Jonathan Bain

This essay is concerned with a number of related proposals that claim there is a link between spacetime topology and quantum entanglement. I indicate the extent to which these proposals can be understood as stating a duality, and then consider two general approaches to articulating such a duality: a “state-based” approach, under which one attempts to identify relevant topological states as dual to quantum entangled states; and an “observable-based” approach, under which one attempts to identify relevant topological observables as dual to quantum entangement observables. Both approaches are faced with issues, essentially due to the ambiguous nature of quantum entanglement, that remain to be addressed.

This book seeks to answer the question "What explains CPT invariance and the spin-statistics connection?" These properties play foundational roles in relativistic quantum field theories, are supported by high-precision experiments, and figure into explanations of a wide range of phenomena, from antimatter, to the periodic table of the elements, to superconductors and superfluids. They can be derived in RQFTs by means of the famous CPT and Spin-Statistics theorems; but, the author argues, these theorems cannot be said to explain these properties, at least under standard philosophical accounts of scientific explanation. This is because there are multiple, in some cases incompatible, ways of deriving these theorems, and, secondly, because the theorems fail for the types of theories that underwrite the empirical evidence: non-relativistic quantum theories, and realistic interacting RQFTs. The goal of this book is to work towards an understanding of CPT invariance and the spin-statistics connection by first providing an analysis of the necessary and sufficient conditions for these properties, and second by advocating a particular account of explanation appropriate for this context.