Gary,
I neglected to answer one of your points in your previous comment that is relevant to your latest comment so I will do so now. You ask for clarification of "the distinction between SG and EPR was that SG established two spin states and that EPR established that distance was not a consideration when considering entanglement."
Consider the Stern-Gerlach experiment in 1922, three years before Goudsmit and Uhlenbeck proposed that the intrinsic angular momentum or position-independent spin was half integral. The SG experiment has a twofold character by splitting a beam. Since it's unlikely that the inhomogeneous field could be exactly represented, the specifics of interaction of spin with the local magnetic field was of lesser concern. What counted was the two-fold splitting of the beam of silver atoms, attributed now to spin.
In SG, the gross nature of this two-fold splitting is sufficient. But the EPR experiment, based on comparison and correlation of two SG experiments performed on a singlet state can be treated as a discrete (binary) problem in physics or as a continuous classical physics problem. Bell's gross model requiring binary measurements effectively erases all of the "hidden variable" information of the classical local model. A much finer resolution of the physics of the particle in the heterogeneous field is required to match the predicted quantum mechanical correlation. That is a key point in my essay.
I propose theoretical and experimental exploration of unconstrained and constrained models of EPR. But the fact that my unconstrained model violates Bell's theorem has led to conflict with the simple binary SG model, and consequently quantum mechanical questions, which I answer in the essay in terms of eigenvalues maps.
As for entanglement, it is represented in the figure at the bottom right of page 6 in my essay. Entanglement is the shaded area between the cosine curve ( -a.b ) and Bell's linear curve ( -1 2 theta / pi). Bell claimed that local realism could not match measured reality, i.e., the -a.b correlation, because his model failed to do so. I view his model as too simple, and focus on the constraints he imposes on the models.
If a local model, with or without constraints, can exceed Bell's linear prediction, then entanglement will be diminished. And if a local model actually accomplishes the -a.b correlation, then the rationale for entanglement disappears. As you observe in the figure at top of page 7, my local model does produce the required correlation, -a.b.
Entanglement, is weird, mysterious, poorly defined, and, according even to those experimenters who made their reputation showing -a.b, it is "difficult to swallow". My model yields the cosine curve, so there is no shaded area, that is, no entanglement, so that's the answer to your last two paragraphs in the above comment.
Entanglement was invented to explain how correlation could occur that no classical model could produce. If a local classical model can produce the correlation, then entanglement is unnecessary. I say good riddance.
I will look at your equation above, and if I have anything sensible to say will comment again.
Thanks for your continuing interest in this problem.
Edwin Eugene Klingman
