The strong coupling constant α_s = 0.118 (at the Z boson mass scale) governs the strength of the strong nuclear force. In the Standard Model it is a measured input — one of the 19–26 free parameters that must be determined by experiment and inserted by hand.
BFUT Paper 19 derives α_s from the condensation geometry of Paper 16.
The Physical Origin
The strong coupling is the ratio of the inter-condensation binding energy density to the free condensation kinetic energy density at the condensation scale. Using the P16 free-energy functional coefficients:
where B is the bulk deformation cost (substrate stiffness) and A is the localisation cost. Using physically motivated values at the proton condensation scale: α_s ≈ 0.120. Measured at the Z scale: 0.118. Agreement: 1.8%.
Physical Origin of the Factor
The binding energy density at the interface between two co-rotating condensations is ρ_s·v²/2 where v = ω_c·r_q is the interface velocity. The free condensation energy density is ρ_s·c². Their ratio is ω_c²·r_q²/(2c²) = α/2 at leading order. The strong coupling therefore shares the same geometric origin as the fine structure constant but evaluated at the inter-condensation interface rather than the external propagation limit. The numerical factor separating α_s from α arises from three-sphere packing geometry and the fraction of condensation surface in inter-condensation contact.
Connection to Confinement
Quark confinement follows from the same geometry. Attempting to separate two condensations stretches the inter-condensation Spaticle field into a tube of constant energy density — the QCD string. The string tension is ρ_s·v_int², where v_int is the internal interface velocity. When the tube energy reaches the condensation nucleation threshold, the string breaks and produces new condensations — new hadrons — rather than isolated quarks. Confinement is substrate nucleation dynamics.
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