Dear Richard Gill,

Thanks for your comments. It's good to hear from you. You are quite knowledgeable about Bell's theorem, and you have grasped a major point of my approach, which is that my theory does confirm Bell's theorem that quantum correlations cannot be matched when Bell constrains the outputs A(a,λ) and B(b,-λ) to ±1 .

My further point is that this mathematical restriction is non-physical, based on Bell's oversimplified model, at least in the case of Stern-Gerlach-based experiments.

Of course you are correct to observe that I should also analyze photon-based experiments, which I hope to do in the future. I am currently attempting to model my proposed SG-experiment and I'm working with others to perform the experiment.

Thank you for including the links to the Christiansen and Giustina experiments, with a brief overview of these. I'll check them out.

I also appreciate your comments on the last 50 years of Bell's experiments and I agree with you that it is likely that a new experimental era of Bell's experiments will make a lot of the discussion of the last 50 years superfluous.

Best regards,

Edwin Eugene Klingman

Thanks Edwin for the appreciation.

Bell's theorem (the inequality part) is mathematically speaking a complete triviality. Hence (of course, IMHO) your model confirms that quantum correlations cannot be matched when the outputs are constrained. Yes. The theorem is about binary outputs.

Some people identify "Bell's theorem" with a metaphysical statement about non-locality of QM. For sure, I believe that the metaphysical consequences are the astounding thing. But, depending on your inclinations, there are a lot of rather different conclusions which can be drawn. The theorem does not, in my opinion, show that QM is non-local. Non-classical, yes; but non-local, no.

A present day conventional statement of Bell's theorem (the metaphysical one) would be that quantum mechanics is incompatible with locality realism no-conspiracy. So if you want to keep QM you still have a choice of three items, (at least) one of which must be rejected. Personally I prefer to reject "realism" which is actually a misnomer - it's a rather idealist standpoint.

Bell points out in his wonderful Bertlmann's socks paper that there are four possible metaphysical stances or positions to take on those consequences. One of them, which he matches to Bohr, is "so what?". Or even "I told you so". That's the one which corresponds to rejecting realism. Bell himself tended to reject locality. He had no sympathy at all with conspiracy (super-determinism). Then it could also be the case that QM is wrong! (That makes four.)

Later Bell admitted that there was a fifth position possible: that the definitive experiment can never be done, because quantum mechanics itself prevents one from creating the required initial conditions. How to create a quantum state of two subsystems far apart, well localised in time and space, which one can moreover measure rapidly and close to ideally.

They've been trying for 50 years, getting close now, but there's still quite a way to go ...

Dear Edwin,

I don't doubt your conclusion that "Bell's 50 year old proof of the non-local nature of the Universe is an over-simplified solution to a complex problem". But I partly disagree with your map/territory analogy, and I disagree with what you say about numbers. (However, I'm glad we both seem to agree that consciousness is fundamental and physically real, and that there is no platonic realm!).

You say that math maps cannot necessarily be trusted, that math maps are "imposed on the physical territory", and that "the physical world can be trusted" to verify or disprove the math maps. Seemingly, your implication is that the nature of the underlying physical world black-box can't ultimately be known. This is what I would dispute - because we ARE reality, we are not separate from reality.

So I contend that every math map is actually somewhat like the territory. I'm not referring to particular mathematical equations, but to the general form of mathematical equations. They are always about 2 basic things: variables/parameters/categories, and relationships between variables/parameters/categories. It's no accident: we ARE reality, and we subjectively experience reality as having this type of fundamental structure. I contend that we can trust that fundamental physical reality has this general TYPE of structure: (what might be described as) categories and relationships.

The other comment I would make is about numbers and counting. I see counting (of things) as being an inherently complex many-step procedure which involves sophisticated comparisons and distinctions of things that are being counted and included versus things that are not being counted or included. Using our sophisticated comparison and distinction abilities, and using our sophisticated knowledge of the properties of materials, we are able to set up machines (e.g. computers) to represent numbers, and to represent counting.

I consider that the apprehension of reality always occurs at a granular, subjective level, rather than at an overall, universe-wide level. So I assume that both counting and computer-like representations are far too sophisticated to be occurring at the foundations of reality (i.e. at the particle level). I consider that there must be maximal simplicity at the foundations of reality, and that the subjective apprehension of categories and relationships is about as basic as you can get. Another issue is that categories of reality like mass cannot be represented by the "counting numbers".

Best wishes,

Lorraine

    Richard,

    I'd like to address several of your points:

    a.) The essential triviality of Bell's inequality, based on binary outcomes.

    b.) The metaphysical implications: realism, locality, logic (or conspiracy).

    c.) The meaning of your fifth case, "that QM is wrong?"

