From Energy to Helical Photon Geometry

Abstract

A photon is a fully specified helical energy flow—radius r = λ/(2π), pitch p = λ—determined by its angular momentum L = ℏ and energy E = ℏω, with no free parameters. Wave and particle properties are projections of this single three-dimensional flow: a sinusoid viewed transverse to the axis, a point-like impact viewed along it. Self-propulsion at c follows from the c-axiom applied to the forward direction of the flow—the forward component is at c by axiom, and that is the propulsion, with no carrier beneath it. The two lateral directions in the plane perpendicular to propagation, also at c independently, generate the angular momentum. Integrating the flow around its axis recovers both measured momenta from one decomposition: the tangential circulation gives the angular momentum ℏ, the axial flow the linear momentum E/c. The full three-dimensional angular momentum is A_m = ℏr, so photons do not all carry the same total; the universal ℏ is its projection onto the axis, and the wavelength-bearing remainder cancels when the helix winds into a target. What is usually called polarization resolves into handedness, phase and coherence—properties of the helices and their alignment, not a separate attribute. Emission and absorption are one local event: flow reaches a node and continues spherically where the local geometry allows and helically where it does not, so each emitted helix is shaped by the state of its source. Applications to moving sources, gravitational deflection and moving clocks are treated in the companion applications paper.