The Problem of Motion: The Statistical Mechanics of Zitterbewegung

TL;DR

This paper explores the concept of Zitterbewegung, proposing that observed particle velocities are time-averaged effects of underlying motion at the speed of light, and derives the relativistic velocity addition rule from this perspective.

Contribution

It introduces a statistical mechanics approach to Zitterbewegung, deriving relativistic velocity addition from probabilistic considerations of light-speed motion.

Findings

Velocity eigenvalues are ±c for Dirac wavepackets.

Observed velocities are long-term averages of light-speed zig-zag motion.

Relativistic velocity addition rule is derived from probability of left/right motion.

Abstract

Around 1930, both Gregory Breit and Erwin Schroedinger showed that the eigenvalues of the velocity of a particle described by wavepacket solutions to the Dirac equation are simply $\pm$c, the speed of light. This led Schroedinger to coin the term Zitterbewegung, which is German for "trembling motion", where all particles of matter (fermions) zig-zag back-and-forth at only the speed of light. The result is that any finite speed less than $c$, including the state of rest, only makes sense as a long-term average that can be thought of as a drift velocity. In this paper, we seriously consider this idea that the observed velocities of particles are time-averages of motion at the speed of light and demonstrate how the relativistic velocity addition rule in one spatial dimension is readily derived by considering the probabilities that a particle is observed to move either to the left or to the right at the speed of light.