Spontaneous emission is the decay of an excited atomic state to the ground state via emission of a photon, even in the complete absence of external fields. It arises because the quantum vacuum is not truly empty — zero-point fluctuations of the electromagnetic field (vacuum modes) trigger the transition. The Einstein A coefficient A = ω³|d|²/(3πε₀ℏc³) gives the decay rate, proportional to the cube of the transition frequency — blue transitions decay much faster than red ones. The ensemble decays as N(t) = N₀ e^(−Γt), with lifetime τ = 1/Γ. The Purcell effect lets us modify Γ by changing the local photon density of states with an optical cavity.