A derivation of the electromagnetic coupling α0 ≃ 137.036

A consistent mathematical derivation is given for the Sommerfeld fine structure electromagnetic coupling 1/α¯0=α0≅1/137.036. Following 't Hooft's holographic principle two complimentary forms of the derivation are given both leading to the E(∞) theoretical value, namely α¯0=(20)(1/ϕ)4=137.082039311. The experimental value is subsequently found by projection as α¯0(exp)=137/[cos(π/α¯0)]≅137.036.