Sean,

I believe it's precisely because of the conformal factor that Rafael Sorkin incorporates the (constant discrete) measure in his "order plus number equals geometry;" i.e., because "order" by itself is not enough to recover the metric. That was part of what interested me about shape dynamics, because throwing in the scale seems artificial. You note that I have to keep repeating "up to a scale factor," in my own essay. Take care,

Ben

Sean,

Also, Lawrence Crowell (who seems capable of instantly making precise remarks about almost any subject) has made some comments on Daniel Alves' thread along the same lines (possible duality/complementarity of symmetric/antisymmetric relations). I'm sure you are following Julian Barbour's thread; there is some relevant discussion there as well. Take care,

Ben

    I'll take a look. I haven't had much time to check the discussions but I will but we just posted our new paper so I will have some time next week. I think there is definitely a connection. It would be nice to make this more rigorous though!

    Cheers,

    Sean.

    Heaven Breasts and Heaven Calculus

    http://vixra.org/abs/1209.0072

    Since the birth of mankind, human beings have been looking for the origin of life. The fact that human history is the history of warfare and cannibalism proves that humans have not identified their origin. Humanity is still in the dark phase of lower animals. Humans can see the phenomenon of life only on Earth, and humans' vision does not exceed the one of lower animals. However, it is a fact that human beings have inherited the most advanced gene of life. Humans should be able to answer the following questions: Is the Universe hierarchical? What is Heaven? Is Heaven the origin of life? Is Heaven a higher order of life? For more than a decade, I have done an in-depth study on barred galaxy structure. Today (September 17, 2012) I suddenly discovered that the characteristic structure of barred spiral galaxies resembles the breasts of human female essentially. If the rational structure conjecture presented in the article is proved then Sun must be a mirror of the universe, and mankind is exactly the image on earth of the Heaven.

    http://galaxyanatomy.com

      Hi Ben --

      I'd just like to register my support for your viewpoint on foundational assumptions. For reasons probably unrelated to yours, I think the "causal set" approach has a lot of promise, and I wish you every success in working out your hypothesis. I find it very impressive that a mathematician would approach physics by doubting the validity of continuous manifolds at a fundamental level! And I've appreciated the very clear and sensible comments you've made to many of the other contest essays.

      My own interest is in learning to describe the physical world that can actually be experienced, whether by us or a measuring device or any other local entity. Traditionally this "view from inside" is treated merely as a means for gaining knowledge of an objective reality that exists in itself. While that's obviously reasonable, I tried to argue in my essay ("An Observable World") that fundamental physics also need to deal with the context-structure of the physical environment that makes information observable. I argue that regardless of the nature of any background reality, the ability of the world to communicate about itself is a basic feature we need to understand.

      So for me, what's important about "the binary relation generating the causal order" is that it describes an element in the structure of observable interaction, in contrast with background-structures like spacetime manifolds, fields and particles.

      I do have one comment on the "causal metric hypothesis" and the problem of the "recovery of established physics at appropriate scales." A basic point made in my essay is that any physical parameter is only measurable in a context defined by other measurable parameters. This suggests that an observable world like ours has to be based on several essentially distinct types of interaction-structure. We can imagine that some of these are more basic than others -- for example, it seems significant that electromagnetic field-structure is largely independent of the metric, and so perhaps reflects a more "primitive" structural layer. But I suspect a successful theory won't just reduce every kind of interaction to a single elementary structure that explains everything at one shot. More likely it will focus on the differences between interaction-modes, explaining what each contributes to the emergence of an observable environment, and perhaps sort them into some sort of evolutionary sequence.

      Again, best wishes for success with your theory -- you have a lot going for you.

      Conrad

        Dear Conrad,

        I appreciate the kind remarks. You make several distinct and important points, so let me itemize my reply.

        1. Regarding the general theory of observation and its importance, my impression is that one reason why it is often neglected even in new theories is simply because the problem is so difficult, and is in some ways unlike the types of problems that physicists and mathematicians are used to solving. This remains true in spite of the attention the "quantum measurement problem" has received over the last generation. I am somewhat guilty of this myself; in my "secret papers" I have written down a lot of thoughts about this subject, but haven't felt sufficiently justified or confident to say much about it publicly.

        2. I am glad you alerted me to the presence of your essay; I have read a fair number of them, but I am sure there are many good ones that have escaped my notice. I will be sure to read yours carefully. I think I agree with what you said in the paragraph above, but I hope to be able to say more after reading it. Let me repeat that I regard the problem as very difficult, however.

