harrylin said:
Does that article agree with Christian's claims, or does it perhaps disagree in some subtle way?
It agrees with Christian's claim that his Clifford algebraic formulation is locally causal.
Castro's showing, in equations 1 through 29 with accompanying annotations, why a Clifford space, Clifford algebraic QM formulation can be regarded as locally causal. But it still has to do with the entangled particles exchanging signals, and it's for this and other reasons that I would guess that most people, including me, wouldn't regard Christian's formulation as a bona fide Local Realistic representation of entanglement.
harrylin said:
To me it sounds like a paper arguing that Pythagoras' theorem is wrong in curved geometry. And then the question is not so much if that argument is wrong (probably not!), but which geometry is the right one for the problem at hand.
That seems like an insightful analogy. And I've found Christian's topological considerations to be interesting in the sense that I hoped that they might be (via some convoluted associations) compatible with my own views on this stuff. But insofar as I don't understand the connection between Christian's approach and reality, or at least my conception of it, then I can only speak to what seems to me to be his motivation and what seems to me to be the relevant features of his formulation and, again superficially, why it doesn't seem to me to explain why the extensions of Bell's theorem to deep reality are flawed.
Bell's work shows, correctly by virtually all assessments as well as imho, that an lhv account of the singlet state is incompatible with the qm account. Subsequent work by others has verified that lhv accounts of entanglement are not only incompatible with qm, but with experimental results. This is a done deal imho and universally accepted by mainstream physicists as being fact. But some have interpreted this to mean, or as proof, that either lhv's don't exist or that nature is nonlocal, and I think it's disagreement with this interpretation that has prompted a closer examination of Bell's work. This is where Christian is coming from.
And yes, he's correct in saying that his formulation can be, in a certain sense, said to be locally causal. But it's a decidedly artificial sense, and as far as I can tell doesn't offer any (readily understandable) insight wrt why Bell's theorem isn't telling us anything about deep reality.
vanesch said:
Maybe I'm simply not sophisticated enough, but there's a version of Bell's theorem which is so terribly elementary, that I don't see how you could "disprove" it. You could just as well try to disprove an elementary theorem in number theory or something.
Of course you're right in saying that the strictly mathematical Bell's theorem (Bell's Inequality) is a proven theorem. But neither Christian nor Castro are claiming otherwise -- at least as far as I can tell.
Bell tests are measuring a relationship between two relationships, and a full accounting of the statistical results doesn't require any reference to local hidden variables (eg., the optical vector of entangled photons is irrelevant wrt determining the joint stats -- it's only the
relationship between paired particles that matters, and this is a global not a local property). If local hidden variables
are used, then you can get the same basic angular dependence predicted by qm, but with a reduced range. However, if local hidden variables are
required to describe an entangled state, then from that you can formulate an inequality that will be violated by qm and experimental results -- none of which contradicts the possibility or assumption of the
existence of local hidden variables or the assumption that nature is locally causal (and wrt to this it helps to keep in mind that Bell showed that qm is quite compatible with a local hidden variable account of individual results).
Is Christian's Bell stuff interesting? Yes, I think so. Is it important in that it clarifies or explains anything? No, I don't think so. But then, I can't claim to fully understand the relationship between the C-space account of entanglement and reality. It would be nice if Christian would spend some time at PF to explain his approach and what he takes to be the meaning and import of his formulation. In lieu of that, I would have to say that Christian's Bell stuff is
not a refutation of Bell's work or disproof of Bell's theorem (that is, wrt the universally accepted minimalist interpretation and unarguable application of Bell's theorem).
The reason I care at all is that I've been thinking about writing something about the MWI and about interpretations in general, and if I ever do that, it would be good to know if this journal has a bad reputation.
