Just a note

I can't find any mathematical write ups on you material , they are too general, so DO you have more concrete material. Thanks

Dear Philip Gibbs,

In your essay you wrote, "If there is indeed a class of many possible solutions for the vacuum, is only one of these real? I think it is more parsimonious to accept that all solutions exist in some higher sense, whether inside or outside our universe. Some physicists have speculated that there is an eternal process of inflation with vacua decaying to different solutions so that our own universe is just one bubble inside a larger arena. Others have looked at evolving universes where the laws of physics evolve in leaps where new universes are born from old. We can learn a lot from thinking about such possibilities whether they are eventually testable or not but we should not get carried away by thinking they are less speculative or more testable than they really are."

If the foundations of physics are mathematical equations that restrict energy and spacetime then there might two basic possibilities: (1) the restrictions cause spacetime to curl up according to energy-density based upon generalized quantum information, or (2) the restrictions cause approximations to energy and spacetime to build up from Fredkin-Wolfram information below the Planck scale. How many fundamental particles need to be added to the roster of the Standard Model of particle physics? My guess is that there 2 basic possibilities: (1) if the Heisenberg uncertainty principle should be generalized to use both hbar and alpha-prime, then some form of supersymmetry is empirically valid, or (2) if Einstein's equivalence principle fails for dark matter then the finite nature hypothesis is empirically valid (because the multiverse has a boundary and an interior). Google "witten milgrom" for more information. What is your opinion of the space roar and the photon underproduction crisis?

    Adel, thank you for the questions. Since you ask I will give you a potted history of how my work developed and you can compare with your own path.

    As a PhD student I worked on Lattice Gauge Theories and wrote programs to do Monte Carlo calculations, much like the Buffon's needle trick except there are many more variables in the calculation.

    I left academia but was still interested in doing some monte carlo simulations on my home computer (a Commodore Amiga) Full blown lattice gauge computations were out of the question but some people were looking at random triangulation models for quantum gravity and I wondered what would happen if it was simplified to just a random graph. I was conditioned to think about symmetries so I thought the permutation symmetry might be spontaneously broken to form an emergent spacetime.

    I found that this was possible but only in contrived ways so I wondered in the adjacency matrix for the random graph could be generalised to a full random matrix so that the permutation symmetry $S_N$ becomes a matrix group like $SO(N)$ or $SU(N)$ which would allow the spacetime symmetry to be unified with gauge symmetry.

    This was in 1987-1990. I had no internet or other way to look at other peoples research so I did not even know that there was a mathematical literature on random graphs and random matrices.

    In 1992 I was working in France and had access to the internet so I found out about arXiv (as we now call it). I did a catch up on string theory and realised that my ideas of emergent spacetime could be relevant to what people were asking about spacetime in string theory and what happened to it in the "topological phase", so I worked on it some more and put some papers on arXiv about random graphs and random matrices with generalisations to include sypersymmetry.

    While random matrices were interesting I saw that they were also limited. I felt that the ultimate model should have complete symmetry so that the field variables themselves are in one-to-one correspondence with the generators of the symmetry. For a matric model this would mean using a single matrix, but single matrix models do not have a rich enough structure, so I started to look at generalisations involving tensors in addition to the matrices. I wanted to produce a random model inspired by string field theory.

    I thought I had done it in 1995 when I heard that an old friend Richard Borcherds had succeeded in using symmetry structures from string theory to prove the Moonshine conjectures so I showed him my string inspired symmetry algebras to ask if there could be a connection. He pointed out with a counterexample that my symmetry did not close. Luckily the counter-example made me realise the way to correct the problem and I published this on arXiv and the Int J Theor Phys.

