WHAT IS A KILOGRAM?

Science seeks new ways to ensure accuracy. The long-running effort to ditch the decaying 19th-century artifact that defines the kilogram nears its conclusion.

As he approached the security checkpoint at Wash ington Dulles International Airport one afternoon last April, Jon Pratt felt on edge. Stufed in his camera bag were four solid-metal cylinders, the sorts of objects guaranteed to draw the scrutiny of wary Homeland Security TSA staf. Each cylinder weighed exactly one kilogram. One of them—a gleaming platinum-iridium alloy about half the size of a can of tuna — was worth at least $40,000. (The price of platinum currently hovers around $1,000 per troy-ounce, a common unit for precious metals.) The other three consisted of finely machined stainless steel.

Pratt’s mission: Deliver them safely— and untouched—to a colleague in a Parisian suburb.

Pratt held documents from the National Institute of Standards and Technology meant to ease his way through security. The paperwork explained that he carried four official U.S. kilograms— the reference masses that serve as the basis for all weight measurements in the country—and speciied that the kilograms should not be touched or removed from their protective canisters.

A slender former punk rocker, Pratt runs nist’s Quantum Measurement Division in Gaithersburg, Md. “The TSA guy was giving me a bit of a hard time,” he says. “But then he read all the literature, and it became this cool thing that made his day.” After a few minutes, Pratt was waved through and boarded the light for the seven-hour trip to Paris, which presented another dilemma: What to do with his costly carry-on if he needed to get up? Should he keep the bag with him at all times, as some colleagues had advised? “I will admit that I left it parked beneath the seat in front of me while I went to the bathroom,” Pratt says. “So it was out of my sight briely, and someone may have come over and rubbed their hands all over the kilograms.”

Such handling would have spoiled many months of careful work devoted to measuring the kilograms to an accuracy of a few parts per billion. Pratt was taking the cylinders to the International Bureau of Weights and Measures (BIPM) in Sèvres, a city just across the Seine from Paris. A few months later metrologists there would compare them with identical metal cylinders from three other countries, along with a one-kilogram sphere of highly purified silicon manufactured at Germany’s national metrology laboratory. It was the latest step in a historic shift in the way the world measures mass.

Since 1889, the same year the Eiffel Tower opened, the kilogram has been defined by the mass of a platinum-iridium cylinder kept underneath three nested glass bell jars in a vault at the BIPM’s headquarters. The International Prototype Kilogram, aka IPK or Le Grand K, is the ur-kilogram from which all other national mass standards are derived. The kilogram is an anomaly; it is the last unit of measurement still tied to a physical object—but not for much longer. By the end of 2018 Le Grand K will be deposed, and the kilogram will have a new deinition based on Planck’s constant, a fixed quantity from quantum theory related to the amount of energy carried by a single particle of light, or photon.

Why force Le Grand K into retirement? For years metrologists have wanted the accuracy and reliability of an international mass standard linked to a fundamental constant of the universe rather than a Victorian-era lump of cosseted metal. But there is a more pressing reason for the change: Le Grand K appears to be losing mass.

Once every 30 years or so Le Grand K is removed from its vault for cleaning and for comparison with six official copies, or temoins (“witnesses”), which are kept in the same vault. When the irst two temoins were compared with Le Grand K in 1889, both matched the original. But measurements made shortly after the World War II and again in 1992 found that the copies outweighed Le Grand K slightly. It seems implausible that the copies would all somehow gain mass while Le Grand K remained unchanged. There is, of course, a more likely explanation. “We could assume,” says BIPM director Michael Stock, “that the International Prototype Kilogram is losing some mass.” That uncertainty is one of the reasons the General Conference on Weights and Measures—the governing body of the bureau—decided in 2011 to establish a new mass standard.

No one knows why Le Grand K might be shedding weight. It is far too valuable to undergo tests that might provide answers. The mystery presents real problems. As technology advances in the decades ahead, precision measurements of mass on the molecular scale and below will become routine in a wide range of industries. “We will want to have ways to measure microgram masses with at least three-digit resolution,” Pratt says. “And with an artifact kilogram, things get really uncertain at small scales.”

