Backflow in relativistic wave equations

TL;DR

This paper demonstrates that backflow is a common feature of wave solutions in both classical and quantum relativistic theories, challenging the notion that it is exclusively nonclassical.

Contribution

It provides simple solutions to relativistic wave equations showing backflow as a universal wave phenomenon, not limited to quantum mechanics.

Findings

Backflow occurs in solutions to Dirac, Maxwell, and gravity wave equations.

Backflow is not a nonclassical effect but a characteristic of wave equations.

The phenomenon appears in both classical and quantum relativistic contexts.

Abstract

We show that, contrary to the statements made by many authors, the backflow is not a nonclassical effect. The backflow is a characteristic feature of solutions of the wave equations: quantum and classical. We present simple solutions of the Dirac equation, Maxwell equations and equations of linearized gravity where the backflow phenomenon is clearly seen. In this work we describe backflow in relativistic theories but this phenomenon can occur in the solutions of all kinds of wave equations: quantum and classical.