Einstein causality of quantum measurements in the Tomonaga-Schwinger picture

Fuente: arXiv
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Autore principale: Fedida, Samuel
Natura: Preprint
Pubblicazione: 2025
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author Fedida, Samuel
author_facet Fedida, Samuel
contents We investigate a generalisation to Lüders' rule à la Aharonov-Albert in those globally hyperbolic spacetimes which allow unitarily equivalent Hilbert spaces to be defined along Cauchy hypersurfaces, thus relying on the existence of an interaction picture à la Tomonaga-Schwinger. We show that under this rule and under the additional assumptions of the integrability and unitarity of the Tomonaga-Schwinger dynamics and the foliation-independence of rays on acausal Cauchy hypersurfaces, selective quantum measurements satisfy a state-independent anyonic commutation relation over spacelike-separated precompact regions. We highlight that this propagates to positive operator-valued measures, where the commutation is necessarily bosonic. In the instantaneous-measurement idealisation, this implies quantum no-signalling for non-selective measurements. We then examine Sorkin's impossible measurements and show that immediate contradictions can be averted as long as collapse-inducing measurements are irreversible. These results reaffirm the consistency of the Tomonaga-Schwinger picture of relativistic quantum theory, for which unitarity, integrability and foliation-independence of the states exclude superluminal signalling despite the ``instantaneity" of a side-cone measurement collapse rule. We finish by discussing the possibility of extending such results beyond the interaction picture.
format Preprint
id arxiv_https___arxiv_org_abs_2506_14693
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Einstein causality of quantum measurements in the Tomonaga-Schwinger picture
Fedida, Samuel
Quantum Physics
General Relativity and Quantum Cosmology
High Energy Physics - Theory
We investigate a generalisation to Lüders' rule à la Aharonov-Albert in those globally hyperbolic spacetimes which allow unitarily equivalent Hilbert spaces to be defined along Cauchy hypersurfaces, thus relying on the existence of an interaction picture à la Tomonaga-Schwinger. We show that under this rule and under the additional assumptions of the integrability and unitarity of the Tomonaga-Schwinger dynamics and the foliation-independence of rays on acausal Cauchy hypersurfaces, selective quantum measurements satisfy a state-independent anyonic commutation relation over spacelike-separated precompact regions. We highlight that this propagates to positive operator-valued measures, where the commutation is necessarily bosonic. In the instantaneous-measurement idealisation, this implies quantum no-signalling for non-selective measurements. We then examine Sorkin's impossible measurements and show that immediate contradictions can be averted as long as collapse-inducing measurements are irreversible. These results reaffirm the consistency of the Tomonaga-Schwinger picture of relativistic quantum theory, for which unitarity, integrability and foliation-independence of the states exclude superluminal signalling despite the ``instantaneity" of a side-cone measurement collapse rule. We finish by discussing the possibility of extending such results beyond the interaction picture.
title Einstein causality of quantum measurements in the Tomonaga-Schwinger picture
topic Quantum Physics
General Relativity and Quantum Cosmology
High Energy Physics - Theory
url https://arxiv.org/abs/2506.14693