Hi David,

My remark "A major question is why these particular gauge symmetries and representations?" refers to the pattern of fundamental particles. Milgrom's MOND is about the rotation of galaxies, so how can it be relevant to that question? Especially since MOND, as opposed to various "dark matter" proposals, doesn't claim to require new fundamental particles, being based on modifying gravity alone.

Nevertheless, MOND is important, but my essay was not about this, you will not find the words "dark matter" or "rotations of galaxies" in it, so I don't think I was being unjust to Milgrom. My essay is about what "fundamental" means.

When we talk about fundamental laws, I think the focus should be on fundamental principles, rather than on approximations and phenomenology. Newton's gravity is an approximation, and so is a modification of Newton's gravity like MOND. A fundamental theory should in particular be generally covariant. But I have good news for Milgrom: there is a generally covariant modification of Einstein's gravity - conformal gravity - which apparently gives as a limit case Milgrom's. I mention conformal gravity for its salient features regarding the Standard Model of particle physics in the endnote #6, but it is also relevant to MOND. So if the final theory will embed conformal symmetry, MOND or something close to MOND will be an approximation of it.

Best regards,

Cristi

A possibility is that distance appeared from a kind of symmetry breaking. For example in a theory where spacetime is a manifold, but the structure group of the tangent bundle is GL(4,R), and it is broken to SO(1,3) by some mechanism. Another possibility is conformal gravity, where you have scale invariance, so angles are invariant, but not the lengths. Note that the Standard Model without masses is conformally invariant. And then the conformal symmetry in conformal gravity is broken to SO(1,3) by some geometric mechanism, which formally is identical to Higgs and endows some of the particles with masses just like in the Standard Model. So yes, it is possible.

It appears that in effect you have CL(3,3) ~ SL(3,C) or U(8) in a Clifford basis. You can break this into SU(3) and SO(3,1). I have similar ideas with SU(2,2) and the occurrence of additional quarks as dark matter.

    Hi Lawrence,

    More precisely, Cl(3,3) is the complex Clifford algebra of a complex 6D space V. The space V can be decomposed as the direct sum of two complex 3D isotropic spaces, which form a Witt decomposition, and we consider them fixed. The transformations of Cl(3,3) preserving this decomposition give the SU(3)xU(1), where U(1) is for electromagnetism. They act by permuting the 8 ideals of Cl(3,3) according to the correct representations of SU(3). On these ideals, the Dirac algebra acts at left in a reducible way, which give room for SU(2) to act as well at left. So the ideals are the spinor spaces for quarks and leptons, and they transform according to the Standard Model group, with the proper representations built in.

    I'm also interested in SU(2,2) and how you used it.

    Best regards,

    Cristi

    SL(3, C) is SU(3) in a tensor product with an 8 dimensional space, or 8 real dimension = 4 complex dimensions. So we can think of this as spinorial or complex valued spacetime with SU(3) principal bundle. The 8 dimensional space is represented only by the trace of a Hermitian matrix or its metric. You then have exp(iS) for S = ∫ds and ds the Gaussian interval. There are three copies of sl(2,C) in the group sl(3,C) which corresponds to three weights or the vector space (e_1, e_2, e_3, f_1, f_2, f_3) which are the 6 dimensional space you talk about.

    I thought I would mention that the conformal diagram you have of the black hole represents one possible slicing. I can slice spatial surfaces any way that I want. I can arrange it that spatial surfaces reach the singularity inside the black hole before they reach i^+ or I^в€ћ. The slicing and how the surfaces reach r = 0 is arbitrary.

    LC

    That's interesting, considering that sl(3,C) has 16 real dimensions, and the Clifford algebra Cl(3,3,C) I used has 64 complex dimensions, and its full spinors have 8 complex dimensions.

