Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

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

Andrew Stewart Caldin

Published Oct 4, 2026• 0 citations
Publisher

Abstract

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

DOI
10.5281/zenodo.23131880

Related papers

Quantum Tunneling and Superposition: Experimental Frontiers, No New Math — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Quantum tunneling and macroscopic quantum superposition are being actively pursued via levitated nanoparticles and atom interferometry, but no new mathematical constant or equation emerges from these search results — they are experimental/educational, not theoretical breakthroughs. | MATH: No new equations or constants extracted. Relevant known formalism: tunneling probability \( T \approx e^{-2\kappa L} \), \(\kappa = \sqrt{2m(V_0-E)}/\hbar\); macroscopic superposition requires maintaining coherence time \(\tau \propto \hbar^2/(m k_B T x^2)\) (decoherence rate scaling). Atom interferometry phase: \(\Delta\phi = (m/\hbar) \oint \mathbf{g}\cdot d\mathbf{r}\, dt\). | CONNECTION: None directly stated. However, note that levitated nanoparticle superposition experiments often use optical lattices — which are periodic structures with crystallographic symmetry (e.g., 1D lattice spacing \(d = \lambda/2\) — ratio 0.5, not golden). No 0.382/0.618/0.786/1.618/2.618 or base-60 appears in Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

•Oct 19, 2026•0 citations

Quantum Superposition and Tunneling at Macroscopic Scales — E8 Intelligence Research

Andrew Stewart Caldin

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

•Aug 25, 2026•0 citations

Quantum Tunneling and Levitated Nanoparticles: No New Math Emerges — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Macroscopic quantum tunneling and levitated nanoparticle superposition push quantum coherence to larger scales, but no new mathematical structure emerges from these sources. | MATH: No explicit equations, constants, or ratios provided in the search results. Standard framework: Schrödinger equation \( i\hbar \partial_t \psi = \hat{H}\psi \), tunneling probability \( T \propto e^{-2\gamma d} \) where \( \gamma = \sqrt{2m(V_0-E)}/\hbar \), decoherence rate \( \Gamma \propto (m v / \hbar)^2 \) for environmental scattering. | CONNECTION: None directly stated. However, the exponential decay in tunneling probability \( e^{-2\gamma d} \) echoes the golden ratio's logarithmic spiral decay rate \( e^{-0.4812\theta} \) — but this is coincidental, not evidence. Levitated nanoparticles in superposition involve optical traps with Gaussian potentials — no crystallographic symmetry. | DEPTH: 3/10 — These are pedagogical or experimental progress reports, not new mathematical discoveries. The h Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

•Aug 30, 2026•0 citations

Macroscopic Quantum Tunneling and Levitated Nanoparticles: Qualitative Review, No New Formalism — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Macroscopic quantum tunneling and levitated nanoparticle superposition are experimentally accessible, but the search results contain no new mathematical formalism — only qualitative descriptions of existing quantum mechanics applied to larger systems. MATH: No new equations, constants, or ratios are presented in the provided sources. The underlying mathematics remains the standard Schrödinger equation \( i\hbar \frac{\partial}{\partial t}|\psi\rangle = \hat{H}|\psi\rangle \), with tunneling probability \( T \propto e^{-2\gamma L} \) where \( \gamma = \sqrt{2m(V_0-E)}/\hbar \). Atom interferometry relies on the de Broglie wavelength \( \lambda = h/mv \). No novel constants or dimensionless ratios emerge from the search summaries. CONNECTION: No explicit geometric harmony ratios (0.382, 0.618, 0.786, 1.618, 2.618), base-60, or crystallographic symmetries appear in the findings. However, the levitated nanoparticle superposition experiments inherently involve trapping potent Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

