the fine-structure constant
/ alpha /
If you had to summarize the strength of electromagnetism in a single number, this is it. The fine-structure constant, written with the Greek letter alpha, is approximately 1/137, or about 0.0073. It is a pure number with no units — it does not matter whether you measure in meters or miles, grams or pounds; alpha comes out the same. That makes it one of the most fundamental and mysterious numbers in nature, a fingerprint of how strongly light and matter interact.
Alpha is built from the electron's charge, the speed of light, and Planck's constant — three of the most important quantities in physics, combined so the units cancel and a bare number remains. Its physical meaning is the probability, roughly, that a charged particle emits or absorbs a single photon. Because that probability is small, each extra photon in a process makes the contribution smaller by another factor of alpha, which is exactly why QED's series of corrections shrinks so reliably and can be computed to extraordinary precision.
The name is historical: the constant was first spotted in the 'fine structure' of atomic spectral lines, tiny splittings in the colors of light atoms emit. Today its value is known to better than a part per billion, and physicists still ask why it has the value it does. There is no accepted explanation for the number 1/137 — it is simply measured. Richard Feynman called it 'one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding.'
When a hydrogen atom emits a photon, the probability per attempt is governed by alpha being about 1/137. If alpha were ten times larger, atoms would be far smaller and chemistry — and life — would look completely different; the value of this one number quietly shapes the entire material world.
Alpha sets the size of atoms and the pace of all light-matter interactions.
The famous value '1/137' is only exact at low energy; because the coupling runs, alpha grows to about 1/128 at the energies probed in high-energy colliders.