Thank you Jonathan,

in my essay, for reasons of space, I only have mentionated few of the recent progresses of the idea. I am writing some new papers that hopefully I will post soon on arXiv.

The technical details (I used essentially: discrete fourier transforms, wave equations, substitution of variables, integration by parts) are the solid support of my arguments. The language of physics is mathematics. After consistent mathematic results it is possible a conceptual interpretation. Thanks to this solid mathematical basis I can state that dynamical cyclic phenomena match ordinary quantum mechanics. As I have shown at FPP10 the correspondence is with the ordinary formulation of quantum mechanics (Schrodinger equation, Hilbert space, commutation relations) as well as with the Feynman Path Integral formulation.

I am in the lucky position that I obtain the same equation and if, as Feynman said, "to the same equation corresponds the same solution" the theory that I shortly describe in my essay can be regarded as a possible new formulation of quantum mechanics, exclusively base on the classical variational principle for relativistic waves.

At the time of FPP10 the formulation of the theory limited to isolated systems though I already showed that interactions, described in terms of variation of the periodicities, provided a remarkable parallelism with AdS/CFT. Today I can state that the variation of periodicity of the field can be equivalently written as gauge interactions, without postulating the local invariance of the fields. At a classical level the corresponding path integral formulation that I obtain is usual one of QED (though I still working with bosons the results can be easily generalized to fermions).

My problem is that I am working alone on this huge project, I have a amazing number of result to publish but I am terribly slow in writing papers (because of my inexperience). For this reason feedbacks like yours are greatly appreciated and I hope more will come with this FQXi contest.

As said in my essay, an assumption of periodicity is already implicit in physics, in fact time is defined by counting the number of cyclic of phenomena supposed to be periodic. The counting process of the cycles is one of the many digital aspects of cyclic phenomena.

I remember where we meet at FPP10 and I thank you again for your support. I am really curious to read you essay and give you comments as soon as possible.

Best regards,

Donatello

  • [deleted]

  • Post #4

Dear Donatello,

I have read your essay. I also believe that de Broglie's original ideas are essential to accomplish unification. You will see similar statements about the non-mathematical aspects in both of our essays. Some of the main ideas in your essay are identical to the ones I pose in my essay, althought the origin is very different. The main differences between your and my description that I could identify are:

1. Page 1. Abstract. Cyclic Space-Time. In my essay time I describe that, under the stated conjectures, time and space are dynamically emerging by the interaction of two fundamental fields. Time is equal to the oscillation period, space dynamically emerges during the highly non-linear oscillation as high-density points of the dynamically combined protofields. This is different from the displacement (motion) of a particle, which should not be equated to dynamically emerging space.

2. Page 1. In the work I cite, there is no need to introduce a lattice, letting N--> infinity, or bosonic fields. The interacting fundamental fields can be describe in terms of state function equation. Its solution can expanded in terms of eigenfunctions, which also results in a 'matrix description, which is in turn equivalent to an effective potential equation. The highly technical analysis of this equation shows that dynamic state function solutions must exist, which give rise to internal spatial randomness.

3. Page 2. The 'uncertainty' relation is derived in the work I cite. However, they are exact relations, not 'uncertain' relations. See QFM-II report on my website.

4. Page 3. Expression 3. You provide an expression for the action in terms of a Langrangian density. Langrangian densities are not needed in the Quantum Field Mechanics I describe because the Lagrangian of a free massive particle has the conventional non-quantum field theory form: L= m_0 sqrt (1 -v sup 2/c sup 2), where m_0 is the rest mass. The particle in a box quantization is not needed. See also QFM-II report on my website.

Finally, I would like to say that there are some very good general observations in the body of your essay and the conclusions!

Best regards.

8 days later

Dear Ben,

thank you for reading my essay. I am happy to see a sort of convergence of views between us. I think that also the Kirilyuk's works will be source of inspirations for my future studies. I particularly I like how you describe the appearance of a particle from the a de Broglie periodic phenomenon. It is what I have found plotting the modulo square of one of my periodic field (see the presentation http://wwwthep.physik.uni-mainz.de/~dolce/tmp/seminario-3.pdf). Moreover I hope you'll find interesting the other discussion given in arXiv:0903.3680v1-v4 (note that v5, i.e. ref.[1], contains only an half of the original paper posted on arXiv nearly 2 years ago).

