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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

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    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two-sentence statement that you quote above (regarding kinematic schemes), this is based on some hundreds of pages of unpublished papers, and hence is an amusingly short abbreviation.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 : )

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          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

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          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

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          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

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          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

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          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

          Dear Pentcho,

          I appreciate that you are spending so much time trying to understand my essay, and I am sorry if you are struggling with aspects of it. You must keep in mind that we only had 12 pages in which to explain our ideas. "Emergence" in physics is not tantamount to deduction. Recovery of established physics means that whatever existing theory describes or explains must also be described or explained by new theory. It does not mean that every detail of every mathematical model appearing in the original theory must appear in the new theory. If this were so, the new theory could not improve on mistaken aspects of the old theory. Take care,

          Ben

          Hello again Ben,

          I have a lot of thoughts to share about causal structure, though I have not finished my first read-through of your essay yet. So I figured I should cross post a comment I left on Robert Spekkens' forum, regarding how we look at kinematics and dynamics. To wit..

          The notion that kinematic states and dynamic evolution are separable seems to carry over from the subject-object distinction in English and other European languages.

          It is a peculiar left-brain dominated preoccupation, which necessitates measures like Korzybski's "the word is not the thing." In Chinese, by contrast; one cannot describe a thing apart from its process, and even the individual strokes in a character tell the story of how that pictogram evolved.

          So this gives you one more thing to reflect on. I'm just returning the favor, since you gave me a lot to think about - in terms of thoughtful questions about my essay content. I have been very busy, this past week or so, but I shall be interested and available to engage on this subject matter as long as there is something worth talking about.

          All the Best,

          Jonathan

          Hello yet again, Ben and everyone;

          I'm following my muse, by sharing a few more thoughts before reading further, as they respond to comments you left on my essay forum and Ian's. First, yes; Twistors are way cool, because they address the objection of Grothendieck, that geometric points omit too much essential information. In twistor theory, rays are more fundamental than points, which I believe are a special case. This strongly suggests a causal element, and incorporates the idea of forward motion in time, revealing that the fabric of spacetime is emergent. As I understand it; the paper by Witten - after his meeting of the minds with Penrose - showed connections with String Theory, but mainly proved the concept and paved the way for others. Work by Nima Arkani Hamed and Freddy Cachazo involving twistors and S-matrix theory has been especially productive.

          But my intuition is that the emergence of spacetime and structure proceeds most simply or elegantly from the octonions, as I mentioned in my essay. One paper by Connes emphatically states "Noncommutative measure spaces evolve with time," but I came to believe that as the Planck scale is approached, geometry becomes non-associative as well - so we must examine the implications of this to have a full understanding of dynamism at the smallest spatial scales and at the universe's time of origin. We know that the octonions are the most general number type, where the quaternions, complex numbers, and reals are a subset thereof. If we assume, as suggested by my departed friend and colleague Ray Munroe, that the imaginary dimensions in octonionic space are at the outset space-like, and the real dimension is time-like - some things fall into place nicely IMO.

          If we interpret the imaginary components of octonions as the freedom to vary by a specified amount, it is natural to consider those dimensions as space-like extents. But making the observation (ontological?) that structures must have a duration in time in order to exist; the last sentence of the preceding paragraph can be seen as a kind of procedural formula. In octonionic space, things can evolve through seven dimensions in sequential relation - as possible directions afforded by a specific range of play - but the next step is always time-like, and this creates specificity or definiteness. Briefly stated; non-associativity makes the octonions not only evolutionary (a la Connes' comments about NCG) but also procedural. Multiplying or dividing with octonions is sort of like putting together or taking apart a watch - where you have sub assemblies that must fit together in a specific way.

          Intriguingly; I've been working on a universal theory of measurement or determination, and some of the behaviors noted above appear to be emergent. For example; the postulates of projective geometry have a connection or can be a generator...

          More later,

          Jonathan

            Dear Jonathan,

            I'm grateful that you have chosen to post this on my thread! Feel free to post thoughts here at any time.

            Your observations raise many important points. As soon as I can, I will get back to you about Fermi/Integral, CDT, causal sets, the missing conformal factor, constant discrete measures, configuration space versus phase space, the Lagrangian as an infinitesimal path functional, path summation over general directed structures, relation and morphism functions as abstract Lagrangians, the generality of (twisted) multiplicativity for phase maps (owing to a cohomological vanishing theorem for noncommutative algebras over sets with partially defined operations), special algebras in quantum information theory, nonassociativity in general relativity...

            But my students are killing me at the moment! Hope to continue this discussion/synthesis soon...

            Take care,

            Ben

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            Dear Ben,

            I have been so busy not understanding your causal metric hypothesis that I have forgot to tell you about my growing understanding of your essay. The first four sections are very well structured and have all the more emerged as chrystal clear. I just needed some re-reading. My troubles arrive when entering section 5. But today I started to once again follow the above conversation, to see what I can get out of it. At present I understand too little to be able to ask you any meaningful questions. Hopefully that will come, because it is part of my idea. I will tell you about it by e-mail.

            Best regards!

            Inger

            Dear Eugeniu,

            Thanks! I don't expect to win... particularly after the ratings chaos yesterday morning, but I appreciate the vote of confidence. Take care,

            Ben

            If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is [math]R_1 [/math] and [math]N_1 [/math] was the quantity of people which gave you ratings. Then you have [math]S_1=R_1 N_1 [/math] of points. After it anyone give you [math]dS [/math] of points so you have [math]S_2=S_1+ dS [/math] of points and [math]N_2=N_1+1 [/math] is the common quantity of the people which gave you ratings. At the same time you will have [math]S_2=R_2 N_2 [/math] of points. From here, if you want to be R2 > R1 there must be: [math]S_2/ N_2>S_1/ N_1 [/math] or [math] (S_1+ dS) / (N_1+1) >S_1/ N_1 [/math] or [math] dS >S_1/ N_1 =R_1[/math] In other words if you want to increase rating of anyone you must give him more points [math]dS [/math] then the participant`s rating [math]R_1 [/math] was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

            Sergey Fedosin