There are always times when things won’t be what we wish, and the Fine Structure Constant is no exception to this rule. We humans usually see what we believe rather than what is, and to that end, it comes straight from nature’s gag reel.
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 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 man. You might say the “hand of God” wrote that number, and “we don’t know how He pushed his pencil…”
-Richard P. Feynman (1985), QED: The Strange Theory of Light and Matter, Princeton University Press, p. 129
Please join me for a highly abridged and cherry-picked tale in the story of modern physics…