Comment on ``The Avez-Seifert theorem for the relativistic Lorentz force equation'' and other related works

Abstract

There exist several approaches that investigate the connectedness of spacetime events through solutions of the Lorentz force equation. These approaches separate into three categories, that consider different equations. We clarify the physical meaning of each equation showing that only one method is based on the Lorentz force equation. The other two approaches lead respectively to a less restrictive equation that defines an electromagnetic flow on the cotangent fiber bundle, or to an unphysical constraint between charge-to-mass ratio and proper length of the solution. We outline the physical meaning of each approach studying the variational formulations and clarifying the results obtained in the explored directions.