Donatello Dolce explains Planck's Blackbox Radiation using de Broglie's Law of Phase Harmony as a Piano

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 http://www.ph.unimelb.edu.au/~ddolce/

 http://unicam.academia.edu/DonatelloDolce

Nearly 90 years ago de Broglie noticed that, in the microscopic world, periodicity and wavelength, T and l respectively, of a relativistic wave can be used to describe the energy momentum, E and p, of the particle through the Planck constant h. That is, E= h / T and p = h/ l (these relations are often written in terms of time frequency and spatial wavenumber).

It is important to bear in mind that, according to de Broglie, the energy E and the periodicity T are “two faces of the same coin”. This means that an assumption of intrinsic periodicity is fully consistent with relativity as long as the relativistic modulations of periodicity associated to relativistic variations of kinematical state are considered. In fact we will describe interaction as modulation of periodicity as for gravitational interaction. Since our world is composed by elementary particles, and elementary particles are intrinsically periodic phenomena, it is natural to assume that reality can be described in terms of elementary cycles.

In particular the de Broglie internal clock associated to an elementary particle, as our ordinary clocks, can be conventionally chosen to be clockwise or anticlockwise. Only the reciprocal combinations of the ticks of these clocks are important. However if invert a single clock with respect to the others we obtain a different physical system. This corresponds to pass from a particle to an antiparticle and vice versa.

As known since Pythagoras, see fig.3a, a system (e.g. a string) constrained in a compact or periodic space can only vibrate with discretized (quantized) frequencies. That is a homogeneous string, which in our case corresponds to a free particle, can be represented as a homogeneous string vibrating with fundamental periodicity T=1 / v , so that the resulting harmonic frequency spectrum is v_n = n v.

It is interesting to note that the theory is the full relativistic generalization of sound theory. Sound theory, developed by the Nobel laureate 1904 Reyleigh, is actually at the origin of the modern quantum formalism. A sound source is an object vibrating along spatial dimensions in a classical wave framework. A quantum system turns out to be an object vibrating along space-time dimensions in a relativistic wave framework [4].

Since temporal-spatial periodicity and energy-momentum are two faces of the same coin, we can equivalently describe the retarded and local variations of energy-momentum occurring during relativistic interactions in terms of corresponding modulations of temporal-spatial periodicity of the elementary particles. In particular we may note that Einstein derived his description of gravitational interaction of general relativity by considering the modulations of temporal-spatial periodicity associated to a Newtonian gravitational potential.

The phase harmony implies that the momentum-energy and the space-time periodicity are dual quantities - they are two sides of the same coin.

In general, the higher harmonics describe the quantum excitations of the particles (e.g. multiparticle states) whereas the fundamental harmonic is the de Broglie matter wave of ordinary undulatory mechanics or field theory - the negative vibrational modes correspond to antimatter ("anti-particles")
Thus, massive elementary particles, with their vibrations in space and time, are the relativistic sources of sound. In fact we have postulated that every elementary particle is a vibrating space-time string.

The "medium" on which this relativistic "sound" propagates is the space-time(s) associated to the fundamental massless particles of the Standard Model, i.e. photons and gravitons.

And similarly:

...the energy-momentum flux will be larger in the blue shifted part than in the red shifted part....In a moving frame, they diverge: the mean internal frequency of the photon will increase; simultaneously the orbital frequency of the photon will decrease due to the relativistic law of the slowing down of clocks. Despite the difference in frequency, at any point in space-time these two oscillations must be in phase....This provides a possible physical origin for the postulated law of the "harmony of the phases" first proposed by de Broglie, which lies at the origin of quantum mechanics. ...In a head-on collision between two photons, the interaction will be essentially between the blue-shifted regions which are converging....This state may then decay back into two photons or into an electron-positron pair.

Is the electron a photon with toroidal topology? J.G. Williamson and M.B. van der Mark, 1997

 The secret of turning the light around - is the virtual micro black hole - as this author, co-wrote with Nobel Physicist Gerard t'Hooft on why Light is Heavy - relativistic mass as superluminal momentum.

Dear Dr. Dolce: Thank you for directly connection "sound theory" from Pythagoras to relativistic quantum physics. I appreciate your explanation of black body radiation using the piano image - excellent. I started piano lessons at age 5 and played a memorized concert at age 18 - and so also studied music theory intensely in high school. I could not accept the normal Western music theory and then I discovered the noncommutative phase secret of music theory that Alain Connes reveals. He relies on the Dirac Operator though while I think your approach is much more fundamental. Have you seen Gerard t'Hooft's protege pdf on whether the electron is a photon that is toroidal? This seems closely tied to your work - I blogged on this at http://ecochoinvasives.blogspot.com Ever since Archytas stated Perfect Fifth plus Perfect Fourth = Octave - this was the wrong music theory as the first logarithmic equation of Western math! Archytas covered up the truth that if C is 1 and octave C is 2 then G is 3 as Perfect Fifth overtone but F is 3 as Perfect Fifth undertone - at the same time! Presto - negative frequency as anti-matter right there - or noncommutative phase as quantum coherence nonlocality. This is the secret of nonwestern meditation. I finished my master's degree doing nonwestern meditation with a Chinese yoga spiritual healer - http://springforestqigong.com - since I realized that Daoism is based on the real Pythagorean (relativistic quantum) harmonics, and so is the "three gunas" of India - the oldest philosophy of India. And this goes back to the original human culture where the music training was the core of the culture to understand reality as spiritual training.

Take care,

drew hempel, M.A.

It is contended further that a photon energy-frequency relation of half that currently accepted is consistent with the quantization of energy of the standing waves mode of a cavity oscillator, as assumed by Planck in his successful theory of the blackbody spectrum....Rather since a standing wave can be regarded as a superposition of two oppositely-traveling waves of equal amplitude, the expected number of photons is twice the number of energy multiples of hv....based on the relativistic Doppler effect. [noncommutative phase as scalar]...a trajectory that reverses in ordinary time may be interpreted as giving rise to pair creation and destruction events.

David C. Lush Composite Photon Energy-Frequency Relation based on de Broglie's Law of Phase Harmony

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