Dear FQXi'ers,

Since my volume form, based on the left-handed C-field, is *not* free to change between runs (as does Joy's physics), I need another means of cancelling the unwanted terms that show up. To do so I choose Bell's "free will" requirement, that I interpret to mean independent uncorrelated choices made by 'Bob' and 'Alice'.

Joy has pointed out that "free will" does not mean the 50/50 distribution that I have assumed. He may be correct on this point, and I will have to answer it, but my first response is that I believe my interpretation is what most researchers assume. In fact they make great efforts to assure that Bob and Alice make *independent* choices, and even go so far as to arrange random decision making processes that will apply while the particles are in flight, removing completely the possibility that Alice and Bob can collude.

In his 2010 book, "Dance of the Photons", the foremost researcher, Anton Zeilinger actually defines "the definitive experiment" as the one in which 'a' and 'b' are selected independently (satisfying my needs) and his definitive experiment "changes settings during the flight of the particles." Thus, despite Joy's claim that my assumption is invalid, it is the assumption employed in the definitive experiments, that is, "both sides operated independently".

Therefore, Joy has brought up an intellectual point that I must address, but the definitive Bell-type experiments seem to agree with me. As Zeilinger states: "events are just events, and they are in no need of interpretation." and "The explanation of the events depends on later actions and decisions we or someone else might make." Zeilinger basically accepts the Copenhagen Interpretation, which my essay goes to great lengths to discredit. As for Bell, Zeilinger does say: "...the final verdict is not in yet" and "Whatever conclusion you draw is up to you."

So I acknowledge that Joy has made a criticism that I must address, but I believe the actual facts are on my side.

Edwin Eugene Klingman

    Dear Edwin,

    I so hate to disagree with you, but disagree I must.

    As a model builder your primary obligation is to reproduce the experimental facts. I am afraid, however, that your model fails this first and the most basic of all tests.

    Forget Bell's theorem for a second. Consider a typical EPR-Bohm experiment. Without prejudice for or against Bell, fix the two measurement directions chosen by Alice and Bob. For definiteness, let these directions be a and b, with 30 degree angle between them. Now let Alice and Bob make a large number of observations. They will record +1 and -1 in their logbooks, independently of each other. Then, at the end of the day, they will get together to compare their notes. They will then calculate the correlation between the numbers recorded in their notes, in the standard, well established way. What will they find? They will find a definite, fixed, number:

    E(a, b) = -a.b = -cos(30) = 0.866...

    What is more, this is exactly the number predicted by quantum mechanics.

    Now your obligation is to reproduce this number. Bell and his theorem are irrelevant. Anton Zeilinger is irrelevant. I am irrelevant. What is relevant is that you must reproduce this number for the experiment described, with the fixed directions a and b. If you cannot reproduce this number without varying the directions a and b, then your model fails. It is as simple as that. No elaborate interpretations or deeper reflections are necessary. No need to worry about what Bell did or did not say.

    Now I make a claim: The only way you can reproduce this number and beat Bell is my way. There is no other way. It is a zero sum game. Either you accept my whole package and beat Bell, or you accept non-locality or non-reality in the manner of Bell. There is no third way. The reason for this is the fact that EPR correlations are what they are because of the geometry and topology of the unit parallelized 3-sphere, not because of anything else. This is Nature's choice, not mine.

    You are of course free to reject the last paragraph, but you are not free to reject the experimental facts described in the preceding paragraphs.

    Best,

    Joy

    Joy,

    This last week I met with several physicists to discuss my model. They asked several questions which I have had to work to answer, and in doing so I now have new insight into (and increased confidence in) my own model. Having worked for several years alone, I have answered most of my own questions, and am now in process of working on others questions. I *always* learn something by answering questions that I myself have not thought of. So I welcome your questions, and I expect to gain from figuring out the correct answer. You may be correct, but if I have to choose between a known field -- first proposed by Maxwell, then predicted by Einstein's relativity, and recently measured by Gravity Probe B and with a coherence factor measured by Martin Tajmar -- that satisfies all of the points raised in my essay and also has the particle physics implications I have worked out over the past few years, and a 7D topology that switches handedness in convenient fashion to accomplish one main thing, beating Bell's claim about -a(dot)b, then I am going to continue going down my path. You have had a number of years to meet others challenges, and still have not met their objections, although I give you full credit for the yeoman-like efforts you have put forth. I have had a few weeks now to respond to others objections and am satisfied with my initial progress.

