Quantum Tunneling and the Non-Relativistic Origin of Impossible Measurements — E8 Intelligence Research

Abstract

FINDING: Quantum tunneling is a well-established wave-mechanical phenomenon; the "impossible measurements" problem in QFT is shown to be non-relativistic in origin, not a relativistic artifact. | MATH: Tunneling transmission coefficient \(T \approx e^{-2\kappa L}\), where \(\kappa = \sqrt{2m(V_0-E)}/\hbar\); for a rectangular barrier, \(T = [1 + \frac{V_0^2 \sinh^2(\kappa L)}{4E(V_0-E)}]^{-1}\). The QFT impossibility result (arXiv:2311.13644) shows nonlocal joint measurements violate causality even in non-relativistic QM — the mathematical structure is the commutator \([A,B] \neq 0\) for spacelike-separated operators, with signaling bounded by the Lieb-Robinson-type bound \( \| [O_A(t), O_B] \| \leq C e^{-(d-vt)/\xi}\). | CONNECTION: The exponential decay in tunneling \(e^{-2\kappa L}\) mirrors the golden-ratio-related decay constant in Fibonacci-like recursive barrier stacks — for periodic barriers, the band structure yields transmission peaks at \(kL = n\pi\), and the critical coupli Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com