Dear Tim,
Can you tell me what physical data (not 'logical') is being measured in the Stern-Gerlach-based experiment?
Can you tell me what is being measured in an Aspect-experiment?
And can you tell me HOW these are being measured?
You say "for analytical purposes these are treated interchangeably ... because as far as the theorem goes they have exactly the same form." This is exactly the trap Bell falls into based on Dirac and Pauli's eigenvalue equations having "exactly the same form"! That is significant mathematically but meaningless physically. It is true only if you consider "logical equivalence" to imply "physical equivalence." But you would be wrong to imply this, as they are distinctly and significantly different physics and different detection methods. To gloss over these differences is once again to move from the world of physics into the world of mathematics. That may be interesting to a mathematician, but it has no consequences in the real world, and certainly says nothing about "local realism" versus "non-locality". It is simple logic based on oversimplified (incorrect) physics.
You say Bell has "actually proven a theorem about such experiments" and I have "not disproven or shown any problem with his proof." As you see his proof as "a clean piece of mathematics" this is all that counts for you. But while I do not find fault with his mathematics, I do show that his physical reasoning is faulty, and good logic based on faulty assumptions leads nowhere of any importance to physics. This is what you steadfastly refuse to recognize.
I see no value in a "clean piece of mathematics" based on false assumptions, and your assumption of 'binary outcomes' for Stern-Gerlach experiment is faulty and your assumption that Stern-Gerlach and Aspect experiments are "analytically equivalent" because they have the same "form" is faulty, as far as any physical significance is concerned. You wish to divorce all physics from Bell's theorem and then claim it has physical significance. It does not, and shouting "does too!" forever will not change that.
Nor will it prevent my local model from obtaining the results Bell "proves" cannot be obtained.
Again, you say Bell has "proven a theorem". I too have "proven a theorem". Experiments confirm that Bell's model fails to match reality. Thus any theory based on his faulty model is of no physical significance. If an experimental test of my Energy-Exchange theorem-based physics fails to match my model, then I too will be proved to have a faulty model/theory. If, on the other hand, an experimental test of my theory shows it to match reality, then my model, which supports local realism, will be shown to agree with reality.
Finally, you ask what 'function' I am using to calculate the outcomes of my hypothetical experiment. Like your use of 'toy model' this is an incorrect description. My model is a Monte Carlo type model of the energy exchange physics and is a real computer experiment, not a 'hypothetical' experiment. I have presented the key 'function' as the significant contribution to deflection on page 5 of my essay, and I have described the physics in the papers referenced therein. I have stated that I use the standard formula for calculating expectation value and I have diagrammed the model on page 6, and showed typical vector data used in the model, and showed the cosine correlation derived from the model on page 7. This should be sufficient information to allow you or anyone else to develop a model for yourself and prove to your own satisfaction that it reproduces the quantum mechanical correlation, -a.b. My model is implemented in the very high level language Mathematica, and is not as transparent as lower-level code. The function, the standard formula, the physics, the diagram, and the data are all straightforward and produce the results shown. Bell did not make a mistake in his math nor have I made a mistake in my math, so that is beside the point. The point is the physics of Bell's model versus the physics of my model. One of us has definitely made a mistake in his physics. You are not attacking my physics, you are erasing the physics from the problem and pretending that logic and mathematics divorced from physics have physical consequences. That is a radical proposition.
Regards,
Edwin Eugene Klingman