Hello again Michael,

I have given considerable thought to what is implied by living inside a 3-sphere, what is seen by folks who reside inside a set of 'compact' dimensions, and so on. We might not notice. Size is relative, not absolute, and interiority/exteriority may be too, if we entertain higher order dimensions where geometry may be non-commutative or even non-associative.

That was part of what I was getting at, in my essay, when I was talking about the universe being inside out of the way we perceive it. We think we are pointing to an edge, or a spot on the universe's periphery, and yet we point at the center.

However; when we think we are pointing directly at the center of the planet, we are only getting the Schwarzschild radius away. This I see as related to the interlocking keyring example used to depict Hopf fibrations of S3. The actual center of the Earth is behind the event horizon, induced by the parallelization of the fiber bundle, it would seem.

My guess is the reason we don't 'see' space as octonionic, but appear to be inside the quaternionic space of S3 relates to the decoupling of matter and energy - which sets a time and distance scale for the universe, as a whole. More later in another missive.

Regards,

Jonathan

    Michael,

    I forgot to mention that is does appear that you have successfully sketched out how Quantum Mechanics could be an emergent theory, rather than fundamental. Since that is the question you ask in your title, I thought I should let you know that it looks like you have indeed proved feasibility for your topological solution, and made significant progress toward a robust formulation.

    Regards,

    Jonathan

      and you insist furthermore with your friends, how can you make this ? just for this papper and your hate and your vanity. You think what my friend ? That your faith is more than mine or what ? let me laugh, never I have crushed even an insect. You are not a scientist , it is not possible, and your firends also are not scizentists, it is not possible. In fact , you are just a team of vanitious false scientists.

      Your maths are so ironical, I ask me even where you have studied our mathjs you and your friends.Frankly, I really suggest that you buy better books of maths. If you made a correct mathemtical improvement ok, but no, you are weak in fact.I just see an ocean of stupidities.In fact your maths and your team do not arrive even at 5 per cent of my works.

      Ironical. Irritating that I arrive at New York soon no? you must become murders or pay people or invent an other strategy, because there, we are going to laugh you know. You know it also in fact :) isn't it ? probably that your hormons are touched , you and your friends, logic for the weak scientists. Even in team and even with your tools and your dtrategy, I continue all days to teach you my theory of spherization.:) I am not arrogant, it is god who said me that.He said me also, pay attention Steve, my son, the human nature is sometimes very bad. I know Father ! I continue just in praying and in showing them what is a real universal heart.

      Hello Michael,

      I am looking forward to settling down with your book (have been traveling and have not been in a position to do so yet). I can already see, however, that it deserves slow and careful reading. Skimming through gives me the impression that the material is quite suitable for at least a 1-semester course ... I hope that you or another instructor can make that happen somewhere, in a physics or philosophy of science curriculum.

      It's especially important, I think, that you emphasize both in the book and in your essay that inductive judgments (such as found in the standard interpretations of QM) cannot be logically closed. We seem to have gotten so far away from the fundamental tenets of scientific rationalism and mathematical completeness -- even I, who am quite familiar with the results of Godel and the philosophies of Popper and Tarski, did not immediately recognize that Bell's choice of measurement domain (S^0) obviates completeness. I only grew to understand the significance by following Joy's argument (reinforced now, by yours). So I do appreciate the breadth of applications of your program across a wide spectrum of disciplines and subdisciplines in physics, the foundations of mathematics, and the foundations of the philosophy of science.

      All best,

      Tom

        Tom,

        Not only "Bell's choice of measurement domain (S^0) obviates completeness" as you put it, but his choice is both a physical and a mathematical non-starter. His measurement functions A(a, L) do not (and cannot) satisfy the completeness criterion of EPR, unless their co-domain is chosen to be a unit parallelized 3-sphere (S^3). For no other choice of the co-domain (in the standard EPR-Bohm case) can Bell's local-realistic prescription A(a, L) for the measurement functions can be EPR-complete. For example, even a round 3-sphere will not do, let alone any other non-compact choice (such as the real line R). Thus Bell's argument is simply a non-starter---a scandal of epic proportions.

        Joy

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        • Post #62

        Joy,

        I'm getting it. :-) New post in my forum on the arithmetic issue.

