# Equivalence and Duality in Electromagnetism

## TL;DR

This paper examines electromagnetic duality through the lens of philosophical and mathematical frameworks, revealing that while it fits some notions of equivalence, it does not preserve empirical content, raising questions about its interpretation.

## Contribution

It applies the concept of categorical equivalence to electromagnetic duality and analyzes its limitations in preserving empirical content.

## Key findings

- Electromagnetic duality fits categorical equivalence but fails to preserve empirical content.
- Duality maps models to models with dual empirical content, not identical.
- Discussion on how to interpret dualities that do not preserve empirical content.

## Abstract

In this paper I bring the recent philosophical literature on theoretical equivalence to bear on dualities in physics. Focusing on electromagnetic duality, which is a simple example of S-duality in string theory, I will show that the duality fits naturally into at least one framework for assessing equivalence---that of categorical equivalence---but that it fails to meet a necessary condition for equivalence on that account. The reason is that the duality does not preserve "empirical content" in the required sense; instead, it takes models to models with "dual" empirical content. I conclude by discussing how one might react to this.