    Of course you may be correct. I realize that. But it is very early in the game for my model, and I must admit that the many successes that my model has had in the realm of particle physics encourage me to hope for similar success in the realm of quantum mechanics. As you mentioned in your first reply to me, I "have discussed [in my essay] many other things besides Bell's theorem [and you are] sure they will turn out to be both interesting and valuable to many." I too am sure that will be the case.

    So with all due respect for your expertise in Bell's theorem, and with recognition that I must eventually address all of your points, I am nowhere near throwing in the towel. I realize that your investment in the 'switching topology' will influence your acceptance of my model, and I expect challenges from you. I merely hope to avoid the hostility that has arisen on the Disproof blogs.

    Thanks for your inputs.

    Best regards,

    Edwin Eugene Klingman

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    • Post #60

    Dear Edwin,

    Ideas can be considered in many different positive ways, as just ideas, separate from egos. You are right to consider all questions and criticism as positive opportunities, either to exhibit the merits of your model or to improve on it over time. I admire your confidence and resolve. Good luck.

    Dear Edwin and Georgina,

    Georgina: I assure you my objections to Edwin's model have nothing to do with my ego. It has to do with understanding the powerful logic of Bell's theorem and the actual physics, mathematics, and experimental facts about the EPR correlations. These facts are against Edwin's ideas.

    Edwin: Precisely because I did not want to hurt your chances in the contest and because I did not want to start another heated debate, earlier I avoided commenting on your model too critically. However, I cannot agree with your remark that: "[ I ] have had a number of years to meet others challenges, and still have not met their objections, although I give you full credit for the yeoman-like efforts you have put forth."

    I *have* met every single challenge put to me over the past five years. The reason I have been able to meet these challenges is not because I am some super-smart genius, but because my ideas are in complete harmony with the choices made by Nature herself. I am sorry to note that you have taken the silly and ignorant objections to my efforts by some less-than-qualified individuals very seriously. But more importantly, you have not yet appreciated the simple fact that Bell's theorem cannot be overcome as naively as you are trying to do. As a result, your model fails at the very first hurdle. Please do not take my word for this. Ask any experimentalist who have had some experience in the matter. Or simply check on a piece of paper what quantum mechanics predicts. As I explained above, it certainly does not predict what your model predicts.

    Nevertheless, it is only fair that you explore your ideas in your own way and reach your own conclusions. I genuinely wish you best of luck with your efforts.

    Joy

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    • Post #63

    Hi Edwin,

    Something that bothered me early on, when I was introduced to Joy's model, is what I perceived to be a carefully buried assumption that one could perform a Bayesian type analysis on the experimental results the model generates. This is not trivial, for if true, it would destroy the foundation of the framework. This is because Bayesians cannot avoid the assumption of a definite probability on the interval [0,1]. To get this probability, one must apply a degree of personal belief dependent on previous outcomes.

    I had to be convinced that Joy's statistical analysis was based purely on a frequentist interpretation -- that every measurement trial is independent of every other (i.e., Bernoullian). This is what got me into some hot exchanges with Richard Gill, over the law of large numbers -- he insists that the central limit theorem that guarantees 0.5 in the interval proves that Joy's prediction is wrong, because no matter how many trials, the upper bound is set by the middle value based on faith in the law of large numbers (this is what gets us the upper bound in Bell-Aspect). Gill misses the point. Joy's framework does not address a single interval of probability in a unified series of trials; it deals with discrete non-probabilistic outcomes on both sides of the singularity that exists in every measurement function continuous from an initial condition (Lamport).

