The fine-structure constant has been a mystery since 1916, when it popped out of Arnold Sommerfeld’s analysis of the hydrogen atom’s quantum mechanical structure. (Niels Bohr had just published his groundbreaking atomic model, with its famous central nucleus and orbiting electrons, three years earlier.) The constant, which Sommerfeld labeled alpha, quantified the strength of electromagnetism, the fundamental force that mediates most of the phenomena evident in our daily lives — from light to electricity to friction to fire.
While Sommerfeld put nascent quantum theory on more solid ground, his constant bedeviled physicists in the century that followed. As its name suggests, it seems to be fixed. Later studies revealed that if its value were somewhat different, a universe with the complex structure needed for life would be impossible. And yet no one knows a good reason for it to actually be fixed. For physicists, who like their theories to be well-motivated, a constant with a seemingly arbitrary value is a major problem. The American physicist and Nobel laureate Richard Feynman once wrote, “All good theoretical physicists put this number up on their wall and worry about it.”
Starting with a paper published by Paul Dirac in 1937, theorists pointed out that changes in fundamental constants such as alpha or the ratio of the proton and electron masses could reveal cracks in some of the bedrock theories of modern physics, such as relativity theory. The fine-structure constant ultimately became one of around two dozen empirical parameters in the Standard Model of particle physics, the wildly successful theory that comes as close as currently possible to describing the universe at its most fundamental level. An inconstant constant could imply the existence of a fifth force — in addition to gravity, electromagnetism, and the strong and weak forces. In other words, alpha could be a window into the unknown.
With that in mind, Flambaum helped Webb analyze his potentially consequential result. But Flambaum knew that physicists wouldn’t accept a changing alpha without serious independent evidence. He realized that a new generation of atomic clocks based on electron jumps in visible wavelengths could provide the needed confirmation. Such “optical clocks,” which pack around 50,000 times more wave peaks into a second than the microwave clocks that currently determine the world’s time, would be so precise that by measuring the constant over just a few years, physicists could get as stringent a result as Webb had from billions of years’ worth of starlight.
Atoms are, in a sense, nature’s clocks. Each time an electron jumps between atoms’ internal energy levels — a concept popularized by the term “quantum leap” — it emits or absorbs light at a unique frequency. A laser tuned close to that frequency can induce the atom to fluoresce, or scatter, photons from another laser. By using the flux of photons to drive a feedback signal, physicists can lock the laser onto the atomic transition. The laser’s successive wave peaks can then be considered ticks of a clock.
Each atomic jump’s frequency is determined by electromagnetic interactions between the atom’s electrons and protons, whose strength is set by alpha. An atomic clock thus implicitly measures the fine-structure constant. Indeed, one could say that every atom in the universe perpetually measures the constant. We just need to figure out how to read the measurement.
It’s a little more complicated in practice, though. Looking for a drift in alpha requires measuring at least two clocks’ frequencies at two times, because a change in just one frequency could reflect either a changing constant or some other shift in the clock or its environment. The ratio of the frequencies of two or more independent clocks, by contrast, is a dimensionless number that depends only on the constants of nature.
In 2004, Ekkehard Peik, a physicist at PTB, Germany’s standards institute, in Braunschweig, took the first big step, comparing an optical ytterbium-ion clock’s ticking rate with that of a microwave cesium clock. To do the experiment, Peik’s team measured both clocks’ frequencies over a couple of weeks to reduce statistical uncertainty, spent a year improving the clocks, then measured them again. The data revealed that alpha could not be changing by more than around 2 parts in 1015 per year. That limit was still about twice as large as the change claimed by Webb’s observations of distant galaxies.
Then in 2008, researchers in David Wineland’s group at the National Institute of Standards and Technology (NIST) in Boulder, Colorado, tightened that limit by almost 100 times, to around 1 part in 1017, by ditching the less accurate cesium clock and using optical clocks based on aluminum and mercury. That put Webb’s changing-alpha result in a tight spot. Last year, Peik’s team tightened the vise even further when they announced preliminary results of a new limit of around 1 in 1018, based on comparisons of an ytterbium-ion clock and a clock made of strontium atoms.
