Dear Alexei Grinbaum,
I very much enjoyed your essay on the mathematical basis and understanding of quantum mechanics. I would call attention to your statement to the effect that
"Mathematical reconstruction of quantum theory... must be complemented with a quantitative bound on the amount of correlations..."
based on what is claimed to be "a fundamental fact about nature: the amount of correlation between distant subsystems is limited by a non-classical bound..."
I realize of course that this is a current statement of the quantum credo, but I would ask that you read my essay in which I present a classical local model that does not respect this bound.
As a good part of the focus of FQXi's essay question is whether mathematics can "trick" physics, I exhibit an instance in which Bell's focus on "hidden variables" has masked his imposition of "hidden constraints".
Bell's math is impeccable. If there were a math problem, it would not have survived for 50 years. But Bell's physics is not impeccable, and could easily survive 50 years given the half-dozen to dozen current "interpretations" of physics, all generally describable by Feynman's comment that "no one understands quantum mechanics", examples of which your essay is full.
Bell begins with a logical contradiction, based on effectively assuming a constant magnetic field which, in turn, yields a null result in a Stern-Gerlach experiment leading to an obvious contradiction.
Given a local model that does reproduce the quantum mechanical correlation, one must ask where the error occurs in Bell's logic. I have analyzed this and attempt to present the answer in nine pages. I hope that you will find the time to read my essay. I realize this goes completely against the quantum orthodoxy, and therefore "cannot possibly be right", but from your own essay it appears that you claim
"All mathematical alternatives to the Hilbert space must fit the experimental value of this bound."
I understand (to some degree) your derivation of the value 2.82537 for bipartite correlations that differs slightly from the Tsirelson bound, but is, as you say, consistent with available experimental results. You also say your model is highly speculative.
The model I develop is consistent with available experimental results and agrees with quantum predicted correlations, while also "in line with Bohr's well-known insistence on the role of classical concepts." Moreover it should be subject to experimental confirmation, as required for all good physics.
Templeton, in providing the funds for FQXi, was not hoping to make assorted professors happy by picking up an easy $10,000 or so for an essay. He was hoping to shake the foundations of physics. We all know how likely this is to occur in the face of fifty-year 'Gospel according to Bell', but I hope you will willingly suspend your disbelief long enough to give my essay a fair reading, and then give me your opinion and feedback.
If Bell's correlation bound is derived from a very good math analysis of very bad (because oversimplified) physics, then it is not at all necessary for reconstructions of quantum mechanics to yield this feature, despite that it is today seen as "as important as the fundamental constants or the mass of the Higgs boson."
My very best regards,
Edwin Eugene Klingman