α=κ/τ : The Geometric Origin of the Fine-Structure Constant

Based on differential geometry and the three-dimensional helical motion model of photons, this paper adopts the Frenet–Serret frame to rigorously derive the curvature κ and torsion τ of photon trajectories. The ratio of these intrinsic geometric invariants yields the relation α = κ/τ, which is logically self-consistent and equivalent to the classical physical definition of the fine-structure constant α = v/c = 2πr/λ.This work for the first time establishes a quantitative expression for the fine-structure constant from a purely geometric perspective, and confirms the century-old conjecture proposed by Dirac and Feynman regarding the geometric essence of α. The whole derivation is logically rigorous, compatible with the existing theoretical physics framework, and constitutes an independent original research breakthrough.