Quantum Lightning: A New Foundation for Quantum Optics — Single-Photon and Biphoton Equivalence with QED in Linear Optics

We state a set of postulates describing the dynamics of a condensate vacuum and its massless transverse vector mode excitations. From these postulates alone, we derive five lemmas establishing that the mode structure, transition amplitudes, detection probabilities, polarisation correlations, and measurement formalism of the condensate framework are identical to those of quantum electrodynamics for single-photon and biphoton experiments in linear optical apparatus. The Born rule is derived from electromagnetic energy flux, condensate fluctuation statistics, and the Poisson limit theorem, without assuming the Born rule or any quantum probability postulate. The fluctuation properties entering the derivation are shown to arise from the classical nonlinear dynamics of the condensate Lagrangian, with no dependence on Planck's constant. Bell inequality violation is derived from the joint vector mode structure of spontaneous parametric down-conversion. The measurement problem is given a physical mechanism: the projection postulate and decoherence emerge as consequences of competitive circuit dynamics. The postulates are stated for any field with current coupling; the photon sector is the first worked example. Extension to fermions is established in a companion paper.