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Bell's theorem - for or against Hidden Variables?
A problem with the topic of "Bell philosophy" is that his original paper, "On the Einstein Podolsky Rosen Paradox", though fine, is not ideal for the discussion. For one thing it emphasizes "nonlocality" which I don't want to do. Instead it's better to consider "Bellist" philosophy. IOW, the general Bell-related theorem and experiments, as (I think) we understand them.

A good place to start is Joy Christian's paper "Macroscopic Observability of Spinorial Sign Changes under 2 pi Rotations", http://arxiv.org/pdf/1211.0784v4.pdf. There he shows that in a typical Bell experiment set-up, if we assume the space of observations is SO(3), then the angular correlation function is linear. See fig.4 and the accompanying discussion in that paper.

Now, let's define a type of Bell-experiment situation we can call "Class 1" - so as not to pre-judge the conclusion. Basically it would be SO(3), and many people would call it realist, local, and classical, but I want to avoid those words. Just call it Class 1. It has an (angular) linear correlation function as Christian's Fig. 4 shows.

Given a class 1 correlation function many inequalities can be derived which must be satisfied. The original Bell inequality, CHSH, others. Let's focus on CHSH since that's most popular.
 
Ok, then the mathematical content of the "Bellist theorem" is as follows. If an experiment is Class 1, it must satisfy CHSH inequality. I claim there's no philosophy or even physics in this statement, nothing to argue about. Everyone agrees with it.

Now, the philosophical content concerns the following. What types of experiments are, in fact, Class 1? Bellists claim any classical, realist, local experiments are. That would include, BTW, Christian's exploding balls. Furthermore, that QM spin experiments (like Bohm's version of Bell) do not satisfy the inequality. Therefore they are not in Class 1 - call that Class 2. This determination rests on physics - which is also somewhat controversial - and philosophy. I won't try to separate the two at the moment.

The above seems the simplest way - given the common understanding we already have - of specifying which part of Bell is indisputable mathematics and which is controversial. "Class 1" is well-defined mathematically, as is the correlation function and resulting inequalities. The problem arises when we try to see how it relates to the physical world (i.e., what it represents physically). Definitions of "real", "local", "classical" all involve and require both physics, and what we might call philosophy. At least, whatever it is, it certainly isn't mathematics.

This should be enough to refute that "Bell’s theorem rests on no foundation except philosophy". It rests on math, physics, [i]and[/]philosophy.

Didn't notice your last post until after previous post.

It's not that I "dismiss" Popper, or disagree with him. I just don't care about him. The reason, everything he says that's worth saying is so obvious I thought of it myself long before reading him. Took me about a minute or so. We can use any of his ideas but I simply don't consider him an authority - the ideas must stand on their own. And please don't call me a Popperian! That's about like calling me a "Dick-and-Jane-ian" because I believe in correct grammar and spelling.
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RE: Bell's theorem - for or against Hidden Variables? - by secur - 09-07-2016, 01:43 PM

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