Luboš defines nonlocality as a violation of relativistic causality—an ability to signal at spacelike separation. (See here and here.) In our present understanding of physics, that is impossible, although, as Luboš has also explained, we may legitimately look for such nonlocal effects in black-hole physics and string-theoretic dualities. At times, physicists and popularizers of physics have been guilty of leaving the impression that quantum correlations are nonlocal in this sense, and Luboš is right to take them to task (for instance, here, here, and here). But we need to distinguish incautious presentation from bad physics. No one really thinks signaling can occur across spacelike separation. Not even advocates of Bohmian mechanics do (although they do think there is a type of Lorentz-violating nonsignaling causation). When Einstein spoke of spukhafte Fernwirkung, he was putting it forward not as an actual physical process, but as the scandalous consequence of claims that Bohr and others had been making.
When I and many other people use the term “nonlocality,” we have in mind a broader definition that includes the nonseparability of entangled states, which violate what Einstein called the Trennungsprinzip. We likewise speak of nonlocality in manifestly gauge-invariant formulations of Yang-Mills theory and in string theory. If we are attuned to these varied usages, I think we will find broad agreement on the physics.
Where we do disagree is the significance of quantum correlations, so let us focus our energies on that. Does the disagreement reflect an outright error or simply a question on which we can agree to disagree? Regarding a pair of electrons in the singlet state, Luboš draws a comparison to Bertlmann’s socks:
When you measure the colors of his socks, there is nothing mysterious about the anticorrelation. It was guaranteed by design because the same brain decided about the two socks in the morning.Remember, when John Bell introduced Bertlmann’s socks, his point was that entangled particles do not behave like socks. Yes, the electrons are correlated by virtue of their joint preparation within the past light cone. But the sock metaphor is realist. We can assign definite colors to the socks, so we have a straightforward explanation of how they develop, maintain, and exhibit their correlation. We know from Bell-inequality violations that we cannot do anything analogous with the electrons. One might still argue that this is not mysterious and that quantum mechanics merely enlarges our conception of the types of objects that populate our world—objects that need not follow classical logic. But you cannot appeal to people’s intuition about matching socks.
The situation is nonlocal inasmuch as we are speaking of joint properties of spatiotemporally separated objects. We know the singlet electrons have a total spin of zero, but we cannot ascribe either particle a definite spin in advance of measurement. If you object to the word “nonlocal” in this context, fine. I would also be happy with “nonseparable,” “delocalized,” or “global.”
The real issue is how to explain the phenomenology of correlations. I know that Luboš does not think highly of the EPR paper (neither did Einstein), but it is the usual starting point for this discussion, so let us focus on the most solid part of that paper: the dilemma it presents us with. Given certain assumptions, to explain correlated outcomes, we must either assign some preexisting values to the properties of entangled particles or we must imagine action at a distance. Einstein recoiled from the latter possibility—he was committed to (classical) field theory. The former possibility was later ruled out by Bell experiments. So, presumably we need to question one of the assumptions going into the argument, and that’s where we go down the interpretive rabbit hole of superdeterminism, Everettian views, and so forth, none of which is entirely satisfactory, either. We seem to be stuck. I personally look to emergent-spacetime models for some help, since those models suggest that the degrees of freedom we see arrayed in space are not fundamental.
Luboš has written:
An action at a distance would be needed in a classical model that would try to mimic the predictions of quantum mechanics.True, but quantum mechanics does not provide a physical picture, either. It tell us that objects should be correlated, but does not tell us how, and it creates a serious tension between correlations and indeterminism. If you disagree, fine. Tell me what is going on. Give me a step-by-step explanation of how particle spins show the observed correlations even though neither has a determinate value in advance of being measured.