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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

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        • 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

        Dear Donatello,

        Congratulations on your dedication to the competition and your much deserved top 35 placing. I have a bugging question for you, which I've also posed to all the potential prize winners btw:

        Q: Coulomb's Law of electrostatics was modelled by Maxwell by mechanical means after his mathematical deductions as an added verification (thanks for that bit of info Edwin), which I highly admire. To me, this gives his equation some substance. I have a problem with the laws of gravity though, especially the mathematical representation that "every object attracts every other object equally in all directions." The 'fabric' of spacetime model of gravity doesn't lend itself to explain the law of electrostatics. Coulomb's law denotes two types of matter, one 'charged' positive and the opposite type 'charged' negative. An Archimedes screw model for the graviton can explain -both- the gravity law and the electrostatic law, whilst the 'fabric' of spacetime can't. Doesn't this by definition make the helical screw model better than than anything else that has been suggested for the mechanism of the gravity force?? Otherwise the unification of all the forces is an impossiblity imo. Do you have an opinion on my analysis at all?

        Best wishes,

        Alan

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          • Post #24

          Donatello,

          I do not know how to rate these essays. First, at this late date I have only read a fraction of the essays. Second there is a wide range of essay "types": there are essays for the general background readers (non-technical), there are technical, accurate, essays that bring no new ideas, there are technical essays that bring up a thousand ideas. Lastly, they are essays like yours that defend a clear point in a technical way. It is difficult to translate ideas in Physics into non-mathematical terms. It is also difficult to show a solid mathematical proof for new ideas. It might be impossible to do both at the same time.

          I did not rate any of the essays.

          Your essay does have QM. I need to go through it a few more times. I think your essay is along the lines of my essay (we are past the voting deadline and my essay is for the general reader).

          All the best,

          Jeff

          Dear Ken,

          thank you for the citation added (even though the long delay) in your paper arXiv:1003.4273 [Time-symmetric boundary conditions and quantum foundations] to my paper arXiv:0903.3680 [Compact Time and Determinism for bosons: foundation].

          As you have already noticed, in my essay (thank you also for the congratulations for this first phase on the contest) I show the possibility of a consistent interpretation of quantum mechanics in terms of boundary conditions, but the validity of my approach is not limited to non relativistic physics like in your case.

          Cheers,

          Donatello

          Dear Alan,

          if you are interested in the unification between electromagnetism and gravity I recommend you to read about the Kaluza's "miracles" or about the Weyl's original proposal for gauge interactions.

          Best regards,

          Donatello

          a month later
          6 days later

          Dear Joe,

          Try to compare with your program the duration of a solar year with the age of the universe, you will see that it is of the same order of the difference between a single period of the cesium clock (~10^-10 s) and a second. Then you may note that it is of the same order of the difference between a single periodic of the internal clock of an electron (~10^-20 s) and the reference periodic of the cesium atom.

          In this way you can figure out that trying to investigate the electron dynamics with a cesium clock, or the other precision clocks now available, is like to study the cycles of the seasons by using the age of the universe as reference cycle. The only way you can describe a system with too fast periodicity with respect you reference clock is a statistical way, just like for a dice rolling too fast with respect to the resolution in time of human senses. 't Hooft noticed that "there is a deep relationship between a particle moving very fast in a circle and the quantum harmonic oscillator". What I have found is that there is actually a deep parallelism between cyclic dynamics and quantum mechanics, the periodicity is the periodicity of the so called de Broglie internal clock.

          Best regards,

          Donatello

          Dear Joe,

          Try to compare with your program the duration of a solar year with the age of the universe, you will see that it is of the same order of the difference between a single period of the cesium clock (~10^-10 s) and a second. Then you may note that it is of the same order of the difference between a single periodic of the internal clock of an electron (~10^-20 s) and the reference periodic of the cesium atom.

          In this way you can figure out that trying to investigate the electron dynamics with a cesium clock, or the other precision clocks now available, is like to study the cycles of the seasons by using the age of the universe as reference cycle. The only way you can describe a system with too fast periodicity with respect you reference clock is a statistical way, just like for a dice rolling too fast with respect to the resolution in time of human senses. 't Hooft noticed that "there is a deep relationship between a particle moving very fast in a circle and the quantum harmonic oscillator". What I have found is that there is actually a deep parallelism between cyclic dynamics and quantum mechanics, the periodicity is the periodicity of the so called de Broglie internal clock.

          Best regards,

          Donatello

          Caro Donatello

          Your paper is highly mathematical, while I like to think in terms of models that one can imagine and illustrate visually and mechanically (not a bad method, Maxwell used it at first !). I found intriguing similarities and basic differences in our approaches. You describe relativistic gears having a "close relationship between the quantum harmonic oscillator with angular frequency ¯ w = 2p /Tt , that is the mode of an ordinary quantum field with energy ¯E = h¯w¯ , and a classical particle moving along a circle of periodicity Tt . By assuming the time period Tt on a lattice with N sites".

          In my fqxi paper and in my earlier 2005 Beautiful Universe proposal on which it is based, I have described a universe made up of a lattice of spinning dielectric nodes interacting with each other as 'slippery' spherical gears transferring angular momentum in units of (h) by induction.

          I think one of the main differences in our approaches (if I understand yours correctly) is that you describe your system using the formalism of (SR) spacetime. I see interactions as absolute in timeless universe, perhaps as you describe in a stroboscopic way, as you nicely describe, but the stroboscope illuminates all the lattice instantaneously. I would greatly value your reading the papers and hearing your expert feedback.

          Best wishes from Vladimir