Second-Order Coherence g²(τ) as the Operational Discriminator of Classical and Quantum Light — E8 Intelligence Research

FINDING: Second-order coherence g²(τ) is the operational discriminator between classical and quantum light — anti-bunching (g²(0)<1) is the signature of a single-photon (Fock) state, bunching (g²(0)>1) of thermal/chaotic light, and g²(0)=1 of coherent (Poissonian) light. | MATH: g²(τ) = ⟨a†(t)a†(t+τ)a(t+τ)a(t)⟩ / ⟨a†(t)a(t)⟩². Fock |n⟩: g²(0) = 1 − 1/n → 0 for n=1. Thermal: g²(0)=2. Coherent: g²(0)=1. HOM dip: coincidence rate ∝ 1 − |⟨ψ₁|ψ₂⟩|², vanishing for indistinguishable photons. | CONNECTION: g²(0)=2 for thermal light is the Bose-Einstein enhancement factor (n+1)/n → 2 at n=1; the factor 2 is the two-photon permutation symmetry of the symmetric group S₂ acting on bosonic modes — the same combinatorial root that gives the 1/2 in spin-statistics and the 2 in the Planck distribution's zero-point term. The HOM dip is the two-photon Hong-Ou-Mandel amplitude |t₁t₂ − r₁r₂|² = 0 for a balanced 50/50 beam splitter (|r|=|t|=1/√2), i.e. destructive interference of the two S₂-symmetric paths Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com