The Kilogram’s Long, Slow Climb to Harmony

The supreme arbiter of mass for humankind is a polished cylinder of platinum alloy just smaller than a golf ball. It was cast in London in 1879, unveiled a decade later in a ceremony in France, and now resides beneath three nested bell jars in a vault outside Paris, somewhere in a manor overlooking the Seine. (Its handlers prefer not to disclose its precise location.) Every scale on earth is calibrated to this artifact. Every dumbbell, every microdose of medicine, and every sack of cement weighs what it weighs, in effect, because the lump of metal weighs what it weighs. The lump is called the International Prototype Kilogram, or I.P.K. As its name suggests, it weighs, precisely and always, by definition, one kilogram.

By international consensus, the kilogram is the world’s universal base unit of mass, the ur-unit from which all others are derived. This rule applies even in the United States, where the government has been quietly using metric units since 1893. Insofar as the notion of the American avoirdupois pound has any official meaning, it is by relation to the kilogram, of which, by law, it is 0.45359237. This is not to suggest that the kilogram possesses some inherent authority. Like all units of measure, it is a tool entirely of man’s making. It exists in nature no more than a pound does, or a unicorn. It is an invented abstraction defined by an invented object. The object is the I.P.K.

Every forty years or so, the I.P.K. is taken out for comparison with the various copies that have been dispatched across the earth to “disseminate” the kilogram. These calibrations insure that the kilogram as the Argentines know it, for instance, matches the kilogram in use in Kenya, and that all kilograms everywhere match the unit defined by the I.P.K. This is a perfectly sensible system, but it depends entirely upon our trust in the I.P.K., and that trust is more tenuous than you might think. On Friday, however, at the general conference of the International Bureau of Weights and Measures, scientists intend to fix the kilogram for posterity.

For a sense of what they will, exactly, be fixing, consider the case of K20—so named because it is copy No. 20 of the I.P.K.—which serves as the primary American mass standard. In 2010, when it was sent to France for calibration at the International Bureau of Weights and Measures, it was discovered to be about thirty-five micrograms heavier than anticipated. This is no more than the mass of two or three thumbprints. But the discrepancy implied that all American mass measurements were slightly off, and metrologists are a fastidious bunch. “This is, for this crowd, very, very high-stakes stuff,” Jon Pratt, a metrologist at the National Institute of Standards and Technology (NIST), in Maryland, told me. NIST, which is responsible for K20, could find no explanation for the increase. Pratt’s boss called the International Bureau of Weights and Measures. “They were a little snarky with her,” Pratt said. “They said, ‘No, no, you’ve got a problem over there at NIST. You’ve got some contamination in your system.’ ” NIST was obliged to issue a correction to the U.S. mass scale, and to recalibrate all high-precision kilogram weights in the country. The process took years.

It turns out the thirty-five micrograms never existed. When K20 was calibrated, in France, it had been compared not directly with the I.P.K. but with the so-called working standards of the International Bureau of Weights and Measures. (The bureau typically goes by its French acronym, B.I.P.M.) In 2014, the B.I.P.M. checked the working standards against the I.P.K. “They do this,” Pratt told me, “and, sacré bleu—thirty-five micrograms! Whoops.” It was not K20 that had gained mass, it seemed, but the working standards that had lost it. The B.I.P.M. concluded that the standards had been worn down, ever so slightly, from being repeatedly placed in balance pans.

That physical objects change and fluctuate is a problem for a mass system that depends upon them, not least because this inconstancy extends to the I.P.K. itself. At the B.I.P.M., the I.P.K. is stored alongside six “witness” kilograms. Over the course of the twentieth century, the I.P.K. and the witnesses diverged steadily in mass. No one knows why. The I.P.K. could be losing mass, or the witnesses could be gaining it, or they could all be changing at once. It’s extremely unlikely, though, that the I.P.K. has the same mass as it did at the outset, and it’s impossible to know how much it has changed.

On its face, the solution seems easy enough. I asked Terry Quinn, a former director of the B.I.P.M., why one could not simply weigh the I.P.K.

“When you say ‘weigh it,’ ” Quinn said, “what do you mean?”

