Mathisson's helical motions for a spinning particle --- are they unphysical?

TL;DR

This paper defends the physical validity of Mathisson's helical motions for spinning particles, clarifying misconceptions about their size and linking their frequency to electron zitterbewegung.

Contribution

It demonstrates that helical motions are physically valid, confined, and gauge-dependent, and connects their frequency to relativistic quantum phenomena.

Findings

Helical motions have finite radius within the centroid disk.

They are gauge-equivalent descriptions of spinning particle motion.

Helical motion frequency matches the electron zitterbewegung frequency.

Abstract

It has been asserted in the literature that Mathisson's helical motions are unphysical, with the argument that their radius can be arbitrarily large. We revisit Mathisson's helical motions of a free spinning particle, and observe that such statement is unfounded. Their radius is finite and confined to the disk of centroids. We argue that the helical motions are perfectly valid and physically equivalent descriptions of the motion of a spinning body, the difference between them being the choice of the representative point of the particle, thus a gauge choice. We discuss the kinematical explanation of these motions, and we dynamically interpret them through the concept of hidden momentum. We also show that, contrary to previous claims, the frequency of the helical motions coincides, even in the relativistic limit, with the zitterbewegung frequency of the Dirac equation for the electron.