Theoretical calculation of the fine-structure constant and the permittivity of the vacuum

Abstract

Light traveling through the vacuum interacts with vacuum fluctuations similarly to the way that light traveling through a dielectric interacts with ordinary matter. And just as the permittivity of a dielectric can be calculated, the permittivity $\epsilon_0$ of the vacuum can be calculated, yielding an equation for the fine-structure constant $\alpha$. The most important contributions to the value of $\alpha$ arise from the interaction of photons with charged lepton-antilepton vacuum fluctuations that appear in the vacuum as on-shell, bound states. Considering these contributions only to first order in alpha, the fully screened $\alpha \cong 1/(8^2\sqrt{3\pi/2}) \cong 1/139$.