Dozens of the top clockmakers in the world convened in New Orleans one muggy week in May 2002 to present their latest inventions. There was not a mechanic among them; these were scientists, and their conversations buzzed with talk of spectrums and quantum levels, not gears and escapements. Today those who would build a more accurate clock must advance into the frontiers of physics and engineering in several directions at once. They are cobbling lasers that spit out pulses a quadrillionth of a second long together with chambers that chill atoms to a few millionths of a degree above absolute zero. They are snaring individual ions in tar pits of light and magnetism and manipulating the spin of electrons in their orbits.
Thanks to major technical advances, the art of ultraprecise timekeeping is progressing with a speed not seen for 30 years or more. These days a good cesium beam clock, of the kind Microsemi sells for about $50,000, will tick off seconds true to about a microsecond a month, its frequency accurate to five parts in 1013. The primary time standard for the U.S., a cesium fountain clock installed in 2014 by the National Institute of Standards and Technology (NIST) at its Boulder, Colo., laboratory, is good to three parts in 1016 (usually written simply as 10−16). That is 2,000 times the accuracy of NIST's best clock in 1975. Successful prototypes of new clock designs—devices that extract time from aluminum or mercury ions instead of cesium—have recently attained accuracy in the 10−18 range, a 100-fold improvement in a decade.
Rock of ages: Stones represent planets in the Orrery, an eight-foot-tall clock prototype showing the relative positions of Earth and its five nearest neighbors. The Long Now Foundation is building a 200-foot-tall version with huge horizontal gears and stone counterweights, designed to run for 10,000 years. Credit: Dan Winters
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Credit: Microsemi Corporation
Credit: CNES/HERVÉ PIRAUD (PHARAO)
Accuracy may not be quite the right word. The second was defined in 1967 by international fiat to be “the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.” Leave aside for the moment what that means: the point is that to measure a second, you have to look at cesium. The best clocks now don't—so, strictly speaking, they don't measure seconds. That is one predicament the clockmakers face.
Further down the road lies a more fundamental limitation: as Albert Einstein theorized and experiment has confirmed, time is not absolute. The rate of any clock slows down when gravity gets stronger or when the clock moves quickly relative to its observer—even a single photon emitted as an electron reorients its magnetic poles or jumps from one orbit to another. By putting ultraprecise clocks on the International Space Station, scientists hope to put relativity theory through its toughest tests yet. But now that clocks have achieved a precision of 10−18—proportions that correspond to a deviation of less than half a second over the age of the universe—the effects of relativity are starting to test the scientists. No technology exists that can synchronize clocks around the world with such exactness.
Inventing Accuracy
So why bother to improve atomic clocks? The duration of the second can already be measured to 14 decimal places, a precision 1,000 times that of any other fundamental unit. One reason to do better is that the second is increasingly the fundamental unit. Three of the six other basic units—the meter, lumen and ampere—are now defined in terms of the second. The kilogram and the mole may be next. “It is just a matter of time before [the kilogram] is redefined,” says Richard L. Steiner of NIST. Using the famous E = mc2 equation, scientists could set the unit of mass to an equivalent amount of energy, such as a collection of photons whose frequencies sum to a certain number. By improving clocks, scientists can improve measurements of much more than time.
Credit: Rolfe Horn Long Now Foundation
More stable and portable clock designs could also be a big boon to navigation, enhancing the accuracy and reliability of the Global Positioning System and of Galileo, a competing system in Europe that recently began initial operations. Better clocks would help NASA track its satellites, enable utilities and communications firms to trace faults in their networks, and enhance geologists' ability to pinpoint earthquakes and nuclear bomb tests. Astronomers could use them to connect telescopes in ways that dramatically sharpen their images. Inexpensive, microchip-size atomic clocks [see "Atomic Micro Clocks" above] are likely to have myriad uses not yet imagined.
To understand why timekeeping has suddenly lurched into high gear, it helps to know a little about how atomic clocks work. In principle, an atomic clock is just like any other timepiece, with an oscillator that “ticks” in a regular way and a counter that converts the ticks to seconds. The ticker in a cesium clock is not mechanical (like a pendulum) or electromechanical (like a quartz crystal). It is quantum-mechanical: a photon of light is absorbed by the cesium atom's outermost electron, causing the electron to flip its magnetic field (and its associated spin) upside down.
Unlike pendulums and crystals, all cesium atoms are identical. And every one will flip the spin of its outer electron when hit with microwaves at the frequency of exactly 9,192,631,770 cycles per second. To measure seconds, the clock locks its microwave generator onto the sweet spot in the spectrum where the most cesium atoms react. Then it starts counting cycles.
