Resolving the Electron Spin Superluminal Paradox: A Composite Model of Multi-Scale Circular Motions

The classical electron spin paradox—$5.13 \times 10^{10}$ m/s at $2.82 \times 10^{-15}$ m \cite{thomson1904}—collapses under a composite ring model in H$_2$. Each electron orbits the bond center at $r_1 = 3.7 \times 10^{-11}$ m ($v_1 = 1.56 \times 10^6$ m/s, $f_1 = 6.72 \times 10^{15}$ Hz), oscillates within at $r_2 = 2.89 \times 10^{-17}$ m ($v_2 = 2.0 \times 10^6$ m/s, $f_2 = 1.10 \times 10^{23}$ Hz), and spans $r_{\text{eff}} = 5.29 \times 10^{-11}$ m via perturbations ($f_3 = 1.4 \times 10^9$ Hz from electron interplay, $f_4 = 1.37 \times 10^{10}$ Hz from proton asymmetry). Velocities peak at $0.05c$, shattering superluminal limits, while $S = \hbar/2$ and $f_{\text{spin}} = 1.40 \times 10^{10}$ Hz match quantum standards \cite{dirac1928, bohm1965}. Rooted in Newton’s laws \cite{newton1687}, this multi-scale framework redefines spin as classical motion, leveraging H$_2$’s molecular dynamics to ground perturbations in tangible interactions. Testable at $10^{-17}$ m via scattering \cite{born1926}, it challenges quantum abstraction with a visualizable alternative—scalable to complex systems. The electron emerges as a ringed titan, its spin a classical dance we can measure and master, bridging intuition and precision in a molecular paradigm.