  Two related problems in relativistic quantum mechanics, the apparent
superluminal propagation of initially localized particles and dependence of
spatial localization on the motion of the observer, are analyzed in the context
of Dirac's theory of constraints. A parametrization invariant formulation is
obtained by introducing time and energy operators for the relativistic particle
and then treating the Klein-Gordon equation as a constraint. The standard,
physical Hilbert space is recovered, via integration over proper time, from an
augmented Hilbert space wherein time and energy are dynamical variables. It is
shown that the Newton-Wigner position operator, being in this description a
constant of motion, acts on states in the augmented space. States with strictly
positive energy are non-local in time; consequently, position measurements
receive contributions from states representing the particle's position at many
times. Apparent superluminal propagation is explained by noting that, as the
particle is potentially in the past (or future) of the assumed initial place
and time of localization, it has time to propagate to distant regions without
exceeding the speed of light. An inequality is proven showing the Hegerfeldt
paradox to be completely accounted for by the hypotheses of subluminal
propagation from a set of initial space-time points determined by the quantum
time distribution arising from the positivity of the system's energy. Spatial
localization can nevertheless occur through quantum interference between states
representing the particle at different times. The non-locality of the same
system to a moving observer is due to Lorentz rotation of spatial axes out of
the interference minimum.