        Tom

        and still the same ironical strategy. oh they are strong, wawww impressing.

        I see an ocean of hate, an ocean of confusions and an ocean of irrationalities.

        If Mr Witten wants, we can discuss about realistic convergences.

        Tom you are really lamentable in fact, you act like a puppet obliged to continue his strategy like a poor frustrated full of hate. It is logic that we do not see real works, if you and your friends you loose your time with the play and the strategies. in fact I have pity in a pure universal point of vue with humility of course.

        A real christian respects his fellowman when he is sincre and entire.The rest is vain. The pseudos shall fall down naturally as is rational the natural sciences.

        ps hello to edwin, James,Jcn,Jonathan, Georgina, Mickael, Ted,Florin, Christi,Don,Tom,George,Joe,Joy,zebitsad,Lawrence,.....good band indeed.

        ironical is a weak word.

        Spherically yours

        Hello Michael,

        I liked your essay very much. You have informed insight into areas of physics that I feel are quite important.

        Joy Christian mentioned my work in one of his responses to you. You can get a good overview of my ideas by reading my essay The Algebra of Everything. Your work is steeped in General Relativity, but perhaps what might be called Octonion Relativity might better connect up with your Octonion component. You will find this in my essay.

        I am very interested in your opinion, especially on the Hadamard structure that is prevalent within the structure of Octonion Algebra. If you could weigh in on my blog, I would be in your debt.

        Regards,

        Rick

        Hi Jonathan

        The way I visualise compact dimensions and why we don't notice them, is that we are spanning them in the same way that our shoulders span a narrow corridor. After a while moving backwards and forwards in such a corridor, you could stop regarding going left and right as constituting a dimension at all! For a closed universe, an analogy would be the experience of a single celled organism living *within* the water film of a soap bubble - it could only move in 2D within the film of the bubble and would have no experience of the 'extra' third dimension because the cell spanned it.

        In a KK theory with compact dimensions, a particle spans these dimensions and experiences changes in the relative orientation of the compact dimensions at different points in space as particle forces. Moving in the direction of these compact dimensions effectively amounts to rotating on the spot - like a hamster going around its wheel and going nowhere - such rotations are the origin of gauge rotations in the dimensionally reduced theory. A consequence of compact dimensions in STUFT is that they provide the 'measuring rod' for all measurements, up to and including the measurement of their own scale. So even if the scale of these dimensions changed, their measured scale in terms of themselves would remain the same - apparently 'constant'.

        Michael

        Hi Jonathan

        Thank you for that acknowledgement of my essay showing how QT can arise as an emergent theory, you are the first to do so.

        It is perhaps not as clear as it could have been, but I had to compress it to fit the word count so that I could put in the follow-up consequence of QT not being fundamental. Which is that physics unification must then be sought in classical physics, and to unify with GR this would seem to imply extending GR with extra dimensions, and there is only one way that adds up in terms of particles as topological defects, the Higgs field and coupling constants - STUFT - which is uniquely defined in terms of the 4 special manifolds S0, S1, S3, S7 and the Relativity meta-principle of 'make no preference'. Without the constraint of QT *having* to be fundamental, STUFT is uniquely the only purely geometrical theory giving the correct charge spectrum of 12 (and only 12) topological monopoles as fermionic particles.

        Another dramatic consequence of this emergent QT proof, is that a similar pattern can systematically occur elsewhere in science under certain conditions - I use these conditions to define the domain of Agent Physics. A general science perspective of the extension of this emergence proof throughout science in given here

        Regards

        Michael

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        • Post #67

        Dr. Goodband:

        Your question about whether quantum mechanics is fundamental is a good one. But implicit in your question is the assumption that QM should be interpreted as a universal theory of all matter. On the contrary, I would suggest QM is rather a mechanism for generating localized particle properties from primary continuous fields (electrons, photons, quarks), where these localized (but not point) particles then follow classical trajectories (as derived from the quantum equations). (Please see my essay "The Rise and Fall of Wave-Particle Duality", http://fqxi.org/community/forum/topic/1296.) Composites such as nucleons and atoms are localized objects WITHOUT wave properties of their own. Beams of neutrons or atoms do not require de Broglie waves for quantum diffraction from a crystal lattice, which instead reflects quantized momentum transfer between the beam particle and the crystal. Remarkably, this reinvisioned quantum picture is logically consistent and avoids quantum paradoxes. Even more remarkably, this interpretation seems to be virtually new in the history of quantum theory, although it could have been proposed right at the beginning. The FQXi contest would seem to be an ideal venue to explore such concepts, but this has drawn relatively little attention.

