Inverse fine-structure constant

Physics has an odd relationship with this number. Eddington argued in the 1930s that it had to be exactly 136, then exactly 137 when measurements moved, and constructed elaborate justifications for both — an episode remembered as a warning about numerology. The measured value is 137.035 999 177(21), which is not an integer and never was.

Modern determinations come from two very different directions: the electron's anomalous magnetic moment compared with a twelfth-order QED calculation, and atom-recoil measurements of ħ/m in caesium or rubidium interferometers. The two routes agreed to a part per billion until caesium and rubidium recoil experiments disagreed with each other by 5σ in 2020, a discrepancy that CODATA 2022 handles by expanding the uncertainty. Because α governs the strength of electromagnetism, a value even a few per cent different would break the stellar triple-alpha process and with it the supply of carbon.