full implications of bell's inequality

[marky3]

The violation of Bell's inequality is often said to imply that either there exists non-locality or there are no hidden variables. In actual experiments it is consistenly found that the inequality is violated by precisely the amount predicted by quantum theory. But quantum theory denies both locality and hidden variables. Therefore aren't we to conclude that the violation of Bell's inequality implies that there is both non-locality and no hidden variables?

[JesseM]

But quantum theory denies both locality and hidden variables.
Why do you think it denies them? It doesn't include any hidden variables, for example, but that's not the same as "denying" them. Quantum theory is just a recipe for making predictions about the probabilities of different measurable events, with no built-in interpretation of where these probabilities come from or what they "mean", so there's no reason in principle it couldn't turn out to be an approximation to some more detailed theory. And we know that conventional nonrelativistic QM makes exactly the same predictions as Bohmian mechanics (http://plato.stanford.edu/entries/qm-bohm/), which does include hidden variables, assigning particles a well-defined position at all times...nothing about the QM formalism rules out the possibility that some other model like Bohmian mechanics could describe the underlying "reality", provided the model makes the same probabilistic predictions as ordinary QM.

[DrChinese]

The violation of Bell's inequality is often said to imply that either there exists non-locality or there are no hidden variables. In actual experiments it is consistenly found that the inequality is violated by precisely the amount predicted by quantum theory. But quantum theory denies both locality and hidden variables. Therefore aren't we to conclude that the violation of Bell's inequality implies that there is both non-locality and no hidden variables?

Could be. I would say that it is highly dependent on your precise definition of non-locality and "no hidden variables". It is generally agreed that with common definitions of each, the answer to your question is NO. But with different definitions - which could also be considered reasonable in some ways - the answer might be YES.