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April 2023 Issue [Letter from Boulder]

In Search of Lost Time

The science of the perfect second
Illustrations by Dima Kashtalyan

Illustrations by Dima Kashtalyan

[Letter from Boulder]

In Search of Lost Time

The science of the perfect second

When I was a kid, in the touch-tone era in the Midwest, I often dialed, for no real reason, the “time lady”—an actress named Jane Barbe, it turns out—who would announce, with prim authority “at the tone,” the correct time to the second. I was, in those days, a bit obsessed with time. I would stare, transfixed, at the Foucault pendulum at Chicago’s Museum of Science and Industry as it swept slow traces through its day; or gawp at the patinaed green clock, topped by a scythe and hourglass-carrying temporal patriarch and marked with a single word—time—that adorned the Jewelers Building on East Wacker Drive. But nothing felt so immediate, so curiously satisfying, as having the exact time delivered through the intimacy of the phone’s earpiece. Yet it left me with a gnawing inquiry: How does she know what time it is? I imagined that time emanated, like the Emergency Alert System, from some secure government facility, possibly underground.

I wasn’t entirely wrong. This summer, after five decades of wondering what drove clock time, I found myself at the nation’s temple of timekeeping: the Joint Institute for Laboratory Astrophysics in Boulder, Colorado. JILA (it rhymes with Willa) is a research institute operated by the University of Colorado and the National Institute of Standards and Technology (NIST), a large and relatively little-known federal agency that plays a significant, if quiet, role in our everyday lives.

The night before my visit, I’d opened, the very official-looking page—headlined official u.s. time—run by NIST and the U.S. Naval Observatory. The site features a map of the United States, divided into time zones, as well as a variety of subsidiary clock displays (Chamorro Standard Time, Aleutian Standard Time) that ticked, at the second level, in seeming synchrony. I noticed that my own watch—the Garmin Forerunner 935, a “premium running watch,” which generally gets its time from four of the thirty-one operational GPS satellites encircling the globe—looked to be a second behind. Why?

This was one of the first questions I put to Judah Levine, an eighty-two-year-old JILA physicist and one of “America’s timekeepers.” “The handheld guys are typically wrong by a second or a half-second,” Levine said. “That’s because the device’s display is not fast enough.” He said this with weary resignation. White-haired, with gold-rimmed glasses, wearing a blue flannel shirt, gray work pants, and sturdy black shoes, Levine reminded me of one of those somewhat cantankerous master craftsmen you still find in certain old quarters of Brooklyn. The shelves of his office were lined with physics textbooks, and an Oregon Scientific clock—which gets a radio signal from NIST—displayed the time in blocky liquid-crystal numbers.

In fairness to my watch, Levine explained that (which had informed me that the laptop I was using had strayed “+0.012 s”) was itself off by a noticeable amount. “It takes a while for the signal to transfer across the network, which we don’t control,” he explained. The actual correct time was on display in a laboratory adjacent to Levine’s office. It appeared as a string of red digits on a device that looked like a high-end stereo amplifier. This was a display of the official time, which is kept by a series of cesium fountain atomic clocks a few miles away, at NIST’s Boulder campus, and sent via satellite to JILA. Here was the seat of temporal power, the nation’s pulsing metronome. I watched the red LED seconds tick away, bathing in their implacable authority. It was then, however, that Levine introduced another complication. The time we were looking at might actually, a month from now, be deemed incorrect.

The official time of the United States is subordinate to what’s known as UTC, or Coordinated Universal Time, which, since the early Sixties, has been the world’s official time standard. Realized and disseminated by the French Bureau International des Poids et Mesures (BIPM), UTC is an aggregate of times gathered from the atomic clocks maintained by more than eighty national agencies across the globe. “UTC,” noted Levine, “is calculated after the fact.” This is done partly because it would be too costly, and too logistically complex, to keep the world’s clocks ticking as one. But there was another reason, he continued: “Clocks often have misbehavior.” Free-running clocks, those that are not frequently recalibrated, begin to subtly “drift,” which can be hard to detect in real time. The advantage of having a “retrospective time scale,” as Levine calls it, is being able to “look back and detect things that you could never detect in real time.”

Levine was awaiting the official time data from the previous month, which comes to NIST and similar institutions via a BIPM publication called Circular T. When Levine and his colleagues receive the report, they discuss its implications, and they do not always agree. After a recent dispute—owing, Levine said, to statistical noise, or what he calls “jiggly wigglies”—they chose to recalibrate what’s called UTC (NIST) so it would match where UTC was the previous month (or, more precisely, where it should have been in the present). Someone was dispatched to NIST room 2051, the clock room, to enter the correction.

