Rob,

Thanks for inquiring about theta. Your statements are correct. In my paper I believe all references in the text are intended to be the angle between the spin lambda and the local field direction, a or b. In other words, for Alice, theta = (a, lambda) and for Bob theta = (b,-lambda). These angles are (on page 4) in Bell's third assumption and implicitly in my equations (2) and explicitly in equation (3), and, on the next page in equation (4). The angles are shown on page 6 as Alice's vectors on the left and Bob's on the right, and very specifically on page 8 between the field of vector B and magnetic moment mu, and on page 9 in the 'physical system' figure on the left side.

However, in Bell's theorem theta is the angle (a,b), that is, the angle between the (remote) directions a and b. And in the figures you ask about, on page 7, theta is Bell's theta, that is, the angle between the remote control settings. I apologize for the confusion, the term theta is typically common to both discussions of precession, independently of Bell, and also, as you note, it is used by Bell as above. Thus it's hard to resolve this issue and still be completely consistent with other sources. I hope the above specifics clarify the meaning sufficiently. My references [2] (135 pages) and [4] (23 pages) give more details on this.

The key results are the ones you ask about on page 7. The local spins in the local fields describe the physics of the problem. Correlations at the top of page 7 derive from my local classical model, and match the QM correlations between a and b and also match the experimental measurements. When I apply Bell's constraints then the second figure on page 7 yields the 'non-local' results which occur when Bell erases the information provided by the local physics. By erasing all local physics information, Bell guarantees that only 'non-local' correlations are obtained. My essay discusses the reasons that Bell made this mistake.

Thank you for continuing to look at my essay.

Best regards,

Edwin Eugene Klingman

Thanks Edwin ! The Website is that of Dr. Ulisse di Corpo (Rome); I mainly thought about his interpretation of the relativity formula and the related work of scientist L.Fantappie. Best: stephen

Edwin,

OK, next question (I'm trying to decide if you and Bell are comparing apples to apples, or apples to oranges)

Exactly how are you computing the correlations?

Are you correlating measured angles? Or are you correlating up/down decisions based upon the measured angles? In other words, to use entangled coins as an example, one could either measure the angles of each coin, relative to some detectors, and then compute the correlations between those angles, or one could be required to declare the coins to be either heads or tails, after the measurements, and then correlate the numbers of heads/tails decisions. What are you correlating?

Rob McEachern

Robert,

Edwin's premise is that Bell assumes a required heads or tails outcome. Those are the constraints he challenges. Apples is. :-) jrc

Robert,

Note page 4 of the Klingman essay; Bell's physical assumptions, line #2

the spin operator is a mixed half-open and closed interval set. So anything that isn't an equal value of plus or minus in the middle of the closed interval portion is excluded. Hence, its all or nothing in counting spin, according to Bell. At least that's how I'm reading it. Onward! through the fog! jrc

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  • Post #61

Rob,

The data of the Stern-Gerlach is shown in the lower figure on page 3. Although Bell interpreted this as +1 or -1, Messiah described it more accurately as a "spread out distribution". The actual measurement is a position measurement, which Bell truncates.

On pages 4 and 5 I discuss the energy-exchange that occurs and calculate the deflection contribution based on the precession energy. From this I calculate Alice's output position A(a,lambda) and Bob's output position B(b,-lambda). It is these outputs that are correlated and that yield -a.b as shown on page 7. The operation of the model is described on page 6. I am correlating the outputs from Alice and Bob's measurements exactly as described by Bell, minus his constraints. When I apply his constraints, then I get his results. When I do not apply his constraints I get the correct results. The rest of the essay explains why Bell was wrong to constrain the local realism model as he did.

As jrc points out, the 'heads and tails' aspect is due to Bell's faulty premise.

Edwin Eugene Klingman

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  • Post #62

Edwin,

Then you are comparing apples to oranges. The triangular correlation function, for the classical case, is only triangular, when decisions, not measurements are correlated. The question remains, when one is "forced" to make up/down decisions in both the quantum and the classical case, and then correlate those decisions, why do the correlation functions differ?

You are claiming that it is possible to make measurements in the quantum case, and then correlate those. But the same is true classically. But that is not the issue that Bell is addressing. Bell's issue, is that it is possible to mimic the quantum decision correlation process (rather than measurement correlation) with a classical system, but they do not yield the same correlation function, for the same decision process. Why?

You have raised another question, about the possibility of measuring quantum systems, instead of making decisions. As interesting as that may be, is not the question Bell is asking.

Rob McEachern

Rob,

It is clear to me that you have not understood what I'm doing, from your questions and your comments. Nor does it appear to me that you understand what Bell is doing. As he is no longer with us we cannot ask him whose interpretation is correct, so we must rely on his own words. Specifically, he asks,

"...if this [quantum mechanical] statistical element can be thought of as arising, as in classical statistical mechanics, because the states in question are averages over better defined states for which the results would be quite determined."

