Volume 1: Hydrodynamic Topology of the Electron and Electric Charge

Abstract

We present a complete derivation of the fine structure constant ($\alpha \approx 1/137$), the weak mixing angle ($\sin^2 \theta_W = 2/9$), the proton-electron mass ratio ($\mu = 6\pi^5 = 1836.12$), and the cosmological constant ($\Lambda \approx 10^{-114}$) from a geometric framework with zero free parameters.

Key Results:

• Unified Action: All physics derives from a single action in 11D ($M^4 \times X^7$) based on G2 holonomy and $W_1$ torsion.

• Geometric Origins: The "arbitrary" constants of the Standard Model are shown to be geometric invariants of a 7-dimensional phase space projection.

• Dark Matter: Predicts a 7.0 keV "dark etheron" (phase-only vortex) corresponding to the unconfirmed 3.5 keV X-ray line.

• Quantum Foundations: Demonstrates that quantum mechanics emerges from classical ether dynamics in 7D phase space, resolving the measurement problem via gravitational phase kicks ($\Gamma \propto m^5$).

This document serves as Volume 1 of a research series, providing the comprehensive mathematical framework and foundational derivations for the specific results published in separate letters.