Violation of Bell inequalities for classical fields?

[Ilja]

Well, to me the fact that QM nonlocality can't be used to send signals is pretty important. I'm not exactly sure what it means, but my feeling is that if there were truly something faster-than-light going on, there should be a way to expose it to experiment.

The point why it is impossible is quite simple, it follows from the logic of the proof. We have Reichenbach's principle of common cause: A correlation requires causal explanation, and there are three possibilities: A causes B, B causes A, and a common cause C for A and B. Then, the whole point of Bell's inequality is to rule out the common cause explanation. That means, two explanations remain, A causes B, or B causes A.

Given that above explanations kill Einstein causality, it is clearly not a defense for Einstein causality that we are, yet, unable to identify with certainty which of the two explanations is correct. Let's not forget that there is only one plausible culprit (what happens earlier in the CMBR frame is the cause), and there is a natural explanation why it is so difficult to identify the culprit: Even if microscopically there is a preferred frame, the symmetry group of the large distance wave equation hides this preferred frame. The simplest example is usual atomic matter, which gives the standard wave equation for acoustic waves in the large distance limit, and the symmetry group for the standard wave equation $(\partial_t^2 - \Delta)\varphi(x,t)=0$ is the Poincare group, which is not the fundamental symmetry group of atomic matter, but only of its large distance approximation.