On the Equivalence Principle and Electrodynamics of Moving Bodies

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.