The fine-structure constant is another example of fine-tuning and design:
In physics, the fine-structure constant, also known as Sommerfeld’s constant, commonly denoted by α (the Greek letter alpha), is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between elementary charged particles.
The definition of α in terms of other fundamental physical constants is:
e is the elementary charge (= 1.602176634×10−19 C);
h is the Planck constant (= 6.62607015×10−34 J⋅s );
c is the speed of light in vacuum (= 299792458 m/s);
ε0 is the electric constant or permittivity in vacuum or free space.
In the early 21st century, multiple physicists, including Stephen Hawking in his book A Brief History of Time, began exploring the idea of a multiverse, and the fine-structure constant was one of several universal constants that suggested the idea of a fine-tuned universe.
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!
— Richard P. Feynman (1985). QED: The Strange Theory of Light and Matter. Princeton University Press. p. 129. ISBN 978-0-691-08388-9.
“When I die my first question to the Devil will be: What is the meaning of the fine structure constant?”
~ Wolfgang Pauli