    To avoid a very long comment, I will limit this comment to a.).

    I certainly agree that (the inequality part) of Bell's theorem is, mathematically speaking, a complete triviality. And, as you note, my local model of spin in a non-constant field shows that quantum correlations cannot be matched when the outputs are constrained. As Tim Maudlin repeats above in many different ways, "the theorem is about binary outputs."

    The question (to a physicist) is what is the relevance of the theorem about binary outputs to physics? The implication seems to be that QM predicts ±1 and that the QM correlation agrees with experiment. Is that true?

    My interpretation of Bell's model is that he applies the wrong quantum mechanical map, Pauli's equation, which is applicable only to a constant magnetic field. The correct QM map would include the deflection energy in the Hamiltonian and would produce a split continuous spectrum of outputs (as observed in Stern-Gerlach), not a binary output. My local model does produce this continuum, and the values are correlated as both QM and experiment imply.

    The first objection to this might be simply that "the binary model of QM works!" But is that a consequence, or is in an obvious coincidence?

    The question is whether the 'binary' (±1) nature of Bell's (mis-)interpretation of Pauli has anything to do with the correlation? I believe it does not.

    Where, in the QM singlet-based expectation value (see eqn (1) in my essay) does the binary nature exhibit itself? One might claim, and even believe, that the sigma-dot-a and sigma-dot-b must be ±1, but the same correlation is obtained from measurements yielding the X cos(θ) values that my model produces.

    Discussion of Bell's theorem seems to assume a quantum mechanical 'calculation' based on actual measurement values (assumed identically equal to eigenvalues.) But that is not how the calculation is performed. Instead, the formal QM expression is written down [see the singlet eqn (1)] and the formalism assumes that the correct eigenvalues are being measured. Then, the usual approach to calculating the expectation value [see Peres, page 162 or JJ Sakurai, page 165] is based on an identity that is essentially a geometric relation, independent of the values of a or b or sigma-dot-a, etc.

    What is often forgotten is that (per MJW Hall) Bell's theorem includes the physical requirement of perfect anti-correlation when a = b. This implies normalization, since the -1 correlation must obtain, whatever the actual energy eigenvalues. [In fact the 'numbers' are E = ±hw/2, not ±1. I.e., normalization is built-in.]

    I think that it is difficult, on a physical basis, to prove that the expectation value -a.b derives from the binary nature of the Stern-Gerlach measurement. And, having briefly looked at the links you provided above, it is also difficult for me to relate the rules:

    '+1' stands for "one or more detector clicks",

    '-1' stands for "no detector clicks",

    to any underlying physics, whatever the statistical significance.

    But, as I have noted, I have yet to perform an equivalent analysis of photon physics [equivalent to my SG-analysis]. On the other hand, Bell's derivation, description, and explanation of his model is primarily in terms of Stern-Gerlach, so I don't think SG can be just 'written-off' as some seem inclined to do.

    Thanks again for your observations,

    Edwin Eugene Klingman

    Dear Lorraine,

    As you rightly note, we agree on the big things, and the small things will work themselves out.

    From my imposition of mathematical 'maps' on physical 'territory', and my trust in the physical world to tell us (in essence, by answering our experimental questions) which maps are valid and which are not, you seem to conclude that I imply that the nature of the underlying physical world cannot be known.

    As a physicist, developing theories to communicate models of reality to others, that is probably a reasonable conclusion. But as a living individual with consciousness, experience, and intuition, I have a personal understanding of the underlying nature of reality. One of the greatest physicists, Richard Feynman, said that, in essence,

    "More can be known than can be proved."

    I generally agree with your third paragraph. As for numbers and counting, I believe you are looking at a level above the actual physical phenomena that counters "do". As I understand biology, there are number of "counting" operations that occur at the protein level. And silicon counting chips are really quite simple, despite that they did not evolve but were designed by complex consciousness. But I think your last paragraph conveys what you're trying to say here. I did not mean to imply that individual fundamental particles count. But I don't think that many particles must be put together before a primitive count, applicable to local circumstances, can occur. The more generalized counting, as performed in computers and brains are of course very high level, as you insist.

    Thanks very much for reading my essay and for giving me these comments.

    My best regards,

    Edwin Eugene Klingman

    Edwin,

    Thank you for the well-written and interesting essay.

    In Einstein relativity, an object must be local, meaning a particle cannot be at one location one moment and a different location the next moment going faster than light in the process. Quantum mechanics is non-local, meaning a particle can be anywhere in its associated matter wave (some locations are more likely than others). Bell's inequality shows that (if quantum mechanics is correct) a local unknown variable cannot exist. Some non-local variable can exist and stay true to Bell's inequality. Some feel that is non-local variable in the form of entanglement could be instantaneous. Although instant communication is not disallowed by Bell's inequality it is not require by the inequality, instant communication does violate relativity and has not been found experientially.

