Symmetry, Structure, and Dynamics in Classical Field Theory

One of the most striking features of physical theory over the past century has been the deep and fundamental role of symmetry. Both Einstein’s General Relativity and the Standard Model of Particle Physics are built on symmetry principles, as are frontier theories, such as string theory. Symmetry principles have guided new theorizing, and they have led to the discovery of new fundamental particles, such as the Higgs boson. This project seeks to uncover why symmetry has been so powerful a tool, by revisiting a cluster of fundamental issues concerning how physicists use mathematics to represent the world. A clearer understanding of why symmetry has been so powerful will provide new insights for interpreting contemporary physics and building the next generation of theories. This work will result in both research articles for a professional academic audience and several articles written for a general audience, exploring the role of mathematics in physics and the meaning of symmetry. It will also support training a diverse cohort of PhD students in contemporary philosophy of science. The goals of this project in the philosophical foundations of physics are to first develop a systematic approach to understanding symmetry in physics, based on the idea that symmetry is (always) a guide to what structure the world must have in order to make sense of the fundamental laws and equations of physics; and second, to explore applications of this account to foundational issues in physics. The account of symmetry will be developed in a series of articles exploring how it relates to the status of laws of nature, mathematical representation, the epistemology of science, and structural realism. The applications considered will include the status of the strong equivalence principle in general relativity, the status of the gauge argument in particle physics, and the status of a class of mathematical theorems that infer the specific form of certain physical laws from assumptions about symmetry. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.