Why Gauge?

TL;DR

The paper asks why gauge theories dominate our description of nature and argues that gauge is not mere mathematical redundancy but encodes relational structure across subsystems. It develops a relational, partial-observables framework in which gauge-variant quantities are measurable only through coupling to apparatus, not predicted by isolated dynamics. Through a simple coupling model and discussions of general relativity, Yang-Mills theory, and time as a gauge degree of freedom, it shows how relational observables arise and how boundary-formalism formalizes measurements. This perspective unifies the treatment of localization, coupling, and measurement in gauge theories, explaining gauge ubiquity while noting open questions in quantum contexts.

Abstract

The world appears to be well described by gauge theories; why? I suggest that gauge is more than mathematical redundancy. Gauge-dependent quantities can not be predicted, but there is a sense in which they can be measured. They describe "handles" though which systems couple: they represent real relational structures to which the experimentalist has access in measurement by supplying one of the relata in the measurement procedure itself. This observation leads to a physical interpretation for the ubiquity of gauge: it is a consequence of a relational structure of physical quantities.