Quantum Tunneling: Exponential Barrier Penetration and Non-Ideal QFT Measurements — E8 Intelligence Research

Abstract

FINDING: Quantum tunneling is a wave-mechanical transmission through classically forbidden barriers, governed by exponential decay of the wavefunction inside the barrier; "impossible" QFT measurements are possible but non-ideal, with signaling constraints. | MATH: Transmission coefficient \(T \approx e^{-2\kappa L}\), where \(\kappa = \sqrt{2m(V_0-E)}/\hbar\); barrier penetration depth \(\delta = 1/\kappa = \hbar/\sqrt{2m(V_0-E)}\). For a rectangular barrier, exact \(T = [1 + \frac{V_0^2 \sinh^2(\kappa L)}{4E(V_0-E)}]^{-1}\). In the WKB limit, \(T \sim \exp\left(-\frac{2}{\hbar}\int_{x_1}^{x_2}\sqrt{2m(V(x)-E)}\,dx\right)\). | CONNECTION: The exponential decay constant \(\kappa\) is a pure inverse length; the ratio of transmitted to incident amplitude involves \(\sinh(\kappa L)\), which for large \(\kappa L\) approaches \(e^{\kappa L}/2\) — yielding the golden-ratio-adjacent asymptotic \(T \propto (e^{\kappa L}/2)^{-2} = 4e^{-2\kappa L}\). No direct 0.618/1.618 ratio emerges from the b Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com