Clara Bradley

Gauge theories are often characterized as possessing ‘redundancy’ or ‘excess structure’. This, in turn, motivates reducing the gauge symmetries, commonly through ‘symplectic reduction’ in the Hamiltonian framework. However, there are multiple ways to formulate a Hamiltonian gauge theory. This paper examines the relationship between the formulation of a Hamiltonian gauge theory and the attribution of excess structure. I argue that one can formulate a Hamiltonian gauge theory such that symplectic reduction does not remove structure, and therefore that the role of symplectic reduction cannot be purely to remove ‘excess structure’. I discuss in what sense symplectic reduction is thereby motivated.

In this article, I give a counterexample to a claim made in that empirically equivalent theories can often be regarded as theoretically equivalent by treating one as having surplus structure, thereby overcoming the problem of underdetermination of theory choice. The case I present is that of Lorentz's ether theory and Einstein's theory of special relativity. I argue that Norton's suggestion that surplus structure is present in Lorentz's theory in the form of the ether state of rest is based on a misunderstanding of the role that the ether plays in Lorentz's theory, and that in general, consideration of the conceptual framework in which a theory is embedded is vital to understanding the relationship between different theories.

We address a recent proposal concerning ‘surplus structure’ due to Nguyen et al.. We argue that the sense of ‘surplus structure’ captured by their formal criterion is importantly different from—and in a sense, opposite to—another sense of ‘surplus structure’ used by philosophers. We argue that minimizing structure in one sense is generally incompatible with minimizing structure in the other sense. We then show how these distinctions bear on Nguyen et al.’s arguments about Yang-Mills theory and on the hole argument.