Dear Jonathan,

Thank you for your message and interesting attachments. Do you have a reference for Einstein's letter expressing doubts about corpuscles?

I have read your attached pdf on decoherence. Also your reported comment by Gerard 't Hooft on quantum gravity in CA. If you will be kind enough to forgive my simplistic assumptions and ideas about these concepts, there is one point that may have been largely overlooked since it was raised some 200 years ago (actually 2500 years, since Democratis's time).

Could it be that at the smallest level there is absolutely no distinction between waves, solid matter, radiation or dark energy etc? I believe that this artificial dichotomy based on everyday perceptions, between particles and waves, is at the heart of a great deal of the foundational problems facing a theory of everything. For example you speak of an ocean vs. a boat, of a person perceiving the ocean differently from land or sea etc. In a CA lattice, particularly in my Beautiful Universe Theory (BU) model, it is all made of the same stuff! Fresnel early on had the right idea of "matter permeable to ether"- and vice verse I might add! - and I think Hertz and others were seeking out a wholly electric ether where Lorentz transformations would account for relativity. Enter Einstein and his photon and constant (c) which inserted a spanner firmly in the these promising works, forcing physics to proceed on his own new tack. And now it is not working!!

With regard to Michael Goodband's comments, and octonions, again please forgive my going into matters I know little of, but is it not possible that 1) The math is asked to cover a physical situation that is far more complicated than it is in Nature? 2) That the math reflects the degrees of freedom in the node of a certain type of CA - I am thinking of my (BU) where each and every node can rotate in any spherical angle, rotate around its own axis, and has polarity, i.e. much as the Bloch sphere of QM - as per attached figure (from my last year Digital or Analog fqxi essay)?

Again thank you for your learned response.

VladimirAttachment #1: FIG5.jpg

    Hi Vladimir

    I like your Beautiful Universe. It is like a Bohr model of space. I think you might be interested in quaternions, which are mathematical extensions of complex numbers. They are associated with spin in quantum mechanics.

    A quaternion can be thought of as four numbers, any one of which may be taken as a reference for the other three. This conceptual link between the numbers leads to a picture of the quaternion as a tetrahedron.

    Your face-centered cube model first struck me as odd since I might have expected simple hexagonal shapes, or the occupation of alternate nodes of a regular grid. The first possibility arose mainly from other investigations, and the second possibility was based on the three dimensional model of a quaternion I had been considering which places the tetrahedron representing the quaternion on four corners of a cube.

    But then on reflection it became clear that the face-centered cube has alternate nodes occupied, and so could very well be related to a 3D structure for a model quaternion. In the attached diagram, the quaternion is shown in a 1/8 segment of a face-centered cube, ie 1/2 x 1/2 x 1/2 of a FCC.

    Mathematically these cubes are assumed to be cyclic like circles or toruses, but that could also correspond to a grid of identical cubes in which case nodes could be placed on other cubes leading to different geometrical configurations of a quaternion, including the condition where the nodes are in the same plane in which case the quaternion bounds no volume, only area.

    If you are interested, download John Baez The Octonions to see where I get this idea, which I readily admit could invite criticism as a gross misinterpretation of the mathematics as physics. First the octonions: they are an extension of the quaternions consisting of eight numbers, double again the size of a quaternion. As Baez puts it, "the octonions are the crazy old uncle nobody lets out of the attic".

    Ignore the math. There are three diagrams on page 7. At the top is a circle with three nodes labeled i, j, k. These nodes correspond to three numbers of a quaternion with the reference number being hidden.

    The second diagram on the page shows a triangular transformation table for the octonion (again not showing the reference number) with an inscribed circle with three nodes e1, e2, e4 on its circumference. I take these to refer to the nodes i, j, k above.

    The third diagram on the page shows a mapping of the eight numbers in an octonion onto the eight corners of a cube. The reference number is now included and labeled with the number '1'. Notice that the reference number and e1, e2, and e4 connect diagonally across the faces of the cube, and occupy alternating nodes. I think that this could be a picture of a quaternion in space, but I doubt if that was intended.