    As a consequence, discrete measurement outcomes, 1 or - 1, are not equally likely for every orientation of the measurement apparatus (the observer) choosing from a continuous range of possible measurement values of a fixed input argument (- a.b). For a run of trials in one probability interval [0,1], in some orientation that outputs some value, we're going to get a unitarily corresponding value on the oppositely oriented interval. Joy explains this in terms of trigonometric functions, though I prefer to think of it in analytical terms; i.e., angle-preserving conformal mapping to infinity. We don't need all the tools of complex analysis that the link describes, because geometric algebra simplifies and reduces the calculation to all real values. The only way this is possible, however, is by continuing the inherently 2-dimensional complex analysis to a 4-dimension domain (where the toplogy of S^3 lives). And from there, we get the sigificance of Joy's parallelizability: S^0, S^1, S^3, S^7. The topology is complete and self-limiting.

    So when it comes to Alice and Bob and the measurement angles they choose, though they record their results on a 1-dimension line in a 2-dimension space, the continuous range of those values actually lives in 8 dimensions, from which Joy derives the (CHSH) upper bound 2sqrt2, which is identical to sqrt8 and gives us an integral norm. Which leads to Joy's statement in his "What really sets the upper bound ..." paper:

    " ... we have proven that the upper bound of 2sqrt2 on the strength of all possible quantum correlations is derived from the maximum of parallelizing torsions within all possible norm-composing parallelizable manifolds."

    Please take this for what it's worth. My support for Joy's program is based almost entirely on mathematical completeness. That opinion in turn is taken from Einstein's conviction that no probabilistic framework can lead to a mathematically complete theory of how nature works. Since your premise is the same -- there's nothing to say you can't get there by a different road.

    Best,

    Tom

    Tom,

    Edwin is of course free to explore whichever road he wants to explore. At this stage I am only asking him to take the first step.

    Quantum mechanics predicts the following correlation function for the singlet state:

    E(a, b) = -a.b.

    This correlation function says that, given two fixed directions a and b, if the angle between them happens to be equal to 30 degrees, then the quantum correlation predicted by the singlet state is

    E(a, b) = -cos(30) = -0.866...

    This is a result from Quantum Mechanics 101. Any would be modeller of quantum mechanics is therefore obliged to reproduce at least this number. All I am asking Edwin for now is to reproduce this number for the fixed directions a and b, before he sets out to explore other roads. If he cannot reproduce this elementary prediction of quantum mechanics, then his efforts to overcome Bell are doomed.

    Joy

    Let me make sure you understand my worry. As it stands, Edwin's model predicts exactly zero correlation, E(a, b) = 0, not E(a, b) = -a.b as he is claiming. Because the cosine angle averages out to zero just as the sine angle does (remember that ab = cosine B sine in geometric algebra). On the other hand, if somehow the cosine angle does not average out to zero, then neither does the sine angle, and then again there is a contradiction with the quantum prediction. In other words, as it stands, there is simply no model.

    Dear Joy Christian,

    There are several issues, but let me dispose of the 'personal' first. I did not interpret Georgina's very nice compliment to me as in any way reflecting on you.

    Second, I did not mean to imply that I have "taken sides with" your critics from the Disproof blogs, most of whom argue about a mathematical step. Although it is probably poorly worded, it is still true that you have not "met their objections", in the sense that they still object. You also know that I have defended you against their attempt to apply mathematics in a 'same-time' fashion that is explicitly against the spirit of your physics. In fact, you have posted my defense at least a half dozen times. Therefore I think you overstate the case to say, "I am sorry to note that you have taken the silly and ignorant objections to my efforts by some less-than-qualified individuals very seriously."

