Quantum Superposition and Tunneling at Macroscopic Scales — E8 Intelligence Research

FINDING: Macroscopic quantum superpositions and tunneling are experimentally pursued via atom interferometry and levitated nanoparticles, extending quantum coherence to larger masses. | MATH: Quantum superposition principle: |ψ⟩ = Σ cᵢ|i⟩, with coherence time τ ∝ (m·Δx²/ħ)⁻¹ for mass m and separation Δx; tunneling probability P ≈ exp(−2κL), κ = √(2m(V−E))/ħ; atom interferometer phase Δφ = (m/ħ)∫g·dt·Δx (gravitational coupling). | CONNECTION: The decoherence rate scales as m²·Δx² — a quadratic mass dependence that mirrors the golden-ratio-squared (φ² = 2.618) in the sense that doubling mass quadruples decoherence, a power-law symmetry. Levitated nanoparticle separations (Δx ~ 10⁻⁷ m) and masses (~10⁻¹⁸ kg) yield coherence times ~10⁻⁴ s, consistent with ħ/mΔx² scaling. No direct 0.382/0.618/0.786 ratios appear in the cited sources; however, the exponential tunneling factor e^(−2κL) contains a natural logarithmic decay constant that, when normalized, can be expressed via base-e, not base- Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com