Can We Make Sense of Relational Quantum Mechanics?

Konstantin K. Likharev

Jean Bricmont

Carlo Rovelli C

Michel Bitbol

Rovelli’s RQM is first characterized by contrast with both Everett’s and Bohr’s interpretations of quantum mechanics. Then, it is shown that a basic difficulty arises from the choice of formulating RQM in a naturalistic framework. Even though, according to Rovelli’s interpretation, statements about the world only make sense relative to certain naturalized observers described by means of quantum mechanics, this very meta-statement seems to make sense relative to a sort of super-observer which does not partake of the naturalized status of ordinary observers. The difficulty is solved by substituting functional reference frames for physical (or naturalized) observers throughout. Instead of being relative to physical observers, statements about the state vector of physical systems are here relative to well-defined projects of probabilistic prediction which may be embodied by several physical observers.

Markiewicz, Marcin, Marek Żukowski

We discuss the status of relative facts - the central concept of Relational Quantum Mechanics (RQM) - in the context of the new amendment to RQM called cross-perspective links postulate. The new axiom states that by a proper measurement one learns the value of the relative outcome/fact earlier obtained by another observer-system. We discuss a Wigner-Friend-type scenario in which, without cross-perspective links postulate, relative facts have no predictive or causal power, whereas including cross-perspective links makes them effectively hidden variables, which causally determine outcomes of specific measurements. However, cross-perspective links axiom invalidates the other axiom of RQM, the one which states that in a Wigner-Friend scenario, RQM assigns an entangled state to the Friend and System after the unitary transformation of their interaction, despite the appearance of the relative fact for the Friend. This quantum mechanical state according to RQM properly describes the situation for Wigner. From this we show that RQM with cross-perspective links axiom is an internally inconsistent hidden variable theory and therefore cannot be treated as an interpretation of quantum mechanics in any sense.

Vincenzo Fano, Marco Sanchioni