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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

    Hi Edwin,

    This is indeed a waste of time for both of us. We will have to agree to disagree. You have made your points and I have made mine. Here is where we stand:

    (1) You claim your model is local. I claim your model is nonlocal in the worse possible sense. It harbors an extreme form of signalling non-locality.

    (2) You claim, or at least thought earlier, that you can reproduce the strong quantum correlations in your model. I claim you cannot---not even the most basic one (-0.866...)---and not unless you embrace my entire framework by recognizing and understanding the true topological origins of the quantum correlations.

    (3) You claim you have produced a counterexample to Bell's theorem. I claim you do not even understand Bell's theorem, let alone producing a counterexample to it.

    (4) You claim I do not understand your model. I claim I understand it enough to say what I have said about it (in fact I understand it much better than you do).

    (5) You pay attention to some silly criticisms of my model made by some uninformed and unqualified people. I pay attention to them only to point out their own errors.

    I think it is best to end this discussion here, as you also seem to be suggesting.

    Best,

    Joy

    Hi Joy,

    I agree that there is no point in continuing this ad nauseam. I disagree with your above points, and I believe you do not understand my model, but as it conflicts with your synchronized switching topology model, I do not expect to change your mind. Hopefully, those who are not committed to your model will continue to give my model a fair critical analysis.

    Best,

    Edwin Eugene Klingman

    Just a small point: If my model is a "synchronized switching topology model", then Obama is the Queen of England.

    Then your model is definitely not a "synchronized switching topology model"!

    But I have essentially characterized it this way many times as my legitimate way of understanding what you are saying, and you have never explained to me how or why the topology switches between experimental runs but not during experimental runs, so I assumed that my characterization was accurate. If you care to do so here, please do so. I am curious about this point. I do not wish to mislead others about the nature of your topological model. I admit that I do not understand the physics of your topology. Since I have apparently mistakenly described it, please fell free to use my blog space to correct this description. I will not comment further on this point.

    Edwin Eugene Klingman

    Hi Edwin,

    Thank you for being generous with your blog space. It is pity that Internet can be such a two-edged sword. It is a blessing in that we can have open discussions like this, but it could also be a scholar's nightmare in that subtle ideas can be misconstrued on the Internet, if they fall into wrong hands.

    In any case, here is what is actually happening in my model. The volume form, mu, is just an outward tool, a garment, if you like, or a representation, of the orientation of the physical space, S^3, which is one of the solutions of Einstein's field equations. Now, mathematically, for any space (not necessarily the physical space) there are always two orientations possible. Let us call them left and right orientations. The choice between them has to do with how the ordered basis of that space is chosen. So, for any space, there exists a natural freedom of choice between left and right orientation. We must make a choice between the two possible orientations before we start solving any mathematical problem within that space. Usually, we instinctively make a choice of the right orientation without even thinking about it, but a choice we must make.

    Now think about the moment of creation of the EPR pair of particles. As soon as they begin evolving, in whatever space they may be evolving, they have to make a choice, as a sheer mathematical necessity, before they can even get started doing whatever they want to do. What I noticed, back in 2007, was that this freedom of choice fits hand-in-glove with the notion of the initial state introduced by Bell in his local-realistic framework. He called this initial state "lambda", the hidden variable. All I have done in my model is equate Bell's lambda with the natural freedom of choice in the orientation of space that exists for any physical system before it can get started doing whatever it wants to do. Now Bell took his lambda to be a random variable. But what could be more random than a 50/50 chance? So I equated Bell's random lambda to the random choice of orientation of the physical space, with 50/50 chance for each of the two options. Despite all the fuss some people have made about this, it is the most natural thing any physicist could have done. In any case, it is hardly "a switching topology", because the topology of the space is the same for both of its orientations. It is more like flipping a coin to decide whether to turn left or right at a forking path, for you can't venture on both paths at the same time.

    Best,

    Joy

    Hello Edwin Eugene,

    I have downloaded, and glanced at, your essay - which I plan to read for detail in the next day or so. It appears that you echo or champion some of the same points I make in my essay, which was submitted 24 hours ago. I also mention JC's ideas and the PBR paper that favors a literal interpretation of the wavefunction.

