Hi Yuri,
I'll try to figure out about your essay.
The idea that the physical world can be described in terms of musical theory has origin in Pythagoras, it also is at the origin of mathematics and harmony in art. This is very fascinating and, according to my essay, I like to think that Pythagoras was the first one to study the laws of QM.
Donatello
Don L,
the real value of de Broglie's ideas are sometimes forgotten or underestimated in modern physics, together with "old" ideas of other great minds of the past.聽
The following historic introduction from your website could have been part of my essay [with some smal variations]: "Schr枚dinger attributed the quantum energies of the electron orbits in the old quantum theory of the atom to the vibration frequencies of electron matter waves around the atom's nucleus. Just as a piano string has 'a fixed tone' [a discrerized frequency spectrum], so an 'electron-wave' [electron-string] would have 'a fixed quantum of' [a give quantized spectrum of] energy. This led to much easier calculations and more familiar visualizations of atomic events than did Heisenberg's matrix mechanics, where the energy was found in an abstruse calculation."
Donatello聽
Dear all,
In this essay I have not included mathematical details, as the proofs of my claims have been peer-reviewed and published on Ann. Phys. and Found. Phys.
For an introduction to the formalism you may consider my essay, IV prize in the 2011 FQXi contest
"Is Reality Digital or Analog?":
Clockwork Quantum Universe by Donatello Dolce
Besides the purely digital or analog interpretations of reality there is a third possible description which incorporates important aspects of both. This is the cyclic interpretation of reality. In this scenario every elementary system is described by classical fields embedded in cyclic space-time dimensions. We will address these cyclic fields as "de Broglie internal clocks". They constitute the deterministic gears of a consistent deterministic description of quantum relativistic physics, providing in addiction an appealing formulation of the notion of time.
Donatello
My essay part 1 devoted to cyclic universe.
What is your attitude to cyclic direction in cosmology?
Yuri,
every system can be described in terms of elementary space-time cycles describing elementary particles. A universe composed by single particle would be cyclic as a pendulum in the vacuum. An universe composed by more non-intearctiong particles, i.e. elementary space-time cycles, has an ergodic evolution. If interaction is also considered, with the corresponding modulations of space-time periodicities, the evolution is chaotic. See for instance subsection "comment and outlook" at the end of sec.1, arXiv:1110.0316.
Title: Compact Time and Determinism for Bosons: Foundations
Author: Donatello Dolce
Journal ref: FOUNDATIONS OF PHYSICS, Volume 41, Number 2 (2011), 178-203
arXiv: 0903.3680
Abstract: Free bosonic fields are investigated at a classical level by imposing their characteristic de Broglie periodicities as constraints. In analogy with finite temperature field theory and with extra-dimensional field theories, this compactification naturally leads to a quantized energy spectrum. As a consequence of the relation between periodicity and energy arising from the de Broglie relation, the compactification must be regarded as dynamical and local. The theory, whose foundamental set-up is presented in this paper, turns out to be consistent with special relativity and in particular respects causality. The non trivial classical dynamics of these periodic fields show remarkable overlaps with ordinary quantum field theory. This can be interpreted as a generalization of the AdS/CFT correspondence.
Keywords: Quantization - Time - Determinism - Compact dimensions - AdS/CFT
TitleGauge interaction as periodicity modulation
Author: Donatello Dolce
Journal ref: Annals of Physics, Volume 327, Issue 6, June 2012, Pages 1562-1592
arXiv: 1110.0315
Abstract: The paper is devoted to a geometrical interpretation of gauge invariance in terms of the formalism of field theory in compact space-time dimensions (Dolce, 2011) [8]. 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 interactions are described as invariance of the theory under local deformations of the boundary. The resulting local variations of the field solution are interpreted as internal transformations. The internal symmetries of the gauge theory turn out to be related to corresponding space-time local symmetries. In the approximation 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 described 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.