    About the black hole singularity, are you referring to this one? Slicing is not unique, of course, that's true in all solutions in general relativity, but the things are not as flexible how you may think. What matters is the atlas, not the particular solution, and the atlas has no preferred slicing. My Schwarzschild solution is analytic and is continued analytically through the singularity, and it remains so even if you apply an analytic change of coordinates and get a different slicing. Moreover, in the paper I find an infinite family of different Schwarzschild solutions analytic at the singularity, and in fact an infinite family of such atlases. But among them there is a unique one which saves the fields at singularity both geometrically and physically in the way I describe here.

    Best regards,

    Cristi

    I was referring to the attached file which appears on your website. The succession of spatial surfaces can appear in any possible way. How I push time forwards is a sort of gauge freedom. I can choose to have the spatial surface slap onto the singularity simultaneous with the disappearance of the black hole as seen outside. this would correspond to the interior observer being coincident with all the Hawking radiation emitted by the black hole. Your figure, which has a bit of an apparent discontinuity at the horizon, has the spatial surface coincident with the singularity as the exterior region reaches I^.

    We then consider this in the light of quantum states on the spatial surface. In your case quantum states on the interior are entangled with Hawking radiation reaching I^. In the case the spatial surface reaches the singularity coincident with the demolition of the black hole as seen in the exterior region entangles interior states with local states. This is curiously similar to what Susskind argues with ER = EPR. The entanglement of Hawking radiation with the interior and later Hawking radiation with the distant I^ are relative, or that in effect interior states are identical to distant Hawking states.

    I think this is a sort of bundle monodromy. The singularity is just a way that a complementary principle is manifested topologically.

    The 16 dimensions of the SL(3,C) is the SU(3) on the 8 dimensional manifold. With the CL(3,3,C) in 64 dimensions ~ U(8) the 8 complex dimensions tied to SL(3,C) in some way.

    Cheers LCAttachment #1: unitary_evaporating_black_hole.gif

    Hi Lawrence. Oh, you mean that animated gif I made back in 2010. Yes, it requires a special slicing of spacetime, and has some other problems which I described here and here. For those reasons I was not satisfied and not interested to write a paper about it, because I wanted something without those problems. The solution I was satisfied with came a year later. I wrote this year about the one from 2010 on my blog, because I saw Maudlin's paper, who rediscovered it independently. Then I showed him my gif and he is using it. He may be satisfied with that solution, but I'm not and was not from the beginning. I find your remarks and the connection with ER=EPR interesting, you may want to send them to Maudlin.

    Best regards,

    Cristi

    7 days later

    • [deleted]

    • Post #17

    Hi Cristinel, I enjoyed your essay when I got into it, rather than just taking a quick look. It is full of interesting ideas that you have clearly explained. I think the question you ponder, about whether fundamental is most foundational; And how foundational should be considered when seeking the fundamental, is good. It seems to me that though material things ultimately reduce to far simpler things, maybe it isn't that 'material essence','quark stuff' and maybe even still potentially differentiate-able existence within that (not yet known), which is (at least by itself) fundamental. In the sense of the 'vital ingredient" in allowing or providing the means for the happening of physics. Or that which is causal for the majority of physics. You are talking about the particles themselves as fields whereas I have been thinking about the matter being differentiated from the ubiquitous existence and there also being fields within that. Affected by and affecting the matter and fermion particles.

    Another section that particularly resonated with me was that about the number of particles of the standard model. It was a subject I had thought of writing about. As I wonder whether all of them exist naturally. As for some, they have been observed (or evidence of them has been observed) under extreme conditions. Which makes me think that they have come into being because of those conditions. There is perhaps also a desire to have a particle for 'everything'. I was thinking about perhaps irreverently comparing the classification to the deities of Terry Pratchett's Discworld. Two I found in particular are Anoia, the goddess of things that get stuck in drawers and Nuggan, in charge of paperclips. (Never mind if it seems irrelevant, it amuses me.)

