Theoretical calculation of the fine-structure constant and the permittivity of the vacuum
G. B. Mainland, Bernard Mulligan
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 $ε_0$ of the vacuum can be calculated, yielding an equation for the fine-structure constant $α$. The most important contributions to the value of $α$ 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 $α\cong 1/(8^2\sqrt{3π/2}) \cong 1/139$.