| Summary: | <p>Gauge theories, by which I mean theories with local dynamical symmetries, are ubiquitous in modern physics, extending across quantum chromodynamics, electromagnetism and (arguably) general relativity. Often philosophers also use the term ‘gauge’ in a broader sense as referring to those theories which contain superfluous structure or, in John Earman’s memorable words, ‘descriptive fluff’. In this sense, symmetries relate models which represent the same physical possibility; I call these <em>invariance symmetries</em>. It is an interesting feature of our theories that gauge symmetries are naturally interpreted as invariance symmetries.</p> <p>An important debate concerns the status of quantities which are not invariant under invariance symmetries, i.e. quantities whose values differ across symmetry-related models. The orthodox position is that such quantities are not physically real, irrespective of their role in theoretical models: this is called the <em>Invariance Principle</em>. However, a question which has not received much attention is whether non-invariant quantities are <em>explanatory</em>. In other words, can interpreting such quantities as physically real increase the explanatory strength of our theories? It is surprising that the relation between invariance and explanation has received so little attention, given that an important reason for interpreting theories is to <em>explain</em> their empirically successful predictions.</p> <p>In this thesis I intend to explore the relation between invariance and explanation, specifically with respect to gauge quantities. The question I set out to answer is: <em>can gauge-dependent quantities play an indispensable role in scientific explanations?</em> This investigation is pressing because if gauge quantities are explanatory, then there are good reasons to interpret them as physically real, contrary to the widely-held Invariance Principle.</p> <p>The standard arguments for the Invariance Principle take the form of a dilemma: either symmetry-related models represent distinct possibilities, or only invariant quantities are physically real. I call the former option absolutism. For example, if there exist absolute positions, then models related by spacetime symmetries represent distinct possibilities. It is argued that absolutism has undesirable consequences, such as undetectability and ind terminism (e.g. the Hole Argument). This leads to the other horn of the dilemma, which necessitates the search for novel ontological posits which are invariant under symmetries. As these are relational quantities, such as relative distances, this position is called <em>relationism</em>.</p> <p>I will argue that this is a false dilemma. In the course of this argument, I develop a novel approach to the interpretation of (gauge) quantities called <em>Quantity-Value Conventionalism</em>. Conventionalism allows us to to interpret non-invariant quantities as physically real without being committed to considering symmetry-related models as physically distinct. It thus avoids theoretical vices such as indeterminism. Quantity-Value Conventionalism is opposed to what I call <em>Quantity-Value Literalism</em>, which is the view that all quantities have determinate values and of which both absolutism and relationism are instances.</p> <p>I then argue in favour of Quantity-Value Conventionalism on the basis that realist interpretations of gauge quantities increase the explanatory strength of our theories. The general claim is that non-invariant quantities explain cosmic coincidences in the instantiation patterns of relational quantities. I develop these arguments in detail with a case study of the Aharonov-Bohm effect, in which I defend a conventionalist interpretation of the gauge-dependent vector potential field. The conclusion of this study is that the vector potential field is a physically real field which interacts with the electron wavefunction to cause the Aharonov-Bohm effect.</p>
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