Subluminality of relativistic quantum tunneling

TL;DR

This paper proves that relativistic quantum tunneling, modeled by the Dirac equation, cannot transmit particles or information faster than light, confirming it as a subluminal process consistent with causality.

Contribution

It demonstrates that the Dirac equation ensures relativistic causality in quantum tunneling, ruling out superluminal transmission of particles or information.

Findings

Quantum tunneling is subluminal when modeled with the Dirac equation.

Particles remain within their future light cone during tunneling.

Quantum tunneling does not allow faster-than-light communication.

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.