On Quantum Indeterminacy
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Quantum Physics arXiv:2605.01103 (quant-ph) [Submitted on 1 May 2026] Title:On Quantum Indeterminacy Authors:Maurice de Gosson View a PDF of the paper titled On Quantum Indeterminacy, by Maurice de Gosson View PDF HTML (experimental) Abstract:We introduce a geometric formulation of quantum indeterminacy from which the standard uncertainty inequalities emerge as necessary consequences. Our approach is based on convex geometry in phase space and on methods from symplectic topology, and does not rely on statistical descriptors such as variances or covariances. Instead, we associate to empirical position and momentum data with convex bodies whose mutual relations encode the fundamental constraints of quantum mechanics. The central tools are h-polar duality and symplectic capacities, which provide intrinsic, coordinate-free bounds on admissible phase-space configurations. Within this framework, the Robertson-Schrodinger inequalities arise naturally as manifestations of deeper geometric and topological principles. This perspective suggests that quantum indeterminacy is not primarily a statistical phenomenon, but rather a structural property of phase space governed by symplectic covariance. The results thus provide a unified and conceptually transparent foundation for the uncertainty principle. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Geometric Topology (math.GT); Symplectic Geometry (math.SG) MSC classes: 53D22, 53D05, 81S10, 81S30, 82C10 Cite as: arXiv:2605.01103 [quant-ph] (or arXiv:2605.01103v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.01103 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Maurice De Gosson Dr [view email] [v1] Fri, 1 May 2026 21:18:25 UTC (19 KB) Full-text links: Access Paper: View a PDF of the paper titled On Quantum Indeterminacy, by Maurice de GossonView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: math math-ph math.GT math.MP math.SG 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?)