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Thanks for your detailed response… I do think we almost have exactly the same perspective about how to make sense of these very experiments. So it’s interesting that I see this perspective as retrocausal, while you merely see it as retrodictive. Let me try once more to see if I can figure out exactly where this divergence comes from.
First of all, however the term “hidden variable” is typically used, and whatever negative connotations you think it may have, I hope we can agree to use it whenever there is *something* to be retrodicted, something that is hidden/unknown, whatever that something might be.
In this case, QM’s maximally-informative preparation of an entangled state (we know it is in a singlet state) does not tell us *everything* there is to know when it comes to the consistent histories viewpoint. I think we agree on that; otherwise you couldn’t even be invoking retrodiction. There is some hidden variable in play, by my above definition.
The hidden variable you’re using seems to have two aspects: (1) which Hilbert-space subspace should be considered (which sample space, which relevant set of consistent histories), and (2) which possibility in this subspace actually occured. We can leave (2) aside, I think, based on your latest response: this part really is retrodiction, at least for this singlet case. The retrocausality is happening for (1).
The evidence for this claim follows from: A) There’s no way to know the right sample space based on the complete QM preparation alone (it’s a hidden variable), B) the right sample space is correlated with the choice of future measurements, and C) this correlation violates the statistical independence condition on this sample space.
Given this (and the arguments I made in the previous post), the only reasonable way to wriggle out of the retrocausality is to claim that the sample space is not properly ontological, that it’s not a real thing which can be associated with causation. But you apparently think that was *does* exist lies within this sample space, and you also clearly stated just now that structures *outside* this sample space do not “exist”. (Even though they *would* exist under a counterfactual future measurement with a different future setting.) This seems to be all that’s needed, then, to deduce that the actual history has been retrocausally influenced by the future decision choice.
Again, this is all precisely compatible with the general approach and specific toy models that I lay out in http://www.mdpi.com/2078-2489/5/1/190 : the future measurement settings/geometry allow one to reduce these huge configuration spaces associated with multiple particles to a reasonable subspace in which one can assign ordinary probabilities. As I see it, this is exactly what you’re doing, just without noting the retrocausal aspect. Do you see any other differences that might explain our divergent interpretations?