Electrodynamics in accelerated frames revisited

TL;DR

This paper reformulates Maxwell's equations in accelerated frames using tetrad fields, clarifying electromagnetic paradoxes by disentangling coordinate and frame transformations to compare fields in different reference frames.

Contribution

It introduces a novel approach to analyze electromagnetic fields in accelerated frames by separating coordinate and frame transformations, providing new insights into classical paradoxes.

Findings

Fields in inertial and accelerated frames are described in the same coordinate system.

The approach clarifies differences in electromagnetic radiation between frames.

It offers a new perspective on classical electromagnetic paradoxes.

Abstract

Maxwell's equations are formulated in arbitrary moving frames by means of tetrad fields, which are interpreted as reference frames adapted to observers in space-time. We assume the existence of a general distribution of charges and currents in an inertial frame. Tetrad fields are used to project the electromagnetic fields and sources on accelerated frames. The purpose is to study several configurations of fields and observers that in the literature are understood as paradoxes. For instance, are the two situations, (i) an accelerated charge in an inertial frame, and (ii) a charge at rest in an inertial frame described from the perspective of an accelerated frame, physically equivalent? Is the electromagnetic radiation the same in both frames? Normally in the analysis of these paradoxes the electromagnetic fields are transformed to (uniformly) accelerated frames by means of a coordinate transformation of the Faraday tensor. In the present approach coordinate and frame transformations are disentangled, and the electromagnetic field in the accelerated frame is obtained through a frame (local Lorentz) transformation. Consequently the fields in the inertial and accelerated frames are described in the same coordinate system. This feature allows the investigation of paradoxes such as the one mentioned above.