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Bell's theorem - for or against Hidden Variables?
The violation of Bell's inequality is considered by many scientists as one of the strongest arguments against Hidden Variable Theories. Last but not least, it forbids a whole class of  such Hidden Variable Theories, usually named (I think misleadingly) "local realistic theories".  

So, it may be a surprise for many people that Bell himself was one of a few, at this time, almost the only one, defender of the most famous Hidden Variable Theory, de Broglie-Bohm theory (dBB), also known as Bohmian mechanics.  How is it possible that a defender of a Hidden Variable Theory is the one who has found one of the most important theorems against Hidden Variable Theories?  A theorem which, as many think, proves that dBB theory is wrong?  This sounds like if the best argument against a theory comes from the only defender of that theory.

Of course, the situation is a little bit different.  Bell's theorem is a problem only for a very special class of Hidden Variable Theories, and the theory defended by Bell is not in this class, thus, not endangered at all by his theorem.  Instead, this theorem solves, in an indirect way, one powerful objection against dBB theory:  The problem is that dBB theory requires a preferred frame. What happens here and now immediately influences what happens far away - immediately, that means, without caring about the speed limit of causal influences imposed by Einstein causality.  

But to violate Einstein causality is a strong argument against a theory - even if it is a Hidden Variable theory.  Hidden or not, the relativistic metaphysics postulates that everything should follow relativistic symmetry. So, the question arises if one can improve dBB theory in such a way that it becomes Lorentz-symmetric too, that means, if there exists an Einstein-causal Hidden Variable Theory.  What Bell has proven is that such a theory does not exist.  So, one cannot make dBB theory Lorentz-symmetric.  It violates Lorentz symmetry, because all Hidden Variable Theories have to violate Lorentz symmetry, because improving it in this direction is impossible.  

As a side effect, Bell's theorem connects the two otherwise quite different classes of Hidden Variable Theories we consider here: Those of quantum theory, which try to revive the classical ideas about reality by introducing hidden trajectories of physical objects, and those of relativity, which try to revive classical ideas about space and time by introducing a hidden preferred frame: If you want hidden variables for quantum theory, you have to have also hidden variables for relativity. 

But there is another aspect, which transforms Bell's theorem even into a strong argument in favour of Hidden Variables. This aspect is hidden behind a popular but wrong simplification of Bell's theorem, namely, that it presupposes the existence of Hidden Variables.  It doesn't.  The existence of these hidden variables is derived in the first part of the theorem.  This is usually ignored, because this first part was only shortly mentioned in Bell's paper - with a reference to the EPR argument.  This first part is, essentially, the EPR argument that Quantum Theory is incomplete, a conclusion derived from a different assumption - the EPR criterion of reality.  

So, Bell's theorem derives Bell's inequality from Einstein causality, together with the EPR criterion of reality.  Once Bell's inequalities are violated, one of the assumptions has to be false.  So, if we postulate the EPR criterion of reality, and use the violation of Bell's inequality as a fact, we can derive that there exists a preferred frame - the Hidden Variable for relativity.  

Even more, for those who think realism is a dubious, questionable assumption, there is a variant which does not mention even realism, but is based on causality alone.  All it needs is Reichenbach's principle of common cause:  If we observe a correlation, there has to exist a causal explanation.  And there are two possible causal explanations: either one event is the cause of the other, or they have a common cause.  What is excluded by Bell's theorem is the causal explanation by a common cause in the past. What remains as a causal explanation is one event causally influencing the other.  Which is the cause, which is the effect, remains unknown by the nature of the argument.  But, if the two events are space-like separated, above remaining explanations violate Einstein causality.  So, there have to exist hidden causal influences violating Einstein causality. 

So, it appears that Bell's theorem provides strong arguments in favor of a hidden preferred frame.

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Bell's theorem - for or against Hidden Variables? - by Schmelzer - 12-20-2015, 07:01 PM

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