Dear Edwin,

To say that it is "de facto true" that Bell's example about spin is just illustrative and no part of the theorem does not address the point. The entire discussion of the detailed model makes no contact with the theorem. The theorem holds of any theory at all that is local (in the sense Bell articulates) and makes certain statistical predictions. That these are predictions about anything called "spin" or anything treated quantum-mechanically is no part of the theorem at all. All one needs are the conditional probabilities for outcomes of certain experiments, which need not be described in any more detail than "Instrument 1 is set to setting A" and "the outcome is outcome 1" or "outcome 2" One can use "spin measurements" in quantum theory as instances of this sort of thing, where the setting is the orientation of the Stern Gerlach magnet and the outcome is a spot on a screen appearing in one place or another. Clearly any theory at all might make such predictions. Since the theorem is only about these sorts of conditional probabilities, it is in no way "about" quantum theory.

Your initial characterization of the question Bell was asking is not accurate. He was not asking whether one could somehow find a theory that predicts the outcomes of experiments deterministically, he was interested rather in whether any local theory at all (deterministic or probabilistic) could recover a certain set of predictions. He insisted on this many times, and complained that his point had been almost universally missed. In fact, the paper relies on an understanding of the EPR argument, which had already established that locality can only be recovered in a situation with perfect EPR correlations if the theory is deterministic, but, as Bell says, "It is important to note that the limited degree to which determinism plays a role in the EPR argument, it is not assumed but inferred. What is held sacred is the principle of 'local causality'-or 'n o action at a distance'. Since the EPR correlation are recoverable by a local theory only if it is also deterministic, one can then ask about constraints on such theories. Bell demonstrates such constraints.

On p. 4, you list what you call "Bell's key physical assumptions". None of these are assumptions or premises of his theorem. The theorem applies to any situation in which the outcomes of certain experiments can be categorized as, e.g., "outcome 1" or "outcome 2", and correlations between the outcomes on different sides predicted. The theorem, which is not particularly about spin, has none of these assumptions as premises, so no discussion of them can have any significance for the theorem.

What is particularly odd about your presentation is that you claim that Bell has a "hidden constraint" in his proof, but nowhere actually discuss the proof itself, but rather only the illustrative example. It would help if you would actually point out where in the proof the supposed constraint appears. Your rather extensive discussion of the toy model makes no direct contact with the theorem itself.

As for your own model, let me try to understand the claim that you make. Your equation 4 has the consequence, as you say, that the deflections produced by Stern-Gerlach magnets will not be quantized, that is, that we cannot, as a practical matter, distinguish the outcomes into two classes, usually denominated "spin-up" and "spin down", determined by the location of the detected particle. If that is correct, then your model certainly does not reproduce the actual phenomenology reported in the lab, nor the predictions of quantum theory. Since the correlations discussed by Bell are correlations between the outcomes on the two sides, which are taken to always be either "spin-up" or "spin-down", and since these are also the predictions of quantum theory, then it would appear that your model actually makes no contact with Bell's topic. You do not explain how the top graph on p. 7 was created, or even what it means. Here is a key sentence from that page: "If I throw away this θ -information by truncating the measurement data, i.e., setting the results to A, B = ±1 , my constrained model cannot produce the correct correlations." The obvious reading of this sentence is that in your model, the outcomes of the experiments are not categorized into two classes, spin-up and spin-down outcomes, and that if one requires such a categorization of the outcomes then you get Bell's result. But it is an observed fact that the outcomes do sort into these two classes, and it is a prediction of the quantum theory that they will, and furthermore if they do not then it is not at all clear what the meaning of "correlation" in your theory is, since the predicted correlations are between these binary results. So you it would help if you could do these things:

1) point out where the supposed "hidden constraint" actually appears in Bell's theorem.

2) Explain, if your model does not predict quantized outcomes for spin experiments, what bearing it has on quantum theory, or Bell's theorem, and what you even mean by a "correlation" between the results on the two sides.

Regards,

Tim

Hi Edwin,

I congratulate your professionally written essay.

In another thread you said:

"I built first in my mind and then built a theory around. I believe modeling physics in your mind and then describing it mathematically is to be preferred to studying math and trying to guess what physics it describes. I believe that much math does not describe 'reality' in the same sense that much fantasy and fiction do not describe reality."

