# Units and the Fine-Structure Constant

The fine-structure constant is defined in terms of the speed of light c, Planck's constant h, and the charge of the electron e. I usually write it as

because I'm a theoretical physicist and use CGS units. (The funny cross on Planck's constant, , is a shorthand for "Planck's constant h divided by two pi".) Experimentalists usually use a different scheme of units. (It's like the Americans used to measure things in feet, and the Europeans in meters: the formulas are different, but the answers are the same.) The formula in SI units is
In either set of units, the value is the same, about 1/137.036.

There is an interesting story about the fine-structure constant. Early on, someone had a theory that it was exactly 1/136. When the measurement got better, he produced an improved theory that it was exactly 1/137. His theory didn't make much sense to people, but it took a much better measurement the second time to disprove him!

It's interesting that g is close to two (it's about 2.001159652188) for an important reason, while is close to 1/137 for no apparent reason at all.