Bell's theorem of course explicitly includes an assumption about hidden variables, so yes, if you want to talk specifically about Bell's theorem, you're going to be talking about hidden variables. (I'll give an explicit example of such talk below.)I don't see how one can talk about Bell's theorem without mentioning hidden variables.
However, Bell's theorem, in itself, says nothing whatever about either quantum mechanics, or the results of actual experiments. Of course Bell knew that QM predicts violations of the Bell inequalities (that's why he went to the trouble of publishing his theorem), and we now know that experiments confirm those predictions of QM. But you can talk about QM and experimental results without talking about hidden variables at all. Hidden variable models are not the only possible models. You can even talk about the fact that QM/experimental results violate the Bell inequalities without talking about hidden variable models.
If you are really unable to see the obvious proof, consider: EM is a local hidden variable model in the sense that Bell's theorem uses that term. (So is classical General Relativity.) Therefore, by Bell's theorem, its predictions must satisfy the Bell inequalities.I claimed that one cannot prove, based on Bell's theorem that EM cannot violate them
If you define "theory of relativity" to only include classical relativity, then you have excluded quantum field theory. In which case your definition of "theory of relativity" is irrelevant to this discussion.There is no other theory of relativity.
No, let's define what "A caused B" means in terms of testable predictions. Otherwise it's just meaningless noise as far as physics is concerned. Can you do that?let's assume for the sake of the argument that A caused B.