On Degenerate Metrics and Electromagnetism

TL;DR

This paper develops a theory of degenerate metrics to unify gravity and electromagnetism, recovering Maxwell's theory with modifications at small scales and proposing a regular Coulomb potential.

Contribution

It introduces a novel degenerate metric framework that unifies gravitation and electromagnetism without ad hoc assumptions about extra dimensions.

Findings

Maxwell's theory is recovered at large scales.

A new regular Coulomb potential formula is derived.

Differences from standard electromagnetism appear only at very small scales.

Abstract

A theory of degenerate metrics is developed and applied to the problem of unifying gravitation with electromagnetism. The approach is similar to the Kaluza-Klein approach with a fifth dimension, however no ad hoc conditions are needed to explain why the extra dimension is not directly observable under everyday conditions. Maxwell's theory is recovered with differences only at very small length scales, and a new formula is found for the Coulomb potential that is regular everywhere.