Relative Facts of Relational Quantum Mechanics are Incompatible with Quantum Mechanics

Abstract

Relational Quantum Mechanics (RQM) claims to be an interpretation of quantum theory [see arXiv:2109.09170, which appears in the Oxford Handbook of the History of Interpretation of Quantum Physics]. However, there are significant departures from quantum theory: (i) in RQM measurement outcomes arise from interactions which entangle a system $S$ and an observer $A$ without decoherence, and (ii) such an outcome is a "fact" relative to the observer $A$, but it is not a fact relative to another observer $B$ who has not interacted with $S$ or $A$ during the foregoing measurement process. For $B$ the system $S\otimes A$ remains entangled. We derive a GHZ-like contradiction showing that relative facts described by these statements are incompatible with quantum theory. Hence Relational Quantum Mechanics should not be considered an interpretation of quantum theory, according to a criterion for interpretations that we have introduced. The criterion states that whenever an interpretation introduces a notion of outcomes, these outcomes, whatever they are, must follow the probability distribution specified by the Born rule.

12 pages, 1 figure

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• An attempt to understand relational quantum mechanics
• A critical analysis of `Relative facts do not exist. Relational quantum mechanics is incompatible with quantum mechanics' by Jay Lawrence, Marcin Markiewicz and Marek Źukowski
• Can a Bohmian be a Rovellian for all practical purposes?