Relational Quantum Mechanics and the PBR Theorem: A Peaceful Coexistence

Caludio Calosi,Andrea Oldofredi

doi:10.1007/s10701-021-00485-2

Abstract

According to Relational Quantum Mechanics (RQM) the wave function psi is considered neither a concrete physical item evolving in spacetime, nor an object representing the absolute state of a certain quantum system. In this interpretative framework, psi is defined as a computational device encoding observers’ information; hence, RQM offers a somewhat epistemic view of the wave function. This perspective seems to be at odds with the PBR theorem, a formal result excluding that wave functions represent knowledge of an underlying reality described by some ontic state. In this paper we argue that RQM is not affected by the conclusions of PBR’s argument; consequently, the alleged inconsistency can be dissolved. To do that, we will thoroughly discuss the very foundations of the PBR theorem, i.e. Harrigan and Spekkens’ categorization of ontological models, showing that their implicit assumptions about the nature of the ontic state are incompatible with the main tenets of RQM. Then, we will ask whether it is possible to derive a relational PBR-type result, answering in the negative. This conclusion shows some limitations of this theorem not yet discussed in the literature.

Highlights

In his seminal essay on Relational Quantum Mechanics (RQM), Carlo Rovelli claims that “the experimental evidence at the basis of quantum mechanics forces us to accept that distinct observers give different descriptions of the same events” ([24], p. 1638)
Rovelli claims that RQM is the most natural result of the unification of these ingredients and their application to the formalism of standard quantum theory taken at face value
Harrigan and Spekkens’ classification cannot straightforwardly be applied to RQM. This fact has a remarkable implication for our discussion: given that the PBR theorem crucially relies on Harrigan and Spekkens’ classification of quantum ontological models, as per the Harrigan and Spekkens Definition of Epistemic States assumption, but the latter cannot be used to evaluate RQM, one can safely conclude that RQM does not lie within the scope of the theorem

Summary

Introduction

In his seminal essay on Relational Quantum Mechanics (RQM), Carlo Rovelli claims that “the experimental evidence at the basis of quantum mechanics forces us to accept that distinct observers give different descriptions of the same events” ([24], p. 1638). According to Rovelli, the wavefunction is considered neither a concrete physical item dynamically evolving in spacetime (or in configuration space), nor an object representing the absolute state of a certain quantum system (cf [24, 25]) In this context, is defined as a useful computational device encoding the information available to a particular observer about a specific system. One would be led to conclude that RQM is in plain contradiction with the PRB theorem In this respect, [13] claims that [T]he wave function, and more in general the quantum state , are interpreted realistically in several presentations of quantum theory. Conforming to this classification, is considered an observer-independent representation of the state of a certain quantum system. This has a remarkable consequence—or so we contend: given

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RQM in a Nutshell

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Harrigan and Spekkens’ Distinction:Ã ‐Ontic andÃ ‐Epistemic Models

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The PBR Theorem

The Peaceful Coexistence

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A Relational PBR Theorem?

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Conclusions