1) I consider that one of the beauty of my theory is that it does not require any hypothetical element not yet observed in nature. It is base only of relativistic space-time and boundary conditions, even the wave nature can be regarded as arising naturally from the assumption of periodicity through Discrete Fourier transform. The most elementary periodic system is a vibrating string and the fields of my theory are exactly the four dimensional generalization of sound waves and sound sources, see ref.[1]. Thus I don't need any pre-field. I suspect that if you tray to formalize your idea of protofield in a consistent way, you'll end up to my periodic field.

2) The lattice assumption was only used to show the connection of my theory with the 't Hooft deterministic model. In my case I have continuos (digital) cyclic coordinates. In your description of field, if you don't use space-time coordinates our only choice left to describe the randomness is to assume hidden variables, with all the problems coming from the no-hidden variables theorems. In my theory there are no hidden variables, the only variables I have are cyclic (analog) space-time and (thus) quantized (digital) energy-momentum.

3) the uncertainty relation as well as the commutation relations are direct consequences of the cyclic space-time. There is not intrinsic (indeterministic) uncertainty. Is the (discrete) process counting of the number of cycles that gives an indeterminacy on the frequency of the ciclic phenomena. To have infinite accuracy of the frequency we need to count an infinite number of cycles, just as in an ordinary wave.

4) A field is a very wide concept and it is perfect to describe periodic phenomenon. The idea comes from de Broglie and evolved in string theory (in my case you can find both these aspects). You say that your theory is base on a protofield, so you should involve some field lagrangian at some point. By the way the field lagrangian and the particle lagrangian are dual if you assume periodicity. You can find the technical proof of this statement for instance in arXiv:0903:3680v4 par.4.1. You will see that a cyclic field, through Poisson summation, can be written a sum of path described by "non-quantum field lagrangians". Moreover the evolution of periodic fields is exactly described by the ordinary Feynman Path Integral and the lagrangian that appears in the exponential is again the "non-quantum field lagrangians".

I really thank you for your interest in my work and you are always welcome for discussions. As you probably noticed, the assumption of intrinsic periodicity opens a new way in physics full of premises!

Best regards,

Donatello

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  • Post #6

Hi Donatello,

As you know, I'm very sympathetic to your general approach of imposing multi-time boundary conditions on continuous systems in order to explain the emergent discreteness of quantum theory. I'm surprised, though, that this picture didn't encourage you to make a stronger stand on whether "reality" was continuous or discrete at the deepest level. Surely if your overall picture is correct, the only possible interpretation would be that "reality" was deeply continuous, but discreteness emerges on a higher level due to an imposed periodicity. Or did I miss some fundamental discreteness assumption you're making...?

Also, using the word "deterministic" in such a context seems dangerous, 't Hooft notwithstanding. Most people equate that word with "pre-deterministic", where the initial boundary fully determines the subsequent events. But I think you are talking about something quite different -- "determinism" on more of a block universe level. Something to think about.

Hope you're enjoying Melbourne!

Ken

    Dear Ken,

    I hope that also this time my explanation can inspire you a new paper as it happened last time for your arXiv:0906.5409.

    The point is that, by constraining a string i a compact (analog) space its frequency spectrum can assume only discrete (digital) value. This is where the quantum discreteness arises - consider for instance the quantization of a particle in a box. You should read carefully the essay.

    Since I am (modestly) doing physics (and not Sci-Fi), the word determinism is meant in a mathematical/physical way as in the 't Hooft theory. In my theory the ordinary Feynman Path Integral arises exactly at a classical level, that is without relaxing the classical variational principle, contrarily to ordinary QM. In fact the Feynman paths in this case are classical paths characterized by different classical number. For instance, a wave in a cylinder (similarly to a wave in a small pool) can self interfere because, every two point in a cylinder geometry are linked by an infinite set of classical paths (for a wave in a pool this corresponds to reflections at the boundaries). As you may probably know fields represent the fundamental elements of our physical description of the universe. When I say clockwork universe (see abstract) I mean that the elementary the fields can be formalized in terms of classical physics, so that they can be regarded as elementary gears similarly to the Newton idea of clockwork universe.

