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I am told that the the violation of Bell's inequalities prove that the universe cannot have local realism. That is to say, the universe cannot both be local and real.

I understand how Bell's theorem can be explained by assuming locality is false, but if we assume locality to be true (and therefore realism is false), how can we interpret the results of Bell's theorem? It seems like Bell's theorem simply disproves locality and nothing else. I have found similar questions on stack exchange, but none of the solutions sufficiently answer my question.

Any help is much appreciated.

Mauricio
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Eli Yablon
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2 Answers2

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In the discussion of the EPR experiment, the word "realism" is used to denote some theory, which nobody has ever described, that explains the result of quantum mechanical experiments in terms of quantities that have a single value at any particular time.

A local realistic theory would be local and realistic and couldn't exhibit correlations as strong as those allowed by quantum theory in the EPR experiment.

Bell's theorem doesn't refute locality because there is a local theory that accounts for the Bell correlations: it is called quantum theory. In quantum theory, physical systems are described by quantum observables that are represented by Hermitian operators, not by single numbers. So quantum theory is not realistic in the sense described above, but it is local since the equations of motion for real quantum systems are local, and so information can only get from one system to another by propagating locally. For more details see

https://arxiv.org/abs/quant-ph/9906007

https://arxiv.org/abs/1109.6223

https://arxiv.org/abs/2008.02328

alanf
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Bell's theorem does not disprove realism. de Broglie-Bohm interpretation of QM is realist, yet it violates Bell's inequality.

In order to understand the consequences of Bell's theorem you need first to understand the EPR argument, since Bell builds on that result.

What EPR has proven was that QM is either non-local or incomplete. In other words, if you want QM to be local you need to "complete" it by adding some other variables. One way to do that is to assume that the measured properties (say the spins of the entangled particles) were already determined at the time of emission. When they are measured you just find out the spins they had all the time.

Bell looked more carefully into this hypothesis and discovered that, if you assume that the hidden variables are not correlated with the settings of the detectors, this idea does not work. Bell's conclusion was that physics is in fact non-local. Here are his words, from his seminal paper "On the Einstein Podolski Rosen Paradox":

"It is the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty."

In conclusion, together with EPR, Bell's theorem restricts the type of possible theories to these classes:

C1. non-local theories

C2. deterministic hidden variable theories where the hidden variables are correlated with the settings of the detectors (superdeterministic theories)

It is important to notice that the standard/Copenhagen interpretation of QM must be non-local as well, since it clearly does not correspond to C2.

What about realism? If you postulate that realism is the same thing as hidden variables (which is not right, since one can be realist about the quantum state itself, like in the many worlds interpretation) then you may say that Bell's theorem restricts the class of possible local "realistic" theories to C2. You can still have non-local realistic theories, like de Broglie-Bohm interpretation, or superdeterministic realistic theories, like 't Hooft's cellular automaton interpretation.

Andrei
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