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Philosophy of Physics

The Problem of Interactions in Relational Quantum Mechanics

James Ladyman, Anthony P. Thompson

Published Jan 1, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.31389/pop.206

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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) 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 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.
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.
The relational approach to quantum states asserts that the physical description of quantum systems is always relative to something or someone. In relational quantum mechanics (RQM) it is relative to other quantum systems, in the (neo-)Copenhagen interpretation of quantum theory to measurement contexts, and in QBism to the beliefs of the agents. In contrast to the other two interpretations, in RQM any interaction between two quantum systems counts as a "measurement", and the terms "observer" and "observed system" apply to arbitrary systems. We show, in the form of a no-go theorem, that in RQM the physical description of a system relative to an observer cannot represent knowledge about the observer in the conventional sense of this term. The problem lies in the ambiguity in the choice of the basis with respect to which the relative states are to be defined in RQM. In interpretations of quantum theory where observations play a fundamental role, the problem does not arise because the experimental context defines a preferred basis.
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.
The relational interpretation of quantum mechanics (RQM), introduced in its present form by Carlo Rovelli in 1996, involves a number of significant departures from other QM interpretations widely discussed in the literature. We begin here by summarizing these unique RQM features, with a focus on those that suggest altered insights into the nature of the randomness exhibited in QM phenomena. One of these RQM features is the assumption that all objects in the universe are quantum objects, regardless of their material complexity. And, the interaction of any two objects can result in new relational quantum states of each of the objects with the other as reference. But such new states do not replace relational states corresponding to previous interactions with other reference objects. In particular, such earlier relational states that include a variable considered to be random do not collapse to define a determined value of the variable, but instead simply take on that specific value in the state relative to the new reference. The concept of randomness associated with quantum state variables in RQM thus differs from that in other QM interpretations. Rather than take the usual pedantic approach of elaborate side-by-side comparisons between the RQM and other common QM interpretations, we illustrate these differences by describing in some detail the well-known "dual-slit" experiment in terms of RQM concepts, pointing out the important advantages over other interpretations along the way. Of course, we suggest no change in dual-slit experiment results, but believe that the interpretative modifications are helpful and profound.