        3. One of the aspects of the manifold assumption that bothers me is precisely that it postulates an entity that cannot possibly be observed, even with arbitrarily advanced technology. However, what bothers me even more is the extremely special structure ("too good to be true"), which makes the mathematics convenient at the expense of assuming a number of properties (least upper bound property? nonmeasurable subsets?!?) that seem obviously irrelevant to physics. In my mathematical work, I spend a lot of time studying things like complex manifolds and algebraic schemes, which constantly reminds me how very special, uniform, and "idealistic" such mathematical objects are. I get the impression that many physics students still get the impression that the shifts of paradigm from Euclidean spacetime to Minkowski spacetime to Riemannian manifolds represent vast and perhaps final generalizations of what is possible, when in fact all these constructs are perched on a tiny ledge over a vast gulf of models that might be relevant at much smaller scales.

        4. I think that your expectation that the observable world "has to be based on several essentially distinct types of interaction-structure" is perfectly reasonable; indeed, it appears this way at ordinary scales, and the radical position, requiring the greater justification, is to assume otherwise. However, there are hints that a simpler picture might be possible. We seem to observe one arrow of time, not several, and to the extent that the arrow of time can be identified with the direction between cause and effect, it seems reasonable to ascribe causality to a single binary relation. If "essentially distinct types of interaction-structure" correspond to multiple distinct binary relations, then from this point of view you would expect "multiple time dimensions," which seems dubious, at least to me. There are several ways in which this chain of reasoning could be wrong, however.

        In any case, I won't remark further on this until I have read your essay! Take care,

        Ben

        Dear Benjamin F. Dribus

        I have liked your essay and I agree with your abandon of the ordinary concepts of symmetry, conservation laws, covariance, and causality in a spacetime context.

        Effectively spacetime is emergent, not fundamental and, therefore, the above assumptions have to be abandoned during the development of a fundamental theory. For instance, the conservation of dynamical quantities in a Liouville space cannot be related to the Noether's theorem, because this theorem is only an approximation and does not apply in the framework of the generalized theory. Another example is causality. We would distinguish between t-causality and tau-causality, with the former being not fundamental as you correctly notice. The more general tau-causality solves several problems of current quantum gravity such as the problem of time (the Hamiltonian associated to tau does not vanish).

        I gave not many details in my reply to your question on what kind of spacetimes we can derive from the Liouvillian approach. I would add now some info that I wait you will find useful. I only commented on the derivation of the more common spacetimes of special or general relativity, but we can take a pure quantum approach and derive a non-commutative spacetime of the kind postulated in string theory and other approaches, with ordinary products being replaced by star products.

        The really interesting is that we can take an intermediate stage between the pure quantum spacetime and the ordinary classical spacetime and obtain the causal and geometrical properties of the dummy spacetime of the quantum field theory:

        "Every physicist would easily convince himself that all quantum calculations are made in the energy-momentum space and that the Minkowski x^\mu are just dummy variables without physical meaning (although almost all textbooks insist on the fact that these variables are not related with position, they use them to express locality of interactions!)"

        --------

        H. Bacry

        "It is important to note that the x and t that appear in the quantized field A(x, t) are not quantum-mechanical variables but just parameters on which the field operator depends. In particular, x and t should not be regarded as the space-time coordinates of the photon."

        ----------

        J. Sakurai

        This very important limitation of the spacetime used in quantum field theory (QFT) is ignored in the textbooks by Weinberg, Kaku, and others --Mandl & Shaw emphasize in their textbook that there is not position operator in QFT but they do not explain why--.

        We can demonstrate that the position operator is not Hermitian (due to QFT deficiences in the direct merge of Lorentz invariance with a Hilbert space structure), explaining why position is not observable in QFT and has to be downgraded to a dummy parameter. We can derive Landau & Lifshitz relativistic uncertainty from first principles confirming that time in QFT is also a dummy parameter.

        Regards

          Dear Benjamin,

          I have an idea that I hope can be of some interest to you. Nothing mathematically fancy, I find that the zero spin quantum field can be reconciled from a system with vibrations in space and time. The model has some unique features that seem to be extendable to gravity and non-locality of quantum theory.

          Is there really no reality in quantum theory

          Best wishes for you in the contest.

          Hou Yau

            Dear Juan,

            I appreciate the details. Actually, I need more details on this subject, because the Liouvillian approach that you describe is something that largely escaped my notice in my program of physics self-education. Let me ask a few more questions:

            1. Where can I read about the derivation of spacetimes in the Louivillian approach?

            2. I am not sure what you mean between t-causality and tau-causality. Is it related to what I call the "causal order" and refinements of the causal order given by "frames of reference?"

