# Electrodynamics and time orientability

## TL;DR

This paper develops a classical framework linking non-time-orientable spacetimes with electromagnetism and gravity, deriving Maxwell's equations and unifying them with general relativity through a U(1) bundle construction.

## Contribution

It introduces a novel classical approach using U(1) bundles on non-time-orientable spacetimes to derive electromagnetism and Einstein-Maxwell equations, explaining electric charge emergence.

## Key findings

- Maxwell's equations derived from spacetime topology
- Electric charges arise naturally from boundary conditions
- Unification of gravity and electromagnetism via topological constraints

## Abstract

On spacetimes that are not time orientable we construct a U(1) bundle to measure the twisting of the time axis. This single assumption, and simple construction, gives rise to Maxwell's equations of electromagnetism, the Lorentz force law and the Einstein-Maxwell equations for electromagnetism coupled to General relativity. The derivations follow the Kaluza Klein theory, but with the constraints required for connections on a U(1) bundle rather than five spacetime dimensions. The non time orientability is seen to justify and constrain Kaluza Klein theories exactly as required to unify gravitation with electromagnetism. Unlike any other schemes, apparent net electric charges arise naturally because the direction of the electric field reverses along a time reversing path. The boundary of a time reversing region can therefore have a net electric flux and appear exactly as a region containing an electric charge. The treatment is purely classical, but motivated by links between acausal structures and quantum theory.