Why Is Number 137 One of The Greatest Mysteries in Physics?

What’s the key to unlocking the mysteries of the universe? If you’re expecting an incantation in some ancient language, uttered by a holy man sitting cross-legged on a mountaintop, this answer may disappoint you.

It might just be the number 137.

Those three digits, as it turns out, have long been the rare object of fascination that bridges the gulf between science and mysticism.

“137 continues to fire the imagination of everyone from scientists and mystics to occultists and people from the far-flung edges of society,” Arthur I. Miller, an emeritus professor of history and philosophy of science at University College London and author of the 2009 book “137: Jung, Pauli and the Pursuit of a Scientific Obsession,” says via email.

The Fine-structure Constant
To physicists, 137 is the approximate denominator of the fine-structure constant (1/137.03599913), the measure of the strength of the electromagnetic force that controls how charged elementary particles such as the electron and muon interact with photons of light, according to the National Institute of Standards and Technology.

The fine-structure constant is one of the key physical constants of the universe. “This immutable number determines how stars burn, how chemistry happens and even whether atoms exist at all,” as Michael Brooks explained in a recent New Scientist article.

And, in a paper published Dec. 20, 2020 in the journal Nature, a team of four physicists led by Saïda Guellati-Khélifa at the Kastler Brossel Laboratory in Paris reported the most precise measurement yet of the fine-structure constant. The team measured the constant’s value to the 11th decimal place, reporting that α = 1/137.035999206.

The new measurement is nearly three times more precise than the previous best measurement in 2018 by a group led by Holger Müller at Berkeley, with a margin of error of just 81 parts per trillion.

The fine-structure constant “characterizes the strength with which matter couples to light, e.g. the probability that an excited atom will decay in a certain time,” Paul Davies, Regents Professor of Physics at Arizona State University and a best-selling author of 30 books on science, explains in an email.

If the constant was bigger, “atoms would decay faster. It is significant too because it is a pure number – a ratio of quantities with equal units. Unlike, say, the speed of light, which is either 186,000 miles per second or 300,000 kilometers per second, depending on which units you prefer.” (Davies wrote this 2016 article on the fine-structure constant for Cosmos.)

In this video, British physicist Laurence Eaves explains that if the fine structure constant was a different value, “physics, chemistry, biochemistry would be totally different – and we might not be around to talk about it.”


But practically from the time of its discovery in 1915 by German physicist Arnold Sommerfeld, who originally rendered it as 0.00729, the fine-structure constant seemed to signify some larger metaphysical truth as well.

The fine-structure constant “determines the distance between an atom’s spectral lines, which are the atom’s DNA,” Miller explains. “And so it is one of those numbers that is at the root of the universe. If it were any other value then the structure of matter would be very different, and so us too. People began referring to it as a mystical number.”

Miller continues: “The language of the spectra – the spectral lines where Sommerfeld found it – is a true music of the spheres within the atom,” he wrote. “People asked why it has this particular value. Physicists could only conclude that it cannot have this value by accident. It is ‘out there,’ independent of the structure of our minds.”

But in 1929, English astrophysicist Arthur Eddington – who played a key role in establishing the validity of Albert Einstein’s General Theory of Relativity and was an early advocate of the Big Bang theory, among other things – began expressing it as 1/137. He also saw it as having larger, spiritual implications.

“Arthur Eddington sought a new mysticism which would emerge from the natural sciences,” Miller says. “Perhaps, he thought, the clue lay in numbers, particularly the number 137. Eddington’s reputation as one of the great astrophysicists of his day put a great deal of weight on this approach.”

Relativity and Quantum Theory
As Miler’s book details, Austrian-born quantum physics pioneer Wolfgang Pauli became fascinated with the number as well, since it figured in the mysterious intersection of relativity and quantum theory that he explored with the help of his friend, psychoanalyst Carl Jung. The scientific fixation on the fine-structure constant was such that in 1936, Nature published an article titled “The Mysterious Number 137.”

But as Pauli learned in the 1950s from a religious scholar, 137 had another significance. It was the number associated with the Kabbalah, an esoteric form of Jewish mysticism – what Miller calls “an extraordinary link between mysticism an

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