“They do not publish very often,” Flambaum said. “But when they publish, it’s really a dramatic breakthrough in accuracy.”
Flambaum wasn’t just waiting around while the clock groups made their painstaking measurements, however. He was busy thinking of other uses for clocks and constants. In 2015, he and a colleague published a paper showing how certain dark matter hypotheses could cause alpha to drift, oscillate or hiccup. He suggested that Ye comb through previously collected clock data for dark matter signatures.
Ye had other ideas. “My thinking is that your proposal can be significantly improved,” he told Flambaum.
Atomic Searches for Unorthodox Dark Matter
Flambaum wasn’t the first to suggest using clocks to hunt for dark matter. In 2014, a pair of researchers realized that another type of atomic clock could be roped into the search for new physics — the kind that has been orbiting Earth for over two decades. The satellites in the global positioning system, commonly known as GPS, use onboard atomic clocks to calculate relative distances to every point on Earth. These clocks use microwave frequencies and lag behind state-of-the-art lab clocks by more than 100,000 times in precision. But they are very reliable, and they are always on. And after their readings were declassified in 1996, geoscientists at NASA’s Jet Propulsion Laboratory in California set up receivers to download and store time data from these clocks; a slight jitter in the interval at which signals were received could indicate subtle shifts in Earth’s crust.
The physicists Maxim Pospelov of the Perimeter Institute for Theoretical Physics in Waterloo, Canada, and Andrei Derevianko, of the University of Nevada, Reno, proposed using the GPS data set as a dark matter search. While dark matter could come in the form of relatively heavy “weakly interacting massive particles,” or WIMPs, which physicists have sought in vain, it could also be made of other weakly interacting stuff.
One hypothesis involves ubiquitous ultralight particles less than 1 millionth of the electron’s mass. These hypothetical dark matter particles could have frozen into massive blobs, strings or walls after the Big Bang. When Earth enters or exits such a dark matter clump, which could be as large as the planet itself, the change would nudge the fine-structure constant, which in turn would tweak the onboard clocks’ ticking rates. A hiccup would roll through the GPS network like a wave. “This is somewhat speculative,” Pospelov admitted. “But at the moment we don’t have a good model for dark matter which you can bet your money on. So we may as well do this almost for free.”
Derevianko, Pospelov and colleagues reported in fall 2017 that they had found no dark matter-induced hiccups in 16 years’ worth of GPS data, tightening the lid on theories of such “topological” dark matter by a factor of 1,000 to 100,000, depending on the size of the theoretical dark matter clumps.
Meanwhile, Asimina Arvanitaki, a theoretical physicist at the Perimeter Institute, was thinking about possible ways to detect dark matter candidates that naturally emerge from theories designed to unify relativity and quantum mechanics — the two great paradigms of modern physics. In such theories, which include the popular string theory, all-pervading fields associated with tiny spinless “dilaton-like” particles affect the values of fundamental constants such as alpha. Because these particles would necessarily interact with normal matter but only weakly, they would form at least part of the mysterious dark sector, Arvanitaki said.
Like all particles, dilaton-like dark matter particles would have associated quantum waves. And like many particles of light coalescing into a laser, vast collections of them — numbering around 1 with 100 zeros after it, in fact — would naturally fall into one large, coherent wave whose frequency and amplitude depends on the particle’s mass. Atomic energy levels — and thus atomic clocks’ ticking rates — would pulse slightly at the wave’s frequency.
Unfortunately, string theory gives no clue about this frequency — it could be a fraction of a second, many years or anything in between. “I wish there was a prediction that there’s a spot in parameter space that would tell you: Look here and you will find it,” Arvanitaki said. Luckily, a mathematical trick called a Fourier transform makes it possible to search any data set for a hidden oscillation of unknown frequency. The only limiting factor is time: The longer experimentalists run two clocks simultaneously and continuously, the broader the range of frequencies they can search. “Everyone who has an atomic clock, in principle, can do it,” Arvanitaki said.