    I would have overlooked this possibility without the diagrams. You have obviously realized the importance of graphics in your essay and website.

    Quaternions and octonions are the basis of modern mathematical physics and I would not be surprised to find them in your model.

    Best wishes and I hope your essay does well.

    ColinAttachment #1: quaternion3D.pdf

      Dear Colin

      Thank you for your kind and timely explanation of Octonions. In Jonathan Dickau's post of Aug. 21 just before yours he refered to octonions and in the last paragraph of my answer I asked a couple of questions about that.

      Thank you for John Baez' paper on octonions, and your explanation of the figures on page 7. I could not help observing that with the great respect I have for Baez's accomplishments us non-academic physicists were a bit scared of being branded by him as cranks when he was on a campaign to expunge our work from the world :) Luckily he did not even notice my papers!

      In his paper Baez refers to Wigner's 1930's interest in octonions. Coincidentally my friend Norman D. Cook reworked an idea of Wigner to build a nuclear structure model based on a Face Centered Cubic FCC . In fact I adopted the FCC in my Beautiful Universe model (over the triangular Kepler packing) thanks to Cook's example. I encouraged Cook to present his work in this fqxi contest. Please have a look at it and his book and simulation software on the same subject published by Springer.

      Its a small world, and with all these efforts I hope something good will jell in the world of fundamental physics.

      With thanks and best wishes,

      Vladimir

        Dear Vladimir

        Your remark about John Baez and cranks hit home. I had a dispute with John Baez over rejecting my first posting to sci.physics.research inquiring about supernova redshift data and got labeled as a crank in the process. He is the inventor of The Crackpot Index. From Wikipedia: "The method, proposed semi-seriously by mathematical physicist John Baez in 1992, computes an index by responses to a list of 36 questions..."

        Petty humiliation can be quite effective. It would be a decade before I posted again. Baez's behaviour was likely symptomatic of a more widespread phenomenon. It seems to me that the situation has gotten worse to the extent that it has become institutionalized, countered for example by VIXRA (thanks to Philip Gibbs) as a reaction.

        Here is a little story coincidentally about John Baez's doctoral supervisor. The late Irving Segal (1918-1998) developed a theory he called chronometric cosmology which called for redshift to vary with the square of the distance to account for curvature, instead of linearly as in Hubble's law. He noted that the data collected to support Hubble's law comprised a small part of the data available. Suspecting selection bias, he embarked on a program to analyze as much data as possible. What he found was that the larger data set clearly supported his model, not Hubble's law. This was found over a wide range of wavelengths and with the collaboration of various researchers in a series of papers. In spite of the data supporting his theory, physicists will tell you that supernova data imply accelerating expansion without even considering Segal. I am not optimistic about the future of physics when the critical work of an established and respected physicist is discounted.

        Colin

        Thanks Colin,

        Yes that's the one - the Crackpot Index! Its funny and makes sense because there *are* some strange ideas out there and I can imagine John was pestered by having to evaluate them.! But I could well imagine how discouraging it can be when successful mainstream physicists put down an idea and its author for no good reason. I had arXiv reject my Beautiful Universe theory paper probably because I have no university affiliation, but I am used to being out there on a limb with my ideas so I took it in stride. And thanks to Philip Gibbs and viXra my papers are online there now. And Philip 'answered' John Baez' Index by his marvelous blog column Crackpots Who Were Right . BTW Philip has participated in this year's fqxi contest and was recently quoted in the news for his knowledgeable comments about Higgs developments.

        All this pales next to some experiences with Physics Forums where rejections of new ideas can range from dismissive to hostile. One researcher told me he was so vehemently attacked by moderators on PF even now many years later he hesitated to promote his ideas even on fqxi, but I think I talked him out of it and he is now writing up a paper for the contest.

        Interesting and typical story about Irving Segal's redshift theory...

        Vladimir

          Hi Vladimir,

          On looking into the Segal story further, it appears there might have been sufficient reason to be suspicious of his rather complicated analysis of the data. Ned Wright's criticism points out some problems.

          Here is a link to Crackpots who were right which was broken. Nicely inspirational.