•Oct 9, 2026•0 citations

Quantum Coherence Scales with Mass, Not Geometry: No Macroscopic Teleportation — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Macroscopic quantum tunneling and levitated nanoparticle superpositions confirm quantum coherence scales with mass, not geometry — no teleportation of macroscopic objects is evidenced, only probabilistic state transfer. MATH: Quantum tunneling probability \( T \propto e^{-2\gamma L} \), where \(\gamma = \sqrt{2m(V_0-E)}/\hbar\). For macroscopic objects, \(m \sim 10^{-3}\,\text{kg}\), \(L \sim 0.1\,\text{m}\), \(V_0-E \sim 1\,\text{J}\) → \(T \sim e^{-10^{30}}\) — effectively zero. Levitated nanoparticle superposition: decoherence rate \(\Gamma \propto (m \Lambda^2 / \hbar^2) k_B T_{\text{env}}\), with \(\Lambda\) = trap wavelength. No new constants or ratios emerge. CONNECTION: None. No 0.382, 0.618, 0.786, 1.618, 2.618, base-60, or crystallographic symmetry appears in any cited work. The only lattice-like structure is the optical trap (periodic potential), but its ratio is arbitrary (laser wavelength), not harmonic. DEPTH: 2 — These are incremental experimental confirma Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

•Oct 10, 2026•0 citations

Quantum Tunneling and Superposition: Scaling Laws Confirmed, No Teleportation Breakthrough — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Quantum tunneling and macroscopic superposition research confirms wave-mechanical scaling laws, but no teleportation-specific mathematical breakthrough is present in these sources. | MATH: Tunneling probability \( T \approx e^{-2\kappa L} \), where \( \kappa = \sqrt{2m(V_0-E)}/\hbar \); decoherence rate \( \Gamma \propto (m \Delta x)^2 / \tau \) for levitated nanoparticles; atom interferometry phase \( \Delta\phi = k_{\text{eff}} g T^2 \) (Kasevich). | CONNECTION: The exponential tunneling exponent contains the ratio \( \kappa L \) — no direct golden-ratio or base-60 link; however, the macroscopic superposition criterion \( \Delta x / \lambda_{\text{dB}} \gg 1 \) echoes scale-invariant ratios (e.g., 0.618 appears only if one imposes harmonic oscillator eigenstate overlaps, which are not stated). Crystallographic symmetry absent. | DEPTH: 3 — These are pedagogical and experimental reviews, not new mathematical discoveries. The transfer-learning paper (arXiv:1912.08278) is algor Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

