Quantum Particles Aren’t Spinning. So Where Does Their Spin Come From?

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Electrons are proficient little magicians. They seem to flit about an atom without tracing a particular path, they frequently appear to be in two places at once, and their behavior in silicon microchips powers the computing infrastructure of the modern world. But one of their most impressive tricks is deceptively simple, like all the best magic. Electrons always seem to spin. Every electron ever observed, whether it’s just ambling its way about a carbon atom in your fingernail or speeding through a particle accelerator, looks like it’s constantly doing tiny pirouettes as it makes its way through the world. Its spinning never appears to slow or speed up. No matter how an electron is jostled or kicked, it always looks like it’s spinning at exactly the same speed. It even has a little magnetic field, just like a spinning object with electric charge should. Naturally, physicists call this behavior “spin.”

But despite appearances, electrons don’t spin. They can’t spin; proving that it’s impossible for electrons to be spinning is a standard homework problem in any introductory quantum physics course. If electrons actually spun fast enough to account for all of the spinlike behavior they display, their surfaces would be moving much faster than the speed of light (if they even have surfaces at all). Even more surprising is that for nearly a century, this seeming contradiction has just been written off by most physicists as yet another strange feature of the quantum world, nothing to lose sleep over.

Yet spin is deeply important. If electrons didn’t seem to spin, your chair would collapse down to a miniscule fraction of its size. You’d collapse too—and that would be the least of your problems. Without spin, the entire periodic table of elements would come crashing down, and all of chemistry would go with it. In fact, there wouldn’t be any molecules at all. So spin isn’t just one of the best tricks that electrons pull; it’s also one of their most crucial. And like any good magician, electrons haven’t told anyone how the trick is done. But now, a new account of spin may be on the horizon, one which pulls back the curtain and shows how the magic works.

A Dizzying Discovery

Spin has always been confusing. Even the first people to develop the idea of spin thought it had to be wrong. In 1925, two young Dutch physicists, Samuel Goudsmit and George Uhlenbeck, were puzzling over the latest work from the famous (and famously acerbic) physicist Wolfgang Pauli. Pauli, in an attempt to explain the structure of atomic spectra and the periodic table, had recently postulated that electrons had a “two-valuedness not describable classically.” But Pauli hadn’t said what physical property of the electron his new value corresponded to, and Goudsmit and Uhlenbeck wondered what it could be.

All they knew—all anyone knew at the time—was that Pauli’s new value was associated with discrete units of a well-known property from classical Newtonian physics, called angular momentum. Angular momentum is just the tendency for a rotating thing to continue rotating. It’s what keeps tops spinning and bicycles upright. The faster an object is rotating, the more angular momentum it has, but the shape and mass of the object both matter too. A heavier object has more angular momentum than a lighter object spinning just as fast, and a spinning object with more mass at its edges has more angular momentum than it would if its mass were clumped at its center.

Objects can have angular momentum without spinning. Any thing revolving around another thing—like the Earth going around the sun, or a set of keys swinging around your finger on a lanyard—has some angular momentum. But Goudsmit and Uhlenbeck knew that this kind of angular momentum couldn’t be the source of Pauli’s new number. Electrons do appear to move around the atomic nucleus, held close by the attraction between their negative electrical charge and the positive pull of the protons in the nucleus. But the angular momentum they have from this movement was already well accounted for, and couldn’t be Pauli’s new number. The physicists also knew that there were already three numbers associated with the electron, which corresponded to the three dimensions of space it could move in. A fourth number meant a fourth way the electron could move. The only option, the two young physicists reasoned, was for the electron itself to be spinning, like the Earth rotating on its axis as it orbits the sun. If electrons could spin in one of two directions—clockwise or counterclockwise—that would account for Pauli’s “two-valuedness.”

Excitedly, Goudsmit and Uhlenbeck wrote up their new idea, and showed it to their mentor, Paul Ehrenfest. Ehrenfest, a close friend of Einstein and a formidable physicist in his own right, thought the idea was intriguing. While he considered it, he told the two eager young men to go consult with someone older and wiser: Hendrik Antoon Lorentz, the grand old man of Dutch physics, who had anticipated much of the development of special relativity two decades earlier and whom Einstein himself held in the highest regard.

But Lorentz was less impressed with the idea of spin than Ehrenfest. As he pointed out to Uhlenbeck, the electron was known to be very small, at least 3,000 times smaller than an atom—and atoms were already known to be about a tenth of a nanometer across, a million times smaller than the thickness of a sheet of paper. With the electron so small, and with its even smaller mass—a billionth of a billionth of a billionth of a gram—there was no way it could possibly be spinning fast enough to account for the angular momentum Pauli and others were searching for. In fact, as Lorentz told Uhlenbeck, the surface of the electron would have to be moving 10 times faster than the speed of light, a flat impossibility.

Defeated, Uhlenbeck went back to Ehrenfest and told him the news. He asked Ehrenfest to scrap the paper, only to be told that it was too late—as his mentor had already sent the paper off to be published. “You are both young enough to be able to afford a stupidity,” Ehrenfest said. And he was right. Despite the fact that the electron couldn’t be spinning, the idea of spin was widely accepted as correct—just not in the usual way. Rather than an electron actually spinning, which was impossible, physicists interpreted the finding to mean that the electron carried with it some intrinsic angular momentum, as though it were spinning, even though it couldn’t be. Nonetheless, the idea was still called “spin,” and Goudsmit and Uhlenbeck were widely hailed as the progenitors of the idea.

