From Energy to Helical Photon Geometry

A helical energy vortex with radius r = λ/(2π) and pitch p = λ emerges from photon angular momentum L = ℏ and energy E = ℏω. The helix appears as sinusoidal patterns from transverse angles and point-like impacts from axial angles, so wave and particle properties are projections of a single three-dimensional structure. Self-propulsion at c follows from the c-axiom applied to the forward direction of the helical flow: the forward component of the photon's energy flow is at c, by axiom, and that is the propulsion. The two lateral components in the plane perpendicular to propagation, also at c independently, generate the angular momentum L = ℏ. Polarization and handedness are geometric features of the helix. Emission and absorption are time-reverses of a vortex nucleation event: motion converging at a high-density node with components in three perpendicular directions exceeds a c/R trigger threshold and produces or absorbs a helix carrying the energy delivered. Applications to moving sources (relativistic Doppler) and gravitational fields (deflection and lensing) are left to future work.