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

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    • Post #77

    Hello,

    You confound really Joy what is the Universal dynamic and its irreversibility and the programmation by computing.

    1 is not equal to -1 at my knowledge, the symmetries are bad understood in their pure physicality.The calsulations are just a mirror in fact, the same results for the same equations, but ....

    all functions do not go to the FUNCTIONS.

    Ans also , the informations are encoded in a pure 3D dynamic !!!The waves and the informations.....=......rotations of spheres !!!

    Edwin, I agree about your words, that said don't forget that the rotating 3D spheres asnwer to all.So the spin and the waves are linked.

    You are right about the physicality of these waves, furthermore the informations also can be encoded in this mass. All is a pure physicality even the informations are under a specific universal dynamic.

    Regards

    • [deleted]

    • Post #78

    Let's play

    Let's speak about the entropy and the information ok ?

    well

    and you speak about predictions ??? and empirical facts ???? you are not rational you know ???

    I ask me how is the model implied to an isothermal system with N molecules like in the ideal gas for example with a volume precise .The increase of information ..."is it proportional with entropy ?"

    You can speak about the maxwell demon you know. And after we shall link with the disorder and the order !

    Dear Joy,

    You say: "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."

    It's pretty clear that you don't understand what I am saying, which is that I calculate the correlation EXACTLY the way it is done in quantum mechanics. But since the implication seems to be that I don't know how it's done in quantum mechanics, I will tell you how I would do it.

    Beginning with equations (4) and (5) in my essay for the time evolution operator and Schrodinger's equation, I would use the appropriate Hamiltonion for the electron spin 'u' in a magnetic field 'B'

    U(t) = exp (iHt/h) => exp (iu.B/h)

    where U(t) is the evolution operator, t is the time, h is Planck's constant, u is electron spin and B is the external magnetic field and the period is the dot operator and the Hamiltonion becomes time independent. This would be applied to the singlet states to evolve the states to Alice's and Bob's respective directions of the magnetic field and the correlation found in the usual way by calculating the expectation value between initial states and the evolved states, where Bob's evolution operator does not affect Alice's particle and Alice's evolution operator does not affect Bob's particle. The result will involve a term of the form

    < singlet | s.a s.b | singlet >

    where s is the Pauli spin matrix and a is the direction of Alice's field and b is the direction of Bob's field.

    Then I would make use of the identity (s.a)(-s.b) = -a.b plus -is.(axb) and Bell (equation 3) claims this results in -a.b

    There may be other ways to explain this, but I believe they are equivalent. Most explanations will involve ensembles and the density matrix, with density rho=(I plus a.s)/2 for an ensemble of spin one-half particles, but the above is about as succinct as I can manage for a text-based comment.

    Joy, it's pretty clear that you will never accept any statement that does not agree that you have the only possible way, and it's also clear that you have not understood what it is that I am saying. I do not wish to turn this into an extension of your 'Disproof' blog, so as far as I'm concerned we can leave it that you do not accept the ideas put forth in my essay. For anyone who has followed all of your blogs, that was a foregone conclusion.

    Best,

    Edwin Eugene Klingman

      Dear Edwin,

      I am sorry, but we cannot leave it at that. As far as I have understood, you are making a claim that your model reproduces quantum mechanical correlations in every respect, but at the same time your model is both *local* and *realistic*, thus providing, in particular, a local-realistic explanation for the singlet correlation, in contradiction to Bell's theorem . If this is not the claim you are making, then I do apologize and withdraw all my comments from this blog.

      However, what you have described above, and in your paper, is neither a local model, nor does it reproduce the observed singlet correlation, -a.b, for the fixed observation directions a and b of Alice and Bob. It is pretty clear that you have not understood Bell's theorem at all. The fact that "Bob's evolution operator does not affect Alice's particle and Alice's evolution operator does not affect Bob's particle" DOES NOT make your model local in any way. Nor does your use of the identity (s.a)(-s.b) = -a.b plus -is.(axb) reproduce the scalar result -a.b for the fixed directions a and b.

      I am forced to say this because you are making a use of my framework and implying that you have improved upon it. As grateful as I am to you for that, I cannot possibly let you misuse my framework the way you are misusing it and not make a comment. So I assert, as clearly as I can: your model is not a local model, and it does not reproduce the singlet correlation for the fixed observation directions of Alice and Bob (or even for the unfixed directions as far as I can see). Therefore your model is not a counterexample to Bell's theorem.