I agree with this statement completely. I followed this procedure to formulate Model Mechanics. Although we have different models of reality, but that is to be expected.

I believe that there are many assumptions in relativity are wrong. Specifically the idea of Relativity of Simultaneity (RoS). Why? Because it is in conflict with the idea that the speed of light is isotropic in all frames.

Regards,

Ken Seto

    Tim,

    Is it your contention that an experiment must result in only outcome A or only outcome B, to be a valid experiment?

    The excluded middle in the spin operator Bell employs constricts vectors to ether parallel or perpendicular to the eigenvector of results. Lambda is constrained to +or- 1 by the artifice of the form of the set of three intervals being mixed half-open and closed. The final sign element is left open ended for the simple expedient of breaking symmetry, but wholly arbitrarily so at 'less than' (however infinitesimally) 180 degrees for either plus or minus rotation; lambda = 1(pi). A different choice of spin operator might conceivably have a form that would produce |0=

    Tim,

    sorry, my post got chopped. I'll continue...

    The point being that Bell's choice of operator was the standard of the industry at the time, which he tried to find a way around. A spin operator of a form producing a continuous relation |0=

    Dr. Klingman, if you will send your email address to genebarbee@msn.com, I will send you an excel spreadsheet with all of the meson and baryon energies and decay times almost perfectly matched.

    OOPS,

    the server is interpreting symbols as commands....

    ...A spin operator with a form producing a continuous relation of equal to or greater than zero, but lesser than 360 degrees, would still break symmetry at 2(pi) being a half-open interval, and the congruent +or- rotations would zero out. The lambda plotting perpendicular to the eigenvector would not experience any growth whether being set at 1 or less than 2. But the dispersion of results would plot different from the typical Bell thin cigar. And in conjunction with the Theta deflection could be expected to produce cluster results for +and- plots which if juxtaposed would approximate the real physical split dispersion pattern of detections in the original Stern-Gerlach experiments.

    I think this is the general point Dr. Klingman's arguments illuminate. Bell cannot be said to generalize to any and all theoretical predictions. Only those which obtain results in the form of only outcome A or only outcome B.

    I don't see John Bell as having been politically niave. He certainly didn't believe the universe to be binary, or reality to be 2-D Hilbert space. He exposed a dichotomy. He was simply being shrewd. jrc

    Dear Tim,

    In the interest of full disclosure, I should probably mention that when I sent you the 130 page precursor to my essay, detailing the local spin model and the Energy-Exchange theorem upon which my model is based, I did not realize that you had written a recent book explaining Bell's theorem and thus my model conflicts with your book. I know this would not cause you to obfuscate or distort my arguments in any way, but readers of the comments can at least realize what is at stake here.

    You are apparently implying that Bell did not have any physics in mind, or any quantum mechanical eigenvalue equations, and made no physical assumptions in analyzing EPR, Stern-Gerlach, spin, and QM correlations, despite that he discusses all of these in detail in his papers, and despite Bertlmann's statements to the contrary. Readers can decide whether this makes sense.

    Your first claim above was that my energy exchange model is global, but as you no longer mention this I assume you now realize it is a local model.

    So let me simply use your terminology. You state that Bell merely assumes an experiment in which there are two outcomes, outcome 1 and outcome 2, plus a probability distribution for outcomes. No constraint should be imposed other than local causality. That is exactly what my local model does.

    One experimenter, Alice, selects control variable a, and the theory ('any' theory, as you state) should yield either outcome 1 or outcome 2, based on actual EPR splitting observed. Any model actually based on physics will use her setting plus the local physics (denoted by lambda) to produce outcome 1, denoted by +A(a, lambda) that belongs to class 'up' or outcome 2, denoted by -A(a, lambda) that belongs to class 'down'. As is both obvious from the SG data and according to a standard QM text at the time, each class is "statistically distributed over a somewhat extended range". [See p. 3]

    Bob's remotely operated experiment also yields two similar outcomes +B(b, lambda) and -B(b, lambda) which are based on the physics of the (any) local physical theory under consideration.