    Best regards,

    Donatello

    5 days later

    Dear All,

    I am wondering if there is something of scientific in the criteria of this contest or if it is only based on popularity.

    Best regards,

    Donatello

      Dear Donatello,

      This is really fascinating work! I find most intriguing the idea of an infinite number of classical paths between two points determined by the wide range of winding numbers for wrapping around cylinders. I also like your stroboscopic analogy for why certain measurements appear discrete rather than continuous. The idea of reproducing the spectral lines and known quantum effects based on a cyclic extra dimension dates back to Oskar Klein's work in the 1920s, so it has a venerable history. Your research seems very promising.

      It seems that though you speak about classical fields, you use terminology from canonical quantum mechanics, such as operators and expectation values. Is that for the purpose of comparing your model to the canonical approach?

      Many best wishes,

      Paul

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        • Post #10

        Dear Donatello,

        I have raised the same concerns regarding the community rating issue, on the essay announcement blog and indirectly on the "time travelers" blog. I was informed by the TT FXQI's blogger that the contestant votes were "hidden this time" in contradiction to fact that we are able to sort according to the community vote. Unfortunately, I did not seek clarification. IMHO there are too many essays for which to vote in too short a time frame, and there are several highly rated essays which do not meet the criteria to validate such a position.

        As for your fine essay, fortunately, I have been able to read it before the voting deadline, for even with my meager QM skills, I have recognized it as pushing the boundaries of knowledge in a rigorous manner and plan to give it the top score it deserves. The only suggestion I could offer as for your current lower than expected rating is that your essay is technically very dense. This is not a problem as far as I am concerned personally, but the essay instructions did say:

        "Accessible to a diverse, well-educated but non-specialist audience, aiming in the range between the level of Scientific American and a review article in Science or Nature."

        So there is that fine line between being accessible and being rigorous.

        As for your theory violating Bell's inequality in principle, I see this as a positive result in the light of Joy Christian's work. I would like to point out the work of Joy Christian, in case you were unaware, which I was introduced on the forum of FQXI's very own website, which seems to support your work, although he concentrates strictly on non-locality. He uses topological and division algebra arguments to conclude "that 'quantum non-locality' is nothing but a make-belief of the topologically naive."

        I believe his fine work only complements your own.

        Wishing you only the best,

        Dan

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        • Post #11

        Hi Donatello,

        I read you reply in the thread of my essay. I also think that periodicity is a very important element to eliminate many of the inconsistencies in current physics and is potentially a promising field of research. There are a few other essays that make references to periodicity, but do not expand upon it as we do in our essays.

        I summarized some aspects of Kirilyuk's original theory on Quantum Field Mechanics (QFM) in my essay and linked it to de Broglie's thinking and current theories. On my website, I have cast Kirilyuk's work in a more accessible form with extensions following from the basic theory.

        About your feedback:

        1. The electromagnetic and gravitational protofields are notions introduced to match observed fundamental interactions with minimal assumptions to construct a theory. They should be viewed as real physical fields of which the detailed characteristics may never be known apart from they way they facilitate particle interaction. They should not be interpreted as mathematical fields.

        2. In QFM-I (see my website) hidden variables indeed appear, but in a completely different fashion than in current theory: they are not measurable since they pertain to the protofield interaction.

