Bell Nonlocality as a Covariance Obstruction in Locally Covariant Quantum Field Theory

TL;DR

This paper reveals a fundamental covariance obstruction in locally covariant quantum field theory that prevents classical past variables from fully explaining quantum correlations without breaking covariance.

Contribution

It formalizes a no-go theorem showing Bell's local causality is incompatible with diffeomorphism covariance in LCQFT.

Findings

Bell correlations cannot be fully explained by covariant classical variables.

The obstruction is distinct from dynamical nonlocality or signaling.

Embedding quantum correlations into classical frameworks requires non-covariant structures.

Abstract

Locally covariant algebraic quantum field theory (LCQFT) satisfies Einstein causality through microcausality and operational no-signalling, yet Bell-type correlations persist in entangled field states across spacelike regions. We demonstrate that this apparent tension reflects a fundamental covariance obstruction: no assignment of classical past variables can simultaneously be covariant under spacetime embeddings, screen off quantum correlations, and reproduce AQFT statistics. This obstruction is distinct from dynamical nonlocality or signalling violations. We formalize this as a no-go theorem in the category-theoretic framework of LCQFT, showing that Bell's notion of local causality -- requiring factorization conditioned on a common past -- is structurally incompatible with diffeomorphism covariance. The failure of Bell locality thus reflects not a breakdown of relativistic causality but the impossibility of embedding quantum correlations into a classical causal framework without introducing preferred foliations or non-covariant beables. This clarifies the conceptual status of nonlocality in relativistic quantum theory.