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Foundations of Quantum Physics III: The Three-Stratum Derivation of Schrödinger Mechanics Constraint, Return, Phase, and the Embedded Einstein Clock

Authors: Needham, Eric;

Foundations of Quantum Physics III: The Three-Stratum Derivation of Schrödinger Mechanics Constraint, Return, Phase, and the Embedded Einstein Clock

Abstract

This restricted record contains the third paper in the ENSO series Foundations of Quantum Physics. The paper proposes that the non-relativistic Schrödinger equation is not merely a postulated dynamical law, but the necessary phase-readable form of constrained dependency under bounded return, once the embedded rest-energy phase is restored to view. The argument is organised into three strata. Stratum I is the time-independent eigenvalue problem, interpreted as a pre-temporal dependency structure among allowed modes, operators, potentials, and boundary conditions. Stratum II is the phase-readability layer: bounded return selects a rotational generator equivalent to the imaginary unit, allowing an admitted mode to be read as recurring phase. Stratum III is the embedded Einstein layer: for massive particles, the full wavefunction contains the rest-energy phase exp(-imc²t/ℏ), whose factoring-out leaves the non-relativistic Schrödinger equation as the slow-envelope equation. The derivation is framed from two declared inputs: a constraint structure and the action scale ℏ. From these, bounded return forces the imaginary phase generator and the Schrödinger form follows. The paper does not claim to derive the full postulate system of quantum mechanics, including spin, measurement update, identical-particle statistics, or the global complex Hilbert-space composition law. It claims that the central wave-mechanical skeleton of non-relativistic quantum mechanics is structurally recovered. The upload includes a Python validation script checking the two directly testable analytic steps: phase readability and rest-energy factorisation. The closure-selection step J² = -I is validated in the companion script for Foundations of Quantum Physics 1. For further information about the ENSO Framework, please contact Eric Needham:ensotheory1@gmail.com 

Keywords

Compton Frequency, Closure, Non-Relativistic Quantum Mechanics, Imaginary Unit, Quantum Foundations, Schrödinger Equation, Embedded Einstein Clock, Quantum Phase, Hamiltonian, ENSO Framework, Wavefunction, Bounded Return, Foundations of Physics, Mathematical Physics, Eigenvalue Problem

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selected citations
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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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