Of course, nothing in quantum physics is really that simple. Complicating things, as usual, is the Heisenberg indeterminacy principle, which puts strict limits on how precisely one can measure the frequency of a single photon. The best clocks now scan a one-hertz-wide sweet spot to find its exact center, plus or minus one millihertz, in every single measurement—despite the Heisenberg limits. “The reason we can do it is that we look at more than a million atoms each time,” explained Kurt Gibble, a physicist at Pennsylvania State University, in New Orleans. “Because it isn't really just one measurement, it doesn't violate the laws of quantum mechanics.”
But that solution creates other problems. At room temperature, cesium is a soft, silvery metal. It would melt in your palm to a golden puddle—although you wouldn't want to touch it, because it reacts violently with water. Inside a cesium beam clock, an oven heats the metal until atoms boil off. These hot particles can zip through the microwave cavity at various speeds and angles. Some move so fast that (because of relativity) they behave as if time has slowed. To other atoms, the microwaves appear (because of Doppler shifting) to be higher or lower in frequency than they are. The atoms no longer behave identically, so the ticks grow less distinct.
Herr Doktor Heisenberg would probably have suggested slowing the atoms down, and that's what clockmakers have done. Several clocks in the world—at NIST, the U.S. Naval Observatory, and the standards institutes in Paris, Teddington, England, and Brunswick, Germany—toss supercooled balls of cesium atoms in a fountainlike arc through a microwave chamber [see “A Chronicle of Timekeeping,” by William J. H. Andrewes]. To condense the hot cesium gas into a ball, six intersecting laser beams decelerate the atoms to less than two microkelvins—almost a complete standstill. The low temperature all but eliminates relativistic and Doppler shifts, and it gives a two-meter-tall fountain clock half a second to flip the atoms' spins. Fountain clocks, introduced in 1996, rapidly knocked 90 percent off the uncertainty of international atomic time.
Time in Space
It takes time to make a good second, and the fountain clocks still rush the job. “We would have to quadruple the height of the tower to double the observation time,” says Donald Sullivan, former chief of the time and frequency division at NIST. Instead of punching a hole through the ceiling of his lab, Sullivan led one of three projects to put fountainlike clocks on the International Space Station. “In space, we can launch a ball of atoms at 15 centimeters per second through a 74-centimeter cavity. So we have five to 10 seconds to observe them,” he explains. The $25-million Primary Atomic Reference Clock in Space (PARCS) project on which he worked was designed to turn out seconds good to five parts in 1017.
PARCS was canceled in 2004, when NASA shifted funding from the space station to programs to send astronauts to the moon and, eventually, Mars. But a device from the European Space Agency called ACES (Atomic Clock Ensemble in Space) is scheduled to launch in 2018 and aims to measure with 99.99997 percent accuracy how much the microgravity of low Earth orbit slows time compared with measurements made on the ground.
Meanwhile efforts to make a third space-faring clock, called RACE (Rubidium Atomic Clock Experiment), helped to refine a newer approach that replaces the cesium so familiar to clockmakers with a different alkali element. “In the best cesium fountains the largest source of error are so-called cold collisions,” explained Gibble—who directed the RACE project, which died along with PARCS in 2004—in New Orleans. At temperatures near absolute zero, quantum physics takes over and atoms start to behave like waves. “They appear hundreds of times bigger than normal, so they collide much more often. At a microkelvin, cesium has nearly the maximum possible cross section,” he continued. “But the effective size for rubidium atoms is 50 times smaller.” That enables rubidium clocks to reach 10−17, one fifth the uncertainty of ACES.
Rubidium clocks offer another advantage: the opportunity to look for fluctuations in the fine-structure constant, alpha (α). Alpha determines the strength of electromagnetic interactions in atoms and molecules. It is very nearly 1/137, a unitless number that falls out of the Standard Model of physics, with no apparent reason for the value it has. Yet it is an important number—change α very much, and the universe could not support life as we know it [see “Inconstant Constants,” by John D. Barrow and John K. Webb, on page 70].
In the Standard Model, the fine-structure constant is immutable throughout eternity. But in some competing theories (such as certain string theories), α could waver slightly or grow as time goes by. In August 2001 a group of astronomers reported preliminary evidence that α may have increased by one part in 10,000 during the past six billion years. But the evidence is equivocal, and the question is a hard one to settle. By analyzing radio signals from a distant galaxy, astronomers in February concluded that if α is fluctuating, it has varied by no more than about one part in a million over the past 2.9 billion years.
