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.
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I would like to express my deep gratitude to Yemima Ben-Menahem and Daniel Rohrlich for their guidance and advice. I thank Yakir Aharonov, Merav Hadad, Ran Lanzet, and Holger Lyre for helpful discussions and comments, and to anonymous reviewers and an editor of the British Journal for the Philosophy of Science for valuable feedback. This publication was made possible through the support of grants from the John Templeton Foundation (Project ID 43297) and the Israel Science Foundation (grant no. 1190/13). The opinions expressed in this publication are those of the author.
© The Authors. Published by The University of Chicago Press for The British Society for the Philosophy of Science.