The Nature of Bell\'s Hidden Constraints by Edwin Eugene Klingman

Dear Lutz,

Thank you for your supportive comment. There are number of experienced players here who agree wholeheartedly with your take on things.

One purpose (as I understand it) of this FQXi topic is to ask whether math has, or can, "trick" physicists in any significant way. My essay answers in the affirmative. Specifically I claim that John Bell's math is impeccable, else his theorem would not have lasted for 50 years as it has. It is his physics that is not impeccable, due to his significant oversimplification.

At first this may sound suspicious. How could physicists be fooled by incorrect physics for 50 years? Is that conceivable? While it is obvious that his math can be, and has been, checked, why not his physics? That is more complicated.

First, there are between half a dozen and a dozen different "interpretations" of physics. Which one should we apply? Second, most physicists accept the paradigm of Goudsmit and Uhlenbeck from 1925 (before there was quantum mechanics) that

"The projection of spin on any axis is +/-1."

This classically makes no sense, and Susskind and others have acknowledged that this is physically incomprehensible. That is, it is part of the "mystical" tradition of quantum mechanics.

Generally speaking, while physicists have no qualms or hesitation about attacking math errors, few are willing to go to war against mystical aspects of orthodoxy which are best summarized by Feynman's quote that

"Nobody understands quantum mechanics."

[Updated by Matt Leifer to: No one understands the quantum state. (see my endnotes)]

And so Bell's seemingly reasonable, simple interpretation along the lines of Goudsmit and Uhlenbeck, remains unchallenged. Even at the expense of giving up local causality!

An ironic aspect of this is Allain Aspect's remarks in his introduction to Bell's book, to the effect that

"The conventional wisdom among physicists was that the 'founding fathers' of quantum mechanics had settled all the conceptual questions."

Aspect claims that

"Bell's example helped physicists to free themselves from the belief that the conceptual understanding that had been achieved by the 1940s was the end of the story."

Today, of course, Bell is the 'founding father' and once again the conventional wisdom is that Bell has "settled all the conceptual questions."

I argue that this is not the case and it is not an argument that those heavily invested in Bell wish to hear. Hence the "hear no evil, say no evil, see no evil" reception that my essay has mostly received from the establishment.

In political terms this was called, "benign neglect", defined generally as "an attitude or policy of ignoring an often delicate or undesirable situation that one is held to be responsible for dealing with."

Edwin Eugene Klingman

Dear Ed,

Thank you for your kind remarks. I was able to follow your link to the 'animated physics' page. The page, as far as I can determine, is strictly about the photon test of Bell's theorem, so it's probably appropriate for me to remark again on this.

My essay of course concerns the Stern-Gerlach scattering of magnetic dipoles in an inhomogeneous field. I have developed the energy-exchange physics of the model and show that the initial angle theta that the spin makes with the field can both predict the individual results of measurement (quantum mechanics cannot do this) and these completely local results can, after the fact, be correlated with the paired remote results to yield the quantum correlation, -a.b, which, again, Bell claims to be impossible. The theta-dependent physics shows up in the distribution of scattering angles, so it is paramount that Bob and Alice's measurements include this physical 'amplitude' information.

Photon experiments are different in nature. The photons trigger a count and the count contains but obscures the corresponding initial value of the corresponding 'hidden variable'. I have not completely analyzed the photon problem as I understand the physics of Stern-Gerlach much better than the physics of photon experiments.

Although some argue this point, Bell discusses Stern-Gerlach and clearly had Stern-Gerlach in mind when he derived his theorem, and as I show, it is the Stern-Gerlach eigenvalue equation that led to his confusion. For practical reasons, most actual experiments have been photon-based, and these results match the quantum predictions (or at least exceed Bell's constrained model.)

All of the statements in the literature that I have seen are a variant of "no local model can match QM." Thus it is only necessary to show one local model that does match the QM correlation to disprove Bell's theorem, and, for the reasons I state above, I have chosen a local model of Stern-Gerlach.

My assumption, which I have not proved, is that if a local model of Stern-Gerlach produces the quantum mechanical correlations, then it is very likely that a local photon model will also violate Bell. But it is not necessary to show this to disprove Bell. My local model does this, and makes clear where Bell went wrong.

Thanks again for your response.

Best,

Edwin Eugene Klingman

Alex,

I think you are completely mistaken that my essay is not on topic. In the first pages I address several FQXi questions that are answered by my essay. Further, FQXi stands for "fundamental questions", and there are few if any questions more fundamental than whether local causality exists, or not. I believe that my essay is exactly what Templeton hoped for when he funded FQXi.

Your other point, that it is not for a "general audience", is somewhat more relevant. Scientific American also supports FQXi; they of course desire essays that can become articles in their magazine. My essay is too dense for most general audiences, but if you read the comments above you will find that the FQXi community finds it appropriate and relevant.

I hope you did not waste too much of your time before discovering it was not your cup of tea.

Sincerely,

Edwin Eugene Klingman

Dear Efthimios Harokopos,

I saw your complaint about scoring on your thread before I commented on your essay, so I knew that you were already upset about scoring. What I had not realized was that you think you can, in general, correlate comments with voting behavior. It is upsetting when low scores are received for no apparent reason. During the first weeks of this contest I was the top paper with a 10 (every time I looked at it I reminded myself that there was nowhere to go but down) and then I received at least two 1s and a couple of 2s. I was of course not happy about this.

There are no rules for how one "should vote". After several essay contests I have a voting strategy that I think is most effective. I typically wish to see all essays before I decide how they should be ranked. I think it is presumptuous for you to assume that my voting behavior should match your ideas of voting but if you are hostile over this point it's probably best you not read my essay.

