The Most Mysterious Number in Physics

Many physical constants determine the structure of the universe. All of them have units or dimensions, such as the speed of light (c) or the gravity constant (G). That is, all of them except one. That one is the fine-structure constant represented by the Greek letter alpha (α). The fine-structure constant seems to be a random number with no units or dimensions, but it keeps showing up in physics calculations. It has been described as the most mysterious number in physics. American theoretical physicist Richard Feynman called it “a magic number that comes to us with no understanding by humans.”

Recognition of the fine-structure constant originated with German theoretical physicist Arnold Sommerfeld in 1916. Chemists can identify different elements in the lab by the spectral lines they emit or absorb when their electrons change energy levels. Astronomers analyze the spectral lines of stars to determine what elements they contain. Some spectral lines are split, showing a fine structure. To explain this, Sommerfeld introduced a new constant into his equations and called it the fine-structure constant. It has no units like the speed of light or other constants. It is just a number – a ratio.

The fine-structure constant shows the strength of the interaction between electrons and photons. It also shows up in many other ratios in physics. The value is approximately 0.007,297,352,569 or 1/137. Physicists consider it mysterious because they don’t know where it came from or why it has that value. They can’t explain why it exists at all. But if you are not a physicist, why should you care about the most mysterious number in physics?

If the fine-structure constant had any other value, life as we know it would not be possible. If you changed that number, you would change the universe. A different value for the fine-structure constant would change the size of atoms and alter chemistry and nuclear reactions. No stable matter, no life, and no intelligent beings would exist. We wouldn’t be here.

Richard Feynman wrote that “all good theoretical physicists put this number up on their wall and worry about it.” Apparently, they worry about where it came from and why it is what it is. Feynman further wrote, “You might say the ‘hand of God’ wrote that number, and ‘we don’t know how He pushed His pencil.”

Feynman was joking about the most mysterious number in physics, but we think it was written by the “hand of God.” We also believe “He pushed His pencil” so that He could create humans for a purpose. More on that tomorrow.

— Roland Earnst © 2023

Feynman quotes taken from The Strange Theory of Light and Matter by Richard Feynman Princeton University Press ©1985