Quantum mechanics is defined here as the theoretical framework crystallised at the fifth Solvay Conference of 1927, comprising five postulates: the wavefunction, the canonical commutation relation [x, p] = iℏ, the Born rule, the Schrödinger equation, and the transition probability rule. We present a complete derivation of all five Solvay postulates from purely classical foundations, starting from the directly observable Coulomb field of the electron. The single empirical input is ℏ—measured from pre-Solvay experiments (Planck 1900—1911, Einstein 1905, Casimir 1948/Lamoreaux 1997) without quantum mechanical interpretation, in the same way G was measured by Cavendish (1798) without general relativity. By Einstein’s photoelectric theory (1905) generalized to all electromagnetic fields, the Coulomb field energy is carried in electromagnetic quanta, each carrying both electric and magnetic fields with energy density ϵ0E^2. The Einstein—Hopf detailed balance condition (1910) uniquely determines the spectral shape ρ(ω) ∝ ω^3. Lorentz invariance confirms this form. The Casimir force measurement gives the total ZPF energy per mode B = ℏ; classical E/B equipartition from Maxwell’s equations gives the electric energy per mode ℏω/2, confirmed by Planck (1911). the central original contribution is the physical justification of the Compton frequency cutoff ωc = mc^2/ℏ: an electron cannot emit an electromagnetic quantum with energy exceeding mc^2, because the residual electron would require negative mass, never observed in nature. Through the Abraham—Lorentz equation, charge e and cutoff ωc both cancel, giving D = ℏ/2m. By Itô’s stochastic calculus and Nelson’s theorem, this gives the Schrödinger equation. The transformation ψ = √ρ e^iS/ℏ linearises the nonlinear Fokker—Planck equation, explaining why superposition holds. All five Solvay postulates emerge as consequences of classical physics plus the single measured constant ℏ. No Solvay postulate is assumed anywhere.