Mathematical expression of Bell's "local realism" I have started this thread to continue a discussion with NateTG that was starting to get a bit off-topic there. I will repeat the base comment and then reply to NateTG's last comment. I would invite anyone interested to please join in! Bell's Theorem rules out local realistic theories, as is well known. Nailing down *exactly* how Bell defines "local" and "realistic" - especially what is necessary for a proof of Bell's Theorem - is a bit more complicated. That is the discussion topic. --------------------- The definition of a "realistic" theory is that particles have observable attributes independent of the act of observation. This is all EPR says; and that is why EPR says QM is incomplete. It is not an assertion of EPR that there are hidden variables that predetermine outcomes. It is that the outcome values themselves exist independent of a measurement. And Bell follows that thinking completely. So if there are 2 simultaneous values for a single particle (corresponding to 2 different measurement settings), then there are 3 as well. a, b and c are different settings to measure observables on a single particle. But such a simultaneous measurement is not possible without disturbing the system under view. So if you measure the particle and a "clone", then you might be able to get 2 values simultaneously. In this example, we are testing the hypothesis - of Bell - that a single particle has 3 simultaneous values. I think your characterization is OK but let me repeat the experimental questions. I. Experimental test of Bell Locality so it does NOT need to be assumed a priori: P(Alice+ (at polarizer setting=a), Bob (any setting b)) = P(Alice+ (at polarizer setting=a), Bob (any setting c)) and similarly (I left this out in the earlier post I think) P(Alice- (at polarizer setting=a), Bob (any setting b)) = P(Alice- (at polarizer setting=a), Bob (any setting c)) We are looking at the variations of the setting for Bob and how it affects things over at Alice, but are not concerned with Bob's outcome in this statement. Because this scenario exactly - word for word - maps to Bell's statement as to his locality assumption. That being that the result at Alice is independent of the setting at Bob. The interesting thing: It just doesn't matter whether there is signal locality or not; if the particles are space-like separated or not; or if there are slower than light influences. None of these can matter in our experiment II IF the experimental result above is first proven. Therefore, there is no need to assume Bell Locality or locality of any kind. In fact, you are free to assume the opposite: that there are such effects because they just won't matter. II. Experimental test of Bell's Inequality This would test correlations between Alice and Bob once we have ruled out - by experiment - that the outcome at Alice is affected by the setting at Bob. So now we can see that the correlations are too strong to obey Bell's Inequality - because there is NO SIMULTANEOUS a, b and c to begin with.