Spreading of relativistic probability densities and Lorentz contraction

TL;DR

This paper derives the laws governing the spreading of relativistic probability densities for a massive particle and demonstrates Lorentz contraction of wavepackets, with implications for particle accelerator design.

Contribution

It provides new analytical laws for the spreading of relativistic wavepackets and confirms Lorentz contraction in quantum probability amplitudes.

Findings

Minimal spreading over long times when momentum width is small

Lorentz contraction of wavepackets demonstrated

Potential applications in particle accelerator technology

Abstract

We find the laws for the spreading of the spatial widths (parallel and transverse to the direction of average motion) of the relativistic position probability density for a massive, spinless particle. We find that when the momentum width of the wavepacket is small compared to the average momentum, there is a long time over which spreading is minimal. This result may be useful in particle accelerator design. We also demonstrate the Lorentz contraction of a wavepacket using relativistic probability amplitudes.