Scientists Are About to Redefine the Kilogram and Shake Up Our System of Measures

After more than 100 years of defining the kilogram according to a metal artifact, humanity is preparing to change the unit based on a constant of nature

The NIST-4 Kibble balance, an electromagnetic weighing machine that is used to measure Planck's constant, and in turn, redefine the kilogram. (Jennifer Lauren Lee / NIST)
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Locked in a vault that requires three keys to open, in the town of Sèvres just to the southwest of Paris, there is a kilogram. Actually, it’s The Kilogram, the International Prototype of the Kilogram (IPK), the kilogram against which all other kilograms must take their measure, Le Grand K. This cylinder of platinum-iridium alloy sits under three protective glass bells, in a temperature- and humidity-controlled environment, in a safe along with six official copies, in the underground vault of Sèvres.

“If you were to drop it, it would still be a kilogram, but the mass of the whole world would change,” says Stephan Schlamminger, a physicist with the National Institute of Standards and Technology (NIST) in Gaithersburg, Maryland.

The IPK only emerges from its vault every 40 years or so, when the golf-ball-sized ingot, exactly a kilogram by definition since 1889, is used to calibrate copies that are shared with countries around the world. But there is a problem. In the vault with the IPK are six témoins, or “witnesses”—the official copies. Over the years, as evidenced by the rare occasions when Le Grand K and its witnesses have been measured, the mass of the IPK has “drifted.”

IPK
The International Prototype of the Kilogram (IPK). (Photograph courtesy of the BIPM)

Most of the witnesses now weigh slightly more—a matter of micrograms, or millionths of a gram—than the IPK (although many of the copies were more massive to begin with). You could say that the IPK is losing mass, only you cannot say that, because the IPK is immutably and unwaveringly one kilogram. Besides, physicists don’t even know if the IPK is losing mass or gaining mass in the long run, just that it is slowly drifting due to imperceptible amounts of material aggregated from the air, or rubbed off during a weighing, or smudged on the silvery surface of the IPK during one of its meticulous baths.

As you can imagine, this minute drifting causes scientists a lot of headaches—not to mention industries that rely on small and precise mass measurements, such as pharmaceutical companies.

“At the moment, the kilogram is defined in terms of the mass of a particular thing,” says Ian Robinson of the National Physical Laboratory (NPL) in South London. “And if that thing is destroyed or changed or whatever, it’s awkward.”

Kilogram Masses
One of NIST's platinum-iridium copies of the IPK, the K92, with stainless-steel kilogram masses in the background. (Jennifer Lauren Lee / NIST)

Fortunately, the metrologists of the world have a solution: redefine the kilogram in terms of a natural, universal constant. Most of the units in the International System of Units (SI) are already defined according to universal constants, such as the meter, which is officially the length traveled at the speed of light in a vacuum in 1/299,792,458th of a second. Of course, this definition relies on the second, which is defined as the duration of 9,192,631,770 periods of a specific frequency of electromagnetic radiation (microwaves in this case) that causes the outer electron of a cesium-133 atom to transition (switch from a quantum measurement of “spin up” to “spin down,” or vice versa).

But the kilogram, the last remaining unit defined by an artifact, has stubbornly resisted redefining—until now. On November 16, at the 26th meeting of the General Conference on Weights and Measures, delegates from 60 member states will gather in Sèvres to vote to redefine the kilogram according to Planck’s constant—a number that relates the frequency of a wave of light to the energy of a photon in that wave. And according to Richard Davis, a physicist with the International Bureau of Weights and Measures (BIPM), “they’re expecting a substantial majority.”

Max Planck and Albert Einstein

In 1879, the IPK was cast by the precious metals company Johnson Matthey in London, a 20-year-old Max Planck defended his thesis On the second law of thermodynamics, and Albert Einstein was born. Though the two scientists did not know it during the courses of their lives, their collective work on the fundamental physics of gravity and quantum mechanics would come to lay the foundation for a 21st century definition of the kilogram.

So what is Planck’s constant? “At a fundamental level, it’s hard to say,” Davis says.

