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arXiv:2403.04069 · Studies in History and Philosophy of Science Part A

Relational Quantum Mechanics, quantum relativism, and the iteration of relativity

Timotheus Riedel

Published Mar 18, 2024• 9 citations
arXivHTMLPDF

Abstract

The idea that the dynamical properties of quantum systems are invariably relative to other systems has recently regained currency. Using Relational Quantum Mechanics (RQM) for a case study, this paper calls attention to a question that has been underappreciated in the debate about quantum relativism: the question of whether relativity iterates. Are there absolute facts about the properties one system possesses relative to a specified reference, or is this again a relative matter, and so on? It is argued that RQM (in its best-known form) is committed to what I call the Unrestricted Iteration Principle (UIP), and thus to an infinite regress of relativisations. This principle plays a crucial role in ensuring the communicability and coherence of interaction outcomes across observers. It is, however, shown to be incompatible with the widespread, conservative reading of RQM in terms of relations, instead necessitating the adoption of the more unorthodox notion of perspectival facts. I conclude with some reflections on the current state of play in perspectivist versions of RQM and quantum relativism more generally, underscoring both the need for further conceptual development and the importance of the iteration principle for an accurate cost-benefit analysis of such interpretations.

DOI
10.1016/j.shpsa.2024.02.007

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The idea that the dynamical properties of quantum systems are invariably relative to other systems has recently regained currency. Using Relational Quantum Mechanics (RQM) for a case study, this paper calls attention to a question that has been underappreciated in the debate about quantum relativism: the question of whether relativity iterates. Are there absolute facts about the properties one system possesses relative to a specified reference, or is this again a relative matter, and so on? It is argued that RQM (in its best-known form) is committed to what I call the Unrestricted Iteration Principle (UIP), and thus to an infinite regress of relativisations. This principle plays a crucial role in ensuring the communicability and coherence of interaction outcomes across observers. It is, however, shown to be incompatible with the widespread, conservative reading of RQM in terms of relations, instead necessitating the adoption of the more unorthodox notion of perspectival facts. I conclude with some reflections on the current state of play in perspectivist versions of RQM and quantum relativism more generally, underscoring both the need for further conceptual development and the importance of the iteration principle for an accurate cost-benefit analysis of such interpretations.
Recent no-go theorems challenging the absoluteness of events have highlighted the possibility that dynamical facts in quantum theory are observer-relative. This thesis examines the metaphysical and conceptual foundations of quantum relativism, focusing on Relational Quantum Mechanics (RQM). It analyzes arguments for relativism through Wigner’s Friend and Extended Wigner’s Friend thought experiments, explores the link between relative physical facts and experiences, and offers the first metaphysical definition of "relative facts." The thesis argues: RQM supports a perspectival retro-determination of past events based on later acquisition of information; Quantum relativists must also relativize facts about observers’ experiences; the strongest arguments for relativism lead to unbounded higher-order relativity, precluding any absolute 'view from nowhere'; Only a metaphysical framework that relativized the composition of reality itself can accommodate such an unrestricted iteration. These conclusions deepen our grasp of a thoroughly perspectival quantum world.
Relational Quantum Mechanics (RQM) claims to be an interpretation of quantum theory \cite{Rovelli.21}. 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⊗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.
This paper discusses perspectivism and relationalism in the two versions of Relational Quantum Mechanics (RQM): that initiated by Rovelli ( Int. J. Theor. Phys. , 35 (8), 1637–1678 1996) and the other, by Adlam and Rovelli ( Philos. Phys. , 1 (1) 2023). To this end, we offer a substantial discussion of this interpretation. We investigate the issue of the disagreement of results between different observers; distinguish four senses of agreement: strong, weak, very weak, and perspectival; and argue that the old version guarantees only the very weak and perspectival agreement, whereas the new version guarantees the weak agreement as well. The problem that individuals in RQM need to be propertyless when they do not interact is also investigated. Concerning the issue of probabilities in RQM, we argue that to express probabilities involving events relative to different systems, a new kind of probability spaces needs to be devised. The final problem that we identify concerns underspecified dynamics; we argue that some additional postulates are indispensable to make RQM’s dynamics fully specified. The last two points lead to the conclusion that, contrary to declarations of RQM proponents, this interpretation requires some modifications of quantum formalism and not merely conceptual changes. Finally, concerning the problem of testimony, while the new version of RQM was devised to solve it, we argue that in the old version, this problem can be alleviated to the extent that perspectivism permits.
Relational quantum mechanics (RQM) explains the world in terms of an ontology of systems and events, where an event consists of a variable of a system taking a value relative to another system. Two strands of RQM may be distinguished depending on whether events are taken to be absolute or relative. The arguments in this paper apply to both, although I assume that the relativity is not infinitely iterated. I argue that, to solve the problem of measurement, RQM needs to offer a specification of the circumstances in which events occur. Current formulations of RQM claim that events occur whenever interactions occur, without further defining what is meant by “interaction”. I develop plausible ways of understanding the notion of interaction, but I show that they fail to provide a satisfactory specification for the occurrence of events. RQM thus leaves the measurement problem unresolved and, in light of these failed constructive efforts, I conclude that developing a solution consistent with the aims of RQM is a formidable challenge.
Relational Quantum Mechanics (RQM) is an interpretation of quantum theory based on the idea of abolishing the notion of absolute states of systems, in favor of states of systems relative to other systems. Such a move is claimed to solve the conceptual problems of standard quantum mechanics. Moreover, RQM has been argued to account for all quantum correlations without invoking non-local effects and, in spite of embracing a fully relational stance, to successfully explain how different observers exchange information. In this work, we carry out a thorough assessment of RQM and its purported achievements. We find that it fails to address the conceptual problems of standard quantum mechanics--related to the lack of clarity in its ontology and the rules that govern its behavior--and that it leads to serious conceptual problems of its own. We also uncover as unwarranted the claims that RQM can correctly explain information exchange among observers, and that it accommodates all quantum correlations without invoking non-local influences. We conclude that RQM is unsuccessful in its attempt to provide a satisfactory understanding of the quantum world.
Abstract This paper examines the role of perspectivism in Relational Quantum Mechanics, situating it within the broader landscape of quantum interpretations and the scientific realism debate. We argue that, while interpretations such as QBism embrace strong forms of perspectivism, Relational Quantum Mechanics adopts a “soft” perspectivism, limiting the observer’s role to selecting experimental contexts without compromising its realist framework. We also explore the historical roots of Relational Quantum Mechanics, showing that relational ideas in the works of Bohr and other pioneers similarly avoided strong perspectivist commitments. By analyzing both contemporary and historical perspectives, we argue that Relational Quantum Mechanics offers a minimalist yet robust relational interpretation, distinct from more subjectivist approaches.