Quantum Physics

Stochastic Electrodynamics of the Photon: Maxwell Equations, Malus’s Law, and the Origin of Photon Randomness from the Electromagnetic Vacuum

Authors: Fusao Ishii

Papers 1—7 of this series derived the Schrodinger equation, the Dirac equation, quantum entanglement, the Coulomb force, the Lamb shift, the anomalous magnetic moment, the hydrogen hyperfine splitting, and the resolution of the double-slit paradox—all for the electron, whose randomness originates in the Zero-Point Field (ZPF) of its own Coulomb interaction. This paper extends the stochastic framework to the photon. The photon has no charge and no rest mass, so the electron’s Abraham—Lorentz equation does not apply directly. We identify the correct photon analogue: the photon’s relativistic (effective) mass meffγ = ℏω0/c^2 replaces the electron rest mass m, and the photon’s own optical cycle τγ0 = 1/ω0 replaces the electron radiation reaction time τ0 = e^2/6πϵ0mc^3. From this photon Abraham—Lorentz equation, equating two independent expressions for the transverse momentum variance gives the photon diffusion coefficient: Dγ = c^2/2ω0 = ℏ/2meffγ, which has exactly the same form as D = ℏ/2m for the electron, with meffγ replacing m. Three major results follow: 1. Maxwell equations are derived from the photon Fokker—Planck equation via the Madelung transformation using the Riemann—Silberstein vector F = √ϵ0E + (i/√μ0)B as the photon wave function. This is the exact photon analogue of deriving the Schrodinger equation from the electron Fokker—Planck in Paper 1. 2. Malus’s law P(pass) = cos(α)^2 is derived from Brownian motion of the polarization angle on the Poincare sphere, without assuming quantum mechanics. 3. Photon randomness originates in the electromagnetic vacuum ZPF—the same field of which the photon is itself a quantum. The coherence volume of a photon equals 2Dγ/ω0 = c^2/ω^2 0 = ¯λ2, consistent with the van Cittert—Zernike theorem. The complete hierarchy of effective descriptions is: Schrodinger (spin- 1/2 , massive) → Dirac (spin- 1/2 , relativistic) → Maxwell (spin-1, massless)—all emerging from stochastic processes driven by the electromagnetic ZPF, differing only in the particle’s mass and spin.

Comments: 28 Pages. This is Paper 8 of a eight-paper series.

Download: PDF

Submission history

[v1] 2026-07-08 22:56:21

Unique-IP document downloads: 24 times

ai.Vixra.org is a AI assisted e-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. ai.Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.