    Getting to Indra's net at the end, mind already boggled, I thought it was fascinating, and bizarre, not as I see it, the way forward. Though it was an incredible journey and I'm grateful for that. Well done. Kind regards Georgina

    Hi Cristinel, I enjoyed your essay when I got into it, rather than just taking a quick look. It is full of interesting ideas that you have clearly explained. I think the question you ponder, about whether fundamental is most foundational; And how foundational should be considered when seeking the fundamental, is good. It seems to me that though material things ultimately reduce to far simpler things, maybe it isn't that 'material essence','quark stuff' and maybe even still potentially differentiate-able existence within that (not yet known), which is (at least by itself) fundamental. In the sense of the 'vital ingredient" in allowing or providing the means for the happening of physics. Or that which is causal for the majority of physics. You are talking about the particles themselves as fields whereas I have been thinking about the matter being differentiated from the ubiquitous existence and there also being fields within that. Affected by and affecting the matter and fermion particles.

    Another section that particularly resonated with me was that about the number of particles of the standard model. It was a subject I had thought of writing about. As I wonder whether all of them exist naturally. As for some, they have been observed (or evidence of them has been observed) under extreme conditions. Which makes me think that they have come into being because of those conditions. There is perhaps also a desire to have a particle for 'everything'. I was thinking about perhaps irreverently comparing the classification to the deities of Terry Pratchett's Discworld. Two I found in particular are Anoia, the goddess of things that get stuck in drawers and Nuggan, in charge of paperclips. (Never mind if it seems irrelevant, it amuses me.)

    Getting to Indra's net at the end, mind already boggled, I thought it was fascinating, and bizarre, not as I see it, the way forward. Though it was an incredible journey and I'm grateful for that. Well done. Kind regards Georgina

      Hi Georgina,

      Thank you for going into my essay, and for sending me your thoughts. I hope you'll write your ideas in an essay for this edition. Also your idea to compare the classification of particles with the deities of Terry Pratchett's Discworld is nice, I think it would be fun if you write about it :) About what's truly fundamental, who knows, many descriptions seem to work partially, to be equivalent sometimes, but I think we know very little and we need fresh ideas.

      Best wishes,

      Cristi

      Hi Cristinel, I have just found out about the origin of 'Indra's' net. I didn't realize 7 was a footnote but thought it was just a reference. Having read the footnote I understand what Indra's net is and why you have chosen to propose it as a model of fundamental physics, tying in with recent ideas in physics about the holographic principle. I really like Francis H Cook's description. "we will discover that in its polished surface there are reflected all the other jewels in the net, infinite in number. Not only that, but each of the jewels reflected in this one jewel is also reflecting all the other jewels". It sounds beautiful. I agree that it is good to explore fresh ideas. My reservation -but what problems does it solve? In what way is it an improvement over other explanations? Plus, of course, personal bias in favour of my own explanatory framework.

      Dear Cristi,

      What an excellent essay, beautifully presented. I particularly like your Isomorphic stories section, and also the notion of Indras Net. Let's assume it is a correct depiction of reality at a fundamental level, so in reality, you have found the way indivisible units operate to create everything within it, including yourself. Do you now know enough about what this reality is? What is still missing?

      Best,

      Jack H James

        Hi Georgina,

        So far, physicists found mathematical descriptions for various phenomena, which cover a large domain. You have equations describing various phenomena, combined together, and it seems that we just need a few more pieces of the puzzle and we will know everything about the fundamental structure of the universe. And maybe continuing like this we will eventually have all these pieces combined together, and covering what we know about the universe, it seems we are close. But I am not satisfied with just a collection of equations combined together. You can put all sorts of things in the Lagrangian, like new unobserved particles predicted by various models. But why these fields, these equations, these terms in the Lagrangian? My dissatisfaction is not only metaphysical or aesthetical. The problem is that the current view gives too much freedom to change the theory if new facts are discovered. I don't trust something that can be adapted so easily. I want something that once found, you can't change. And if there are new phenomena, I want those to result from that model because they are there, not because you can add them by hand. A theory that can't be adjusted has much more predictive powers, so higher chances to be falsified, and if not falsified by any conditions, to be true.

