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

Dear Tejinder, Anshu,

Thank you for reading and thinking about my essay. As the issue of Bell's theorem and physics is quite complex and exceedingly important, it's wise to revisit it until it is understood and can be accepted or rejected. References [2] and [4] contain much supporting physics. I do hope you find time and are motivated to understand my treatment of Bell. I believe the key fact is that my local model has produced the correct correlation, -a.b, which Bell claims to be impossible.

It is very important for everyone to understand that experiments do not "prove" non-locality. They prove only that Bell's models do not work correctly. The question is why? I contend, and offer evidence, that it is Bell's constraints that force any such local model to fail. This is an artifact due to incorrect choice of mathematical 'map', not a feature of physical reality.

You also ask, given that I establish the fundamental physical nature of counters and counting -- based on fundamentally physical logical operations NOT and AND that provide all arithmetic operators -- how I "build the number system, as well as geometry and algebra." Although many here trace the history of math, I rely upon Kronecker, who said "God made the integers, all else is the work of man." As you note in your essay, after analytical geometry every geometric object and operation can be mapped to numbers.

You also state in your essay "pattern recognition, with inputs from arithmetic, is the basis of algebra." The robot is designed with robust pattern recognition capability, and rich algorithmic resources. You mentioned "hardwired" human primordial perceptions such as object, size, shape, pattern and change..." The robot is hardwired to extract such features from numeric data and to build a "best" (using entropy extremization) feature vector, which is a 'primordial' Hilbert space representation. I used a US colloquialism which is probably inappropriate. I interpret 'persuasion' here as 'type'. The equations that conserve the eigenvalues [features] are eigenvalue equations.

Finally you ask whether there is a parallel with the cognitive processes you discuss. There is not in terms of the robot, which is assumed to lack conscious awareness. Of course the robot was designed by intelligence, but my purpose was to show that, based simply on the physical reality of logic gates/operators, one can go all the way to classical and quantum mechanics without conscious awareness, given sufficient measurements and appropriate pattern recognition and arithmetic processing capabilities. I have treated consciousness in an earlier FQXi essay, but the robot is not assumed to be conscious nor to evolve toward consciousness, only to be capable of very sophisticated mapping of numbers into features.

As you observe, there is much more information in The Automatic Theory of Physics. Thank you again for your comment and your questions.

I hope you reach some conclusion on Bell.

Best,

Edwin Eugene Klingman

Dear Steve,

Thanks for reading and commenting. I would agree with you about 'useful discourse', but Bell has had such a profound effect on our physics, it is necessary to discuss him, useful or not. And I'm glad you were pleasantly surprised by the flaws in Bell's approach. Some responses to these flaws are not so pleasant.

I have found Hestenes' approach very worthwhile, as every entity in his math has both a geometric definition and an algebraic definition, which is a far greater coupling than exists in other maths.

I'm not sure how empty space emerges from action, but I tend to view space as containing at least the gravitational field and hence not being truly 'empty'. But obviously, this aspect of reality is one of the less agreed-upon features of modern physics.

Thanks again. I'm glad you found my essay understandable. That was my main worry.

Best regards,

Edwin Eugene Klingman

Dear Miss Sujatha Jagannathan,

While I have stated that intuition should guide our choice of the many mathematical maps applied to physical reality, you are correct that I did not emphasize the conceptualization of intuitive notions. Yet the classical model that yields QM correlation is very intuitive, and it contradicts Bell's extremely non-intuitive concept of non-locality.

Thanks for reading and commenting. I look forward to reading your essay.

Best,

Edwin Eugene Klingman

Dear Vladimir,

Thanks for your comment. That is a very interesting question! Einstein of course contributed when he confused 'synchronicity' with 'simultaneity', and again when he replaced the gravitational field with "curved space-time". But I believe the biggest disconnect between the math of physics and the intuitive trust in physical reality probably occurred when physicists began believing in "superposition" as if it were a physically real condition rather than a mathematical artifact. I think that's where the train left the tracks. After that physicists felt comfortable simply introducing another 'quantum field' or equivalent whenever a new problem needed to be solved. Today no physicist knows exactly how many 'fields' there are in physics, nor has any idea which fields are 'real'. As so many essays and comments here state, finding physics to fit the math is the wrong way to go. Much better to use math to describe real physics.

My best regards,

Edwin Eugene Klingman

Dear Vladimir,

I have looked at the interview with Alexander Zenkin. He begins by noting the super-abstractionism of the Bourbaki, leading to two mathematicians working in neighboring rooms but unable to understand each other. Almost all of my math education took place at the peak of the Bourbaki school, and I have been trying to overcome this handicap ever since. The rigor and rigidity is the antithesis of what a physicist should use math for.

As I've noted in a number of places, I do not believe infinity 'exists' in physical reality, so (except for my early math education) I have paid no attention to mathematical treatments of infinity. In the paper Zenkin mentions that Cantor designates 'a series without end' by the symbol omega and then, skipping through the potential infinity of the series, continues to count further: omega +1, omega +2, ... Any logic based on such a scheme would seem to bear little relevance to physics.

In short, I am very much in sympathy with the views expressed in the paper.

