• Ultimate Reality
  • Classical Spheres, Division Algebras, and the Illusion of Quantum Non-locality:

I wish to mention a recent preprint of mine---this one---which is about the prevalent (but false) belief in "quantum non-locality." I am, in fact, required to post this link here, because this preprint is part of my forthcoming book on Bell's Theorem and Quantum Entanglement, which is kindly supported by FQXi through a generous mini-grant.

Let me begin by mentioning that Michael Atiyah---that wise old sage of mathematical physics---gave a provocative seminar last November, at IAS, Princeton, with the following thesis: There are four fundamental forces of nature, and there are four division rings over the reals (connected with the parallelizability of four classical spheres): the real numbers, the complex numbers, the quaternions, and the octonions. Therefore---according to Atiyah---one should expect all four of these division algebras to play a role in the ultimate theory of physics, allowing octonions, in particular, to account for gravitation. As one would expect from someone like Atiyah, this was not an idle speculation. He described some specific steps in this direction, substantiated his ideas, and made some deep connections. Now you may wonder what this has to do with quantum non-locality. Well, rather astonishingly, the division algebras have popped up in my own work on Bell's theorem quite unexpectedly. When I started out my critique of Bell's theorem some four years ago, the division algebras were the last thing on my mind. I was simply trying to clean up the argument by John Bell, which I thought was far too sloppy---at least topologically---to lead to any radical conclusions about the nature of physical reality. But this cleanup operation has led me to uncover a profound connection between quantum correlations and the division algebras. The preprint linked above (and also this one) brings out this connection in a somewhat technical language. My main conclusion---after some four years of battle against the conventional wisdom---is that "quantum non-locality" is nothing but a make-belief of the topologically naive.

    • [deleted]

    Hi Bee,

    Yes, a new mother of two beautiful baby girls! As far as I know, she is not writing a book. ;-)

    J.C.

    6 days later
    • [deleted]

    Joy,

    I recently found your papers on Arxiv and am working through them. This is quite a radical, but exciting development in the foundations of QM. I am still trying to work out the wider implications for QM hidden variables and so on. Also your latest paper relates the results to Torsion in the spaces. By coincidence I have also just been trying to understand the role of Torsion in (extended) GR. So there could be several convergences at work here: not just the Division Algebra story.

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      Roy,

      Thanks for your note. I too find the connection of my work to teleparallel gravity (i.e., torsion) quite intriguing (hence the last sentence of my latest paper). I am also exploring some other avenues unrelated to either gravity or division algebras---so watch this space, as they say.

      J.C.

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      I eagerly look forward to the book. I found Joy's article through Wikipedia, when I was following up issues raised in the 'Bell's Speakable and Unspeakable' last year. My first impression was very positive, in that it seemed to point out a simple flaw in the Bell's original paper, which overturned 60 years of accepted wisdom on non-locality. I expected to find lots of discussion at a very high level in physics on such a fundamental issue.

      Instead, I found relative silence. I understand that a paper is slowly making its way through the Physics Review channels. I did not expect the time to get such a new critical idea accepted or effectively refuted to take so long.

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      Graham,

      Four years ago I too had such an innocent view of science. Sadly, today I have lost that innocence. I now appreciate that evidence in science---no matter how starkly presented---can be misinterpreted, denied, effectively neutralized, or simply ignored if the scientific community does not like it. Even in mathematics a theorem is not a theorem until the social act of its acceptance. And foundations of quantum mechanics is clearly not as exact a science as mathematics. Recall how von Neumann's theorem against general hidden variables was believed in by the physics community for 30 years despite its clear-cut refutation by Grete Hermann in 1935 (and despite the existence of explicit counterexample to the theorem by Bohm). It was not until John Bell rediscovered Hermann's objection in 1965 that the importance of her work began to be appreciated by the community.

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      The idea that one should expect all four division algebras to play a role in the ultimate theory of physics, on the basis that there are four fundamental forces of nature, ``allowing octonions, in particular, to account for gravitation'' sounds very convincing, were it not for the fact that according to our modern -- i.e. post-1915 -- views on gravitation, the latter is not a force at all, but rather an aspect of spacetime structure. However, if the gluons (8), resp. electroweak vector bosons (4), are somehow associated with resp. the octonions and the quaternions, one should expect that there are exactly three Higgs bosons, being associated with the remaining two normed division algebras, namely the real and complex numbers. Alternatively, since the mean dimension of the five exceptional Lie algebras is 105, and there are only 25 known fundamental particles -- one of which is still elusive -- one should expect the discovery of 80 new fundamental topologically nontrivial EPR elements of reality at LHC sometime very soon.

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        Your sarcasm is not entirely unjustified, but it distracts from my main point. While I wholeheartedly endorse the thesis that "gravity is not a force" (see, e.g., some of my older papers on the arXiv), to be fair to Atiyah his arguments were not as simplistic and naive as your comments seem to suggest.

        But all that is beside the point. The main concern of my note is the prevalent but false belief in "quantum non-locality", not the true nature of quantum gravity. And whatever else one may discover at LHC, it certainly won't be "non-locality", unless LHC is capable of discovering figments of imagination.

        • [deleted]

        Right, well I find it very amusing to read that my ``sarcasm is not entirely justified'' coming from a person with such fantastical ideas. It seems to me you are taking Feyerabend a little too seriously.

