One of the great physicists of this century is a man named Richard Feynman, who teaches at CalTech and knows as much about the way the Cosmos works as any man alive. Feynman has participated in half a dozen extraordinary theoretical developments and won a fistful of prizes, including the one you get from Sweden. Even so, he likes to tell people that physics has not accomplished as much as some physicists like to brag, and that we are not as close to a great universal theory of matter and energy as some theorists like to think. Indeed, Feynman has said, physicists ought to put a special sign in their offices to remind themselves of how much they don't know. The message on the sign would be very simple. It would consist entirely of one word, or, rather, number: 137.

One hundred thirty-seven is the value of a number called the fine-structure constant. This constant, 137, is the way physicists describe the probability that an electron will emit or absorb a photon. Because this is the basic physical mechanism of electricity and magnetism, the fine-structure constant has its own symbol, the Greek letter a, “alpha.”

Now, alpha is nothing more, nothing less than the square of the charge of the electron divided by the speed of light times Planck’s constant. Thus this one little number contains in itself the guts of electromagnetism (the electron charge), relativity (the speed of light), and quantum mechanics (Planck’s constant). All in one number! Not only that, this number isn’t like the gravitational constant or the universal gas constant, full of meters and kilograms and degrees Celsius. Alpha is a pure, dimensionless number — little wonder that people have been fascinated.

Physicists would like to believe that these phenomena fit together tidily in accordance with one big plan. They would like the ratio of electromagnetism, relativity, and quantum mechanics to be a number like one, or maybe two times pi. They do not like its being 137 — a prime number, for heaven“s sake!

The significance of alpha was first spelled out in 1915 by a physicist named Arnold Sommerfeld — at the time, measurement errors made the value closer to 136 — and physics ever since has been littered with efforts to explain it. the most famous attempt was that of Sir Arthur Eddington, a prominent astronomer who believed that such constants could be used to produce a theory of the universe. He built a huge 16-dimensional equation full of these constants and claimed that alpha could be calculated from the number of terms: (162 - 16) / 2 + 16 = 136.

Unfortunately, experiments quickly showed that alpha was really closer to 137. Plucky Arthur Eddington was not dismayed. He said he had forgotten to add one more factor — alpha itself — and made the value 137. For thus, Punch magazine dubbed him Sir Arthur Adding-One. But Eddington was not deterred. Proudly he proclaimed that the firmament contains exactly (137 - 1) x 2256 protons. Of course, the old man may have been right; nobody has yet been able to count them all.

Throughout the Thirties and Forties, the greatest scientists of the day tried and failed to figure out the magic number 137. The great Werner Heisenberg told his friends that the problems of quantum theory would disappear only when 137 was explained, and spent years trying to explain it; fortunately, the problems did go away despite his failure. One of Heisenberg’s friends, theorist wolfgang Pauli, wasted endless research time trying to multiply pi by other numbers to get 137; Edward Teller, now a prominent advocate of star wars, derived alpha from gravitation; and a dotty Japanese showed that the difference in the masses of the proton and delta particle is equal to alpha. All this shows is that there are many ways you can multiply and add a bunch of numbers to get 137. The closest any of these people got to the answer, perhaps, was when Pauli died — in hospital room 137.

The best explanation of the mystery ever given to Victor Weisskopf, another leading theorist from that time, was provided by Gershom Scholem, one of the most eminent scholars of Jewish mysticism. When Scholem met Weisskopf, he asked about the prominent unsolved problems in physics. Weisskopf said, “Well, there's this number, 137....” And Scholem's eyes lit up! He said, “Did you know that one hundred thirty-seven is the number associated with the Cabala?”

After physicists slam into a problem for a few decades, they tend to go into greener pastures. Alpha calculating has been out of fashion for a while. Physics is making progress without it. But it is comforting to know that if you're at a party, and some know-it-all is talking about how great the progress of science is, you can always say, “That’s true, my man. But why is alpha equal to one hundred thirty-seven?”

— Charles C. Mann
copyright © 2001 by Charles C. Mann



Charles C. Mann is a contributing editor for both Science and The Atlantic Monthly. He also writes for The New York Times Magazine, The Sciences, and Smithsonian. The recipient of an Alfred P. Sloan Foundation Science Writing Prize, he is the co-author (with Mark L. Plummer) of:

Noah’s Choice: The Future of Endangered Species

The Second Creation: Makers of the Revolution in Twentieth-Century Physics

The Aspirin Wars: Money, Medicine, and 100 Years of Rampant Competition

He also wrote a book about particle physics called The Second Creation (rev. ed., 1996, Rutgers University Press) that discussed 137.

His book, @Large: The Strange Tale of the Internet’s Greatest Invasion was published in 1997 by Simon & Schuster.

A number of Mann“s articles appear elsewhere in cyberspace, including “Brave New World”

These articles were co-authored with Mark L. Plummer:

“Empowering Species”
“Are Wildlife Corridors the Right Path?”
“The Butterfly Problem”

The Feynman Webring

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