The Theory of Every Thing: Toward a Symmetry-Based Metaphysics of Matter

Abstract

In modern physics, almost everything about the material constituents of the world (such as particles) can be inferred from claims about the symmetries of the world. For example, recent breakthroughs in particle physics are almost entirely due to claims about symmetries. This gives rise to an intriguing metaphysical vision according to which the symmetries of the world are fundamental, whereas the material constituents of the world are ontologically derivative of them.

This dissertation develops a general framework for a metaphysics of modern physics that underwrites this vision: an account according to which symmetries correspond to fundamental ontological items and which details how every non-fundamental claim about the material constituents of the world can be accounted for in terms of claims about those items. This account provides a template for an ontology for a wide range of current and future physics and promises to explain the enormous success of symmetry techniques in the recent history of physics.

In the first two chapters, I develop ontological hypotheses that give this metaphysical vision a precise metaphysical underpinning in the relatively simple settings of classical particle mechanics and non-relativistic quantum mechanics, respectively. These views amount to proofs of concept: they show how every relevant claim about material constituents—point particles in the classical setting and wavefunctions in the quantum setting—can be reduced to some claim about symmetries. The third chapter showcases an important instance of the explanatory power and metaphysical utility of symmetry-based metaphysical theorizing. By developing an account of the physical entities that correspond to symmetry groups—the mathematical objects that are used to systematize types of symmetry transformations, such as rotations—this chapter demonstrates how symmetry-fundamentalist ontological theorizing allows us to provide deep, hitherto unavailable explanations of important features of physical properties, such as the fact that quantum-mechanical spin is discrete. The fourth and final chapter develops a perspicuous account of what it is for a physical property to be invariant under a symmetry.