When I suggested that Levine and his colleagues are not so much telling time as forecasting it, he nodded excitedly. “It is exactly forecasting!” This is particularly true given the emergence, a few years ago, of so-called rapid UTC, a weekly provisional dissemination of the world’s official time (considered in retrospect) from the authorities in France. NIST, like other laboratories, uses that provisional time to make predictions of where the time will be in the future, but like any forecast, it comes with the risk of being imprecise. If I’d gone to Boulder expecting to find some unassailable master clock, surrounded by druidic time lords reverently conveying its results—the sacred source that had so captured my childhood imagination—what I found instead was rather disconcerting: Time, it would seem, is quite often out of joint.

In addition to keeping the national time, NIST helps maintain the International System of Units—meters, kilograms, and the like. Its headquarters occupies a sprawling sylvan campus in Gaithersburg, Maryland (as the story goes, it was moved from Washington in the Sixties to avoid being destroyed in a nuclear strike). The agency is difficult to categorize. Its workforce is filled with experimental and theoretical physicists, but it is technically part of the Department of Commerce. It is a purely advisory, not regulatory, body, and the standards it works on are not those you might imagine: NIST does not tell industry groups what the strength or the tolerance of their materials should be, it determines how the strength or tolerance of those materials should be measured. The agency’s job, according to Katrice Lippa, the chief of NIST’s Office of Weights and Measures, is to “publish the standard of how the inspectors are supposed to test devices.” In other words, it orchestrates the metastandards.

NIST conducts metrology, the science of measurement. Scientists there measure everything from the blockchain to cloth face masks at a variety of scales. They possess both the world’s smallest ruler—a silicon chip used in X-ray diffraction that is accurate to 0.000000000000001 meters—and the world’s largest deadweight machine—a towering stack of fifty-thousand-pound stainless steel discs capable of generating up to a million pounds of force. If you need to know how granite holds up after a century you can go to the monumental wall at NIST, which is composed of 2,352 stones taken mostly from a nineteenth-century collection of quarry samples. Care to gawk at one of the world’s last surviving original radium standards, a glass ampoule filled with 20.28 milligrams of radium chloride prepared by Marie Curie in 1913? NIST has it in the basement, encased in a steel bathtub, buried under lead bricks.

NIST is a sort of acropolis of the average, a Parnassus of the prototypical. Nowhere is this more evident than in its Standard Reference Materials (SRM) division. Picture a low-lit warehouse whose metal shelves are stocked with thousands of small jars whose sober labels announce contents like “New Jersey Soil Organics and Trace Elements,” “Oyster Tissue,” and “Domestic Sludge.” Every measurable attribute of these materials has been endlessly scrutinized and calibrated, providing benchmarks for the testing of other things. Steven Choquette, the director of the Office of Reference Materials, calls them “truth in a bottle,” a sample of which can fetch up to four hundred thousand dollars. Lately, Choquette says, the division has been focusing on biopharmaceuticals, and working on NIST’s first SRM for a living material: a Chinese hamster ovary cell line. It is also busily developing “Human Whole Stool” (it’s powdered).

For all these painstakingly curated artifacts, some of the most involved work at NIST goes into standardizing and calibrating things that are no longer things: the units of measurement themselves. The International System of Units—ultimately overseen by BIPM—consists of seven “base units.” These are: the meter, the kilogram, the ampere, the candela, the mole, the kelvin, and the second. Until relatively recently, one of the most familiar of these units, the kilogram, was calibrated with reference to a physical object. For more than a century, the kilogram was realized by the International Prototype of the Kilogram (IPK), a platinum-iridium cylinder, nearly four centimeters tall, housed in a vault in France. For years, NIST researchers would carry kilogram prototypes overseas to compare them with the IPK. But transporting the kilogram to and fro risked wear and tear that could compromise its mass. In 2019, the kilogram became defined in terms of Planck’s constant—a hard value derived from quantum mechanics—making it the last of the base units to surrender its physical artifact.

