Subluminality of relativistic quantum tunneling

Abstract

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.Comment: 14 pages, 6 figures, published on PRA (see https://doi.org/10.1103/PhysRevA.107.032209