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Since the issue of a retro-causal qtwo came up, I thought this might be a good place to mention Rod Sutherland’s model. I’m not at all convinced by a number of the claims that he’s made with that, but I still find his model interesting, in the sense that it provides a simple example of a retrocausal qtwo. Just have two universal wave functions, the usual one evolving forwarad in time from some big-bang-ish initial condition, and then the second one, evolving backwards in time from some ???- (maybe heat-death-) -ish final condition. And then I think the dynamics of the particle configuration can be defined to depend in a kind of symmetrical way on the two wave functions.
(Note that, as I finally learned after lots of discussion and confusion, this is not actually how his model works. But I think you can generalize his one-particle toy model into a qtwo in this way.)
Two quick points about this idea:
1. I’m pretty sure that the picture will give nonsense for all but the earliest and latest times. The particle configuration in the middle will be a big mess. Nothing like the macro-world we actually observe. So I think that, while interesting in so far as it’s maybe an example of a true retrocausal qtwo (but see 2.), it’s not an empirically viable theory.
2. I’m not sure it’s even retro-causal. This is really the main point I wanted to get at. Despite how I described it above, I don’t see why one should think of this theory as any more retro-causal than ordinary BM. It’s just that there are two wave functions, which jointly influence the particle velocities, instead of one. But so what? Whatever differential equation the new, supposedly backwards-evolving wave function obeys could just as easily be read as normal, forward-in-time evolution. Just because you solve some problem by specifying a boundary condition at t_final, doesn’t make it retro-causal. You’d have, I think, exactly the same theory if you instead had two wave functions that jointly influence the particles, one evolving forward in time from some kind of thermodynamically low entropy initial condition, and the other evolving forward in time from some high entropy initial condition. So my point here is: I literally lose sight of what it’s even supposed to mean to call a theory like this retro-causal. And so part of the big worries that I meant to be expressing before, is the worry that, at the end of the day, and in the context of something like a qtwo where you don’t sneak things in by treating observation/measurement in a special way, I’m really not even sure what retro-causality means. At some very abstract level, the theory just says what happens “in the block” (or maybe gives some kind of probability distribution over possible histories of what happens “in the block”). It makes me a little uncomfortable that not only the idea of retro-causation, but also the idea of forward-causation, kind of crumbles to dust from this point of view. But it seems to me that it does. Or might. So that’s the other thing I’m worried about. Is there anything left for retro-causality to even mean, if we zoom out from the toy models to something like a qtwo, where there are no longer any “external interventions”??