  We challenge the widespread belief, originated by Newton and Wigner (Rev.
Mod. Phys, 21, 400 (1949)) that the incorporation of special relativity into
quantum mechanics implies that a massive particle cannot be localized within an
arbitrarily small spatial extent, that there is a minimum width approximately
equal to the Compton wavelength. Our argument is in four parts. First, the
scalar function used by Newton and Wigner as a measure of localization is not a
position probability amplitude. The correct relativistic position probability
amplitude becomes a delta function for a state vector localized according to
the criteria of Newton and Wigner. Second, the possibility of Lorentz
contraction as observed from a boosted frame means that the wavepacket width in
the boost direction can take arbitrarily small values. Third, we refer to the
work of Almeida and Jabs (Am. J. Phys. 52, 921 (1984)) who show that the long
time wavepacket spreading rate for relativistic position probability amplitudes
is always less than the speed of light no matter how small the initial width of
the wavepacket. Lastly, we show that it is a simple matter to construct scalar
amplitudes with spatial widths smaller than the supposed minimum.
