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arXiv · 1411.1854

The Problem of Motion: The Statistical Mechanics of Zitterbewegung

Kevin H. Knuth
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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.

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Kevin H. Knuth. 2014-12-19. The Problem of Motion: The Statistical Mechanics of Zitterbewegung. https://doi.org/10.1063/1.4906026

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