“We’ve dematerialized all of our units,” said Leon Chao, a NIST researcher. “Now all of our measurements are derived from universal constants.” During the dematerialization process, standards were democratized—there was no “one kilogram” in a vault in Paris—but the measurement devices themselves lost their intuitive connection to the things they were measuring. Kevin Chesnutwood, a mechanical engineer with NIST’s Mass and Force Group who oversees the deadweight machine, told me that he used to tell schoolchildren on field trips, “Hey, we have this kilogram, and we take it to Paris every few years and compare it against the master.” The dematerialized system is much more difficult for the students to grasp, so he tries not to focus on it. “I mean, hell, we can’t even understand half of it,” he joked.

Of all the units that NIST metrologists work on, only one has never had a physical artifact: the second. Listening to NIST scientists, one gets the sense that the second has also stood apart in other ways. Theoretically, “the physicists could argue there is only one fundamental unit,” Chao told me, with a hint of tentativeness in his voice. “And I think that’s time, or frequency.”

Frequency, whose base unit is the hertz, could be understood to support all the other standards. “It’s very fundamental,” Darine El Haddad, a researcher in NIST’s Quantum Measurement Division, said. “If you want to measure everything precisely, you have to measure in terms of frequency.” The exact measurement of mass is aided by frequency but not vice versa. And there was one final thing, El Haddad told me: “It’s the unit you can measure most precisely.” There are clocks functioning at an uncertainty level that metrologists working with other units could only dream of.

In this world of metrology, which has left behind the dusty archives of physical things in favor of fundamental properties of the universe, it seems a kind of cosmic joke that this intangible, evanescent unit is the one that is understood most accurately. Even so, there is something amiss in the world of the second, the world of time. In a world of staggering exactitude, there are new timepieces on the horizon, capable of even more accuracy, clocks that are moving beyond mere measurement and opening new inquiries into time, into the universe itself. These machines have helped to drive a creeping suspicion that the second—that fundamental base unit upon which our temporal kingdom is built—despite all the synchronous activity of the world, despite the advent of clocks whose fidelity could theoretically outlast human civilization itself, is not being realized as exactly as it could be. Having come in search of the origin of time, I was learning that the very thing that drives it—the standard second—is flawed.

What makes a second a second? To the mind, a second is fleeting—by the time we pay attention to it, it’s already gone. We know it tautologically: a second is a second because our clocks tell us it is (or, perhaps, like children, we count “one, one thousand,” at a speed we inexactly deem to be second-like). If pressed, we intuit that it derives from some astronomical interval, which, indeed, it used to. For much of the twentieth century, the second was based on a nineteenth-century standard derived from astronomical calculations: 1/86,400 of a mean solar day. This may sound reassuringly simple and authoritative, but it’s built on artifice. Because of Earth’s tilt and elliptical orbit, the movement of the sun through the sky produces days of varying lengths. The mean solar day, to smooth out inconsistencies, is derived from the movement of an idealized, hypothetical sun. But this model is not optimal on account of the daily fluctuations in Earth’s rotation.

In 1960, a new standard—the ephemeris second—was created, derived from Earth’s annual orbit in the tropical year 1900. A tropical year is the length of time it takes Earth to orbit around the sun. Confusingly (like many things in the world of time), it is slightly longer than a calendar year. And if the year 1900 seems an odd choice for a standard made in 1960, it turns out that it’s the first year charted in the influential 1898 book Tables of the Motion of the Earth on Its Axis and Around the Sun, written by the Canadian-American astronomer Simon Newcomb.

The ephemeris second was less prone to variation, but it had one huge limitation: it could not be seen in action. “From the standpoint of practical metrology, it was a disaster,” said Levine. “Okay, the second is defined based on the length of the year 1900—what am I supposed to do with that?” In 1967, at the thirteenth Conférence générale des poids et mesures, it was declared “inadequate for the present needs of metrology.”

By then, the world had taken significant strides toward atomic time. The idea of marking frequency via the vibration of hydrogen or sodium particles—which promised to trade the vagaries of the heavens for the unchanging frequencies of atoms—had been theorized since the nineteenth century. By 1949, the first atomic clock was up and running. A decade later, a cesium clock at NIST was supporting the U.S. frequency standard. In 1967, when the Conférence finally killed the ephemeris second, it redefined the second as “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 caesium 133 atom.”