Le Grand K’s shortcomings are not limited to measurements of mass. Units of force and energy are ultimately derived from it as well. “We are now at the point where we would see values of fundamental constants change because the IPK changes,” Stock says. “And that makes no sense.”

THE NEW STANDARD

the kilogram is the latest of the metric system’s seven basic units to be revamped, but it will not be the last. Besides the kilogram, the International System of Units, or SI, comprises the meter, the ampere (for electric current), the second, the candela (a measure of the intrinsic brightness of a light source), the mole (which relates the weight of a substance to the number of atoms it contains), and the kelvin (for temperature).

Two of the SI units were redefined decades ago. In 1983 the meter, formerly gauged by the distance between two lines etched in a solid platinum-iridium bar stored in the same vault as Le Grand K, became instead the distance traveled by light in 1/299,792,458th of a second. And with the advent of improved atomic clocks in the 1960s, the second—which had been defined as a fraction of a day—was reset in terms of a speciic frequency of microwave radiation emitted from a cesium atom. The mole, kelvin and ampere are all slated for an overhaul in 2018 as well.

The current (so to speak) state of the ampere is especially odd. Its oicial deinition, part of which involves two infinitely long, one-dimensional, massless wires, is so abstract that it cannot be replicated in a lab. That will change in 2018 when the ampere is redefined in terms of the charge of an electron, an advance made possible by the development of nanotechnology devices capable of counting individual charged particles moving through a circuit. “If we look to the next redefinitions, they might include a quantum mechanically based candela for light and maybe an optical definition of the second instead of a microwave definition,” says Alan Steele, Canada’s chief metrologist. “But those are at least 15 years away. Maybe longer.”

The redefinition of the kilogram is the centerpiece of an effort to create a truly universal system of measurement that is not bound to parochial, earthly conventions. In principle, the new units would make sense to intelligent beings anywhere, from here to Andromeda. For metrologists, these are heady times. “This is a once-in-a-lifetime thing,” Steele says. “The last time we attempted anything this fundamental was when the meter was redefined. This is the time to be a chief metrologist, I’ll tell you that. It’s not like world peace or anything, but it’s pretty cool.”

THE VAULT

Le Grand K was not the irst oicial kilogram. It has a predecessor, made during the French Revolution, when the entire metric system was born. Before the revolution, local custom determined nearly all of France’s weights and lengths. Standards varied from one town to the next, burdening the country with more than 700 diferent units of measurement. A toise, for example, was the equivalent of an English fathom: the distance between a man’s outstretched arms. But a Parisian toise (which equaled 72 pouces ) might not have matched one used in Marseilles. Savants, as the French then called their scientists, sought to end the chaos by creating a new system “for all people, for all time,” a motto memorialized on a contemporary plaque.

“Their idea in 1791 was that the standards should be based on natural and invariable phenomena,” says Richard Davis, a retired director of the BIPM’s mass division, which is responsible for maintaining Le Grand K. “We’re still doing that,” he says. The diference is that now metrologists are turning to natural constants that really are invariant.

We are sitting in Stock’s oice in the Pavillon de Breteuil, an elegant 17th-century building on a verdant hilltop overlooking the Seine in Parc de Saint-Cloud, once a royal hunting reserve for French kings. Marie Antoinette’s rose garden is still carefully tended here. It has been the headquarters of the international bureau since the Meter Convention of 1875, a treaty signed by 17 nations.

“Did you notice the island on the left as you walked across the bridge to Sèvres this morning?” Davis asks. The island, he says, once housed a Renault factory that built tanks for the German army in World War II. American bombers repeatedly targeted it. After one bombing run rattled the Pavillon de Breteuil, Le Grand K was placed in a special shockproof container.

Although the temoins had been evacuated to an underground safe in the Bank of France for most of the war, the Meter Convention specified that Le Grand K must always remain at the bureau.

When Le Grand K was removed from its vault after the war, in 1946, for cleaning and comparison with the six copies, it was found to be 30 micrograms lighter than the temoins. By the time of the next cleaning, 45 years later, the diference had increased to 50 micrograms—the weight of a ly’s wing.

