The Philosophy and Physics of Duality

Abstract

This monograph discusses dualities in physics: what dualities are, their main examples—from quantum mechanics and electrodynamics to statistical mechanics, quantum field theory and string theory—and the philosophical questions that they raise. Part I first conceptualises dualities and discusses their main roles and themes, including how they are related to familiar notions like symmetry and interpretation. It also discusses the main simple examples of dualities: position-momentum, wave-particle, electric-magnetic and Kramers-Wannier dualities. Part II discusses advanced examples and their inter-relations: particle-soliton dualities, electric-magnetic dualities in quantum field theories, dualities in string theory, and gauge-gravity duality. This Part ends with discussions of the hole argument, and how string theory counts the microstates of a black hole. Part III is an in-depth discussion of general philosophical issues on which dualities bear: theoretical equivalence (two theories ‘saying the same thing, in different words’), scientific realism and the under-determination of theories by data, theory succession and the M-theory programme, explanation and scientific understanding. It proposes a view of scientific theories that it dubs the geometric view of theories. The book’s treatment of the examples is at the advanced undergraduate and graduate level, starting from elementary and progressing to more advanced examples. The discussions of philosophical topics, such as referential semantics, theoretical equivalence, scientific realism and scientific understanding, are both self-contained and in-depth. Thus the book is aimed at students and researchers with an interest in the physical examples and philosophical questions about dualities, and also in how physics and philosophy can fruitfully interact with each other.