Planck’s constant is a very small number: 6.62607015 x 10-34, to be exact, as will be officially defined at the November 16 meeting. In 1900, Max Planck calculated the number to fit models of light coming from stars, matching the energy and temperature of the stars to their spectrums of electromagnetic radiation (collectively known as blackbody radiation). At the time, experimental data suggested that energy is not free flowing at any value, but rather contained in bundles or quanta—from which quantum mechanics takes its name—and Planck needed to calculate a value for these bundles to fit his blackbody radiation models.

Einstein and Planck
Five Nobel Laureates, from left to right: Walther Nerst, Albert Einstein, Max Planck, Robert Millikan and Max von Laue, gathered for a dinner hosted by von Laue in 1931. (Public Domain)

Five years later, Albert Einstein published his theory of special relativity, which would come to be expressed as the famous equation E = mc2 (energy equals mass times the speed of light squared, an epiphany that energy is fundamentally bound up in all the matter of the universe). He also calculated the theoretical value of a single, fundamental quantum of electromagnetic energy—now known as a photon—which resulted in the Planck-Einstein relation, E = hv. The equation states that the energy of a photon (E) equals Planck’s constant (h) times the frequency of electromagnetic radiation (v, which is the Greek symbol nu rather than a “v”).

“You know you have the energy of a photon, which is hv, but you also know you have the energy of a mass, which is mc2. [So], E = hv = mc2. Right there you can see how you can get a mass from h [Planck’s constant], v [the wave frequency] and c [the speed of light],” says David Newell, a physicist at NIST.

But this is not the only place that Planck’s constant shows up. The number is needed to describe the photoelectric effect which solar cells are based on. It is also used in Niels Bohr’s model of the atom, and it even appears in the Heisenberg uncertainty principle.

“It’s like saying, well, what about Pi?” Davis says. “What’s Pi? Well, it’s the circumference of the circle divided by the diameter of the circle. But then Pi shows up everywhere in mathematics. It’s all over the place.”

The key connecting Planck’s constant to the kilogram is its unit, the joule-second, or J·s. The constant gets this unique unit because energy is measured in joules and frequency is measured in Hertz (Hz), or cycles per second. A joule is equal to a kilogram multiplied by meters squared divided by seconds squared (kg·m2/s2), so with a few clever measurements and calculations, one may arrive at the kilogram.

But before you can convince the world to change the definition of the standard unit of mass, your measurements better be the best ever taken in the history of science. And as Newell puts it, “measuring something absolute is damn hard.”

Measure for Measure

We often take for granted that a second is a second, or a meter a meter. But for the majority of human history, such measures of time, length and mass were rather arbitrary, defined according to the whims of local customs or rulers. One of the first decrees that national measurements must be standardized came from the Magna Carta in 1215, which states:

“Let there be one measure for wine throughout our kingdom, and one measure for ale, and one measure for corn, namely “the London quarter”; and one width for cloths whether dyed, russet or halberget, namely two ells within the selvedges. Let it be the same with weights as with measures.”

But following the Enlightenment, as scientists began to untangle the physical constraints of the universe, it became apparent that varying standards of measure presented a dire impediment to the advancement of the species. Scientists spread across the globe in the 18th and 19th centuries, measuring everything from the precise shape of the Earth to the distance to the sun—and every time a German lachter (about two meters, depending on region) had to be compared to an English yard (which also varied for most of its existence), uncertainties and miscommunications abounded.

A copy of the first meter standard, sealed in the foundation of a building at 36 rue de Vaugirard, Paris. (Ken Eckert / Wikimedia Commons CC 4.0)

The French finally had a revolution—not just of politics, but also of measures. As the 18th century drew to a close, the Kingdom of France is estimated to have had some quarter million varying units, making it impossible to keep track of them all. Urged by the National Constituent Assembly, which formed during the outset of the French Revolution, the French Academy of Sciences set out to establish a new unit of length that would become the official measure for the country: the meter, defined as one ten-millionth of the distance from the North Pole to the Equator.

