Dear Janko,

Thanks for the feedback. I will see if I can find what Feynman said about this... I always appreciate his point of view.

Regarding Machian ideas and shape dynamics, a number of us (me, Lawrence Crowell, Sean Gryb, Flavio Mercati, Daniel Alves) have been discussing the possibility of a duality or complementarity between causal theory and shape dynamics. Shape dynamics derives an arrow of time essentially from an asymmetry in configuration space, whereas I take it to be fundamental, but these two ideas need not necessarily contradict each other. Part of that discussion is on my thread, and part of it is scattered about on the other threads.

Regarding the recovery of relativity, many the ideas specific to relativity (as opposed to Newtonian mechanics) are clear in causal theory; in fact, causal theory is more a generalization of relativity than anything else, since it is in relativity that the primacy of the causal structure and the ideal of background independence are clearly embodied. The technical difficulty comes in recovering manifold structure, and the point of view is that this is really unnecessary to all the important physical ideas of relativity. This will take work, because these ideas are currently expressed in geometric language. If Riemann had been around to advise Einstein rather than Minkowski and his friends, he might have showed him that there are many possible formalisms for expressing his physical ideas that don't involve continuum manifolds.

I don't know enough about consciousness to agree or disagree with anyone about it, though I think it can't be deterministic. I like to read about it, though! Also, I appreciate the rating! Take care,

Ben

Dear Sergey,

250 is quite impressive; I have not managed to understand that many so far. At this rate, you will have read every entry in the contest within another week or so. I appreciate the rating. Take care,

Ben

  • [deleted]

  • Post #187

Dear Ben and Daniel,

So do I, thanks to your conversation above.

Best regards,

Inger

Dear Michael,

Thanks for the feedback! The complex numbers are undoubtedly the workhorse of much of modern physics, and avoiding them, if it's even possible to do so, will certainly require a great deal of work to achieve the same explanatory power, let alone surpass it. You might ask, "why, then, abstain from the complex numbers at all, if they are so useful?" The important word here is "useful." Many of the properties that characterize the real number continuum, and by extension the complex numbers, are mathematically "useful" without having any clear physical meaning. Even if there were not physical reasons to doubt that spacetime is infinitely divisible (of which there are many), properties like the least upper bound property of the real numbers would never be directly relevant to physics. Even worse, paradoxes like the Banach-Tarski paradox (you can pull apart a solid sphere into nonmeasurable sets and reassemble them into two spheres identical to the original sphere) show that the real and complex numbers have properties that are not only physically irrelevant, but also physically absurd.

But I am not sure if this answers your question? (I suspect it doesn't!) In any case, I see that you have an essay here about an interesting subject, so I will read what you wrote before making any further remarks. Take care,

Ben

  • [deleted]

  • Post #189

Benjamin,

Since you want Minkowski spacetime to emerge from your "causal relations", you will have to assume, additionally, constancy of the speed of light:

John Norton: "That the speed of light is a constant is one of the most important facts about space and time in special relativity. That fact gets expressed geometrically in spacetime geometry through the existence of light cones, or, as it is sometimes said, the "light cone structure" of spacetime. (...) So if we mean a spacetime that also behaves the way special relativity demands, then we have a Minkowski spacetime."

Then it may turn out that your "causal relations" are superfluous - Minkowski spacetime emerges from the assumption that the speed of light is constant and that's it.

Pentcho Valev

    Dear Pentcho,

    I have heard of a certain company that offers to name distant celestial objects after its clients in exchange for a fee. Calling the causal relations of the universe "mine" would be an even more absurd presumption of ownership.

    I'm afraid that suggesting that causal relations are superfluous because spacetime is a large-scale manifestation of them is like suggesting that the pixels on your screen are superfluous because they form a picture. Try doing without them!

