Coincidence Interpretation of the Born Rule: The Two-Photon Bound State as the Physical Origin of \( |\psi|^2 \)

The Born rule assigns probability density \( |\psi|^2 = \psi^* \psi \) to a single wavefunction. It is postulated here that this interpretation, while computationally successful, conflates two physically distinct situations. For a bound state, \( \psi^*\psi \) is not the square of a single wavefunction but the coincidence product of two independent conjugate wavefunctions \( \psi_1\psi_2 \) — one incident, one its counter-propagating conjugate — simultaneously present. Detection of a quantum event requires the coincidence of these two conjugates at the detection point; a single wavefunction alone cannot populate a bound energy state or trigger detection. Stated carefully, the postulate is a bilinear detection law: detection is postulated to depend bilinearly on two conjugate field amplitudes through their product, rather than on an independently squared probability for each field. Under stated hypotheses this law reproduces standard results of quantum mechanics — the double slit interference pattern in the pair-arrival regime, and an invariant composite rest mass for the bound pair — without wavefunction collapse. A complete account of Bell correlations is not claimed: a locally factorizable coincidence model cannot reproduce the quantum correlations for arbitrary analyzer settings, and constructing a CHSH-complete treatment is registered as the central open problem of the interpretation (Section 5). The two-photon electron of Delta-c Mechanics provides the mechanical realization of this postulate: the electron is formed by two conjugate photons in counter-propagating circular orbit, their combined flow density forming a standing wave that is Lorentz invariant by construction. A structural correspondence between the Feynman path-integral hierarchy and this standing-wave construction is proposed in companion work; the exact amplitude mapping remains open. A Thomson scattering experiment capable of distinguishing the coincidence interpretation from standard QM is identified and described in a companion paper.