Dear Lawrence,

Thanks for the comments. I particularly appreciate your remarks about the FERMI/INTEGRAL experiments; I knew about these but don't feel very confident in interpreting the results. You're right of course that experiment is the final arbiter, but with the caveat that one must be sure what the experiment means.

Torsten's approach is fascinating and is worth understanding at a deeper level. I'll also point out that Jerzy Krol's essay is worth looking at in this regard; the two of them have been collaborating and their submissions are complementary. Jerzy discusses nonstandard models of number systems and their role in defining exotic smoothness structures.

You have the advantage of being well versed in the string/M-theoretic technology, which I am rather a novice at. Superficially, the 4d-to-7d duality of exotic structures you suggest sounds intriguing and perhaps gives another glimpse of why dimension 11 is special, although I'm not qualified to remark further on this. I do note that string/M-theory has been recently assimilating aspects of other approaches (noncommutative geometry, entropic gravity, twistor theory, etc.) in a way that suggests that the serious approaches to QG and unification may prove more amicable than previously thought. The causal theories (causal dynamical triangulations, causal set theory) seem perhaps left out of this picture to a degree, which gives me pause considering that causal theory is my own favorite approach. Take care,

Ben

Ben,

"The central new principle I propose is the causal metric hypothesis, which states that 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, which I will call a universe, and that the phase associated with a congruence class of directed paths in the con guration space of such universes is determined by the causal relations of its constituent universes"

How can you imagine let alone model causal relationships of a multiverse? Are the attributes of gravity shared between universes? I struggle with your esoteric essay.

Jim

    Dear Jim,

    Well, I would rather not call it a multiverse because that is often understood these days to refer to the string-theory multiverse, which means something entirely different. My "causal configuration space" is a "way of talking about the superposition principle of quantum theory in a background independent setting." For some context, in 1948 Richard Feynman showed that you could explain quantum theory by thinking of all the possible paths a particle could follow between two points in space and time. Since general relativity says that the structure of spacetime responds to matter and energy moving through it (background independence), different particle paths correspond to different spacetime structures; i.e., different "universes." So you see that in this context, "universe" doesn't mean "all that exists," it just means a particular classical causal structure.

    The fact that the causal configuration space itself has a similar structure to the individual "universes" is a nice thing, in my opinion, but the relationships among the "universes" aren't "causal" in the usual sense. The point of the causal metric hypothesis is that you can describe a lot of different things (causality, spacetime "geometry," the superposition principle, etc.) by means of a single type of structure. I

    I hope this helps! Take care,

    Ben

    Thanks Ben,

    The supreme example of the mathematician-physicist is Newton - and of course you are right about the 3 piggies metaphor being inexact - perhaps at the most basic level physics and mathematics are equally artificial, but in conjunction try to describe Nature the best they can. As an artist and inventor I built my physics model using geometry and physically realistic interactions. I suppose topology, knot and graph theory can all be used to describe such models, but I am satisfied with understanding how it works as a sort of mechanical linkage. (I was inspired by Kenneth Snelson's concept of tensegrity - I urged him to present his ideas about the atom in this contest and am glad he did - at age 85!)

    I hope that my model can be tested by computer simulation but I had better update my research and present it more succinctly.

    Following your remark about gravity and entropy: In one of the discussions of this contest I suddenly realized (and wrote) that my Beautiful Universe model explains why entropy occurs - it is the same causal local mechanism of diffusion of energy as a wave pattern in the lattice, which simultaneously explains probabilistic behavior and uncertainty! But what about solitons? how would entropy be manifested in their behavior?

    Thank you for rating my essay, (as I did yours). Last year I also participated in the fqxi contest, and one participant used to sign his messages: Have fun!