    I agree with Joy's comment just above, that there is an inherent choice built in to the topology of spaces, and I actually address this briefly in my endnotes - assuming my paper posts as-is. But I feel it is not only possible, but essential to forge links between the geometric approach and approaches involving the wavefunction.

    While some folks tend to feel that you can't have it both ways, I tend to believe that it has to work both ways, being internally consistent within both sides of a dual representation - for it to work in nature at all. That is; the wave-like portion needs to follow the rules for waves and the particle-like aspect needs to follow particle rules - but it's not like we can choose one or the other and know the whole picture.

    However; Dieter Zeh clearly argues that the wave-like representation can tell you what is really happening better than the discrete view. More comments will follow once I've read for detail.

    Good Luck!

    Jonathan

      Hi Jonathan,

      Very good to see you back. I do look forward to reading your work. I have just read and given a glowing comment to Ulf Klein's essay and think you might like it also.

      Too bad our friend Ray Munroe is not here this year, but here's to his memory.

      I very much look forward to your comments after you've read my essay.

      Edwin Eugene Klingman

      Hello again,

      I've digested more of your paper and glanced at Ulf Klein's and Stanley Reiter's - noting connections across a common theme. I'm putting together a brief paper reviewing my conceptual approach to decoherence, and comments about the wavefunction, so I don't end up recreating the same information in 3 or 4 places.

      Expect some comments soon, regardless.

      Jonathan

      Hello Edwin Eugene,

      Here is some food for thought; the first few pages of the document promised above, with thoughts on decoherence and the wavefunction. It may turn into something that can be published, when complete, but now is just a draft of a Physics letter.

      I'll likely have some specific comments on your paper later or tomorrow.

      JonathanAttachment #1: DecoherenceReviewDraft.pdf

        Jonathan,

        Great! I'll be reading this while you look at my essay. I'm glad several of us are focused on quantum mechanics and wave function issues. Michael Goodband just posted another, asking if "quantum theory is as fundamental as it seems", but his is very complex and I've only read it once.

        Edwin Eugene Klingman

        Hi Tom,

        Thanks for the comment. I find it very interesting that you say Joy's 7 (or 8) dimensions are artifactual. I would assume we mean the roughly the same thing by this term, [and my 'only' was not meant in any derogatory fashion, as 'mere']. But your definition is not quite clear to me, although your example is perfectly clear.

        I know, and have been aware for at least a year, across the many "Disproof" blogs, that you have a picture in your mind that makes sense to you. Whether it's the same picture Joy has is another question, one that I certainly can't answer and I don't believe he has committed to either way. I recall our extensive conversation over Lamport, and the result that neither of us changed the others mind (as usual!) I find it fascinating that our approaches share a great deal (based in continuity) while we somewhere make a 90 degree turn and go off into some other dimension of understanding. You use the words correctly, good grammar, expressive terms, but I often can't grasp what you are saying. Your idea that " ... all possible quantum correlations is derived from the maximum of parallelizing torsions within all possible norm-composing parallelizable manifolds", is understandable as English, but doesn't do it for me as physics. When trying to understand the basis of our disconnect I've wondered if it's as simple as: you try to fit physics to math, I try to fit math to physics. It's probably nothing so simple.

        For instance, Joy's last response to me, in which he corrected my characterization of his idea as a "synchronous switching topology" was succinct and probably his best brief description of the way he sees things. I now realize why my characterization was inappropriate. On the other hand, his description seems to me to be purely mathematical with no physics content. I buy it as a math approach to kill unwanted terms, but not as a theory of the physical universe. Similarly, your claim above that "his topological framework obliterates the distinction between local and global" is just so many words to me. I am quite sure that you have something in your head that goes beyond the words, but it's not in my head.

        Also your words about probability. The wave function may be continuous, but it can describe discrete states based on local conditions; the ground state is different from excited states. The existence of these different states lends itself to a 'state'-istical approach and the probability of these different states is related to their energy. I don't see how you can ignore the fact that quantum mechanics is based on and makes good use of these probabilities. I have simply tried to relate the mathematical probability amplitudes to the ontological physical waves induced by the particle.

