# Theoretical Equivalence and Duality

## TL;DR

This paper explores the relationship between theoretical equivalence and duality, proposing that duality's schema implies an isomorphism-based construal of equivalence, with applications to Maxwell's electromagnetic theory.

## Contribution

It clarifies how duality informs a model-based understanding of theoretical equivalence, extending the schema's interpretative constraints to physical sciences.

## Key findings

- Duality suggests an isomorphism-based view of equivalence.
- The schema's interpretative constraints are applicable to physical theories.
- Illustrations include various formulations of Maxwell's electromagnetic theory.

## Abstract

Theoretical equivalence and duality are two closely related notions: but their interconnection has so far not been well understood. In this paper I explicate the contribution of a recent schema for duality to discussions of theoretical equivalence. I argue that duality suggests a construal of theoretical equivalence in the physical sciences. The construal is in terms of the isomorphism of models, as defined by the Schema. This construal entails interpretative constraints that should be useful for theoretical equivalence more generally. I illustrate the construal in various formulations of Maxwell's electromagnetic theory.