On the notion of "the same physics in all spacetimes"

TL;DR

This paper examines whether the category-theoretic formulation of local covariance in quantum field theories ensures consistent physics across all spacetimes, introducing a new criterion called dynamical locality.

Contribution

It introduces the concept of dynamical locality as a new criterion to ensure theories represent the same physics in all spacetimes, and analyzes its implications.

Findings

Dynamical locality is incompatible with covariantly choosing a preferred state.

The BFV notion of local covariance does not guarantee the same physics in all spacetimes.

Dynamically local theories satisfy a specific condition that ensures consistent physics across spacetimes.

Abstract

Brunetti, Fredenhagen and Verch (BFV) have shown how the notion of local covariance for quantum field theories can be formulated in terms of category theory: a theory being described as a functor from a category of spacetimes to a category of $(C)^*$-algebras. We discuss whether this condition is sufficient to guarantee that a theory represents `the same physics' in all spacetimes, giving examples to show that it does not. A new criterion, dynamical locality, is formulated, which requires that descriptions of local physics based on kinematical and dynamical considerations should coincide. Various applications are given, including a proof that dynamical locality for quantum fields is incompatible with the possibility of covariantly choosing a preferred state in each spacetime. As part of this discussion we state a precise condition that should hold on any class of theories each representing the same physics in all spacetimes. This condition holds for the dynamically local theories but is violated by the full class of locally covariant theories in the BFV sense. The majority of results described form part of forthcoming papers with Rainer Verch.