Indefinite Causal Order from Failure-to-Glue: Contextual Semantics and Parametric Time
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Quantum Physics arXiv:2601.16494 (quant-ph) [Submitted on 23 Jan 2026] Title:Indefinite Causal Order from Failure-to-Glue: Contextual Semantics and Parametric Time Authors:Partha Ghose View a PDF of the paper titled Indefinite Causal Order from Failure-to-Glue: Contextual Semantics and Parametric Time, by Partha Ghose View PDF HTML (experimental) Abstract:Indefinite causal order (ICO) has been studied via higher-order quantum processes (e.g.\ the quantum switch), process matrices, and quantum-gravity proposals involving superposed causal structure, yet the meaning of ``indefiniteness'' and its relation to definite-order explanations often remain opaque. Part~I develops a category-theoretic formulation of definite-order explainability as a gluing problem: each definite causal ordering (a partial order/DAG type) is treated as a context, and causal separability amounts to a consistent global section (possibly after convex mixing), whereas causal nonseparability is a failure-to-glue. We also introduce a compact seven-valued contextual classifier -- an intuitionistic elaboration -- that separates variation across contexts from genuine indeterminacy. Part~II applies this framework to a quantum-gravity motivated setting where the fundamental time is a parametric ordering variable $\tau$, distinct from geometric (spacetime) time. Adopting a stochastic-quantization perspective on spin-network dynamics (Hilbert space not assumed fundamental) and reading the Wheeler--DeWitt condition as an equilibrium/stationarity constraint, we interpret ICO as indeterminacy of the parametric order of coarse-grained relational interventions, even when the microscopic update process is globally ordered by $\tau$. Together, the two parts provide a common language for comparing ICO criteria and for stating precisely what ``no hidden definite order'' means. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.16494 [quant-ph] (or arXiv:2601.16494v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.16494 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Partha Ghose Professor [view email] [v1] Fri, 23 Jan 2026 06:44:44 UTC (458 KB) Full-text links: Access Paper: View a PDF of the paper titled Indefinite Causal Order from Failure-to-Glue: Contextual Semantics and Parametric Time, by Partha GhoseView 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?)