  It is known that relativistic wavefunctions formally propagate beyond the
light cone when the propagator is limited to the positive energy sector. By
construction, this is the case for solutions of the Salpeter (or relativistic
Schr\"odinger) equation or for Klein-Gordon and Dirac wavefunctions defined in
the Foldy-Wouthuysen representation. In this work we investigate quantitatively
the degree of non-causality for free propagation for different types of
wavepackets all having initially a compact spatial support. In the studied
examples we find that non-causality appears as a small transient effect that
can in most cases be neglected. We display several numerical results and
discuss the fundamental and practical consequences of our findings concerning
this peculiar dynamical feature.