    The Lie algebras I had constructed for discrete strings were a form of necklace Lie algebra, but these were not known to me at the time so I did not use that term until later. That is probably why you cant find them in my work. see http://arxiv.org/abs/hep-th/9510042 http://arxiv.org/abs/hep-th/9609118

    These papers generated a little interest at the time from people like Leonard Suskind who wrote to me to say that he was also looking at discrete strings while trying to solve the black hole information paradox. Soon after he published him Matrix Theory. Where I spoke of spacetime events he spoke of instatons so nobody noted the connection with my event-symmetry. Another group did play on the connection between the permutation symmetries and diffeomorphism invariance but there was never any mention or citation of my work so nobody follows the idea through to the necklace lie algebras.

    Much later in 2006 the idea of quantum graphity arrived which reinvented the idea of random graphs using permutation symmetry. Again there was no reference back to my work so nobody followed to where I had taken the idea (Later they did give me a citation)

    So for twenty years I have been sitting on this idea of Necklace Lie Algebras. The maths is very tidy. It falls into place naturally and can be generalised through an iterative process that I think is related to multiple quantisation. The complete symmetry is just what would be needed to formulate a holographic theory that everybody is puzzling over. I learnt that necklace lie algebras similar to mine are of interest to mathematicians. Even that the free lie algebra can be arranged into the form of a necklace lie algebra and there are ways of mapping this through iterated integration to spacetime. The amplituhedron also uses Yangian symmetries with a linear structure and they scratch their heads wondering how these might be extended to string theory.

    So each year I write an FQXi essay and try to promote my ideas in different ways, but always everyone knocks it down and the winners are safer ideas with nothing very new or radical. I dont mind because I would rather write about what is meaningful to me than something safe and accepted that other people already agree with.

    I think eventually people will see that necklace lie algebras, multiple quantisation, complete symmetry and all that fit in, perhaps in another twenty years time it will happen. From my experience so far I expect that when they do they will use a different language and a different interpretation and so they will not recognize the connection to my work even then. That is what happen when you work independently outside the system. I dont mind that. I am happy that I have known stuff for over twenty years that other people are still confused about and I may have another twenty years of it before they finally get it.

    So my advise to you is keep working on your stuff yourself is nobody else will listen. Make sure your results are out there somewhere permanent and dont be disappointed if nobody joins in to work on it with you. Just enjoy the pleasure of having a different way of looking at things that others cant see yet.

    Allow me to just point out that Geometric Algebra \neq Algebraic Geometry. I got confused about that at one point when I was a Ph.D. student and started learning some Geometric Algebra when what I really needed was Algebraic Geometry. Still, it was a very interesting diversion to see the mathematics of spinors presented in terms of GA.

    Hi Philip,

    Your central thesis that mathematics and physics converge due to universality is very intriguing to me. However, it still leaves open the question of why the meta-laws should exhibit such universality. We still have a "miracle" to deal with, but just at one higher level than Wigner's miracle of the effectiveness of mathematics. Of course, all answers to Wigner's question will open their own new questions, so I do not see this as a defect of your view. However, I think that maybe if we take into account that human knowledge is developed by a social network of individuals, that might help to explain why universality should inevitably emerge in our fundamental laws. It is perhaps a bit controversial to bring social factors into the analysis of fundamental physics, but I think we can safely admit that knowledge is partly shaped by the society that generates it without descending into full-scale social constructivism.

      David, thanks for these points. I feel they go beyond the subject of my essay which does not have much to say about details in cosmology. The anomalies (dark roar and photon underproduction) you mention are very interesting and not ones that I am familiar with. I fear that the resolutions will be rather mundane but I hope there will turn out to be something fundamental at work and I will keep an open mind on it until more compelling data is available either way.

      I follow the digital physic and finite nature ideas which are very interesting to someone like me who sees information and qubits as fundamental but I dont agree with some of the stronger claims or theories about cellular automata. This is because I steer away from the idea that simplicity has nay part in determining the laws of physics and use universality instead. Nevertheless digital physics is also interesting from the point of view of universality.

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      • Post #93

      Interesting points. I dont claim to have all the answers. These are the Marianas Trench of philosphical questions and the bottom is still a long way down. However, I am guided by the idea that there cant be any miracles. There must eventually be some way to understand our experience without harking back to something more fundamental, even something like simplicity is too much of a human construction.

