The Problem of Motion: The Statistical Mechanics of Zitterbewegung
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 ±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.
Knuth K.H. 2015. The problem of motion: the statistical mechanics of Zitterbewegung. Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Amboise, France, Sept 2014, AIP Conference Proceedings, American Institute of Physics, Melville NY. arXiv:1411.1854 [quant-ph]