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While i don't know all the mathematical/experimental specifics i know enough about entanglement/bell's theorem to know the general ideas of what's going on. It's definitely interesting but i'm not sure how the "hidden variable" argument can ever be ruled out. I definitely understand why it is thought that bell's theorem says what people think it does but i still can't get around the idea that any possible result we find simply being a product of some sort of "preprogamming" if you will. Doesn't the concept of programming allow for any possible result?

Yogi DMT
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As previously said (e.g. in this answer), you’re right, any possible physical theory can be described by hidden variables. The whole point of Bell inequality is to look at some properties of these hidden variables. The bell tests rule out local hidden variables. But non-local hidden variable are still allowed, and quantum physics can be seen as a non-local hidden variable theory, with the state being the non-local hidden variable.

The main interesting point of hidden variables is in their generality. Since any theory can be described in a hidden variable framework, you can define “natural” constraints (like locality) and test experimentally these constraints without further assumption. Taking again the canonical example of the Bell inequalities, it allows to properly define the set of all possible local physical theories (local hidden variables, or LHV), and show that

  • there is no way to rephrase quantum mechanics as a LHV, because the exeprimental prediction of qunatum mechanics are different than a LHV

  • we can (and did) effectively test Nature is described by a LHV or not, without assuming the validity of quantum mechanics.

So one can exclude some broad categories of hidden variable theories, but never all such theories. But that is not the point.

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Frédéric Grosshans
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