        I was attracted by holomorphic functions since I first learned about them as undergraduate student. On the one hand when I read that you can use them to represent the electric field in 2D. Moving to 4D spacetime and replacing the complex field with the Clifford algebra of spacetime reveals that you can include other equations of physics, but including the other forces and the particles from the Standard Model shows that even this needs to be replaced with something richer, and I think, as I explained, that this is a larger algebra, perhaps a larger Clifford algebra, like the complex Clifford algebra Cl(3,3), or maybe another one. Different things we know in physics seem to be regained from such a structure already, without having to add them manually, and without giving us too much freedom to adjust. So I believe that such a structure exist, which naturally includes what we know and what there is to be found, but in a rigid way, so that you can't and don't need to adjust it. No mobile parts, maximum rigidity. And the most rigid mathematical fields seems to me to be the holomorphic ones.

        When physicists talk about simplicity, at first sight one may think that it is about using simple constituents which are similar to what our intuition can grasp easily. But to physicists, "simple" is not "easy". On the one hand simple means the smallest number of principles, equations, and free parameters. On the other hand, it means simplicity in the mathematical sense of indecomposability. So what appears to us as being different fields, to be just different components of one thing. This sort of simplicity means rigidity.

        The fact that holomorphic functions have this property the full information about the field is contained in any point was something that I found cute and aesthetically appealing, but didn't think of it from the beginning as being relevant. Later, when I found out more about things like quantum holism, the holographic principle, and the holistic ideas of Bohm, I realized that these may just be consequences of this analyticity of holomorphic functions. And only last year I found out about Indra's net, which I thought it was a good metaphor for this. And I thought this idea may be interesting for the theme of this essay contest, since it introduces an interesting type of fundamentalness.

        Kind regards,

        Cristi

        Dear Jack,

        Thank you for reading and for the comments. You ask:

        > Let's assume it is a correct depiction of reality at a fundamental level, so in reality, you have found the way indivisible units operate to create everything within it, including yourself. Do you now know enough about what this reality is? What is still missing?

        The point of science is to advance in understanding as much as possible. But there is no guarantee that the scientific method based on testability of hypotheses can lead to this. There's no guarantee that every truth about the universe is in our range of testability and in our range of understanding. As for the proposals I made in this essay, they are still in the phase of being mere hypotheses, supported by some arguments like those I mentioned, but far from being proven. Much is still missing, the resulting description will have, in my opinion, to be complete, without mathematical or logical inconsistencies, without parts that can be changed or replaced (see this previous comment for more details). But even so, we may never know that we found the ultimate truth and nothing is missing :)

        Best regards,

        Cristi

        Hi Cristi and Mr Brown,

        I have difficulties with this MOND , like Verlinde also has made.The fact to change this gravitation seems so odd.On the other side we search this quantum weakest force and we could insert this dark matter in encircling this standard model by this gravitation governing this universe. The fact to consider only photons like primordial informations seems odd.The problem I am thinking humbly is that the geometrical algebras consider only these photons and consider only a photonic space time.Of course this E8 for example is interesting but it lacks some foundamentals like the spherical volumes and their motions and this matter not baryonic.The quantum gravitation needs a kind of revolution of our standard model.Now in a pure philosophical point of vue, I am doubting that this infinite consciousness having created a physicality has only created photons.It is not a prison at my humble opinion where we cannot travel between our cosmological sphères due to this special relativity. The fact to consider that a cosmological central singularity produces a gravitational aether playing with the cold and heat with a kind of finite serie seems more foundamental. We are Young still and our knowledges also and perhaps it is time to insert and superimpose this matter not baryonic to our standard model.Imagine simply that we have a serie of quantum BHs farer than nuclear forces implying forces stronger and now let's insert these particles of gravitation them encoded weaker than our electromagnetic forces.We see that this gravitation encircles our standard model, that can answer to many things and at all scales.Insisting on only photons is like a prison, I liked your essay Cristi , it is general and it is always a pleasure to read your lines of reasonings. Lol lie and Clifford drink a belgian beer and discuss about what is an electron, Hestenes and Bohr them try to find the good operators , vectors and scalars in fractalising the forces, Hamilton and schrodinger and lagrange arrive and tell that after all it is just a question of good parameters and how we interpret them.Now after these beers, the take a belgian chocolate and it is a catalyser of reasonings,the truths appear in choosing the spherical volumes said Tesla, Newton and Einstein lol

        friendly

        Hi Cristi ,

        You tell us in your essay that waves are essential, I agree.That said you tell that these waves and oscillations can give all the shapes.It is a reasoning for the strings in fact.Can we be sure about this ? if the 1D primordial field is nt photonic and that the particles are notpoints and strings , so there is a problem because the spherical volumes and their motions witha finiet serie of spherical volumes where space disappears, we have also the combinations to create all shapes.