Keywords: Gauge invariance; Relativistic Geometrodynamics; QED; Semi-classical methods
Title: Classical geometry to quantum behavior correspondence in a virtual extra dimension
Author: Donatello Dolce
Journal ref: Annals of Physics, Volume 327, Issue 9, September 2012, pp 2354-2387
arXiv: 1110.0316
Abstract: In the Lorentz invariant formalism of compact space-time dimensions the assumption of periodic boundary conditions represents a consistent semi-classical quantization condition for relativistic fields. In Dolce (2011) [18] we have shown, for instance, that the ordinary Feynman path integral is obtained from the interference between the classical paths with different winding numbers associated with the cyclic dynamics of the field solutions. By means of the boundary conditions, the kinematical information of interactions can be encoded on the relativistic geometrodynamics of the boundary, see Dolce (2012) [8]. Furthermore, such a purely four-dimensional theory is manifestly dual to an extra-dimensional field theory. The resulting correspondence between extra-dimensional geometrodynamics and ordinary quantum behavior can be interpreted in terms of AdS/CFT correspondence. By applying this approach to a simple Quark-Gluon-Plasma freeze-out model we obtain fundamental analogies with basic aspects of AdS/QCD phenomenology.
Highlights: ► Quantum behavior is related to the intrinsic periodicity of isolated systems. ► A periodic phenomenon can be parameterized by a virtual extra dimension. ► KK modes are used to describe the quantum excitations. ► 5D classical geometry encodes 4D quantum behavior. ► Geometrodynamical description of AdS/QCD as modulation of space-time periodicity.
Keywords: Compact dimensions; Kaluza-Klein theory; Semi-classical methods; Relativistic geometrodynamics; AdS/CFT correspondence; Quark-Gluon-Plasma
Dear all,
please, in evaluating my essay consider the difference between unproved conjectures or speculations and proved mathematical results scientifically certified through peer-review in leading physics journals. See papers above or my other publications on the subject in arXiv
best regards,
Donatello
Hi Donatello,
Intriguing Essay. I am going to give you an high score.
You know that, together with collaborators, I try to formulate an alternative to black holes in this Essay Contest within the framework of the debate on determinism versus randomness. On the other hand, I recently tried to put some order also in the framework of black hole evaporation. In fact, Parikh and Wilzcek have shown that Hawking radiation cannot be strictly thermal. I recently used their result to show that this implies that Hawking radiation cannot be strictly continuous too. In this way, black hole's entropy becomes a function of the black hole's quantum excited state see http://arxiv.org/abs/1205.5251. In other words, there is an order in the process of black hole evaporation!!
Good luck for the Contest.
Cheers,
Ch.
Hi Christian,
as I wrote in the discussion of your essay, your idea is also intriguing, as well as 't Hooft studies on black holes. It has fundamental relations with my description of elementary system as periodic phenomena, though this is link is not trivial and it is not mentioned in my essay. I hope we will find occasion to share our ideas.
Good luck,
Donatello
Hello thinkers,
Hello Mr.Dolce and Mr.Danoyan,
I like so much these kind of discussions.After all, the spiritual universality is essential.It is the sister of the consciousness and the mother of the universal love. The rest is vain in fact.
The partitioning is relevant considering the oscillations correlated with spherical volumes of the uniqueness serie, more the rotations and motions.
The 3 motions of spheres can be understood. The pure thermodynamics and heat are essential when the groups of uniqueness are finite and precise. Pythagore and his theorems are relevant. Thales also was relevant. They had understood a lot of things for this period.
The harmony of the generality in fact was their torch. The partitioning, universal is purelly correlated with the rotating spheres. I am a musician, I play guitar and îano. The waves at my knowledge are spherical. Put a simple mass on the water.The 2d is for the plane.See the water but don't forget that the 3D spherical waves are a reality. It is there that it becomes very relevant for the convergences with the 2D and the 3D.
The Universal sphere and its spheres composes and plays the universal spherical partition of spherization in a pure general harmony.
It is fascinating indeed. The spheres play the melody of pure 3d spherization harmonization. They turn so they are.....The universal partition is still young. We evolve towards this universal eternal sphere and its spheres, quantic and cosmologic. Fascinating is a weak word.The death does not really exist. The life is eternal.:) fascinating, wonderful,the truth in fact.
Thanking you
Regards
Donatello,
If I understood you correctly, you are not ready for a radical break space from time?
Donatello
Thank you for that essay. I have been hoping to find one such as this. It also opens the door to connections with others who are realizing that music has much to do with physics, especially quantum physics.
In your essay you mention:
In physics the most groundbreaking ideas are the simple ones.
