A few trivia about the fine structure constant

Clifford Pickover

In a post I published in this blog over three years ago, I talked about the fine structure constant and some of its physical peculiarities. In this post I am going to talk about some of its mathematical peculiarities. I have taken them from a book I have mentioned on other occasions: A Passion for Mathematics, by Clifford A. Pickover.

As we know, the most exact value of this constant is this:

α = 1/137.035999206

Pickover points out that Eric W. Weisstein, in his World of Physics website, offers two mathematical approximations incredibly close to this value:

The fine-structure constant

Arnold Sommerfeld

One of the latest scientific advances of 2020 was a new, more precise measurement of the fine-structure constant. The last value officially accepted in 2018 by the Committee for Data on Science and Technology (CODATA) is equal to 1/137.035999084. The value obtained in December 2020 is equal to 1/137.035999206. It will be seen that the difference with the previous value is very small and affects only the seventh decimal place.

But what is the fine-structure constant? It's a dimensionless constant, defined by the following formula: