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Is Time a Cyclic Dimension?

Dolce, Donatello

Published Jan 1, 2025• 0 citations
Publisher

Abstract

If “quantization is an art”, it can be greatly refined through the formalism of cyclic time. In past papers, we have demonstrated the effectiveness of a unified formulation of quantum and classical physics based on cyclic relativistic time. In this paper, we show, using theorems from Geometric Quantization, that the Poisson brackets of intrinsically cyclic time dynamics, classical in essence, lead naturally to the canonical commutation relations and the other quantization rules of standard Quantum Mechanics. Our results suggest that canonical quantization can be interpreted as an implicit imposition of closed time paths on classical dynamics, without explicitly stating that time is a cyclic dimension.

DOI
10.6084/m9.figshare.30812804

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Dolce, Donatello

If "quantization is an art", it can be greatly refined through the formalism of cyclic time. In past papers, we have demonstrated the effectiveness of a unified formulation of quantum and classical physics based on cyclic relativistic time. In this paper, we show, using theorems from Geometric Quantization, that the Poisson brackets of intrinsically cyclic time dynamics, classical in essence, lead naturally to the canonical commutation relations and the other quantization rules of standard Quantum Mechanics. Our results suggest that canonical quantization can be interpreted as an implicit imposition of closed time paths on classical dynamics, without explicitly stating that time is a cyclic dimension.

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If “quantization is an art”, it can be greatly refined through the formalism of cyclic time. In past papers, we have demonstrated the effectiveness of a unified formulation of quantum and classical physics based on cyclic relativistic time. In this paper, we show, using theorems from Geometric Quantization, that the Poisson brackets of intrinsically cyclic time dynamics, classical in essence, lead naturally to the canonical commutation relations and the other quantization rules of standard Quantum Mechanics. Our results suggest that canonical quantization can be interpreted as an implicit imposition of closed time paths on classical dynamics, without explicitly stating that time is a cyclic dimension.
If "quantization is an art", it can be greatly refined through the formalism of cyclic time. In past papers, we have demonstrated the effectiveness of a unified formulation of quantum and classical physics based on cyclic relativistic time. In this paper, we show, using theorems from Geometric Quantization, that the Poisson brackets of intrinsically cyclic time dynamics, classical in essence, lead naturally to the canonical commutation relations and the other quantization rules of standard Quantum Mechanics. Our results suggest that canonical quantization can be interpreted as an implicit imposition of closed time paths on classical dynamics, without explicitly stating that time is a cyclic dimension.
In Elementary Cycles theory elementary quantum particles are consistently described as the manifestation of ultra-fast relativistic spacetime cyclic dynamics, classical in the essence. The peculiar relativistic geometrodynamics of Elementary Cycles theory yields de facto a unification of ordinary relativistic and quantum physics. In particular its classical-relativistic cyclic dynamics reproduce exactly from classical physics first principles all the fundamental aspects of Quantum Mechanics, such as all its axioms, the Feynman path integral, the Dirac quantisation prescription (second quantisation), quantum dynamics of statistical systems, non-relativistic quantum mechanics, atomic physics, superconductivity, graphene physics and so on. Furthermore the theory allows for the explicit derivation of gauge interactions, without postulating gauge invariance, directly from relativistic geometrodynamical transformations, in close analogy with the description of gravitational interaction in general relativity. In this paper we summarise some of the major achievements, rigorously proven also in several recent peer-reviewed papers, of this innovative formulation of quantum particle physics.
Wave-particle duality, together with the concept of elementary particles, was introduced by de Broglie in terms of intrinsically periodic phenomena. However, after nearly 90 years, the physical origin of such undulatory mechanics remains unrevealed. We propose a natural realization of the de Broglie periodic phenomenon in terms of harmonic vibrational modes associated to space-time periodicities. In this way we find that, similarly to a vibrating string or a particle in a box, the intrinsic recurrence imposed as a constraint to elementary particles represents a fully consistent quantization condition. The resulting cyclic dynamics formally match ordinary relativistic Quantum Mechanics in both the canonical and Feynman formulations. Interactions are introduced in a geometrodynamical way, similarly to general relativity, by simply considering that variations of kinematical state can be equivalently described in terms of modulations of space-time recurrences, as known from undulatory mechanics. We present this novel quantization prescription from an historical prospective.
Elementary Cycles Theory is a self-consistent, unified formulation of quantum and relativistic physics. Here we introduce its basic quantum aspects. On one hand, Newton's law of inertia states that every isolated particle has persistent motion, i.e. constant energy and momentum. On the other hand, the wave-particle duality associates a space-time recurrence to the elementary particle energy-momentum. Paraphrasing these two fundamental principles, Elementary Cycles Theory postulates that every isolated elementary constituent of nature (every elementary particle) must be characterized by persistent intrinsic space-time periodicity. Elementary particles are the elementary reference clocks of Nature. The space-time periodicity is determined by the kinematical state (energy and momentum), so that interactions imply modulations, and every system is decomposable in terms of modulated elementary cycles. Undulatory mechanics is imposed as constraint "overdetermining" relativistic mechanics, similarly to Einstein's proposal of unification. Surprisingly this mathematically proves that the unification of quantum and relativistic physics is fully achieved by imposing an intrinsically cyclic (or compact) nature for relativistic space-time coordinates. In particular the Minkowskian time must be cyclic. The resulting classical mechanics are in fact fully consistent with relativity and reproduces all the fundamental aspects of quantum-relativistic mechanics without explicit quantization. This "overdetermination" just enforces both the local nature of relativistic space-time and the wave-particle duality. It also implies a fully geometrodynamical formulation of gauge interactions which, similarly to gravity and general relativity, is inferred as modulations of the elementary space-time clocks. This brings novel elements to address most of the fundamental open problems of modern physics.