    Then, as you note, Bell takes the correlation between the outcome of the two sides (in pairwise fashion) using the standard formula for expectation values. The standard formula, applied to my model's local outcomes, and plotted against the angle between Alice's and Bob's control settings, yields the top figure on page 7, exactly as predicted by QM. This is the cosine curve -a.b that Bell claims to be impossible for any local theory.

    Now you ask where in his theorem do Bell's constraints appear. They appear in his first equation (1) where he states that +A(a, lambda) must equal +1, and -A(a, lambda) must be constrained to -1. There is no valid reason for these constraints, as they have the effect of throwing away the actual physics applied by (any) physical theory. I have explained why he erases this information in my essay and in more detail in my reference [4].

    It is Bell's constraints, imposed on any local physical theory, that results in failure to match QM predictions. My local model does produce QM predictions.

    Your use of 'toy model' is also incorrect, as toy models are 'reduced dimension' models. My model is full 3D and is a real physical model. Your statements about 'spin up' are also misleading, as I have explained in detail in reference [4]. In short, my model does predict quantized outcomes for spin, but the outcome of the experiment is not a direct measurement of spin, but a position measurement that reflects the physics of the spin scattered by the inhomogeneous field. Failure to recognize this has led to 50 years of non-intuitive nonsense about non-locality.

    Regards,

    Edwin Eugene Klingman

    Hi Ken Seto,

    Thanks for your nice comment. Based on your essay I'm not surprised that you agree that modeling physics in the mind and then describing it mathematically is to be preferred to searching for physics in mathematics. It is hard to think of any significant physics that was not found in this way.

    As for your comment about special relativity, have you seen the following:

    ">Scientists slow the speed of light](https://www.bbc.com/news/uk-scotland-glasgow-west-30944584

    )

    The arXiv paper is here: Photons slower than speed of light

    This may shakeup things, but then, some things certainly need to be shaken up.

    My best regards,

    Edwin Eugene Klingman

    Dear basudeba,

    Thank you for reading and for your fine comments. I will address specific statements. You recalled Messiah's quote that "the initial states are statistically distributed over a somewhat extended domain." This fact is interpreted differently according to the two eigenvalues maps usually associated with spin. These interpretations are discussed in detail in Spin: Newton, Maxwell, Einstein, Dirac, Bell.

    Then you note that my local model does produce the correct correlation, based on energy-exchange physics, and remark that some assumptions of quantum mechanics become questionable, as a statistical model cannot ensure that all relevant parameters have been woven into it.

    That is correct, as quantum mechanics does not take note of the initial spins upon entering the field, which determine the scattering or deflection of the particle is it traverses the non-constant field. Thus, as Einstein suggested, quantum mechanics is not complete. This conflicts with the Quantum Credo believed in by many physicists.

    Quantum mechanics is a marvelous statistical machine for those situations in which only certain outcomes occur, with energy-based distribution according to the partition function. In such cases it (apparently) cannot fail to predict the statistical outcome. But it is incomplete and there is an underlying level of reality that quantum mechanics does not see. That is in contrast to the current consensus belief that the classical world is a statistical overlay on QM. I discuss these interpretations on pages 104 - 113 in Quantum Spin and Local Reality

    Thanks for your, as always, informative comments.

    My best regards,

    Edwin Eugene Klingman

    Hi Edwin,

    Doing the math before the physics is the main problem of current string theories. All string theories posit extra space dimensions and there is no experiment to confirms the existence of these extra dimensions.

    Regards,

    Ken Seto

    Dear Sir,

    We appear to have agreement at the fundamental level. You may recall, after the black hole firewall paradox appeared during July 2012, it is no longer easy to say that both relativity and quantum mechanics (especially entanglement) are correct. One of them must be wrong. We question relativity as conceptually flawed and a wrong description of reality, but question only some of the interpretations of quantum mechanics. But why is the scientific community shying away from accepting facts boldly? If the points raised and examples given in our essay are wrong, it should be openly told and not bye passed. If they are correct, they should be accepted.

    Regards,

    basudeba

    The main thing that I get from your essay is that you have essentially a classical model of the electron. The factoring out of cosθ is due to the fact the quantum measurement of spin does not measure a part of the angular momentum projected along an axis of measurement. That can happen classically, but experimentally this has never been found. So this factoring out is motivated by experiment that is in agreement with quantum physics.

