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I understand that this is a much debated issue, so I will try to be precise in order to narrow the question. Bell inequality violation rules out Local Realism. From this, I understand that by giving up just one of the two conditions (Locality or Realism) one could generate a viable model. My questions:

  1. Could we provide a local and non realistic model that reproduces the observed correlations? (in particular I do not see how a local theory can reproduce correlations outside of the light cone)
  2. Could we provide a non local and realistic model that reproduces the observed correlations?
  3. What about QM? I this (non) local and/or (non) realistic? Is this just a matter of interpretation?

Claims on these points in the literature are often unclear and (to me) confusing (see for example http://www.physics.drexel.edu/~bob/Entanglement/aspect_nature446.pdf) so I would like to see explicit model for my points 1. and 2.

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  • $\begingroup$ What exactly do you mean by "local" and "non-local"? Note that it is possible for a theory to be non-local (in the sense that it produces correlations between spacelike-separated events that break the CHSH bound) while also non-signalling (i.e. no action of Alice can affect local measurements of Bob at a spacelike-separated event). This category includes quantum theory, but also stranger beasts like Popescu-Rohrlich boxes. Theories with signalling are not that interesting (as they break causality if you allow relativistic motion) but there's a long way from non-signalling to local. $\endgroup$ Apr 10 '15 at 13:50
  • $\begingroup$ thx emilio, trying to translate it to my own language you are saying that: QM is non-local (i.e. out of light cone correlated) and non-realistic (i.e. no "element of reality" thx to Bell inequality violation) what I try to understand is whether we could interpret QM by breaking just one of the conditions. $\endgroup$ Apr 10 '15 at 14:03
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    $\begingroup$ The short answer is yes: Bell violations imply that if a model reproduces QM it cannot be both realistic and local; in other words, you can get away with only breaking one of them. The detailed answer, however, depends on what you mean by "(non-)local" and "realistic". Specifically: do you consider a non-signalling realistic theory which violates CHSH to be nonlocal? $\endgroup$ Apr 10 '15 at 14:57
  • $\begingroup$ Let's try with these definition: 1. Locality: different measures at space-like separations are uncorrelated 2. Reality: (the einstein one) if the outcome of a measure can be predicted with 100% confidence than it is a real property of the system It seems that the answer to your last question in my definitions is yes, isn't it. $\endgroup$ Apr 10 '15 at 15:26
  • $\begingroup$ That definition of locality is much too strict - you can easily beat it within classical physics. Say Charlie takes a pair of gloves, puts them in different boxes, sends you and me the boxes at random, and we open them simultaneously. If I have a right-hand glove, I can immediately conclude that yours is a left-hand one - there's a perfect (anti)correlation between our spacelike-separated measurements. There's no mystery there! The problem is if our measurements of the boxes start to beat CHSH bounds on their correlations, which the sock model cannot do. $\endgroup$ Apr 10 '15 at 15:38
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1.) You have to give up not only Einstein-locality (locality itself would be unproblematic), but also causality, because there are variants of the proof which rely on causality only, with Reichenbach's principle of common cause as the base. I do not think theories which reject causality and realism make sense for a scientist, who wants to study the real world and find causal explanations for unexplained correlations. But, in principle, one could use the minimal interpretation of QT for this.

2.)+3.) There are realistic interpretations of QT, namely the de Broglie-Bohm interpretation.

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There are a number of local theories that violate Bell's inequality. This is partially because there are lots of hidden assumptions in Bell's theory which are well described by Wiseman.

The best example I know of is a Event-based simulation of quantum physics experiments where they show that a simple classical event-based simulation can reproduce Bell-CHSH inequalities. It can also be done with negative probabilities. Neither of these are a complete theory, however.

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