Space and time ambiguities in vacuum electrodynamics

TL;DR

The paper introduces a transformation in vacuum electrodynamics that exchanges space and time roles, resulting in a new Lorentzian metric influenced by the electromagnetic field, with potential applications and implications discussed.

Contribution

It presents a novel transformation that maps electromagnetic fields to new metrics with exchanged space-time roles, expanding understanding of vacuum electrodynamics.

Findings

The transformation produces a Lorentzian metric depending on the electromagnetic solution.

Examples demonstrate explicit computation and analysis of the new metrics.

Discussion includes potential applications and future research directions.

Abstract

It is shown that every regular electromagnetic field in vacuum identically satisfy Maxwell equations in a new manifold where the roles of space and time have been exchanged. The new metric is Lorentzian, depends on the particular solution and forces the flow of time to tilt somehow in the direction of the field lines. We give a detailed description of the transformation and discuss several of its properties, both in the algebraic and differential settings. Examples are given where the new metrics are explicitly computed and carefully analyzed. We conclude with possible applications of the transformation as well as future perspectives.