Essay Abstract

Max Tegmark, exploring implications of the External Reality Hypothesis that there exists an external physical reality completely independent of us humans, claims that physics is so successfully described by mathematics because the physical world is completely mathematical, isomorphic to a mathematical structure, and that we are simply uncovering this bit by bit. In this essay we have tried to discover that mathematical structure. We start from the correspondence rule as it has a potential to look at the vast existing empirical domain from a different angle. We do not need new data nor new mathematical structures. We need only this different angle - a paradigm shift. If Geometrical Universe Hypothesis is correct, then the empirical domain and the correspondence rule are redundant in the sense that they can be inferred from Thurston geometries. In his well-known essay, Wigner claimed that "the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious", and that "there is no rational explanation for it". The GUH provides this explanation and more: makes the testable prediction that is uncovered in the conclusion.

Author Bio

Freelance researcher, studying mathematical physics. Innovations don't typically come from the experts, says Evernote CEO Phil Libin. Instead, it comes from fresh eyes that can look at a problem in new ways... Innovation sometimes comes when you have just enough knowledge about a subject to feel it in your gut but not enough to be trapped by its established rules.

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Dear Jack Safuta,

I enjoyed your essay and found that I will have to ponder on it for a while. This was my first exposure to the idea Thurston geometries so I need a little time to research and think about it.

I liked the chart of fundamental particles and the brief history of physicists' opinions on the aether.

If you get a chance, please have a look at my essay here where I present specific models of the fundamental particles of the standard model. The geometries I use are a little different, but are approached purely from the perspective of matching the properties of the particles.

Good luck with the essay contest and thank you for the thought provoking ideas.

Regards,

Ed Unverricht

    Dear Jacek,

    Geometry is certainly a good way to explore relations in Physics. You have chosen this path and that is good. So, should you learn in detail classical physicists who are using geometry, came to the uncontested achievements. It is not easy, not least due to the archaic ways of speaking in their time, or because of inadequate translation from the Latin. Readable and a brief statement of Boskovic's work goes in English, see link: http://www.lulu.com/shop/roger-anderton-and-dragoslav-stoiljkovich/roger-boscovich-the-founder-of-modern-science/paperback/product-21684660.html Or you can find on the internet, if you write Boskovich Stoiljkovich or Anderton Boskovich. What is wrong with your work is that you waste time adding dimensions. Classics of physics, who used geometry, They have no extra dimensions in their natural philosophies. Your essay is noteworthy and deserves a good rating.

    Best Regards,

    Branko Zivlak

    Dear Jacek,

    As I told you in my Essay page, I have read your peculiar Essay. Here are my comments:

    1) I do not think that your statement that gravity is transmitted instantaneously is correct. In general relativity the speed of gravitational interaction is finite, presumably equal to the speed of light. One can indeed show that the problems that you suppose to exist, i.e. unstable planetary and stellar orbits (aberration of gravity), are not suffered by a static field in general relativity.

    2) I did not know the Thurston geometries. Thanks for pointing out it to me in your Essay.

    3) In your table in page 3 you claim that the spin of gravity is not applicable. Why? Although we do not have a full theory of quantum gravity in the weak field approximation gravitons have spin 2.

    4) One of the greatest problems obstructing the geometrization of the electromagnetic interaction is that there is no electromagnetic counterpart of the equivalence principle which is the foundation of metric theories of gravity. This is because, while the ratio between gravitational and inertial mass is universal, the same does not apply to the ratio between electrical charge and inertial mass. How do you think to circumnavigate this problem?

    5) Concerning your proposing the evolution of information concept, how holographic principle does enter in your geometric picture? Is there room for it?

    In any case, I found your Essay interesting.Thus, I will give you a high score.

    I wish you best luck in the Contest.

    Cheers, Ch.

    Hi Ed,

    Your essay is excellent. Full of great pictures. You present an approach that I was waiting for. I mean: a visual language, independent, universal and baggage-free description. The last notion is explained in Max Tegmark's very inspiring letter "The Mathematical Universe" (arXiv:0704.0646v2) where he says: "a description to be complete, it must be well-defined also according to non-human sentient entities (say aliens or future supercomputers) that lack the common understanding of concepts that we humans have evolved, e.g., "particle", "observation" or indeed any other English words. Put differently, such a description must be expressible in a form that is devoid of human "baggage".

    I think that visual imaging could be the answer.

    You say: Usefulness is also high if the model can be represented in a number of different ways and leads to a predictive power. My essay delivers the predictive power that five out of Thurston geometries remain to be uncovered in nature. These are five exotic Riemannian manifolds, which are homogeneous but not isotropic: the geometry of S2 ﾃ-- R, H2 ﾃ-- R, the universal cover of SL(2, R), Nil geometry and Solv geometry. Maybe you could prepare visualizations of these geometries?

    Obviously our, humans, problem is that some geometrical structures we are not able to imagine in our brains e.g. S3 and H3. Unfortunately it needs to take a look from R4 perspective. But we can create some projections on R3 or cross-sections. You have tried to help to imagine quarks. It is really interesting... Do not stop in your useful work. Your rating is unfair. You deserve much more.

    Regards,

    Jacek

    Dear Cristi,

    Thank you for careful analysis and very important questions! I cannot ignore the issues of such importance. This will keep me busy for a long time. Thank you very much.

    Responding immediately on the geometrization of the electromagnetic interaction I would evoke the Kaluza-Klein framework. However I have to study this question very carefully.

