Electric charge in hyperbolic motion: the early history

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.

Electric charge in hyperbolic motion: the special conformal transformation solution

“…The electromagnetic field produced by an electric charge in hyperbolic motion was calculated a long time ago by Sommerfeld [5], based on the retarded electromagnetic four-potential of Liénard and Wiechert. His geometrical derivation takes place in Minkowski space, where a point has coordinates (x, y, z, ict).…”

“…The same Minkowski metric applies to both Minkowski space and flat conformal space. The notation, the Minkowski diagrams, and the calculations in this paper are related to calculations from 'Electric charge in hyperbolic motion: the early history' [8], and a reading of this article is suggested before proceeding further.…”

“…as explained in 'Electric charge in hyperbolic motion: the early history' [8]. Assuming that e>0, the magnitude of the electric field is…”