Unveiling the structure of protons and neutrons through quark dynamics and the fine-structure constant

This paper presents a unified semi-classical framework that bridges quantum mechanics and relativity to investigate nucleon structure through quark dynamics, introducing the Quantum Turning Point—a fundamental threshold defined by the product of an elementary particle’s mass and classical radius that distinguishes quantum-scale from classical-scale. By anchoring this threshold to Planck-scale parameters, we demonstrate that nucleon masses emerge not from quark rest masses alone but from relativistic quark dynamics, characterized by large Lorentz factors (γu ≈ 968, γd ≈ 3871) reflecting near-light-speed motion. A key achievement is the derivation of the proton-to-electron mass ratio (∼1837) from first principles, aligning with empirical observations and suggesting a deeper connection between fundamental constants. Remarkably, our unified nucleon mass formula incorporates the fine-structure constant (α) as a scaling factor, revealing an unexpected interplay between electromagnetic and strong interactions in nucleon mass generation. The empirical factor 0.476 in this formula further reflects a geometric symmetry in quark binding, explaining the near-equality of proton and neutron masses despite their differing quark compositions (Nu = 2, Nd = 1 vs. Nu = 1, Nd = 2). These results challenge the conventional separation of forces in the Standard Model, proposing instead that constants like α may emerge from internal particle dynamics rather than being externally imposed. While heuristic, our framework offers numerically consistent predictions and opens new pathways to unify quantum mechanics, relativity, and subatomic structure. This study advances our understanding of nucleon mass origins and hints at a deeper geometric or dynamical symmetry underlying fundamental physics.