Mass-Squared Decoherence: Quantum Coherence Fades Exponentially, Not Abruptly — E8 Intelligence Research

FINDING: Macroscopic quantum tunneling and levitated nanoparticle superposition reveal that quantum coherence scales with mass via exponential suppression, not a hard classical boundary. MATH: Tunneling rate ∝ exp(−2γ/ℏ) where γ = ∫√(2m(V(x)−E))dx (WKB); decoherence rate Γ ∝ (m·Δx)²/τ_env; superposition lifetime τ ∝ 1/(m²·Δx²·k_BT); no new constants — only ℏ, m, Δx, T. CONNECTION: The exponential decay of coherence with mass² mirrors the golden-ratio-adjacent scaling in dissipative systems: Γ ∝ m² suggests a quadratic form, linking to root system B₂ (square lattice symmetry) in phase space — not 0.618 directly, but the exponent 2 is the rank of the B₂ root lattice. DEPTH: 6 — confirms known quantum mechanics at larger scales, but no new mathematical structure; the mass² scaling is a consequence of harmonic oscillator commutators, not a novel ratio. FINDING: Atom interferometry (Kasevich) uses matter-wave superposition to measure gravitational acceleration with precision ~10⁻⁹ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com