Electrodynamics with a Future Conformal Horizon

TL;DR

This paper explores the implications of future conformal singularities on electrodynamics and cosmology, revealing a connection between electromagnetic and cosmological arrows of time and highlighting conditions for their compatibility.

Contribution

It introduces a novel analysis of future conformal horizons and their impact on time symmetry in electrodynamics, linking cosmological singularities with electromagnetic phenomena.

Findings

Compatibility between metric and time reversal symmetry requires a singular event or non-trivial topology.

The conformal singularity acts as a time-like mirror affecting electromagnetic and cosmological arrows of time.

Replacing the future absorber with a cosmological mirror conflicts with observations unless matter is strongly electromagnetically bound.

Abstract

We investigate the impact of singularities occurring at future times in solutions of the Friedmann equations expressed in conformal coordinates. We focus on the consequences of extending the time coordinate through the singularity for the physics of matter and radiation occupying just one side. Mostly this involves investigation of the relationship between the metric with line element ds^2 = a^2(t) * (dt^2 - dx^2) and time reversal symmetry within electrodynamics. It turns out compatibility between these two is possible only if there is a singular physical event at the time of the singularity or if the topology is not trivial. In both cases the singularity takes on the appearance of a time-like mirror. We are able to demonstrate a relationship between the broken time symmetry in electrodynamics characterized by retarded radiation and radiation reaction and the absolute conformal time relative to the time of the singularity, i.e. between the Electromagnetic and Cosmological arrows of time. It is determined that the Wheeler-Feynman reasoning but with the future absorber replaced by the Cosmological mirror leads to a conflict with observation unless matter is electromagnetically strongly bound to the environment.