“As opposed to comparing its mass with the others,” I said. “You know, placing it on a scale that reads out to a high degree of—”

“Well, there’s no such thing,” he said. “Today, every balance in the world that gives a number when you put something on it, that number is ultimately linked to the I.P.K.”

“So if that balance tells you that the I.P.K. is not a kilogram, it’s the balance that’s wrong, and not the I.P.K.,” I said.

“Well,” Quinn replied, “it can never tell you that the I.P.K. is not a kilogram.”

In a mass system derived from a physical artifact, the unit accommodates the artifact, and not the other way around; which is to say the unit is constantly subject to change. It is a relief to mass metrologists, then, that the unit is about to be revised. On Friday, the kilogram will receive a new definition.

The kilogram, and the metric system to which it belongs, are products of the utopian rationalism of the French Revolution. Ancien régime France, like most nations of the time, contained a mess of competing systems of measurement, with standards varying by region, town, and trade. At the revolution, the countrys philosopher-scientists proposed a unified system, the units of which would be derived from an eternal feature of the natural world; they would be intelligible across all times, it was hoped, and by all peoples.

As the system’s basis, the Academy of Sciences settled on the quarter-meridian, the distance from the equator to the North Pole. The new, “natural” unit of length, to be called the mètre, would be defined as one-ten-millionth of this distance. The new unit of mass would be derived from the metre, and would be natural by extension; it would be equal to the mass of a cube of pure liquid water, one-tenth of a metre high, deep, and wide, and would come to be known as the kilogramme. Both units would be scaled in tens, and would together compose the système métrique décimal. “Never has anything grander and simpler and more coherent in all its parts come from the hands of men,” Antoine Lavoisier, the celebrated chemist, declared in 1793.

The meridian had to be measured precisely before the new units could be fixed, though, and it was another six years before the surveyors returned to Paris with a number. It has since been determined that their measurement was slightly short, but from it the metre was calculated, and then the kilogram, and a platinum prototype of each was presented to the French legislature on June 22, 1799. (The date was recorded as 4 messidor, year VII, the metric system being just one of the revolution’s many social innovations. Another, the guillotine, had claimed Lavoisier a few years earlier.) The president of the upper chamber hailed the Academy’s “immortal service” to the French Republic and the “kindness it has done for mankind.” The metric system, he said, ought to “breach the borders that separate the peoples of the world.”

And so it did, if slowly at first. The Netherlands was among the first; Spain, Brazil and Mexico followed not long after. The United States regarded the system with a sort of reluctant fascination from the start. In an 1821 report to Congress, John Quincy Adams, then Secretary of State, declared the metric system “the greatest invention of human ingenuity since that of printing,” though he also recommended against imposing its use. It was made legal, but not compulsory, in 1866. In 1875, the U.S. signed the Metre Convention, the treaty that created the B.I.P.M. Copies were made of the original French metre and kilogram, and, in 1889, at its first general conference, the B.I.P.M. approved these as the world’s official international prototypes: the I.P.M. and the I.P.K.

From the beginning, though, scientists were unhappy with the system’s reliance on physical objects. In principle, the metre and kilogram were immutable; in practice, they were defined by two fickle bits of metal. In 1960, the metre was redefined in terms of wavelengths of light, and the metal bar was retired. Two decades later, the metre was redefined again, this time as the distance travelled by light in a very specific fraction of a second. To make this possible, the speed of light, c, first had to be assigned a fixed value; otherwise, the length of the metre would not be constant, and a variable metre is exactly what the metal bar had been. (At the time, c was known to be constant, but there was no consensus as to its precise value.) In 1983, the B.I.P.M. resolved that c would be defined as 299,792,458 metres per second, exactly. The metre, by the definition still in place, was therefore the distance travelled by light in one 299,792,458th of a second. If this seems circular, it’s because it is. But if you intend to define a unit of measure in relation to a natural constant, it’s the only available method. It is sometimes called bootstrapping, and it is precisely how the kilogram will be redefined.

