Indefinite Causal Order from Failure-to-Glue: Contextual Semantics and Parametric Time
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| Format: | Preprint |
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2026
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| author | Ghose, Partha |
| author_facet | Ghose, Partha |
| contents | 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 $τ$, 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 $τ$. Together, the two parts provide a common language for comparing ICO criteria and for stating precisely what ``no hidden definite order'' means. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_16494 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Indefinite Causal Order from Failure-to-Glue: Contextual Semantics and Parametric Time Ghose, Partha Quantum Physics 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 $τ$, 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 $τ$. Together, the two parts provide a common language for comparing ICO criteria and for stating precisely what ``no hidden definite order'' means. |
| title | Indefinite Causal Order from Failure-to-Glue: Contextual Semantics and Parametric Time |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2601.16494 |