Hi Harlan,

Thanks for the feedback! Those are good questions, and I can only partially answer them. Let me itemize.

1. Regarding the prediction of the dimension, the first question is how you even define the dimension of a causal relation. It will be emergent, only making sense at large enough scales, and it won't be an integer in general, although it must be very close to 4 at appropriate scales. Fractal dimension is relevant here. There is actually a fair bit of literature on the dimensions of causal sets, but these papers tend to use hypotheses that seem to obscure part of the structure. I have made some progress on this for structures I consider relevant, but it is not yet developed to my satisfaction.

Then, of course, you have to predict it. One of the greatest difficulties with causal theories like causal set theory and some versions of my own ideas is that there are a lot more "obviously nonphysical" universes than physical ones. This is usually described as an "entropy problem," in the sense that nonphysical solutions tend to dominate just like "disordered" solutions dominate in classical statistical thermodynamics. One way around this is to use a Lagrangian approach which (potentially, hopefully!) selects for "physical" behavior by means of an action principle and interference effects. The million-dollar question is then, "what is the 'correct' Lagrangian/action?" Again, I have some ideas about this, but I don't yet know the answer.

2. Regarding antimatter, I can understand it in the context of causal theory only in a very indirect way. In quantum field theory, the necessity for antiparticles "falls out" of the elementary representation theory of the Poincare group, which is the symmetry group of Minkowski space. In causal theory, the Poincare group is replaced with families of refinements of binary relations, and an analogous "representation theory" must be developed. If anyone has done this, I haven't been able to find it, so I am in the beginning stages of doing it myself. There are some aspects of causal theory that make me confident matter-antimatter asymmetry should ultimately be inevitable from this point of view, but I can't explain that at the moment.

3. Regarding the relativity of simultaneity, this is one of the most natural aspects of causal theory. Different frames of reference, rather than merely involving different orderings of spacelike-separated events, ARE different orderings of spacelike-separated events. This prunes away "imaginary geometry" governing what happens, and leaves behind only what actually does happen.

Take care,

Ben

Ben -- congrats with your essay. It places IMHO a healthy focus on the key question "How to get an emergent metric from a local causal relationship?"

Two more opportunities I would like to stress: Firstly, seeking recovery of a Lorentzian manifold is indeed a key challenge, but an emergent De Sitter manifold might be the true target that would allow you to get 'dark energy' to be emergent. Secondly, you don't mention unitarity as a key assumption. You might get some further mileage from entertaining the inevitable question "Is unitarity really required?"

Good luck at the contest, I would be disappointed if your contribution doesn't score well!

    Hello Mr. Dribus,

    I am understanding. no I have no publications. I am isolated at home without job, without nothing, just my personal probelms. I have not published.I have understood Mr Tegmark, ok. You can make what you want afterr all.I have made my works me, I have shown my theory to the world.If people copies or wants the prizes, you can have them Mr Tegmark and Mr Aguire.I thought that Fqxi was there to help the real innovators.I see simply a strategy. I am sad simply. You can with your friends, have a good life, and travel in private airplanes and buy opulences.Make what you want, me I sleep quiely and serenity. Of course I have neurological probelms and also I have a kind of depression due to my difficult life.But I have faith in God me, I have faith in this universal kindness and universal love. I have faith in this universal sphere. I am going to continue to read and discuss on fqxi. I forgive you all after all, you are simply persons loving monney and vanity.Perhaps you can evolve in a pure universality.

    It is the life, it exists a little of all on this planet, good people, bad people, universal people,envious,vanitious,.....the real importance for me is my faith in God.

    ps Mr Dribus, the entropy , it is god ! It is simple you know the truth !

    Regards

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    • Post #32

    Hi Ben,

    I want to understand the meaning of "causal metric" hypothesis better. I found on another web page "The causal-metric hypothesis, if correct, greatly simplifies and clarifies theoretical physics. In particular, it is the purest possible version of background independence. A theory is background independent if its entire structure is dynamical, rather than relying on a static embedding space in which the dynamical entities of the theory reside."

    I am trying to understand this in contrast to GR now (without Lambda). What is the background that the structure isn't independent from, spacetime?

    Regards,

    Jeff

      Jeff,

      Thanks for the feedback! Yes, that's my website... I don't know how you found it because its not ready for primetime yet and I've done nothing to try to promote it (no time; dissertation year!), but anyway...