    The holographic principle refers to string theories. These are also geometric in background but in completely different way. I cannot accept M theories as so far they do not generate predictions (there are some claims recently) and they demand more than 4 dimensions and I assume that 4 is enough.

    I have claimed that the spin of graviton is not applicable as I am convinced (not in 100%) that gravity is not a fundamental but emergent phenomenon so graviton does not exist.

    Not only your essay but also your honest approach and important notices deserve a high rating. I have not got my voting code yet. Guys responsible are out of the office.

    Best regards,

    Jacek

    Dear Jacek,

    Thanks for your reply.

    Actually, the holographic principle has general character. In fact, it was introduced in a famous t' Hooft's Essay where, following Susskind it was found that "the combination of quantum mechanics and gravity requires the three dimensional world to be an image of data that can be stored on a two dimensional projection much like a holographic image". Extension of holographic principle to string theory was mainly due to the Maldacena conjecture.

    I am surprised that you have not got your voting code yet. I received it in the Fqxi email confirming my submission.

    Also kindly notice that I am Christian Corda, not Cristi Stoica, although I am in friendship with Cristi and I appreciate his research work.

    Cheers, Ch.

      Dear Christian (sorry for Christi),

      I have made a complaint and finally received my code.

      You can see the effect right now! Congratulation.

      Jacek

      Hi Jacek,

      at first I skimed over your essay and found it interesting. Actually I used the exceptional geometries (NIL, SOLV, SL2) in my work. In a previous paper I described the interaction with them (see the paper). The idea is simple: the connection between the knot complements (=fermions) are torus bundles and there are only 3 types of torus bundles which can be identified with interactions (weak, strong and EM). In this paper you will also find the identification of bosons to the geometries.

      Currently I think about the SL2 geometry and the Ricci flow.In the past I thought that the Ricci flow is something to do with the measurment process in quantum mechanics but now I changed my mind. I have to go over your essay more carefully. Thanks for your words.

      Best Torsten

        Hi Torsten,

        Could you please give me the link described above as "(see the paper)" as it does not work and I am really interested in.

        Thanks,

        Jacek

        Hi Jacek,

        try http://arxiv.org/abs/1006.2230 and download the PDF (it is the published version). Secion 8 discussed the gauge group and explains the geometry.

        Unfortunately, I see now that I don't mention the geometries (I think the referee don't want to see them and ask to remove them).

        Here it is:

        finite order = E3 (Eucledian)

        Dehn twist = NIL

        Anosov = SOLV

        Best Torsten

        Dear Jacek,

        I congratulate as you wrote a brilliant essay. I enjoyed reading it from the beginning until the ending.You described your theory well and I would say it is NOt contradictory to KQID but it is KQID in different clothing with its different symbols, and story. Beneath it, we are in complete agreement. You should read carefully my essay again and you will discover similarity like below statement in which KQID has identical proposition.

        You wrote:

        "We propose the evolution of information concept. To explain it very shortly, we have to apply the theory of Darwinism beyond its original sphere of organic evolution on Earth. The organic evolution refers to some pieces of DNA (a kind of information) and not to species (what is the most common misconception). Going further beyond information carried by pieces of DNA (that are sets of molecules), we observe only the waves (information) possessing long-term existence and stability."

        If I may add we must fight for diversity, tolerance and inclusivity and we must fight against uniformity, intolerance and exclusivity. We are for "harmonious unity" or unity in diversity of ideas, races, languages, cultures and civilizations,

        Best wishes and hope you will do well and I vote according to my favorable view,

        Leo KoGuan

          Dear Leo,

          Thank you very much for your kind comments.

          I fully support your emphasis on diversity, tolerance and inclusivity.

          I will try to read your essay again. As you see so many essays were published in last few days that it is hard to be careful. And to be honest, we shall try to take a look for all of them.

          Best regards,

          Jacek

          Dear Jacek,

          My essay proves that forces are instantaneous, and from that fact QM naturally arises. I hope you know some programming.

          Essay

          Thanks and good luck.

            Dear Adel,

            I will take a look at your essay asap.

            Unfortunately I do not know programming.

            Best regards,

            Jacek

            6 days later

            Dear Jacek,

            I read with great interest your essay. I totally agree with you that only the language of geometric representations can lead to an adequate model of the Universe as a whole and the new paradigm, as you stated: "We need this different angle - a paradigm shift." My high score. Philosopher and mathematician Vasily Nalimov said that only on the basis of the language of geometric representations can construct a model of "self-aware universe."

            Fundamental knowledge, mathematics and physics, requires a deep ontological justification (basification). In fundamental physics is necessary to introduce an ontological standard justification (basification) along with the empirical standard. I invite you to see and appreciate my analysis of the philosophical foundations of mathematics and physics, the method of ontological constructing a new basis of knowledge and new unifying paradigm - the basic generating structure, "La Structure mère" as the ontological framework, carcass and foundation of knowledge, the core of which - ontological (structural, cosmic) memory.

            Kind regards,

            Vladimir

              Dear Vladimir,

              Thank you for your appreciation. I will read your essay with great interest asap.

              Best regards,

              Jacek

              15 days later

              Dear Jacek,

              I finally got to your essay, and I enjoyed it very much. I like the Geometrical Universe Hypothesis (GUH), since geometry is involved at all levels of fundamental physics. Very well written, with excellent ideas.

              Best wishes,

              Cristi

                Thank you very much Cristi,

                I was convinced that no one is still interested in the contest.

                I am very glad that your essay is so much appreciated and I could contibute in that score. Congratulations!

                Jacek