        3. No comments.

        4. You state that 'You say that your theory is base on a protofield, so you should involve some field Lagrangian at some point.' The basic theory (see QFM-I on my website) describes protofield interaction and from that dynamically emergent space and time. It does not rely on a Lagrangian yet, since it addresses the existence of particles. The next layer of the theory (QFM-II) introduces physically rationalized action conditions to describe electron motion (with stationary state is a special case), from which eventually the Lagrangian of a free electron follows. This does not seem to be a very important result, but a free electron can be viewed as the prototypical particle of nature given its stability and low complexity. A correct physical description of this case should be viewed as a stepping stone for subsequent theoretical work. I have attempted to come up with a 'simple description' of more complex massive particles in line with some of the results of QFM, but this description remains to be compared to measurement results. This is clearly work in progress and can be criticized in some areas.

        I will take a look at the references that you mentioned since I'm always interested to learn something new.

        Best Regards.

        Dear Paul,

        thank you very much for your support. It is very important to me to have feedbacks.

        You are right about the analogy with the Klein's idea. I briefly mention this aspect and the dualism with extra dimensional theories on a paper which I have submitted to PRD few days ago. I will post it on arXiv as soon as possible.

        An extract from the introduction:

        "Nevertheless it must be

        noted that Klein's original proposal was to use 5D field theory

        in an attempt to interpret Quantum Mechanics (QM). In

        his famous paper Quantentheorie und funfdimensionale Relativitatstheorie

        \cite{Klein:1926tv} he noticed that Periodic Boundary Conditions

        (PBCs) at the ends of a compact XD provide an analogy with the Bohr-Sommerfeld

        quantization condition - in particular he used this hypothetical cyclic XD to interpret the quantization of the electric charge. Similarly, it is well known that the solution of the

        mass spectrum of an XD field theory is performed by

        a mathematical procedure which turns out to be parallel to the one used for the semi-classical determination

        of the energy spectrum of simple Schrodinger problems. Examples are

        the analogies between the resolution of: the mass spectrum of a

        Kaluza-Klein (KK) theory and the quantization of a ``particle'' in an infinite well

        potential \cite{Randall:1999vf}; the mass spectrum for an XD theory

        with mass or kinetic lower dimensional terms at the boundaries of a compact XD and the Schrodinger problem with a Dirac delta potentials \cite{Dvali:2001gm,Carena:2002me};

        the mass spectrum with soft-walls or dilatons and the semi-classical quantization of the harmonic oscillator \cite{Karch:2006pv}.

        The KK mass spectrum in a given compact XD background is in fact fixed by imposing

        consistent Boundary Conditions (BCs), whereas the evolution along

        the XD is described by bulk Equations of Motion (EoMs) which play the role

        of the Schrodinger equation of the problem \cite{Dvali:2001gm,Carena:2002me}. We may also note that an XD sector contributes to other typical quantum phenomena such

        as the anomalous magnetic momentum, the lamb shift, the Casimir effect

        and so on \cite{Hong:2009zw,Brodsky:2008tk,Hosotani1983193}."

        What I am actually trying to do is to show that there is a matching between classical fields with intrinsic periodicities and ordinary quantum field theory. I have found that classical fields can be described in Hilbert space, with the Schrodinger equation and commutation relations, the space-time evolution is described by the ordinary Path Integral. The parallelism is surprising and goes from elementary aspects of QM mechanics to more evolved aspects of modern physics. For instance, the correspondence between classical fields (dual to XD fields) and quantum fields is of the same kind of the AdS/CFT correspondence. The theory resemble also string theory....

        There is a lot to say and this seems to be only the beginning of a long story...

        Best regards,

        Donatello

        Dear Donatello,

        That sounds fantastic! I thought perhaps that there was a deep connection between your research and Klein's work. I was also reminded in your essay of the AdS/CFT correspondence, so I'm glad you go into more details in your article. Your ideas do seem highly original and interesting!

        I'll look forward to your article on arXiv (and hopefully also in Physical Review D).

        Best wishes,

        Paul

        An excellent paper!

        The biggest problem is that it starts out at warp speed. As I told another author in this contest, you would benefit from having a more extended description of your motivations for writing this paper, and how the goals of your research fit with the goals of this contest, for this venue, as that would push the first Math down on the page.

        Your research is indeed relevant to the essay subject. It really is quite a good fit; as you are saying that the continuous reality of a cyclical universe maps onto our local framework in a discrete way. It looks like you are still at the 'working model' phase, in some regards, but your program is well along.

