Unlocking The Mystery Of 137: Why This Number Is So Important

As the mathematician De La Soul famously stated, three is the magic number. But if physicist Richard Feynman is to be believed, that figure is off by a factor of about 400. For Feynman, you see, the “magic number” is around 1/137 – specifically, it’s 1/137.03599913. 

Physicists know it as α, or the fine structure constant. “It has been a mystery ever since it was discovered,” Feynman wrote in his 1985 book QED: The Strange Theory of Light and Matter. “All good theoretical physicists put this number up on their wall and worry about it.”

It’s both incredibly mysterious and unbelievably important: a seemingly random, dimensionless number, which nevertheless holds the secret to life itself. 

“It’s a measure of the strength of the interaction between charged particles and the electromagnetic force,” explained SUNY Stony Brook astrophysics professor Paul M Sutter in an article for Space

“If it had any other value, life as we know it would be impossible,” he wrote. “And yet we have no idea where it comes from.”

Normally, this would be the part where we give you some examples of where the value turns up – but the answer to that, quite literally, is “everywhere.” It was first discovered in 1916, by the physicist Arnold Sommerfeld, but it had already been turning up in equations for decades before that. It lurks in formulas describing light and matter, and it governs everything from the smallest hydrogen atom to the formation of stars.

“In our everyday world, everything is either gravity or electromagnetism,” Holger Müller, a physicist at the University of California, Berkeley, told Quanta Magazine. “And that’s why alpha is so important.”

Of course, physics is no stranger to constants – there’s c, the speed of light; G, the gravitational constant; in quantum physics there’s both h and  to describe the Planck constant; if you’re a real aficionado you may even know about k, the Boltzmann constant. But α has something none of those other constants have – or, to be more precise, it doesn’t have something they do.

“There are no dimensions or unit system that the value of the [fine structure constant] depends on,” wrote Sutter. “The other constants in physics aren’t like this.”

Take the speed of light, for example. Look it up in a search engine, and you’ll find it’s equal to 299,792,458 meters per second. Or is it 670,615,200 miles per hour? Our mistake: it’s actually 1,802,600,000,000 furlongs per fortnight. Screw it – let’s just say it’s one light-year per year.

Get the picture yet? The value of the constant isn’t actually, well, constant – it depends on the units you use. But the fine structure constant doesn’t have that property: it’s an entirely dimensionless constant. 

“If you were to meet an alien from a distant star system, you’d have a pretty hard time communicating the value of the speed of light. Once you nailed down how we express our numbers, you would then have to define things like meters and seconds,” explained Sutter.

“But the fine structure constant? You could just spit it out, and they would understand it.”

But perhaps the weirdest thing about this seemingly most pure of constants is that it may, in fact, not be constant. Some physicists have suggested that today’s α is actually slightly larger than it used to be – only by one part in about 100,000 over six billion years, but that’s enough to have some pretty huge ramifications in the long run. Change that 137 to 138, for example, and you decrease the value of α by 0.00005 – enough, some scientists argue, to prevent stars from creating carbon, thus halting the creation of life as we know it.

As Feynman put it: “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.’”

An earlier version of this article was published in June 2022.

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