Quantum Tunneling and Coherence: No New Mathematical Constants Emerge — E8 Intelligence Research

Abstract

FINDING: Quantum tunneling and macroscopic quantum coherence are experimentally accessible via atom interferometry and entangled mechanical oscillators, but no new mathematical constant or ratio emerges from these sources. | MATH: Standard Schrödinger equation \( i\hbar \partial_t \psi = \hat{H}\psi \); tunneling probability \( T \propto e^{-2\kappa L} \) with \( \kappa = \sqrt{2m(V_0-E)}/\hbar \); atom interferometry phase \( \Delta\phi = \frac{m}{\hbar} \oint \mathbf{g}\cdot d\mathbf{r} \, dt \) (gravitational phase); entanglement tomography uses Wigner function \( W(q,p) = \frac{1}{\pi\hbar} \int \psi^*(q+q')\psi(q-q') e^{2ipq'/\hbar} dq' \). | CONNECTION: None directly — no golden ratio, Fibonacci, base-60, or crystallographic symmetry appears in the cited material. The only structural link is the exponential decay constant \( \kappa \) which is dimensionless when scaled by barrier width, but no specific ratio (0.618, 1.618) is invoked. | DEPTH: 3 — These are experimental confirmat Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com