          Colin

          Hi Colin

          Thanks for the corrected link to Philip's blog. Segal may have been wrong, but that is all part of the advance of science. The case of Einstein's photon being a point particle on the other hand may yet be classified under Great Scientists Who Were Wrong.

          Read Eric Reiter's current fqxi essay for the details (also one of the foundational questions in my fqxi essay). It seems Planck opposed the point photon early on giving an alternate loading theory, then Compton himself offered an alternate wave explanation for his scattering experiments...all neglected by physicists for a century. I had an inkling that the light quantum in space was just a wave, based on my streamline diffraction researches. Eric has independently and more importantly experimentally proven it...after he struggled alone for years neglected by the physics community.

          Vladimir

          Thanks Vladimir,

          Regarding Einstein's doubts, aside from the page visible in the slide behind Zeilinger, I have no clue as to the origin of the reference. I can write Anton, and see if I get a reply.

          As to decoherence, I agree that waves and particles are a somewhat artificial distinction, and my conceptual model attempts to show that. If we believe Zeh, there are no particles and only the wave-like aspect is real. Geometrically speaking; Grassmann's prescription involves putting points, lines, and planes, on an equal footing - rather than trying to derive extended forms from simpler bases.

          Regarding CA based theories of Physics; I asked 't Hooft at FFP10 how his CA based QG theory fares in light of the Planck satellite results showing high and low energy gamma ray photons from a distant supernova arriving almost simultaneously - demonstrating Lorentz invariance. Our discussion became the topic of 4 or 5 slides in his FFP11 talk in Paris, where he explained why it is a rather difficult matter to make a CA based theory Lorentz invariant.

          More in the next entry.

          Regards,

          Jonathan

          Hi Vladimir,

          Sorry it took me a while to process your response to my remarks. I have made some comments above, in reply to your questions. I shall make some comments in feedback to your contest essay some time soon.

          Jonathan

            Hello again,

            In regards to CAs based on your figure depicting polarized spheres, I think the proper analogy is to quaternions and the 3-sphere - because that correctly encodes the order of operations dependent nature of QM.

            I like your BU idea, and I think it has potential to inform us about reality. It would be nice if it was that simple. But I agree with Michael Goodband's statements above, that you need to have at least 7 extra dimensions in a KK formulation to obtain or explain all the observed symmetries.

            So perhaps what would allow that to be represented would be more like a cluster of seven interlocking spheres. The description of half-overlapping figures in Michael's comment above comes to mind, as a base configuration for one node. Einstein was noted to say that we should keep things simple, but not try to make things more simple than they really are.

            My working assumption after talking with 't Hooft, and then discussing possibilities with a number of colleagues, is that the Octonions may be the minimal starting place. That is; we can craft an emergent description of Physics, as you do with your Beautiful Universe theory, but to see all of the observed forms and symmetries come out - you need enough degrees of freedom to start with.

            Regards,

            Jonathan

            Cool Beans,

            I like your comments, Colin. It seems that with Michael, you, and I all making comments relating to quaternions and octonions, Vladimir will certainly get some useful insights about them to aid his research.

            All the Best,

            Jonathan

            Yes Steve,

            You do irritate sometimes, especially when you challenge my comments on other people's pages. But I just found a gem in a paper by Aubert Daigneault, where he cites Mark Peterson's comments about Dante's version of the theory of spheres.

            "Astonishingly, Riemann’s nineteenth century description of the universe as a three dimensional sphere appears to have been anticipated much earlier by the Italian poet Dante for whom the universe encompasses the material world as well as Paradise, Inferno and Purgatorio. In his celebrated work ‘The Divine Comedy’ (Canto 28, lines 1-129) the thirteenth-century Florentine writer views the Universe from a point in the Primum Mobile [the equatorial 2-sphere] where he stands with his beloved Beatrice who shows him, on the one hand, Paradise which he calls the Empyrean, [an hemi-hypersphere, indeed a three-ball] consisting of a sequence of two-spheres of decreasing radii, lodging angels of all orders, all the way to God [standing at a pole of the 3-sphere] and, on the other hand, the material world [the other hemi-hypersphere; indeed the other three-ball] made of another sequence of two-spheres also of decreasing radii, dwellings of the stars, the planets and the earth with Satan at its centre [the antipodal point of the first pole on the three-sphere]."

