The hidden geometry of electromagnetism

TL;DR

This paper investigates a hidden geometric structure in electromagnetic field lines that could potentially eliminate singularities in classical electrodynamics and address the self-force problem.

Contribution

It introduces a novel geometric perspective on electromagnetic fields that aims to resolve classical singularities and self-force issues.

Findings

Preliminary results suggest a new geometric framework for electromagnetic fields.

Potential to eliminate singularities in classical electrodynamics.

Progress towards a consistent treatment of self- and external fields.

Abstract

Nearly all field theories suffer from singularities when particles are introduced. This is true in both classical and quantum physics. Classical field singularities result in the notorious self-force problem, where it is unknown how the dynamics of a particle change when the particle interacts with its own (self) field. Self-force is a pressing issue and an active research topic in gravitational phenomena, as well as a source of controversies in classical electromagnetism. In this work, we study a hidden geometrical structure manifested by the electromagnetic field-lines that has the potential of eliminating all singularities from classical electrodynamics. We explore preliminary results towards a consistent way of treating both self- and external fields.