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

A J Paton

Published Mar 28, 2026• 0 citations
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Abstract

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.

DOI
10.5281/zenodo.19276402

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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.
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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.
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.
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.
This paper derives Schrödinger evolution as a structural consequence of coherent persistence rather than as a postulate of quantum mechanics. Starting from minimal requirements for viable propagation—linearity, norm preservation, and continuity—we show that admissible evolution must be unitary and generated by a self-adjoint operator. The resulting Schrödinger equation describes reversible propagation within the space of viable states, while irreversible selection arises separately from the return operation. This separation clarifies the relation between unitary dynamics and measurement without introducing collapse mechanisms or stochastic dynamics. Schrödinger evolution thus emerges as the unique form of continuous, coherence-preserving propagation compatible with structural closure and return, completing the dynamical layer of the Structural Coherence framework.
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.