I Confused by nonlocal models and relativity

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There's no wave function for photons!
Ok, then substitute "quantum state", which is more general and allows for the somewhat different mathematical objects that model photons in QFT.

If your criticism is that, strictly speaking, QFT has no invariant concept of "the quantum state of an extended system at an instant of time", that is true, but you can still pick a particular frame, such as the overall rest frame of the system + measurement apparatus in the experiment under discussion, and construct the quantum state of an extended system such as the multi-photon system in the experiment at an instant of time in that frame. That is implicitly what is being done when we talk about the "wave function" of the multi-photon system.

Also, as has been pointed out, you could do a similar experiment with electrons moving at non-relativistic speeds. Such an experiment could be modeled using only non-relativistic QM, in which the description in terms of wave functions is unproblematic and the issues you appear to be raising with photons not having wave functions do not arise.
 

vanhees71

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The point is that photons have no position observable to begin with. All you can measure are probabilities to register a photon (with given properties depending on the measurement you do).

Surely you can do such experiments in principle also with electrons though I guess for technical reasons neutrons are better candidates. The formalism is nearly the same (up to electrons/neutrons being fermions rather than bosons).
 
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There was a recent experiment where superposition of photons were photographed just ran across it last night. Thought it interesting and applicable in this thread

 
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The point is that photons have no position observable to begin with.
Nor is one needed for the experiments under discussion. The states you wrote down earlier, where photons are distinguished by having momentum in different directions, with no position observable anywhere in sight, are quite sufficient to analyze the experiments.
 

vanhees71

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Sure, that's what I'm saying!
 

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