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arXiv:2510.17513 · Annals of Physics

Quantum mechanics relative to a quantum reference system: A relative state approach

M. J. Luo

Published Mar 9, 2026• 0 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2026.170431

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We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical language to introduce and study quantum reference systems, showing that the orthodox "absolute" quantities are good representatives of observable relative quantities if the reference state is suitably localised. We use this relational formalism to critique the literature on the relationship between reference frames and superselection rules, settling a long-standing debate on the subject.
We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical language to introduce and study quantum reference systems, showing that the orthodox “absolute” quantities are good representatives of observable relative quantities if the reference state is suitably localised. We use this relational formalism to critique the literature on the relationship between reference frames and superselection rules, settling a long-standing debate on the subject.
The standard description of the state of a spin in quantum mechanics presupposes externally fixed directions -- a classical background. Can a spin be fully described instead in relation to other quantum mechanical systems? Poulin suggested twenty years ago group averaging over rotations the joint state of a fundamental spin and a reference spin with large angular momentum which, however, yields a classical bit in a probabilistic mixture. We revisit this idea and show that when the quantum reference system is augmented to \emph{two} large spins, the standard quantum mechanical description of a spin is recovered in the limit of large quantum numbers for the reference system.
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.