      GR is usually taken as the prototype for background independence (in contrast to QFT and most versions of string theory) because spacetime interacts dynamically with matter-energy in GR. However, the whole point of background-independence is not taking things for granted, particularly things that by their very nature can't be observed, and GR does retain some traces of this. For instance, spacetime is still viewed as "containing" matter-energy even though the two interact; it's not that there is no background, just a dynamical background. This is better than a static background, but it's still something you can't observe; you can only ascribe properties to it by the behavior of matter-energy inside it. The causal metric hypothesis says that there is no background at all; spacetime and matter energy (at the classical level) are two aspects of a single structure.

      The potential for paradoxes in GR (time-travel etc.) comes from clashes between two a priori different structures: a metric structure and a causal structure. The causal metric hypothesis says that there is only one structure. In particular, causal cycles are still possible, but they're not paradoxical. Take care,

      Ben

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      • Post #34

      Ben,

      I can see now why you would like to do away with the manifold structure. It would seem that our essays run counter to each other, which is great for me to develop an understanding of your intended meaning. To me, the constant multiple of the metric represents a static potential for curvature (a potential for energy) whereas the tensor (i.e. Einstein tensor) represents the dynamic portion which gives rise to what we perceive as matter and energy moving in spacetime.

      As an analogy, for me it is the derivatives within the fabric and not the fabric itself that is important, but the fabric does exist, whereas you would like to propose that the fabric itself doesn't exist even if the derivatives do?

      BTW, I hope you rate my essay as highly as I have yours.

      Regards,

      Jeff

      Jeff,

      Well, I don't absolutely object to differentiable manifolds, though I find anything so uniform rather hard to believe in at the fundamental scale. However, one had better recover a Lorentzian structure at large scales and low energies, or the idea won't work. That's part of the task for my approach, but there is good reason to believe that it can be done. What worries me more (but also interests me more) is recovering the representation theory that describes the particles in the standard model. This requires some mathematics that appears to be very little developed and should be a lot of fun to get a handle on. In any case, tensor fields would be emergent, just like the geometry they refer to.

      I find the whole rating thing a bit embarrassing, because I'd prefer to just learn about other people's ideas rather than presume to judge the quality of their work. However, I feel justified in giving high ratings to essays that lead me to think about things in new ways, and your essay certainly did. Take care,

      Ben

      Johannes,

      Thanks for those suggestions... both of them are right on target. Take care,

      Ben

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      • Post #37

      Benjamin, you wrote:

      "The fi rst few assumptions I reject are that spacetime is a manifold, that systems evolve with respect to an independent time parameter, and that the universe has a static background structure."

      I reject too.

      See my essay

      http://fqxi.org/community/forum/topic/1413

        Dear Ben, I liked your idea of casual metric very much. You said in my thread that "you and I have perhaps different ideas on the nature of time" but I don't think so. In my mind, time is the expression of changes in energy state, and what can be more causative than that?

        Our major difference lies in you regarding matter and space as a single structure --like a true mathematician!-- and on a certain scale and at certain energies this is right. But there is also an intermediate scale, at low everyday energies, where this approach is not well suited, imo.

        Here are the quotes from your essay that especially resonated with me:

        Re : "These phenomena suggest the promise of physical models that naturally incorporate scale-dependence,.."

        Agree with you: scale is everything.

        Re : "The first few assumptions I reject are that spacetime is a manifold, that systems evolve with respect to an independent time parameter, and that the universe has a static background structure."

        Agree again: time as an independent parameter is suitable only on macro scales, while on the quantum scale, I believe, the micro-processes themselves (not 'particles'!) define spacetime volumes they trace, which can be mapped into time and distances at different scales. As for the universe having a static structure -- who actually thinks so? I can't even fathom it.

        Re : "Dimension becomes an emergent property, and is no longer assumed to be constant, nondynamical, or an integer."

        I see it exactly the same way.

        Re : "If spacetime has a sufficiently simple structure, "...

        Yeah, what is spacetime?

        Re : "Finally, the dimension of space as well as its curvature might vary with energy density, "...

        Just my thoughts. See, we have more in common than it seemed at first.

