A dimensionless fundamental constant of the universe, shown as α or αe with the ‘e’ for ‘electromagnetic’. Its value is approximately 1/137. α is a coefficient on the expression for how likely it is that an electromagnetic interaction will take place between two charged particles. In a Feynman diagram, each photon vertex introduces a factor of α attenuation in the probabalistic magnitude (in addition to a couple other matters).

There are similar constants for the other forces, but they are more complicated to use since the other forces are mediated by bosons which have mass. This gives equations mass terms, which really mucks them up since then you have to integrate over all possibilities of the momentum they could transfer. Photons have no mass, so they carry any amount of energy equally well, so the integration is far far easier.

The fine structure constant's full significance was (pretty much) discovered by Richard Feynman. Since 'Feynman' is pronounced including the sound 'fine', this connection should be easy to remember. However, it isn't quite that simple. The value of the fine structure was known to spectroscopists from the fine splitting and ultrafine splitting of hydrogen emission lines before its full significance was discovered. That is where it got its name. Now, it is known to be the fundamental electromagnetic interaction coefficient, and 'fine structure constant' doesn't really do it justice.

Ignoring electroweak unification

ugah174: I don't consider this 'derivation' to be at all significant. If the electromagnetic force has this strength for geometrical reasons, why aren't the other four force constants the same thing? They're equally constrained by geometry. Also, the derivation increases the number of magic numbers from one real number to two integers. Why aren't there 29 forces then?