Richard Feynman told physicists to hang 137 on the wall because 1/137, the fine-structure constant, is one of the deepest unsolved puzzles in physics. It is the number that sets how strongly light and electrons interact, it has no units, and nobody can explain why it has the value it does. In his 1985 book QED: The Strange Theory of Light and Matter, Feynman wrote that “all good theoretical physicists put this number up on their wall and worry about it.” More than forty years later, nobody has taken it down.
The passage in QED
Feynman’s book was written for general readers, which makes the passage all the more striking. He introduces a number he calls “the amplitude for a real electron to emit or absorb a real photon”, and then explains that his physicist friends won’t recognise it, “because they like to remember it as the inverse of its square: about 137.03597”. That is the famous 137, and one over it is the fine-structure constant, α.
Then he admits what nobody knows. The number, he wrote, has been “a mystery ever since it was discovered more than fifty years ago”. Is it related to π, or 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.” — Richard Feynman, QED: The Strange Theory of Light and Matter, 1985
Why 1/137 is worth worrying about
The number was already old when Feynman wrote. Arnold Sommerfeld introduced it in 1916, to explain a tiny split in the red light of hydrogen: one line that turned out to be two, a hair apart. He gave it the Greek letter α, and its value came out at about 1/137, more precisely 1/137.036.
What makes it strange is what it lacks. A speed comes in metres per second, a mass in kilograms, and those numbers change when you change your rulers and clocks. α has no units at all. Any civilisation, using any units, would measure the same number.
And it is not an ornament. α sets how strongly light and electrons interact, and that decides the size of atoms and the colours of the light they give off. A different α would mean different atoms, and a world that looked different.
Measured to twelve digits, still unexplained
Since Feynman wrote, the measurements have only grown sharper. The 2022 recommended value of 1/α, from CODATA, is 137.035999177: twelve digits. That is where the Short ends, and it is the heart of the matter: precision is not understanding. Nobody has ever derived α from deeper principles; every attempt to build 137 out of pure numbers has failed, and it can only be measured.
That is why the advice still stands. The full story, from Sommerfeld’s split red line to the two best modern measurements that refuse to agree, is in why 137 haunts physics.
We know what the number is. We still do not know why it is 1/137.