      I am able to accept that the range of logical possibilities is an acceptable starting point which does not require any miracle. Mathematics is just the analysis of these logical possibilities. We can start from there and try to find a bridge that takes us to physics without putting in any miracles. Universality is just that bridge. It must be there because we got here somehow.

      I dont know exaclty how the bridge is constructed but I use metaphors from complexity theory to try and get some ideas. Most of the things we know about universality in complexity theory exist within some bigger context. Everything has to be intrinsic rather than extrinsic. We have to avoid the need for some measure on the moduli space of possible theories because that measure would need an explanation itself. I think some forms of universality such as the universality of computability do not need such a measure. I think there is a similar universality principle at work in category theory but it is harder to find.

      I dont think social constructs are involved in forming these meta-laws. I do think that social constructs such as anthropomorphic selection is relevant in selecting the solution to the meta-laws that forms our experience of reality. So there can be no fine-tuning in the meta-laws. They must be perfectly natural.

      Dear Philip Gibbs,

      In your essay you wrote, "Today the more progressive physicists take a different view. Space and time are seen as emergent from a yet unknown new way of looking at the universe that must go beyond the bounds of standard quantum field theory, but that much is widely accepted and therefore is not the defining feature of the new paradigm. What is harder to accept is the multiplicity of the vacuum - the idea that there may be more than one stable solution for cold empty space and that the one we know is nothing special or unique." If spacetime needs to be replaced, there might be 2 basic possibilities: (1) there exists a continuous, non-commutative geometry for the string landscape with different Lagrangian formulations of quantum field theory; (2) quantum field theory is an approximation generated by Wolfram's automaton via approximations to string vibrations on a finite lattice. Could there be a third alternative? According to Jacob Bekenstein, "The present paper introduces TeVeS, a new relativistic gravitational theory devoid of a priori fields, whose nonrelativistic weak acceleration limit accords with MOND while its nonrelativistic strong acceleration regime is Newtonian. TeVeS is based on a metric, and dynamic scalar and 4-vector fields (one each); it naturally involves one free function, a length scale, and two positive dimensionless parameters, k and K. TeVeS passes the usual solar system tests of GR, predicts gravitational lensing in agreement with the observations (without requiring dark matter), does not exhibit superluminal propagation, and provides a specific formalism for constructing cosmological models." -- J. Bekenstein, "Relativistic gravitation for the MOND paradigm", 2004, arxiv.org

      What is my fundamental objection to TeVeS? I doubt that it makes sense in terms of string vibrations. Digital physics might, or might not, be empirically valid. In any case, MOND is empirically valid -- on the basis of the work of Milgrom, McGaugh, Kroupa, and Pawlowski. MOND might suggest 2 basic possibilities: (1) the equivalence principle is 100% correct but the concepts of gravitational mass and inertial mass need to be slightly changed by a complicated modification of Einstein's field equations; (2) the equivalence principle is 100% correct for particles that are measured but fails for dark matter. Why do I think that the first alternative in the preceding statement is wrong? If you modify GR by adding two or more new mathematical mechanisms then you need to explain the modifications in terms that make sense to most physicists. You also need to explain what went wrong in Einstein's original derivation. I say that the -1/2 in the standard form of Einstein's field equations should be replaced by -1/2 + dark-matter-compensation-constant. This means that the multiverse has a boundary and an interior and that gravitational energy is lost from the boundary; the process eventually results in an instantaneous collapse of each matter universe and each antimatter universe into a synchronized big bang that occurs every 81.6 ± 1.7 billion year. Let us suppose that the fundamental string domain really is 10-dimensional in empirical reality. If nature is infinite, the 10 dimensions somehow curl-up into 4 spacetime dimensions. If nature is finite, the 10 dimensions DO NOT curl-up. There are 4 dimensions of spacetime in a universe composed primarily of matter, 1 dimension of Wolframian time that determines the nonmeasurable clock speed of Wolfram's automaton in a matter universe, 4 dimensions of spacetime in a universe composed primarily of antimatter, and 1 dimension of Wolframian time that determines the nonmeasurable clock speed of Wolfram's automaton in an antimatter universe. The Wolframian time is needed to explain the discrepancy between astronomical time and atomic time. Here "astronomical time" and "atomic time" are as described by Fernández-Rañada and Tiemblo-Ramos.