•Oct 20, 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 \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
FINDING: Quantum tunneling and macroscopic quantum superposition are being actively pursued via levitated nanoparticles and atom interferometry, but no new mathematical constant or equation emerges from these search results — they are experimental/educational, not theoretical breakthroughs. | MATH: No new equations or constants extracted. Relevant known formalism: tunneling probability T≈e−2κL T \approx e^{-2\kappa L} T≈e−2κL, κ=2m(V0−E)/ℏ\kappa = \sqrt{2m(V_0-E)}/\hbarκ=2m(V0​−E)​/ℏ; macroscopic superposition requires maintaining coherence time τ∝ℏ2/(mkBTx2)\tau \propto \hbar^2/(m k_B T x^2)τ∝ℏ2/(mkB​Tx2) (decoherence rate scaling). Atom interferometry phase: Δϕ=(m/ℏ)∮g⋅dr dt\Delta\phi = (m/\hbar) \oint \mathbf{g}\cdot d\mathbf{r}\, dtΔϕ=(m/ℏ)∮g⋅drdt. | CONNECTION: None directly stated. However, note that levitated nanoparticle superposition experiments often use optical lattices — which are periodic structures with crystallographic symmetry (e.g., 1D lattice spacing d=λ/2d = \lambda/2d=λ/2 — ratio 0.5, not golden). No 0.382/0.618/0.786/1.618/2.618 or base-60 appears in Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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
FINDING: Macroscopic quantum tunneling and levitated nanoparticle superposition push quantum coherence to larger scales, but no new mathematical structure emerges from these sources. | MATH: No explicit equations, constants, or ratios provided in the search results. Standard framework: Schrödinger equation iℏ∂tψ=H^ψ i\hbar \partial_t \psi = \hat{H}\psi iℏ∂t​ψ=H^ψ, tunneling probability T∝e−2γd T \propto e^{-2\gamma d} T∝e−2γd where γ=2m(V0−E)/ℏ \gamma = \sqrt{2m(V_0-E)}/\hbar γ=2m(V0​−E)​/ℏ, decoherence rate Γ∝(mv/ℏ)2 \Gamma \propto (m v / \hbar)^2 Γ∝(mv/ℏ)2 for environmental scattering. | CONNECTION: None directly stated. However, the exponential decay in tunneling probability e−2γd e^{-2\gamma d} e−2γd echoes the golden ratio's logarithmic spiral decay rate e−0.4812θ e^{-0.4812\theta} e−0.4812θ — but this is coincidental, not evidence. Levitated nanoparticles in superposition involve optical traps with Gaussian potentials — no crystallographic symmetry. | DEPTH: 3/10 — These are pedagogical or experimental progress reports, not new mathematical discoveries. The h Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Macroscopic quantum tunneling and levitated nanoparticle superposition are experimentally accessible, but the search results contain no new mathematical formalism — only qualitative descriptions of existing quantum mechanics applied to larger systems. MATH: No new equations, constants, or ratios are presented in the provided sources. The underlying mathematics remains the standard Schrödinger equation iℏ∂∂t∣ψ⟩=H^∣ψ⟩ i\hbar \frac{\partial}{\partial t}|\psi\rangle = \hat{H}|\psi\rangle iℏ∂t∂​∣ψ⟩=H^∣ψ⟩, with tunneling probability T∝e−2γL T \propto 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. Atom interferometry relies on the de Broglie wavelength λ=h/mv \lambda = h/mv λ=h/mv. No novel constants or dimensionless ratios emerge from the search summaries. CONNECTION: No explicit geometric harmony ratios (0.382, 0.618, 0.786, 1.618, 2.618), base-60, or crystallographic symmetries appear in the findings. However, the levitated nanoparticle superposition experiments inherently involve trapping potent Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Macroscopic quantum tunneling and levitated nanoparticle superpositions confirm quantum coherence scales with mass, not geometry — no teleportation of macroscopic objects is evidenced, only probabilistic state transfer. MATH: Quantum tunneling probability T∝e−2γL T \propto e^{-2\gamma L} T∝e−2γL, where γ=2m(V0−E)/ℏ\gamma = \sqrt{2m(V_0-E)}/\hbarγ=2m(V0​−E)​/ℏ. For macroscopic objects, m∼10−3 kgm \sim 10^{-3}\,\text{kg}m∼10−3kg, L∼0.1 mL \sim 0.1\,\text{m}L∼0.1m, V0−E∼1 JV_0-E \sim 1\,\text{J}V0​−E∼1J → T∼e−1030T \sim e^{-10^{30}}T∼e−1030 — effectively zero. Levitated nanoparticle superposition: decoherence rate Γ∝(mΛ2/ℏ2)kBTenv\Gamma \propto (m \Lambda^2 / \hbar^2) k_B T_{\text{env}}Γ∝(mΛ2/ℏ2)kB​Tenv​, with Λ\LambdaΛ = trap wavelength. No new constants or ratios emerge. CONNECTION: None. No 0.382, 0.618, 0.786, 1.618, 2.618, base-60, or crystallographic symmetry appears in any cited work. The only lattice-like structure is the optical trap (periodic potential), but its ratio is arbitrary (laser wavelength), not harmonic. DEPTH: 2 — These are incremental experimental confirma Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum tunneling and macroscopic superposition research confirms wave-mechanical scaling laws, but no teleportation-specific mathematical breakthrough is present in these sources. | MATH: Tunneling probability T≈e−2κL T \approx e^{-2\kappa L} T≈e−2κL, where κ=2m(V0−E)/ℏ \kappa = \sqrt{2m(V_0-E)}/\hbar κ=2m(V0​−E)​/ℏ; decoherence rate Γ∝(mΔx)2/τ \Gamma \propto (m \Delta x)^2 / \tau Γ∝(mΔx)2/τ for levitated nanoparticles; atom interferometry phase Δϕ=keffgT2 \Delta\phi = k_{\text{eff}} g T^2 Δϕ=keff​gT2 (Kasevich). | CONNECTION: The exponential tunneling exponent contains the ratio κL \kappa L κL — no direct golden-ratio or base-60 link; however, the macroscopic superposition criterion Δx/λdB≫1 \Delta x / \lambda_{\text{dB}} \gg 1 Δx/λdB​≫1 echoes scale-invariant ratios (e.g., 0.618 appears only if one imposes harmonic oscillator eigenstate overlaps, which are not stated). Crystallographic symmetry absent. | DEPTH: 3 — These are pedagogical and experimental reviews, not new mathematical discoveries. The transfer-learning paper (arXiv:1912.08278) is algor Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com