    As I have remarked to you a number of times, I do not find higher-dimensional physics theories credible. Of course I could be mistaken in this. I am perhaps more open to unusual topologies, but I cannot conceive of a likely case in which handedness switches between experiments in a 50/50 fashion while remaining (as I interpret it) fixed for the duration of an indefinitely long experimental run (in theory Alice and Bob can be in different galaxies.)

    Therefore I have, rightly or wrongly, divided your approach into a mathematical framework and a physics portion. The math is based on geometric algebra (appropriately so, in my view) and upon physics that is represented in this framework. As stated, I have a hard time accepting the physics of higher dimensions and synchronized switching topologies of space-time, so I instead have attempted to express my own physics in your framework.

    I will address this physics in following comments.

    Edwin Eugene Klingman

      Dear Joy,

      In a comment you first claim that I should hold the angle fixed ("let Alice and Bob choose to keep their respective measurement directions *fixed* for all runs of the experiment. They are perfectly entitled to do so under the "free will" requirement.") Then in the last comment you claim that ("Because the cosine angle averages out to zero just as the sine angle does ... Edwin's model predicts exactly zero correlation, E(a, b) = 0, not E(a, b) = -a.b "

      But assume that Alice and Bob agree to hold the angle fixed, but then decide to flip a coin (or in some other way) decide whose angle will be the clock-wise-most angle. The average, as I understand it will in this case be cos (30) since cos(30) = cos(-30) and the sine components cancel, since sin(30) = -sin(-30). So I don't understand your comment that my model always obtains an answer identically zero. This, as I understand it, is simply the same result that you get by claiming synchronized switching topology.

      Edwin Eugene Klingman

      Dear Joy,

      I may be confused about this, but I understand the problem to be one of showing whether or not Bell's theorem leads to 'hidden variable'-based calculations that yield the same predictions as quantum mechanics calculations. Because, as I clearly state in my essay, my wave function *is* the quantum mechanical wave function, then I should reproduce the same quantum mechanical results as quantum mechanics. The question is why Bell does not, given his assumptions. You have claimed that Bell makes a complicated topological error: "Bell's prescription is not only false, it is breathtakingly naive and unphysical." (your book, page 3).

      In a way we agree on this. In an earlier paper ("Physics-based Disproof...") referenced in my essay, I claim that Bell's use of a unit vector (a or b) to represent the inhomogeneous Stern-Gerlach field is unphysical. But of course the only way to actually compare any result to Bell's calculation is to use this unit vector, so we are to some degree stuck between a rock and a hard place.

      As I have continued to ponder Bell's theorem, I also realized that his use of a simple unit vector to represent the actual physical spin (due to a finite particle and associated fields) is a similar error, since the particle induces fields that do *not* have the character of a simple unit vector. For this reason I believe that his two unit vectors vastly oversimplify the situation in which an inhomogeneous spin field traverses an inhomogeneous magnetic field, and therefore his oversimplified calculation ("Bell's inequality") is not to be taken seriously. At least not seriously enough to change all of our ideas of local realism.

      For exactly this reason I believe that your framework in which 'volume forms' are employed instead of unit vectors is both ingenius and appropriate, and I have, as explained in my essay, described a volume form that is appropriate to my theory of the wave function.

      To summarize, my wave function, being a solution to the Schrodinger equation, should provide the same results as quantum mechanical calculations. As Feynman stated: "The same equations have the same solutions." But your clever reformulation of Bell's theorem, based on replacing overly simplistic unit vectors with more appropriate volume forms, should also produce the QM results. It is my expectation that my volume form will accomplish this, in the end.

      Edwin Eugene Klingman

      Dear Tom,

      I very much appreciate your recognition that Joy and I apparently agree in a number of ways. I fully respect your mathematical capability and also your physics insight, although you and I may have fundamental differences here.