          Thanks for the thoughtful feedback! I re-read your section on time, and it does seem that we are in closer agreement than I thought at first. In particular, your concept of time seems to arise from local properties of the "fundamental energy units," while the overall order emerges from a tendency toward uniformity, which seems like a description of some sort of potential energy or entropic condition. I tried to suggest something similar in my essay, but only very briefly, since I don't know how to describe this condition precisely yet. You also describe "things in space" as a way of talking about alterations or defects of the structure, which I completely agree with.

          Also, when I said "if spacetime has a sufficiently simple structure," I guess I was being lazy... what I meant was "if the underlying structure, from which what is commonly called spacetime emerges, is sufficiently simple..."

          Take care,

          Ben

          Yuri,

          Thanks for the feedback. I just read your essay, which I found interesting in several regards. I note that you mention the idea that space can be described in terms of angles. Julian Barbour suggests something similar with his "shape dynamics," but doesn't suggest quantization.

          You point out that the strong, weak, and electromagnetic interactions are of similar strengths and that gravity is much weaker. This is true, of course, but it's also interesting to think about the size scales on which these interactions dominate. The strong and weak interactions have very short range, while electromagnetism dominates up to about the everyday scale, where gravity takes over.

          You also point out some interesting numerical relationships. There is much speculation about the dimensionality of space and the number of particle generations, but the 18-degree thing is something I have not heard of before. Take care,

          Ben

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          • Post #41

          I suggest that 3:1 ( examples #1,#2,#3) is enclosed in a total interaction of Bose and Fermi particles or fields, and it is a bootstrapping relationship between mentioned evidences.

          Surprisingly, the container(space-time), content(fermions-bosons), content (energy-matter) obey the same law 3:1.

          http://www.fqxi.org/community/forum/topic/946

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          • Post #42

          See also http://www.fqxi.org/community/forum/topic/946

          Benjamin,

          Wonderful dose of sense and lack of maths for a mathematician. Sound approach to the issues and nicely presented. I also agree most assumptions are reasonable, but I think you fall short of the path to the holy grail. First some favourite bits;

          "...complete unification of relativity and quantum theory was gradually understood to be a particularly intractable problem..." and;

          "...a variety of unexplained phenomena have been recognized." also;

          "Recovery of a Lorentzian manifold from a physically relevant causal relation is necessary at some level of approximation."

          Lastly on Dark matter; "However, this phenomenon does behave like ordinary matter in many respects, as observed in the collision of galaxies and in certain examples of gravitational lensing." I think this last point has started to be forgotten.

          Certainly worth a good score. But I'd also like to invite you to study the mechanisms embodied in my own essay, which I think finds the R postulates direct from a long known QM. I hope you are well versed in logic. I referred to PDL but had to omitt Truth propositional Logic, the exact hierarchical structure of which I've found applies to my emergent model on (non manifold) dynamic space-time frames.

          Please do study and see if you can assimilate the ontological structure from the components discussed. I throw in a bit of theatre just to help visualisation.

          Best of luck in the scoring. I hope mine will help.

          Peter

            Peter,

            Thanks for the feedback! I'll be sure to have a careful look at your essay when I get back from my trip. I won't be too discouraged if my approach "falls short of the path to the holy grail," as you put it; I believe it's fine to think, speculate, and theorize about the biggest questions, but I'm not quite that ambitious about my ideas; at best they're part of the story.

            Your ideas sound interesting as you describe them here, though I haven't yet had a chance to read your submission. Of course I have studied the common aspects of mathematical logic and some of the particular ideas applied to quantum settings, but I'm by no means an expert on this. Hopefully I can at least understand what you propose. Take care,

            Ben

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            • Post #45

            You wrote: "The strong and weak interactions have very short range, while electromagnetism dominates up to about the everyday scale, where gravity takes over".

            I think because c and G speed variation the same. See my essay part.3

            h is eternal constant and Planck unite of mass also eternal.

            Yuri,

            Let me make sure I understand. So you think that the ratio c/G is constant, but neither G nor c are independently constant? Do you mean constant in "space" or constant in "time?" Take care,

            Ben

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            • Post #47

            Variation constants in time.Within a single cycle.

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            • Post #48

            Big Bang; Present; Big Crunch

            c=10^30; c=10^10; c=10^-10

            G=10^12; G=10^-8; G=10^-28

            h=10^-28; h=10^-28; h=10^-28

            alfa =10^-3; 1/ 137; 1

            e=0,1 ; e=e ; e=12