  We exploit the reparametrization symmetry of a relativistic free particle to
impose a gauge condition which upon quantization implies space-time
noncommutativity. We show that there is an algebraic map from this gauge back
to the standard `commuting' gauge. Therefore the Poisson algebra, and the
resulting quantum theory, are identical in the two gauges. The only difference
is in the interpretation of space-time coordinates. The procedure is repeated
for the case of a coupling with a constant electromagnetic field, where the
reparametrization symmetry is preserved. For more arbitrary interactions, we
show that standard dynamical system can be rendered noncommutative in space and
time by a simple change of variables.
