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.
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) 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 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.
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.
This paper examines the metaphysical foundations of Relational Quantum Mechanics (RQM), with special attention to its compatibility with scientific realism. We argue that RQM faces a dilemma. In its original formulation, RQM secures a sparse ontology of relative quantum events, but lacks the world-building structure needed to explain how these events jointly constitute a single, coherent reality of the kind presupposed by scientific realism. Recent discussions have already emphasized the difficulties that RQM faces concerning intersubjective agreement, communication, and the emergence of stable facts. Our contribution is to diagnose these difficulties as symptoms of a deeper metaphysical problem: RQM provides relative facts, but no clear account of what makes them facts of one world. We then assess the revised formulation proposed by Adlam and Rovelli, centered on the Cross-Perspective Links (CPL) principle. While CPL aims to restore intersubjective agreement by guaranteeing consistency across perspectives, we argue that it does so at a significant cost. It introduces observer-independent facts, persistent information-bearing structures, and global consistency constraints that sit uneasily with the relational spirit of the original interpretation. Thus, RQM either remains thoroughly relational but metaphysically too weak to support robust scientific realism, or it repairs this weakness by compromising its own relational foundations.
The projection postulate and spectral representation of observables remain central in quantum theory but describe only an idealized measurement limit. Realistic measurements may be inefficient, unsharp, weak, indirect, adaptive, destructive, or informationally incomplete. Positive-operator-valued measures (POVMs) provide the probability rule for processes, whereas quantum instruments specify state transformation. This review traces the hierarchy from von Neumann projective measurement to generalized measurement, emphasizing distinctions among effects, instruments, channels, and implementations. Naimark dilation realizes arbitrary POVMs through unitary coupling to an ancillary meter and projective readout. Stinespring dilation represents completely positive trace-preserving dynamics by unitary evolution on an enlarged system followed by partial trace. A qubit–ancilla interaction yields a partial-measurement instrument, its POVM effects, and its information–disturbance trade-off. It compares projective, generalized, and ancilla-mediated schemes; examines compatibility, instrument incompatibility, and disturbance; and surveys applications to state discrimination, tomography, control, and error correction. Recent developments in dynamic-circuit measurements and noisy-POVM compatibility are integrated with questions concerning measurement back-action and outcome definiteness. The review stresses that a POVM does not uniquely determine state update, dilation theorems establish realizability rather than unique mechanisms, and operational measurement theory does not settle definite outcomes, arguing quantum instruments provide a complete description of measurement.