    Vladimir

    Dear Benjamin,

    Studying the question of connection of entropy and gravitation, I found Lorentz-invariant formula for entropy in the book: Fizika i filosofiia podobiia ot preonov do metagalaktik. Perm, 1999, 544 pages. ISBN 5-8131-0012-1. In short the question is described in the book: The physical theories and infinite nesting of matter. Perm, 2009-2012, 858 pages. ISBN 978-5-9901951-1-0 in such way: Using the stress-energy tensors for the substance and the gravitational and electromagnetic fields allows us to write the equations of thermodynamics explicitly in the Lorentz-invariant form. As a result the entropy, the amount of heat, the chemical potential, the work and thermodynamic potentials can be represented as tensor functions of microscopic quantities, including the electric and gravitational field strengths, the pressure and the compression function. This allows us in § 21 to find out the meaning of the entropy as the function of the system state - it is proportional to the ratio, taken with the negative sign, of the absolute value of the ordered energy in the system to the heat energy, which is chaotic by nature. The ordered energy means the energy of directed motion of the substance, the compression energy from pressure and the potential energy of the substance in the gravitational and electromagnetic fields. When the system achieves equilibrium, part of the orderly energy inevitably is converted into thermal form and the entropy obtains a positive increment. I hope it may be interesting also for Vladimir F. Tamari and others authors in the contest.

    Sergey Fedosin

      Dear Ben,

      I am in general agreement with your critique in regard to the foundational problems. My view is that the problems you have highlighted are secondary, tertiary derivatives that have emerged due to the original foundational problems that Newton (and others) introduced when he intentionally developed Mechanics on a makeshift basis as a stepping stone for what he called the "Truer Method of Philosophy".

      You have quite rightly pointed out that although certain foundational problems are realized by eminent physicists, they do not know how to rectify them.

      For instance you wrote in reply to Frank: "Regarding the continued use of widely doubted assumptions, the reason I mentioned this is because I wanted to make clear that I wasn't offering anything new by rejecting these particular assumptions; of course people have known for years that there are issues with manifold structure, background-dependence, etc., and plenty of people are working on these problems. I don't think that well-educated physicists continue to use these assumptions because they are trying to make them "fit a preconceived model," but rather because they don't yet know what to use in their place. .....".

      This is because there is no single foundation presently. When the problems arose on the original foundation, without analyzing and rectifying them, other foundational concepts (even contradictory ones) were overlaid, while retaining some of the problematic ones (like the point mass) and this process has continued. My view is that the solution to the present crisis must begin with going back to the original foundation of Newton and rectifying its mistakes.

      I have done this to a certain extent. I have not only pointed out what the foundational problems are, but I have offered solutions.

      I request you to have a look at my essay and comment: http://fqxi.org/community/forum/topic/1549

      Since the diagrams have not come out properly in the above pdf version, I am attaching the MS Word version also.

      I will continue on this with another post making some introductory comments about my essay.

      Best regards,

      VirajAttachment #1: 9_A_TREATISE_ON_FOUNDATIONAL_PROBLEMS_OF_PHYSICS2.doc

        Continuing:

        Hi Ben,

        The following are some matters I wish to bring to your attention about the contents of my essay: http://fqxi.org/community/forum/topic/1549

        1. I have listed out a number of assumptions that Newton made that have turned out to be foundational errors.

        2. I have not only listed the errors, I have found a new approach to overcome these errors (guided by notions of Newton, Maxwell, Einstein) and provided accurate quantitative solutions.

        3. I have discussed that these wrong assumptions of Newton have been carried over to the foundations of Quantum Mechanics and Theory of Relativity and these too are afflicted by the same problems.

        To quote from the essay: "We may note that among the problematic foundational concepts created by Newton that have congenitally infected RT and QM are a) the primacy of the concepts of space and time, b) representation of bodies as mass-points without internal structure, c) consideration of centrifugal force as a pseudo-force, d) the closed system with the consequent inability to account for inflow and outflow of energy between the system and the field etc. e) Not recognizing that it is by the two quantities of energy (Mc2 and pc) fusing together to form a system that motion occurs. f) the omission of the fact that a fraction of the applied energy of motion pc gets usurped for the co-movement with the location. g) Not developing the theory with state changes of energy as the basis of its physical geometry. With these congenital foundational problems being inherent in these two progeny theories as well, it should be obvious that revamping of physics must begin from where the problems originated".