      Having said that, I have no objections to your model explaining---in a different and perhaps more enlightened (but ultimately *non-local*) way---some of the physics usually described by quantum theory. That is very nice. But your claim of producing a local model for the singlet correlation is simply false. You are nowhere near accomplishing that.

      Best,

      Joy

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      • Post #81

      Hi Edwin,

      " ... 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?"

      They are. It would be wrong, though, to say "only" so, as if to imply "mere." What I mean by "mathematical artifact" is a term that instantiates meaning without changing meaning. By the same token, Einstein's famous equation doesn't change meaning if the statement is truncated to E = m -- as an equation of state, though, E = mc^2 tells us that the rest state of matter contains more energy as kinetic potential (atomic binding energy) than is evident until we actually measure the excess, which of course, is the source of atomic power.

      Joy's expectation (or correlation) value E(a,b) = -a.b is also an equation of state. That is, it prescribes a measurement limit, just as the constant c^2 in special relativity. And just as we expect a precise quantity of energy to be released from identical quantities of mass every time we "split" an atom, one should expect a precise correlation between an observer's potential result and her actual measure result at the limit, which turns out to be identical to quantum mechanical correlations.

      When you speak of the Hilbert space and probability functions, you are out of the domain in which Joy's framework lives. One can't derive the orientability that obviates every probability function, from that basis. One gets it only in the limit of topology that Joy has described: " ... all possible quantum correlations is derived from the maximum of parallelizing torsions within all possible norm-composing parallelizable manifolds."

      Just as binding energy is "hidden" in the potential kinetic energy of mass, the correlation function of quantum pairs is hidden in the topology of parallelizable spheres. Just as the measured potential of binding energy is realized at the kinetic limit as a local and real phenomenon, quantum correlations are realized at the topological limit as a local and real phenomenon. The self-limiting mathematical artifact in each case tells us that we have arrived at a closed logical judgment -- the result (value) will always be covariant with the (argument) limit; i.e., dependent on topological orientation and initial condition.

      How we (you and I) arrive at a non-probabilistic wave function has nothing to do with Joy's framework. We use the term because we need a local artifact to describe a continuous function independent of discrete measurement results (a real continuous function is never probabilistic). Joy doesn't need it at all -- his topological framework obliterates the distinction between local and global. "All physics is local," as Einstein said.

      You wrote, " 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."

      It doesn't work for the wave function, and can't. The wave function is continuous; there is no continuous probability function.

      Tom

      Hi Edwin,

      On a second thought, I am afraid I will have to take back my comment that at least as a non-local model your model may be nice. In fact even as a non-local model it blatantly violates relativistic causality, because it blatantly violates parameter independence (parameters a and b have to be randomized in harmony to get the correlations right even for the non-fixed a and b). In other words, your model harbors signal non-locality that is even worse than that of Bohm's theory, even if we ignore the manifest backward causation between a and b. This is on the top of the fact that the model cannot reproduce the most basic experimental observations without randomizing a and b. Oh, well.

      Joy

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      • Post #83

      "Criticism like rain should be gentle enough to nourish a person's growth" Geoffrey Moss

      I am all for that.

      But I have also learned that sometimes gentle criticism is misconstrued as room for wiggling out of it. I did make a very polite, very respectful, and very gentle criticism of Edwin's model, deliberately away from his author's blog. This was neither understood nor taken too seriously by him. Gradually I had to turn up the heat when he repeatedly refused to recognize his error. And believe you me, what I have written is not even a fraction of what I actually think of Edwin's model (here I only mean his model for the EPR correlation, not his essay as a whole). But I consider him a friend and a supporter of my work, and I like him as a person. Therefore I have tried extremely hard to be as gentle and polite as possible.

      Hi Joy,

      You make several points. I still do not believe you understand my model. Since I propose that the wave function is a circulation in a local field induced by a mass current in accordance with the weak field equations of relativity, I think it's clear that the model *is* a local model. As I note above, the PBR No-Go theorem seems to imply a real physical field as opposed to an 'information-only' wave function, and the latest experimental measurements of the wave function also seem to imply this.