I have constructed a local model with better defined states whose outputs are quite determined and whose average or statistical element matches the quantum mechanical statistical element, -a.b.

Bell further states that:

"The vital assumption is that the result B for particle 2 does not depend on the setting a, of the magnet for particle 1, nor A on b."

I completely satisfy that assumption in my local model.

Bell's Theorem, stated frequently in the physics literature, is that "No local model can produce the QM correlation, -a.b." Contrary to Bell, I have done this and exhibit the results here. I further explain why Bell came to this conclusion, and why it is incorrect. I regret that this does not match your own interpretation of what Bell is doing, but the history of Bell discussions on FQXi seem to show that there are strongly held opinions of what Bell was doing that are irreconcilable.

In the Oct 2014 issue of 'Physics Today', the monthly magazine of the American Physical Society, Zurek mentions the Quantum Credo. A credo is a statement of religious belief. Unfortunately that is to be taken seriously for some, which removes most hope of logical resolution of differences.

Finally, you are entirely incorrect to state that I am claiming it is possible to make measurements in the quantum case, and then correlate those. I make no such claim. You appear to be seeing both Bell and my essay through your own lens, for your own purposes. As I suggested earlier, I suspect we have quite a different understanding of quantum mechanics.

It appears that we simply need to agree to disagree, because I do not expect to convince you that Bell meant what he said.

Edwin Eugene Klingman

Edwin,

I am an empiricist; observations always trump hypotheses. Since all the actual experiments attempting to test Bell's ideas, have been carried out with decisions, rather than measurements, any experiment that purports to get a different result, when compared to the actual, existing experimental results, must correlate the same thing; decisions, not measurements. Otherwise, they are not comparable - of course one can get a different result, when one measures an entirely different thing.

Note that your first quote from Bell, begins with an "if" clause. My point is, that the clause is false. Classical statistical mechanics never deals with entities encoding only a single bit of information. That is what makes the quantum case so peculiar, in comparison. When there is only one bit of information in a message, there is nothing to average over, there are no better defined states, precisely because there are no other states at all, by definition of what is meant, by a single bit of information. Since such entities are never encountered in the classical realm, we have no intuitive understanding of how such things behave. But we seem to be observing such behavior, in the quantum case.

Rob McEachern

Dear Rob,

This comment is out of sequence as the FQXi bug will (again) not allow me to enter this comment where it belongs above. I encourage you to write up your view of Bell and QM. You and I have a different understanding of quantum mechanics. Thanks for presenting your perspective. It is not my perspective.

As I noted on your thread, I do find your ideas expressed in your current essay quite interesting, and wish you luck in the contest.

Best,

Edwin Eugene Klingman

    Gentlemen,

    This has been an interesting and informative exchange, as polite differences generally are. Thank-you. Bell's Theorem seems to be the one topic which concentrates attention on the elusive characteristic of spin. And I say characteristic because it is only because of characteristic behavior both of electromagnetic and particle-like phenomenon that suggests some fundamental physical property. Yet I've found nothing anywhere that seems definitive of what that might be.

    It isn't physical rotation, though its treated that way. As a purely classical puzzle it seems to me to be as much about the question of what is it in a field that exhibits apparent motion, as whether there is an induced angular motion in a particle or waveform. It intuitively seems that Spin is more a measure of a physical property that doesn't undergo a coherent rotation. It's weird! :) jrc

    jrc,

    Glad you enjoyed it. Rob has internalized the information theory perspective and usually has unique and interesting insights into various fields of physics.

    While my local model is essentially classical, and, FAPP may be considered a spinning particle, the QM and QFT 'point-based' particles do have difficulties with this perspective. It's interesting that Dirac's 4-component point-based electron does not yield an eigenvalue equation for spin. Only after the Foldy-Wouthuysen integral transformation to a 2-component wave function as an average over a "Compton-volume" does the fundamental helicity eigenvalue equation fall out. I do have a view of particle physics that is not entirely weird, but I want to stay strictly focused on Bell in this forum. Thanks again,

    Edwin Eugene Klingman

    Rob,

    Although I have hinted that we should terminate this exchange, I think so highly of your basic information theory approach that I've tried to understand where our basic disagreement lies. To this end I reviewed your 2012 essay, in which, discussing Bell's theorem, you state, "when 'spin' was discovered, it was assumed to be analogous to a quantized version of angular momentum... [and] to be describable via multiple components... like an ordinary three component vector." You then imply that it is not a 3-D vector but "a single bit of information", and go into your 'two-sided coin' discussion.

