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Symmetry

Particle Mixing and Quantum Reference Frames

Antonio Capolupo, Gabriele Pisacane, Aniello Quaranta

Published Jan 19, 2026• 0 citations
Publisher

Abstract

We discuss the problem of defining rest frames for mixed particles, showing that Quantum Reference Frames are necessary to incorporate mass superpositions. This approach reveals a strictly frame-dependent nature of entanglement. We investigate the phenomenological impact on neutrinos and neutral mesons, demonstrating that the transition to the rest frame generates entanglement.

DOI
10.3390/sym18010181

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We discuss the problem of defining rest frames for mixed particles, showing that Quantum Reference Frames are necessary to incorporate mass superpositions. This approach reveals a strictly frame-dependent nature of entanglement. We investigate the phenomenological impact on neutrinos and neutral mesons, demonstrating that the transition to the rest frame generates entanglement.
In physics, every observation is made with respect to a frame of reference. Although reference frames are usually not considered as degrees of freedom, in all practical situations it is a physical system which constitutes a reference frame. Can a quantum system be considered as a reference frame and, if so, which description would it give of the world? Here, we introduce a general method to quantise reference frame transformations, which generalises the usual reference frame transformation to a "superposition of coordinate transformations". We describe states, measurement, and dynamical evolution in different quantum reference frames, without appealing to an external, absolute reference frame, and find that entanglement and superposition are frame-dependent features. The transformation also leads to a generalisation of the notion of covariance of dynamical physical laws, to an extension of the weak equivalence principle, and to the possibility of defining the rest frame of a quantum system.
In this paper, we discuss the concept of transformations among reference frames (classical or quantum). Usually transformations among classical reference frames have sharply defined parameters; geometrically they can be considered as pure states in the parameters’ space, and they form a group. It is however possible that the distributions in the parameters’ space are mixed states; such states form a semigroup. Similarly, transformations among quantum reference frames can be either pure or mixed. This gives rise to interesting consequences: the state of a system can be pure with respect to a reference frame and mixed with respect to another; we concretely discuss this in the framework of Galilei transformations in 1+1 dimensions. In particular, if the state of a reference frame with respect to another frame is thermal at some temperature, a quantum particle in the pure (improper) rest state with respect to the first frame will appear in a thermal state with a related nonzero temperature with respect to the other. This can also be discussed in relation to the time/energy uncertainty relation.
We investigate the physics of quantum reference frames. Specifically, we study several simple scenarios involving a small number of quantum particles, whereby we promote one of these particles to the role of a quantum observer and ask what is the description of the rest of the system, as seen by this observer? We highlight the interesting aspects of such questions by presenting a number of apparent paradoxes. By unravelling these paradoxes, we obtain a better understanding of the physics of quantum reference frames.