In another thread, the issue of perfect anti-correlation in the EPR-Bohm setup and Dr. Bertlmann's socks came up. If you are unfamiliar with Dr. Bertlmann's socks, then I recommend reading chapter 16 of Bell's book. The following is a variant of Bell's amusing example of Dr. Bertlmann's socks, which I recently posted in another thread:

Joy Christian wrote:

"Imagine you are walking from your home in winter and midway to your destination you reach out in your pockets for hand-gloves, but you find only one of them. At that moment you instantly know that you forgot the other one at home. Not only do you know that, but you also instantly know that the one you forgot at home is a lefthand glove if the one you pulled out from your pocket happens to be a righthand glove. Note that this is true even if your home happens to be in the far corner of the Universe. You have instant information about the handedness of the glove you forgot at home by simply looking at the glove you just pulled out from your pocket. That is perfect anti-correlation and it has nothing to do with nonlocality of any sort. It is just simple classical physics. The same is true for the anti-correlation of spins in the EPR-Bohm setup."

Here I want to stress the importance of this example in my 3-sphere (or quaternionic) model for the singlet correlations. The mathematical details of this model can be found in this paper. But the point I want to make here is that ALL correlations are Dr. Bertlmann's socks type classical correlations within my 3-sphere model, not just the perfect anti-correlations. You may wonder: How is that possible? Well, recall that the perfect anti-correlations are ensured by the condition A(a)B(b) = -1, where A(a) and B(b) are results observed about the measurement directions a and b. On the other hand, the singlet correlations predicted by quantum mechanics are of the sinusoidal form: << A(a)B(b) >> = -a.b. That requires sign flips from A(a)B(b) = -1 to A(a)B(b) = +1 for at least some of the directions a and b. How is that possible for Dr. Bertlmann's socks type correlations? Well, it is indeed not possible if we assume that we live in a flat Euclidean space R^3. But it is possible to have such sign flips naturally within a quaternionic 3-sphere. The sign flips from A(a)B(b) = -1 to A(a)B(b) = +1 are induced by the twists in the U(1) bundle over S^2 constituting a quaternionic 3-sphere. In my view, the strong correlations we observe in Nature are proof that we live in such a quaternionic 3-sphere. Let me reproduced an essential page from an influential paper. It discusses the twists in the U(1) bundle over S^2. It is from page 272 of T. Eguchi, P. B. Gilkey, and A. J. Hanson, Physics Reports, Volume 66, No. 6, pp 213-393 (1980):

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