Edwin,

Very interesting read. I agree with your fundamental argument, however I believe it was Bell's intent to define a state of locality in a non-localized field, thereby introducing the constraint as +/- 1. I believe, or my intuition tells me, we are led to a fuzzy paradox when attempt to constrain any bounded state of locality.

I do feel we often describe things in mathematics that we truly can not in physics. Idealistically my argument would contend we only use mathematics as a model to physical reality.

Nevertheless, it was a good essay. Kudos!

Best Regards,

D.C. Adams

    Edwin,

    In regards to Bell, let me give you something to think about, in the realm of truly macroscopic objects like idealized coins, rather than electron spins.

    The correlation given for classical entities is a triangular function. The correlation given for quantum entities is a sinusoid. A triangular function has a Fourier spectrum, consisting of odd harmonics of the sinusoidal fundamental. Consequently, even a crude lowpass filter (smoothing operation) applied to the triangular function, will convert it into a sinusoid. Thus, the only difference between the triangular and sinusoidal correlation functions, is a lowpass filter.

    Now Shannon's Capacity theorem, reduces to the uncertainty principle, when only a single bit of information is recoverable from a message. Any such message is inherently band limited (lowpass filtered). But was the filter applied at the transmitter or the receiver? If it was applied at the transmitter, then the "single bit" is an intrinsic property of the entity being received, not the apparatus being used to receive it.

    Now consider making a very noisy, time-bandwidth limited measurement (limited at the transmitter, to contain only a single recoverable bit of information), and then trying to "decide" whether the measurement is +1 or -1. As noted above, a simple lowpass filter will convert a triangular function into a sinusoidal one. But does one apply the filter to the measurements or the discrete decisions derived from the measurements? And how, exactly, did one make the decisions? More importantly, in this limiting case of only a single bit being present, can one even separate the measurement and the decision making processes, and thus which data set, the measurements or the decisions, are to be filtered? If filtered decisions are used as input to the correlation computation, the result will be sinusoidal, though perhaps not "normalized".

    My point is that, the correlation may result from the peculiar nature of attempting to "decide" the difference between a measurement and a decision/index based on the measurement, when only a single bit of information exists, rather than from any considerations of the physics per se, which is merely the carrier of the one-bit message.

    Rob McEachern

      Dear Demond,

      Thanks for reading my essay and commenting on it. I'm not sure I understand your comment, but the consensus of Bell's supporters seems to be that the +1 or -1 are simply eigenvalues and that measurements must produce eigenvalues. That is why I have focused on this argument and attempt to show that Bell confused Dirac's fundamental eigenvalue equation with Pauli's provisional eigenvalue equation, which is clearly inappropriate in that it leads immediately to a contradiction.

      You say "I believe, or my intuition tells me...". Like you, I do regard intuition as meaningful. Some, as Phil points out above, distrust intuition, and attempt to suppress it from all considerations. There are arguments for both approaches.

      You also say we only use the mathematics as a model of physical reality. I agree with this and refer to it as the 'map' that represents the 'territory' in the Korzybski sense.

      Thanks for your kind remarks, and good luck in the contest.

      Edwin Eugene Klingman

      Dear Rob,

      I agree that the correlation given for 1-bit classical entities is a triangular function, versus the sinusoidal quantum correlation. But the classical 1-bit entities do not experience the energy-exchange that yields an analog result.

      This "dissipation" can be viewed, as you say, as a low-pass-filter, and this is the difference between the binary result obtained without dissipation and the continuous spectrum obtained with the non-constant field.

      You discuss Shannon capacity and the uncertainty principle in the case when only a single bit of information is recoverable from a message. The local classical model is not a one-bit model but a continuous distribution (quantum magnitude but arbitrary 3-D direction). You make a very interesting point that, if the filter is applied to the transmitter, then the 'single bit' is an intrinsic property of the entity, not the 'filter' (the apparatus). But, as I discuss, the actual result is not a single bit, but a continuous spectrum. So I don't see this as applying.

      Your next paragraph is more complex, but seems to again assume (as did Bell) a one-bit measurement. As the local model is not one bit I don't see this logic directly applicable (as I understand it) since the assumption that only a single bit exists is not correct. Moreover, as I point out, this physical 'fact' should be experimentally testable, and I plan to work toward testing it.

      In other words, Bell's 'one-bit' assumption is inappropriate, based on his over-simplification of the problem, which was itself based on his confusion between the Dirac fundamental helicity eigenvalue equation and Pauli's provisional precession eigenvalue equation.

      Thus while I do agree with your analysis (as I understand it) it is premised on "when only a single bit of information exists", which is Bell's fundamental mistake. The physics of the local model (which produces correct results) is not "merely the carrier of the one-bit message".

      Thanks for your insightful comment,

      My best regards,

      Edwin Eugene Klingman

      Edwin,

      I am not assuming a single bit. I am talking about "constructing" a classical object that only has a single bit. Imagine a coin, to which "noise" is added, via surface imperfections, after which, the surfaces are then blurred, by a physical lowpass filtering operation, to such an extent that, even if you held the coin in front of you, you cannot tell if you are looking at the "head" or tail side. The only process that can tell, is a carefully constructed "matched filter" type of operation, that knows, a priori, exactly what other filter must be correlated against the entire surface of the coin, to "decide" if the surface under consideration is heads or tails; a sort of carefully weighed average over the entire surface, for which the weighting function must be known, a priori, in order to recover the bit without error.

      By carefully adjusting the noise level and bandwidths of the lowpass filter, the coin is being constructed such that it obeys Shannon's Capacity relation, for an entity from which only a single bit of information, can ever be recovered (in regards to the heads vs. tails observation) In this regard, it is quite unlike other classical objects. My belief, is that it is not small physical size, but small information content, that cause most of the oddities in quantum observations. Hence, if one were to construct a macroscopic object, that intrinsically has a small information content, similar oddities will occur, when one attempts to determine its observable state.

      Rob McEachern

      Rob,

      I understand that you are "constructing" a classical object that has only a single bit. This is the 'classical' example of the coin as model of spin one-half.

      But my point is that it is this model that is inappropriate. My classical model of spin is not constructed 'of' or 'as' a one-bit entity. It is a continuous entity in that it can point in any 3-D direction. Nor is the measurement one-bit, as can be seen from the iconic 'postcard' data. Instead, it is Bell's assumption of a one-bit entity, and a one-bit measurement that is the focus of my essay.

      I'm not arguing with your constructing a classical object that has only a single bit, nor your analysis thereof. I am saying that it is not the appropriate description of my local model which I have constructed as a continuum-based entity, and which I show can and does produce a correlation that Bell claims to be impossible. Nor did I make any claims about small size having any relevance.

      I suggest that you have not understood my essay or my comments derived from it, as your arguments seem to miss the point.

      Edwin Eugene Klingman

      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

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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