Philosopher Tim Maudlin writes What Bell Did:
On the 50th anniversary of Bell's monumental 1964 paper, there is still widespread misunderstanding about exactly what Bell proved. This misunderstanding derives in turn from a failure to appreciate the earlier arguments of Einstein, Podolsky and Rosen. I retrace the history and logical structure of these arguments in order to clarify the proper conclusion, namely that any world that displays violations of Bell's inequality for experiments done far from one another must be non-local. Since the world we happen to live in displays such violations, actual physics is non-local.He also just posted a Reply to Werner. He does not reference the Werner criticisms, and the closest I could find was this Reinhard F. Werner post:
The experimental verification of violations of Bell’s inequality for randomly set measurements at space-like separation is the most astonishing result in the history of physics. Theoretical physics has yet to come to terms with what these results mean for our fundamental account of the world. ...
Unfortunately, many physicists have not properly appreciated what Bell proved: they take the target of his theorem — what the theorem rules out as impossible — to be much narrower and more parochial than it is. Early on, Bell’s result was often reported as ruling out determinism, or hidden variables. Nowadays, it is sometimes reported as ruling out, or at least calling in question, realism. But these are all mistakes. What Bell’s theorem, together with the experimental results, proves to be impossible (subject to a few caveats we will attend to) is not determinism or hidden variables or realism but locality, in a perfectly clear sense. What Bell proved, and what theoretical physics has not yet properly absorbed, is that the physical world itself is non-local.
I am one of those who see in “local realism” a conjunction of two concepts: locality and realism. Bell’s argument shows that this conjunction is not in agreement with the observed facts. The separation between the concepts is not difficult, something that I expect students to understand. Quantum mechanics as I understand it takes the local option, in the sense of not containing spooky signals. Of course, if you insist on a classical “realist” description they are all over the place. It is clear that if you are altogether unwilling to even debate realism (or “classicality”) you can soak your language in it to such a degree that it would seem like an undeniable demand of basic logic. But that is just sloppy thinking, which is not improved by any degree of shouting or religious devotion.(Maudlin was replying to a different Werner essay, but that is not online yet, according to the comment below.)
“Realism” has a double meaning in this context. On one hand, it is a basic principle of science, the demand to check any claims against reality, to go for empirical content rather than storytelling. On the other hand, it stands for a particular way of constructing a theory, namely assuming that every individual system has an in principle complete description in terms of its properties (“classicality”). The irony of quantum mechanics is that it brings these two into conflict. Those insisting on the second kind of realism, like the Bohmian school, thereby lose sight of the first: Bohmian trajectories have no connection to empirical fact, and even the Bohmian theory itself claims no connection. So they are just a piece of fantasy. You may call the trajectories the reality givers (I even heard “realizors”) of the theory, and base an “ontology” on them. But they are still but a figment of your imagination.
Werner is on the mark here. There are two kinds of realism here. Quantum mechanics is contrary to the sort of realism associated to classical or hidden variables.
Maudlin and the other Bell fans yearn for some sort of classical realism, and prefer to reject locality. However it is foolish to conclude that "the physical world itself is non-local." If that were true, then Nobel prizes would have been given to Bell and his followers long ago.
Finally, it has become fashionable to say that another way to avoid Bell’s result and retain locality is to abandon realism. But such claims never manage to make clear at the same time just what “realism” is supposed to be and just how Bell’s derivation presupposes it. I have heard an extremely distinguished physicist claim that Bell presupposes realism when he uses the symbol λ in his derivation.That distinguished physicist is correct. Bell assumes λ parameterizes a hidden variable theory that functions according to classical (non-quantum) rules. If realism means that thew world is ruled by classical hidden variables, then realism has been disproved by quantum mechanics and Bell's theorem.