Borns Rule from Reversible Evolution and Irreversible Outcomes
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Quantum Physics arXiv:2604.07418 (quant-ph) [Submitted on 8 Apr 2026] Title:Borns Rule from Reversible Evolution and Irreversible Outcomes Authors:Oskar Axelsson View a PDF of the paper titled Borns Rule from Reversible Evolution and Irreversible Outcomes, by Oskar Axelsson View PDF HTML (experimental) Abstract:We show that the quadratic measure need not be postulated, but follows from the compatibility of two structural features of physical processes: linear reversible evolution prior to the formation of persistent records, and multiplicative composition of outcome weights once such records are established. Reversible evolution combines configurations additively at the level of a compatibility parameter, while the formation of persistent records induces a multiplicative structure on the weights assigned to physically realized outcomes. Requiring consistency between these two regimes constrains the admissible weight assignment to be quadratic in the associated amplitude. The Born rule therefore emerges as the unique measure compatible with reversible linear evolution and irreversible record formation, without assuming a probabilistic interpretation or a specific quantum formalism. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.07418 [quant-ph] (or arXiv:2604.07418v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.07418 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Oskar Axelsson [view email] [v1] Wed, 8 Apr 2026 14:44:34 UTC (7 KB) Full-text links: Access Paper: View a PDF of the paper titled Borns Rule from Reversible Evolution and Irreversible Outcomes, by Oskar AxelssonView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?)