            So apparently; even Dante's version requires higher-dimensional Math.

            Regards,

            Jonathan

            Thank you Jonathan. I read your comments above about quatrenons and, as with Colin, the necessity of having 7 dimensions and 't Hooft's comments about CA. As you have probably figured by now I am still a learner! At 70 I am not as mentally agile as I was when I first started my physics self-study, but with so many wonderful contacts on the Internet, and through discourse with first-class thinkers here and elsewhere I could see where and how my model agrees or does not with other established theories and ideas, and will be mulling all these things and adjusting my model accordingly.

            Quatrenons or octonons might be the answer but I know my own mind - I simply do not think algebraically, and would rather use the energy required to learn them to work things out geometrically and leave it to you whizzes (Colin included) to establish the math for such ideas.

            I wonder if the 7 symmetries required are all 'basic'. In my Beautiful Universe theory I have seen how leaving special relativity (i.e. c constant and the use of 'spacetime' as a starting premise) out of GR can lead to an utterly simply scenario of space with a density matrix refracting e/m energy. If that is indeed so, I sincerely hope that some such simplifications in assumptions (as per my fqxi essay 'Fix Physics!' could one day show that the required symmetries are emergent from the simple symmetries of a model like BU.

            I looked up Lorentz Invariance..more things to study. I do not know which CA 't Hooft had in mind, but surely there are many different models that use discrete self-assembled nodes? If he thinks of CA as simple 'on' off' nodes then yes I agree, but in my BU the nodes have these degrees of freedom: A scalar internal rotation ie density a 2- dimensional spherical orientation that should include ( -) spin orientation, apart from the 3 dimensions of their location in the grid . That is six, will that work? OK nice try perhaps but I am thinking a lot about other possibilities. I am now considering the concept of spherical surfaces in the lattice where the nodes are aligned 180 degrees twisted in relation to and caused by the original 'locked' matter nodes. Atoms as black holes...a google shows the atom as a black hole is by no means a new idea!

            By the way I think the Einstein quote in your slide may have been the old chestnut (I paraphrase from memory ) about any fool thinking he knows what a photon is, but it is still a mystery.

            Yes Ste*ve is irritating - his rambling off-subject comment was inappropriate, but you were more tolerant and generous by offering your Dante quote.

            Best wishes and appreciation, Vladimir.

            Hello Vladimir,

            Gerard 't Hooft's CA-based theory is described in some detail in the following paper. Entangled quantum states in a local deterministic theory Of course; the model has likely been evolved somewhat, since that writing, by Gerard himself. But that paper provides a suitable snapshot of his recent work in that direction. It also gives some insight into what works and what doesn't

            There is an article somewhere on the FQXi site that refers to this work, but I don't have the link right now. I'm sure that Googling the good professor's name, along with the words Cellular Automaton would produce some interesting results, as when 't Hooft announces significant new work, people like to comment. It is notable that his famous paper on Dimensional Reduction in QG also utilized a CA.

            A notable feature is that including Gravity is what makes it work.

            Regards,

            Jonathan

            Thank you Jonathan,

            I tried to understand the best I can 't Hooft's paper you kindly provided the link to. I have no doubt it is as he tells it *within the scheme of the Standard Model, SR and other aspects of physics as we know it*. But try to convince dreamers like me with half-cooked ideas that starting from completely different first principles, the picture could be very different and many points made in the paper may simply not be relevant!

            He uses the concept of gravitons, a concept that does not exist in a model like BU where gravity is the result of systematic topological twists in the lattice node field betsween particles. He discusses Bell's Theorem, a whole world built on the supposition of say, photons being point particles with quantum probabilities. Read Eric Reiter's fqxi essay to see a very different view of such particles and sensing scenarios, and my papers about why I think quantum probability is an emergent description of an ordered micro structure.

