A Natural Derivation of the Fine-Structure Constant from Electron–Planck Geometric Ratios

The fine-structure constant, α ≈ 1/137, is one of the most fundamental andmysterious dimensionless constants in physics. In this work, we propose a remark-ably simple and physically meaningful relation that expresses α purely in terms of four universal constants: the electron mass me, the classical electron radius re, the Planck mass mp, and the Planck length lp. We show that the ratio α ≈ (me × re) / (mp × lp)not only numerically reproduces the measured value of α with high precision, butalso allows a physical interpretation of α as the dimensionless resonance coupling between the matter structure and the quantized spacetime background.