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

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 \( i ∂/∂ t|ψ = Ĥ|ψ \); tunneling probability via WKB approximation \( T ≈ e^{-2∫x_1x_2 √2m(V(x)-E)/^2 dx} \); single-photon interference follows \( P(x) = |ψ(x)|^2 \) with \( ψ = {1}{√2}(ψ_1 + ψ_2) \). | CONNECTION: The WKB exponent contains an action integral — its stationary phase condition yields \( ∮ p\,dq = n h \) (Bohr-Sommerfeld quantization), which for harmonic oscillators gives energy levels \( E_n = ω(n+1/2) \). The ratio of successive tunneling amplitudes in a periodic potential (Kronig-Penney) produces band gaps whose widths relate to \( cos(ka) = cos(α a) + P{sin( Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com