Infrared Lorentz Violation and Slowly Instantaneous Electricity

TL;DR

This paper explores a Lorentz-violating modification of electromagnetism where electromagnetic waves are massive but static Coulomb forces remain unchanged, allowing for faster-than-light electrical signal transmission over large distances.

Contribution

It introduces a novel Lorentz-violating theory where electromagnetic waves are massive yet Coulomb forces are unaffected, enabling instantaneous electrical communication at large scales.

Findings

Photon Compton wavelength bound of 6000 km

Electromagnetic signals can be transmitted instantly over large distances

Coulomb force remains Coulomb despite wave mass

Abstract

We study a modification of electromagnetism which violates Lorentz invariance at large distances. In this theory, electromagnetic waves are massive, but the static force between charged particles is Coulomb not Yukawa. At very short distances the theory looks just like QED. But for distances larger than 1/m the massive dispersion relation of the waves can be appreciated, and the Coulomb force can be used to communicate faster than the speed of light. In fact, electrical signals are transmitted instantly, but take a time ~ 1/m to build up to full strength. After that, undamped oscillations of the electric field are set in and continue until they are dispersed by the arrival of the Lorentz-obeying part of the transmission. We study experimental constraints on such a theory and find that the Compton wavelength of the photon may be as small as 6000 km. This bound is weaker than for a Lorentz-invariant mass, essentially because in our case the Coulomb constraint is removed.