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arXiv:2003.03121 · Foundations of Physics

Completing the Quantum Formalism in a Contextually Objective Framework

Philippe Grangier

Published Jun 30, 2021• 15 citations
arXivHTMLPDF
DOI
10.1007/s10701-021-00424-1

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We introduce the Contextual Projection Framework (CPF), in which quantum phenomena are understood as manifestations conditioned by contextual projection structures rather than as consequences of ontological dualities, dynamical collapse, or retrocausal effects. The framework reformulates measurement, complementarity, delayed choice, quantum erasure, and decoherence as consequences of structural incompatibility between contextual projections defined on the Hilbert space. Without modifying the standard quantum formalism, the CPF unifies these phenomena under a single geometric principle and yields a general No-Paradox Theorem: quantum paradoxes arise exclusively from the simultaneous application of incompatible contextual frameworks.

•Dec 15, 2025•0 citations
Abstract Quantum contextuality represents a fundamental form of nonclassicality in quantum mechanics. To provide a more complete characterization of nonclassical properties in quantum systems, we adopt a logical perspective and propose a mathematical framework based on exclusive partial Boolean algebras. This framework enables a unified description of contextuality and nonclassicality across finite general, quantum, and classical systems. We establish a unified and minimal classical counterpart for any finite general system. Within this framework, we formalize major categories of quantum contextuality, demonstrating that: 12 projectors suffice to generate Kochen–Specker scenarios; 10 projectors suffice to witness state-independent contextuality; and 3 observables suffice to witness quantum contextuality. Finally, we prove that contextuality is a sufficient but not necessary condition for nonclassicality.
Quantum theory and general relativity are extraordinarily successful within their demonstrated domains, yet their standard formalisms are not straightforwardly unified. Layer Before Law asks whether part of that difficulty may arise one conceptual step earlier: before selecting the physical law that governs a state, has the relevant object, context, admissibility structure, and scale been typed correctly? Within the McLaughlin-Kairos Unified Field Theory (MKUFT) research programme, the proposal is an addressed architecture rather than a completed theory of quantum gravity. A complete effective state carries substrate participation, informational and relational structure, physical expression, observer-positioned registration, contextual address, and retained load-bearing history. A compatibility map constructs an admissibility descriptor; a law assembler then constructs the active physical-law object. Physical propagation, measurement or registration, and readdressing of the next effective possibility object follow. The paper adds a property-relative law-ownership gate and bidirectional scale readdressing, separates higher-law failure from constitutive closure and recoverability, applies the framework to entanglement as a worked constraint case, states explicit Bell/local-hidden-variable and no-signalling requirements, and defines recovery obligations for quantum and gravitational regimes. It does not derive the Born rule, Bell correlations, quantum field theory, Einstein dynamics, or a fundamental quantum-gravity theory. Its contribution is a typed, falsifiable research architecture for testing whether relational and contextual structure performs independent work beyond the strongest adequate physical-state, history, and boundary description.
We introduce the Contextual Projection Framework (CPF), in which quantum phenomena are understood as manifestations conditioned by contextual projection structures rather than as consequences of ontological dualities, dynamical collapse, or retrocausal effects. The framework reformulates measurement, complementarity, delayed choice, quantum erasure, and decoherence as consequences of structural incompatibility between contextual projections defined on the Hilbert space. Without modifying the standard quantum formalism, the CPF unifies these phenomena under a single geometric principle and yields a general No-Paradox Theorem: quantum paradoxes arise exclusively from the simultaneous application of incompatible contextual frameworks.