[Paper Review] Eliminating the "impossible": Recent progress on local measurement theory for quantum field theory

Maria Papageorgiou, Doreen Fraser|arXiv (Cornell University)|Jul 17, 2023

Quantum Mechanics and ApplicationsPhysics and Astronomy3 citations

TL;DR

This paper investigates the 'impossible measurements' problem in quantum field theory (QFT), where standard measurement rules lead to superluminal signaling. It analyzes three approaches—detector models, algebraic QFT with Fewster-Verch framework, and histories-based formalisms—and shows that dynamics and non-operational interpretations of local algebras are essential to rule out such scenarios, offering new foundational insights into measurement in relativistic quantum theories.

ABSTRACT

Arguments by Sorkin arXiv:gr-qc/9302018 and Borsten, Jubb, and Kells arXiv:1912.06141 establish that a natural extension of quantum measurement theory from non-relativistic quantum mechanics to relativistic quantum theory leads to the unacceptable consequence that expectation values in one region depend on which unitary operation is performed in a spacelike separated region. Sorkin labels such scenarios "impossible measurements". We explicitly present these arguments as a no-go result with the logical form of a reductio argument and investigate the consequences for measurement in quantum field theory (QFT). Sorkin-type impossible measurement scenarios clearly illustrate the moral that Microcausality is not by itself sufficient to rule out superluminal signalling in relativistic quantum theories that use Lüders' rule. We review three different approaches to formulating an account of measurement for QFT and analyze their responses to the "impossible measurements" problem. Two of the approaches are: a measurement theory based on detector models proposed in Polo-Gómez, Garay, and Martín-MartÍnez arXiv:2108.02793 and a measurement framework for algebraic QFT proposed in Fewster and Verch arXiv:1810.06512. Of particular interest for foundations of QFT is that they share common features that may hold general morals about how to represent measurement in QFT. These morals are about the role that dynamics plays in eliminating "impossible measurements", the abandonment of the operational interpretation of local algebras as representing possible operations carried out in a region, and the interpretation of state update rules. Finally, we examine the form that the "impossible measurements" problem takes in histories-based approaches and we discuss the remaining challenges.

Motivation & Objective

• To address the foundational problem of 'impossible measurements' in relativistic quantum field theory, where standard measurement rules imply superluminal signaling.
• To analyze how different measurement frameworks—detector models, algebraic QFT, and histories-based approaches—respond to the 'impossible measurements' problem.
• To clarify the role of dynamics, the interpretation of local algebras, and state update rules in eliminating non-physical signaling in QFT.
• To explore how the absence of a consensus measurement theory in QFT constitutes a foundational challenge, particularly in algebraic QFT.
• To identify shared structural features across successful frameworks that may generalize to a broader understanding of measurement in QFT.

Proposed method

• Formalizes Sorkin-type 'impossible measurement' scenarios as a reductio ad absurdum argument, showing that naive extension of Lüders' rule leads to superluminal signaling.
• Reviews the detector model approach (Polo-Gómez, Garay, Martín-Martínez) that uses smeared field operators and detector-specific interaction regions to define local measurements.
• Analyzes the Fewster-Verch (FV) framework in algebraic QFT, which uses scattering isomorphisms and expectation values over spacetime regions to define state updates.
• Examines histories-based approaches, where decoherence functionals and multi-time histories represent physical predictions, though the 'impossible measurements' problem remains unresolved.
• Compares the three frameworks by focusing on how they interpret local algebras, state updates, and the role of dynamics in preventing superluminal signaling.
• Emphasizes that state updates in both FV and detector models are not physical state changes but represent changes in observer knowledge or counterfactual expectations.

Experimental results

Research questions

• RQ1 How do Sorkin-type 'impossible measurements' arise from the naive extension of Lüders' rule in relativistic quantum theories?
• RQ2 Why is microcausality alone insufficient to rule out superluminal signaling in QFT with standard measurement rules?
• RQ3 How do detector-based models and the Fewster-Verch framework avoid the 'impossible measurements' problem through their treatment of dynamics and state updates?
• RQ4 What is the role of spacetime smearing functions in detector models, and how do they relate to the physical region of interaction?
• RQ5 To what extent can the interpretation of local algebras in QFT be operational, and why must this interpretation be abandoned in light of the 'impossible measurements' problem?

Key findings

• The 'impossible measurements' problem arises when expectation values in one spacetime region depend on unitary operations performed in a spacelike-separated region, violating relativistic causality.
• Microcausality alone does not prevent superluminal signaling in QFT if Lüders' rule is applied naively, demonstrating that causality requires more than just algebraic commutativity.
• The Fewster-Verch framework resolves the problem by interpreting 'in' and 'out' states as counterfactual, with state updates being manifestly Lorentz covariant and not representing physical state changes.
• Detector models avoid the problem by treating state updates as changes in observer knowledge, not physical changes in the field, and by using spacetime-smearing functions that reflect holistic detector-field interactions.
• Both the FV framework and detector models reject the operational interpretation of local algebras as representing possible operations in a region, instead treating them as mathematical structures encoding expectation values.
• The absence of instantaneous states-at-a-time in all three frameworks suggests that expectation values and correlation functions are the fundamental physical representatives of the state in QFT, not Hilbert space vectors.