On the foundations and necessity of classical gauge invariance

TL;DR

This paper argues that gauge invariance in classical field theories arises from measurement limitations, introducing a new geometric framework that generalizes principal fiber bundles to accommodate novel models with variable metrics and interaction speeds.

Contribution

It provides a foundational perspective on gauge invariance as a consequence of measurement constraints and introduces a generalized geometric model for classical field theories.

Findings

Gauge invariance stems from measurement limitations.

New models with signature-changing metrics are proposed.

Generalized principal fiber bundles are introduced.

Abstract

We argue that, ideally, the ways to measure magnitudes in non-quantum theories of physics (spacetime, field theory), limit drastically their possible mathematical models. In particular, gauge invariance in the Yang-Mills framework, is a necessity of our way of measuring rather than an a priori imposition on symmetry. A general postulational basis for the geometric aspects of classical field theories is introduced, and the permitted models are studied. Some of them (for example, compatible with signature-changing metrics or variations of the speed of interactions) are new, and require a generalization of the concept of principal fiber bundle, which may be of interest both, physically and mathematically.