        Thank you.

        Alan M. Kadin, Ph.D.

          Hello Michael,

          I am re-posting a comment I made elsewhere, with minor edits, as it pertains to your work.

          I thought this might be a good place to raise the question of whether viewing particles and spaces as topological objects might account for the observations of Jenkin and Fischbach of varying decay rates for nuclei, depending on Sun-Earth distance. Apparently this has taken on a new dimension recently, as with more sensitive measurements it works as a kind of early warning system for solar storms.

          This would argue heavily for the interpretation that the fabric of spacetime is of the nature of S3, topologically speaking. Or at least; I think that a topological description with a non-trivial twist in the fibration might easily account for such an effect as follows. When there is a mass ejection, this is a ripple in the topological fabric in the region of the Sun, in effect it is a rapid partial eversion of the Sun's mass. And this ripple propagates because of the topological connectedness.

          Would you care to comment? Is this relevant here?

          All the Best,

          Jonathan

          Hi Jonathan,

          You raise a very interesting point that I hadn't registered. I was just adopting the standard closed universe picture of GR and not registering it implied that S3 space-time must be a fibre-bundle, which as you suggest could result in unexpected effects. Further non-standard effects could arise in my model because the electroweak vacuum is of the form of a twist in the compactified dimensions in going all the way around the universe. So the sort of ripples you suggest might also involve changes in the electroweak vacuum, which could result in changes to the decay rates of particles. Such results could well be relevant, and perhaps provide a test for the topological structure of space-time. The problem I would have is that the particle masses and particle family mixing angles are not calculable in my model, which is a bit of problem for calculating changes to particle decay rates.

          With particles being topological defects in my model, simple heuristic arguments say that neutrinos must have a non-zero mass, which is suggested in the link as being a possible factor. The topological defect particles take the form of compactified rotating black holes, which means particles would have rotational frame-dragging that should give non-standard spin interactions - but with a cross-section that would be too small to be of relevance for particle decay effects.

          Another non-standard thought that occurred to me reading Joy Christian's book is that S3 can occur as a flat sphere with zero curvature - so could the universe be closed and flat at the same time?

          I did enjoy, thanks!

          Michael

          Hi Michael,

          You asked: "...could the universe be closed and flat at the same time?"

          Indeed it can. And I claim that it is. That is the message coming out of my work, as you seem to have gathered.

          Without the universe being closed as well as flat, the strength and origins of the quantum correlations are impossible to understand in local-realistic terms.

          Joy

          Dr. Kadin

          I apologize for not having yet commented on your essay, I am woefully behind!

          I agree with you that seriously reconsidering quantum theory is drawing much less attention in this FQXi contest than it should be - it is as if it is the assumption that still cannot be questioned, even when all other assumptions are up for grabs! My essay makes a rather more serious challenge to the assumptions of quantum theory than is perhaps initially apparent, and proceeds to show that QT isn't fundamental as its mathematical form can be derived by a change in mathematical representation.

          It is not just us essay contestants who are encountering problems challenging the assumption of quantum theory. Joy Christian's work shows that Bell's theorem doesn't prove that QT has no replacement - which effectively seems to me to amount to a proof that QT isn't fundamental - and has been getting serious stick, as opposed to being ignored. My essay outlines a totally independent proof of the same thing. In strict physics terms this opens the door to seriously questioning the status of QT, and hopefully this may happen before the end of the contest.

          I think your closing lines nicely capture what's gone wrong with physics:

          "Generations of physicists have been educated to ignore physical intuition about the paradoxes, while focusing on mathematics divorced from physical pictures. In response, the field of theoretical physics became more mathematically abstract, straying far from its origins explaining the behavior of real objects moving in real space."

          Incidentally, the same is also true of general relativity, which has become something of a mathematical map detached from its physical territory - a trend which looks as though it is set to get a lot worse with notions of emergent dimensions.