This is the inscrutable, hyperaccurate, modern second that governs our lives today. It represents the culmination of more than a century’s effort to standardize and synchronize time frequency, even to fashion it as a commodity. As the historian Peter Galison notes in Einstein’s Clocks, Poincaré’s Maps, it was not until the nineteenth century that minute hands became a common feature of clocks. Time was fluid, subject to local idiosyncracies; passengers at French railway stations were served by a panoply of differing temporal displays (local time, Paris time, train time). But by the late nineteenth century, accuracy was prized. Parisian owners of pneumatic clocks—calibrated by puffs of compressed air sent through pipes—fretted about the fifteen seconds it took the air to reach the clocks. “Synchronized time intervened in peoples’ lives the way electric power, sewage, or gas did,” writes Galison, “as a circulating fluid of modern urban life.” The clock became the “key-machine of the modern industrial age,” as Lewis Mumford wrote, enabling the vast expansion of the capitalist mode of production. The uneven, irregular experience of time—what Henri Bergson called durée—gave way to an experience of time as a regimented, “independent world of mathematically measurable sequences.”

There are clocks at NIST’s Boulder laboratory that are projected neither to lose nor to gain a second in three hundred million years. But who needs this kind of staggering precision, this infinitesimal punctuality? Forget the millisecond: most of us, as Levine told me, are not even “one second people.” Few things in life are calibrated to such a degree—we don’t arrive at a doctor’s appointment or a bus stop thinking in intervals of less than a minute. Human awareness of any discrete moment is thought to max out at a tenth of a second. (Nineteenth-century psychology termed this “the personal equation.”) By its own account, NIST’s timescale “typically differs from UTC by less than three billionths of a second,” an error far beyond the perception of most. NIST traffics in the nanosecond, a unit of time comprehended only by machines and relevant only to “serious users,” as Levine calls them, those who “care at the nanosecond level,” like Wall Street traders, who pay upward of one thousand dollars per month to have a more precise picture of time than the general public.

But even for the rest of us, the second plays a larger role than we might think. Consider GPS: it not only enables any number of essential services in our daily lives—our car’s navigation system, our Fitbits, our smartphones—it is one of the means by which standard time is distributed across the globe (the several dozen satellites that make up the system each maintain their own timescales). Synchronizing clocks at a distance has long been a problem. Several decades ago, the process of comparing NIST’s master clocks with the time standard involved flying to Paris with two fifty-pound iridium clocks as carry-on baggage. Roughly twice a year, Levine or one of his colleagues would travel from Boulder to France, stopping off at Washington Dulles to check the clocks against the Naval Observatory’s timepieces. Once in Paris, Levine would hustle to the offices of the Bureau international de l’heure (the clocks had a twenty-four-hour battery life). There, the clocks would be compared—not by something so crude as the human eye, but by a special machine known as a time interval counter. The clocks thus synced, Levine would return to Boulder. He did this for years, until 1978, when the Air Force launched the first GPS satellite.

For GPS to work, it needs ultra-exact timing: accuracy within fifteen meters requires precision on the order of fifty nanoseconds. The 5G networks powering our mobile phones demand ever more precise levels of cell-tower synchronization or calls get dropped. Meanwhile, increasingly interconnected electrical grids rely on nearly instantaneous timing to provide efficient power delivery and avoid network failures. Any online gamer will be well aware of his system’s latency, measured in milliseconds. And as Mumford could have predicted, nowhere has time become so fetishized as in the financial sector, with the emergence over the past decade of algorithmic high-frequency trading. Donald MacKenzie, the author of Trading at the Speed of Light, estimated in 2019 that a trading program could receive market data and trigger an order in eighty-four nanoseconds, or eighty-four billionths of a second. This is a far cry from the Nineties, when many of the clocks at brokerage houses time-stamped transactions at a one-minute level of granularity. No, we are not “one-second people.” We live in a world that moves much faster than that.

The beating heart of the nation’s time is the NIST-F1, one of the cesium fountain clocks that help maintain the standard tick. It has a steampunk vibe, all copper and aluminum and wires and tubes; a joking sign nearby it reads no playing in or around the fountain. As Elizabeth Donley, the chief of NIST’s Time and Frequency Division, described it, a ball of cesium atoms, introduced into a vacuum and cooled with lasers, are tossed up and fall back down through a tubular chamber, as in a fountain, while being “interrogated” at the midpoint of their journey by a series of microwaves. “Then you detect the atoms at the end to see if they’ve changed state,” Donley said, which is done by probing them with a laser to see whether they emit light. The interrogating microwave is adjusted to resonate with the atoms. When that resonance is reached, NIST counts, using another instrument, a staggering 9,192,631,770 periods of the microwave field. That’s the frequency established in France in 1967; in other words, the second as we know it.

