On the intrinsically cyclic nature of space-time in elementary particles

TL;DR

This paper proposes a framework where elementary particles are modeled as intrinsically cyclic entities, linking their quantum behavior to space-time periodicity and revealing a geometrodynamical aspect of gauge interactions.

Contribution

It generalizes the de Broglie hypothesis by formalizing particles as cyclic phenomena, connecting relativistic quantum mechanics with space-time periodicity and gauge interactions.

Findings

Particles exhibit intrinsic space-time periodicity.

Relativistic interactions modulate de Broglie periodicity.

Gauge interactions have a geometrodynamical interpretation.

Abstract

We interpret the relativistic quantum behavior of elementary particles in terms of elementary cycles. This represents a generalization of the de Broglie hypothesis of intrinsically "periodic phenomenon", also known as "de Broglie internal clock". Similarly to a "particle in a box" or to a "vibrating string", the constraint of intrinsic periodicity represents a semi-classical quantization condition, with remarkable formal correspondence to ordinary relativistic quantum mechanics. In this formalism the retarded local variations of four-momentum characterizing relativistic interactions can be equivalently expressed in terms of retarded local modulations of de Broglie space-time periodicity, revealing a geometrodynamical nature of gauge interaction.