          Michael

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          • Post #73

          always a poor team still of strategists full of hate, still a poor band of frustrated, probably that your young life at school was difficult, probably that you makes a kind of revenge in making the bad. Jonathan , I have pity my friend and for your frustrated friends also. You are not foundamental, nor universal, nor relevant and still less an imrpover. Let me laugh in seeing your poor strategy and your hate increasing. I love USA and I am christian.

          What is your poor probelm ? the vanity. I don't know me, buy a bibble and makes a redemption.I don't know, you are not relevant in fact even in your strategy.

          Become a murder, it is better you know. And we shall see how shall be your humility in front of our god. You are a comic.Ok he said, ok.

          Hi Joy,

          I am currently reading your book, and it is the highlight of my year! - unless I am completely missunderstanding it ;-)

          Your disproof of Bell's theorem seems to me to be effectively amount to a proof that QT is not fundamental, as your model demonstrates that a local classical physics theory *can* exist, would I be correct? If so, then my proof is a totally independent proof that QT is not fundamental. Now that I am coming to understand your work better I think that my work is related - I have come from the physics side, whereas you have come from the maths side.

          It seems to me that the usage of the word 'local' is causing problems, because it can have several meanings. This is the point I was trying to make with my diagram in the attachment below. Your usage of the word 'local' seems to correspond to the physics intuition of a continuous path of subluminal causation, whereas there is also 'local' space-time separation in relativistic dynamics and the two won't be the same if the background metric changes. The illustration seems to provide the only way I can think of squaring physics intuition 'local' with apparent non-local space-time separations. Since your analysis is for R3, is it possible that such a relativistic change in metric signature is being captured in the global structure of the S3 function space?

          Chapter 7 gives the general case as being a local function of the form

          A(x,l): X*L -> Y sub Z

          Where x is some orientation in the space X, and Z is constrained to be either S3 or S7. For the common case of spin orientation - which is an internal particle property - x is a 3-vector and X=R3. It seems to me that the same argument would apply to the gauge orientation x of the internal particle property space of gauge symmetries. As the isospin group space is S3 and electromagnetism is S1, the option of Z=S3 is too smal ... which *only* leaves S7. Is this correct?

          I register that this S7 could also be flat as well. I don't yet know how this would square with my S10 unified field theory as I am currently on chapter 7.

          MichaelAttachment #1: 2_Local_to_nonlocal.pdf

          Hi Michael,

          Thank you for your kind words. I think we are on the same page as far as the understanding my central message is concerned, but we may have different views about some of the details.

          In particular, you are correct to read my disproof as a proof that QT is not fundamental. The credit for this observation, however, must go first to Einstein, and then to Bell, before my work is even considered. Einstein argued most of his life that QT is not a fundamental theory, and Bell's work (which is based on the earlier work on hidden variables by von Neumann) clarified and quantified Einstein's position tremendously. My work is entirely in the tradition of Einstein, von Neumann, and Bell, but of course these giants do not consider going beyond the algebra of the real line, whereas both you and I consider the most general division algebra possible, namely the octonionic algebra, associated with S7. I too feel that our work is related, but I must admit that I haven't had time to digest some of your arguments (these days I am preoccupied in clarifying the relationship between SU(2) and SO(3) even further to understand the issue of "flatness" you alluded to above).

          You have rightly raised the question about my usage of the word "local." I have used a very precise definition of "local" provided by Bell. This definition is theory-independent. In particular, it is independent of relativistic considerations. On the other hand, it may not remain valid if the space-time metric itself changes its signature during the course of dynamics, say, of an EPR pair. I am not sure whether a relativistic change in metric signature of the kind you have considered is captured in the global structure of the S3 function space. My feeling is that if such a change in signature is allowed then strong quantum correlations would be wiped out. That is not such a bad thing, however, for we do observe both quantum as well as classical correlations. In fact, more often than not we observe classical correlations rather than quantum correlations.

          I think you are right to think that the same argument would apply to the gauge orientation x of the internal particle property space of gauge symmetries, with S7 substituted for S3. But the details here are beyond my field of expertise, so I am unable to be all that confident about this.

          The octonionic S7 is indeed flat, and it is this discipline of "flatness" of S7 that is responsible for the strong quantum correlations. That is my claim in any case.

          Thanks again for your kind words about my book. It is good to be appreciated.

          Best,

          Joy