How to Be a Relativistic Spacetime State Realist

Abstract

According to spacetime state realism (SSR), the fundamental ontology of a quantum mechanical world consists of a state-valued field evolving in four-dimensional spacetime. One chief advantage it claims over rival wave-function realist views is its natural compatibility with relativistic quantum field theory (QFT). I argue that the original density operator formulation of SSR cannot be extended to QFTs where the local observables form type III von Neumann algebras. Instead, I propose a new formulation of SSR in terms of a presheaf of local state spaces dual to the net of local observables studied by algebraic QFT. 1. Introduction2. Spacetime State Realism in Quantum Field Theory 2.1. Equivalence thesis3. Entanglement and the Type III Property 3.1. No-Go Lemma 13.2. No-Go Lemma 24. State Space Axioms for Quantum Field Theory 4.1. Revised equivalence thesis5. Discussion