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Paper I — Ordered Dynamics and Operational State Spaces

Paul Cooney

Published Dec 14, 2025• 0 citations
Publisher

Abstract

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

DOI
10.5281/zenodo.17925620

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Paper III — Relativistic Extension of Ordered Information Locality DescriptionExtending the operational locality framework into a relativistic regime, this paper demonstrates how Lorentz-compatible dynamics emerge from ordered information constraints. Without presupposing Minkowski spacetime, relativistic causal structure arises from invariant bounds on influence propagation. This work situates special relativity as an emergent consistency condition within the Ordered-Dynamics Reconstruction Program rather than a fundamental geometric assumption. Keywordsrelativity; Lorentz invariance; operational locality; causal structure; emergent spacetime; quantum foundations

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Paper VI — Entanglement Information Locality and Many-Body Structure

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Paper XII - Emergent Spatial Locality from Bounded Influence

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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 III — Relativistic Extension of Ordered Information Locality DescriptionExtending the operational locality framework into a relativistic regime, this paper demonstrates how Lorentz-compatible dynamics emerge from ordered information constraints. Without presupposing Minkowski spacetime, relativistic causal structure arises from invariant bounds on influence propagation. This work situates special relativity as an emergent consistency condition within the Ordered-Dynamics Reconstruction Program rather than a fundamental geometric assumption. Keywordsrelativity; Lorentz invariance; operational locality; causal structure; emergent spacetime; quantum foundations
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
We develop a pre-geometric reconstruction framework in which quantum mechanics, entanglement structure, gauge symmetry, locality, Lorentzian spacetime geometry, gravitation, and physical constants emerge from recursively stabilized coherent Hilbert-relational organization. The framework begins from a primitive coherent substrate consisting of compositional accessibility relations and complex transport amplitudes. No background spacetime manifold, metric geometry, or particle ontology is assumed fundamentally. The central proposal is that coherent Hilbert structure is more fundamental than spacetime geometry. Observable spacetime emerges through projection stabilization: a physical stability-selection mechanism dynamically selecting recursively stable coherent sectors from deeper relational structure. Quantum mechanics emerges from norm-preserving coherent transport. Entanglement emerges from nonfactorizable relational closure. Gauge symmetry emerges as redundancy of coherent transport representation. Classicality emerges through decoherence and stability selection. Lorentzian geometry emerges statistically from projected accessibility organization. Gravitation emerges thermodynamically as equilibrium relaxation of projected geometry. The framework is presented not as a completed unified theory, but as a reconstruction program aimed at explaining why physical reality organizes itself through Hilbert structure, gauge redundancy, locality, spacetime geometry, and thermodynamic gravitational dynamics.
We develop a conditionally closed reconstruction of quantum mechanics from exactly three physical axioms: microscopic ontic definiteness and finite localization, physical reality of the spacetime--vacuum substrate, and persistent causal source--response coupling. Wave functions, Hilbert spaces, complex amplitudes, density operators, the Born rule, commutation relations, Fock spaces, path integrals, completely positive maps, and Markovian dynamics are introduced only as derived mathematical or operational structures, not as additional physical axioms. The construction distinguishes the actual finite carrier and its causal history from the quantum state used to represent preparations, transformations, and measurement probabilities. It derives unitary dynamics from self-adjoint Hamiltonians, formulates spectral observables and probability currents, and states the explicit equilibrium, additivity, noncontextuality, and calibration conditions required for the Born representation. Measurement is described through instruments, pointer dynamics, stable records, weak values, continuous monitoring, diffusive and counting trajectories, and operational error--disturbance relations. Quantum trajectories remain record-conditioned predictive representations rather than automatically ontic paths. Composite systems, identical particles, spin, entanglement entropy, purification, steering, Bell correlations, dense coding, and no-broadcasting are developed on declared tensor-product and symmetry domains. Open-system dynamics are formulated through causal Volterra equations, memory kernels, initial-slip terms, auxiliary-mode realizations, and unitary dilations. Existence, positivity, complete positivity, trace preservation, no-signalling, and energy closure are treated as logically distinct properties. Semiclassical pseudodifferential calculus, controlled path-integral convergence, Ehrenfest-time bounds, semiclassical measures, decoherence, and macroscopic-record stability define the quantum--classical interface. Topological phases, defect-bound states, relativistic wave equations, infrared dressing, and effective quantum-field-theory domains are incorporated with explicit applicability and error conditions. Numerical spectral certification, statistical model comparison, twenty-five benchmark models, theorem-status ledgers, and a complete experimental statistical protocol provide falsification and replication criteria. The resulting framework preserves standard quantum mechanics on its validated domain while isolating finite-core and historical corrections as conditional, quantitatively bounded, and experimentally testable extensions. **Keywords** Quantum foundations; topological quantum mechanics; historical memory; three-axiom reconstruction; Born rule; quantum measurement; weak measurement; quantum trajectories; entanglement; spin and statistics; open quantum systems; Volterra equations; semiclassical limit; quantum topology; numerical certification; experimental falsification.
We establish two foundational results concerning time and irreversibility within an operational framework where physical measurements correspond to distinguishable, persistent record states. First, we prove that no physical clock can ground time as a fundamental parameter: any clock-induced ordering necessarily reduces to a preorder defined by reachability among record states via admissible transformations. Second, we prove that bounded recording capacity forces accessible irreversibility: any system capable of recording more distinct events than its accessible register capacity must exhibit non-invertible operations at the accessible level. These results are derived without assuming time, entropy, or thermodynamic principles as primitives. Together, they establish that temporal structure and irreversibility are not independent physical laws but emerge from operational constraints on physical memory and distinguishability. The framework is compatible with globally unitary microscopic dynamics while explaining effective irreversibility for bounded observers. We conclude that time is a representational index for record structure rather than an ontological primitive , establishing the necessary foundation for the failure of deterministic prediction addressed in companion work [3]