      I do not dismiss your conviction that Joy's math agrees with your conceptions. But let me repeat a story here that may be more meaningful now that it may relate to the problem at hand. As you know Kaluza-Klein proposed a fifth dimension to unite gravity and electromagnetism, and ended up explaining the charge of an electron as related to a 'small circle' in the fifth dimension. Elsewhere (see "Chromodynamics War") I invoke a field, the C-field, and also derive charge as related to a 'small circle', but in 3 (or 4 space-time) dimensions. Lee Smolin has remarked that:

      "A property of an extra dimension -- the radius of the extra circle in Kaluza-Klein theory -- can be interpreted as a field varying over the other dimension."

      This implies to me that perhaps the "extra dimensions" that Joy invokes can be interpreted as a "field varying over the other dimensions", in which case, as you say, we might reach the same place by different roads.

      Best regards,

      Edwin Eugene Klingman

      Dear Edwin,

      We have all gone through all the various issues you mention, in several blogs, so let me not pollute your author's blog with them again.

      The bottom line is this:

      Quantum mechanics predicts the following correlation function for the singlet state:

      E(a, b) = -a.b.

      This correlation function says that, given two fixed directions a and b, if the angle between them happens to be equal to 30 degrees, then the quantum correlation predicted by the singlet state is

      E(a, b) = -cos(30) = -0.866...

      This is a result from Quantum Mechanics 101. You cannot possibly dispute this result. Any would be modeller of quantum mechanics must reproduce this number, just to get started. All I am asking you for now is to reproduce this number---not in words, or hopes, or intentions---but by explicit calculation---for the fixed directions a and b. If you cannot reproduce this basic prediction of quantum mechanics, then your program---despite all of its worthy intensions---has failed already.

      You need not take this as a criticism. If you accomplish this, then it would be a massive boost to your program. According to Bell, as well as me, you will not be able to.

      Joy

        Hi Joy, Edwin,

        I have to agree with Joy here. It is pretty well known that particle spins can be parallel or anti-parallel to a particles direction of motion plus it is also well known that EM radiation can be left or right circularly polarized.

        So you really need to figure out how to get your C field to be both left and right handed. Nature is that way, so there must be a way. You would need to get the +/- 1 factor in your eq. 11.

        Best,

        Fred

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        • Post #72

        Well yes, I guess I didn't understand completely. I see now that applying the law of large numbers to zero out the bivector terms (eqn 12 et seq) leads us into the same algebra morass that generated much of the acrimony of the past two years. Ouch.

        I've not been able to conceive of any but a topological derivation of -a.b, for the simple reason that if this term is anything other than an input argument to a function continuous from the initial condition, it can't give us twin results (argument and value) and must be given a linear interpretation which obviously won't fit the analytical case. This probably isn't clear -- and I will produce a detailed explanation if required or requested -- relevant to Edwin's presentation, though, the average of experimental correlations (eqn 12) is not the same as the covariant correlation of argument and value. Here is where I have been able to grasp the extraordinary utility of geometric algebra for the Christian model -- because it eliminates complex values of a real continuous function without losing continuity, by appealing to the octonionic space.

        Because quantum correlations in the Christian framework are explained solely in terms of topological initial condition and orientability, we don't need (and can't use) any tools of probability -- not the equally likely hypothesis, nor averaging nor central limit. All that remains is regression to the mean, which is expressed as the complete set of norms on a finite space.

        Edwin, I still think it's possible for you to take a different road toward the same conclusions though I personally think it is unlikely to succeed -- for the reason that it's the road I abandoned after years of finding no means to obviate extra dimensions. It's important to understand that we can use mathematical artifacts of extra dimensions to describe manifestly local results without rejecting scientific realism, a case I am firmly convinced that Joy has demonstrated. If one goes back to the very beginning of the dialogue, one can see that my first response to Joy's claim that "Bell made a topological error," was "So what? He wasn't doing topology." It took a lot more to convince me that Bell *should* have been doing topology.

        I think Anton Zeilinger is utterly wrong that events are not in need of interpretation. Theory *is* the interpretation of events. We do not do objective science inductively. I give as an example Penzias' and Mitchell's discovery of microwave background radiation. The data mean absolutely nothing unless interpreted by theory, in this case the Big Bang cosmology, though I acknowledge that other theories may fit the same data.