The kilogram will be bootstrapped from the Planck constant. There is nothing self-evident about this choice. The Planck, which is commonly known as h, connects energy to frequency in quantum mechanics. It is no more obviously related to the kilogram than is, say, the speed of light. But various scientific advances have made it possible to link h to mass, and to measure it relatively accurately. “It’s opportunistic,” Terry Quinn told me. “You have this long-term idea to link all our things to constants of nature. And you look around and see what turns up.” What turned up was h.

The difficulty, over the past few decades, has been to establish a sufficiently precise value for it, one that can be trusted as the basis for every mass measurement on earth. Researchers have developed two methods. The first involves the use of an exquisitely complex and sensitive apparatus known as a Kibble balance. In its broadest lines, the Kibble balance is a sort of quantum-mechanical equal-arm balance. A kilogram standard is placed on one side; on the other, balancing the kilogram, is a motor, and a value for the Planck constant can be derived from precise measurements of the electrical force this motor produces. In the U.S., NIST has built one of the world’s handful of functioning Kibble balances; it took three decades to produce a sufficiently accurate measurement of h.

The second method for measuring h involves counting atoms. An international coalition of metrological laboratories known as the Avogadro Project has produced silicon spheres of near-perfect purity and crystal structure, each weighing precisely one kilogram. The spheres are also thought to be the roundest objects on earth. “Maybe the roundest in the universe,” Joachim Ullrich, the physicist who runs the German metrological institute and oversees the Avogadro Project, told me. The largest imperfections are on the order of fifteen or sixteen nanometres; if the spheres were the size of the earth, the distance from the peak of the highest mountains to the bottom of the deepest seas would be about two metres. This extreme uniformity allows for a precise estimation of the number of atoms in each sphere, which allows for a precise calculation of h. The Avogadro Project has been at this for thirty years, as well.

That these very different experiments have produced nearly identical values for h suggests that the numbers are right. “That is absolutely astonishing when you think of the different physics involved,” Quinn said. “It shows that classical physics and quantum physics at that level agree.” On Friday, the B.I.P.M. will set the value of h at 6.62607015 x 10^-34 metre-squared-kilograms per second; it follows that the kilogram may be defined as the mass that results in this value, when h is expressed in the units above. A limpid definition in mathematical terms, if not exactly handy for the rest of us.

Still, a kilogram will stay a kilogram. Its size won’t change; the average human won’t notice a thing. But the Planck-constant kilogram will come with its advantages. The unit will now be entirely stable. It will, in principle, liberate science and industry from their reliance on centrally maintained mass standards. In an ideal future, end-users will be able to make precision mass measurements directly on the Kibble balances they keep in their pockets, without having first to fly to France to have their mass standards calibrated. (We’re not there just yet. NIST’s Kibble balance is about eight feet tall and relies on a magnet system that weighs a metric ton.) The new definition is expected to be of particular use to researchers working at extremely small mass-scales. Mostly, though, no one has the faintest idea what advances the redefinition could make possible. “This is the way it is,” Quinn said. “You make a step forward, and then clever people come up and think, Oh! Now I can do this and that!”

Utility is not all, though, even in metrology. “Our passion for this, our drive, is really on the aesthetic side,” Jon Pratt, of NIST, told me. “It’s just so much more beautiful to think about tying all measurement to these things that are—as far as we understand the universe—constant.” On his left forearm, Pratt has a tattoo of a nineteenth-century French metrology medallion. (He was a punk guitarist before he was a scientist.) Along the bottom edge is a value for h that his team at NIST calculated. The words along the top edge read, “À tous les temps, à tous les peuples”: for all times, for all peoples.

The redefined kilogram approaches this ideal as closely as man-as-measurer ever has. Concretely, though, it’s just a new way to express the mass of an old lump of metal, one that is not and really never was the ideal kilogram it was supposed to be. The I.P.K. doesn’t weigh what it did a hundred and thirty years ago, at least not exactly. And, given the mismeasurement of the meridian, even the original French kilogram didn’t weigh quite what it should have. The Planck-constant kilogram will inherit the flaws of its predecessors, just as it inherits their aspirations to harmony and truth. For the purposes of measurement, it will be excellent. As ever, harmony and truth remain just out of reach.