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Paper V — Angular Information Locality and Spin

Paul Cooney

Published Dec 14, 2025• 0 citations
Publisher

Abstract

Paper IV — Local Interactions and Potentials from Operational Locality DescriptionThis paper shows how local interaction terms and effective potentials arise from operational locality constraints. By analyzing admissible deformations of free ordered dynamics, we derive interaction structure without invoking classical force laws or background geometry. The results clarify why local potentials dominate physical dynamics and how interaction terms reflect operationally constrained information exchange. Keywordslocal interactions; emergent potentials; operational physics; quantum dynamics; reconstruction theory; locality

DOI
10.5281/zenodo.17925681

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We present a structural framework for analyzing dynamics in background-independent theories based on admissible transport on configuration spaces. The approach reformulates canonical evolution not in terms of a fixed Hamiltonian, but via constrained transport maps acting on an admissible subspace of states, preserving constraint closure and covariance by construction. Within this setting, we show that admissible dynamics admit a dual description in terms of state transport and observable transport, related by an adjoint pairing, and we establish conditions under which validation metrics are invariant under this duality. We further prove that admissibility enforces contraction bounds on accumulated deviations under composition, providing a structural explanation for stability without specifying a particular microscopic dynamics. The framework is applied to canonical Loop Quantum Gravity as a consistency analysis rather than as a proposal for new dynamics. We clarify how transport-based formulations relate to existing spin- network and spin-foam constructions, and we identify precise conditions under which such formulations remain anomaly-free. No claim is made to resolve the full dynamics problem or to derive novel physical predictions. Instead, the results provide a controlled language for distinguishing structurally stable evolutions from inadmissible ones in background-independent quantum theories. This work is an information-theoretic framework concerned with admissible transport and stability of information under composition. Physical theories, including Loop Quantum Gravity (LQG), are used solely as structured test cases rather than as the primary object of study. LQG serves as a representative background-independent information system. This manuscript is information theory under constraints, not physics. CIFT is an information-theoretic framework in which conserved quantities are measured in bits and are conditional on explicit admission and boundary exchange.

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Paper IV — Local Interactions and Potentials from Operational Locality DescriptionThis paper shows how local interaction terms and effective potentials arise from operational locality constraints. By analyzing admissible deformations of free ordered dynamics, we derive interaction structure without invoking classical force laws or background geometry. The results clarify why local potentials dominate physical dynamics and how interaction terms reflect operationally constrained information exchange. Keywordslocal interactions; emergent potentials; operational physics; quantum dynamics; reconstruction theory; locality
Paper IV — Local Interactions and Potentials from Operational Locality DescriptionThis paper shows how local interaction terms and effective potentials arise from operational locality constraints. By analyzing admissible deformations of free ordered dynamics, we derive interaction structure without invoking classical force laws or background geometry. The results clarify why local potentials dominate physical dynamics and how interaction terms reflect operationally constrained information exchange. Keywordslocal interactions; emergent potentials; operational physics; quantum dynamics; reconstruction theory; locality
Paper VI — Entanglement Information Locality and Many-Body Structure DescriptionThis work extends ordered-dynamics locality principles to composite systems, deriving entanglement structure and many-body correlations from operational constraints. Entanglement emerges as a necessary feature of jointly constrained information propagation, not as an added axiom. The paper clarifies the operational meaning of non-separability and establishes the foundations for multi-particle quantum structure within the ODRP. Keywordsentanglement; many-body systems; quantum correlations; operational locality; information theory; quantum foundations
Paper I — Ordered Dynamics and Operational State Spaces DescriptionThis paper inaugurates the Ordered-Dynamics Reconstruction Program (ODRP) by introducing the foundational concept of ordered dynamics as a pre-geometric, pre-spatiotemporal substrate for physical theory. Without assuming spacetime, Hilbert space, or quantum postulates, we construct operational state spaces from minimal ordering and distinguishability requirements. The paper establishes the core axioms governing records, operational comparison, and bounded influence, providing the primitive framework from which locality, dynamics, and physical observables will later emerge in the series. Keywordsordered dynamics; operational state spaces; foundations of physics; pre-spacetime physics; information theory; reconstruction programs
Paper II: Operational Information Locality and Schrödinger Dynamics Description: Following the derivation of kinematics in Paper I, this paper constrains the admissible forms of free dynamics. It introduces the axiom of Operational Information Locality (OIL), a universal bound on how quickly free evolution can convert momentum uncertainty into spatial distinguishability4. The paper proves a rigidity theorem showing that OIL is equivalent to a global Lipschitz bound on group velocity, forcing the dispersion relation to have uniformly bounded curvature5. Schrödinger kinetics (H=P2/2mH=P^2/2mH=P2/2m) emerges as the saturating, constant-curvature case of this admissible class, uniquely selected by tightness and monotonicity refinements6.
We present a structural framework for analyzing dynamics in background-independent theories based on admissible transport on configuration spaces. The approach reformulates canonical evolution not in terms of a fixed Hamiltonian, but via constrained transport maps acting on an admissible subspace of states, preserving constraint closure and covariance by construction. Within this setting, we show that admissible dynamics admit a dual description in terms of state transport and observable transport, related by an adjoint pairing, and we establish conditions under which validation metrics are invariant under this duality. We further prove that admissibility enforces contraction bounds on accumulated deviations under composition, providing a structural explanation for stability without specifying a particular microscopic dynamics. The framework is applied to canonical Loop Quantum Gravity as a consistency analysis rather than as a proposal for new dynamics. We clarify how transport-based formulations relate to existing spin- network and spin-foam constructions, and we identify precise conditions under which such formulations remain anomaly-free. No claim is made to resolve the full dynamics problem or to derive novel physical predictions. Instead, the results provide a controlled language for distinguishing structurally stable evolutions from inadmissible ones in background-independent quantum theories. This work is an information-theoretic framework concerned with admissible transport and stability of information under composition. Physical theories, including Loop Quantum Gravity (LQG), are used solely as structured test cases rather than as the primary object of study. LQG serves as a representative background-independent information system. This manuscript is information theory under constraints, not physics. CIFT is an information-theoretic framework in which conserved quantities are measured in bits and are conditional on explicit admission and boundary exchange.