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On the Zitterbewegung and light-like internal dynamics of the electron

Olivier Rousselle

Published Aug 18, 2026• 0 citations
Publisher

Abstract

This paper focuses on the understanding of the electron and its intrinsic properties. We analyze the Zitterbewegung motion, that gives information about the internal dynamics of the electron (with internal motion at the speed of light with an amplitude at Compton scale). This approach with field explains the origin of the spin and mass, while being compatible with quantum physics. This article is in the continuity of De Broglie and Einstein ideas to make quantum physics realistic (with real trajectories and physical waves) and to define a geometrical structure to the electron.

DOI
10.13140/rg.2.2.15680.70405

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This paper focuses on the understanding of the electron and its intrinsic properties. We analyze the Zitterbewegung motion, that gives information about the internal dynamics of the electron (with internal motion at the speed of light with an amplitude at Compton scale). This approach with field explains the origin of the spin and mass, while being compatible with quantum physics. This article is in the continuity of De Broglie and Einstein ideas to make quantum physics realistic (with real trajectories and physical waves) and to define a geometrical structure to the electron.
Zitterbewegung and de Broglie matter waves are both phenomena associated with the quantum-mechanical properties of the electron, but they are usually discussed in different contexts. Zitterbewegung is understood as a rapid oscillatory motion appearing in the Dirac equation, whereas the de Broglie matter wave is understood as a wave corresponding to the linear momentum of a particle. Some previous studies have attempted to derive the de Broglie matter wave from an internal clock of the electron or from Zitterbewegung. In the present study, however, no causal relation in which the matter wave is generated by Zitterbewegung is assumed. Instead, the two are regarded as different geometrical representations of a common phase degree of freedom. Specifically, Zitterbewegung is interpreted as a phenomenon corresponding to an internal rotational degree of freedom, while the de Broglie matter wave is interpreted as spatial phase progression associated with linear momentum. and are interpreted, respectively, as the rates of phase progression in the temporal and spatial directions. Furthermore, using the relation introduced in previous work, and reinterpreting it as the ratio of the internal rotational velocity to the external propagation velocity, this study shows the possibility of describing internal rotation, translational motion, matter waves, and the fine-structure constant within a common phase geometry.
We show that the Zitterbewegung of the electron arises as a real internal motion when spin is treated as a classical bivector rather than as a point-fermion of the Dirac equation. In the Bivector Standard Model, physically meaningful dynamics reside in the body-fixed frame where two orthogonal internal angular momentum vectors counter-precess about a torque axis. Their rigid rotation generates a time-dependent chord whose magnitude oscillates at twice the Compton frequency, 2ωC, and whose orientation precesses at ωC. When projected into the laboratory-fixed frame, this internal rotor produces the characteristic trembling motion of the Zitterbewegung and traces a horn torus envelope without additional assumptions. The internal clock defined by this cyclic bivector motion unifies the origin of spin properties and the de Broglie modulation. It distinguishes complementary parity sectors that cannot be related by Lorentz transformations. The Zitterbewegung is therefore not an interference between positive- and negative-energy spinors, but the visible shadow of a real, energy-conserving internal rotation inherent to the bivector structure.
The Zitterbewegung model of an electron offers a classical interpretation for interference and diffraction of electrons. The idea is very intuitive because it incorporates John Wheeler’s idea of mass without mass: we have an indivisible naked charge that has no properties but its charge and its size (the classical electron radius) and it is easy to understand that the electromagnetic oscillation that keeps this tiny circular current going – like a perpetual current ring in some superconducting material – cannot be separated from it. In contrast, we keep wondering: what keeps a photon together? Hence, the real challenge for any realist interpretation of quantum mechanics is to explain the quantization of light: what are these photons? In this paper, we offer a classical quantum theory for light. The intuition behind the model is the same as the one we developed for an electron: we think of the photon as a harmonic electromagnetic oscillator, and its elementary cycle determines its properties, including spin and its size (the effective area of interference).
Dirac's Relativistic Wave Equation implies a measured electron velocity of ±c\pm c±c in any direction, in contradiction to Special Relativity and observation. It is shown in this article that this anomalous electron velocity reveals an internal structure of the electron whereby the mass and the charge of the electron cannot be described by the same position operator. The measured velocity of electron mass is always less than ccc in any direction but charge can be displaced at the speed of light. This speed is realizable only when the electron is in a state that is a superposition of positive and negative energy states, also known as a zitterbewegung state. It is shown that in zitterbewegung it is the charge and not the mass that undergoes rapid spatial oscillation, and that there are measurable consequences of this charge zitterbewegung. Zitterbewegung of charge also occurs in an entangled electron-positron pair created by a strong electric field.
For a free Dirac electron, the Heisenberg equations define an internal dynamical system in the rest frame, isomorphic to a finite three-dimensional oscillator with a compact SO(5) phase space, such that the spin of the electron is the orbital angular momentum of the internal dynamics (Barut and Bracken 1980, 1981a). In the present work, the change in this internal dynamics due to an external magnetic field is studied. In order that the internal motion can be distinguished from the centre of mass motion, the solutions of the corresponding Hamilton and Heisenberg equations for the relativistic classical motion and the relativistic quantum mechanical spinless motion are also presented. The solutions for the electron exhibit the effect of the spin terms both in the internal motion and external motion, and we are able to identify the properties of the Zitterbewegung in the external field.
The spin of an electron is an intrinsic quantum property that cannot be explained using classical mechanics. Nevertheless, it is possible to conceive semiclassical systems with internal degrees of freedom that exhibit spin-like properties. Building on the analysis of phase modulation by elliptical gears and kinematically equivalent antiparallelogram linkages, we present a novel semiclassical model of Zitterbewegung, a rapid oscillatory motion closely connected with spin. The kinematical analog is based on including the internal rotation of the linkage represented in spacetime. The system’s dynamics is related to two-center electron models, which describe the constant momentum of the center of mass and the lightlike oscillation of the center of charge at twice the Compton frequency for a particle at rest. A two-dimensional extension provides an intuitive illustration of topological spin properties and can be used to calculate the spin and magnetic moment of an electron.