I already figured it out some years ago.
QM gets -a.b according to Susskind (ref
https://www.youtube.com/watch?v=XlLsTaJn9AQ: I think that is the correct lecture Part but I am too ill to want to look it up)
As I have said elsewhere, Susskind's argument is really only a double Malus experiment and not a Bell experiment. Susskind takes a particle vector pointing at alice=0 degrees (so A=1) and then the opposite vector is dropped or projected onto the vector bob=theta to find the result B= 1 or -1.
When A=1 and B= + or -1, then that is a Malus situation.
One might think that if we take A=-1 aand B = + or -1 and say we aggregate these two circumstances together then we get a Bell situation overall. This may be true but I have yet to see a proof that a general vector theta, not equal to alpha or beta, will project onto alice and bob angles giving the correct Bell result. It would be a Bell result in this circumstance.
I wrote it up here:https://vixra.org/pdf/1610.0327v4.pdf
on page 10 in 2016/7
Extracts:
As a back-of-an-envelope check, the quantum mechanics calculation used by Susskind for 0.073 had as its final line the expression 0.25 ∗ (1 − 0.5 ∗ √2). A similar expression can be derived using simple algebra and the constraints on a 2x2 symmetrical table, given the target correlation.
etc etc
"= - 0.707 = − 0.5 ∗ √2
=> 2 * (N++) - 0.5 = - 0.5 * 0.5 * √2
=> (N++) = 0.25 ∗ (1 − 0.5 ∗ √2)
=> (N++) = 0.073 "
Maybe someone can point me to the QM proof of the generalised correlation of vector projections for the Bell case rather than the Malus case?
Another issue is "where is the physics, Fred?" This whole thread looks like merely maths. I do understand your pleasure at finding a maths-only apparent breaking of something. (However, surely it has to break or disobey CFD.) I distrust the chopping and changing of strings of outcomes. My own approach to Bell's theorem hinges on my idea of what the physics might be. If the particle vector is say a precessing vector (surely the detector would cause a precession? I followed maths of that some years ago), only exact projections would cause a correl of -0.707 at theta=45 deg. And we cannot allow exact projections in the laboratory or even in the theory. I have tried to prove (unsuccessfully) that the maximum abs correlation is 0.707, by using incremental changes to the projections. But it seems very obvious that it is a maximum. So I looked for a method that bypassed the Bell inequalities instead of breaking them. And that is retrocausality. Bell's theorem does not even apply to my retrocausal version of what is really going on the laboratory in a Bell experiment.
Also, are your graphs showing that Bell's Inequalities are broken? Every once in a while you state that nothing can break the Bell Inequalities. So what is the conclusion?