    LC

      Lawrence,

      With great respect for your acumen in math, could you elaborate enough to make it clear where the physical distinction lies in factoring out (cosTheta/cosTheta) as pertains to Quantum measurement not including a coeffeciency of measure along the spin axis. Doesn't this impose an assumption of a true circular orbit of precession?

      Arguably any precession would be physically ellipsoid, or at some point on the axis of rotation, change of direction would become instantaneous. If any precession would naturally follow a 'wobble' of that point avoiding instantaneous angular change, then the statement that it 'has not been experimentally found' is a fallicy of substitution. Classically, it is consistently found that deflection occurs as a three vector, which QM simply does not try to predict. Again, we encounter the arbitrary +or-1, which in this case limits vectors along the axis projection to extend only in parallel to the extention of the eigenvector of results, and excludes any local values between that and perpendicular. Genuinely asked, jrc

      The theory of angular momentum is that the value of the angular momentum measured is a projection from L to -L in increments of 1. A spin 1/2 system can then only have -1/2 and 1/2 along a basis. A boson can have -1, 0, 1 if the boson is massive, and the 0 case is gone for a massless particle. Quantum mechanics does not permit one to measure a spin = 1/2cosθ for some angle other than 0 or π. That is the point of the whole division by |cosθ|. A classical angular momentum, where there is not much meaning to a classical intrinsic spin, can have the angular momentum vector pointed differently than the direction the observer chooses to measure it.

      LC

      Dear basudeba,

      I only addressed specific issues in your above comment, but I found your comment extremely well written, and very insightful. I would like to address your remark that

      "Contrary to general belief, entanglement does not extend infinitely, but breaks down after some distance like a rubber band..."

      Susskind at Stanford regularly states that entanglement is weird because it tells us about the whole while we know nothing of the parts. Before Bell that was simply conservation of energy/momentum, and there was nothing weird about it.

      As I point out in several places, the current version of entanglement is associated with non-locality, as Bell thought he had proved that no local model could produce QM correlations, in which case there is a need for something that does account for the correlation.

      But, as no one understands the physical mechanism of entanglement (or anything at all physical about it) is also confused with local interaction. For example a recent article "entanglement on a chip" seems to imply the reality of entanglement. In my theory, which holds that momentum and intrinsic spin are separable (a tensor product), momentum produces a real, physical deBroglie-like wave aspect for a particle. If two (or more) such particles interact in close proximity then they do affect each other, potentially changing their states, and becoming effectively "entangled". This interaction-based interdependence is not Bell's non-local entanglement, but I believe that is pointed out nowhere.

      You ask why the scientific establishment shies away from recognizing the shaky ground of current science. It is because, as in all human enterprises, 'establishment' dominates 'science'. This is as old as mankind, and no one should expect it to change. Planck said that science progresses 'funeral by funeral', but today the establishment is too big for this to hold. But this will not prevent new challenges, like the 'slow photons', from arising.

      Thank you again for your excellent comments.

      Edwin Eugene Klingman

      Lawrence,

      Thank-you for your time and attention in response. I'll give it some read. Much obliged, jrc

      Lawrence,

      Despite what some Bell defenders say, Bell really was asking whether a classical model could produce quantum predictions. He did not insist on "classical" because he would have been interested in any non-classical theory, if only someone could imagine one that works.

      The main point I am addressing is the constant refrain in the literature that:

      "No local model can reproduce the quantum correlations."

      I show a local model that can and does unless subject to Bell's irrational constraints, and I explain why (in my opinion) Bell imposed these constraints. This should have implications for 'entanglement' and for the credo that "information is not lost". The initial spin information is lost in the Stern-Gerlach apparatus and Bell erases it in his theory. Yet the quantum mechanical predictions are reproduced by my theory.

      That you are not happy with a 'classical' model does not change the fact that it does produce the supposedly impossible quantum correlations, which is what I set out to prove.

      The Quantum Credo, mentioned by Zurek in his Physics Today article on Quantum Darwinism is truly a religious belief in that it is not subject to rational argument. Those who believe (but think they 'know') that the classical ('real') world statistically arises from the mystical quantum world are not open to argument. They have their credo and to hell with anyone who questions it.

