Measurement as Sheafification: Context, Logic, and Truth after Quantum Mechanics
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Quantum Physics arXiv:2512.12249 (quant-ph) [Submitted on 13 Dec 2025] Title:Measurement as Sheafification: Context, Logic, and Truth after Quantum Mechanics Authors:Partha Ghose View a PDF of the paper titled Measurement as Sheafification: Context, Logic, and Truth after Quantum Mechanics, by Partha Ghose View PDF HTML (experimental) Abstract:Quantum measurement is commonly posed as a dynamical tension between linear Schrödinger evolution and an ad hoc collapse rule. I argue that the deeper conflict is logical: quantum theory is inherently contextual, whereas the classical tradition presupposes a single global, Boolean valuation. Building on Bohr's complementarity, the Einstein--Podolsky--Rosen argument and Bell's theorem, I recast locality and completeness as the existence of a global section of a presheaf of value assignments over the category of measurement contexts. The absence of global sections expresses the impossibility of context-independent description, and Čech cohomology measures the resulting obstruction. The internal logic of the presheaf topos is intuitionistic, and the seven-valued contextual logic proposed by Ghose and Patra is exhibited as a finite Heyting algebra capturing patterns of truth, falsity and indeterminacy across incompatible contexts. Classical physics corresponds to the sheaf case, where compatible local data glue and Boolean logic is effectively restored. Measurement is therefore reinterpreted as sheafification of presheaf-valued truth rather than as a physical breakdown of unitarity. Finally, a $\sigma$--$\lambda$ dynamics motivated by stochastic mechanics provides a continuous interpolation between strongly contextual and approximately classical regimes, dissolving the usual measurement paradoxes and apparent nonlocality as artefacts of an illegitimate demand for global truth. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2512.12249 [quant-ph] (or arXiv:2512.12249v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.12249 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Partha Ghose Professor [view email] [v1] Sat, 13 Dec 2025 09:15:20 UTC (26 KB) Full-text links: Access Paper: View a PDF of the paper titled Measurement as Sheafification: Context, Logic, and Truth after Quantum Mechanics, by Partha GhoseView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 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?)