            By the way, I downloaded 5 or 6 papers of yours from viXra, but haven't got a chance to read them yet. Perhaps some of the information is there.

            Thanks again, and take care,

            Ben

            Dear Hou,

            Thanks for pointing out your essay to me. As it happens, I had already seen from reading the abstract that your essay was interesting and had it highlighted to read more carefully. I will post some remarks about it over on your thread in a day or two when I have looked at it in detail. Take care,

            Ben

            Dear Ben,

            i now read your essay and it is indeed interesting. You begin with very clear and well-ordered introductions to the whole problem fields of modern physics and you clearly write what are rejected assumptions for you and what you consider as working hypothesis. I enjoyed reading your essay, albeit not understanding every line of reasoning you made during your elaboration.

            I found it intelligent to explicitely write about some phenomenons in the way that the community "interprets" them as "...". This clears up a lot and makes the whole argumentation of yours very easy to follow.

            As i understood it at this point of my reading, your approach is in some way a reinterpretation - surely with the important! fact of abandoning some "fundamental" principles and adding! some interesting new ones - of large parts of the common deduction sheme that is incorporated into classcial physical thinking.

            In some way you "play" - in combination with thoughtfull reasoning - with the building blocks of the classical physical framework and this is exactly what seems interesting and creative to me.

            Nonetheless, in my opinion, wether we interpret some building blocks as "universes", as "virtual Feynman paths" or something other, it seems to me that the ontological meaning of the whole building blocks stays somewhat ambigious for the reader. Therefore i would prefer to explicitely state that the very foundation of your framework is in its essence a logical (mathematical) and therefore "non-physical thing". For me i understood it as an informational theoretic approach that is at its core deterministic in the same sense the Everett worlds are. Moreover, at the end of your essay you outline the difficulty to decide/test the hypothesis, - please don't get me wrong - your approach deserves further examination, surely more examination than my own approach/interpretaion does. I write this to be intellectually honest and because i know the problem of reinterpreting the commonly used framework and at the same time give some reasonable proof of the exclusiveness of such a reinterpretation.

            All in all, i wish you good luck with your work and because you gave me some inspiring new points to think about, i thank you having visited my page and left a commment.

            All the best,

            Stefan

              Dear Stefan,

              I appreciate your kind remarks! Regarding your impression of my approach as largely involving reinterpretation, I would prefer to think of it in the way you describe than to think of it in terms of simply throwing out all that we've learned over the last 500 years and starting over. There are often many steps separating original physical ideas from the formal theories eventually used to describe them, and I think that a lot of the great scientists of previous eras had many physical ideas more or less perfectly correct without necessarily having the tools necessary to make them precise.

              Regarding the mathematical nature of my approach, through my many discussions here I have come to realize that to some extent I have failed to communicate what I view as the proper perspective on the relationship between the physical and mathematical ideas involved. As a mathematician trying to do physics, my goal is to not allow mathematics to be a limiting factor in the expression and description of physical ideas. In other words, I have tried not to be influenced by the mathematical convenience of particular models, but rather by which models I feel express the physical ideas in the purest way and with the least baggage. One possible result of abandoning mathematical convenience is, of course, that the mathematics can become very difficult and can lead into mathematical fields and topics that most people, including myself, have never heard of before. For this reason, the whole approach can create the false impression of focusing too much on the mathematics itself. The intention, however, is just the opposite: to begin with the simplest of physical ideas (such as cause and effect) and then simply bring to bear whatever mathematical machinery is necessary to adequately describe the resulting theory. Take care,

              Ben

              Dear Ben,

              You have gone through my paper extentsively. Thanks. Pls give me some time to go through yours once again and make my comments.

              I will have to respond to your comments part by part, since the posts cannot be too long. In this post I will take up your comment about "Lorentz invariance".

              You wrote: "5. I agree that Lorentz invariance as Einstein conceived it is not exactly right, but it is close enough to being right that I prefer to regard it as an approximation of the correct principle. This is what I mean when I discuss "reinterpreting the principle of covariance" in my essay. "Covariance" is usually understood to mean "Lorentz invariance," i.e., group symmetry. I do not think group symmetry is the right way to think about this principle".

              Let us look at this issue from a historical point of view. And also let me quote Einstein in regard to his own views on evolutions of concepts.

              'The concepts originate from experience by way of 'abstraction' i.e. through omission of a part of its content... (They) easily achieve so much authority over us that we forget their earthly origin and take them for something immutably given. They are then stamped as 'necessities of thought', 'a priori given', and so on. The path to scientific progress is often obstructed by these errors for a long period of time. It is therefore no idle amusement at all, when we are preoccupied with analysis of concepts that have been current for a long time and with showing, upon what circumstances are dependent their justification and utility and how they emerge, individually, from experiential data. Thereby their excessively great authority is broken down. They are omitted, if they cannot be made properly legitimate; corrected, if their co-ordination with the given objects was too carelessly established; or replaced, if it is possible to construct a new system which we, for some reason prefer" (4, p.19).