        4. I have shown from Newton's writings (Preface to the Principia) that he intended to create only a makeshift theory (Mechanics) as a stepping stone until a "Truer Method of Philosophy" (a geometric theory based on the behaviour 'least particles') is found.

        5. I have shown from Einstein's writings that he considered both Newtonian foundation as well as that of his own theory are based on fictitious concepts.

        6. I have shown that Einstein has pointed that the 'Right Way' is yet to be found which would be based on simplest conceivable mathematical ideas connecting laws with phenomena.

        7. I have shown why Einstein could not find the 'Right Way' himself which he was desperately in search of, by expanding the thermodynamic approach into whole of physics.

        8. I have shown that Maxwell chartered an outline of a program for the future development of science, based on the paradigm that all phenomena are based on state changes of energy, and inflow and outflow of energy from a system (i.e. based on open systems).

        9. By assimilating the intuitive notions of all the founders, in regard to the future development of physics should take, I have initiated to develop a new approach.

        10. It a) provides the equation of motion for a particle at any velocity (slow or near light velocity) thus the schism in physics between Newtonian mechanics and SRT is removed. b) Explains how gamma-factors arise, c) why it requires momentum gamma-Mv for a particle to be set in motion with momentum Mv. d) provides the physical basis of the Lorentz transformation, e) the physical basis of the constancy of the velocity of light g) why physical processes slow down when a particle is in motion. h) From where the energy underlying the centrifugal force comes.

        (This is all I could squeeze in within the 25,000 characters permitted by the contest. Elsewhere I have derived Lorentz force, gravitational time increase of a GPS clock, Compton scattering, explanation of Michelson's experiment by recognizing TDE changes frequency while keeping velocity constant etc.).

        Hoping to hear from you.

        Best regards,

        Viraj Fernando

        Dear Viraj,

        It appears that the first few assumptions you reject ("the primacy of the concepts of space and time," etc.) are the same as mine, although we use different words (I would say "the manifold structure of spacetime," or "an independent time parameter.")

        Some of the other assumptions you reject (for instance, those regarding centrifugal force and some of the statements about energy) I would expect to disappear automatically once the usual assumptions about space and time are rejected.

        I had better not make any more specific remarks until I have read your essay, however. One thing I will say is that it appears as if you made an honest effort to answer the question posed by the essay contest rather than just writing down your favorite ideas about physics. You will notice that I made a similar effort. Take care,

        Ben

        Dear Sergey,

        That's quite a book... 544 pages. Is any of this material posted online? If not, I understand... I have hundreds of pages of unpublished stuff myself. Also, I regret that the only languages I can read are English and a little French and Spanish. Take care,

        Ben

        The Fermi X-ray, gamma ray test of relativity can be found in this review This measurement was followed up by the ESA Integral spacecraft.

        There is a lot of confusion over Verlinde's entropic gravity. Gravity as a dynamic force is conservative. The force in the Newtonian limit is given by F = -∇Φ(r), which is conservative. This means the force evaluated around a closed loop, such as an orbit, is zero. Thermodynamics gives nonzero evaluations for such forces. This is related to the matter in differential geometry that a p-form ω is exact if dω = 0, but a subset of them are closed when ω = dσ, or d^2 = 0. There is some cohomology behind this. The force is determined by the coboundary operator on a 0-form and we have by Stokes law

        ∫F•dr = ∫∫∇xF•da. da evaluated in the region enclosed by the closed loop.

        Yet we know that ∇x∇Φ(r) = 0 (curl-grad = 0 or d^2 = 0) and so the force is conservative.

        Verlinde's entropic gravity does not involve the dynamics of a particle in a gravity field. It involves the dynamics of an event horizon or holographic screen. The main idea is that the force on the screen over some unit distance is equal to the work

        ∫F•dr =W,

        and this work is equal to the increase entropy of an event horizon. This by the Bekenstein theorem is S = k A/4L_p^2, for L_p = sqrt{Għ/c^3} --- the Planck length. So the entropy is a measure of how many Planck units of area there on the horizon. So the Verlinde hypothesis is

        ∫F•dr =TS,

        or a force that displaces the horizon some increment gives

        F•δr = TδS.

