Why α ≈ 1/137 is arguably the most mysterious number in Physics

And why it shows up everywhere from spectra to metrology

Fine-structure constant, often denoted by ‘α’ is a dimensionless number that sets the strength of electromagnetism. At low energies, α⁻¹ ≈ 137.035999. Think of it as the single knob that scales how strongly light and charged particles interact. Sommerfeld introduced α in 1916 while explaining the fine splitting of hydrogen’s spectral lines. In SI form,

graphics by the author

Its small size (≈ 0.007297) is why atomic structure is mostly orderly and chemistry is stable: electromagnetism binds atoms tightly enough to exist, but not so tightly that everything collapses.

The number picked up lore. Eddington argued — wrongly — that α⁻¹ is exactly 137. Pauli disliked numerology but still joked about “137,” and the famous story about his hospital room number stuck. Nice anecdotes, not physics.

QED turned α from a curiosity into a workhorse. The 1947 Lamb-shift measurement forced the community to adopt renormalisation: charges get “dressed” by virtual particles. Since then, α has been the expansion parameter in precision QED. The electron’s anomalous magnetic moment g−2 is predicted as a power series in α (now through five loops) and matches experiments to staggering precision. When theory and…