2025/06/17 by Samuel Fedida, Fedida, Samuel
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Radioactive Decay and Measurement Techniques
paper · pdf · doi:10.48550/arxiv.2506.14693
openalex publication_date 2025/06/17 · openalex created_date 2025/10/09 · openalex updated_date 2026/08/01
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.