Hamiltonian Evolution as Structured Admissible Continuation: A Structural Placement within the Paton System

A J Paton

Published Mar 28, 2026• 0 citations

Abstract

This paper clarifies the structural role of Hamiltonian evolution within the Paton System. Without introducing new physical laws or modifying classical or quantum mechanics, Hamiltonian dynamics are interpreted as describing structured admissible continuation of system states. The Hamiltonian is treated not as a physical substance, but as a generator of structured pathways through admissible state space. This interpretation separates structural evolution from physical interpretation while remaining fully consistent with established formalism.

DOI: 10.5281/zenodo.19278319

Related papers

Wave Equation as Propagation of Admissible Structure: A Structural Placement within the Paton System

A J Paton

This paper clarifies the structural role of the wave equation within the Paton System. Without introducing new physical laws or modifying wave mechanics, the equation is interpreted as describing the propagation of admissible structure through a system. Rather than treating waves as moving objects, this framework interprets them as the transmission of structural relations under constraint. This distinction resolves interpretational ambiguity while remaining fully consistent with established physical formalism.

Mar 28, 20260 citations

Schrödinger Equation as Admissible Evolution: A Structural Placement within the Paton System

A J Paton

This paper clarifies the structural role of the Schrödinger equation within the Paton System. Rather than introducing new physical laws or modifying quantum mechanics, the equation is interpreted as governing admissible evolution of system states prior to observational selection. The wavefunction is treated as a representation of recursively evolving admissible structure within Tier-5 (continuation), while observation occurs at Tier-4 as a constrained projection of that structure. This distinction resolves common interpretational ambiguity by separating continuous evolution from discrete observation without altering established quantum formalism.

Mar 28, 20260 citations

Quantum State Admissibility

A J Paton

This paper interprets quantum mechanical state evolution through the admissibility framework of the Paton System. Rather than treating quantum states purely as mathematical vectors evolving under probabilistic measurement rules, the admissibility interpretation recognises that only states satisfying the governing constraints of the quantum system are structurally permitted. Quantum state space therefore represents a constrained admissible manifold in which physical evolution occurs. Measurement outcomes correspond to admissible state transitions within this constrained space. This perspective clarifies why quantum systems exhibit stable statistical behaviour while remaining fundamentally probabilistic: probability operates only within the geometry of states that are structurally permitted to exist.

Mar 9, 20260 citations

Quantum Measurement as Admissibility Collapse: A Structural Interpretation within the Paton System

A J Paton

This paper presents a structural interpretation of quantum measurement within the Paton System framework. Quantum systems are described as occupying sets of admissible configurations prior to measurement. Measurement is treated as a constraint interaction that reduces the admissible configuration set to a single outcome. Collapse is understood as the reduction of admissible configurations under constraint rather than as an additional physical mechanism. The observed outcome corresponds to the configuration that satisfies the combined constraints at the point of interaction. This framework does not modify quantum mechanics and introduces no new ontology. It provides a pre-theoretical structural lens describing measurement as the resolution of admissibility under constraint.

Mar 23, 20260 citations

Entanglement as Constraint-Linked Admissibility: A Structural Interpretation within the Paton System

A J Paton

This paper presents a structural interpretation of quantum entanglement within the Paton System framework. Entangled systems are described as sharing a constraint structure that governs admissibility jointly rather than independently. Admissibility is therefore evaluated at the level of the composite system rather than its individual components. Measurement outcomes in entangled systems reflect constraint-linked admissibility across the joint system. A measurement applied to one subsystem restricts the admissible configuration of the other through the shared constraint structure, without requiring signal transfer. This work does not modify quantum mechanics and introduces no new ontology. It provides a pre-theoretical structural lens in which entanglement is understood as shared constraint determining admissible configurations. It complements prior work on quantum state admissibility and quantum measurement as admissibility collapse without duplication.

Mar 24, 20260 citations

The Schrödinger Equation as Closure Evolution - Hamiltonian Admissibility, Phase Preservation, and Partial Closure Dynamics

Philip Lilien

Paper 1 established quantum mechanics as the mathematics of partial closure within Atomic Continuum Ontology. This second paper develops the first major formal bridge: the Schrödinger equation as closure evolution. Rather than interpreting the wavefunction as a particle-cloud, ghostly object-wave, or hidden object-state, this paper interprets ψ as a phase-bearing partial-closure profile within the atomic continuum. The Schrödinger equation is then translated as the differential law by which partial closure remains dynamically admissible under Hamiltonian constraint. The Hamiltonian becomes a closure-admissibility operator; i expresses phase-rotation structure; ℏ functions as the quantum scale of closure-action; eigenstates become stable closure modes; eigenvalues become disclosed energy residues; and unitary evolution becomes phase-preserving closure flow. This framework preserves the standard quantum formalism while shifting its ontological reading from object motion to partial-closure dynamics. Measurement is not treated as ordinary Schrödinger evolution, but as a later reclosure transition, thereby preparing the transition to Paper 3.

Jul 9, 20260 citations