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Philosophy of Physics

Relational Quantum Mechanics does not Resolve the Problem of Measurement

Paolo Faglia

Published Jan 1, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.31389/pop.209

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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) purportedly resolves the measurement problem by the postulate that physical variables can take determinate values that are relational in the sense that they are indexed to particular systems. Physical variables take on relational definite values if and only if two systems interact. The discrete nature of interactions required creates an ambiguity as to whether quantum events take place in the context of weak and continuous measurements and interactions. We provide a careful analysis of this problem, explain what a full solution to this problem would require, and then analyse certain proposed resolutions - finding all of them to be insufficient in their present form. Since ‘interactions’ (and the quantum events they underpin) are central to all versions of RQM, no version of RQM presented in the literature so far resolves the measurement problem.
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.
The relational interpretation (or RQM, for Relational Quantum Mechanics) solves the measurement problem by considering an ontology of sparse relative events, or "facts". Facts are realized in interactions between any two physical systems and are relative to these systems. RQM's technical core is the realisation that quantum transition amplitudes determine physical probabilities only when their arguments are facts relative to the same system. The relativity of facts can be neglected in the approximation where decoherence hides interference, thus making facts approximately stable.
Abstract The standard formulation of Relational Quantum Mechanics (RQM) models events through projective measurements, thereby importing idealisations that fail to capture generalized quantum measurements. We show that this limitation is not intrinsic to RQM but to the PVM framework. By identifying relational events with effects—the elements of POVMs that encode physically implemented interactions—RQM becomes fully POVM-native. Events are effect-ascriptions, and relational state updates follow the general Kraus rule, with no appeal to projectors or Hilbert-space dilations. This reformulation constitutes an initial step toward dissolving the “Problem of Generic Measurements” recently raised by Calosi and Riedel [11], thereby naturally accommodating weak, noisy, and continuous measurements. We conclude our analysis by identifying at least three possible metaphysical candidates for our POVM-native formulation of RQM.
Relational quantum mechanics (RQM) is an interpretation of quantum mechanics based on the idea that quantum states do not describe an absolute property of a system but rather a relationship between systems. There have recently been some criticisms of RQM pertaining to issues around intersubjectivity. In this article, we show how RQM can address these criticisms by adding a new postulate which requires that all of the information possessed by a certain observer is stored in physical variables of that observer and thus is accessible by measurement to other observers. This makes it possible for observers to reach intersubjective agreement about quantum events that have occurred in the past. We suggest a possible ontology for a version of RQM employing this postulate; this ontology upholds the principle that quantum states are always relational, but it also postulates a set of quantum events that are not strictly relational. We show that the new postulate helps address the preferred basis problem in RQM.
This paper examines the explanatory adequacy of formulations of relational quantum mechanics by distinguishing two levels of relationality. Intra-event relationality concerns the specification of a fact that obtains relative to a system in a particular interaction; inter-event relationality concerns the constraints connecting an event to subsequent events, physical records, and a relational history. Using established results from measurement theory, we show that an effect can specify the statistics of the current outcome without uniquely determining the conditional operation or the statistics of subsequent sequences. Likewise, a fixed coupling and ready state do not uniquely determine the structure of retrievable records unless the readout is specified. We accordingly introduce a task-relative criterion of explanatory adequacy: the required structures must be assessed against the particular explanatory role that a formulation assigns to an event, a relational fact, or a link between perspectives. The conclusion is not that RQM must derive instruments, dynamics, or linking rules from relational principles. A formulation that explicitly incorporates these structures can be fully adequate for the task in question. The paper contributes a distinction between intra-event and inter-event adequacy, a unified criterion for the division of explanatory labor, and a task-relative definition of an architectural deficit.