Borns Rule from Reversible Evolution and Irreversible Outcomes

Quantum Physics [Submitted on 8 Apr 2026] Borns Rule from Reversible Evolution and Irreversible Outcomes Oskar Axelsson 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: 9 pages, 1 figure. Derivation of the Born rule from compatibility between reversible evolution and irreversible outcomes 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 Submission history From: Oskar Axelsson [view email] [v1] Wed, 8 Apr 2026 14:44:34 UTC (7 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)