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

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  • 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.

          Hi Gene,

          Thank you for the comments and for the interesting information. I guess that the masses of the particles, the mixing matrices for leptons and quarks, and the coupling constants should emerge from something deeper, but we can still try to find the rules even if we don't know the deepest explanation.

          Best regards,

          Cristi

          Hi Cristi,

          one thing I always find striking in these contests is that there seem to be certain currents of thought that find echoes in different ways in different presentations. In some sense, it seems as though there's something in the air that many different authors are trying to capture in their different ways, some more successfully than others.

          That's not to say I don't think your ideas are original---they are, very much so, and you display both breadth and depth in your work---but the general direction they hint at seems shared with various other submissions to this contest.

          One theme, broadly, is that the notion of 'fundamental' isn't an absolute one, but relative to a given context---you focus on isomorphisms and dualities between (at first sight) strikingly different objects. If two theories apparently start from completely different premises, yet both end up having, in an appropriate sense, the same content, then neither on its own can be considered 'fundamental'---rather, the fundamental must lie in the way they mutually reflect one another.

          Your idea of 'seeds' takes this notion to the extreme---perhaps to its logical conclusion. I can still vividly remember the shock I felt when I first learned that to reconstruct a full ('well-behaved') function, all that's needed is the data (including all the derivatives) at one single point. That seemed like magic to me: how does the data over here know what the function looks like all the way over there? How can the way I look I be completely described by just the tip of my nose?

          That the universe could be like that is an interesting thought (as is your proposal for algebraic unification---although I guess I'll have to read the essay again in order to really understand the connection between the two ideas). I'll have to mull it over some more, but it's getting late. For the moment, I'll just be contented with the fact that I'm not the only one working some concepts from Eastern philosophy into their essay. ;)

            Hi Jochen,

            Thank you very much for the comments.

            You said "there seem to be certain currents of thought that find echoes in different ways in different presentations. In some sense, it seems as though there's something in the air that many different authors are trying to capture in their different ways, some more successfully than others.".

            I guess it must be floating in the air, because when I submitted mine there were no essays posted yet :) But I am very interested in this subject, so I would be interested to put at the top of my reading list essays with related ideas, which would you recommend? (I was not active in this contest so far because I had some strong deadlines, but now I will have more time to read them)

            I also added yours in the top of my reading list, because it seems very appealing to me. As it happened, I found Lao Zi shortly after the '89 revolution (previously it was very difficult to find such writings), and about the same time I learned about holomorphic functions, so I felt the two of them are connected (it seemed to me at that time similar to the idea of manifest and unmanifest Dao). It was only later when I found about Bohm's ideas, and the holographic principle papers by 't Hooft and Susskind appeared a bit after. But the main reason for me to pursue the idea of holomorphic functions for Clifford algebras was in the similarities between Maxwell's and Dirac's equations with the Cauchy-Riemann equations. In fact, I think that the seed of this idea of holomorphic fundamentalness connects together most of my work in physics - to fix the singularities in GR, the discontinuous collapse in QM, and the Clifford algebra model of particles and forces, the sheaf theoretical perspective, as well as other things I wrote which seem disconnected but to me are part of a long term direction I pursue. Now coming back to Lao Zi, I look forward to read your essay carefully, both because of the theme, but also because I liked your previous essays :)

            Best wishes,

            Cristi

            Cristi,

            Nice essay. I stick to the prose ... You present the "germ" which is all the derivatives of a dynamic process. In my essay, I submit that only a dynamic process can come from nothingness, without failing the primitive rule of non-contradiction.

            A single quantum "spark" could start the dynamic process but, after a number of iterations of the dynamic process, the excitation would return to its point of origin and the whole thing would collapse back to nothingness.

            This is why, I "think/believe" that it requires two "quantum sparks" in order to produce a self-sustaining dynamic process. The first spark starts/creates a dynamic process that would normally evolve in symmetry, returning to its point of origin. But a second spark would disturb the normal evolution of the process making it non-symmetric. The dynamic process would not return to its point of origin and the last iteration would become the new "spark".. for another germ, which contains and maintains the asymmetry imparted by the original second spark..

            Such a two quantum sparks event is most likely exceedingly rare ...

            All fun and games,

            All the bests,

            Marcel,

              Hi Cristi,

              well, there's always a question of how much leeway we allow ourselves in seeing similarities---with enough coarse-graining, everything starts to blur together, so maybe I'm just muddling things together that are, in fact, quite different.

              But for instance, Sebastian de Haro's essay talks about 'relative fundamentality', you about the 'relativity of fundamentalness' (and both of you highlight the reason for why there are some clumsy formulations in my essay: should it be fundamentality, or fundamentalness?).

              This is also something that plays a role in the thinking of Philipp Gibbs, I think: in my discussions with him, the point that there is some mutual relationship between what we think the world is like, and what we are like, has cropped up a fair number of times. As an illustration, take a post-measurement quantum state: the measurement apparatus registers 'up' relative to the electron's spin being 'up', and it registers 'down' relative to that spin being 'down'.

              My own take on this is comes from (algorithmic) information theory: a set may contain a vanishing amount of information, but the information content of a subset may be arbitrarily large, but will always be equal to that of its complement---thus, relative to that subset, its complement has a certain information content (which I more or less equate with what's 'fundamental'), and vice versa, but their union has none.

              And for an example not from this contest, I think it's Jeff Barrett who points out that Everettian quantum mechanics can be understood as positing that 'facts are relations', in the sense of the example I give above---it's neither a fact that 'the electron's spin is up' nor that 'the electron's spin is down', but rather, the factual content of quantum mechanics concerns the relations between electron spins and measurement apparatus states.

              All of this, to me, seems to be similar to the idea of Indra's net: every bead reflects every other; and moreover, the whole of the character of any given bead is exhausted by the reflection it shows. There's a sort of mutual dependency here, as with the measurement apparatus and the electron's spin.

              But it may be that I'm getting carried away here; I do sometimes have the tendency to overemphasize the connections I see. And similarly, don't expect my essay to be an orthodox reading of Lao Zi---mostly, I use concepts from Daoist and Buddhist philosophy in the same sense that one might use Democritus' atoms today, that is, unified at best by a continuity of theme, not furnishing a literal interpretation.

              Still, I'd be very curious to read your comments on my essay!