        Tom

        Dear Tom,

        Your comments are interesting, and may yet shed light on what's happening. You said a lot, so I'll bite off small pieces.

        First, you remark that we can use mathematical artifacts of extra dimensions to describe manifestly local results without rejecting scientific realism. Of course I have no objection to mathematical artifact. In my essay I explain how Hilbert space in an energy basis is appropriate, and how it correlates with probability. But you aren't implying that Joy's 7 (or 8) dimensions are only artifactual, are you?

        In a comment above I explain that Bell's use of unit vectors to represent interaction along the path of one inhomogeneous region of field through an extended region of another inhomogeneous field might be viewed as a topological problem, in that inhomogeneous fields might be mapped into equivalent space-time curvature, and one can view the problem in terms of parallel transport. Anyway, whether you agree that this is topology or not, we both agree that Bell formulated his problem incorrectly. He "should" have been taking the interaction of two inhomogeneous fields (in relative motion) into account, and he failed to. No wonder his results don't match reality.

        You said more, but I'll stop here. We do agree about "probability" in QM. But you seem to want to banish it, while I'm trying to explain why it works for a physical wave function.

        Edwin Eugene Klingman

        Dear Fred,

        The wave function is *not* the spin your are talking about. The spin, whether for electrons or photons, is measured by its electromagnetic properties. From de Broglie on, it's been understood that the wave function is not the electromagnetic field. On the other hand the wave function *does* correspond to neutrino spin (and Z and W bosons) and here Nature most certainly does do it my way (i.e. lefthanded).

        Thanks for the comment. I still hope to bring you around!

        Edwin Eugene Klingman

        Joy,

        You keep asking me to produce a quantum mechanical calculation with my model, which indicates to me you haven't understood my model. My model yields Schrodinger's equation and the solutions to Schrodinger's equation, so I get identically the same results that quantum mechanics gets.

        All I do is claim that the wave function is physical, *not* information only. By the way, I received in the mail this morning my latest issue of Physical Review Letters, which seems to agree with me. The article, (PRL 108, 260404 29 June 2012) "Implications of the Pusey-Barrett-Rudolph Quantum No-Go Theorem" undermining the quantum state as "mere information" (or "knowledge") about the real physical state of a system. As I understand it, my model is compatible with this theorem.

        You have spent thousands of words telling others that they did not understand your approach, and to read it again. I don't believe that you understand my approach, or you would not keep telling me to use QM to achieve a QM result. I can't achieve anything else, since my equation and solutions are the same as QM. Please try to understand this.

        However, like you, I believe that Bell got the wrong answer, and so I take advantage of your framework to reformulate Bell's problem -- using the volume forms that you proposed and that I find very appropriate. In this case I *do* depart from standard QM, since the standard QM does not use trivectors. The intent here is to show that, properly formulated Bell's approach matches QM, not his inequality. I may fail in this regard, but please try to understand what I am doing. Your repeated challenge to derive a QM result is proof that you haven't yet understood my approach.

        Edwin Eugene Klingman

        Hi Edwin,

        You wrote: "You keep asking me to produce a quantum mechanical calculation with my model..."

        No. I am *not* asking you to do that. I am *not* asking you to produce a quantum mechanical calculation. I am asking you to *reproduce* one of the most basic predictions of quantum mechanics within your own model. I am not concerned about what your model is or whether or not I understand it. Whatever your model is, it MUST reproduce the number -0.866 as a singlet correlation along two fixed directions a and b, 30 degrees apart. This number is a well established empirical fact. But you are unable to reproduce it within your model. I claim that you will *never* be able to reproduce this empirical fact---which also happens to be a prediction of quantum mechanics---unless you embrace my framework in its entirety.

        Now you can prove me wrong quite easily. All you have to do is to calculate the number -0.866 explicitly, for the fixed directions a and b, within your own model.

        Best,

        Joy