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arXiv:2604.12094

Why does the wavefunction 'collapse' in relational approaches to quantum mechanics?

Emily Adlam

quant-phphysics.hist-phSubmitted Apr 13, 2026• Announced Apr 15, 2026• 0 citations• Revised Oct 13, 2026 (v2)
v1 · Apr 13, 2026v2 · Oct 13, 2026
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Abstract

I argue that there is a straightforward way to understand the occurrence of wavefunction collapses or 'quantum events' in relational approaches to quantum mechanics: we necessarily encounter a discontinuity in our description when a system interacts with the reference relative to which we are describing it, since the reference system cannot be described relative to itself. This makes it clear how recent concerns around quantum events in relational quantum mechanics should be resolved. However, the solution requires accepting that quantum mechanics is not a complete description of all physical facts, and moreover I argue that this is most likely inevitable if we want to be able to give a precise description of quantum events.

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Updated version to include a comment on 2510.11349

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I argue that there is a straightforward way to understand the occurrence of wavefunction collapses or 'quantum events' in relational approaches to quantum mechanics: we necessarily encounter a discontinuity in our description when a system interacts with the reference relative to which we are describing it, since the reference system cannot be described relative to itself. This makes it clear how recent concerns around quantum events in relational quantum mechanics should be resolved. However, the solution requires accepting that quantum mechanics is not a complete description of all physical facts, and moreover I argue that this is most likely inevitable if we want to be able to give a precise description of quantum events.
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.
Wavefunction collapse is usually seen as a discontinuous violation of the unitary evolution of a quantum system, caused by the observation. Moreover, the collapse appears to be nonlocal in a sense which seems at odds with general relativity. In this article the possibility that the wavefunction evolves continuously and hopefully unitarily during the measurement process is analyzed. It is argued that such a solution has to be formulated using a time symmetric replacement of the initial value problem in quantum mechanics. Major difficulties in apparent conflict with unitary evolution are identified, but eventually its possibility is not completely ruled out. This interpretation is in a weakened sense both local and realistic, without contradicting Bell's theorem. Moreover, if it is true, it makes general relativity consistent with quantum mechanics in the semiclassical framework. Quanta 2016; 5: 19–33.
The collapse postulate in quantum mechanics is problematic. In standard presentations of the theory, the state of a system prior to a measurement is a sum of terms, with one term representing each possible outcome of the measurement. Many dynamical collapse theories imply that the quantum wavefunction is fundamental, and that particles are just a temporary “bunching up” of the fundamental wave-like entity. Quantum mechanics is often taken to be an indeterministic theory. Quantum mechanics represents the state of a system in various ways, but the representation that is most perspicuous for understanding collapse theories uses a wavefunction. Consistency with special relativity is, therefore, a problem for dynamical collapse theories, but perhaps not an insuperable one. Some have argued that the wavefunction needs to be supplemented to counteract the effects of the novel quantum vagueness introduced by dynamical collapse theories. The ontological consequences of dynamical collapse theories remain an area of active debate.
Quantum mechanics describes certain systems as being in superpositions of their properties, yet every measurement on every system that we are able to perform yields a determinate result. The “orthodox” formulation of the theory builds this in by including a postulate that such superpositions “collapse” at the time of measurement. This strategy fails to really explain why such measurements are determinate, is unacceptably imprecise, and makes observation basic in fundamental physical theory, which looks like the wrong sort of process for the job. The problem of the interpretation of quantum mechanics is the problem of finding a more satisfactory understanding of the formalism in This project began in an independent study with Craig Callender, who provided much help in terms of direction, discussion, comments, and continuing support. Thanks also to Jerey Barrett for reading and commenting on an earlier draft of this paper, including helping me find some clearer and more economical way of putting some crucial points.
The probability of occurrence of an event or that of the existence of a physical state has no relative existence in the sense that motion is strongly believed to only exist in the relative sense. If the probability of occurrence of an event or that of the existence of a physical state is known by one observer, this probability must be measured to have the same numerical value by any other observer anywhere in the Universe. If we accept this bare fact, then, the probability function can only be a scalar. Consequently, from this fact alone, we argue that the quantum mechanical wavefunction can not be a scalar function as is assumed for the Schroedinger and the Klein-Gordon wavefunctions. This has fundamental implications on the nature of the wavefunction insofar as translations from one reference system to the other is concerned.
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.