An unexpected theoretical structure that could explain quantum-mechanics postulates like the Born rule and the wave-function reduction
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Quantum Physics arXiv:2601.12092 (quant-ph) [Submitted on 17 Jan 2026] Title:An unexpected theoretical structure that could explain quantum-mechanics postulates like the Born rule and the wave-function reduction Authors:Léon Brenig, Marc Vincke View a PDF of the paper titled An unexpected theoretical structure that could explain quantum-mechanics postulates like the Born rule and the wave-function reduction, by L\'eon Brenig and 1 other authors View PDF HTML (experimental) Abstract:A unique postulate is shown to underly the whole quantum mechanics theory: the invariance of the Heisenberg uncertainty inequality under a group of special nonlinear gauge transformations (NLGT). With this postulate, the quantum mechanics of a free particle is derived from classical mechanics, including the statements of the postulates of quantum mechanics, except for the wave-function-collapse postulate. An explanatory mechanism for the latter postulate is derived by performing an analytical continuation of the NLGTs. This extension results in a Schrödinger-bridge process, intertwined under the NLGT with the standard unitary quantum evolution, and revealing non-quantum (or beyond-quantum) phenomena. Mechanisms of that latter kind, like the ones associated to the quantum measurement process, occur in a new space-like dimension and hence are non causal in nature, in opposition to a time evolution. The present exercice focusses on the free particle in order to highlight the features of the performed derivation in the simplest possible way. Work is in progress to extend the performed derivation beyond that simple case. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.12092 [quant-ph] (or arXiv:2601.12092v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.12092 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Léon Brenig [view email] [v1] Sat, 17 Jan 2026 16:04:55 UTC (64 KB) Full-text links: Access Paper: View a PDF of the paper titled An unexpected theoretical structure that could explain quantum-mechanics postulates like the Born rule and the wave-function reduction, by L\'eon Brenig and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)