Symmetries in physics, metaphysics, and logic

Thesis

This thesis examines the idea that when a physical theory contains symmetries, the theory should be interpreted in such a way that symmetry-related models represent the same physical state of affairs. It argues that we can best do so by drawing on analogies to ideas in philosophy of logic and language: specifically, by thinking of symmetries as a means of translating a theory into itself. It consists of six chapters, together with an introduction and conclusion.

In Chapter 1, I set up the main ideas needed to more precisely frame the question at hand: namely, the notions of symmetry, interpretation, and possibility. I make some remarks about how I take these to be connected.

In Chapter 2, I argue that isomorphic models should be interpreted as equivalent. After giving some motivations for doing so, I consider the main obstruction: how to provide an account of de re modality. I review how counterpart theory may be used to overcome this obstruction, and clarify how counterpart theory relates to other positions in the debate over modality de re.

In Chapter 3, I show that the metaphysical debate over quidditism can be made precise by drawing on notions of translation from model theory, and argue in favour of an anti-quidditist attitude towards interpreting theories. I then consider the special case of translating a theory into itself: how such a theory should be interpreted, and what reformulations of the theory such an interpretation suggests.

In Chapter 4, I turn my attention to physics. I define the notion of an internal symmetry for a theory, and argue that they may be regarded as translations from a theory into itself (in the sense of Chapter 3); and, hence, that symmetry-related models should be interpreted as equivalent. Drawing on the analogy further, I look at how the theory may be reformulated to take this interpretation into account.

In Chapter 5, I look at external symmetries. I argue, drawing on ideas from Chapters 2 and 3, that models related by external symmetries should also be interpreted as equivalent. I discuss how implementing this interpretational lesson bears on finding the spacetime structure appropriate to a theory.

In Chapter 6, I consider a specific external symmetry: the accelerative symmetry of Newtonian gravitation. I show that one can reformulate the theory to take this into account, setting gravitation on a spacetime structure that has absolute rotation but no absolute acceleration.

Authors: Dewar, N

• DOI: 10.5287/ora-j07xoxaxg
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: Equivalence; Symmetries; Translation
• Subjects: Philosophy