Relative Facts of Relational Quantum Mechanics are Incompatible with Quantum Mechanics

Quantum 7, 1015 (2023).

https://doi.org/10.22331/q-2023-05-23-1015

Relational Quantum Mechanics (RQM) claims to be an interpretation of quantum theory [20]. 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.