Within weeks of Arvanitaki’s paper hitting the scientific preprint site arxiv.org, Dmitry Budker, a physicist at the University of California, Berkeley, told her that he was looking for evidence of such oscillations in data he had collected from measurements of electron jumps in dysprosium atoms. A short while later he posted his results — no evidence of an oscillation. The work tightened the theoretical constraint on the interaction between dilaton-like dark matter and ordinary matter by a factor of 10,000. Less than two years later, a group at the Paris Observatory used data from their cesium and rubidium microwave clocks to tighten that limit by another factor of 10.
Experimentalists often take years to improve a theoretical constraint by one order of magnitude. So jumps of 10,000 or more are major advances. “There’s a lot of low-hanging fruit,” Arvanitaki said. “You can make a lot of progress by doing simple things.”
Like going back over old data. After David Hume, a physicist at NIST, read Budker’s paper and got an email from a colleague of Flambaum’s, he started reanalyzing his lab’s aluminum-mercury clock data from the mid-2000s. He discovered that he already had the world’s best constraint on dilaton-like dark matter. He’s now gearing up for new clock runs that will do even better. The measurements will also test whether the fine-structure constant has drifted over the past decade, possibly even improving on Peik’s latest result.
Ye received Flambaum’s 2015 email just as he was perfecting a strontium clock that would soon break his group’s own record for the world’s most accurate. He was excited by the dark matter proposal, but he put a new spin on the idea. Instead of comparing his strontium clock’s frequency to that of another clock, he decided to compare it to the length of the exquisite single-crystal silicon cavity that he uses to stabilize his laser. The cavity itself, Ye reasoned, would measure any change in the fine-structure constant, because it is a certain number of Bohr radii long (the Bohr radius sets the natural length scale of an atom), and the radius, like any atomic transition frequency, has the constant embedded in it. In late 2017, he launched what may be the world’s first dedicated search for dilaton-like dark matter. He has taken two months’ worth of data and believes the experiment will constrain dark matter theories beyond published limits.
And there is no shortage of ideas about how to improve clock-based dark matter searches even further. Ye hopes to probe additional dark matter hypotheses, including the hiccups from Flambaum’s 2015 email, by running his newest clock at the same time as an equivalent setup at PTB. Derevianko imagines going a step further by connecting the world’s best clocks via fiber-optic cables and running them simultaneously — a scheme that he calculates could test topological dark matter 10,000 times more sensitively than the GPS satellite clocks. A fiber-optic network has already linked clocks in London, Paris and Braunschweig for the past two years, though expanding beyond Europe would require advances in fiber-optic or satellite communication technology. Derevianko and Budker are also trying to persuade atomic physicists to publicly archive precision measurements, to enable future searches as new theoretical ideas emerge.
This everything-but-the-kitchen-sink approach is the right strategy when no theory is a clear standout, physicists say. “I think one has to look everywhere one can for new physics,” said Marianna Safronova, a theoretical physicist at the University of Delaware. But atomic clocks may have an edge, because physicists have already been refining them for decades in the quest for more accurate timekeeping. “We are not building a big new machine for some dedicated physics experiment,” Peik said.
Several research groups, including Peik’s, are eyeing a proposed clock based on a jump not between atomic electron levels but between energy levels in the atomic nucleus. Most nuclear transitions occur at extremely high frequencies, but by an accident of physics, one isotope of thorium has a nuclear jump whose frequency is within the range of lasers. The exact frequency still needs to be found, and lasers need to be improved. But a clock based on this transition would theoretically beat today’s top optical clocks in accuracy by an order of magnitude. More advanced clocks could potentially detect gravitational waves and test theories of quantum gravity, Ye said.
Indeed, Arvanitaki said, such a clock “would be an extremely sensitive probe of basically everything.”