The Electron – A Round Arrow of Light: An Effective Mass Model of the Electron Using Arrows of Light

n all of modern physics the electron is a point particle with no internal structure. Arrow numbers, with a real and an imaginary part, give us a new physical perspective, and let us look inside the electron, and inside we see the light. This continues the atomic view of the Greeks, who looked for smaller and smaller elementary parts of matter, except that the parts are now waves. Besides straight-arrow motion, uniform in a line, we propose a new type of free motion, given by a round arrow of light: an arc, measured in the same unit as a straight arrow, on which the light runs with no outside force. A wave carried once around a ring by the half-angle arrow comes back reversed, so the light closes on the ring when half a wavelength fits: the radius ℏ/2mc = 1.93 × 10⁻¹³ m, half the reduced Compton wavelength, the energy mc² and the spin ℏ/2 follow, with no half quantum assumed. Its effective mass holds the ring: confined there, the light has the dispersion of a particle whose rest mass is the electron’s. Of all the rings the closure allows, the electron’s arrow pair takes only the lowest, which is why no excited electron is seen. The charge stays a point at the centre, as scattering sees it; the ring carries the energy. The same arrows lead from Fermat’s least time to Maxwell’s equation, from Maxwell’s current read on the wave to the Klein–Gordon equation, and from its flow to the arrow Navier–Stokes law: three laws of one mathematical form, the double arrow differentiation of an arrow of matter. In hydrogen the arrow laws give Sommerfeld’s levels and the Lamb shift, 1057.70 ± 0.01 MHz against the measured 1057.845 MHz. Every statement is checked by a script with a control that must fail. This record holds the preprint (v0.7.56), its LaTeX source, and the check scripts in Python and Julia: every statement marked "(Checked.)" in the paper has a script with a control that must fail. The Julia checks use the author's arrow package ArrowCalc, to be released separately.