    Is this still your assumption, that underlies your above comments? It appears to me to be so. In your last reply to me above: on Jan. 27, 2015 @ 15:41 GMT you say:

    "Classical statistical mechanics never deals with entities encoding only a single bit of information. That is what makes the quantum case so peculiar, in comparison. When there is only one bit of information in a message, there is nothing to average over, there are no better defined states, precisely because there are no other states at all, by definition of what is meant, by a single bit of information. Since such entities are never encountered in the classical realm, we have no intuitive understanding of how such things behave. But we seem to be observing such behavior, in the quantum case."

    In other words, although I have clearly stated that we are not discussing a single bit of information, you seem to insist that we are. If that is the case, we cannot possibly come to an agreement. You ignore the QM assumption of a 3-component vector, putting your own interpretation in its place, and then insist that my treatment, based on the QM assumption is wrong.

    Am I misunderstanding you?

    Edwin Eugene Klingman

    Thanks Doc,

    That summation directs to good reading and really helped me connect dots in your argument. :-) jrc

    Edwin,

    I am not ignoring "the QM assumption of a 3-component vector", I am disputing it, as a misinterpretation of reality. The problem is not that the quantum world behaves oddly, but that the classical world behaves much more oddly than people suppose.

    The reason people suppose they understand classical behavior, is simply because they have never, ever encountered the one type of classical behavior that they do not understand at all; an object encoding only a single bit of information. Like highly unstable, radioactive atoms, such objects do not exist in the natural world. Hence, they have never been observed; but they can be created. And they do not obey the triangular correlation function, so often discussed in regards to Bell's theorem, in order to claim that quantum and classical behaviors differ.

    Furthermore, the hallmark, the signature, the fingerprint of such an entity, is that it will exhibit only two states, when one attempts to observe it, and it MUST obey the uncertainty principle (which, contrary to popular belief, has nothing to do with QM, but is a purely mathematical consequence of Fourier analysis). This is easily demonstrated if one considers the very poorly understood meaning of Shannon's capacity theorem, and the resulting uncertainty principle.

    Shannon's capacity theorem is virtually always derived and discussed in such a way as to completely obscure its simple meaning:

    The maximum number of bits of information that can be recovered from a signal, cannot exceed the number of bits of digitized data, required to completely reconstruct the continuous signal, to an arbitrary highly degree of accuracy. The latter number is simply equal to the number of samples, multiplied by the number of bits per sample, needed to reconstruct the continuous signal. The number of bits per sample is determined by the signal-to-noise ratio; that is the log-base-two-2 in the expression for Shannon's capacity. The number of samples is the product of the time-duration and the bandwidth; that reduces to the uncertainty principle, in the following special case:

    Consider a signal in which the bandwidth is so restricted, that all samples within the time duration of the signal, have become so highly correlated, that there is only one independent sample. Then suppose that the signal-to-noise ratio is equal to 1.0, so that the single independent sample has only one significant bit. That is the origin of all observations that obey the uncertainty principle, and exhibit only two states; an entity encoding only a single bit of information.

    Here is how to construct such a signal classically:

    1) Create a polarized coin such that one semi-circle of one side is red, and the other semi-circle of the same side is green.

    2) Represent each pixel in the image of the coin by +1 for red, -1 for green.

    3) Correlate the coin against rotated versions of itself, to "decide" if the correlation is better aligned with green of red.

    4) Now compute the decision correlation statistics versus rotation angle; you will get a triangular function

    5) Now add noise and blur the image, such that only a single bit of information remains.

    6) You will not be able to see the polarization visibly, the image is too noisy and blurry.

    7) But you can correlate a clean image against the blurry one and compute the correlation statistics

    8) But you will not get a triangular function.

    Rob McEachern

    Dear Edwin,

    There are many claims in your paper that need to be discussed, but perhaps it is best to start with the main one. You claim to have produced a local theory that nonetheless predicts violations of Bell's inequality. But the theory simply does not appear to be local in Bell's sense. Of course, if one enforces certain global conservation restrictions on a system, that will have consequences for what is observed. The perfect anti-correlation between results for spin measurements in the same direction on particles prepared in the singlet state, for example, is predicted by enforcing 0 net spin for the system. But if each particle is not in a state which predetermines the outcome of the experiment, and is completely unaffected by whatever distant experiment is carried out, then enforcing the global conservation means that theory is not local in Bell's sense.

    Let's put is more directly. Suppose that a system has two, widely separated parts and I carry out experiments on the parts at space-like separation. And suppose that as a consequence of carrying out an experiment on one part, the energy of that part changes. If I now enforce global energy conservation, so the energy that disappears from one side must appear on the other space-like-separated side, then the theory is not local in Bell's or Einstein's sense. Calling this non-local interaction between the sides "energy exchange" does not change this: energy exchange between space-like separated subsystems is a violation of locality. So it is not a surprise that your model can generate violations of Bell's inequality: it is not a local model.

