The Paradox of the Third Particle is classical

Quantum Physics arXiv:2607.15351 (quant-ph) [Submitted on 16 Jul 2026] Title:The Paradox of the Third Particle is classical Authors:Ladina Hausmann, Renato Renner View a PDF of the paper titled The Paradox of the Third Particle is classical, by Ladina Hausmann and Renato Renner View PDF 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. Comments: Subjects: Quantum Physics (quant-ph); General Relativity and Quantum Cosmology (gr-qc) Cite as: 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) Submission history From: Ladina Hausmann [view email] [v1] Thu, 16 Jul 2026 18:01:07 UTC (487 KB) Full-text links: Access Paper: View a PDF of the paper titled The Paradox of the Third Particle is classical, by Ladina Hausmann and Renato RennerView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-07 Change to browse by: gr-qc References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)