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Wow! It’s very nice to hear we’re in agreement about both the framing of the problem and what the solution must look like. Apart from a single word, I’m also in agreement with:
“…it [had] better turn out that the boundary conditions on S’ *imply*, via the application of the basic dynamical postulates of the theory, the same sort of “internal facts” that were instead imposed by hand, as boundary conditions, when you analyzed S. That’s, I think, the “block universe consistency” that’s needed.”
My one-word-nitpick, unsurprisingly, is the word “dynamical”. The sort of account I’m discussing is only going to make sense when analyzed “all-at-once”, not where causation is “flowing in” via some differential equations. I know you’re skeptical that there’s an essential difference, but that means you don’t really have anything against “all-at-once” accounts, you just don’t see that they’re needed.
And the problem of achieving Block Universe consistency, in the way we both agree is necessary, is precisely where an all-at-once account *is* needed. If I could get you thinking along the lines of “history counting” as a way to determine effective dynamics, I think you’d be a lot more optimistic about a solution. In fact, given such a framework, solving your biggest concerns here would almost be trivial.
Take the best analog to my proposed 4D-history-counting: 3D-state-counting in stat. mech. Consider a sequence of systems, all touching, with each new system much smaller than the last. At each system interface, the smaller system would effectively be constrained by a boundary condition from the neighboring larger system, as if the larger system was effectively a thermal reservoir. Zooming into some small part of this story, one could find this result by simply state-counting. (The more ways something could happen, the more probable.) Zooming out, one gets the same answer, for the same reason. This sort of logic is consistent at all scales.
This works in 3D, and I see no reason why it won’t work in 4D as well, if one gives up law-like dynamics. In stat. mech. the likelihood of each macrostate is just given by counting microstates. Similarly, for my 4D Block Universe extension, if you get rid of law-like dynamics and just count microHistories, you automatically get exactly the consistent account that we both agree is needed.
A much harder task is to address the other point at which you’re skeptical: showing that one can use retrocausality to get all the beables back into spacetime, for any possible entangled state. (That’s getting all my attention at the moment, and I’m cautiously optimistic I’ll either have it solved soon, or show that it can’t be done.) This measurement-problem issue, in comparison, I think is going to be relatively straightforward.
One last comment: I guess I sort of understand your concerns with comparing my nice-sounding-prose to perhaps similar arguments people make about decoherence or other proposed measurement-problem-solutions in standard QM. But standard QM is *doomed* to fail to address the measurement problem, because of how systems get blurred together into configuration-space. For all your interest in spacetime-local-beables, I’m still not sure you see how many of the central problems of QM are solved, in one fell swoop, by separating out everything in spacetime and getting rid of action-at-a-distance. (Maybe that last part is the key, because in your approaches there’s still action-at-a-distance going on…)
Thanks for the great discussion!