This is a principle held by many, including Einstein. However, the mathematics used to define such things as quantum mechanics is horrendous. When we consider fields as continuous in nature and mass as composed of infinitesimal points it follows that the mathematics will be very complex.
Musical mathematics, although it can become quite complex, can be reduced to very simple precepts. The structures of music are defined by the Enharmonic System. If you look up enharmonic in a dictionary it will define enharmonic as - notes that sound the same but are written differently. This is the exact opposite of what enharmonic actually means. In an enharmonic system we are dealing with notes that are written the same but sound differently.
Even a simple scale, called a diatonic scale in music, has intervallic problems. It actually takes three diatonic scales to create perfect harmony. It takes 38 scales to allow for proper tuning of the chromatic system. Most musicians do not understand the enharmonic system. If they did we certainly would not have the tonometric system. I described the tonometric system in the essay. Let me reiterate a simple example. In the tonometric system the perfect fifth (with the exception of the octave the most basic interval) looks like this:
Whereas the perfect fifth is simply:
Not only can everything in music be defined by positive integers the entire enharmonic system is comprised of the powers and multiples of just three numbers; 2, 3 and 5.
I cannot help wondering that if so much of quantum mechanics appears to be musical in nature how much could it be simplified if we really used musical principles.
Apparently my math examples were left out. No problem as they were not really that important.
Donatello
While in many ways the interior of a concert hall behaves like the interior of an instrument such as, say a trombone there is a difference that bothered me for a long time. That remarkable standing wave that was created when we performed in the Chapel of the Resurrection in Valparaiso Indiana was created by the resonances of the voices and instruments of the performers.
In a voice or an instrument the air chambers that contain the resonances are small and the wave would form virtually instantaneously. In an area the size of the Chapel there should have been a delay. The delay in that area should have been greater than a tenth of a second and would have easily be sensed but the lovely sound started immediately.
Then I remembered the first moon landing where they crashed the LEM into the surface of the moon. This caused a resonance (NASA called it resonance which is to their credit). According to NASA the moon rang like a bell for a considerable time. If the resonance was progressive the size of the moon should possibly have made the resonance impossible but apparently the resonance was instantaneous, just as with the interior of the Chapel.
The only explanation is that the resonance was already sounding. There is plenty of ambient energy in just about anything, solids, air, whatever.
On the moon it was an impulse function, much like clapping to elicit a resonance. This is usually what is done in places like Stonehenge and the old Greek theaters (not the best method) but it words to a degree. The chapel had such a dramatic response because the pitch of our performance was at or very near the fundamental frequency of the already existing resonance of the chapel.
I cannot help wondering about the resonance of an elementary particle and is it a simple as the resonance of macroscopic body.
This could be a great over-simplification or perhaps it could be something worth thinking about.
Thanks again for that great article.
Tom
Yuri,
In relativity space and time mix each other. QM is telling us that space-time is intrinsically cyclic in elementary systems, the periodicity is described by undulatory mechanics (think to wave-particle duality). When this is used to describes the non-relativistic limit it is possible to see the radically difference nature of time w.r.t. spatial coordinates. This limit is obtained by putting the mass to infinity (rest energy) and the momentum to zero. In undulatory mechanics, through the Planck constant, this correspods to put the time periodicity to zero and the spatial periodicity to infinity. in classical mechanics, time is extremelly compactified whereas the spatial dimensions have infinite compactifications. Thus we have an effective 3D description in which the flow of time is an emerging (relational description) phenomenon associated to the tiny periodicities of these elementary cycles (i.e. the elementary particles).
regards,
Donatello
The holographic principle associates each bit within a spacelike
three volume with a two-dimensional Planck-scale area on the surface of that volume.
Donatello
You wrote: "In relativity space and time mix each other".
My approach is opposite: space and time need break from each other.
The problem with speculative thinking is that it is too easy to overlook a basic premise. While I think I am correct about the existence of a natural resonance in the moon I overlooked the fact that a resonance is not self-sustaining. There has to be an initial vibration if a resonance or a cascade of resonances if the resonance is sustainable. There must be a vibration and a feedback occurring in the moon and I will leave the argument there as I am not sure we have enough data about the internal structure of the moon.
My apologies for this but it does in no way challenge my basic argument.