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Quantum Tunneling and Single-Photon Proof: Quantum Mechanics Rules All Scales — E8 Intelligence Research

Andrew Stewart Caldin

Published Aug 29, 2026• 0 citations
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Abstract

FINDING: The 2025 Nobel Prize in Physics centers on experimental proof of macroscopic quantum tunneling and single-photon quantum behavior, confirming that quantum mechanics governs all scales — not just microscopic. | MATH: Central formalism is the Schrödinger equation \( i\hbar \frac{\partial}{\partial t}|\psi\rangle = \hat{H}|\psi\rangle \); tunneling probability via WKB approximation \( T \approx e^{-2\int_{x_1}^{x_2} \sqrt{\frac{2m(V(x)-E)}{\hbar^2}} dx} \); single-photon interference follows \( P(x) = |\psi(x)|^2 \) with \( \psi = \frac{1}{\sqrt{2}}(\psi_1 + \psi_2) \). | CONNECTION: The WKB exponent contains an action integral — its stationary phase condition yields \( \oint p\,dq = n h \) (Bohr-Sommerfeld quantization), which for harmonic oscillators gives energy levels \( E_n = \hbar\omega(n+\tfrac{1}{2}) \). The ratio of successive tunneling amplitudes in a periodic potential (Kronig-Penney) produces band gaps whose widths relate to \( \cos(ka) = \cos(\alpha a) + P\frac{\sin( Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI
10.5281/zenodo.22154640

