A Two‑Dimensional Zero‑Volume Ontological Model of the Photon Based on Self‑Consistent Conditions of Maxwell Field‑Source

Abstract

Classical electromagnetic theory directly identifies freely propagating electromagnetic waves with the homogeneous zero‑source solutions of Maxwell’s equations, assuming ρ=0, J=0 for vacuum electromagnetic fields. This paradigm successfully describes macroscopic wave phenomena, yet confuses two physically distinct kinds of light‑speed electromagnetic fields: bound fields originating from sub‑luminal material charges, and the intrinsic radiation field of free photons. From Maxwell equations and the d’Alembert equation, this paper distinguishes bound electromagnetic waves (ρ=0, J=0) and free electromagnetic waves (photons, ρ≠0, J≠0). For stable dispersion‑free propagation at speed of light, the photon’s equivalent charge‑current source must be confined within a two‑dimensional surface with zero three‑dimensional volume, so that the total integrated charge remains zero. Outside the photon plane there exists no electromagnetic field; otherwise bound‑field contradictions would appear. The traditional electromagnetic field energy density formula encounters conceptual conflict with this model, because it is not directly derived from Maxwell’s equations. A critical experimental prediction is given: the cross‑section of two‑photon annihilation γ+γ→e⁺e⁻ depends on the relative angle between the two photon planes, an angular dependence absent in standard QED. Observation of this effect can test the two‑dimensional intrinsic geometry of photons.