Hi Peter,
I guess I mis-read what you were doing here… But given your clarification, I think you should be careful about simply assigning the outcome of the future measurement as a hidden variable. Huw has already talked about exactly this kind of minimal-ontology (see section 5.2 of 1002.0906 ), and the obvious downside is that such accounts are doomed to fail as a deeper explanation of the outcomes (the outcomes are not “explained” by the hidden variables if they are simply identical!)
With this in mind, you may want to consider my mis-interpretation of your ontology, after all… There’s at least hope for some deeper explanatory account if you associated the hidden variables with particular directions, rather than just the actual measurements.
And yes, there are always “problems lurking” when one is talking about measurements – although at least in retrocausal block-universe scenarios everything lives in spacetime. But, problems still lurk. In order to get retrocausality, measurements can’t just be *correlations* between the device the system, they actually have to be *constraints* (or else one can’t recover retrocausation, right?).
Travis Norsen was mentioning on one of these threads (as he has to me, personally) that even for retrocausal accounts, he doesn’t see how there can be a special role for measurement devices, if those devices are supposed to obey the same rules as the systems themselves. Why are some interactions treated as external constraints, and other interactions treated as mere correlations?
This is an excellent and still unresolved question, but I don’t think it’s unresolvable. Large conductors are treated as constraints in electrostatics, in a way that individual charges are not. So long as there’s some *ultimate* constraint (i.e. a cosmological boundary condition), I think there’s a path to making it all work.
The most detailed hand-waving explanation I’ve written was a FQXi essay from a while back: see pages 5 and 6. The question that standard QM has trouble with is basically whether a single atom interacting with a photon should be viewed as a “measurement/constraint” on the photon or not. The nice thing about retrocausal accounts is that the answer to this question can depend on the bigger-picture, and what happens later.
That said, I also think it’s fair to put these questions aside for now, and simply assume that macroscopic measurements work as boundary constraints on microscopic systems (as you’re basically doing!). So I think it’s fine to treat a non-invasive/intermediate Stern-Gerlach apparatus as an external boundary condition — just one that shouldn’t need to introduce any discontinuity at that point, at least in the models I most prefer.
Cheers! -Ken
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