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I have a problem. I'm giving a lecture tomorrow on the EPR experiment and Bell's theorem and so on.

I had the feeling I really understand the essence of the EPR thought experiment.

However, a few hours ago I just had a disturbing thought (while practicing the lecture in front of a wall!) that made me stutter. I'll try to shortly explain my problem:

The formulation I'll have in my lecture consist of correlated photons and aligned polarization filters. I hope it's familiar to you / obvious why it's analog to the famous spin one.

The idea, as I understand it, is that by measuring the first photon's polarization we immediately know precisely what the polarization of the other photon is, although it might be light years away. Assuming locality is held, we conclude that the faraway photon always had this specific polarization - therefore QM isn't a complete theory, for it failed to assert that in the first place. (simply put, of course I won't portray it as simplistic)

My problem: QM predicts that the wave function collapses to either "horizontal" or "vertical" eigenstates (for example |x>1|x>2), assuming the filters are for example aligned with the x-axis. So in the EPR thought experiment, if we assume the first photon is transmitted, we infer that the second one has a polarization in the x-axis direction.

QM always end up saying "second photon is polarized horizontally" or "second photons is polarized vertically". But as I understand EPR's logic, the polarization could be in any direction whatsoever? The claim that by measuring the first photon's polarization we discover the real value of the second one's polarization - but not create it. How do they therefore explain this binary result? How come the second photon never turns out to be polarized in an angle of 45 degrees (for example).

I hope my problem is clear. It doesn't contradict their claim or anything, it just looks like another indication for a "collapse" of the wave function, which they opposed, and I wonder what their view on the subject was, and I can't seem to find a reference to it anywhere.

For me, they either have to treat this problem, or it could be that I'm misunderstanding something.

Thanks a lot,

Tomer.