Unification of Force and Substance

TL;DR

This paper explores the deep significance of gauge invariance in Maxwell's equations, discusses its role in unifying fundamental physics, and considers future prospects for further unification inspired by this concept.

Contribution

It provides a broad interpretation of gauge invariance's physical meaning and discusses potential future unification theories building on Maxwell's foundational ideas.

Findings

Gauge invariance has profound physical significance.

Potential for new unification theories based on gauge symmetry.

Maxwell's vision of unity may be realized at a deeper level.

Abstract

Maxwell's mature presentation of his equations emphasized the unity of electromagnetism and mechanics, subsuming both as "dynamical systems". That intuition of unity has proved both fruitful, as a source of pregnant concepts, and broadly inspiring. A deep aspect of Maxwell's work is its use of redundant potentials, and the associated requirement of gauge symmetry. Those concepts have become central to our present understanding of fundamental physics, but they can appear to be rather formal and esoteric. Here I discuss two things: The physical significance of gauge invariance, in broad terms; and some tantalizing prospects for further unification, building on that concept, that are visible on the horizon today. If those prospects are realized, Maxwell's vision of the unity of field and substance will be brought to a new level.