      8 days later

      Phil,

      Count me among your admirers. Though I haven't always understood what you're saying, I find this essay crisp, clear and abundantly meaningful.

      "What then would happen if we treat the whole of mathematics as a statistical physics system or as a path integral over the moduli space of all possible theories [4]? Would some universal behaviour emerge that could describe the meta-laws of physics?"

      I think so! Taking your reference to chess-playing aliens, one finds that that every chess game, as complex as the game is, has a critical point where the game can go either way, or to the equilibrium state of a draw. I agree also with your view of vacua -- my conclusion is that nature cannot respect any vacuum state without respecting all vacuum states.

      Years ago I suggested that even mathematics (at the level of analysis) is a self organized system. You get my highest score, and I hope you can read my essay when you get a chance.

      All best,

      Tom

      Hi Philip,

      I am just curious how you think an AI could invent the concept of real numbers. If everything a computer can deal with is computable, how could a computer handle uncomputable real numbers (as opposed to computable reals such as pi or e) which have an infinite amount of information and cannot be referred to in any unambiguous way? The information content of most "real" numbers cannot be compressed. How would a computer define operations such as addition on these types of numbers?

      Please check out my Digital Physics movie essay if you get the chance. I'd be interested to hear your thoughts.

      Thanks,

      Jon

      Dear Philip,

      Thank you for the comments you left on my essay's page. About a week ago, following a reference at the end of Jonathan Dickau's essay, I came upon your almost twenty-year-old essay Theory of Theories, and I found your extension of the idea behind Feynman's path integral to the space of all possible theories absolutely fascinating. Quoting from that essay:

      "We might well ask if the same can be applied to mathematical systems in general to reveal the laws of physics as a universal behavior which dominates the space of all possible theories and which transcends details of the construction of individual theories."

      I then reread your entry in this year's contest, where you expand upon this idea, whose significance I had missed on first reading, and followed your reference to the recent paper by Seth Lloyd and Olaf Dreyer, The universal path integral.

      If I were to rewrite my essay today, I would certainly mention these ideas. I totally agree with you that, if all possible mathematical/physical universes have potentially the same existence as ours, the anthropic principle is not enough by itself to explain why we find ourselves living in a universe that is so regular and relatively simple. Something like your Theory of Theories could "collapse" the chaotic ensemble of all mathematical possibilities, via something like a path integral, to a reduced set of relatively well behaved "coherent" scenarios, on which the anthropic principle would then act. The principle of stationary action has always been my favorite idea in all of physics, and to think that something similar could play a role in "regularizing" the "smorgasbord" of the multi/Maxiverse is very appealing to me!

      I agree with you that a future FQXi contest on the relationship between consciousness and physics would be absolutely fascinating! In this year's contest, we have splits between mathematical platonists and anti-platonists, as well as the usual split between the "let's evolve physics from the current accepted theories" crowd and the "bring back local realism and/or absolute space-time" crowd. Imagine if we add a split between "consciousness-first" and "matter-first" views, and between the "free-willers" and the "free will is an illusion" camp... Oh what a wonderful, delicious and mad cacophony this would be! :)

      Marc

      P.S. I have also posted this on my essay's page, and I will be back with a proper review of your essay, hopefully within the next few days!

        Dear Philip,

        Following our previous conversations, I just reread your essay. Indeed, we share a lot of the same views.