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FINDING: The 2025 Nobel Prize in Physics centers on experimental proof of macroscopic quantum tunneling and single-photon quantum behavior, confirming that quantum mechanics governs all scales — not just microscopic. | MATH: Central formalism is the Schrödinger equation ( i\hbar \frac{\partial}{\partial t}|\psi\rangle = \hat{H}|\psi\rangle ); tunneling probability via WKB approximation ( T \approx e^{-2\int_{x_1}^{x_2} \sqrt{\frac{2m(V(x)-E)}{\hbar^2}} dx} ); single-photon interference follows ( P(x) = |\psi(x)|^2 ) with ( \psi = \frac{1}{\sqrt{2}}(\psi_1 + \psi_2) ). | CONNECTION: The WKB exponent contains an action integral — its stationary phase condition yields ( \oint p,dq = n h ) (Bohr-Sommerfeld quantization), which for harmonic oscillators gives energy levels ( E_n = \hbar\omega(n+\tfrac{1}{2}) ). The ratio of successive tunneling amplitudes in a periodic potential (Kronig-Penney) produces band gaps whose widths relate to ( \cos(ka) = \cos(\alpha a) + P\frac{\sin( Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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FINDING: The 2025 Nobel Prize in Physics centers on experimental proof that quantum mechanics governs macroscopic phenomena — specifically quantum tunneling and the "quantumness" of reality — with Google's Quantum AI and MIT single-photon experiments as corroborating evidence. | MATH: No new fundamental equation is presented in the titles/descriptions; the core mathematics remains the 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−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. The MIT single-photon experiment confirms the Born rule P=∣⟨ϕ∣ψ⟩∣2 P = |\langle \phi | \psi \rangle|^2 P=∣⟨ϕ∣ψ⟩∣2. | CONNECTION: The tunneling exponent e−2κL e^{-2\kappa L} e−2κL is a decaying exponential — its characteristic decay length 1/κ 1/\kappa 1/κ has no inherent ratio to 0.618 or 1.618. However, the *macroscopic* tunneling demonstrated (likely in superconducting qubits or Josephson junctions) involves phase coherence, where Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: The 2025 Nobel Prize in Physics centers on macroscopic quantum tunnelling, with supporting single-photon experiments confirming quantum theory's non-classical statistical structure. | MATH: Quantum tunnelling probability T≈e−2γd T \approx 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; single-photon interference follows Born rule P(x)=∣ψ(x)∣2 P(x) = |\psi(x)|^2 P(x)=∣ψ(x)∣2, with photon statistics obeying Poisson distribution P(n)=λne−λn! P(n) = \frac{\lambda^n e^{-\lambda}}{n!} P(n)=n!λne−λ​. | CONNECTION: The tunnelling exponent e−2γd e^{-2\gamma d} e−2γd is a decaying exponential — no direct golden-ratio or base-60 link. However, the single-photon interference pattern's fringe spacing Δx=λL/d \Delta x = \lambda L/d Δx=λL/d (double-slit) yields ratios that in certain symmetric setups (e.g., d=λ d = \lambda d=λ) produce Δx=L \Delta x = L Δx=L, and the phase accumulation ϕ=2πdsin⁡θ/λ \phi = 2\pi d \sin\theta/\lambda ϕ=2πdsinθ/λ involves 2π 2\pi 2π — a full circle, echoing base-60's 360° division. No crystallographic symmetry or root-system struct Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: 2025 Nobel Prize in Physics confirms macroscopic quantum tunneling and universal quantum behavior; MIT single-photon experiment validates quantum theory at fundamental level. | MATH: Quantum tunneling probability T≈e−2γ T \approx e^{-2\gamma} T≈e−2γ where γ=1ℏ∫2m(V(x)−E) dx \gamma = \frac{1}{\hbar} \int \sqrt{2m(V(x)-E)} \, dx γ=ℏ1​∫2m(V(x)−E)​dx; Planck constant h=6.62607015×10−34 J⋅s h = 6.62607015 \times 10^{-34} \, \text{J·s} h=6.62607015×10−34J⋅s; reduced Planck constant ℏ=h/2π \hbar = h/2\pi ℏ=h/2π; Schrödinger equation iℏ∂∂t∣ψ⟩=H^∣ψ⟩ i\hbar \frac{\partial}{\partial t} |\psi\rangle = \hat{H} |\psi\rangle iℏ∂t∂​∣ψ⟩=H^∣ψ⟩. | CONNECTION: No explicit geometric ratios (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 or crystallographic symmetries reported in these findings. The quantum tunneling exponent involves no golden ratio or harmonic constants. | DEPTH: 7 — Confirms universality of quantum mechanics and macroscopic tunneling, but mathematical structure is standard quantum formalism without new geometric or harmonic constants. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: The 2025 Nobel Prize in Physics confirms quantum mechanics as the fundamental framework of the universe — specifically via quantum tunnelling and the experimental proof that all physical reality is quantized, not continuous. | MATH: The core mathematical structure is the **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 the tunnelling probability given by the **WKB approximation**: T≈e−2∫x1x22m(V(x)−E)ℏ2dx T \approx e^{-2\int_{x_1}^{x_2} \sqrt{\frac{2m(V(x)-E)}{\hbar^2}} dx} T≈e−2∫x1​x2​​ℏ22m(V(x)−E)​​dx. The Nobel work (Aspect, Clauser, Zeilinger lineage; 2025 extension) relies on **Bell's inequality** violation: ∣E(a,b)−E(a,b′)∣+∣E(a′,b)+E(a′,b′)∣≤2 |E(a,b) - E(a,b')| + |E(a',b) + E(a',b')| \leq 2 ∣E(a,b)−E(a,b′)∣+∣E(a′,b)+E(a′,b′)∣≤2, experimentally broken to 22 2\sqrt{2} 22​ (Tsirelson bound). The single-photon MIT experiment confirms **photon statistics** obey g(2)(0)<1 g^{(2)}(0) < 1 g(2)(0)<1 (anti-bunching), proving quantized field modes. | CONNECTION: The tunnelling exponent ∫V−E dx \int \sqrt{V-E} \, dx ∫V−E​dx is a **path integral over imaginary time** Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: The 2025 Nobel Prize in Physics centers on macroscopic quantum tunnelling, with supporting single-photon experiments confirming quantum theory's non-classical predictions. | MATH: Quantum tunnelling transmission coefficient T≈e−2κd T \approx e^{-2\kappa d} T≈e−2κd, where κ=2m(V0−E)/ℏ \kappa = \sqrt{2m(V_0-E)}/\hbar κ=2m(V0​−E)​/ℏ; single-photon interference visibility V=(Imax−Imin)/(Imax+Imin)→1 V = (I_{\text{max}}-I_{\text{min}})/(I_{\text{max}}+I_{\text{min}}) \to 1 V=(Imax​−Imin​)/(Imax​+Imin​)→1 in the MIT experiment; no new fundamental constants introduced — the framework remains Planck's constant h=6.62607015×10−34 J⋅s h = 6.62607015 \times 10^{-34} \, \text{J·s} h=6.62607015×10−34J⋅s and the Schrödinger equation iℏ∂tψ=H^ψ i\hbar \partial_t \psi = \hat{H}\psi iℏ∂t​ψ=H^ψ. | CONNECTION: The tunnelling exponent e−2κd e^{-2\kappa d} e−2κd is a decaying exponential — its characteristic decay length 1/κ 1/\kappa 1/κ relates to the golden ratio via κd=ln⁡(ϕ)≈0.4812 \kappa d = \ln(\phi) \approx 0.4812 κd=ln(ϕ)≈0.4812 when the barrier width equals the golden-ratio-scaled de Broglie wavelength; however, no explicit geometric ratio (0.382, 0.618, 0.786, Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com