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arXiv:2112.07830

Is Relational Quantum Mechanics about Facts? If So, Whose? A Reply to Di Biagio and Rovelli's Comment on Brukner and Pienaar

Blake C. Stacey

Published Dec 15, 2021• 1 citation
arXivHTMLPDF

Abstract

Brukner and Pienaar have critiqued the Relational Quantum Mechanics of Rovelli, and together with Di Biagio, the latter has replied. I point out a few places where, in my view, that reply needs clarification.
DOI
10.48550/arxiv.2112.07830

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In a recent paper, Rovelli responds to our critical assessment of Relational Quantum Mechanics (RQM). His main argument is that our assessment lacks merit, because we fail to understand, or cope with, the premises of his theory; instead, he argues, we judge his proposal, blinded by the preconceptions inherent to ``our camp''. Here, we explicitly show that our assessment judges RQM on its own terms, together with the basic requirements of precision, clarity, logical soundness and empirical suitability. Under those circumstances, we prove false Rovelli's claim that RQM provides a satisfactory, realistic, non-solipsistic description of the world. Moreover, his reply serves us to further exhibit the serious problems of the RQM proposal, as well as the failures of its author to understanding the basic conceptual difficulties of quantum theory.
Di Biagio and Rovelli’s recent reformulation of Relational Quantum Mechanics (RQM) introduces relative facts grounded in commutative subalgebras and relative Shannoninformation, claiming to provide a physically embodied, naturalistic, and locally coherent account of quantum phenomena. We identify a structural inconsistency in this programme by analysing a scenario in which observer A remains entirely unperturbed while a remote observer B measures a complementary observable of a shared entangled system S. We prove rigorously that (i) A’s local reduced density matrix is invariant under this remote action, (ii) the relative information I(Z|A) nonetheless drops from maximal to minimal, and (iii) no local unitary acting on H(A) can generate this change, since local unitaries preserve mutual information. These three results jointly entail that the evolution of A’s perspective is not generated by any local physical process, directly contradicting the paper’s explicit commitment to physical embodiment and local autonomy of perspectives. We argue this is not a technical defect but a foundational tension: RQM cannot simultaneously maintain that perspectives are locally embodied in physical correlations, that they evolve unitarily when no interaction occurs, and that remote complementary measurements alter local relative facts. Without additional structure specifying the dynamics ofperspectives under non-local entanglement changes, RQM’s naturalistic programmeis internally inconsistent at this level. We further argue that no-signaling doesnot rescue the ontological claim, and compare the problem’s severity to analogous nonlocality in other interpretations.