    The claim that your model is local is critical part of the paper: if it were true, then you wold have shown that there is some flaw in Bell's reasoning. As for your remarks on Bell's argument, you seem to have mistaken an illustrative example that he gives for part of the theorem itself, which it is not. The theorem is about any theory--whether the theory uses quantum-mechanical formalism or a completely different formalism in which there is no talk at all of eigenstates or eigenvalues--that makes certain predictions about correlations between outcomes of distant experiments. Because of this complete generality, it is not even correct to us the term "hidden variables" to describe the theorem, since that term itself is used only in connection with quantum theory. Peres, who you cite, has it right here. Since Bell's theorem only refers to the results of experiments and their correlations, he makes no assumptions at all of any kind about the theory predicting those results, save that it is local. His theorem does not apply to "energy exchange physics" because in this setting the energy exchange would not be a local process, and the theory would not be local. It is therefore not a counterexample to Bell's theorem.

      Tim,

      "If I now enforce global energy conservation, so that the energy that disappears from one side must appear on the other space-like-separated side..."

      Where does he say that? A particle need not refer to a point exterior of itself to know its initial orientation to its state of motion. That is clearly implied by our definition of inertia globally, regardless of relative local energy transfers. If you are in a closed spacecraft intergalactically and the interior appears to be tumbling around you, is it? Gently, jrc

      Dear Edwin,

      Thank you, your reply deserves a careful and thought-out response. Unfortunately, the next couple weeks or so will be very busy for me, so let me just say that I wish to continue our discussion, but there will be a little time lag time before I have a chance to fully engage in it. I do want to do it because this may well be one of those (relatively rare) kinds of discussions where both parties can learn from each other.

      Best wishes,

      Armin

      Rob,

      Thanks for your reply. You confirmed my last comment, as I was sure you would. You are effectively ignoring the QM assumption of a 3-component vector by replacing it with your own 1-bit interpretation of reality.

      Thus all your arguments are based on your own idea of 1-bit events that match your fixation on Shannon and agree neither with the quantum mechanical interpretation nor with my local model. As your results will never agree with the 3-D realistic world we can only agree to disagree on spin.

      I still find your view of superposition generally compatible with mine and hope to address this later, but there's no point in responding to the details of your above comment because they concern a different model of reality.

      Thanks very much for your clarification,

      Edwin Eugene Klingman

      Dear Tim,

      Thanks for reading my essay and responding. As I understand your comment you make three points:

      1. Global energy conservation across space is non-local.

      2. Bell's suppression of theta physics is illustrative, not basic.

      3. Bell's theorem is about any theory, not just quantum mechanics.

      If I understand you correctly, you state that global conservation (compatible with the perfect anti-correlation case) will have consequences for what is observed, but is not local in Bell's sense.

      Then you claim that "if I now enforce global energy conservation, so the energy that disappears from one side must appear on the other space-like separated side, then the theory is not local in Bell's or Einstein's sense."

      While this is probably a true statement, it has nothing to do with my model, in which there is no hint of energy disappearing from one side and appearing on the other.

      My model assumes local conservation of energy; (which, I believe, generates global conservation of energy,) energy does not "disappear" locally. It transforms, which is the meaning of my Energy-Exchange theorem. The precession energy, which locally is transformed into deflection energy is not "lost" locally. It is converted into deflection energy, and can be measured by the position measurements that Stern-Gerlach performs, yielding the initial angle that spin makes with the local field, which is the "hidden variable" in my model.

      You also claim that Bell's suppression of this theta physics is merely an illustrative case, and not part of his theorem. While technically this may be true, it is a de facto result of the constraints he imposes in his theorem, and it also illustrates his thinking that underlies his model. The results are the same, whether one considers the suppression of theta a basic assumption or a consequence of another basic assumption.

      As for your statement, which agrees with Peres, that Bell's theorem is about any theory, whether the theory uses quantum mechanical formalism or is a completely different formalism in which there is no talk of eigenstates or eigenvalues, I would ask you to explain just how the +1 and -1 constraints show up in a non-quantum-mechanical theory.

      To summarize the 3 points:

      1. is a mistaken interpretation of my model.

      2. the logic is the same whether theta suppression is a basic assumption or follows from another basic assumption.

      3. is an editorial point, and has bearing on the logic of my argument only if you can explain why 'any' theory must erase information in a way that mimics imposition of QM eigenvalue constraints.

      Finally, I sincerely thank you for stating that if my model is local then I have shown a flaw in Bell's reasoning. You claim my model is not local because "energy-exchange physics" is not local. But that is mistaken because the energy exchange in my model is completely, 100%, local.

      Thanks again for your consideration,

      Edwin Eugene Klingman