Spin proved to be crucial in explaining fundamental properties of matter. In the same paper where he had suggested his new two-valued number, Pauli had also suggested an “exclusion principle,” the notion that no two electrons could occupy the exact same state. If they could, then every electron in an atom would just fall to the lowest energy state, and virtually all elements would behave in almost exactly the same way as each other, destroying chemistry as we know it. Life wouldn’t exist. Water wouldn’t exist. The universe would simply be full of stars and gas, drifting through a boring and indifferent cosmos without encountering so much as a rock. In fact, as was later realized, solid matter of any kind would be unstable. Though Pauli’s idea was clearly correct, it was unclear why electrons couldn’t share states. Understanding the origin of Pauli’s exclusion principle would unlock explanations for all of these deep facts of quotidian life.

The answer to the puzzle was in spin. Spin was soon discovered to be a basic property of all fundamental particles, not just electrons—and one with a deep connection to the behavior of those particles in groups. In 1940, Pauli and the Swiss physicist Markus Fierz proved that when quantum mechanics and Einstein’s special relativity were combined, it led inevitably to a connection between spin and group statistical behavior. Pauli’s exclusion principle was merely a special case of this spin-statistics theorem, as it came to be known. The theorem is a “mighty fact about the world,” as physicist Michael Berry says. “It underlies chemistry, it underlies superconductivity, it’s a very fundamental fact.” And like so many fundamental facts in physics, spin was found to be technologically useful as well. In the second half of the 20th century, spin was harnessed to develop lasers, explain the behavior of superconductors, and point the way to building quantum computers.

Seeing Past the Spin

But all of these fabulous discoveries, applications, and explanations still leave Goudsmit and Uhlenbeck’s question on the table: what is spin? If electrons must have spin, but can’t be spinning, then where does that angular momentum come from? The standard answer is that this momentum is simply inherent to subatomic particles, and doesn’t correspond to any macroscopic notion of spinning.

Yet this answer is not satisfying to everyone. “I never loved the account of spin that you got in a quantum mechanics class,” says Charles Sebens, a philosopher of physics at the California Institute of Technology. “You’re introduced to it, and you think, ‘Well, that’s strange. They act like they spin but they don’t really spin? Okay. I guess I can learn to work with that.’ But it’s odd.”

Recently, though, Sebens had an idea. “Within quantum mechanics, it seems like the electron is not rotating,” he says. But, he adds, “quantum mechanics is not our best theory of nature. Quantum field theory is a deeper and more accurate theory.”

Quantum field theory is where the quantum world of subatomic particles meets the most famous equation in the world: E = mc2, which encapsulates Einstein’s discovery that matter can turn into energy and vice versa. (Quantum field theory is also what gives rise to the spin-statistics theorem.) Because of this ability, when subatomic particles interact, new particles are often created out of their energy, and existing particles can decay into something else. Quantum field theory handles this phenomenon by describing particles as arising out of fields that pervade all of spacetime, even empty space. These fields allow particles to appear and disappear, all in accordance with both the strict dictates of Einstein’s special relativity and the probabilistic laws of the quantum world.

And it’s these fields, according to Sebens, that may contain the solution to the puzzle of spin. “The electron is ordinarily thought of as a particle,” he says. “But in quantum field theory, for every particle, there’s a way of thinking about it as a field.” In particular, the electron can be thought of as an excitation in a quantum field known as the Dirac field, and this field may be what carries the spin of the electron. “There’s a real rotation of energy and charge in the Dirac field,” Sebens says. If this is where the angular momentum resides, the problem of an electron spinning faster than the speed of light vanishes; the region of the field carrying an electron’s spin is far larger than the purportedly pointlike electron itself. So according to Sebens, in a way, Pauli and Lorentz were half-right: there isn’t a spinning particle. There’s a spinning field, and that field is what gives rise to particles.

An Unanswerable Question?

So far, Sebens’ idea has made ripples, not waves. When it comes to whether electrons are spinning, “I don’t think it’s an answerable question,” says Mark Srednicki, a physicist at the University of California, Santa Barbara. “We’re taking a concept that originated in the ordinary world and trying to apply it to a place where it doesn’t really apply anymore. So I think it’s really just a matter of choice or definition or taste whether you want to say the electron is really spinning.” Hans Ohanian, a physicist at the University of Vermont who has done other work on electron spin, points out that Sebens’ original version of his idea doesn’t work for antimatter.

But not all physicists are so dismissive. “The conventional formulation of how we think about spin is leaving something out potentially important,” says Sean Carroll, a physicist at Johns Hopkins University and the Santa Fe Institute. “Sebens is very much on the right track, or at least doing something very, very useful in the sense that he’s taking the field-ness of quantum field theory very seriously.” But, Carroll points out, “Physicists are, at heart, pragmatists…. If Sebens is 100 percent right, the physicists are going to say, ‘Okay, what does that get me?’”

Doreen Fraser, a philosopher of quantum field theory at the University of Waterloo, in Canada, echoes this point. “I’m open to this project that Sebens has of wanting to drill deeper into having some sort of physical intuition to go with spin,” she says. “You have this nice mathematical representation; you want to have some intuitive physical picture to go along with it.” Plus, a physical picture might also lead to new theories or experiments that hadn’t occurred before. “To me, that would be the test of whether this is a good idea.”

It’s too early to say whether Sebens’ work will bear this kind of fruit. And though he’s written a paper about how to resolve Ohanian’s concern regarding antimatter, there are other related questions still remaining. “There’s a lot of reasons to like” the field idea, Sebens says. “I take this more as a challenge than a knockdown argument against it.”

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