I would also point out to you that Eckard Blumshein's essay has just posted, dealing with similar aspects of mathematics and its relevance to physics. I highly recommend his essay and think you will enjoy it.

Best,

Edwin Eugene Klingman

Dear Eckard,

I caught the misspelling immediately but didn't want to put another comment merely to draw attention to it. I use voice recognition software which is surprisingly good on well-known names but can make the type of error that you saw on some names. Of course it is my duty to edit my own comments so I can't really blame software. Usually I simply try to cut and paste names in to guarantee correct spellings, but sometimes I screw up.

Thanks for your feedback on the omega +1, omega +2, etc. I always like to receive your blessings on this type of issue.

I am curious as to any feedback you could give me on the technical content of my essay. Did you feel that you understood it? Did you find any minor mistakes? Do you have any comments?

I believe I saw a few weeks ago a comment that you have personal issues taking up a lot of your time, and I realize that my essay is time-consuming. So if that's the case ignore my above request for such comments.

Best,

Edwin Eugene Klingman

Dear Vladimir,

It's good to see you back. Thank you for your comment. You are correct that the anti-parallel spins retain their correlated directions until they reach the remote measuring instruments. This used to be known as conservation of momentum, rather than entanglement. Once in the measuring device the energy exchange process that I describe provides a further correlation between their initial spin and the direction of instrument, and this is the correlation that yields the -a.b result that both quantum mechanics and actual measurements provide, and that Bell says cannot be provided by local models. Although my local model proves Bell wrong and I explain exactly why and how he is wrong, his word has been gospel for 50 years and that's a brick wall to come up against.

The interesting thing, in terms of this essay contest on math and physics, is that Bell got his math right, but his physics is wrong because he oversimplified the problem. Apparently most of the fighting has been over his math and in the end everyone agrees that his math is correct. As you have noted, the physical analysis of the actual, more complex, phenomena is rather complicated. In fact, even Bell's oversimplification is complicated, so unless one has lots of time and interest in this problem it's just too complicated to fool around with. Nevertheless, it is a problem of major importance, and I am producing more results and working toward an experiment and I'm not going away.

I won't try to explain the theta-dependent experiment here, but it's really a rather minimal variation on the standard Stern-Gerlach experiment. Considering that was done in 1922, I'm sure we should be able to do a reasonably accurate experiment today.

And of course I always look forward to your beautifully illustrated and interesting essays.

My very best,

Edwin Eugene Klingman

On another thread Tim Maudlin noted that "The reason that people stop responding to your incorrect claims about Bell is that you do not pay any attention to what they say."

I responded as follows:

Dear Tim Maudlin,

There is quite a difference between "not paying attention" to what you say, and "agreeing with what you say." For example you have said approximately 15 times that the Stern-Gerlach-type experiments describe:

"Binary outcome space" , or

are "coded as +1 or -1", or

are "outcome1 and outcome2", or

are "spin up and spin down", or

"red light went on" versus "green light went on", or

are "above the midline" or "below the midline".

It's pretty hard to miss that you believe the experiment is based on binary outcomes.

What you have missed, and missed a number of times, is that this suppresses the physics of the situation.

As an example, when particles are collided at LHC, some of the collision products come out 'above the midline' and some of them come out 'below the midline'. Nobody cares -- there is no physics in analyzing LHC scattering experiments in such a simple manner.

I've tried to tell you, in a number of different ways, that Bell ignores the physics going on in the Stern-Gerlach apparatus. And by constraining the outcomes to be simple binary outcomes he throws away the information that can be derived from the physics of the experiment. Physicists care (or should care) about this information. The fact that when this information is thrown away the physical model cannot match reality, is significant. Applying correct math to incorrect physics makes no sense, but that is exactly what Bell has done.

As John Cox remarked, as an academic philosopher, you find it easy to take the physics out of math while leaving the math in physics. As a physicist I don't find it that simple. You have twice stated that I pay no attention to what you say. I have reviewed our comments and find it is difficult to discover any response from you to my valid points. And when I supplied data that contradicted your statement about neutron results, and asked you for any data that would support your position, you said you couldn't imagine why anymore time should be spent on the argument.

In fact, having reviewed your comments, I do have more responses.

Edwin Eugene Klingman

Dear Jim,

Thank you for your kind remarks. Yes, it's a pretty dense essay, but you clearly know the secret - which is found in multiple readings. Unfortunately not everyone has the time to read an essay more than once. But that's the only way to understand very complex issues. I thank you for doing so.

As I mentioned to Vladimir above, even Bell's oversimplified analysis is complex. When one tries to deal with the more complicated physics going on when a magnetic dipole interacts with the non-homogeneous field, and view this interaction from the perspective of classical determinism while at the same time keeping in mind the quantum mechanical perspective, it gets, as you say, pretty dense.

Why would anyone even care? Only because Bell, on the basis of correct math applied to incorrect (because oversimplified) physics concluded that nature is non-local. And because no one could find error in his mathematical proof the world at large accepted his physical conclusion. A perfect example of what this essay contest was designed to bring out - the tricks that math can play on physics when one is not paying close attention.

I look forward to reading your essay and commenting on your thread.

Best,

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