    Regarding the constancy of the speed of light, "speed" means "change in distance per unit time." Distance and time are both metric concepts. When one begins with something other than a metric, "speed" must be viewed as a secondary, rather than a primary, concept. No assumption must be made about it whatsoever. Take care,

    Ben

    Dear Michael,

    I realize after reading your essay that my answer to you above was mostly irrelevant. Hence, I have left some additional remarks on your thread. Take care,

    Ben

    Dear Benjamin,

    I found your essay to be one of the most all-encompassing in the contest. The paper paints a fairly complete picture of the current state of things and yet it is not lacking in details. It surely merits the high rating it has received.

    One comment I can pick out that especially triggered a response is:

    "Causality is often formalized at the classical level as an irreflexive, acyclic, transitive binary relation on the set of spacetime events."

    I agree. Though the approach I wrote about is classical or semi-classical, and therefore embedded solely in U(1) topology, the rigorous consideration of rotations really requires formulation in SU(2) or higher topologies because of the difference in rotational characteristics of the electric and magnetic fields, path dependencies and the cyclic nature of waves. Then the algebra accommodates reflections and cyclic relations. And there the non-commutative nature of the algebra naturally leads to quantization.

    It's hard to picture just what you mean when you make this intriguing statement:

    "I will call the relation induced by these transitions the universal relation, and each of its subrelations a kinematic scheme. Under suitable assumptions, a pleasing fractal picture emerges, in which kinematic schemes share most of their abstract properties with the causal relations of their constituent universes, and quantization becomes an iteration of structure, at least locally"

    Perhaps that is related to the point made in the essay at note 1. The statement conjured up reflections on an interesting but perplexing book "Fourier Analysis on Finite Groups and Applications" by Audrey Terras. I've not yet fully fathomed its nuances but the author demonstrates how Fourier Analysis and associated sets can be used in a surprisingly general series of applications where the domain can be interpreted as having some type of cyclic basis. She doesn't mention Quantum Mechanics, as I recall, but maybe there is a natural fit there.

    Congratulations on a fine essay,

    Steve

      • [deleted]

      • Post #193

      Dear Ben,

      Earlier today I made a short comment (hard for you to to find) related to your conversation with Daniel Burnstein. Forget about it. What I wanted to say was that I'm hopefully beginning to begin to grasp your very interesting ideas. As you already know, I'm neither a physicist nor a mathematician. But re-reading your essay today, and following the above conversation, has been most instructive. It also gave me an idea, which I will come back to later, after more reading and thinking. I very much look forward to follow this conversation further. I have so much to learn!

      Best regards,

      Inger

        • [deleted]

        • Post #194

        Hi Benjamin,

        I think I made an interesting discovery. Check out my post of 9/19/12. Let me know what you think!

        Regards,

        Steve

          Dear Steve,

          Thanks for bringing this to my attention. I had checked your thread a couple of times after I posted there originally, but there are so many to look at that I missed seeing this. I don't know if you saw the discussion about antimatter antigravitation in my thread above or my brief mention of the possibility in my essay, but this is something I find very interesting. Take care,

          Ben

          Dear Inger,

          Thanks for the kind remarks. I found your essay interesting too, and have read it more than once. Don't forget to pass that idea along when it is ready! My email address is on my essay. Take care,

          Ben

          Dear Steve,

          Thanks for the kind remarks. I will have to find a copy of the book you mentioned. Regarding my two-sentence statement that you quote above (regarding kinematic schemes), this is based on some hundreds of pages of unpublished papers, and hence is an amusingly short abbreviation. Conceptually, it boils down to a precise statement of the point Robert Spekkens makes in his essay, that kinematics and dynamics in causal theory cannot be separated.

          At any rate, you can see now why your discussion of Lorentz invariance interested me! Take care,

          Ben

          Hello Ben,

          I finally responded to your comments on my forum page. I have also started reading your essay, which looks very interesting so far. I shall try to finish up quickly and have a few proper comments once I am done. I noted Lawrence's comments about the Fermi and Integral experiments above, and I think that addressing that data is going to be a crucial step for showing the viability of your theory.