        Good Luck,

        Jonathan

          Dear Dan,

          thank you for the clarification about the community rating. I was fearing that nobody considered my work.

          My essay is dense, but I have a lot to say and many other important and technical results has been omitted for the sake of simplicity. The mathematics I use is the mathematics of the most elementary and fundamental system in physics, that is a classic string in compact dimensions, plus integration by parts and substitution of variables. With this I describe the elementary mathematics of quantum mechanics and special/general relativity. This is the minimum for a rigorous discussion.

          Your forum and Joy Christian's paper seems very interesting. I will study them as soon as I will find the time.

          I strongly appreciate your encouragement, it helps me a lot to carry on my researches.

          Best wishes.

          Donatello

          Thank You Again Jonathan,

          I understand what you mean, but from my experience I know that, since my hypothesis is a little bit unusual, people do not take it properly in consideration if I don't use mathematics proofs. The mathematical proofs give me shelter from unfair criticisms. Then there is a lot to discuss on the conceptual level but I prefer to have a solid base to my motivations.

          The mathematics I use is the mathematics of a vibrating string in four dimensions and Hilbert notation, this should be familiar even to non experts.

          The theory is starting to be more than a 'working model'. The published papers refer to results of 1-2 years ago. I have briefly mentioned the new results that I am try to write it into papers, but it is not easy for a researcher with few experiences in publications to write papers and at the same time carry on such a huge project. I have already too much results than I can handle.

          Good Luck to you as well!

          Donatello

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          • Post #17

          Donatello,

          You've got my "10" vote. I feel bad now, that I wasted a lot of time debating with nonsense, while a true gem languished below the cutoff.

          I am a real fan of a quantum interpretation of classical determinism. I had not known of that 1910 Einstein quote. It reminds me, however of what Carl Jung said: "Whatever happens in a moment of time has the properties of this moment in time."

          If you get a chance, I hope you read my essay, too.

          Tom

            Dear Tom,

            thank you for your vote. Independently on this FQXi contest your opinion is by itself a big support to my research plan.

            I have found the quotation in the Barbour's FQXi essay on the nature of time. As I read it I

            seid to myself "I could not state the idea in a better way".

            Best regards,

            Donatello

            Donatello,

            I have read the first two section of your paper and the ending, though rather hurriedly I must confess. This does look rather interesting. My only pause with the gravitational part is how degrees of freedom are counted, but this seems to be a comparatively minor issue at this time.

            Cheers LC

              • [deleted]

              • Post #21

              Ciao Donatello,

              I'm glad you made it. Good luck. Interestingly, going back over your paper, for one of I expect many times to come -- your observation in the intro about 't Hooft quantum determinism and continuation over infinite lattice sites echoes some dialogue I had with Ray Munroe (see my essay forum for link) over a paper I wrote a few years ago, in which I hint at an arithmetic proof strategy for the Poincare Conjecture, whereby continuous curves are exchanged for discrte points. If the points could be represented as point particles ... anyway, you might find it interesting.

              All best,

              Tom

              Dear Lawrence,

              thank you for your interest in my essay. Of course there is a lot more to say about general relativity and gravity. In the essay I only tried to give a heuristic argument to show how to conciliate GR with the assumption of intrinsic periodicities. When I say new degree of freedom I mean that the metric g(x) must be regarded as an additional dynamic field in the theory and therefore a kinetic terms associated to that field must be introduced. This is similar to gauge theory where the assumption of gauge invariance introduces a gauge field as a new dynamical field in the theory (a new d.o.f. according to my terminology) and then we infer that its dynamics must be described by the kinetic terms F_{\mu\nu}F^{\mu\nu} with appropriate coupling (that the parallelism between gravity and gauge theory is indeed very deep). I understand your concern, in fact the term d.o.f. in field theory is usually refereed to the d.o.f. of the field (for instance a gauge field in a gauge invariant theory has 2 d.o.f.). In my case with the term d.o.f. I mean a new dynamical field.

              Best regards,

              Donatello