        I like the way you begin your essay by considering the shortcomings of the "univacuum assumption". I googled "univacuum" and I think you are the first to use the term in this context. I would say that I am clearly in the camp of the "multivacuers"... but I think there are many "univacuers" out there! You say that the idea of the multiplicity of the vacuum "bruises the egos of particle physicists who thought that the laws of physics they were unveiling were special in a very fundamental sense." This echoes the final sequence in the third of my "This Is Physics" videos (submitted to the recent FQXi video contest) where I claim that "Most physicists don't like the idea of the Multiverse, because if it is true, it means that they have devoted their lives to master only ONE physics of ONE universe instead of THE physics of THE universe."

        I agree with you when you explain that it is more "parsimonious" to accept that "all solutions exist in some higher sense, whether inside or outside our universe." I claim essentially the same thing in my essay when I discuss the issue of Occam's razor (the "law of parsimony") in the context of the multi/Maxiverse.

        Like I said in the most recent reply to my conversation with you and "En Passant" on my essay's page, maybe we are obscuring the issues by insisting in labelling as "mathematical" or "physical" the fundamental structures that make up reality. In your essay, you take a safe and wise approach when you simply talk about the "timeless and spaceless" ensemble of "all things that are logically possible".

        For me, the highlight of your essay is when you say that "Universality brings together all the logical possibilities of mathematics under one metaphorical path integral". Indeed, emergent universal behavior, as expressed by the Meta-Laws of physics, is what we need to understand better if we are to explain why, in the space of all possible worlds, we find ourselves living in a universe that obeys stable and relatively simple laws. I like how you use the concepts of path integrals and critical points in the context of finding out the Meta-Laws of physics.

        Finally, you nicely address the subject of this year's essay directly when you explain that "mathematicians and physicists are attracted towards the same critical point of universality".

        Great job!

        Marc

        P.S. As you say, the fact that the Monstrous Moonshine Conjectures have been studied by using the methods of string theory is an astounding demonstration that "there are deep relations between ideas from physics and mathematics". I have to confess that I'm having some difficulty understanding clearly the complicated concepts behind the Monstrous Moonshine Conjectures and Borcherds' approach. Do you know of any (relatively) accessible sources that deal with this fascinating topic?

        My use of the word "metaphorical" when talking about the path integral is deliberate. We get an intuitive idea feel for universality when we think of it as a sector of the path integral that dominates or where phases do not cancel out, as in maximum entropy or the classical limit. But even in quantum mechanics that is not the whole story. The path integral for fermions works differently through some less intuitive algebraic mechanism.

        Universality of the concept of computability is another example that is less intuitive. Some people do not even recognise it as the same use of the word universality, but I think it is. The universailty that I am looking for in this essay may also be more subtle than just a path integral dominated by some kind of comonality, but it is a good metaphor and possibly a source of toy models that might be instructive.

        The monstrous moonshine conjectures are quite deep and a bit beyond my expertise, but you can get an idea by learning a little about the Golay code and the Leech Lattice and the related groups. There are a lot of mathematical ideas mysteriously connected by the number 24 which are also connected to the number of dimensions in bosonic string theory. John Baez wrote some easily understandable articles about that.

        6 days later

        Dear Phillip,

        There are opinions that Euler's identity is of particular importance for physics. In this competition is very rarely mentioned. I have no idea about it, but I see the possibility of complementarily exp(i*pi), (from Euler's identity) and exp(2*pi), which I use in my essay, under the name cycle. I ask: what you think about the possible progress in using Euler identity in physics?

        Regards,

        Branko

          Dear Brabko,

          Euler's identity was an early example of the surprising connectedness of ideas in mathematics and physics. It linked [math]e[/math] and [math]\pi[/math] in a surprisingly direct way where previously they seemed unconnected. Now we take it for granted because it is part of complex analysis that is common place in maths and physics, for example it is used in Fourier analysis. However it is a good idea to use it in this contest.

