Is it possible to describe an electron by the evolution of a single point?

TL;DR

This paper proposes a geometric model where an electron is represented by a moving point that describes its charge center, explaining spin, magnetic properties, and interactions through differential equations and relativistic considerations.

Contribution

It introduces a novel geometric framework modeling the electron as a point with a specific motion, linking charge dynamics to fundamental quantum and relativistic properties.

Findings

Electron's charge center moves at the speed of light.

Spin and magnetic properties arise from charge motion.

Interaction parameters relate to the fine structure constant.

Abstract

The answer to the title-question is affirmative. The analysis of the geometry of continuous and differentiable curves in three-dimensional Euclidean space suggests that the point represents the location of the center of charge of the electron, satisfies a system of ordinary differential equations of fourth order, and moves at the speed of light. The center of mass of the electron is a different point and will be determined by the evolution of the center of charge. It is the relative motion of the center of charge around the center of mass that gives rise to the spin and magnetic properties. The invariance of the mass and the absolute value of the spin for the center of mass observer imply that in the interaction of the electron with an external electromagnetic field the particle has to radiate. The analysis of a Poincar\'e invariant interaction of two electrons implies that the only relevant parameter that characterizes the interaction in a natural system of units, is the fine structure constant. The fundamentals of General Relativity have to be revisited.