Compact Time and Determinism for Bosons: Foundations

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.

Elementary cycles of time

“…Free elementary particles can be regarded as reference clocks for a more accurate operational definition of the time unit. A formalization of elementary particles as ECs provides natural solutions to controversial questions of physics as well as a novel concept of time [1][2][3].…”

“…They are dual descriptions of the kinematical state. The instantaneous temporal and spatial periodicities of a particles can be written in a contravariant tangent four-vector T µ = {T t , λ x }, [1]. Indeed every particle can be formally represented by phasors or waves, in which the space-time coordinates enter as angular variable with periodicity T µ .…”

“…A description of nature in terms of ECs has remarkable conceptual and physical implications [1][2][3]. From a conceptual point of view, it implies that every particle can be regarded as a reference clock: the so-called "internal clock".…”

“…In recent publications [1][2][3] we have proposed a formalization of relativistic Quantum Mechanics (QM) in terms of relativistic Elementary Cycles (ECs). This description can be justified, for instance, by the wave-particle duality introduced by de Broglie in terms of a "periodic phenomenon" attributed to every elementary particle [4].…”

“…By assuming ECs in space-time, the recurrence of elementary particle can be implemented directly at the level of space-time geometry. Technically this is realized in terms of compact space-time dimensions with periodic boundary conditions [1][2][3]. The resulting description provides elegant solutions of central problems of modern physics such as a unified semiclassical geometrodynamical description: of quantum and classical mechanics [1], of gauge and gravitational interaction [2], as well as of Maldacena's conjecture [3].…”