          Hi Phil,

          It is a pleasure to meet you again in FQXi Essay Contest. Even this year, you made an excellent work as I found your Essay very interesting and enjoyable. I must confess that I have read your Essay after reading a nice sentence of yours reported in the Essay of our friend Jonathan J. Dickau which claims that "the laws of physics are a universal behaviour to be found in the class of all possible mathematical systems". In any case, here is a couple of comments on your nice Essay:

          1) Some years ago I discussed in San Marino with two great physicists, i.e. Hagen Kleinert and Alexander Burinski, on the new paradigm that is emerging in fundamental physics concerning the new way of looking at the universe. All of us three agreed that gravity is the key. We think that gravity goes beyond string theory and quantum field theory.

          2) I disagree on the issue that the holographic principle is required to resolve the black hole information loss puzzle. This assumption by Susskind is based on the Maldacena conjecture. But I agree with Mathur's criticisms, see here and here. The key point is that the AdS/CFT duality works only for low energy processes, where black holes do not form. In other words, if we force the gravity theory to be the dual of a given CFT, then we cannot assume that black holes will form in the theory. Thus, the duality seems to break down in presence of black holes.

          In any case, I still remark that I find your Essay very intriguing. Thus, I give you a deserved highest score.

          I hope you will have a chance to read my Essay .

          I wish you best luck in the Contest.

          Cheers, Ch.

            Christian, It is good to see you here again.

            I agree that gravity and spacetime is an important key. For me it is about how to understand that the geometry of gravity emerges from somthing more algebraic and abstract, but there are other ways to see it.

            I dont think the holographic principle is really based on AdS/CFT. The principle was formulated by 't Hooft and Susskind before the Maldacena conjecture and is independent of that or string theory. The problem is to know the general context in which the conjecture could be true. For that I have suggested that "complete symmetry" is the required element. Of course it is not unreasonable to be skeptical of the principle. It is speculative, as is string theory. I am sure it will be many years and there will be many interesting discussions and revelations before any consensus is formed.

            Philip,

            Heavy stuff. As some politicians would say, "I am not a scientist specializing in quantum gravity, so ..." Well, what they say is simpler.

            "All is possible in the quantum realm but there is a hierarchy of classical limits ... these limits define worlds in which math rules are played out according to the law of quantum averages."

            Can we simply start with trying to explain a mystery in the classical world, for example, how European robins navigate N and S seasonally. A theoretical physicist and a molecular genetics professor did this. They combined a receptor for the avian chemical compass with a protein capable of generating entangled electrons that interacted with the Earth's magnetic field. Does their study impose a classical limit which utilizes what they know about quantum mechanics?

            I know I am cherry-picking your quotes but I am struggling to understand.

            Incidentally what does a successful BICEP2 discovery of a primordial B-mode cosmic inflation caused by gravitational waves do for quantum gravity?

            Like to see your thoughts on my essay: http://fqxi.org/community/forum/topic/2345.

            Jim

              Phil,

              Well up to you usual high standard and with signs of greater maturity of view. I hope my score helps keep you at the top. I particularly like your identification that the question can be just as well reversed (why is it that physics...). I do however have a couple of questions;

              1) Do you really believe there must be a greater or 'super' symmetry hiding away behind the 'dipole' symmetry considered 'breaking' by Green and most particle physicists? ..and what would it bring. Do you think of the concept that the dipole may perhaps be the very quiescence of 'matter' (inc anti) as opposed to (maybe dark?) 'energy' alone?

              2) This may be semantic, but suggesting a 'map of all things logically possible" would seem to many to be excluding QM and non-locality. Do you suggest QM; a) CAN have a 'logical' explanation. Or b) ??

              Re 2; I hypothesise a 'quasi classical' mechanism that seems to reproduce it and reveal the mathematical 'sock switch' trick that hides it in my essay, so prefer a).

              I hope you get to read mine. I feel that in 'stabbing in the dark' I've felt something, but how can we then expose what it really is when each of us has a different vision? Perhaps the value of reading these a essays is in converging those vision.

              Well done, and very best of luck with the definitive judging.

              Peter