“Fifty micrograms—over a century,” Stock says, as we look at a graph of the changes on his oice computer. “You can see it’s very small.” For now, he says, the discrepancy does not present any practical dificulties. “But if we continued like this, one day this would lead to problems.”

In the realm of nanotechnology, 50 micrograms is a huge number. Moreover, the uncertainty in the kilogram’s mass would ripple through a long chain of fundamental units: the metric unit of force—the newton—is defined in terms of the kilogram, and the newton, in turn, defines the joule—a unit of energy—and the joule defines the watt, and so on. Ultimately a small question mark would taint nearly every measurement of the physical world.

Cleaning and comparing Le Grand K with the test masses is not a routine task—especially because it has been done only four times since 1889. First Le Grand K must be removed from its caveau, or vault, which requires the presence of three people to open three locks that are arranged vertically. Inside the vault sits a large safe with a combination lock that holds the Le Grand K, which rests under the three nested bell jars. The safe also shelters the six copies. Only three people in the world hold keys to the vault: the BIPM director, the director of the National Archives in Paris and the president of the International Committee for Weights and Measures (CIPM), which supervises the bureau’s work. Because each key is different, all three oficials must be present to unlock the vault.

“I’m only the second person outside of Europe in the history of the Meter Convention of 1875 that’s been elected president of the CIPM,” says Barry Inglis, an Australian electrical engineer. “I asked them what happens if I’m traveling home over the Indian Ocean and the plane goes down: ‘How are you guys going to manage?’ But I’m sure there’s a locksmith that could pick the old lock without too much trouble.”

Few of the bureau’s staff have ever glimpsed Le Grand K, and there are rumors that its oicial photographs depict a stunt double. “I’ve seen it once,” says Susanne Picard, who has worked at the BIPM since 1987. The three key holders open the vault once a year to look at—but not touch— Le Grand K to make sure it is, well, still there.

After entering the inner sanctum of Le Grand K, a technician picks up the shiny cylinder with chamois-padded tongs and carries it to a cleaning station, where it is rubbed with a chamois cloth soaked with alcohol and ether, followed by a rinse from a jet of doubly distilled water. A inal puf of nitrogen gas removes any remaining water droplets. The entire process takes about an hour. The bureau has experimented with different cleaning techniques on test masses—using ultraviolet radiation, for example—but those methods actually made the alloy too clean. “They seem to remove more dirt than our technique,” Stock says. “But afterward the mass is unstable because it is so clean that the surface becomes highly reactive.” And that would only make Le Grand K less reliable as a standard, so the bureau remains committed to its chamois-rub-and-water-rinse method.

After their baths, Le Grand K and the temoins are taken to a clean room and put on a device called a mass comparator, a $500,000 instrument that can measure diferences in mass as small as one microgram. The mass comparator and 10 so-called working standard kilograms are the workhorses of the BIPM’s mass division; they are used for most day-to-day calibrations, with Le Grand K and the temoins trotted out only once every few decades for verifying national prototype kilograms from diferent countries.

As the conversation with Davis and Stock winds down, I ask them if I can see the outside of the vault where Le Grand K resides; I know there is no chance of seeing the regal master cylinder itself. They burst into laughter, shaking their heads: “No, no, no, no!” “It’s not the irst time we’ve been asked,” Davis says. “It is here on the grounds, right?” I ask. “Yes,” Davis answers, “that much is public knowledge.”

A TOUGH MEASUREMENT

soon Le Grand K will be a historical curiosity, and the new international definition of mass will be based on Planck’s constant. Planck’s constant includes units of both energy and time and can be expressed in terms of mass by massaging the equation E = mc². Like G, the gravitational constant, Planck’s constant arises from theory, but its numerical value can be determined only by experiment. And with better instruments, our measurements of natural constants are steadily improving.

To make the transition to the new quantum standard, the BIPM devised a two-part strategy. First, the national metrology labs of five different countries will ix a numerical value for Planck’s constant, weigh their national kilograms in terms of that value and then see how well their kilogram measurements match. This is the test that the bureau ran last summer.