        Nevertheless, I enjoy hearing about how you see things, and hope you find my views equally interesting.

        Best,

        Edwin Eugene Klingman

        Hi Edwin,

        I cannot help making some further corrections in your view of my model. You wrote: "I buy it as a math approach to kill unwanted terms, but not as a theory of the physical universe."

        This sentence is wrong and misguided on several counts. To being with, the idea that I am somehow "killing unwanted terms" is offensive to me. As I have said before, it shows that you have fallen for the mischaracterizations of my work by Gill and Moldoveanu, and that you have not understood---or understood only very superficially---what my program is all about. I am not killing any unwanted terms, but calculating the physical correlations among the physical events occurring within our physical space. The term you call unwanted, namely a /\ b, is actually the most wanted term in my model. It represents the torsion within the physical space, modelled as a parallelized 3-sphere, and hence it is responsible for the violations of the Bell-CHSH inequality (I explained this to you in one of my very first responses to your questions on the Disproof blog). Moreover, 3-sphere is a solution of Einstein's field equations of GR (it is one of the Friedmann-Robertson-Walker solutions of the standard cosmology), and thus my model can hardly be called "a math approach." I am aware of your strong prejudice against what you consider extra dimensions, but there is nothing "extra" about the dimensions of the 3-sphere, which is a three-dimensional physical space. When it comes to quantum correlations more general than the EPR correlations, all seven dimensions of the 7-sphere do come into play, but the correlations like those exhibited by the GHZ state are a direct physical evidence for these "extra" dimensions. In fact, even in this case I see nothing extra about the dimensions of the 7-sphere. Thus, the way I see it, your reservations are based on some misunderstandings of my framework as well as on your insistence on separating what you consider physical from what you consider mathematical. In short, in my view, your sentence I have quoted above is completely unjustified.

        Best,

        Joy

        Jonathan, -- a very brief review looks as if we have the universe bracketed!

        Joy, I plead guilty to not understanding your model. I have told you that for quite a while now. I have read your book and all your papers, but I do not see physics the way that you do. While I am not an expert on FLRW models, some of the other essayists seem to be and seem to, if not dismiss them, at least downplay them. Tom quoted Einstein, "All physics is local" and that is what I tend to focus on as all discussions of global topology or global wave function or global anything seem to exceed my imagination, or a least my ability to grasp the reality enough to take it seriously as other than a mathematical exercise. Probably my failing. The fact that I do not understand your model physically is not an insult to you and has never been intended to insult you. I have actually invested a lot of time and effort trying to understand your model. I wish people would do the same for my model. One option of course is to say nothing at all about your model, but you may recall that on your Disproof blogs I often served the purpose of bringing the discussion back from endless haggling over whether or not a sign error exists to questions of a more fundamental nature. I recall that you thanked me at least once for this. And you posted a pdf containing my defense of model in almost half a dozen places.

        Joy I bear you nothing but good will. You said to Georgina that I am a friend who has supported your work. I hope that is true. The fact that I do not have the picture that you have, nor the picture that Tom has is not an attack on either you or Tom, it's just a simple fact. I am not against topology, in fact I now have, as part of my theory, a topological model of spin one-half particles that I searched for decades to understand. So I believe in topology in its place, I just don't understand yours. I was not trying to demean your ideas when I said that I now see why 'synchronized switching topology' is inappropriate, but your explanation of the choice of handedness occurring at every event seems unphysical to me. Of course now that you have explained (again?) that you are not trying to get rid a^b I also see that my remark about unwanted terms is also inappropriate. I'm glad you have an interpretation for those terms in your model. I have decided that I would like to be able to explain the a^b in my model. At the moment I have no such explanation. And you are correct that I separate the physical from the mathematical, which may account for much of this impasse.

        Anyway, feel free to correct any misstatement on my part about your model. I do not make them to antagonize you.

        Best,

        Edwin Eugene Klingman