn implies the rest of the quantum formalism (e.g. the use of Hilbert space and noncommutative operators for observables); but I believe he needs to actually exhibit some simple solutions to general relativity containing time loops, and show how to obtain the Schrodinger equation from the application of probability theory to such a class of simple solutions, before his argument can be taken seriously.
Energy conditions (well, the topological censorship, really) in classical GR prevent only traversable wormholes, and only in 3+1 dimensions. Non-simply connected spacetimes are otherwise allowed in a covariant formulation of GR, though they do not arise in an initial value problem with a simply connected spacelike initial surface.
Additionally, changing one’s past is absolutely incompatible with GR, as there is a unique metric tensor associated with each spacetime point, not two or more different ones, one for each go through a closed timelike curve. The only way time travel can happen in GR is by unwrapping these time loops into some universal cover. And there is a heavy price to pay for that, but that discussion is straying too far afield, so feel free to PM me if you want to talk further.