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arXiv · 2607.15351

The Paradox of the Third Particle is classical

Ladina Hausmann·Renato Renner
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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.

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Ladina Hausmann, Renato Renner. 2026-07-16. The Paradox of the Third Particle is classical. https://arxiv.org/abs/2607.15351

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