Assuming the results, expected early this year, are satisfactory, the study participants will reverse the process and use their national kilograms at their home facilities to ine-tune their measurement of Planck’s constant. The exacting new value for Planck’s constant will then be used to permanently redeine the kilogram.

Most of this work will involve the use of an exceedingly complex device called a Kibble balance. Until last year, Kibble balances were known as watt balances. Metrologists decided to rename them after the death of their inventor, British physicist Bryan Kibble, in 2016. Kibble-balance experiments are so diicult that in 2012 the journal Nature listed them among the ive toughest undertakings in physics, right up there with detecting the Higgs boson or gravitational waves.

One day last May, Stephan Schlamminger of nist drove me to the white two-story building on the edge of the institute’s woodsy 235-hectare campus that houses the older of its two Kibble balances, now essentially mothballed since the completion of a newer model in 2014. “It’s like the Little House on the Prairie, ” Schlamminger jokes as we pull up in front of the isolated structure. It is here that most of nist’s measurements of Planck’s constant occurred, and the new model will work in much the same way.

Any resemblance to a farmhouse vanishes when we step inside. The interior looks like a setting for a steampunk novel, with walls sheathed in copper all the way to the second-floor ceiling. “See all the brass hardware?” Schlamminger says. “No iron.” The copper and brass shield the instrument from external magnetic fields. But the magnetic fields generated inside the building are powerful enough to erase credit cards. In the middle of a room on the irst loor stands a tall support column with a superconducting magnet at its base. When operating, the magnet is cooled with liquid helium.

The actual balance mechanism is on the second floor. It consists of a half-meter-wide aluminum wheel mounted vertically with balance pans suspended by wires from either side. During measurements, one balance pan holds a kilogram mass; a coil of wire is suspended directly below that same pan by three four-meter-long rods. The pan on the other side of the balance holds a counterweight and an electric motor. Two distinct operating modes of the balance are needed to acquire all the values used in the equations that link mass to Planck’s constant.

In “weighing mode,” the downward gravitational force on the test mass is exactly ofset by a magnetic field generated by running a current through the coil suspended below the pan. In “velocity mode,” the test mass is removed from the pan, and the coil is lifted by the motor in the opposite pan at a steady velocity through a magnetic field created by the balance’s superconducting magnets, which induces a voltage in the moving coil.

The current measured in the weighing mode and the induced voltage from the velocity mode are then plugged into equations from quantum theory that relate current, voltage and electrical resistance to Planck’s constant. In short, starting with a known mass of one kilogram, the Kibble balance can determine Planck’s constant. Then, with an accurate value for Planck’s constant in hand, the balance can be used to measure mass without the need for any kind of physical artifact.

For accurate results, Schlamminger and his colleagues need to account for local fluctuations in air pressure and gravity. The precession of Earth’s axis must be included, too, along with tides. “If you don’t correct for tides,” Schlamminger says, “it’s about a 100-parts-per-billion error.” Despite its complexity, he observes, the device reminds him of something from another era. When his team was measuring Planck’s constant, valves had to be opened and closed in careful order; the pressure inside tanks full of liquid helium had to be checked constantly. “You felt as if you were driving a steam engine,” Schlamminger adds, “yet you were doing experiments measuring quantum-mechanical quantities!”

AU REVOIR, LE GRAND K

What happens next depends on the results from last year’s test. Kilogram measurements by three of the ive participating national metrology labs must match within 50 micrograms—the current fly-wing uncertainty in the mass of Le Grand K. After the pilot study results are published, work on the redefinition will begin in earnest.

If all goes well, the kilogram will then be defined in terms of Planck’s constant. The BIPM has set stringent standards for the redefinition: not only must all the measurements of Planck’s constant agree to within 50 parts per billion, but at least one must have an uncertainty below 20 parts per billion—a level the Canadians have already surpassed. For the redefinition to take efect in 2018, all the new measurements of Planck’s constant must be accepted for publication by July 1, 2017.

