Incompleteness of the particle dynamics in microcosm and the skeleton conception of elementary particles as overcoming of this incompleteness

TL;DR

This paper proposes a skeleton conception of elementary particles that overcomes the limitations of conventional particle dynamics in discrete space-time geometries, leading to a unified, geometrized, and relativistic description of particle behavior.

Contribution

It introduces a skeleton-based model of particles in discrete space-time, replacing differential equations with a geometric, monistic approach that unifies quantum and relativistic physics.

Findings

Discrete space-time geometry leads to stochastic world chains.

Statistical analysis yields the Schrödinger equation.

Particle dynamics are fully described by space-time geometry.

Abstract

The skeleton conception of elementary particles is considered in the paper. Conventional particle dynamics is formulated in an unaccomplished form, which is adequate only in the continuous space-time geometry. The conventional differential equations of the particle motion cannot be written in the discrete space-time geometry. In the discrete space-time geometry the particle world line is replaced by the world chain. The world chain links has a finite length (not infinitesimal). The world chain appears to be stochastic. Statistical description of stochastic world chains leads to the Schr\"{o}dinger equation, if the elementary length of the geometry is chosen in a proper way. The quantum principles are founded by existence of the discrete (and multivariant) space-time geometry and lose the role of prime physical principles. In the skeleton conception the particle is described by its skeleton (several rigidly connected space-time points). Skeleton conception of the elementary particles realizes a proper description of the particle state, which appears to be adequate in a discrete space-time geometry. The particle dynamics takes the form of a monistic conception, which is described completely in terms of the world function of the space-time geometry. The skeleton conception accomplishes the transition from nonrelativistic physics to the relativistic one and realizes the total geometrization of particle dynamics.