  In relativistic theories the principle of microscopic causality states that
``information cannot travel faster than the speed of light'' \cite{kaku}. In
the present work we show that the time evolution of relativistic wave functions
violates this principle. We consider here the wave functions of massless and
massive particles. In the case of massless particles the wave functions which
violate the microscopic causality have an analytic form while in the case of
massive particles we have to rely on numerical calculations. In both cases the
wave functions which are strictly localized at $t=0$, at later times do not
vanish {\it outside} the future light cone. \end{abstract}
