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The frontiers collection

Of Buckey Balls and SQUIDs: Observing Decoherence in Action

Published Jul 27, 2007• 0 citations
Publisher
DOI
10.1007/978-3-540-35775-9_6

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Bridging Quantum to Classical: Tunneling, Decoherence, and Thermalization — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Macroscopic quantum tunneling and superposition are being experimentally pursued via levitated nanoparticles and atom interferometry, with quantum chaos/thermalization as the theoretical bridge to classicality. | MATH: Quantum tunneling probability \( T \sim e^{-2\gamma L} \) where \( \gamma = \sqrt{2m(V_0-E)}/\hbar \); macroscopic superposition decoherence rate \( \Gamma \sim \Lambda^2 / \hbar^2 \) (where \( \Lambda \) is the action difference between branches); eigenstate thermalization hypothesis (ETH) — for an observable \( O \), matrix elements \( \langle E_\alpha | O | E_\beta \rangle = O(\bar{E})\delta_{\alpha\beta} + e^{-S(\bar{E})/2} f(\bar{E},\omega) R_{\alpha\beta} \), with \( S \) the entropy. | CONNECTION: The decoherence rate scales as \( \Lambda^2 \propto (m v L)^2 \) — the action difference. For a tennis ball (m≈0.06 kg, v≈10 m/s, L≈0.1 m), \( \Lambda \approx 6\times10^{-2} \) J·s, so \( \Gamma \sim 10^{34} \) s⁻¹ — utterly classical. For a levitated nanopartic Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

•Oct 4, 2026•0 citations
FINDING: Macroscopic quantum tunneling and superposition are being experimentally pursued via levitated nanoparticles and atom interferometry, with quantum chaos/thermalization as the theoretical bridge to classicality. | MATH: Quantum tunneling probability T∼e−2γL T \sim e^{-2\gamma L} T∼e−2γL where γ=2m(V0−E)/ℏ \gamma = \sqrt{2m(V_0-E)}/\hbar γ=2m(V0​−E)​/ℏ; macroscopic superposition decoherence rate Γ∼Λ2/ℏ2 \Gamma \sim \Lambda^2 / \hbar^2 Γ∼Λ2/ℏ2 (where Λ \Lambda Λ is the action difference between branches); eigenstate thermalization hypothesis (ETH) — for an observable O O O, matrix elements ⟨Eα∣O∣Eβ⟩=O(Eˉ)δαβ+e−S(Eˉ)/2f(Eˉ,ω)Rαβ \langle E_\alpha | O | E_\beta \rangle = O(\bar{E})\delta_{\alpha\beta} + e^{-S(\bar{E})/2} f(\bar{E},\omega) R_{\alpha\beta} ⟨Eα​∣O∣Eβ​⟩=O(Eˉ)δαβ​+e−S(Eˉ)/2f(Eˉ,ω)Rαβ​, with S S S the entropy. | CONNECTION: The decoherence rate scales as Λ2∝(mvL)2 \Lambda^2 \propto (m v L)^2 Λ2∝(mvL)2 — the action difference. For a tennis ball (m≈0.06 kg, v≈10 m/s, L≈0.1 m), Λ≈6×10−2 \Lambda \approx 6\times10^{-2} Λ≈6×10−2 J·s, so Γ∼1034 \Gamma \sim 10^{34} Γ∼1034 s⁻¹ — utterly classical. For a levitated nanopartic Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com