Chapter 71: The Neutron Lifetime: Crown of the Cascade

The free neutron decays with a lifetime τ_n ≈ 879 s—roughly fifteen minutes. This single number encodes the entire calibration cascade of Book IV: it depends on the fine structure constant α, the electron-to-neutron mass ratio R, the weak sector coupling κ(A;1), the Cabibbo angle, and the phase space integral that counts the kinematically allowed decay products. No other derived quantity in the microcosm touches as many layers of the framework. The neutron lifetime is the crown of the cascade: the most complex readout from the single input ι_τ. This chapter derives τ_n within τ³, confronts the “bottle vs. beam” experimental discrepancy, and explains why τ_n closes the calibration programme by connecting geometry to a macroscopic timescale.