THE DERIVATION OF SCHRÖDINGER'S EQUATION FROM SCALE-EXTENDED GEOMETRY

Koenig, Andy, Karma

Published May 24, 2026• 0 citations

Abstract

We present a complete derivation of the Schrödinger equation from scale-extendedgeometry. The central claim is that quantum mechanics is not fundamental — it is thelow-energy effective theory obtained by projecting scale-extended dynamics onto theobservable slice ζ=0. The wavefunction Ψ(x,ζ,t) lives in an extended Hilbert space whereζ = ln(E/E0) is the logarithmic energy scale coordinate. The scale Laplacian L_K, withweight K(ζ) = |ψ_KB(ζ)|2 given by the graviton probability density, has a computedground state eigenvalue μ0 = 8.41×10−9. Projecting the scale-extended Schrödingerequation onto this ground state yields the standard Schrödinger equation, with the Born rule emerging from the projection measure K(ζ) rather than being postulated. The near-degenerate pairs in the spectrum (μ2≈μ3, μ4≈μ5, ...) correspond to particle/antiparticle doubling from the odd symmetry of ψ_KB. The action principle is written explicitly.Every algebraic step is shown in full. Full Portolio at: https://drive.google.com/drive/folders/1fdKdo3edGqXVx95IntIumXlzKq22s-yw?usp=drive_link

DOI: 10.5281/zenodo.20360171

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