Historically, "non-locality" is one of the aspects of QM that has been put forward by opponents of realism as evidence that no "common-sense" physical interpretation of the theory is possible.
"Non-Locality" and Realism: A Brief Discussion
By Travis Norsen (May 2002, Part 5 of 5)

[OBJECTIVE SCIENCE.COM] Many realist-minded people are bothered by this observation of a non-local interaction between the two entangled particles.  Indeed, historically, "non-locality" is one of the aspects of QM that has been put forward by opponents of realism as evidence that no "common-sense" physical interpretation of the theory is possible.  But do non-local interactions really undermine realism? 

The short answer is:  of course not.  One cannot undermine realism with something that is real.  (And I assume it goes without saying that one doesn't get far undermining realism with the unreal, either.) 

The longer answer is that no valid principle of metaphysics rules out the possibility of faster-than-light physical causation among particles.  Philosophy tells us that whatever exists has identity.  So a proper commitment to realism allows one to veto out of hand any assertion that, for instance, micro-physical processes lack identity, or that quantum systems exist in an indeterminate state of limbo until a measurement is made.  But in rejecting "local realism," we need reject only the "locality" aspect, not the "realism" aspect. [13]  A theory which regards quantum systems as perfectly determinate, well-defined, and identity-possessing, but which simply includes faster-than-light interactions among entangled particles, is entirely consistent with all the facts – both the facts observed in the lab, and the ones observed everyday in reality which underlie our philosophical commitments. [14] 

The most one can say is that these faster-than-light influences seem to violate the prohibitions of relativity theory.  But to reject the evidence for non-locality based on relativity alone is to treat that theory as a kind of sacred cow -- a status which it does not deserve. After all, relativity theory is essentially just a set of mathematical transformation laws that tell us how "appearances" differ for observers in relative motion.  The physical fact at the root of the theory, namely the universality of the measured speed of light, is a fact which the theory itself takes as an unexplained axiom.  But without a physical explanation of this axiom (or in other words, without an understanding of the causal meaning of the equations of relativity) one cannot know exactly where and to what extent the formalism of relativity should apply.  At very least, one can not be certain a priori that the formalism of relativity will apply to a surprising new kind of interaction that was never part of the experimental context that gave rise to relativity in the first place.  

Until the causal mechanisms involved in both relativity and entanglement are better identified, one simply cannot claim that they contradict each other.  In all likelihood, it will be found that the formalism of relativity has only a limited domain of validity, or that a specific type of interpretation of the formalism (which allows for faster-than-light interactions) is forced on us. [15] 

So, to summarize:  Do the experimental results conflict with Bell's inequalities?  Yes.  Does this mean that the LRHVTs are wrong?  Yes.  Does this mean we must reject identity, causality, reality, Objectivism?  No, of course not.  It simply means that there is a new kind of physical interaction which maintains entanglement between spatially separated particles.  This kind of "weird new physics" is hardly unprecedented in the history of science.  Nature repeatedly surprises us with her exotic implementations of the law of identity. 

Many thanks to Eric Dennis for a year's worth of discussions on these and related issues.  My understanding was significantly improved by these exchanges. 

References and Notes:

[13]  And remember, we're not even really rejecting "locality", but only the weaker claim that causal effects always propagate with speeds slower than the speed of light.  As discussed in an earlier footnote, it is reasonable (and certainly not contradicted by experiment) to think that all interactions are "local" in the stronger sense of the term.  All that is being claimed here (because this is all we are able to infer from the experiments) is that entangled particles interact via some faster-than-light mechanism.  Currently, the lower limit on the speed is many times the speed of light.  As mentioned before, it is hoped that as this limit is pushed, we will eventually discover the exact speed at which these interactions propagate.  Assuming this occurs, we will be able to say again that physics is completely local (in the strong sense) but that nature's speed limit is actually quite a bit higher than the speed of light. 

[14]  Some version of Bohm's theory is the obvious example of such a theory.  See, e.g., Bohm's book "The Undivided Universe" or Peter Holland's book "The Quantum Theory of Motion". 

[15]  The Lorentz Ether Theory is the obvious example here.  The best (and perhaps only) decent reference for this theory is the textbook by Janossy, "Theory of Relativity Based on Physical Reality", 1971. 

Travis Norsen recently finished his PhD in theoretical physics, and is currently teaching physics and astronomy at a liberal arts college in New England. He remains interested in and philosophy of science and the foundations of physics, and is engaged in several research and writing projects on these subjects.

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