A surveying expedition led by French mathematicians and astronomers Jean Baptiste Joseph Delambre and Pierre Méchain triangulated the distance of a portion of that length, stretching from Dunkirk to Barcelona, in order to calculate the new meter. The survey measurements were completed in 1798, and the new standard was soon adopted in France.

The meter came to represent a fundamental unit of measure, defining the liter (1,000 cubic centimeters) and even the kilogram (the mass of one liter of water). By 1875, the world was ready to adopt the metric system, and the Metre Convention of that year saw representatives of 17 nations sign the Treaty of the Metre, creating the International Bureau of Weights and Measures and providing for new mass and length standards to be cast in platinum-iridium alloy, defining the meter and the kilogram for the world.

But as a wave of 20th century scientists such as Planck and Einstein began to poke and prod at the Newtonian structure of physics, discovering new laws among the vastness of the cosmos and the fundamentals of the atom, the system of measure needed to be updated accordingly. By 1960, the International System of Units (SI) was published, and countries around the world established metrology institutions to continually refine the official definitions of our seven base units of measure: the meter (length), kilogram (mass), second (time), ampere (electric current), kelvin (temperature), mole (amount of substance) and candela (luminosity).

Silicon Sphere
An Avogadro sphere of pure silicon-28 atoms. By measuring the volume of the sphere and the volume of a single silicon-28 atom, meteorologists can measure the mass of a single atom in the sphere, providing a method to calculate the number of atoms in a mole, called Avogadro's number, which can be used to calculate Planck's constant. (Photograph courtesy of the BIPM)

From these base units, all other units may be calculated. Velocity is measured in meters per second which can be converted to mph and other speeds; the volt is measured in terms of amps of current and resistance in ohms; and the definition of the yard is now proportional to 0.9144 of a meter.

Today, as during the 18th century, the matter of refining such measurements is at the forefront of scientific capability. Though the redefinition of the kilogram is unlikely to change your daily life, the ultimate effects of defining a more accurate system of measure are often widespread and profound.

Take, for example, the second. Since 1967, the definition of a second has been based on the frequency of a microwave laser, and without this precision, GPS technology would be impossible. Each GPS satellite carries an atomic clock, critical to correct for the fact that time passes infinitesimally but measurably slower on our satellites as they orbit the Earth at high speeds—an effect predicted by Einstein’s theory of relativity. Without the new definition, we could not correct for these tiny fractions of a second, and as they grew, GPS measurements would drift farther and farther off course, making everything from Google Maps to GPS-guided munitions nothing but science fiction.

The relationship between the second and GPS reveals the fundamental entwining of metrology and science: advancing research requires and allows for new standards of measure, and those new standards of measure in turn allow for more advanced research. Where this cycle will ultimately take our species is unknown, but following the death of the meter bar and the abandonment of the second as defined by a fraction of a day, one thing is clear: the IPK is next up to the guillotine.

The Kibble Balance

NIST-4
The NIST-4 Kibble balance, operated by the National Institute of Standards and Technology. Unlike earlier Kibble balances, the NIST-4 uses a balance wheel that operates like a pulley rather than a beam. The balance measured Planck's constant to within an uncertainty of 13 parts per billion. (Jennifer Lauren Lee / NIST)

Physicists have known for decades that the kilogram could be defined in terms of Planck’s constant, but it was not until recently that metrology advanced enough to measure the number with such precision that the world would accept a new definition. By 2005, a group of scientists from NIST, NPL and the BIPM, whom Newell calls “the gang of five,” started to push the issue. Their paper on the matter is titled, Redefinition of the kilogram: a decision whose time has come.

“I consider it a milestone paper,” Newell says. “It was very provocative—it annoyed people.”

One of the key technologies to measure the Planck constant identified in the paper is a watt balance, first conceptualized by Bryan Kibble at NPL in 1975. (After his death in 2016, the watt balance was renamed the Kibble balance in Bryan Kibble’s honor.)

The Kibble balance is, at a fundamental level, the evolution of a technology that dates back more than 4,000 years: balance scales. But instead of weighing an object against another to compare the two, a Kibble balance allows physicists to weigh a mass against the amount of electromagnetic force required to hold it up.

