Essay Abstract

Relativity, if rigorously interpreted, only fixes the differential structure of space-time without giving any particular prescription about the boundary of the space-time dimensions. On the other hand the boundary conditions have played a fundamental role since the earliest days of quantum mechanics. Wave-particle duality suggests the introduction in physics of the principle of intrinsic periodicity so that elementary particles turn out to be described as modulated harmonic vibrations of compact space-time dimensions. This enforces the undulatory nature of elementary particles and the local nature of relativistic space-time. For instance, as mathematically proven in recent publications, this conciliates special relativity with quantum mechanics [Found.Phys.,41:178,2011], gauge interactions with gravitational interaction [Ann.Phys.,327(6),1562,2012], and pinpoints a fundamental aspect of the Maldacena conjecture [Ann.Phys.,327(9),2354,2012]. Here, we present some conceptual elements of this innovative and elegant interpretation of the quantum world giving some historical and philosophical motivations.

Author Bio

Dr. Donatello Dolce has obtained his PhD in high energy physics at the Florence Univ., in 2007 after a PostDoc at J. Gutenberg Univ. of Mainz, Germany, he is concluding a PostDoc at the University of Melbourne, Australia. Despite his main research field is Phenomenology, he has dedicated most of his time and efforts in foundations of physics, convinced that novel natural testable ideas are necessary in modern physics. He has proposed a principle of intrinsic periodicity of elementary systems, obtaining and publishing a new theory with a realistic unified description of physics.

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Dr Donatello Dolce

Why is nature playing that particular string chord?

Because Creator is Great Musician.

See my essay and listening music too...please.

http://fqxi.org/community/forum/topic/1413

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Donatello,

Everyone pays hommage to deBroglie. He predicted the wave nature of the electron! And then he gets left to history as the person who showed the dual nature of particles, when in reality he showed us pretty much the complete nature of particles.

I think of your essay as picking up where deBroglie left off.

I have a theory (digital wave theory) that is similar to yours but goes off the deep end in several ways.

You will know what I am about by taking a look at: http://www.digitalwavetheory.com/DWT/20_Experiments-_QM.html

Best of Luck

Don L.

    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.

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      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

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        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

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          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

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          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