The number that fascinates physicists above all others

[Sanguine]

 It is the fine-structure constant denoted by the Greek letter alpha. Paul Davies explains.

"God is a pure mathematician!” declared British astronomer Sir James Jeans. The physical Universe does seem to be organised around elegant mathematical relationships. And one number above all others has exercised an enduring fascination for physicists: 137.03599913.

Let me explain. When scientists measure any quantity they must specify the units being used. The speed of light, for example, is either 186,000 or 300,000 depending on whether it is expressed as miles per second or kilometres per second. Likewise your weight might be 150 or 68 according to whether you are measuring in pounds or kilograms. Without knowing the units being used the number is meaningless – unless it is a pure number.

The best known example of a pure number comes from combining three of nature’s most fundamental quantities: the speed of light, the electric charge carried by a single electron and Planck’s constant of quantum mechanics. In symbols, that’s c, e and h. Put them together as follows, hc/2πe2, and the units of c, e and h cancel out to leave a pure number, 137.03599913. If c, e and h were measured by Vulcan scientists using Vulcan units, they would still get 137.03599913. This curious number is therefore a universal constant of nature – “God given” Jeans might have said.

In view of its importance, hc/2πe2 has acquired a name and a symbol all of its own. For historical reasons the inverse, 2πe2/hc = 1/137.03599913, is used. It is known as the fine-structure constant and is denoted by the Greek letter alpha (α).

What is α good for? It is used to measure how strongly charged particles such as electrons interact with electromagnetic fields. For example, it determines how quickly an excited atom emits a photon. If  were twice as big, atoms would decay twice as fast. Alpha also determines the trajectory of a charged particle moving through an electromagnetic field – this was the basis of old-fashioned TV projection...

While it is too soon to rewrite the textbooks, the prospect that one of nature’s critical pure numbers might turn out to be variable has created considerable controversy. If James Jeans were alive today, he might conclude that God may well be a pure mathematician, but one with a whimsical bent.

https://cosmosmagazine.com/mathematics/number-fascinates-physicists-above-all-others