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I agree with Mark that you have the right idea for a Block Universe, but Mark’s last paragraph doesn’t really address the key questions in that last paragraph of yours. (Mark: I would say that the whole point of the Block Universe is that everything ontological can be described “all-at-once”, so mentioning all of these different “processes” is obscuring the point, I would think.)
So to answer Bob’s final questions: a Block Universe could certainly be compatible with a stochastic theory. In that case “the Block” is a single world filled with what actually occurs. (An agent might not know which block is the real one, and might assign probabilities to various imagined blocks, but only one Block happens.) The big question is whether this “one 4D universe” is compatible with quantum theory, essentially the last questions that you lead up to.
Now, almost everyone will take a look at entangled states on one hand, and the Block Universe framework of SR/GR on the other, and decide that the “existence” of entangled states rules out any possibility of a Block Universe. But this section of this forum happens to be filled with the 20-odd people for whom retrocausality is a live option, which sheds some doubt on this usual conclusion. In principle, retrocausality provides a way to rescue the Block Universe (entangled states would have to be epistemic, not ontic, for starters, but this isn’t enough; retrocausality is needed to resolve the no-go theorems). Here’s a recent talk I gave about precisely this issue:
But… surprisingly to me, many of the people who are interested in quantum retrocausality do not like the idea of a Block Universe, and do *not* want to rescue this framework of SR/GR. Certainly Ruth Kastner would be in this camp, and perhaps also Eliahu Cohen and Avshalom Elitzur, based on their “meta-time” comments in this forum. I’m not sure about John Cramer (John, if you’re reading this, I’d like to hear where you stand on this…). I’m also not sure about Yakir Aharonov and other people involved with retrocausal interpretations of the two-state-vector formalism. The multi-particle states in that formalism continue to reside in configuration space, not spacetime, and I haven’t seen much discussion of whether they even want to resolve this issue.
Perhaps it would be good to hear from some retrocausal-minded people (Ruth?) who don’t particularly want to recover a Block Universe, and what they are hoping to recover instead.