        As a result some input of mass-energy into a black hole increases entropy, and this force is what evolves the event horizon, or equivalently the holographic screen.

        Event horizons and screens have units of area, and in naturalized units with c = ħ = 1 the gravitation constant G is an area. So this measures the amount of information entangled with the black hole, or the entanglement entropy.

        Cheers LC

        Hi Ben,

        I report my reply to your questions about my essay Elementary Time Cycles. I have justpresente the theory in DICE2012, Castiglioncello, Italy where I have received entusistinc feedback. I will read asap your assay and let you know my opinion.

        -----------

        Thank you for your comments on my essay. I present a new idea and it is not immediate to figure it out, though eventually it turns out to be extremely intuitive. The theory indeed works spectacularly. So many mathematical results cannot be a coincidence, they point out a conceptually fascinating description of the quantum word. This description is different from our ordinary description but absolutely compatible.

        I will reply to your question but for a more detailed description please refer to the section "comments and outlooks" of arXiv:1110.0316, in particular the one at the end of par.1.

        1) Right! I am saying that our flow of time is a relational or effective description at "large scale" of the phases of the elementary time cycles, i.e. of the elementary particles. The vibrations of the space-time dimensions with characteristic periodicity describe through the Planck constant their kinematical state of what de Broglie called elementary parcel of energy and that we today simply call elementary particle. A free particle, i.e. constant energy, has persistence time periodicity. As a pendulum in the vacuum, every elementary particle can be used to define a time axis on which describe events. That is, as in an ordinary calendar or stopwatch, different presents or events are characterized by the combination of elementary time cycles of the elementary particles This is a very familiar description of time flow because in our in everyday life we use the cycles of the Moon and the Earth, or their approximation that we call years, months, weeks, days .... Every particle or observer, depending on its kinematical state, describes a different combination of phases, i.e. a different present (relativistic simultaneity). Interactions, i.e. events in time, are variations of energy and thus of periodic regimes of the elementary clocks, So that we can establish a before and an after and order event in time. The periodicity of the clocks and the energy of the corresponding particle are two faces of the same coin, as we known from ordinary undulatory mechanics. The retarded variations of the energy prescribed by the relativistic framework of the theory means that the periodicity varies with the retarded potentials and this yields a reinterpretation of causality as retarded and local modulation of periodicities. This formulation in which every particle is a reference clocks enforces the local nature of relativistic time, and solves some of the issues related to the problem of time symmetry. Since every particle is a reference clock, every particle can be used to define our external (and artificial) relativistic time axis, so that the inversion of the (arbitrary) helicity of a single clock does not imply to invert all the other clocks. We just invert the axis defined from that clock but the chain of events in time, i.e. the combination of the phases of the other clocks remains the same. Thus we describe the same flow of time. The difference in this case is that the inversion of a single clock corresponds to describe the corresponding antiparticle, i.e. antiparticles are clock with inverted helicity. I could continue for pages to describe the elegance and the naturalness of this description of the flow of time, please read my papers.

        2) In undulatory mechanics, according to the wave-particle duality, we represent a particle as a phasor. This implicitly says that the (space-)time coordinates in elementary particles are angular (cyclic) variables. In our atomistic description of nature every system is in fact described in terms of a set of elementary particles, thus every system can be parametrized by a set of cyclic coordinates (whose minimal topology describing the quantization of the energy-momentum is S^1 if we neglect a possible spheric symmetry and the corresponding quantization of the angular momentum).

