I can follow the derivation of the maths, but I'm hard pressed to come up with an analogy that accurately captures what's being said by them. When you rotate particle B by some angle, you modify the correlation between particles A and B (how often they'll point in opposite directions, for example). Classically (with local realism), that would be proportional to B's rotation angle, and quantum mechanically, we find it's proportional to the negative cosine of that angle.

From a maths perspective it seems like you can say that the probabilities used in the CHSH inequality calculation must either be non-local (ie, the parameters of measurement must be non-locally communicated between systems) or that there is not a hidden variable 'phase space' being integrated over for the probability.

But what does that all mean, physically, if we can think of such a thing?