stevendaryl said:
I consider Bertlmann's socks to be an illustration of exactly the opposite conclusion. Bertlmann's socks is an example of an apparent nonlocality that disappears when you are given more information about local conditions. That's the whole point of the search for hidden variables: You have a correlation that is apparently nonlocal, but you can eliminate the nonlocality if you can find local information that make the same predictions as the nonlocal information.
The correlation doesn't suddenly become local once you found a hidden variable that explains it. It is still a non-local correlation, the numbers haven't changed. Non-locality of correlations is a relation between numbers. The point is that the correlation can be explained by a common cause in the past. The socks were separated in a local region and then sent to Alice and Bob at a slower speed than the speed of light. Thus neither the discovery of the red sock causes the blue sock to be blue nor does the discovery of the blue sock cause the red sock to be red. Instead, there is a common cause in the past.
If you can't find such variables, then you're stuck with a nonlocal theory.
Only under the assumption that the world is classical (i.e. realistic). If the world is classical, the common cause explanation is not possible and thus the discovery of the spin-up particle would have caused the other particle to have spin-down and the other way around: The proof of Bell's inequality assumes realism (modeling on a combined probability space) and locality. Thus a violation of Bell's inequality implies that not both realism and locality are true (by the logical principle of contraposition), which means that realism or locality or both are false. If we know that the world is realistic, must conclude that the locality assumption in the proof must have been false. However, if we don't assume a realistic world (for example a quantum mechanical world), then we can't infer that the locality assumption is false. Neither can we infer that it is true. We just don't know it.
That's only because nobody really knows what "causation" means.
Well, in the case of a Bell-test experiment, we can explain the non-local correlations if we accept that the world is quantum mechanical: The entangled quantum particles had been created locally in the past and then sent to Alice and Bob respectively at a speed lower than the speed of light. This is a perfectly causal explanation as soon as we accept that the world is quantum mechanical and quantum objects just happen to exist. If we hadn't entangled the particles in the past, before we sent them to Alice and Bob respectively, we wouldn't have seen the perfect correlations in the Bell-test experiment. A classical physicist couldn't accept such an explanation. But for a quantum physicist, who accepts that the world behaves quantum mechanically, it is not problematic. It's only the classical thinking that makes it seem weird.
That's a huge difference. In the socks case, we know that our nonlocal description is incomplete, that a complete description of Alice's and Bob's situation is local. So the apparent nonlocality is due to our ignorance about the state of the system. The nonlocality is in principle eliminable. That's not the case with QM.
I agree that it is a huge difference and the non-local correlation of quantum objects are very different from the non-local correlations of classical objects. But I don't agree that this implies that quantum mechanics is non-local, because for non-locality, it's the
cause that matters, not the
correlation. Quantum mechanics is not complete, but that doesn't imply that non-local correlations can't be explained causally.
In the one case, the most complete description of reality is local. In the other case, it's not.
In the other case, it's also local, because I can also give a common cause explanation for the non-local correlations. It just involves quantum objects rather than classical objects. The only thing you need to accept is that using quantum objects as if they did really happen to exist in the universe is a valid way of reasoning. And given the success of quantum mechanics, I don't find this assumption unreasonable.
stevendaryl said:
If you know everything there is to know about the local region near Bob, you can never do better than 50% probability of spin-up, 50% probability of spin-down.
That's right. Quantum mechanics is not complete. But completeness isn't required for locality. It's an entirely different concept.
If, in addition, you know that Alice measured spin-up at angle \vec{A}, then you can predict with certainty that Bob will measure spin-down along that axis.
That's also right. Non-local correlations exist, just as they do in classical theories (see Bertlmann's socks). In both cases, they can be explained by common cause explanations in the past, although in the quantum case, you must resort to quantum reasoning.
So the quantum facts are nonlocal; the best prediction for what Bob will measure may involve facts about the situation far away from Bob.
The facts are non-local, just as in the classical case. The explanation is local (i.e. causal) in both cases.
Are you suggesting that it is possible to predict Bob's results using some kind of quantum local variables that fail to belong to a combined probability space?
No, we can neither predict Alice's nor Bob's results. We can however predict the non-local correlations and we can explain them causally. No FTL is involved. The reason for the correlation lies in the past light cone of both Alice and Bob.