Lasers Rule
Indeed, the development of ion clocks in recent years has made clocks based on fountains of atoms seem almost obsolete. In August 2001 Scott A. Diddams and his colleagues at NIST reported an initial trial run of something many clock builders had thought they might never live to see: an optical atomic clock based on a single mercury atom. It may seem like a natural idea to graduate from microwaves, at frequencies of gigahertz, to visible light, well into the terahertz part of the spectrum. Optical photons pack enough energy to bump electrons clear into the next orbital shell—no need to fuss with subtleties like spin. But although the ticker still works at terahertz frequencies, the counter breaks.
“Nobody knows how to count 1016 cycles per second,” observes Eric A. Burt of NASA's Jet Propulsion Laboratory. “We needed a bridge to the microwave regime, where we do have electronic counters.”
Enter the optical ruler. In 1999 Thomas Udem, Theodor W. Hänsch and others at the Max Planck Institute for Quantum Optics in Garching, Germany, figured out a way to measure optical frequencies directly, using a reference laser that pulses at a rate of one gigahertz. Each pulse of light is just a couple of dozen femtoseconds long. (A femtosecond is a very, very small amount of time. More femtoseconds elapse in each second than there have been hours since the big bang.) A laser puts out a continuous beam of only one color, but pulse that laser, and you get a mixture of colors in each flash. The spectrum of a femtosecond pulse is a bizarre thing to see: millions of sharp lines spanning the rainbow, each line spaced exactly the same distance from its neighbors—like tick marks on a ruler. “That you could make a laser that pulses a billion times a second and whose constituent frequencies are all stable to one hertz is just short of unbelievable,” Gibble said in New Orleans, shaking his head.
Diddams's group at NIST has built a rudimentary optical clockwork around mercury ions, which they immobilize in an electromagnetic trap [see "Extracting Time from an Atom" graphic above]. Because each atom is missing an electron, the ions carry a positive charge. They repel one another, so collisions are no longer a problem. The device is stable to better than six parts in 1016 over the course of a second. Over longer periods the uncertainty could approach 10−18. “Mercury is not an ideal element to use,” Sullivan acknowledges. “The clock transition we use in it can shift with magnetic fields, which are hard to eliminate completely. But there is a transition in indium that looks attractive.”
Udem and Hänsch are one step ahead of him. They have been investigating the indium ion, and indeed it seems quite capable of carrying clocks down “into the 18's,” as Gibble put it. Groups at the Federal Institute of Physics and Metrology in Brunswick, Germany, and elsewhere are experimenting with uncharged calcium atoms. Because neutral atoms can be crammed more densely into the trap than ions can, the signal soars higher over the noise. And in 2015 a NIST-led team reported the successful demonstration of an optical lattice clock based on atoms of strontium 87; the uncertainty was pegged at two parts in 1018. A German research group reported in 2016 on a precision almost as good, of 3.2 parts in 1018, from a system based on a single ion of ytterbium 171. The NIST group also used ytterbium for a lattice clock that achieved an accuracy of 1.6 parts in 1018.
Inconstant Time
But there's that word again: accuracy. These new clocks “move away from the atomic definition of the second, which is based on the properties of cesium,” Sullivan points out. For the newest and best clocks to be strictly accurate as keepers of the time to which we set our watches, that definition will have to change. Sullivan says the time committee of the International Bureau of Weights and Measures (BIPM), which decides such things, accepted his proposal to allow “secondary” definitions that state the equivalence of a cesium frequency to that of other atoms. If the full BIPM assembly approves the idea, the definition of the second will be broadened but also weakened.
Clock builders will not get around relativity so easily. Clocks accurate to one part in 1017—a millisecond in three million years—will be easily thrown out of whack by two relativistic effects. First, there is time dilation: moving clocks run slow. “A frequency shift of 10−17 corresponds to a time dilation due to walking speed,” Gibble said.
The other confounder is gravity. The stronger its pull, the slower time passes. Clocks at the top of Mount Everest pull ahead of those at sea level by about 30 microseconds a year. When NIST researchers synchronized two quantum logic clocks and then raised one of them 33 centimeters, they found that the clocks were perceptibly out of sync. Raising a clock 10 centimeters changes its rate by one part in 1017. And elevation is relatively easy to measure, compared with variations in gravity caused by local geology, tides or even magma shifting kilometers underground.
Ultimately, Gibble said, “if you take our ability to split spectral lines with microwave clocks and extrapolate to optical rulers, that puts you at uncertainties of order 10−22. I certainly would not claim that we are going to get there anytime soon, however.” There is no particular rush: no one has the first idea how to transfer time that precisely between two clocks. And what good is a clock if you can't move it and can't check it against another?