  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.
