Derivation of the fine-structure constant
Source: FSC Alpha Derivation 24 June 2026. Standard Model treats α as a measured input. BFUT derives ħ from condensation geometry, then α from the standard electromagnetic definition with that ħ.
Coefficients (no measured constant)
E(R) = A/R² + B·R² + C·R + D/R
A = 1/2 exact. D = 1 exact. C = −1/3 from C3v symmetry. B = 0.56308 from void-filling geometry.
R0
dE/dR = 0 gives R0 = 1.27348221. No measured constant enters.
SI anchor and ħ
r_p = 0.8414 fm (PDG 2022) is the length anchor. ħ = m_p · c · r_p / (π · R0) = 1.054577 × 10⁻³⁴ J·s. Measured 1.054572 × 10⁻³⁴. Difference 0.00048%.
α
α = e² · R0 / (4ε0 · m_p · c² · r_p) = 1/137.0367. Measured 1/137.0360. Difference 0.00048%.
Where the residual sits
The whole residual is the gap between R0 from geometry (1.27348221) and R0 back-computed from measured constants (1.27348831). That is an identified open problem in the geometric derivation of B. It is not a fitted parameter.
Measured inputs to α: m_p and r_p. Exact inputs: e and c. ħ and α are outputs.