Unifying Classical and Quantum Malus Laws via Cosine-Squared Intensity — E8 Intelligence Research

FINDING: Malus's Law — both classical (light polarization) and quantum (spin-1/2) — reduces to a cosine-squared intensity law, with the quantum case requiring a quasi-probability distribution that can go negative, revealing a deep algebraic identity between SU(2) spin projections and classical polarization geometry. | MATH: Classical: \(I(\theta) = I_0 \cos^2\theta\) (Malus, 1809). Quantum spin-1/2: for a spin state \(|+\rangle_n\) measured along axis \(m\), probability \(P = \cos^2(\theta/2)\), where \(\theta\) is the angle between axes \(n\) and \(m\). Equivalently, \(P = \frac{1}{2}(1 + \cos\theta) = \frac{1}{2}(1 + \mathbf{n}\cdot\mathbf{m})\). The quantum Malus law is formally identical to classical if one uses a Wigner-like quasi-distribution \(W(\theta)\) that can be negative; the classical case has \(W(\theta) = \delta(\theta - \theta_0)\) (positive). Generalization to spin-\(j\): \(P_j(\theta) = \left[\cos^{2j}(\theta/2)\right]\) for extreme eigenstates, with intermediate proj Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com