Richard Feynman, one of the originators and early developers of the theory of quantum electrodynamics (QED), referred to the fine-structure constant in these terms:
There is a most profound and beautiful question associated with the observed coupling constant, e – the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455 (My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.)
Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by humans. You might say the "hand of God" wrote that number, and "we don't know how He pushed His pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out*– without putting it in secretly!
https://en.wikipedia.org/wiki/Fine-structure_constant#Numerological_explanations_and_multiverse_theory)
My comments:
*
it comes out of the sign-flip algorithm I developed in the early 1980s at University of Cincinnati
The roots of the characteristic equation (Full Rydberg Equation) from the simultaneous solution of the Bohr and Schrรถdinger atomic models for a single electron hydrogen atom at 0K gives the fine-structure constant as one of the roots and it can be calculated to any desired precision.
©2021 Mark Eric Rohrbaugh & Lyz Starwalker © 2022
I enter it as a seed value and use a numerical method to solve for the roots of the full Rydberg equation - an equation from quantum mechanics that related energy and frequency and the spectral lines. Fine-structure constant deals with the fine lines as mentioned in wikipedia copy/pasta above.
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