Electric charge in hyperbolic motion: arcane geometrical aspects

TL;DR

This paper explores the geometrical aspects of an electric charge in hyperbolic motion, emphasizing a time symmetric formulation that relates to electrostatic four-force calculations.

Contribution

It introduces a geometrical model using infinitesimal worldline elements and connects it to Fokker's time symmetric electrostatic four-force.

Findings

The geometrical model closely matches electrostatic four-force calculations.

Time symmetric formulation offers advantages in describing electrodynamic interactions.

The approach provides new insights into the geometry of charges in hyperbolic motion.

Abstract

We look at an electric charge in hyperbolic motion, and we describe some arcane geometrical aspects of the electrodynamic interaction. We discuss the advantages of a time symmetric formulation in which the material point particles are replaced by infinitesimal length elements along their worldlines. We show that the four-force obtained from our geometrical model is very closely related to the "electrostatic" four-force obtained from Fokker's time symmetric action.