And what of Le Grand K? It will remain in its vault. Given the complexity of Kibble balances, though, we probably have not seen the last of kilogram artifacts. Rather than regularly making arduous Kibble-balance measurements, the world’s metrology labs will, in the decades ahead, use a new generation of prototypes for day-to-day work. The new prototypes are already taking shape at the bureau. But they will be calibrated by Kibble balances, not Le Grand K. So is this the end of the story? Do we now have a kilogram for all people, for all time? Stock is reserving judgment.

“One of my predecessors, a Nobel laureate named Charles Edouard Guillaume, thought the present kilogram would work for 10,000 years,” he says. “This was of course overly optimistic. I’m not sure this will be the last redefinition, but it should be good for some time. Maybe not for the net 10,000 years".

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CHANGING MEASURES 

The International System of Units (SI), otherwise known as the metric system, rests on a foundation of seven base units. (Another 22 units are built from those seven.)

In 2018 the International Committee for Weights and Measures is expected to redefine the majority of the base units in the biggest overhaul of the metric system since 1960.

The move would tie the seven base units to invariant natural constants. The meter, the second and the candela will remain essentially the same, but the other four will be fundamentally reconceived.

Currently Defined in Terms of Physical Constants

1. Unit: Meter
Abbreviation: m
Measures: Length

Current deinition (established in 1983):

The distance light travels in a vacuum in 1/299,792,458 of a second.

Historical note:

When the French Academy of Sciences proposed the metric system in 1791, it defined the meter as one ten-millionth of one fourth of Earth’s circumference, which in turn was defined as a meridian that runs from the North Pole to the equator through—where else—Paris.

2. Unit: Second
Abbreviation: s
Measures: Time

Current definition (established in 1967):

The second is “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.”

Historical note:

The original definition is the familiar one: a second was 1/86,400 of the “mean solar day,” or the time it takes Earth to rotate relative to the sun. The committee gave the second its current, quantum-mechanical definition in 1967.

3. Unit: Candela
Abbreviation: cd
Measures: Luminosity

Current definition (established in 1979):

A candela is the “luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian,” which is the SI unit for a solid angle.

Historical note:

In the early 20th century the U.S., France and the U.K. defined the candela by referring to the luminosity of a carbon-filament lamp.

In 1933 metrologists made the deffinition more precise by basing it on blackbody radiation. Such a definition was adopted in 1948 and later replaced with the current one.

Still To Be Redefined

1. Unit: Kilogram
Abbreviation: kg
Measures: Mass

Current deinition (established in 1889):

For now the kilogram is still defined by reference to Le Grand K, the platinum-iridium cylinder hidden in a vault in Paris.

Proposed redefinition:

If eforts remain on schedule, in 2018 the kilogram will be pegged to Planck’s constant, a fixed quantity from quantum theory that specifies the amount of energy carried by a single particle of light, or photon.

2. Unit: Ampere
Abbreviation: A
Measures: Electric current

Current definition (established in 1946):

The ampere’s current deinition, which involves, among other things, “two straight parallel conductors of infinite length, of negligible circular cross section ... placed 1 meter apart in vacuum,” (is impossible to replicate exactly in the lab).

Proposed redefinition:

The ampere would be simplified by fixing the numerical value for the charge carried by one proton (the fundamental constant known as the elementary charge).

3. Unit: Kelvin
Abbreviation: K
Measures: Temperature

Current definition (established in 1967):

Today one kelvin is equivalent to “1/273.16 of the thermodynamic temperature of the triple point of water” — the combination of temperature and pressure at which ice, water vapor and liquid water can coexist.

Proposed redefinition:

Basing the kelvin on a fixed value for the Boltzmann constant, which relates the average kinetic energy of a gas’s molecules with its absolute temperature, would improve the accuracy of extremely low-and-high-temperature measurements.

4. Unit: Mole
Abbreviation: mol
Measures: Amount of substance

Current definition (established in 1971):

“The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12.”

Proposed redefinition:

The mole’s link to the kilogram would be severed, and the unit would be defined by fixing the numerical value for the Avogadro constant, which refers to the number of molecules, atoms or any other small, discrete quantities of matter in one mole of substance.

By Tim Folger in "Scientific American", USA, vol.316, n. 2, February 2017, excerpts pp. 46-53. Adapted and illustrated to be posted by Leopoldo Costa.