  We prove that the classical Dirac equation in the presence of an external
(nondynamical) electromagnetic field is a relativistically causal theory. As a
corollary, we show that it is impossible to use quantum tunneling to transmit
particles or information faster than light. When an electron tunnels through a
barrier, it is bound to remain within its future light cone. In conclusion, the
relativistic quantum tunneling (if modeled using the Dirac equation) is an
entirely subluminal process, and it is not instantaneous.