          Causal structures can be problematic, in terms of Lorentz invariance. CDT may have been ruled out by Fermi and Integral and I had thought it was quite promising. Most of what you see for that subject in Wikipedia was written by me, largely unchanged though now in need of an update. I had interesting discussions about this topic with Gerard 't Hooft at FFP10 and with some Loop Quantum Gravity people at FFP11.

          I commented on my essay page that - concerning the summing over paths approach - you may want to learn about Hamiltonian Phase Space Path Integrals. The conventional Lagrangian PIs treat particles as things, in effect, or deal with them kinematically. Re-casting the problem in the Hamiltonian form focuses instead on the dynamics and allows for the uncertainty to be factored in up front, but reduces calculations to a simpler functional integral later on.

          See the attached paper.

          Regards,

          JonathanAttachment #1: 0912.0006v2.pdf

            Dear Benjamin,

            I tried to read your essay but despite my interest in what you had to say by the time I got to new principles, the really interesting part, it was no longer at all comprehensible to me. I recognise it as English but not much more than that. That is not meant in an unkind way but an honest reflection of my personal experience. You seem to be doing very well in the ratings so perhaps it is only a reflection of my own intellectual shortcoming. You also appear to have had a lot of feedback on your essay, so you are obviously doing something right. Kind regards Georgina : )

              • [deleted]

              • Post #200

              Benjamin,

              I thought your theory was deductive. That is, "causal relations" can be formulated as an assumption (analogous to Einstein's 1905 assumptions) from which (and possibly from other assumptions) you are going to deduce conclusions, Minkowski spacetime in particular. Now I see I was wrong: there is no deductive theory.

              The following wisdom of yours is breathtaking:

              "Regarding the constancy of the speed of light, "speed" means "change in distance per unit time." Distance and time are both metric concepts. When one begins with something other than a metric, "speed" must be viewed as a secondary, rather than a primary, concept. No assumption must be made about it whatsoever."

              Pentcho Valev

              • [deleted]

              • Post #201

              Dear Pentcho,

              You were right the first time. I do assume the causal relations to be fundamental. Minkowski space is not "deduced," but recognized as a large-scale approximation. No assumption is made (or needed) about the speed of light because it is not a fundamental concept. Take care,

              Ben

              • [deleted]

              • Post #202

              Dear Jonathan,

              Thanks for the feedback! You raise some excellent points that give me an excuse to talk about certain technical issues that might otherwise have been considered overkill. I must hurry to go teach my class, but will get back to you later today. Thanks also for the paper. Take care,

              Ben

              • [deleted]

              • Post #203

              Dear Georgina,

              Thanks for the message. The last two sections were a little compressed because of the length requirement, and I could only state short versions of my ideas in a rather formal way without much explanation. That part represents several hundred pages of my own work. You certainly should not feel any personal shortcoming from not understanding the details, because by itself that part raises more questions than it answers. Since the topic of the essay contest was which existing assumptions are wrong, I didn't feel justified in spending more than a few pages at the end introducing new theory. Anyway, thanks for persevering through it! Take care,

              Ben

              • [deleted]

              • Post #204

              Then don't mislead the reader by saying in the essay that you will "recover" established physics from your new principles:

              "Recovery of established physics at appropriate scales from these principles is a challenging problem due to their parsimony, with the standard model likely more dicult to recover than general relativityｮ ｨｮｮｮｩ ﾅmergence of ﾍinkowski spacetime is the first step toward the standard model as well as toward relativityｮｮｮ｢ｼｯpｾｼpｾﾁt least in my understanding this means that you first state your new principles and then physicsｬ ﾍinkowski spacetime in particularｬ somehow emerges from themｮ ﾔhis is tantamount to deductionｮ ﾉf it is notｬ you will have to justify your original ｨeuphemismｩ theoretical approachｮｼｯpｾｼpｾﾐentcho ﾖalev