        Best Regards

          Hi Steve,

          Thank you for the remarks you made here and above, under David Brown's comment. And for the questions.

          In my essay I don't favor photons and exclude the other particles. All fundamental particles evolve in time like waves, they propagate and interfere and interact. The difference is that those with mass have an additional mass term, so they are if you want like waves which don't propagate at the speed of light. Even leptons and quarks are governed by a wave equation like this with an additional mass term, obtained by applying once again the Dirac operator to the Dirac equation.

          Best regards,

          Cristi

          You are welcome,

          It is relevant because we arrive still to what is an electron in fact.Dirac has made a wonderful equation, we could improve it in adding this gravitation and all these motions and oscillations of spherical volumes.The positron, the electron the photon in fact are more than we can imagine.If we insert this matter nt baryonic and if my equation is correct E=m(b)c²+m(nb)l² we could extrapolate to this weakest force , the quantum gravitation but with an equation of electron but nt relativistic.Because if all is gravitationally coded and that the finite series of spherical volumes are the key.We can consider that the method can be the same with the wave functions at the difference that they are nt relativistic.We just consider particles of gravitation instead of photons and we consider them nt relativistic and perhaps also we insert this cold.We can insert the reduce planck constant and we imrpove with the spherical volumes and we insert also the motions orbital and spinal.The dirac equatin can be improved and can permit to reach this gravitation.Photons are just like a fuel.It is not easy to find all this puzzle, if we could see the truth like that it could be well lol like a picture giving us the real truths but we are far.Friendly

          Cristi,

          A couple of things about your essay caught my attention. I developed a model of the proton by reducing data and using it to understand some aspects of atomic physics and cosmology. Admittedly, I didn't have all the theory. Your 3*3 group indicates that 1/3 charge is related to 3 dimensions. I kept coming up with logarithms that are multiples of N=0.0986, which I wanted to understand. I did not have the relationship to Schrodinger's equation until Edwin Klingman encouraged me to look at fundamentals of E=e0*exp(N), where N is a natural logarithm. Derivation of the relationship is in: Barbee, Gene H., Schrodinger Fundamentals for Mesons and Baryons, October 2017, vixra:1710.0306v1.

          I use probability 1 for P=1=exp(iet/H)*exp(-iet/H).

          The logarithm associated with the electron is N=10.136 and with the known mass 0.511 MeV we can evaluate e0.

          e0=0.511/exp(10.136)=2.02e-5 MeV

          With your theory, N=0.0986 is associated with fractional charge 1/3 for each of three dimensions, the value 10.431-0.0986-0.0986-0.0986=10.136 (the -1 charged electron) and E=e0*exp(0.295)=27.2e-6 MeV (the electromagnetic field energy).

          In high energy collisions, the electron can revert to a quark by absorbing an anti-e neutrino and kinetic energy. I associate N=10.333 with the mass of a quark. But N=10.431 is neutral and 10.431 -0.0986=10.333 is the fractional charge (-1/3) for the quark. Four units of 2.02e-5*exp(10.33)= 0.622=2.49 MeV, the standard model mass for the Up Quark (PDG) is 2.2 MeV.

          Aside: In my model, the dimensions don't split until after the neutron is formed (by Schrodinger based quads). When they do split, neutrons proliferate (probability 1 is maintained) and the gravitational coupling constant (1/exp(90)) is established. Your concept that the rules are everywhere the same is correct and fractional charge is related to dimensions.