What Price Fiber Bundle Substantivalism? On How to Avoid Holes in Fibers

TL;DR

This paper examines the philosophical implications of fiber bundle structures in physics, proposing a method to reformulate gauge theories and general relativity that avoids the hole argument and substantivalist issues.

Contribution

It introduces the Dressing Field Method as a way to reformulate gauge and gravitational theories invariantly, addressing hole arguments and substantivalist concerns.

Findings

Dressing Field Method provides a gauge-invariant reformulation.

Reformulation clarifies the conceptual structure of gauge and gravitational theories.

Method helps avoid hole-type arguments in fiber bundle frameworks.

Abstract

On a mathematically foundational level, our most successful physical theories (gauge field theories and general-relativistic theories) are formulated in a framework based on the differential geometry of connections on principal bundles. After reviewing the essentials of this framework, we articulate the generalized hole and point-coincidence arguments, examining how they weight on a substantivalist position towards bundle spaces. This question, then, is considered in light of the Dressing Field Method, which allows a manifestly invariant reformulation of gauge field theories and general-relativistic theories, making their conceptual structure more transparent: it formally implements the point-coincidence argument and thus allows to define (dressed) fields and (dressed) bundle spaces immune to hole-type arguments.