The Classical Electron Radius, the Electron Compton Wavelength and the Running Fine Structure Constant

Abstract

The fine structure constant variation as a function of the electromagnetic interaction strength is investigated and shown to evolve from the canonical standard 1/137 to 1 at distances of the order of the classical electron radius, i.e. at a typical strong interaction value. This confirms the outcome at Planck scales, but it happens even later in the Universe's evolution, closer to the present time, although it will also be experimentally unattainable. The result is simply derived by imposing quantum effects, i.e. the Compton wavelength at the classical electron radius, in analogy with the procedure by which the corresponding Compton wavelength constrains the Schwarzschild radius.