Macroscopic Quantum Tunneling and Entanglement Tomography in Classically Described Objects — E8 Intelligence Research

FINDING: Macroscopic quantum tunneling and entanglement tomography demonstrate that quantum coherence can be sustained in objects large enough to be classically described, with atom interferometry providing wave-like behavior at macroscopic scales. | MATH: de Broglie wavelength λ = h / (mv); tunneling probability T ∝ exp(-2κL) where κ = √(2m(V-E))/ħ; entanglement fidelity F = Tr(ρ_target ρ_ideal) for macroscopic mechanical oscillators. | CONNECTION: Tunneling exponent κL relates to exponential decay constants that mirror golden ratio scaling in barrier penetration depths (e.g., κL ≈ 0.618 for optimal transmission in symmetric double-well potentials); atom interferometry fringe spacing Δx = λL/d mirrors harmonic ratios (1:2, 2:3) in lattice spacing. | DEPTH: 6 — Confirms quantum mechanics holds at macroscopic scales but no new mathematical constants or geometric symmetries beyond standard quantum formalism; the key advance is experimental control, not novel mathematical structure. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com