The Paradox of the Third Particle is classical

Abstract:The Paradox of the Third Particle arises when particles are described relative to one of them serving as a reference frame. Although it is typically attributed to quantum superpositions, we show that the paradox and its ramifications$\unicode{x2014}$such as the relativity of subsystems$\unicode{x2014}$already occur classically. In light of this insight, we establish a no-go theorem that holds whenever physical subsystems, whether classical or quantum, are used as reference frames: if one demands that frame transformations be information-preserving, then it is impossible to meaningfully partition the world into subsystems, like individual particles, from the perspective of each frame.

arXiv:2607.15351 [quant-ph]

(or arXiv:2607.15351v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.15351 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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