Using our recently published electron’s charge electromagnetic flux manifold fiber model of the electron, described by analytical method and numerical simulations, we show how the fine structure constant is embedded as a geometrical proportionality constant in three dimensional space of its charge manifold and how this dictates the first QED term one-loop contribution of its anomalous magnetic moment making for the first time a connection of its intrinsic characteristics with physical geometrical dimensions and therefore demonstrating that the physical electron charge cannot be dimensionless. We show that the fine structure constant (FSC) α, and anomalous magnetic moment αμ of the electron is related to the sphericity of its charge distribution which is not perfectly spherical and thus has a shape, and therefore its self-confined charge possesses measurable physical dimensions. We also explain why these are not yet able to be measured by past and current experiments and how possible we could succeed.
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