            Hope this makes some sort of sense? Meanwhile I will keep trying, but not too hard, to understand aspects of the prevailing paradigm. I feel it is more important for me to keep building my model to the point it may be properly simulated and tested. It may sound like building perpetual motion machines but its fun, and as such dreamers always hope , "it just might work"!

            Vladimir

              Of course,

              The paper from 't Hooft has value for you now mainly as a reference point. It is better that you try something new, rather than try to emulate what he did. The relevance of the discussion about Bell's theorem in that paper is mainly to show the context of the term 'locally realistic theory' so you know his understanding of that concept. The the thing is; adding gravity to the mix in the CA formulas is what makes the model locally realistic.

              Gravity resulting from topological twists is arguably very different from using gravitons, so that would send your simulations off in a different direction. Always something to learn!

              all the best,

              Jonathan

              Thanks Jonathan for your understanding, encouragement, and pointing out relevant information. Vladimir

              Hi Vladimir,

              聽As an artist your mind is open and critical; it is natural for you to query and present alternate points of view. 聽Furthermore, you have studied physics at university, combining the acquired knowledge with your natural talent to be at your best; you composed an excellent essay asking the right questions and presenting points of view that many can agree with.

              聽I really enjoyed your rendition, the written as well as the drawn - they say a picture tells a thousand words so we are thankful 聽that these artistic words were never counted.

              Regards and good luck - Anton聽

                Dear Anton,

                Thank you very much for sharing your enjoyment of my essay. The advantage of an artistic mindset in science is that it encourages the use of imagination, and also a respect for the characteristic of beauty, which Dirac emphasized was a quality physical theories must posses to be right.

                My university studies in physics in the late 50's gave me a foundation in method and basic maths, but by the 1980's when I started self-study in optics, most of what I had learned had been superseded by new theories and developments.

                I enjoyed reading your paper immensely. The first thing that struck me about it was the superb typography and attention to details such as fonts and layout. The pdf says you used the font Palladio, designed by the Einstein of typography Herman Zapf. Excellent choice.

                The second thing I enjoyed was your reference to Poincaré's ideas. I found new respect for him after reading how Poincaré's book influenced both Einstein and Picosso's thinking . Try to read Miller's book it is fascinating.

                I will comment on your paper on your page. With warm regards and best wishes,

                Vladimir

                9 days later

                • [deleted]

                • Post #108

                Dear Vladimir,

                I wish I could write elegantly like you, full of substance mingled with the touch of humour. It is enjoyable and gives the critique of the post 19th century theories succinctly within the limited space of the essay.

                You have come out with the metaphor of the buildings which have been built one on top of the other but with little or relation to one another. You have commented mostly about the superstructures, but written hardly anything about short comings of the primary building.

                Do you think if this primary building was constructed properly, with a resilient and a deep foundation, that the superstructures (the derivatives) would have taken to form that they are now? Is it not because the first building was inadequate and did not allow for a continuity of its structure, that other structures have been erected on it haphazardly? From the first derivatives (SRT and QM), second, third, fourth derivatives have come up, and these later order derivatives are trying to unify physics!!

                So where should we begin to Fix Physics? Should we not look at the Problems in Newtonian Foundation of Physics?

                I quote the list of problems from my essay :

                http://fqxi.org/community/forum/topic/1549

                "We may note that among the problematic foundational concepts created by Newton that have congenitally infected RT and QM are a) the primacy of the concepts of space and time, b) representation of bodies as mass-points without internal structure, c) consideration of centrifugal force as a pseudo-force, d) the closed system with the consequent inability to account for inflow and outflow of energy between the system and the field etc. e) Not recognizing that it is by the two quantities of energy (Mc2 and pc) fusing together to form a system that motion occurs. f) the omission of the fact that a fraction of the applied energy of motion pc gets usurped for the co-movement with the location. g) Not developing the theory with state changes of energy as the basis of its physical geometry. With these congenital foundational problems being inherent in these two progeny theories as well, it should be obvious that revamping of physics must begin from where the problems originated".

                I have not only listed out the problems, I have provided some solutions. (I have a lot more solutions to offer which I could not include within the 9 pages of the essay).

                I request you to read my paper and give your comments, if you can find the time for it.

                Best regards,

                Viraj