      Therefore I don't believe that you can argue, as you appear to, that my model is not local. What you might argue is that I cannot successfully map this model into quantum mechanics. I believe that the fact that the free particle solution in my model is almost identical to the quantum mechanical free particle suggests that I *can* perform this map. On the other hand all real QM representations assume a Schrodinger 'wave packet' and thus a Fourier superposition that ususally entails a Gaussian apodization function and a close analysis of my equation appears to imply a slightly different apodization function, so there still results a 'spread' of momenta in both models that may or may not be equivalent. Since A. Zee remarks that "a significant fraction of papers in theoretical physics consists of performing variations and elaborations of this basic Gaussian integral" I do not believe that there is a 'God-given' apodization function for QM and therefore my apparently equivalent formulation seems acceptable as a wave function.

      You ignore the fact that the actual physical mechanism I postulate in my theory *automatically* makes the wave function local, and therefore your insistence that it is not is misplaced. Also you claim that my use of the identity does not reproduce the scala -a.b, but my claim was that my use is identical to the standard QM use, so does, or does not, that produce -a.b?

      You say that I am using your framework and claiming to improve on it, therefore you are forced to comment. I have in a number of places acknowledged your right to comment on this, and do so now, although at some point it becomes a waste of time. Those who see an error in your math certainly could not 'wait you out' as you have never accepted even the possibility that you made an error. As I also mentioned, it is early in the game for my model, and while I am willing to face the fact that I may have made an error, I am not ready to concede that it is irrevocable. So no matter how much you protest, I will simply try to understand your point and determine to address it, either now or in the future.

      You claim that I do not understand Bell's theorem as well as you do. But if your contention is correct -- that Bell made a fundamental mistake -- it does not really matter whether or not I know exactly where he is wrong (although as I note above, I think I do know.) If he is wrong, then his inequality that is the primary basis for his claim of non-locality is also wrong, and cannot be used to argue for non-locality, as you seem to be doing against my model. I repeat, I think you are confused about my model. It is not surprising, as you have been twisting your own brain around your topological ideas for years now, while I have been doing similar based on my understanding for a while also. Where you have an advantage on me is that you have been defending against challenges much longer than I, and so have worked out, at least to your own satisfaction, what the answers are.

      As I mentioned in an earlier comment, I welcome questions that I have not thought of, as I always learn something from answering these question, or at least trying to.

      Since my model is, on its physical face, local, then I must try to translate all of your claims that it is non-local into some understanding of what you could mean, and that is made difficult by the fact that you don't even understand that the field is local. This could go on for a while.

      Bst Edwin Eugene Klingman

        Dear FQXi'ers,

        Comments above indicate that clarification is needed to connect my real physical model of particle plus wave with the 'standard' quantum mechanical correlations. Specifically, I note that the physical field induced by the (non-point) particles satisfies the Schrodinger equation for the free particle and can even be used to 'derive' the Schrodinger equation. The essay then develops the relation between this physical wave and the mathematical wave function, explaining the correlation of the normalized probability amplitudes and the non-normalizable wave. Quantum Mechanics, per se, is still calculated in terms of the probability amplitudes and thus results in the same answers that have been obtained since Schrodinger first formulated his equation, and Born interpreted the waves as probability. Because many physicists believe that non-locality is implicit in the configuration space formulation of QM I discuss the origin of this concept and show that it derived from the mistaken belief that physical waves propagate without particles. But since Bell also claims to show that non-locality is implicit in QM --- based on his oversimplified analysis (I think Joy and I agree on this statement?)-- I also attempt to show how my model, in Joy Christian's volume-form-based formulation, results in the correct correlation. Joy, not surprisingly, disputes these results, as they do not require or imply his synchronous switching topology. I believe that he is wrong in some of his statements above, but of course I will continue to work on this application of my model to his framework to try to address all criticism.

        While I assume that it is possible some combination of my local physical wave function and Joy's topological analysis could both be true, this seems an unlikely and awkward solution to the problem.

        I thank Joy for his development of a 'volume-form'-based approach to Bell's theorem and for his fighting the good fight against a non-local (and nonsensical) interpretation of quantum mechanics.

        Edwin Eugene Klingman