Clockwork Quantum Universe by Donatello Dolce

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 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

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 Vladimir,

thank you for your interest in my work and, though I am very busy with the publication of new papers based on the same idea, I'll try to read your paper. At a first scan it looks a huge work and I highly appreciate your effort to interpret QM.

By the way I would like to point out that I am not assuming a time period on a lattice, in my model the space-time coordinates are analog, though they are cyclic. If I well understand your wonderful pictures the analogy with your idea can be obtained by associating to every space-time point (to a field in a space-time point) intrinsic space-time periodicities, depending on the content of four-momentum in that point and according to the relativistic geometrodynamics. This maybe are what you call dielectric nodes and I call, oversimplifying, relativistic gears.

In the conclusion, I give some remarks about the flow of time as emerging from the particular "coincidences" of the phase of all these gears. This aspect is rather philosophical and conceptual, I should expand this idea in some future work.

Best wishes to you,

Donatello

Ciao V. P.,

my road brought me to Melbourne and I ready to continue it.

Dear all,

I would like to thank the FQXi community for this fourth prize. It represents an important encouragement to continue in the extremely hard (and urgent) task of promoting original ideas in physics.

What quantum mechanics is telling us is that elementary systems are intrinsically and dynamically cyclic.

I hope this idea will continue to stimulate discussions.

Best regards,

Donatello

Hi Sridattadev,

thank you for interest in my idea. The derivation of your equation zero = i = infinity is not exactly what I mean for "mathematics". By the way ...

...love,

Donatello

PS: You should read about Augustine of Hippo.

IMPORTANT UPDATE: my recent publication on Ann. Phys. (2012) confirms the importance of a cyclic interpretation of elementary systems in physics. From the conclusion, two of the main results are:

► gauge interaction can be derived from the invariance of the theory under local transformations of variables as gravitational interaction can be derived by requiring invariance under diffeomorphisms.

► field theory in cyclic 4D, without any further assumption than intrinsic

periodicity, provides the possibility of a geometrodynamical and semi-classical description of scalar QED

--------------------arXiv:1110.0315 --------------------

Gauge Interaction as Periodicity Modulation

Donatello Dolce,

Annals of Physics (2012), Received 6 November 2011. Accepted 13 February 2012. Available online 22 February 2012.

The paper is devoted to a geometrical interpretation of gauge invariance in terms of the formalism of field theory in compact space-time dimensions [arXiv:0903.3680]. In this formalism, the kinematic information of an interacting elementary particle is encoded on the relativistic geometrodynamics of the boundary of the theory through local transformations of the underlying space-time coordinates. Therefore, gauge interaction is described as invariance of the theory under local deformations of the boundary, the resulting local variations of field solution are interpreted as internal transformations, and the internal symmetries of the gauge theory turn out to be related to corresponding local space-time symmetries. In the case of local infinitesimal isometric transformations, Maxwell's kinematics and gauge invariance are inferred directly from the variational principle. Furthermore we explicitly impose periodic conditions at the boundary of the theory as semi-classical quantization condition in order to investigate the quantum behavior of gauge interaction. In the abelian case the result is a remarkable formal correspondence with scalar QED.

Highlights

► Gauge interaction is inferred from local space-time geometrodynamics.

► Gauge symmetries are related to local space-time symmetries.

► Scalar QED is derived semi-classically as modulation of periodic phenomena.

► Quantum mechanics is associated to a cyclic nature of elementary systems.

► Every free elementary particle can be regarded as a reference clock.