Edwin,

If it obeys the uncertainty principle, then there is only a single bit of "information" present, regardless of how many data bits are in the measurements. The meaning of the uncertainty principle, is that regardless of how much data one collects, that data is all so highly correlated from one measurement to the next, that there is only a single bit of information buried in all the redundant data. If this is not true, then the data does not obey the uncertainty principle, and is not of interest quantum mechanically.

Think of it in terms of a time-bandwidth product, which is what the uncertainty principle is:

The limit in time means there is a limited time duration during which the signal is present and able to be measured. The limited bandwidth means that the "signal" has been lowpass filtered, which introduces correlations between any closely spaced measurements. The uncertainty principle says there is an inverse relation between the time-period and the correlation period, such that only a single independent measurement can be made; all other measurements are non-independent and entirely correlated with the first measurement, such that they are devoid of any additional "information". Furthermore, that single measurement, is only accurate to 1 single bit. This latter fact can be seen by setting the signal-to-noise ratio in Shannon's Capacity, equal to 1, in which case the expression for the capacity just becomes equal to the uncertainty principle; the uncertainty principle is simply the special, limiting case, in which the information carrying capacity of the "message", consists of a single bit of information.

Also, keep in mind that most of the experimental tests of Bell's theorem, do not even employ particles with spin, or use magnetic fields. They are performed by measuring the polarization of photons.

Rob McEachern

Dear Rob,

I have the highest regard for your information theory perspective, which usually agrees with my own info perspective. But this is not the perspective in terms of which John Bell developed his theorem. I have just performed a hurried review of all the references in John Bell's 'Speakable and Unspeakable in Quantum Mechanics', which is the "Bible" of Bell's theorem, and have not found a single reference to Shannon. I know that you tend to see everything in terms of Shannon's info theory, and I generally think this is quite appropriate.

But Bell's theorem is special. For 50 years physicists have been told that no local theory of hidden variables can produce the quantum correlation, -a.b. In my essay I have shown a local theory that does produce these correlations. Bell was searching for a local classical physics explanation of quantum correlations, not an information theory-based explanation. I have provided the local physics-based explanation. The problem is quite complex and, based on about six months of discussion of these problems, I have found that Bell's supporters finally fall back on the eigenvalue arguments that I present in my essay. From above comments on my thread you can see that some of my readers claim they need more study to understand it.

As I view Bell's theorem as one of the most significant aspects of modern physics (non-locality versus locality) I am quite interested in clarifying this problem. I find it very difficult to clarify in the standard perspective that Bell developed. I simply do not believe your comments are clarifying, but, for most physicists, may be more confusing. Your remarks are now on record, and available to the readers of my essay, some of whom may find them enlightening. They do not, in my view, contribute to understanding my local model, nor the error that Bell made in interpreting Dirac vs. Pauli eigenvalue equations. Bell's theorem is not normally viewed as an uncertainty principle problem, and I do not find your first paragraph above relevant to my local model, either in your premise or your conclusions. Nor do I find your second paragraph any more enlightening. I strongly believe Bell's theorem is best discussed in Bell's framework, not your framework as laid out above. The fact that you twice put "information" in scare quotes tells me that the argument you make is not a simple one or transparent. I do not believe your argument about the uncertainty principle applying to 10,000 measurements of local variables as you imply. I suspect our understanding of quantum mechanics differs.

Finally, I have elsewhere addressed the fact that most experiments have been based on photons. It is not necessary to present both a local Stern-Gerlach particle-based model and a photon-based model to counter Bell's claim that NO local model can produce the correlation. I will address photons later, but it is not required to counter Bell's claim.

In short, for a few souls, your translation of the problem may be enlightening. It may be very well worthwhile for you to write a paper presenting your unique perspective. But I do not wish to take a perspective based on John Bell's framework and attempt to reformulate it into your perspective. I don't see that as efficient or effective, nor likely to be successful.

Edwin Eugene Klingman

PS. This comment is not in-line as the FQXi software is having problems with my browser.

    Dear Edwin ! Profesionally, your : Thermodynamics of Freedom, is of great (!)importance to my work. The Bell Essay, about map and territory, is very distant from my knowledge base, although I've the intuition that it could help me in these social science problems as well. I can imagine that: www.lifeenergyscience.it could interest you. Even 'simple nature' does not behave like classical physics, so pleae visit the mentioned website. Best wishes and cordially: stephen

      Dr. Klingman,

      Your bio says it all, your recent focus has been on issues of Bell's Theorem, which is quite daunting to the uninitiated. It is clear however that your conclusions which come from questioning Bell's underlying assumption of constraints which essentially impose arbitrary unity in the formulation of his arguments, produce the same results as did Joy Christian's questioning of his choice of topological measurement space. However mathematically contrived, spin is related to identifying rotation as a measurement function, firstly on a complex plane, and the integer and half integer values really only assign which quadrant to look in. Your argument that a continuous rotation in 3 dimensions is not a simple bit of information, is I think self-evident. I'm only qualified to 'watch and learn', as the laggards say on construction crews, so I'll gladly rate with the community. Best Wishes, jrc

        Dear Stephen,

        I'm pleased that you found my ToF essay useful to your work. I've looked at your site, but syntropy to Bretton Woods covers quite a bit of territory, and there's more there, so I've not absorbed all your information. Although I'm sure we will differ on details, I believe that, particularly in your field, going in the right direction is more important than getting all the small details right. Thanks for your comment and my best wishes,

        Edwin Eugene Klingman

        Dear jrc,

        I've read many of your comments over the years and very much appreciate the above comment. As you note, Bell's theorem is quite daunting to the uninitiated, and not that transparent even to those who study it. I'm glad this FQXi contest allows me to present the ideas contained in my essay. I agree with your statements about spin, from Bell, to JC, to 'not a simple bit of information', and I am happy to have you "watching".

        My best regards,

        Edwin Eugene Klingman

        Edwin,

        I have to admit that I am a bit puzzled by your paper, and the angle theta. In your paper, you seem to be defining theta to be the angle between the spin direction and some measurement angle. But in Bell's plot of the correlation vs. theta, theta is the angle between Alice and Bob's detectors, and is completely independent of the spin direction, the magnetic field direction, or the angle of either Alice or Bob's detectors relative to the spin and/or field.

        In your figures on page 7, what is the theta angle that you are plotting the correlation against?

        Rob McEachern

        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

        • [deleted]

        • 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

        • [deleted]

        • 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