NIST-F1 does not run all the time. Donley said it acts more as a “tuning fork” that calibrates the masers, or microwave lasers, helping to keep them in sync. Masers are a part of the timescale to determine the national standard. There is, in fact, no single clock that keeps official time in the United States. NIST has an ensemble of some twenty atomic clocks, mostly masers and some cesium clocks, spread across its campus, to ensure redundancy in the event of an outage. These all feed into a small room filled with flashing machines. Jeff Sherman, a researcher in NIST’s Time Realization and Distribution Group, explained that all the signals coming in—none of which, he said, have “the absolute correct frequency”—are used to calculate a sort of moving average, with the more predictable clocks given a higher weighting. He pointed to a bank of flashing lights. “These devices are really simple,” he said. “They just count five million oscillations, flash a light, count five million oscillations.” He pointed to one particular blinking light, which, he noted, “indicates the beginning of the second in the United States.”

While F1 does not look anything like a traditional clock, or run constantly, it is not, in broad terms, that dissimilar from any other timepiece. “We mark off time by counting periodic events,” Donley said. “Whether it’s the Earth orbiting the sun to make a year or the Earth spinning to make a day or a pendulum swinging.” This one just happens to count the nine-billion-odd times an alkali metal is excited and calls that a second. In the Twenties, Sherman told me, researchers looking for a better resonator for radio frequencies hit upon quartz crystals, which vibrate at a generally reliable frequency. “It was off to the races,” he said. Quartz-powered clocks appeared soon after. The idea was to trust objects whose internal rhythms were more stable than those of Earth’s movement. And the most stable objects are atoms. What makes them so appealing from a timekeeping perspective, Sherman explained, is that “the hydrogen in Boulder is the same as the hydrogen in Paris and it’s the same as the hydrogen we might get twenty years from now. They don’t need batteries, they don’t wear out. They don’t change when you look at them—in their structure, anyway.”

Sherman compared atoms to bells. All bells will sound a note when struck, but that note will vary depending on the shape of the bell. When atoms are struck, they produce charged energy; the wavelengths of that energy will vary depending on the shape of the atom. The frequency at which an atom like cesium oscillates is, he said, “kind of arbitrary, and doesn’t have anything to do with the second or the hour or the minute. We’ve just decided we’re going to count time by counting those oscillations.”

When time was based on astronomy, Levine has written, frequency was a “derived quantity that was implicitly defined by astronomical observations.” That began to change as new technologies arrived, like radio waves, that depended more upon frequency (how many events happen in a given time period) than time itself (a way of marking when events happen). For instance, when you listen to KROQ-FM in Los Angeles, at 106.7 on the radio dial, the radio sine waves powering that music are being pumped out at 106,700,000 cycles per second; your radio tuner, set to that station, will resonate at the same frequency. With the rise of frequency, as well as quantum mechanics, time began to be constructed from the ground up, using the infinitesimal frequencies of atoms, rather than from above, using the movement of celestial objects. All this makes F1 staggeringly accurate: it will gain or shed only one second every 100,000,000 years. Since the days when time was defined astronomically, the accuracy of the second is estimated to have increased by a magnitude of eight.

Given our exquisitely realized second, one might assume that the time and frequency folks have moved on to other matters. But the second still suffers from two distinct problems. The first is one of continuity. Every time the second has been redefined, an effort has been made, typically through protracted calculation, to link it to previous versions of the second. Despite the dominance of atomic time, astronomical time scales still exist, and the two are kept in harmony. Levine thinks the most recent handoff presented some issues. “Cesium clocks immediately began running fast with respect to the astronomical timescale,” he said. As a result, the international time community has had to insert periodic leap seconds into the scale. Atomic time essentially stops for a full second to allow astronomical time to catch up. (Adding to the confusion, some clocks beat 23:59:59 twice, while others pause at 24:00:00.) Not everyone does it this way. “Places like Google, for example, they smear it out,” Donley told me. In other words, rather than stop time, they will subtly adjust the frequency of atomic clocks, “to catch up.”

The second, more substantial issue is that even though the current cesium fountain clocks at NIST have seen their accuracy increase by a factor of ten since their inception, there is a new generation of optical clocks that are, according to Donley, about one hundred times more accurate still. Optical clocks work much like atomic clocks, except the interrogating waves are comprised of an optical frequency—i.e., light—that is some one hundred thousand times higher than that of microwaves. The more ticks, the more information, the more precision.

