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 Jin,

    Thanks for informing me of your paper. 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

      • [deleted]

      • Post #110

      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

        • [deleted]

        • Post #113

        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

          • [deleted]

          • Post #115

          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

            Dear Viraj,

            Thanks for reposting this here. Since this part of the discussion is about your work, I will post any further remarks about it over on your thread. Take care,

            Ben

            • [deleted]

            • Post #117

            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

            Dear Pentcho,

            Perhaps. But so long as one is aware of the possibility of one's own ignorance, there remains at least some chance of repairing it. Take care,

            Ben

            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

              Dear Vladimir,

              You mentioned this before, and I will have to think about this idea further. The correct definition and use of entropic principles is one of the things I am a bit hung up on in my own approach. Take care,

              Ben

              • [deleted]

              • Post #122

              Hi Ben and thanks for a very interesting essay.

              I realise I share your view of the universe in some key aspects of your hypothesis and must read it once more to give you some useful comments on it. Here is a first:

              "...the metric properties of classical spacetime, up to overall scale, arise from a binary relation, which I will call a causal relation, on a set..."

              Well formulated !

              The problem I have in accepting it is not that it contradicts observations, but the mind-nuking number of "binary relations" involved. Intuition tells me this cannot be right and that there has to be a simpler model, but then again, I do not trust intuition very strongly in these matters.

              If you have an hour of lesure time, I think you would enjoy this youtube-video:

              http://www.youtube.com/watch?v=YfYon2WdR40

              PS.

              My first impression of you, extrapolated from your written posts on several essays, was that you were 60 years old. But since you present yourself as a Ph.D student, I suspect that is not the case.

                • [deleted]

                • Post #123

                No, I am sorry but there are a lot of probelms. Indeed I am parano. and you know it all. I have known FQXi at the begining. I have shared my theory in a total transparence. I don't understand the comportment of Tom, Joy, Christi,Jonathan Dickay, Brendan, Lawrence, and friends , I am stopping there for the names. I beleive in fact that it is a team trying for their vanity and hormons.Probably that they like this play. The Universal integrity is more than these comportments with superimposed algorythms for the confusions and the strategy. I continue even with your strategy. In fact, all is false. You have made a bad thing. For your knowledge, the laws exist and it is important for the good governances. The real integrity is essential. If these persons trying to discriminate, or to profit, or to steal, or to superimpose the algorythms are in a bad boat, it is not my probelm. The lawz are the laws. You are not generalists, just persons competent for the computing, it is totally different. Me without tools and strategy and alone, and you with all that.let me laugh , frankly it is ironical. I know the team behind. it is what the probelm, they want the nobel, because they need funds and investments, because they are not able to ponder works like mine, it is what the probelm?

                I love FQXi , it is important for me,I respect Mr Wilszec,Mr Tegmark,Mr Witten,Mr Guth and friends. So don't try with your discriminations between Canada,USA and Netherlands.

                You know, you do not imagine how I forgive this play of Tom, Jonathan ,joy and friends. and if people utilizes false names, be sure that I see it .No probelm dear team. each thing at its times.

                They have hacked my computer, they check all.and what? where is the probelm?

                You know Ben, I have been already lsot in the past in my country, due to bad people, they have caused me a bankrupcy. I have worked hard for my theory of spherization,I have learned a lot.and always I have people who are bad with me.always I have been nice and kind, always Ben. My economical situation, my health, mysocial situation are catastrophic.My state of mind is very weak. I am not well. I am isolated at home without job. This society disgusts me you know. I am tired.My theory is all my life.I just would sharing it in a total transparence.I would simply find partners and friends.I would like just finding a job also.I just would a little of recognizing for my works.and even on net, it is corrupted.Oh my god, but what is this circus. I am shocked by this planet. I have found FQXi and I said me, it is cool, a platform of physics for the theoretical physics. I am happy, I will can show my theory and I will find a job and coachs and mentors. and I see all this play from a team. It is sad. The technology of information is a tool, and this tool must be utilized with wisdom and universality. The cyber criminality msut be punished for the well of all in fact.

                But where are the good persons ? on an other planet or what ?

                I have 48 inventions ben and my theory of spherization, a revolutionary theory, general and rational and deterministic. I just want to evolve correctly with good persons. I search even my mentor. I need to learn more.Personally I will be honored if Mr Penrose, Mr Hawking, Mr Solomon or Mr Wilcszec could be my mentor. I need to evolve, there I don't evolve. I just decrease my health. I must move. I become crazy in fact there at home with my problems.

                FqxI is a wonderful platform. so why ?

                Dear Andreas,

                Haha... well, actually I'm 32, which I admit is a bit long in the tooth for a graduate student, but I've had a rather interesting and non-traditional journey to this point.

                Thanks for the feedback and the video suggestion...I will be sure to take a look!

                Regarding the number of relations, one must make a distinction between "binary relation," of which there is precisely one for each classical alternative in my approach (and a single higher-level binary relation for the entire quantum picture), and "relation between elements," which refers to a particular ordered pair of elements which are "related" by the binary relation.

                I'm not sure what could be simpler than cause and effect as a basic building block for physical interactions. Of course, there are going to be a huge number of cause-and-effect relationships, but this will be true in practically any model you can think of, whether that model takes causality to be fundamental or not. In particular, if the universe is infinite, its hard to imagine how there could not be an infinite number of causal relationships.

                If you mean that the number of "classical universes," each with its own binary relation, is large, then yes, there is an infinite number of such binary relations, representing the infinite number of possible histories. I call these "classical universes" not in the sense of "THE Universe," but in the sense that each is self-contained as a classical causal network. Then entire ensemble of these possible classical histories is a way of talking about THE Universe in my view.

                Again, on the subject of simplicity, I believe that the sum-over-histories view is by far the most conceptually simple view of quantum theory. Without it, you have to take for granted mathematical objects like Hilbert spaces and operator algebras. Of course, many people would still like to believe that quantum theory is somehow wrong, and that a single deterministic picture underlies everything. While I can understand and sympathize with this view, my own opinion is that quantum theory really does play a fundamental role,and that trying to do without it raises much worse problems, particularly in the philosophy of science.

                Anyway, thanks again for the feedback! Take care,

                Ben

                Jonathan,

                Thanks. I would be grateful your feedback, both on my questions and on my own work. However, I do see that you have a few messages piled up on your thread, so I won't be impatient! Take care,

                Ben