        • [deleted]

        You have misread my sentence. Please read it again and recognize your error. As for my "ideas", there is nothing fantastical about correcting the incorrect mathematics used within a fallacious theorem. That is all I have done. You will recognize that if you actually read my papers.

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        Or worse still....you really do believe you have actually disproven Bell's theorem. As for your point about incorrect mathematics, I indeed found that to be a nuisance when attempting to read your work. For instance, in one of your more recent pamphlets you mention that ``a 2-sphere is not homeomorphic to R2 (or to R for that matter, for both R and R2 have the same cardinality)''. However, the accompanying figure which is supposed to demonstrate this only shows that stereographic projection is not a homeomorphism, not that there exists no such homeomorphism. That, in fact, there exists no homeomorphism between R2 and S2 can for instance be shown as a simple consequence of the fact that the latter space is compact, while the former is not. The fact that R2 and R have the same cardinality is completely irrelevant here. According to your reasoning, R would not be homeomorphic to itself, since it is not homeomorphic to R2 (i.e. replace S2 by R in the above quote). Now, I can go on and mention (many) other similar exmples, but perhaps some other time. Anyway, I think my point is clear. Before accusing Bell -- or anyone else -- of sloppy mathematics, please check your own.

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        I am sorry you found reading my work a nuisance, but I thank you for reading it in any case.

        "...the latter space is compact, while the former is not."

        Indeed ... my point is as trivial as that, and I have said precisely that in one of my previous "pamphlets" (see especially my talk posted on this site). But this simple point was not understood by some, prompting me to add a figure to explain the issue.

        Now I have reread my sentence you have quoted, and I do not see how anyone can infer what you are inferring from it. My sentence is correct as it stands, and within the context of my paragraph it makes perfect sense. I will let the reader decide who is in error here.

        In any case, it is perfectly clear from my discussion in that paragraph that the type of functions proposed by Bell are simply not capable of accounting for all possible measurement results, and hence Bell's argument does not even get off the ground.

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        For example I have invented a new universal equation between all physical spheres.(quant.and cosm.)

        m mass V volume v1 vel.spin.of rot. v2 vel.orb.of rot. more the others rotations of the system......if you take these elements you have an universal constant....mvV= CONSTANT.............now of course all that is in 3D for the respect of our proportionalities of evolution, the SPHERIZATION OF QUANTUM SPHERES ....COSMOLOGICAL SPHERES ...INSIDE A BEAUTIFUL 3D SPHERE IN OPTIMIZATION TOWARDS THE PERFECT HARMONY BETWEEN ALL THESE SPHEERS AND LIFES AND COSCIOUSNESS.....LOGIC DEAR SCIENTISTS LOGIC......THE OCTONION AND THE QUATERNION ARE UNDER THE LAWS OF THE SPHERE!!!!!!!

        Regards

        Steve

        • [deleted]

        I think the sentence that you seem to be confused about is quite clear. No logical inference intended, so if you choose to read it differently that is simply an error on your part.

        • [deleted]

        Thanks. You have confirmed what I assumed to be the case - the simple inertia of introducing new ideas into the system. There must be a strong desire to keep hold of spookiness - it makes good stories.

        However, I would have hoped that your work at Oxford Uni and the Perimiter Institute would have acorded you a little more respect than having to respond to the charges of 'fantastical ideas' below. It is hard to understand how adding a few extra dimensions to balance Bell's equation is unfavourably compared with instantaneous action at a distance.

        Hopefully more people will simply read the paper for what it is, and appreciate the problem it attempts to solve. Hope you don't have to wait as long as Grete.

        • [deleted]

        Dear Dr Christian,

        I am a bit confused regarding your critique of Bell's theorem. While I don't claim to understand your work in detail, it appears on first sight that you allow geometries that not necessarily approximate flat metric, or any metric at all, on small scales. You bring the example of a torsion tensor, and - unless I am mistaken - one could also mention some noncommutative geometry as another example. Doesn't that mean that your work begins on a somewhat different premise as compared to conventional formulation in physics would? It appears to me that giving up "metric" as central concept to guarantee universal applicability of physical law, that indeed there will be far reaching consequences. That would make your work a very interesting opportunity for restricting validity of Bell's theorem to incomplete subspaces of a more general, "complete" geometry of nature. Am I off?

        Thanks, Jens

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          Dear Dr. Koeplinger,

          Thank you for your comments. I am not doing anything unconventional in my work, apart from correcting the incorrect topology of the co-domain of the local-realistic functions presumed by Bell. This change has nothing to do with the spacetime geometry, or the geometry of the quantum state space. It only amounts to completing the space of all possible measurement results, in the EPR sense, within the orthodox local-realistic framework of Bell. So, I am afraid, you are indeed "off."

          J.C.

          • [deleted]

          Thank you for responding so quickly! I'll have to study this and your work a bit.

          There's one more thing I'd like to ask: You mention Sir Atiyah's talk from Simons Center last year. Many people wonder about it, as do I; but beyond the slides I couldn't even find the reference list ... Since you're hinting at it, I thought I'd ask what you're referring to when you wrote about specific steps and substantiated ideas. Sorry for the indiscretion :)

          Thanks, Jens

          (no Dr/PhD)

          • [deleted]

          Jens,

          I myself was not present at Atiyah's talk and know about its contents only through secondary sources. I have written to him directly and perhaps he will respond (although he is an extraordinarily busy man, as you can imagine). Beyond that I rather not go into details about his talk, because the last thing I want to do is to misrepresent his carefully thought-out argument.

          Joy