For Young Minds, Tired Physicists, and Curious Mathematicians
r_oct = (sqrt(2)-1)/2 = 0.20711 The octahedral void radius. The bigger gap between touching spheres.
r_tet = (sqrt(6)-2)/4 = 0.11237 The tetrahedral void radius. The smaller gap between touching spheres.
Lambda_QCD = 220 MeV The QCD energy scale. The only measured input.
From these three numbers: everything.
alpha_0 = r_oct x r_tet / pi = 0.0074081 1/alpha = 1/(alpha_0 x (1 - 2*alpha_0)) = 137.018 Measured: 137.036. Error: -0.013%. Zero free parameters.
alpha (fine structure constant) Determines the strength of electromagnetism, size of atoms, colour of light, reason chemistry works. Nobody knew where it came from. BCT derives it from sphere gaps in three lines. BCT: 1/alpha = 137.018. Measured: 137.036. Er