        Thus a system of (non-quantized) free elementary particles is represented for example (considering only time periodicity) by sin[E_1 t_1 / hbar], sin[E_2 t_2 / hbar], sin[E_3 t_3 / hbar], ... , sin[E_n t_n / hbar] where t_1, t_1,... ,t_1 are independent cyclic coordinates of periodicity h/E_1, h/E_2, ... , h/E_n, respectively. Now, every phasor (persistent periodicity) is a reference clock that can be used to define an external time axis t \in R so that t = t_1. But we also can now use the external time t to parametrize every phasor so that the phasor are sin[E_1 t / hbar], sin[E_2 t / hbar], sin[E_3 t / hbar], ... , sin[E_n t / hbar] ... of periodicities h/E_1, h/E_2, ... , h/E_n. Thus, since we can compare the periodicities of the different clocks, every cyclic coordinate can be parametrized by a common coordinate t whose periodicity is related to the periodicity of that particle, and the description can be reduced to a single time. I hope this answers your question - with a little of imagination.

        3) and 4) The dimension around the cylinder is the time dimension of an elementary particle (in case of interaction the cylinder should be deformed, see fig.5 to have an idea). In an intrinsically periodic phenomenon, such as that associated to an elementary particle, the evolution from a given initial configuration to a final configuration is described by the interference of all the possible paths with different windings numbers. It is possible to show that this sum over such classical paths associated to a cylindrical geometry reproduces the ordinary Feynman Path Integral. That is, by imposing periodic boundary conditions to a field, the field can self-interfer as it evolves. This means that in the Feynman path integral only the periodic paths are really relevant. Intuitively these are the only paths having positive interference, the others fade out for distructive interference as the anharmonic modes of a vibrating string where only the harmonic modes with frequency n/L remains.

        5) This fits perfectly we relativity because the periodicity is relative as time. For instance consider a particle in a Gravitational potential. The energy of such a particle w.r.t. a free one differs as E' = E (1 - G M /r). By means of the Planck constant and undulatory mechanics this means that the periodicity of the internal clock of that particle differs as transformed periodicity T' = T (1 G M / r) w.r,t. a clock outside the gravitational well, that is time runs slower inside the gravitational well, as well-known. The mathematical reason for the consistency with relativity is because GR is about the metric but does not give any prescription about the boundary conditions, For instance, there are many action describing the Einstein equations as equations of motions, but all these actions differ by boundary terms. If we play with boundary conditions consistently with the variational principle it is possible to derive exactly QM from relativity. This is mathematically proven in my papers.

        6) and 7) Experimental time resolution is too coarse to detect the internal clock at the time of the fathers of QM (but sufficient to determine the constancy of the speed of light a to give rise to relativity). Today we are reached the resolution in time sufficient to detect the internal clock. The internal clock of the electron has been already observed indirectly in 2008, see ref. [12] Search for the de Broglie Particle Internal Clock by Means of Electron Channeling, P. Catillon, et.al,

        Found.Phys.38(2008)659 of my essay. Such an experimental resolution when reached will open a new frontier in physics. it will allow us to control the quantum dice with unimaginable applications. This is a prediction. I have some precise ideas on the possible predictions of the theory that I cannot anticipate here because, as you say, my essay is already too dense. I hope to find soon a job opportunity that will allow my to present this predictions in a scientific form.

        Best regards,

        Donatello

        view post as summary

          Ben,

          Thanks for acknowledging that my essay is strictly in context of the topic of the contest. Actually, you may note that I have gone a bit further by, finding alternative solutions, which would confirm my contentions about the identified wrong assumptions.

          I am awaiting your comments about my essay. I hope being a young person with an open mind free of dogmatic views on exisitng theories, you would find it easier to understand the point of view I am presenting.

          BTW, LSU in which city are you in. I was in Shreveport recently for some time.

          Best regards,

          Viraj

          Dear Lawrence,

          I appreciate the insight. This is the sort of thing that would require me a lot of time and effort to piece together myself. If there is any connection between Verlinde's entropic description of gravity and my speculative application of entropy to determine transition amplitudes, it's a coincidence, since I didn't even know about Verlinde at the time. I suppose that the hypothesis "gravity is entropic" can mean a lot of different things. My idea came from results in graph dynamics, and entropy in this case is determined by the cardinality of a particular automorphism group. If this works at all, it requires some finiteness assumptions. (I assume you transposed "closed" and "exact" above, unless you were referring to something different than the usual definition of de Rham cohomology.) Take care,

          Ben

          Dear Ben,

          I found your essay very inspiring especially it deals with excellent mathematical arguments. Generally, your presentation is convienced and very good, this more that you touch so many important things on so limited number of pages. Let me comment on some important for me point.

