How to interpret Bell's theorem correctly

[entropy1]

There's something I don't quite get about most illustrations about Bell's inequality theorem. I will explain what:

Consider a pair of entangled photons fired at two arbitrarily oriented polarizers. I most explications, it seems the author suggests that the hidden variable represents the binary value (yes/no) that determines if the photon is, or is not, going to pass the filter, independent of the oriëntation of the filter.

This seems a little silly to me however. If that would be the case, either the photon already 'knew' the position of the filter, or the filter has no influence whatsoever! It would make more sense to me if the hidden variable was a prescription of 'how to act' if it would encounter the filter in a certain spatial oriëntiation. Then the filter in conjunction with the hidden variable would determine if the photon would pass or not!

The proof would still hold because the decision to pass or not would still be local.

So, what is the correct interpretation of Bell's theorem?

 

[Heinera]

There's something I don't quite get about most illustrations about Bell's inequality theorem. I will explain what:

Consider a pair of entangled photons fired at two arbitrarily oriented polarizers. I most explications, it seems the author suggests that the hidden variable represents the binary value (yes/no) that determines if the photon is, or is not, going to pass the filter, independent of the oriëntation of the filter.

Not at all. In Bell's original papers (and all later refinements) the binary value (i.e. outcome) can in general depend on both the orientation of the fiter and the value of the hidden variable.

 

[entropy1]

Not at all. In Bell's original papers (and all later refinements) the binary value (i.e. outcome) can in general depend on both the orientation of the fiter and the value of the hidden variable.

That's my interpration too!

UPDATE: I see now that I misinterpreted the explanations. It is a subtle use of language, and english is not my motherlanguage, as you may have guessed... And also, it probably is very difficult to explain!