Tone Theory: Boundary Trapping and Soliton Formation
Authors/Creators
Description
Abstract
The primary goal of this paper is to unify the micro-vortical mechanics of localized electronic
bound states and the non-linear transport of boundary-constrained photonic solitons within the Tension
Optimized Newtonian Entropy (TONE) framework. We present two independent mathematical and
computational constructs: a discrete 2D spatial matrix simulation of the ground-state hydrogen atomic
orbital yielding the empirical Rydberg limit, and an analytical Korteweg-de Vries (KdV) boundary-
clamped model of a photon wavepacket traveling down a metallic waveguide. We demonstrate that
both systems, though fundamentally different in their macroscopic configurations, are governed by the
identical fluid-mechanical parameters of an elastic manifold interface. By enforcing a hard universal
kinematic viscosity limit equal to the fine-structure constant (α ≈ 1/137.035999), we mathematically
show how localized atomic orbits reach structural stability and why waveguide boundary constraints
deterministically slow the group velocity of light without causing wavepacket dispersion.
PACS Codes: 03.65.Ge, 42.65.Tg, 47.10.ad, 02.40.Dr, 84.40.Az
Keywords: Tension Optimized Newtonian Entropy, Ground-State Atomic Matrix, Waveguide Solitons,
Viscous Damping, Boundary-Value Problems, Rydberg Constant
Copyright © 2026 Anthony Santana. All Rights Reserved. Copyright Pending.
DOI: 10.5281/zenodo.21881473