There is a heady competitive rustle in the world of optical clocks, with each research group touting their preferred element—ytterbium! strontium! mercury!—as the One True Frequency. Each has its own virtues and weaknesses. Some are more costly, some are easier to operate. Strontium clocks are stable, which is good for precision measurements. Aluminum ion has one of the lowest systematic uncertainties, but takes a long time to measure. “It’s a really odd situation that we have so many clocks that are performing better than the standard can,” said David Hume, a NIST physicist who is working on an aluminum ion clock. “That’s not the normal thing when working on new measurement standards.”

And so, in the labs and conferences and Zoom calls of the metrology world, a conversation has begun once more about how to redefine the standard. Levine broke down the options. “Number one, everybody’s got their favorite clock and we declare one to be the winner, all the others to be ‘secondary representations,’ equal at the 99 percent level,” he said. “Number two, I take an average of all the winners and that’s the winner. Number three, I don’t define a standard of frequency anymore.” In other words, define frequency indirectly through some other constant, such as the mass of the electron—except, he says, we can’t measure any of these things accurately enough. “My personal vote,” he said, “is for the first choice.”

It isn’t likely that we’ll see a new standard second before the end of the decade. International consensus has yet to be forged, the optical clocks are still prototypes, and it is impossible to compare clocks in separate locations without degrading their performance. And for the needs of present industry and society, the current second is fine. But who knows what technologies will come along, and what levels of precision they’ll require?

Yet the more precisely time is measured, the less it starts to feel like time at all. Cutting-edge timekeepers, as Sherman told me, “are not really counting seconds,” at least not in the sense we would recognize. Rather, physicists studying higher-order problems are “comparing rates of different bells. They want to study the structure of an atom and they need to compare the ringing to our ringing, which is kept to some kind of a standard.” He suggested that subtle variations in these ticks might open doors onto “new physics,” perhaps helping us to better understand phenomena such as dark matter, that mysterious body that makes up some 85 percent of the total mass of the universe. “A clock accurate to a second over the age of the cosmos,” Patrick Gill, a physicist at the U.K.’s National Physical Laboratory, is quoted as saying in New Scientist, “would allow tests of whether physical laws and constants have varied over the universe’s history.”

For now, such clocks can at least confirm the old physics. “If you were to lift this clock up a centimeter of elevation,” Hume told me, “you would be able to discern a difference in the ticking rate.” The reason is Einstein’s theory of relativity: Time differs depending on where you are experiencing it. When standing upright, your head exists at a slightly different timescale than your feet. But with this accuracy comes a sobering reality. “There are not just two times,” notes the physicist Carlo Rovelli in The Order of Time. “Times are legion: a different one for every point in space.” What we think of the present, he writes, “does not extend throughout the universe.” Rather, “it is like a bubble around us.” The “well-defined now,” as he calls it, “is an illusion.”

Relativity raises the question of whether we can ever, ultimately and incontrovertibly, know what time it is, or whether it even makes sense to ask. On more than one occasion, in my conversations with physicists, we would get to some nettlesome issue about time, and they would pause and say something along the lines of, “Well, now here it gets philosophical.” But they would inevitably retreat to the safe harbor of metrology. “What we think about time,” as the NIST book From Sundials to Atomic Clocks puts it, “is less important to defining it than how we measure it.” I had come looking for certainty, but I kept finding its opposite. “In metrology,” Chao told me, “the name of the game is, at the end of the day, what’s your uncertainty?” Accuracy, in measuring the kilogram or the second, is perhaps less about knowing you are right than about having an achingly exact understanding of how often you are likely to be wrong.

Toward the end of my visit, in the small room where hydrogen masers pump out the precise aggregate time we now live by, Sherman explained the various issues a clock can face—temperature, magnetic fields, humidity. These were technological issues with technological fixes. But, as with seemingly every aspect of the measure of time, there was a caveat. Deriving time from atoms, Sherman said, is limited by the fact that when you measure an atom, you get one bit of information—whether it is in its ground state or not. “If you have a finite number of atoms,” he said, “you can only have a finite amount of knowledge about frequency.” Even if we could somehow marshal all the atoms in the universe to build two clocks, “they will immediately wander off by a very small amount.” All clocks drift.

“So what do you do about that?” Sherman asked, not waiting for my answer. In the end, measuring time by counting periodic processes will always have fundamental limitations. “This statistical aspect of quantum mechanics tosses one more thing in the rubbish bin, which is a conceptually perfect clock,” he said. “It can’t exist.”

 is the author, most recently, of Beginners: The Joy and Transformative Power of Lifelong Learning.

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