Lorentz-Covariant Bi-Photonic Kinematics: Deriving Optical Polarization and the Born Rule from Internal Constrained Dynamics

(Dated: November 7, 2026) Standard quantum electrodynamics (QED) treats the photon as an unstructured, point-like excitation of a gauge field. In this orthodox framework, when light encounters a measurement device, its continuous wave description abruptly and unpredictably reduces to a single discrete detector click. The statistical likelihood of recording that click is calculated by squaring the overlap between the incoming wave state and the detector state—an operational prescription universally known as the Born rule (P = |⟨ϕ|ψ⟩|2). The persistent inability of spontaneous collapse hypotheses, context-free hidden-variable schemes, and many-worlds branching to eliminate fundamental unpredictability stems from treating abstract state vectors as irreducible primitives of nature. Here, we formulate a relativistic, composite two-particle (bi-photonic) model of light in which a single optical packet consists of a phase-locked pair of conjugate sub-elements (γA, γB) executing internal transverse orbital motion on a light-cone surface. Using relativistic Hamiltonian mechanics with algebraic constraints (Dirac constraint mechanics), we prove that the negative internal binding potential exactly cancels the positive transverse orbital kinetic energy inside the invariant mass operator.