      I briefly discuss a broader picture on pages 104 - 113 in Quantum Spin and Local Reality, but a 9 page essay precludes such discussion. Matt Leifer's quote on page 10 in my endnotes accurately summarizes the current confused state of quantum mechanics (after 90 years!)

      I currently have about 200 pages on spin that cover far more than the 9 page essay. I point out that spin is connected (in QM) to a deBroglie-Bohm-like particle only as a tensor product (see top of page 9):

      |ps> = |p> x |s>

      where |p> is the momentum wave function and |s> is spin. It is a mistake to fail to differentiate the intrinsic angular momentum from the other momentum, linear or angular. My current essay focuses only on the intrinsic spin. That does not mean my model does not address non-spin quantum mechanics.

      But it is difficult to think new thoughts, much easier to dismiss a model as "classical", despite that my spin model is quantized, and my momentum model does induce deBroglie-like 'waves'. My model also seems to explain the recently reported photons that go slower than light in vacuum. I believe that QM as it stands and relativity as it stands are not up to explaining current and expected (by me) experimental results.

      Many physicists have simply rejected mystical religion to create a new mystical science, where they can be the high priests. They become more conservative, even regressive, as their hold on power erodes, and their mysticism becomes even more esoteric. There is no way not to offend such believers, and I reject political correctness. Like jrc, I do not question your mathematical acumen, but you already know that I question your physics. It's no surprise that you question mine. FQXi offers us both the platform. But, like Phil, I don't want you telling me how you voted for me. Much better to simply discuss ideas found in essays.

      In your second comment, you state that quantum mechanics "does not permit one to measure a spin for some angle other than 0 or n." My energy-exchange theory should be subject to experimental test that would measure just such an angle, and I plan to push for such a test. FQXi is offering grants for (The Physics of What Happens). Such a grant could start the ball rolling. If theta is measured, then that will simply prove QM is incomplete. That will come as a shock to believers in the Quantum Credo.

      Edwin Eugene Klingman

      For some reason the above post does not show a reply box.

      You have a classical model of the electron that does what you say. If you are doing this business of not taking Fcosθ --- > Fcosθ/|cosθ| then you really do not have quantum mechanics. Later text appears to show similar ideas with ellipses and the like.

      LC

        Lawrence,

        Despite our history of five years of disagreements, you say that I have a classical model of the electron that does what I say. Thank you. What I say is that it yields the quantum mechanical correlation that Bell claims to be impossible for any local theory.

        Then you say I really do not have quantum mechanics. As I've stated, my intention was to design a local theory that yields quantum mechanical correlations, which I have done. It implies that quantum mechanics is incomplete.

        You said above "Quantum mechanics does not permit one to measure a spin = 1/2cosθ for some angle other than 0 or π." My response is that my energy-exchange theory should be subject to experimental test that could measure just such an angle, and I plan to push for such a test. FQXi is offering grants for The Physics of What Happens. My model explains what happens when the particle is scattered by a heterogeneous field. If θ is measured, then that will simply prove QM is incomplete.

        Thank you for observing that the model does what I say.

        Edwin Eugene Klingman

        You don't have QM in the standard way. The Stern-Gerlach experiment in your setting would not have the discrete sets of spins. You have a local realism where the spin has projections along an axis that can be less than 1/2.

        You have a "war" against QM and nonlocality, and of course this is a physics case of Don Quixote on his quest. FQXI has a large number of people who hang on the blogs and contribute to the essays who have similar ideas. There are further people with anti-relativity biases as well. As a result your essays always attract loads of attention and votes. The problem is that science is not really a democracy, and these contests tend to operate that way. I don't have time right at the moment to look this up, but there are a couple of famous videos of Richard Feynman talking about this. In one of them he talks directly about the sort of ideas you advance and in one of them he talks about "if you don't like it go somewhere else."

        Actually, if you really think about it, QM is not what is so strange. What is really strange is that on a large scale there is this classical world, which is coarse grained physics built up from QM. QM can't be understood in a classical sense. The strangeness of QM is due to our insistence on shoving it into a classical setting. Trying to converse to build the classical world from QM is difficult as well, and we might find this not entirely tractable either.

        LC