Hi Michael,
What is shocking about the 500-pound canary sitting in Bell's very first equation is not the canary itself but some people's determined refusal to see it even after it has been repeatedly pointed out to them (for example in my Chapters 1, 4, 6, 7, 8, and 9). A(a, L) = +1 or -1 and B(b, L) = +1 or -1 are supposed to be mathematical functions. As such, they take values from their domain and churn out numbers that live in their co-domain (which is of course different from the actual image points, or measurement results such as +1, -1, etc.). It is then abundantly clear that any correlation between the numbers A(a, L) and B(b, L) is entirely determined by the topology of their co-domain. Now one may insist that the co-domain of A(a, L) and B(b, L) is simply the binary set { +1, -1 }. But then the completeness criterion of EPR can never be satisfied, as I have demonstrated in my book. Even if we disingenuously pretend that Bell's argument is somehow meaningful independently of the EPR argument, the set { +1, -1 } is by no means the only possible choice of a co-domain that can satisfy all the other requirements of Bell. One such set is a parallelized 3-sphere, which is a simply-connected collection of the zero spheres { +1, -1 }. The topology of this set then *necessitates* that the correlation between A(a, L) and B(b, L) cannot be anything but -a.b. One does not have to be Einstein to recognize this elementary fact. But instead of recognizing it some people's reaction is to reach out for the gun and shoot the messenger: How dare you point out the 500-pound canary in Bell's argument?
The above observation is actually not unrelated to your observation of a shift in the meaning of lambda in Bell's equations (1) and (2). The zero sphere { +1, -1 }, or even a collection of all such zero spheres, can only be a *totally disconnected* set. The set S3, however, is a simply-connected set, and hence more akin to the real number system rather than the natural number system. It is therefore not surprising that EPR correlations are entirely determined by the topology of S3. The shift from a frequency interpretation of lambda in Bell's equation (1) to the probability interpretation of lambda in his equation (2) goes hand-in-hand with the shift from a totally disconnected co-domain { +1, -1 } to the simply-connected co-domain S3. This shift is then the 500-pound canary in his equation (1).
Your advice to put Bell in the frame is very wise, but if diplomacy were my strong point I would not be in this position of having to defend my work and career (you are aware of the kind of names I have been called by the lesser minds). Besides, I did try to put Bell in the frame (see, for example, my Chapter 3), but that only produced kneejerk reactions and shut-outs from the mediocrity (the public attempts to crucify me is only a fraction of what has been going on behind the scenes since 2007).
More importantly, it is not surprising that QT predicts SO(3) correlation for my experiment. In fact I am counting on that. I am counting on the fact that most people would not expect to see strong correlation. What my work (and your work) shows, however, is that QT is an incomplete theory of nature (in the EPR sense). What is more, in my view quantum correlations are the evidence that the physical space we "live in" respects the geometry and topology of a parallelized 3-sphere (more generally, 7-sphere). If so, then we should expect strong correlations between objects rotating in tandem even in the macroscopic domain. And that is what I am expecting to see in my experiment.
Best,
Joy
