# Faster-than-light signalling in the rotating-wave approximation

## TL;DR

This paper investigates causality violations caused by the rotating wave approximation in quantum optics, revealing that these violations decay polynomially with distance and persist even over long interaction times, challenging the approximation's compatibility with relativity.

## Contribution

The study demonstrates that the rotating wave approximation leads to polynomially decaying causality violations that do not vanish over long times, questioning its use in relativistic regimes.

## Key findings

- Causality violations have fat tails, decaying polynomially with distance.
- Violations persist even in long interaction time regimes.
- The approximation is unsuitable where relativistic causality is critical.

## Abstract

We present new results on the causality violations introduced by the rotating wave approximation commonly used in quantum optics and high-energy physics. We find that the causality violations and faster-than-light signalling induced by the approximation have `fat tails', i.e., they are polynomially decaying with the distance from the light-cone of the emitter. Furthermore, we also show that the fundamental problems with the incompatibility between the approximation and relativity are not cured even in the long interaction time regime (where the approximation is often taken). This renders the approximation unsuitable for any regime where we are concerned about relativistic causality and information transmission via the electromagnetic field.