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thank you very much for your comments. It’s nice to get feedback from someone who is so skilled in this area.
Let me try to briefly respond to your points:
1) You are right, the model – as it stands with the 1st order dynamics – is actually not time-symmetric! That’s why I also had to change the title btw. 😉
I don’t think the (appearent) asymmetry in the measurement process is the problem, though, since I believe that, when properly analyzed, (quantum-)measurements turn out to be irreversible in a thermodynamic sense.
Concerning the dynamics, the “solution” that I have in mind – rather than going 2nd order – is that, in the end, you will still need something like a wave-function or quantum state to manifest the structure of entanglement. And this object, whatever it is, may itself have a nontrivial transformation under time-reversal. E.g. in Bohmian mechanics, the guiding equation is first order but the wave-function get’s complex conjugated under time-reversal, compensating for the sign.
Anyway, in order to make the points I was trying to make, it was more convenient to work with a toy model that involves advanced and retarded actions in an asymmetric way. But of Course I believe that if one considers a more serious retrocausal theory, it should be motivated by time-symmetry.
2) You’re right, if you have free fields, the distinction between the advanced and retarded part is somewhat arbitrary. However, I don’t believe in free fields. 😉
3) Yes, absolutely! As I said, the toy-model doesn’t actually explain or account for “entanglement”, i.e. why a pair of particles should be able to interact over arbitrary distances without being disturbed by others. The problem is not the light-cone structure, though. The light-cone structure is a good thing, as it makes the interactions intrinsically relativistic. However, I believe that any more serious theory will need additional ingredients, to account for a structure of entanglement.
4) A colleague of mine is working on such “history space” measures in a somewhat different context. I agree that this is probably the way to go for a statistical analysis of time-symmetric theories, but it’s not that easy. If you have more references on that I’d be very interested.
5) I wasn’t familiar with Gerchberg-Saxton, I’ll look it up! References are very welcome.
6) I agree. The ontological level matters most when assessing whether a theory is “conspiratorial”. In my brief discussion, I was trying to make the connection between the ontological level and the formal “no conspiracy assumption” which enters the derivation of Bell’s inequality. I’m not sure how well I succeeded, though.
Thanks again for your comments!