Gauge and Ghosts

This article suggests a fresh look at gauge symmetries, with the aim of drawing a clear line between the a priori theoretical considerations involved, and some methodological and empirical non-deductive aspects that are often overlooked. The gauge argument is primarily based on a general symmetry principle expressing the idea that a change of mathematical representation should not change the form of the dynamical law. In addition, the ampliative part of the argument is based on the introduction of new degrees of freedom into the theory according to a methodological principle that is formulated here in terms of correspondence between passive and active transformations. To demonstrate how the two kinds of considerations work together in a concrete context, I begin by considering spatial symmetries in mechanics. I suggest understanding Mach’s principle as a similar combination of theoretical, methodological and empirical considerations, and demonstrate the claim with a simple toy model. I then examine gauge symmetries as a manifestation of the two principles in a quantum context. I further show that in all of these cases the relational nature of physically significant quantities can explain the relevance of the symmetry principle and the way the methodology is applied. In the quantum context, the relevant relational variables are quantum phases.1 Introduction 2 Spatial Symmetries and Their Methodological Role 2.1A symmetry principle2.2A methodological principle2.3A ghost in classical mechanics 3 A Toy Theory 4 Quantum Theory and Gauge Symmetries 4.1The representations of a quantum system4.2Relative variables: quantum phases4.3Gauge transformations 5 The Gauge Argument 5.1The gauge argument: what makes it work?5.2Interpretation and observability of gauge symmetries