Steve,
One needs to be careful about what is meant by "refuting" a theorem. One way to do that is to demonstrate that the theorem's conclusion does not follow, logically, from its premises. But that is not the only way. When the theorem is also being claimed to have some relevance to the real, physical world, then it is not sufficient to merely prove that the conclusion follows from the premises, because it must also be true that the premises are actually relevant to the real, physical world, and not just some idealistic world that exists only in some thought experiment.
The refutation of Bell's theorem is of the latter form; there is no error in the logic being used to derive the conclusion. The error is not a mathematical one, it is a physical one; the premise of "identical particles" seems to be irrelevant to the real world - there do not appear to be any such perfectly "identical" entities, existing outside of idealistic thought-experiments.
The "philosophical origin" of the EPR paradox lies in the trivially-obvious fact, that if you measure two different objects, in the same manner, and ever expect to get exactly the same result, each and every time, regardless of what you choose to measure, then the two different objects had better be "identical", otherwise you run into the age-old problem of foolishly comparing "apples" to "oranges". So, in the EPR paradox, Einstein proposed a very simple technique for avoiding the problem of having the first measurement of one object, disturb that object so much, that a second measurement of its "original" state will no longer be possible; just make the second measurement on a different (hence undisturbed) object, that just happens to be "identical". That is where the interest in "entangled" pairs of particles originated - pairs of identical particles, that ought to yield the exact same result, whenever they are measured in the exact same manner. Easy to say, in a thought experiment, but not so easy for "Mother Nature" to create, in the real world.
But when the entangled particles happen to be non-identical, then the entire experiment, every Bell test experiment - turns out to be just an unrecognized case of foolishly comparing "apples" to "oranges", rather than a case of "non-local" correlations existing between "apple to apple" measurements.
In that case, Bell's theorem is "Not even wrong", to use Pauli's famous expression. It is simply, entirely, irrelevant to any world (such as the one in which we appear to find ourselves) in which pairs of entangled "particles", may not be as absolutely "identical" as has been naively assumed, for the past, entire century. In that case, it is easy to demonstrate that the cause of "Bell correlations" is entirely due to the "non-identicality" of the entangled pairs, rather than any supposed "non-locality" of the real world, in which those entangled pairs actually exist.
Rob McEachern