    All the best,

    Jeff Schmitz

      Jeff,

      Thank-you. That is the most comprehensible concise statement I've read about the Bell controversy. jrc

      Dear Jeff,

      Thanks for reading my essay and for your thoughtful comment. I agree with your statement about relativity being local. The question of the non-locality of quantum mechanics is less clear and would appear to be interpretation-dependent. A key question is whether the wave function is ontological or epistemological, which, according to my endnotes quotation from Matt Leifer, is currently not known. My own opinion is that the wave function is ontological, and further, is induced by the linear momentum of the particle, |p> providing both real particle-and-wave aspects, as opposed to particle-or-wave. In this perspective, although the actual location of the particle may be known (quantum mechanically) only probabilistically, it is in reality relatively local. My picture is 'Bohm-like' but is not identical to Bohm's.

      Of significance in this picture of a local particle-plus-wave is the particle's spin |s>. As I point out on page 9 of my essay the standard QM wave function |ps> is actually a tensor product |ps> = |p> x |s> which is a mathematical trick to keep these separate entities joined-at-the-hip while making sure that the mathematical operations on the entities remain separate. Although the same quantum formalism is applied to linear momentum |p>, and intrinsic angular momentum, |s>, I do not perceive spin as inducing the deBroglie-like "matter-wave". Much of the weirdness of quantum mechanics is actually associated with the treatment of spin 'as-if' it also had an associated matter wave.

      In other words, I view quantum mechanics as a powerful statistical theory of real particles, not an essentially mathematical, almost non-physical, and rather mystical phenomenon. I agree with jrc that you have concisely summarized the prevailing perspective on QM. If, as I propose in my essay, Bell's model is actually oversimplified, then it is not clear what physical significance Bell's theorem actually has. Of course until I can treat the case of photons, most physicists seem reluctant to doubt Bell. As you noted in your response to my comment on your page, "a useful model is a wonderful thing".

      All the best,

      Edwin Eugene Klingman

      Edwin,

      Thank you for the vote of confidence. I am doubly glad that you did vote, because I had read your essay early on, and neglected to rate it, so I am happy to do that now that you brought it to my attention..

      I just couldn't think of what more to say. Though our mathematical methods differ widely, there are many physical principles on which we agree.

      All best in the competition,

      Tom

      Edwin,

      Many thanks for the encouragement. I see that part of your voting strategy is to vote late. You are a wise man:-)

      Best Regards and Good Luck,

      Gary Simpson

      Hi Edwin,

      Your response clarifies the situation for me. Although I cannot evaluate the details of your argument, it seems to me that you are making a point which is specific enough and clear enough that it should be possible for physicists to reach a definitive answer. Your essay has received a large number of comments, and a large number of ratings, mostly favorable in each case. These figures, and the content of the discussion, suggest that your ideas on this matter have a good chance of becoming accepted in physics. As I said, I do not have the background to be able to make an independent judgment, but the outlook does seem promising.

      Best wishes,

      Dear Laurence,

      Thanks for the very gracious comment. I yesterday spoke to Zeilinger, who was presenting a talk at Stanford. I noted that Bell derived and described and explained his theorem in terms of particles in Stern-Gerlach, and he concluded that "NO local model could produce the QM correlations." I asked whether, despite the fact that most experiments are done on photons, it would be significant if a local model of spin in Stern-Gerlach could produce the QM correlations. He answered, "It would be fun."

      What a difference from the usual response I get from theoretical physicists! Maybe I need to spend more time with experimentalists.

      Thanks again for your comment and your wishes.

      Edwin Eugene Klingman

      11 days later

      Dear Edwin Eugene Klingman,

      Thank you very much. Not just do the 315 postings concerning your essay so far clearly demonstrate the by far dominating interest in your essay. I also appreciate the very numerous and utterly helpful comments on essays by other contestants. Here you did not just address the essence quickly and precisely. You even decided to read some essays again after a while and provide an even more expert judgment.

      I see you the uncrowned king of the contest.

      All the best,

      Eckard

      2 months later

      Dear Edwin Eugene Klingman,

      I don't know if a post after the conclusion of the contest will reach you, but I am hoping it will.

      In retrospect, your essay was the most substantive for me because it dealt with quantum entanglement. I have a speculation about the role of dual reference frames in reference to entanglement. Might you care to read it? It is posted on ResearchGate as Entropy, Dimension, Reference Frames. I would be interested in your views because your article seemed to be skeptical about the 1982 experiment in a learned way, and because some of your comments in the article seem to resonate with ideas in the RG article I posted.

      Best wishes

      Bob Shour

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