On the Equivalence Principle and Electrodynamics of Moving Bodies

TL;DR

This paper extends Einstein's elevator thought experiment to charged bodies in electromagnetic fields, deriving an observer-dependent metric that reproduces the Lorentz-force law and aspects of radiation reaction, linking gravity and electromagnetism.

Contribution

It introduces a novel approach to incorporate electromagnetic effects into the equivalence principle by deriving an observer-dependent metric that aligns with charged particle trajectories.

Findings

Derived an observer-dependent metric consistent with electromagnetic forces.

Reproduced the Lorentz-force law within a geometric framework.

Connected radiation reaction effects to the extended equivalence principle.

Abstract

We consider a certain extension of the Einstein's elevator thought experiment by assuming that the elevator is charged and falls into an electromagnetic field. We argue, on grounds of the Equivalence Principle, that an observer-dependent metric should exist, for which the geodesics coincide with the trajectories of the charged body in the electromagnetic field. We give a solution to this problem by finding such a metric and hence we are able to recover the Lorentz-force law. Recovery of the leading terms of the radiation reaction force is also possible with this approach.