In classical physics, a vacuum is a total void—a true manifestation of nothingness. But quantum physics says that empty space isn’t really empty. Instead, it’s buzzing with “virtual” particles blipping in and out of existence too quickly to be detected. Scientists know that these virtual particles are there because they measurably tweak the qualities of regular particles.
One key property these effervescent particles change is the miniscule magnetic field generated by a single electron, known as its magnetic moment. In theory, if scientists could account for all the types of virtual particles that exist, they could run the math and figure out exactly how skewed the electron’s magnetic moment should be from swimming in this virtual particle pool. With precise enough instruments, they could check their work against reality. Determining this value as accurately as possible would help physicists nail down exactly which virtual particles are toying with the electron’s magnetic moment—some of which might belong to a veiled sector of our universe, where, for example, the ever-elusive dark matter resides.
In February, four researchers at Northwestern University announced they had done just that. Their results, published in Physical Review Letters, report the electron magnetic moment with staggering precision: 14 digits past the decimal point, and more than twice as exact as the previous measurement in 2008.
That might seem like going overboard. But there’s much more than mathematical accuracy at stake. By measuring the magnetic moment, scientists are testing the theoretical linchpin of particle physics: the standard model. Like a physics version of the periodic table, it’s laid out as a chart of all the particles known in nature: the subatomic ones making up matter, like quarks and electrons, and those that carry or mediate forces, like gluons and photons. The model also comes with a set of rules for how these particles behave.
But physicists know the standard model is incomplete—it’s likely to be missing some elements. Predictions based on the model often don’t line up with observations of the real universe. It can’t explain key conundrums like how the universe inflated to its current size after the Big Bang, or even how it can exist at all—full of matter, and mostly absent of the antimatter that should have canceled it out. Nor does the model say anything about the dark matter gluing galaxies together, or the dark energy spurring cosmic expansion. Perhaps its most flagrant flaw is the inability to account for gravity. Incredibly precise measurements of known particles are therefore key to figuring out what’s missing because they help physicists zero in on gaps in the standard model.
“The standard model is our best description of physical reality,” says Gerald Gabrielse, a physicist at Northwestern University who coauthored the new study, as well as the 2008 result. “It’s a highly successful theory in that it can predict essentially everything we can measure and test on Earth—but it gets the universe wrong.”
In fact, the most precise prediction the standard model makes is the value of the electron’s magnetic moment. If the predicted magnetic moment doesn’t match up with what’s seen in experiments, the discrepancy could be a clue that there are undiscovered virtual particles at play. “I always say that nature tells you what equations are correct,” says Xing Fan, a physicist at Northwestern University who spearheaded the study as a Harvard University graduate student. “And the only way you can test it is if you compare your theory to the real world.”
The electron lends itself to testing because it’s stable, making it possible to measure the particle for long periods of time in a well-controlled environment. “Often in physics, it happens that something can be calculated very well but it can’t be measured very well, or vice versa,” says Holger Müller, a University of California Berkeley physicist who was not involved in the work. But this is a rare case where it’s possible to do both, he says, which makes it a chance to put the standard model to the test.
To measure the magnetic moment, the researchers trapped a single electron inside a metal chamber using an ultrastable magnetic field, which made the electron twirl like a top. They measured the frequency of this motion and its difference from the frequency of the electron’s spin—a kind of intrinsic angular momentum. The ratio between those values is proportional to the electron’s magnetic moment. The value they came up with was 1.00115965218059, a number so precise, Fan says, it’s like measuring a person’s height with a margin of error a thousand times smaller than the diameter of an atom.
This measurement matches up with the standard model’s predicted value at least up to 12 digits past the decimal point. That means the standard model is safe—for now. “When I saw the paper come out, my first takeaway was a sense of relief,” Müller says.
But whether the last two digits agree is still a mystery, one that can’t be solved until physicists figure out a related value called the fine structure constant, which is a measure of the strength of the electromagnetic force and is used to compute the standard model prediction of its magnetic moment. (Whether this constant is truly the same throughout the entire universe will be another clue to the standard model’s accuracy.) There are currently two leading values for it—Müller measured one of them—but those pop out different answers for what the electron’s magnetic moment should be. “They’re working to try and figure out what went wrong,” Gabrielse says. “And we’re anxious for them to fix it.”
There’s another particle that scientists are closely measuring for clues: the muon, an unstable cousin of the electron. It’s over 200 times heavier, which makes it much easier to scrutinize. Two years ago, researchers at Fermilab measured the muon’s magnetic moment and found it to be inconsistent with what the standard model predicts, an enticing hint that undiscovered particles might be in the mix. But that result isn’t nearly as precise, Gabrielse says—the uncertainty is about one part per million, contrasted with the electron measurement at a part per trillion. So it’s still not clear whether the muon’s discrepancy points to new physics or an experimental error.
Compared to the muon, the electron’s lighter mass makes it 40,000 times harder to search for new particles with its magnetic moment. But Fan thinks an upgraded electron-trapping instrument will help the team overcome this difficulty. Improving the accuracy by another factor of 2 could land them in the realm of uncharted physics, he says.
The field as a whole is entering its precision era, moving beyond just slamming particles into each other to see if they throw off new subatomic bits and adopting meticulous techniques to probe their properties. “The old way of doing particle physics was smashing things together and seeing what fragments come out,” Müller says—like hitting a clock with a hammer to see what’s inside. These days, he says, scientists are also carefully studying the way it ticks and gleaning information from there.
The Northwestern team has already done a proof of concept that shows how measuring the electron’s magnetic moment with their instrument can help them search for dark photons, hypothetical particles that interact with dark matter similarly to the way regular photons interact with ordinary matter. In the future, they plan to redo this experiment with the positron—the antimatter version of the electron—whose magnetic moment hasn’t been measured for the past 35 years. If that value ends up being different from the electron’s, it could be a smoking gun in another longstanding physics mystery: the question of how antimatter all but disappeared after the Big Bang, leaving us in a matter-rich universe.
The team is pleased with how accurately they’ve measured the electron’s magnetic moment so far. “We’re excited about this factor of 2,” Gabrielse says, referring to the way the new paper doubled its predecessor’s level of precision. But next time, he thinks they can do a lot better: “We’re going for another factor of 10.”