              There are a lot of mathematical baggage that has been overlaid in trying to interpret the EMPIRICAL EQUATION for the DISPLACEMENT that Lorentz discerned by TRIAL AND ERROR by ITERATING the data of Kaufman's experiments on fast moving electrons. By 'interpret' I mean what mainly Poincare (and Einstein too) did to give it a twist to make it fit into his line fictitious thinking of about the "nature of SPACE and TIME". (Note: Displacement is what is measured directly, "SPACE" is where the displacement occurs). Now people have been so indoctrinated that they cannot discuss LT in simple terms as an expression for displacement, without getting confused into using this mathematical baggage concerning the 'nature of space'.

              So if we are to understand what Lorentz transformation really means, we must forget all the interpretations that have been assigned to it, and consider its point of birth by 'curve fitting' of data, " showing, upon what circumstances are dependent its justification and utility and how it emerged, individually, from experiential data".

              What has happened is when Lorentz curve fitted data for particles moving at NEAR LIGHT VELOCITIES (v/c tending to 1) he had unknowingly missed out the term v/c which should have belonged to that empirical equation. Then this equation with the v/c term deficient was taken over by Einstein as true and perfect and made it into a postulate of the theory.

              If you consider the equation x' = gamma (x - ut), it gives very accurate results when v/c is almost equal to one. As a result when the empirical equation of Lorentz conforms to the DISPLACEMENTS of particles at very fast velocities, the credit goes to SRT. But everybody forgets that every time x' gets confirmed, time does not correspond to t' = gamma. t(1- ux/c2) as SRT contends, but SRT gets a free pass on this.

              However, as the velocity declines to 0.9c, 0.8c, 0.7c there is a progressive degeneration of the accuracy x' in a non-linear manner. Below 0.5c the degeneration becomes more marked. And at much lower velocities the degeneration of results reach exponential proportions.

              We can now understand why the theory has been named "special" theory. It is valid only for the special condition of v/c tending to 1. So there is a schism in physics, SRT [meaning displacement x' = gamma(x -ut) and gamma' F for force] for very fast motion and Newtonian mechanics (meaning x= vt for displacement and F for force). But this leaves out the vast middle ground between very slow and very fast motion. Should not there be an equation that covers the whole range of velocities from very slow to very fast?

              From the above observations (about the degeneration of results with declining velocities) we can re-construct the equation to be valid for all velocities v by following simple logic. If the LT equation is valid for the condition v/c = 1, then the equation that will be valid for all values of v will be

              x' = gamma. (v/c)(x - ut) or x' = gamma .vt(1- u/c).

              This then is the general equation of motion valid for all velocities. It can be verified by the computer analysis of all the relevant experiments done in the last century.

              Your next comment: "6. I agree that "all inertial frames are not equivalent, but..." is closely connected with why the discrepancy (wrt classical x = vt) in a straightforward displacement measurement had to be interpreted as arising from the "nature of space and time". I will touch upon this in my next post.

              (My essay: : http://fqxi.org/community/forum/topic/1549)

              Best regards,

              Viraj

                Ben,

                You wrote: "Regarding the constancy of the speed of light, my guess would be that a concept like this only makes sense at sufficiently large scales. (...) You'll have to remember that my background is mostly mathematical, and therefore I'm inclined to consider the possibility of things that most physicists "know" are wrong. This might be useful in some cases; in others it only reflects my own ignorance."

                Insofar as "the constancy of the speed of light" is concerned, I am afraid your last statement is relevant, Ben.

                Pentcho Valev

                Hello Ben,

                I thank you for the gracious comments you left on my essay forum page. I'll answer your queries shortly. Your points are well taken and very much appreciated. Unfortunately; I've been sidelined with unexpected responsibilities, but I do hope to get to read your essay soon and respond to your comments sooner. However I am still catching up elsewhere, so it may be a little bit.

                All the best,

                Jonathan

                  Dear Sergey and Benjamin

                  A lot of fascinating ideas seem to have emerged and are emerging in Russia - but unfortunately I do not have the language either! I have newly discovered that entropy emerges naturally in the same mechanism - diffusion - explaining uncertainty and probability) in my Beautiful Universe model, where also e/m and gravity are realized in local causal building blocks of a universal lattice.

                  Vladimir