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Very interesting paper! It was very useful to read for a fuller account of your views, after only seeing your presentation in Cambridge last summer.
Some thoughts that occurred to me as I read through the paper:
– After using time-symmetry as a motivation for this general style of approach, I was surprised to see (3) in your model which looked quite time-asymmetric, essentially distinguishing past and future. Can you comment on whether you see any tension here?
– Model step #5 also seemed strangely time-asymmetric. “Towards the orientation antipodal to its own” seems to require a preferred direction of time to parse properly. (When time-reversed, this is a rotation *away* from the antipodal orientation.) This leads to the problem you explicitly note at the beginning of section 2.1, and even though I strongly agree that going to second order equations is the way to go, the other option is just to flip one of the signs in Equation (5). Have you tried this? Does this not work properly?
– Typically the concepts “retarded” and “advanced” have some subjectivity to them, at least when you’re talking about the fields. In E+M, it’s always possible to reframe any retarded field as free+advanced fields, and possible to reframe any advanced field as free+retarded fields. And yet you’re using these terms as if they have a clear objective meaning. Actually, since you’re just using retarded and advanced *times* in this work, I think you’re generally okay on this front, but something to be careful about.
– Putting the interaction between the two particles on light-like lines is nice, but raises the possibility that such interactions can be *shielded*, destroying the entanglement via some intermediate blockage. Are you worried about this, or do you see this as such a general toy model that this isn’t a big concern?
– In 4.1, you are (rightly!) worried about the state space measure… Have you considered looking the whole history for a natural “history space” measure, rather than at instantaneous slices?
– If you’d like to start actually *solving* such two-time-boundary problems, the best framework I’ve found is something called the Gerchberg-Saxton algorithm in E+M. Let me know if you want more details on how it might apply to such cases as these.
– I’ve found it useful, in separating retrocausal accounts from conspiracy/superdeterministic accounts, to outline the superdeterministic story on the ontological level, not just at the level of correlations. Sure, at the level of observable correlations, these two accounts look quite similar, but “under the hood” they are wildly and essentially different.
Thanks again for a useful and well-argued paper!