          It is certainly something that should be rejected in manifold's model for the space-time valid on every physical scales. But my personal view is that we do not understand or even know at present whole net of mathematical structures related with manifolds. Let it be two things: 4-d smoothness and logico-categorical perspective. Both indicate on discrete and noncommutative structure of smooth 4-manifolds. This discretness does not change or replace the manifolds, it is rather an ever-present leyer of smooth manifolds. Besides, the dimension 4 is crucial here. Fundamental gravity can be, thus, related with the curvature of exotic R4 (standard R4 can be flat exotic can not) where discretness appears naturally. I think that again mathematics shows us the way which is not, however, quite clear yet.

          These commentaries expresses rather my personal point of view but I was inspired by your great essay. Congratulations and good luck.

          Jerzy

            Dear Ben,

            Thanks for your impartial comments on my essay, on my thread and rating it.

            http://fqxi.org/community/forum/topic/1549

            However I am responding to it on your thread because I think it has come out incomplete. Can you please check and do the needful if neccesary.

            You wrote: "My belief is that its standing will improve as more serious authors read it". I do not think even 10% of the authors will give an unbiased rating. Firstly,because they will not understand what my essay is about with their own pet ideas in their minds, and secondly they will be interested to up their position by rating others low. (As for me I still have not rated even my own essay. I am reading through them and will rate all of them on their merit at a later date).

            This points to the facct that all those who have got high Community ratings for their essays seems to have achieved them not by the ratings of authors but from the FQXi 'Community'.

            But the big question is how do I get the attention of the "Community". The FQXi, highlights "Top Essays" some authors to the Community, but when I posted some highlights about my essay in that blog to draw their attention, it was removed by the administrator saying that Competitor ads are not allowed. So all competitors are not playing on a level playing field.

            Best regards,

            Viraj

              yes of course and Verlinde who speaks whith Johan and Brendan, of course of course.

              The team is known band of comics frustrated and loving money and opulences.

              The team is a small team from usa,canada and Netherlands. In fact , they need funds simply.So they try , it is logic for the persons needing funds due to our global crisis. You like money band of comics.Me no, you dislike me, me no I like you.You imply diffamations and calomnias and lies and strategies.Me no.You are in team with tools, me no.and what ? There is a probelm?

              academicain of nothing yes.You do not improve, you decerease the velocity of evolution. It is totally different.The suit does not make the monk !!! my knowledges are above yours. Even with my literal english, I give you courses all days.Me I learn all days everywhere even in seeing a fly of a bee. and you want what, a bridge between netherlmands and usa for the convergences with Canada. let me laugh.

              You want really that I give a list of people of this badteam on net.

              here is the team band of comics.Lisi, Brendan,Lawrence, Tom,Christi,Don, Benjamin dribus,Jens,Verlinde,Rick,Goodband,joy,Jonathan,Johan,.........

              Mr Witten, Mr Wilczec,Mr Tegamrk,Mr Guth please don't be corrupted by the businessmen.They imply the chaos.Just due to their vanity and their unconsciousness. Don't accept these comportments. I will go at MIT .and I will show in live what are the truths.

              Regards

              Steve,

              I'm not sure what I did to offend you, but a penniless graduate student such as myself is far more interested in keeping my health insurance next year than being part of any "team" of people whom I have never met and have only conversed with online in the last few weeks.

              If you recall, my first remark to you (on a different thread) was an expression of sympathy for the loss of your piano, since I am a fellow musician. When you posted on my thread, I asked if you had an essay or any paper online, and would gladly have looked at your ideas, as I have everyone else's.

              Kindly leave me off the "team." Most of the people you name are way out of my league anyhow. Take care,

              Ben