Topological Optics from Global Realism: A Three-Axiom Reconstruction of Photon Genesis, Causal Propagation, Matter Response, and Classical–Quantum–Nonlinear Optical Dynamics

Abstract

Abstract We construct topological optics as the optical sector of global realism from three foundational axioms: microscopic ontic definiteness, the physical and causal reality of the spacetime-vacuum substrate, and persistent coupling between every localized matter excitation and that substrate. The inherited finite-core topology, energy functional, electromagnetic projection, retarded historical-field operator, and coarse-graining interfaces are organized into one noncircular dependency system. The resulting optical state contains finite matter world tubes, covariant electromagnetic response, weakly protected radiative packets, constitutive memory, detector records, and a quantitative approximation ledger. We prove an explicit axiom-to-action descent. The three axioms cannot select one universal numerical Lagrangian without geometric, constitutive, boundary, and resolution data. Nevertheless, every admissible optical case possesses an axiom-traceable action equivalence class through a direct variational formulation, a conservative reservoir dilation, or an auxiliary multiplier embedding. Compatible case actions satisfy overlap conditions and form one global optical theory. Regularity and scale conditions are theorem domains; unevaluated coefficients are microscopic calculation obligations carrying residual bounds, not additional postulates. Photon structure is derived rather than assumed. Reduction of the radiative symplectic form gives \(E=\omega J\); single-valued closure of the projected topological phase gives \(J=n\hbar_{\mathrm{top}}\); hence the minimal separated radiative packet obeys \(E_\gamma=\hbar_{\mathrm{top}}\omega\). Local detection is the inverse reconstruction of that packet in finite matter. Positivity, locality, phase invariance, degree-two response, and orthogonal additivity force a positive-operator quadratic detection weight, while the derived disturbance-guided dynamics makes its normalized measure equivariant and entropy attracting. The optical commutator, number ladder, and packet Fock representation then descend from the same symplectic structure and action unit. From this foundation we derive, within one causal and energetic architecture, geometrical and wave optics, interference and diffraction, polarization, coherence and imaging, dispersive and structured media, spectroscopy and scattering, photoelectric and Compton processes, nonlinear conversion, solitary pulses, lasers, photon statistics, entanglement, optomechanics, thermal radiation, moving-media optics, and curved-spacetime propagation. Classical, quantum, nonlinear, statistical, and relativistic optics are therefore controlled sectors of one matter–substrate dynamics rather than independent foundations. Every proposed correction is tied to a recovery limit, an identifiability condition, a residual estimate, and a falsifiable measurement. Topological optics is thus an axiomatic reconstruction of the physical content of light, not an interpretive supplement to inherited optical formalisms. Keywords **Global realism; topological optics; photon genesis; spacetime-vacuum substrate; historical disturbance field; finite-core topology; causal propagation; optical memory; nonlinear photon interaction; quantum detection; Born rule; optical media; photon statistics; curved-spacetime optics; axiomatic reconstruction.**