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Bell's theorem - for or against Hidden Variables?
Gill1109 wrote:

"Whether a theory is local or non-local depends, I think, on what you consider to be real. If you want to consider the outcomes of not-performed measurements as real, then QM is non-local. If you want to consider the wave-function as real, then QM is non-local. But if you accept only the reality of actual outcomes of performed measurements, and accept irreducible randomness as a fundamental part of reality, then it seems to me that QM is local.

But I am not a professional philosopher, nor a physicist, just a mathematician. I think we should not worry so much about locality and non-locality. Maybe it is time to forget some distinctions which used to be considered important. Perhaps the phenomena are trying to teach us that some old distinctions have less meaning than we thought. It seems to me that successful Bell experiments are teaching us that reality is non classical. Things apparently happen in these experiments which cannot be explained in a mechanistic way. QM allows some things which classically would have been thought to be impossible; but it also forbids other things. Reality is *different* from what we thought. Different from how evolution has programmed our brains to imagine reality. Right now I think we should reject local-realism but that the idea that one of the two (locality or realism) has to be rejected and the other can be kept is too simplistic. It's more useful to explore the possibilities offered by QM and maybe adapt our ideas of locality and realism accordingly."

Thanks Gill1109,

"Non-local" has different meanings in different applications. In the current context "local" means "within the past light cone". Modern Bell experiments are designed so that when Alice and Bob make their spin measurements their stations are non-local in one key sense: their detector settings can't be known at the other station, because they're spacelike separated. In fact no observer in the universe can know both those settings, when the detections are made. Those two angles are "non-local" with respect to each other.

To me the phrase "QM is non-local" means the following in this context. When we analyze and predict mathematically the results of the experiment, those two non-local variables must appear together in the same equation. In fact, we must use the cosine of the sum of the angles (or, the dot product of vectors representing the detector settings) to predict the correlations of Alice and Bob's two detections (or a series thereof). This happens nowhere else in physics! To analyze any other experiment, and predict its results - or a function of the results, like correlation coefficients, or moments - it's always sufficient to use only the information available in the past light cone. Except in this one case. Here we must use two variables that no possible single observer could have known, at the time of the measurement. This very peculiar and unique situation can reasonably be called "non-local".

What does one do when confronted with a paper which claims to reproduce the results of a Bell experiment, like Christian or Hess? One knows that somewhere hidden in the math, those two variables have been used together. Maybe a key subscript has been dropped, or maybe a limit is taken to two separate values at once, or whatever. When you find it, you find their mistake (or trick). So my definition of "non-local" is an operational, practical definition.

Since the term "non-local" makes people uncomfortable, we can call it "property X" instead: the mathematical analysis must use, in the same equation, variables which are not within each other's past light cones.

As we've seen, Property X can be rigorously defined just by looking at the math. But the question inevitably arises, what does it mean physically? One might suppose that some "influence" travels between Alice and Bob detector stations faster than light. But other explanations are available under the general heading of "non-realism". There's rejection of counterfactual definiteness, rejection of "free will" and determinism, "nature conspiracy" ideas, "consistent histories", and others I've never heard of. Ontological issues arise: is the wave function real? Is irreducible randomness real? Epistemological issues arise: is the "collapse of wave function" a change in real physical information, or just a change in our knowledge? As far as I know, it's a complete waste of time to debate these questions. Instead we should ask, what hypotheses can be formed, and what experiments performed, that might help decide the issue?

Here's an example. Suppose the hypothesis is that an FTL signal of some sort travels between the two detector stations, between the two entangled particles, to ensure they get the right correlations. If it can't be tested, then it's mere philosophy. But we could try to block the signal by shielding. What if we put a thick slab of lead, or a powerful EM field, between the two stations? Does the correlation fail? I'm almost certain it wouldn't. I bet you could put a billion light years, and a supernova or active quasar, between them: QM would still work as advertised. But in the unlikely event that shielding destroyed the correlation, you see, that would support the hypothesis that an FTL signal travels between them. Such an experiment would be real physics, and even with the expected null result, far more useful than any amount of ontology.

I offer this only as an example, no doubt you can think of more useful experiments. The main point I hope we can agree on: don't worry about philosophy, much less terminology. Instead concentrate on math and experiments.

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RE: Bell's theorem - for or against Hidden Variables? - by secur - 07-26-2016, 06:47 PM

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