Bell's theorem: Local realism v. counterfactual determinism

[zvi]

This is kind of an offshoot from:
https://www.physicsforums.com/showthread.php?t=369328

Assume for a second that the controversial experiments are valid and Bell's theorem is true of the universe.
I have often seen the philosophical analysis that if Bell's Theorem is true then either local realism OR counterfactual determinism must be violated.
E.g. http://en.wikipedia.org/wiki/Counterfactual_definiteness

But all the interpretations of quantum mechanics I know do involve some breech of locality - namely there is entanglement.

So (1) can we say that Bell's Theorem proves that the world is not local (i.e. that there is entanglement) and if not what is the counter example of a theory which is totally local and yet is consistent with Bell's inequality and with the predictions of QM?

(2) if locality is indeed violated does anyone know of a really clear lay explanation for how locality can be broken but in such a way that it does not allow non-local signalling.

Hope my question is clear!

ThanksPS I just saw an older related thread
https://www.physicsforums.com/showthread.php?t=361173

However I don't see a conclusion there. Does there/can there exist a theory compatible with the predictions of QM which is abandons realism but is completely local (no entanglement). I have not seen such a theory. And if not can we not say that Bell=>nonlocality? Thanks.

 

[DarMM]

So (1) can we say that Bell's Theorem proves that the world is not local (i.e. that there is entanglement) and if not what is the counter example of a theory which is totally local and yet is consistent with Bell's inequality and with the predictions of QM?

Copenhagen and other non-representational views like QBism. They retain locality by giving up the idea that values of Quantum Observables are outcomes on a single sample space.

(2) if locality is indeed violated does anyone know of a really clear lay explanation for how locality can be broken but in such a way that it does not allow non-local signalling.

Typically our ignorance of the precise conditions of the particle masks any possible signalling. I have heard that the non-local nature of Bohmian Mechanics actually produces the limit of experimental precision needed for this masking. @Demystifier can undoubtedly say more.

 

[facenian]

Copenhagen and other non-representational views like QBism. They retain locality by giving up the idea that values of Quantum Observables are outcomes on a single sample space.

This is equivalent to abandoning one of the Bell inequality hypothesis, i.e., "Measurement independence"
$$p(\lambda|a,b)=p(\lambda)$$
Copenhagen does not necessarily mean that we have to abandon this "no conspiracy" assumption.