06-06-2016, 08:35 AM
No, they used no inequality at all, but computed what quantum theory predicts. The result was something greater than 2, thus, violated the Bell-CHSH inequality, which would hold in a Einstein-causal realistic theory.
The whole point is that QT is not equivalent to any Einstein-causal realistic theory. So, of course, if they compute the QT prediction, they use the QT rules and not some inequality which holds for Einstein-causal realistic theories.
Of course, nothing can violate mathematical proofs, which is a triviality. But you can have theories which violate the assumptions of the Bell-CHSH theorems, thus, can violate the resulting inequalities.
The whole point is that QT is not equivalent to any Einstein-causal realistic theory. So, of course, if they compute the QT prediction, they use the QT rules and not some inequality which holds for Einstein-causal realistic theories.
Of course, nothing can violate mathematical proofs, which is a triviality. But you can have theories which violate the assumptions of the Bell-CHSH theorems, thus, can violate the resulting inequalities.