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 I have hundreds of pages of unpublished stuff myself.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

        Dear Jerzy,

        I really appreciate the kind remarks! As a matter of fact, you and Torsten have convinced me to reconsider a lot of my tentative beliefs about fundamental physics, as have some of the shape dynamics folks and a few others.

        The last time I really thought carefully about low-dimensional manifolds was a few years ago, and that was before I was properly aware of noncommutative geometry. I never took nonstandard models seriously until I read Connes, and as you have seen, I still have only the vaguest ideas about them.

        I feel fortunate to have perhaps half a dozen serious new directions to think about once the exchange of ideas slows down a bit. Take care,

        Ben

        Ben,

        Indeed I interpolated closed and exact. I have done this in the past as well.

        I read last night Barbour's essay and had some thoughts about this that I will relay to Julian later today. This touches on ideas of graphs, causal sets and dynamic triangulation.

        Cheers LC

        Dear Viraj,

        You're absolutely right... the form evidently won't accept a "less than" sign without putting it in a latex environment, and it deleted everything below, which was 80 percent of my post. I finally got it right, but there was another abortive post in between. I apologize for cluttering your thread, but all the comments are there now at least!

        Regarding your remarks about the contest and the rating, there are many more than 35 good essays among the 270 or so in the contest, so no one should be too disappointed if his or her own submission isn't a finalist. For a complete outsider and first-time contributor like myself, the whole point of participating in this contest is to have the opportunity to discuss many interesting ideas with serious and original thinkers, and to make contacts with other scientists of similar interests.

        In my opinion, the final community ratings are unlikely to look anything like what they do now; probably most people have not yet voted and it wouldn't be surprising if submissions in the top 10 now finish out of the top 100. The FQXi membership includes many of the most distinguished physicists in the world, and I imagine most of them are very busy. I seriously doubt if they are paying very close attention to this contest on a daily basis or have read or rated most of the essays.

        In my view, the ratings are not worth worrying about too much, since doing so only distracts from the science. A high rating would be nice, but I would prefer to try to understand other people's ideas, circulate my own, and let the chips fall where they may. Take care,

        Ben

        Lawrence,

        Thanks... I'll be sure to look at that. There are at least two other essays involving shape dynamics that I think are interesting, the one by Sean Gryb and Flavio Mercati, and the one by Daniel Alves. My general inclination is to regard this form of relationism as less well-motivated and compelling than the causal versions, but it has some attractive qualities, and some of the authors here have expressed it quite well. Take care,

        Ben

        Hi Ben,

        Quite an ambitious essay indeed! If we ever meet, I suspect we will have many interesting discussions.

        I applaud your courage for trying to reject so much structure and still try to reproduce the rich structures of GR and the Standard Model. It is certainly not an easy task as is evidenced by the efforts of the Causal Sets people. However, I have always found that these approaches are well motivated. Good luck with your approach and in this competition!

        Sean.

          Hi Ben,

          Thanks for re-posting your message in my thread.

          About your other comments:

          It is not that I am dead keen to get a good rating. I too am in the 'contest' more to use it as a forum to get to know people and ideas, and to circulate my own. You know the long forgotten motto of the Olympics - "Not to win but to take part".

          But an important aspect of taking part amounts getting the attention of independent parties (eminent scientists who are FQXi members) to my essay for whatever it is worth, as much my reading other participants' essays. But the avenue to reach FQXi members is blocked, while 'Top Essays' are freely advertised in the Main blog. It is also a fact that the content of some of these "Top Essays", do not conform to the context of the topic of the contest.

          This is a genuine concern I have about the way the "Contest" is run.

          However, I am not worried about the 'contest'. If things are left for chance without manipulations, I know the chips would have fallen in a cetain way, but the way things are it appears they won't. It is just the instinct in me not to take things sitting down that bugs me.

          Quite apart from the contest and FQXi community, do you know of any scientists who are likely to take an interest on essays like ours concerning fundamental problems of physics. If you feel it appropriate I request you to let me know.

          My email: virajplf@yahoo.co.uk

          Best regards,

          Viraj

          Dear Sean,

          Thanks for your kind remarks. I think you have characterized the obvious advantages and disadvantages of an approach like mine quite correctly: it's well-motivated and would be terrific if it worked but may fall well short of the level of structure necessary to describe the real world.

          One remark I will make (I said something similar on Daniel Alves' thread) is that perhaps one way to think about the relationships among approaches such as causal sets, causal dynamical triangulations, shape dynamics, and my approach, is to consider the symmetry, antisymmetry, or asymmetry of the relations involved. Shape dynamics seems to involve symmetric relations, since separation does not specify order. Causal sets involves strictly antisymmetric relations because of the acyclicity hypothesis. Causal dynamical triangulations uses both symmetric and antisymmetric relations, and my approach uses mostly antisymmetric relations, although I admit the possibility of cycles. Of course, shape dynamics assigns weights (separations) to the symmetric relations, which gives more information. Anyway, maybe this is wrong, and I'm certainly a fool to talk about shape dynamics two weeks after first learning it existed, but it seems on the surface that there might be dualities among appropriate versions of some of these theories. Oh well, just a wild thought. Take care,

          Ben

          "Regarding the constancy of the speed of light, my guess would be that a concept like this only makes sense at sufficiently large scales."

          No it makes sense locally. See this:

          "vO is the velocity of an observer moving towards the source. This velocity is independent of the motion of the source. Hence, the velocity of waves relative to the observer is c vO. (...) The motion of an observer does not alter the wavelength. The increase in frequency is a result of the observer encountering more wavelengths in a given time."

          This author teaches that the speed of light is VARIABLE (varies with the speed of the observer). If he thought it was constant, he would have written:

          "vO is the velocity of an observer moving towards the source. This velocity is independent of the motion of the source. The velocity of waves relative to the observer is constant,c, because the motion of the observer alters the wavelength. The increase in frequency is a result of the motion of the observer altering the wavelength."

          Pentcho Valev

          Interesting thought.

          I don't know much about the difference between symmetric and anti-symmetric relations so I can't comment much. However, I would just point out that, in shape dynamics, the conformal factor of the metric is pure gauge, up to a constant. Because of this, the causal structure is really the main information that we are keeping aside from the total volume. Thus, I suspect that there is a way to map causal structure onto shape space. Indeed, this could have something to do with the isomorphism between the de Sitter group and the conformal group. Probably there is a way to map the conformal structure of de Sitter to the isometries of the conformal sphere in one less dimension. Then one could use a framework similar to what Flavio and I are discussing the paper we're about to post to understand this better in gravity. The discreteness is another issue but I have some ideas about that as well. There may be a way to make some connections.

          Cheers,

          Sean.