Pragmatists and Purists on CPT Invariance in Relativistic Quantum Field Theories

Abstract

Philosophers of physics are split on whether foundational issues in relativistic quantum field theory (RQFT) should be framed within pragmatist approaches, which trade mathematical rigor for the ability to formulate non-trivial interacting models, or purist approaches, which trade the ability to formulate non-trivial interacting models for mathematical rigor. This essay addresses this debate by viewing it through the lens of the CPT theorem. I first consider two formulations of the CPT theorem, one purist and the other pragmatist, and extract from them a set of problems that clarifies the distinction between pragmatism and purity. I then apply this distinction to Greenberg's ([2002]) influential claim that the violation of CPT invariance in an interacting RQFT entails the violation of (restricted) Lorentz invariance. I show how this claim rests on an unsuccessful attempt to mediate between pragmatism and purity. I then evaluate another attempt at such mediation in the form of causal perturbation theory. This approach suggests that a focus on renormalized perturbation theory as a way of distinguishing pragmatists from purists may be misleading.