[Paper Review] Classical elementary particles, spin, zitterbewegung and all that

M. Rivas|ArXiv.org|Dec 17, 2003

Quantum and Classical Electrodynamics3 citations

TL;DR

This paper proposes a classical model of the electron as a point-like charge undergoing zitterbewegung—rapid oscillatory motion at the speed of light—linked to spin and magnetic moment via a rotating structure. By analyzing the kinematics of inertial observers tracking the particle's state, it derives a consistent classical picture that reproduces key quantum features like spin-1/2, magnetic moment, and Compton-scale oscillations, offering a unified classical foundation for electron properties and suggesting new insights into photon and neutrino structure.

ABSTRACT

After a revision of the main features of the structure of the Dirac electron a plausible definition of elementary particle is stated. It is shown that this definition leads in the classical case to a picture which produces a very clear correspondence between the classical and quantum mechanical features of the electron. It is analyzed how the classical spin structure and zitterbewegung are related to the classical variables that define the kinematical state of the particle.

Motivation & Objective

• To clarify the theoretical definition of an elementary particle as a system without excited states.
• To establish a classical mechanical picture of the electron that reproduces quantum features such as spin and zitterbewegung.
• To relate classical spin and magnetic moment to rotational dynamics of a point charge undergoing relativistic oscillations.
• To explore the classical Lagrangian structure of spinning particles and extend it to massless systems like the photon.
• To address inconsistencies in classical models of spinning particles, particularly radiation from accelerated charges, by redefining the center of mass and charge dynamics.

Proposed method

• Defining the kinematical state of an elementary particle through the consistent measurement by consecutive inertial observers.
• Modeling the electron as a point charge with a velocity eigenvalue of ±c, derived from the Dirac equation’s α matrices.
• Introducing zitterbewegung as a high-frequency oscillation of the position operator, with amplitude ~ħ/mc (Compton wavelength scale).
• Using a rotating structure model where spin arises from angular momentum of a charge rotating at speed c, with frequency ν = mc²/h.
• Deriving classical expressions for electric and magnetic dipole moments from time-averaged fields of the oscillating charge.
• Formulating a Lagrangian for spinning systems, including the photon as a massless, spin-1 system with H² − P²c² = 0.

Experimental results

Research questions

• RQ1 How can a classical model of the electron reproduce the intrinsic spin-1/2 and magnetic moment without quantum postulates?
• RQ2 What is the classical origin of zitterbewegung, and how does it relate to the Compton wavelength and relativistic velocity?
• RQ3 Can the classical motion of a charge undergoing zitterbewegung produce a time-averaged field that matches the Coulomb and magnetic dipole fields of the electron?
• RQ4 How does the classical model resolve the radiation paradox of an accelerated charge while preserving energy conservation?
• RQ5 What classical dynamics underlie the photon’s spin and massless nature in this framework?

Key findings

• The zitterbewegung motion of the electron’s position at speed c produces a classical oscillation with amplitude ~ħ/mc, matching the Compton wavelength.
• The time-averaged electric field of the oscillating charge is Coulomb-like at distances ≥3 Compton wavelengths and vanishes at the origin, avoiding singularities.
• The time-averaged magnetic field corresponds exactly to a magnetic dipole moment μ = eħ/2m at the origin, matching the Bohr magneton.
• The classical model predicts that spin and magnetic moment are parallel for both electrons and positrons, contradicting the usual quantum picture but consistent with time-averaged dynamics.
• The model allows classical tunneling for properly polarized electrons and predicts bound states of spin-1 from electron pairs, suggesting relevance to ferromagnetic superconductors.
• The photon is described as a massless spinning system with H² − P²c² = 0, where spin arises from circular motion at speed c with frequency ν = mc²/h (zero mass limit).