You have written an essay in an earlier contest, and you should therefore be aware that no one is happy with FQXi voting. There is always some vote trading going on and the best policy is not to discuss votes in comments and not to combine the timing of comments and votes to 'send messages'.

Your implication that I would give high praise and low scores is unwarranted, and there is no basis for you even to suggest this. The fact is that I have not scored your essay, nor most essays, as I have my own policy or voting strategy. I think your complaint about voting is valid, but your assumptions about how I should vote are invalid and not appreciated.

Edwin Eugene Klingman

Dear Bob Shour,

Thank you very much for your kind remarks. I consider giving helpful feedback and voting separate issues. This issue never goes away, and there has been extensive discussion about voting problems after several of the contests closed. Many policies have been suggested, but no panacea has been found. An optimistic view is that 'the wisdom of crowds' will prevail, and that the shenanigans will average out, but who knows. At least as serious a problem, is that the judges often ignore top ranked essays that go against the party line, and the FQXi membership appears to take care of itself quite well thank you. Therefore, even if we could find a just and fair way to vote, it would just be overridden by the judges, all of whom are part of the establishment and see as part of their job protecting the establishment under the guise of "keeping FQXi from becoming a joke."

FQXi offers a rare opportunity to tackle serious issues in a serious venue that is, for the most part, operated professionally and civilly and even enjoyably. Even more important it forms a permanent record of one's thoughts, theories, and comments. In addition the cross stimulation of ideas from very knowledgeable and creative people is worth its weight in gold. I would not keep coming back year after year if I did not think FQXi's good points far outweigh the bad points.

Thank you again for your supportive comment.

My very best wishes,

Edwin Eugene Klingman

Hi Jonathan Tooker,

You are correct that quite a bit of explanation is included in the above comments, but it takes a while to plow through them. The short version is that Stern-Gerlach is not measuring spin directly; it is measuring spin-dependent scattering from an inhomogeneous field. And the inhomogeneous field is not described by Pauli's simple eigenvalue equation, due to the non-zero and non-trivial gradient of the field that must be included in the Hamiltonian. Instead, depending on the specifics of the gradient, there is a continuum of eigenstates, not binary eigenstates.

When the physics of the particle interactions are taken into account, the amplitude predicted by the local model can be correlated (in pairwise fashion) and the result (as shown on page 7) is the quantum correlation -a.b. Bell claims this is impossible, and the consensus today as evidenced by numerous statements in the physics literature is that "no local model can produce the quantum correlation". Bell assumes that the particle only precesses, but this is true only in a constant field, which yields null results and thus a logical contradiction. Bell apparently believes that he is measuring spin directly, and assumes spin can only have two possible results +/-1, thus he throws away the actual measurement data and replaces it with an abstraction, the +/-1 dichotomy. This prevents his constrained model from ever obtaining the correct correlation. In other words he is applying the wrong map, Pauli's (provisional) precession eigenvalue equation in a situation where it does not apply and it is likely that he is doing this because he is confusing the Pauli equation with the Dirac equation as I explain in the essay.

Believing that there is a difference between what local models (as constrained by Bell) and quantum models can produce in terms of correlations, physicists have looked for an explanation for that difference. They have settled on entanglement as the explanation of the difference. If a local model can produce the correct correlation, as mine does, then there is no difference between the local and quantum correlations, and this would seem to have some significance for entanglement. And as quantum mechanics does not contain the initial spin, and cannot predict each local result, but only the correlation, then quantum mechanics is incomplete, in Einstein's sense. My model should be capable of being tested experimentally, and this issue decided.

Thank you for your comments. I hope this short summary answers your questions and of course will be happy to try to answer any other question.

Best regards,

Edwin Eugene Klingman

Dear George Rajna,

Thank you for your most gracious comment.

Edwin Eugene Klingman

Dear Leo Vuyk,

I see that you have put some effort into studying Stern-Gerlach. I was somewhat surprised by your statement of 'no smearing' of particle impacts on the screen, as there appears to be visible 'smearing' on the iconic postcard that Stern-Gerlach sent to Bohr, and Messiah (a primary QM text at the time of Bell) describes "the appearance on the screen of a more or less spread out distribution of impacts..." indicating that the atoms are not all in the same initial condition and implying a statistical distribution.

But I see you are referring to the lack of a continuous distribution with no separation. Please note that this is compatible with my model and can be explained with classical physics when energy-exchange between precession-mode energy and deflection-mode energy is taken into account.

I do understand your suggestion, and I find it both interesting and well thought out, based on belief in entanglement as a fundamental phenomenon.

My approach is not to deny entanglement as a starting proposition, but to explore Bell's conclusion that no local model can produce the QM correlation. I have presented a local model that does produce the QM correlations, unless Bell's constraints are imposed. This would seem to call Bell's constraints into question, and so I have analyzed the reason why he might have imposed such constraints. My essay offers an explanation, based on confusion of Dirac and Pauli eigenvalue equations, and assumptions of eigenvalue measurements. If this analysis is valid, then the rationale for entanglement is called into question.

But if one assumes entanglement from the start, then I believe your analysis is reasonable. The good news is that we have proposed two experiments that should be able to settle the question. As the belief in non-locality is certainly one of the most major challenges to intuitive understanding of physics, it seems very important to perform these experimental tests. I am beginning efforts to have my experiment performed, and I hope you are doing the same.

Thank you very much for reading, thinking, and commenting.

Best,

Edwin Eugene Klingman