Elementary Time Cycles by Donatello Dolce

Hi Thomas,

Thank you for your detailed reply. What you say is really fascinating. Though I cannot see your attachments, I can figure out what you say. But I would rather say that if the structure of music is defined by the Enharmonic system, the structure of sound is described by the harmonic system of a vibrating string for example. That is to say on Pythagoras studies. According to my mathematical results the axiomatic (and not intuitive) structure at the base of our description of QM can be elegantly and simply derived from the physics of a harmonic system...after all this idea is also behind orthodox string theory, though this theory is absolutely not simple from a mathematical point of view.

This also means that the other aspects of music or sound that you describe, if correctly generalized to 4D, can be used to describe important quantum phenomena in a very elegant way, an resolve some of the quantum paradoxes that we have.

Please give a look to the caption of the pictures in my web page: http://www.ph.unimelb.edu.au/~ddolce/

regards,

Donatello

Hi Tom,

Probably the system that I would like to describe to explain the mass of the carrier of information and therefore the gauge symmetry breaking that we observe at LHC is more similar to the air chamber of a instrument rather than of a Chapel...but this are just hits that I am trying to work out.

I keep Reyleight's book close to my desk and I am sure that there I will find help for my hints...actually in that fundamental book about sound theory it is possible to see how an apparently abstract mathematical tool such as the Hilbert space has a very simple description and application in describing the harmonics of a sound source.

regards,

Donatello

Dear Roger,

I do not agree with the thesis of your essay Nature Has No Faithful Mathematical Representation by Roger Schlafly. Deny the possibility of a mathematical description of reality is deny the possibility to find general objective rules to describe nature. This would be the end of natural philosophy and science of Pythagoras and Galileo. This means to give up with the effort to understand nature. It is reductive to say that the scientific method is all wrong without giving alternative frameworks or proposing new assumptions. You use the complexity of quantum mechanics to claim that nature has no faithful mathematical description, but quantum mechanics is the demonstration that mathematics works by far better than our physical intuition. The amazing accuracy of the predictions of the anomalous magnetic momentum of the electron is an absolute demonstration of the power and correctness of our mathematical description of quantum mechanics. The problem of quantum mechanics is that we have not grasped the underlying physical meaning of QM, i.e. the physical meaning or geometrical description of QM. Copernicus's revolution and Kepler have taught us that a geometrical or mathematical problem apparently impossible or extremely difficult to formalize in simple roles, if approached with the correct physical assumption, e.g. by using the Sun as origin of the coordinates of the system, suddenly simplifies in an elegant mathematical equations or geometrical elements (try to describe planet motions using the Earth as origin of your coordinates, the equations are so complex that the underlying symmetries are completely hidden). A physics hypothesis is true as long it describe consistently our observations.

In my essay Elementary Time Cycles I discuss how all the fundamental aspects of quantum mechanics and relativity are conciliated in an elegant mathematical form. This has the same form of the system which originated mathematics with Pythagoras and it is at the base of the all modern theory of physics: this is the mathematical description of a vibrating string with all its harmonics. In my papers, published in leading scientific journals, I show with rigorous mathematical demonstrations, certified with peer-review in the better scientific tradition, that the "missing link" for a consistent description of the most fundamental aspect of quantum world is an assumption of intrinsic periodicity of isolated systems, as implicit suggested nearly a century ago by the fathers of quantum mechanics (de Broglie, Bohr, Sommerfeld, Schrodinger, Fermi, Dirac, ...). The mathematics is correct, and this is easy to check. Nevertheless in some cases I had the funny comment that my results are (a long series of) "mathematical coincidences". My question is: What is not a mathematical coincidence in physics?. A mathematical coincidence, if exists, is only something that works mathematically but it is not well understood conceptually.

Hi Ben,

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