A generally covariant measurement scheme for quantum field theory in curved spacetimes

TL;DR

This paper introduces a covariant measurement scheme for quantum field theory in curved spacetimes, enabling local, consistent, and causal measurements of quantum fields via probe systems within the algebraic quantum field theory framework.

Contribution

It develops a new, local, covariant measurement framework for QFT in curved spacetimes using probe systems, with a formula for post-measurement states and causal consistency.

Findings

The measurement scheme is local and covariant.

Induced observables are localized within the causal hull of the coupling region.

The framework ensures causal consistency and can be explicitly calculated.

Abstract

We propose and develop a measurement scheme for quantum field theory (QFT) in curved spacetimes, in which the QFT of interest, the "system", is dynamically coupled to another, the "probe", in a compact spacetime region. Measurements of observables in the probe system then serve as proxy measurements of observables in the system, under a correspondence which depends also on a preparation state of the probe theory. All our constructions are local and covariant, and the conditions may be stated abstractly in the framework of algebraic quantum field theory (AQFT). The induced system observables corresponding to probe observables may be localized in the causal hull of the coupling region and are typically less sharp than the probe observable, but more sharp than the actual measurement on the coupled theory. A formula is given for the post-selected system state, conditioned on measurement outcomes, which is closely related to the notion of an instrument as introduced by Davies and Lewis. This formula has the important property that individual measurements form consistent composites, provided that their coupling regions can be causally ordered and a certain causal factorisation property holds for the dynamics; the composite is independent of the causal order chosen if more than one exists. The general framework is amenable to calculation, as is shown in a specific example. This contribution reports on joint work with R. Verch, arXiv:1810.06512.