“The balance works by passing a current through a coil in a strong magnetic field, and that generates a force, and you can use that force to balance the weight of a mass,” says Ian Robinson of NPL, who worked with Bryan Kibble on the first watt balances from 1976 onward.

The balance operates in two modes. The first, weighing or force mode, balances a mass against an equal electromagnetic force. The second mode, velocity or calibration mode, uses a motor to move the coil between the magnets while the mass is not on the balance, generating an electric voltage which gives you the strength of the magnetic field expressed as a measure of electrical force. As a result, the force of the mass in weighing mode is equal to the electrical force generated in velocity mode.

The electrical force can then be calculated as a function of Planck’s constant thanks to the work of two Nobel-winning physicists, Brian Josephson and Klaus von Klitzing. In 1962, Josephson described a quantum electrical effect related to voltage, and von Klitzing revealed a quantum effect of resistance in 1980. The two discoveries make it possible to calculate the electrical force of the Kibble balance in terms of quantum measurements (using Planck’s constant), which, in turn, equates to the mass of a kilogram.

In addition to the Kibble balance, the “gang of five” paper addresses another way to calculate Planck’s constant—by crafting spheres of virtually pure silicon-28 atoms, the most perfectly round objects ever created by humanity. The volume and mass of a single atom in the sphere can be measured, which allows metrologists and chemists to refine the Avogadro constant (the number of entities is one mole), and from Avogadro’s number, one can calculate Planck’s via already-known equations.

“You need two ways of doing this so that you get the confidence that there isn’t a hidden problem in a single method,” Robinson says.

White Board
A white board at NIST explains how a Kibble balance can equate a mechanical measure (the weight of a kilogram mass) to an electrical measure (the force of electric current required to hold up the kilogram, expressed as a function of Planck's constant). (Jay Bennett)

In order to redefine the kilogram, a change that will be implimented on May 20, 2019, the General Conference on Weights and Measures required at least three experiments to calculate the Planck constant to an uncertainty of no more than 50 parts per billion, one of which must calculate the value to within an uncertainty of 20 parts per billion. The international silicon sphere effort has become precise enough to achieve an uncertainty of only 10 parts per billion, and four Kibble balance measurements also produced values within the required uncertainty.

And as a result of all these measures, much more than the kilogram is about to change.

The New International System of Units

More than redefining the kilogram, the 26th meeting of the General Conference on Weights and Measures (CGPM) is setting a fixed value for the Planck constant, and as a result, enacting the largest transformation of the International System of Units since its inception in 1960. Previously, Planck’s constant was measured incessantly, averaged with other measurements across the world, and a list of new values was delivered to research institutions every few years.

“No one will measure the Planck constant once this [vote] has passed, because its value will have been defined,” Davis says.

In addition to the Planck constant, the Avogadro constant will be set at a fixed value, as will the elementary charge (e, the charge of one proton), and the triple point of water (the temperature at which water can exist as a solid, liquid or gas, to be defined as 273.16 degrees Kelvin, or 0.01 degrees C).

By setting the Planck constant as an absolute value, scientists are turning away from conventional mechanical measurements and adopting a suite of quantum electrical measurements to define our fundamental units. Once the constant is defined, it can be used to calculate a range of masses from the atomic level to the cosmic, leaving behind the need to scale the IPK down into smaller measurable parts, or up to enormous masses.

“If you have an artifact, you only anchor your scale at one point,” Schlamminger says. “And a fundamental constant doesn’t care about the scale.”

Mark II Kibble Balance
Ian Robinson with the Mark II Kibble balance. Built by the National Physical Laboratory (NPL) in the U.K., Mark II was later acquired by the National Research Council (NRC) of Canada, where it was used to measure a value of Planck's constant to within an uncertainty of 9 parts per billion. (Image courtesy of NPL)

The new value for Planck’s constant also changes the definitions of our electrical units, such as the 1948 definition of the ampere. Physicists have long used the Josephson and von Klitzing effects to calculate electrical values with precision, but these measurements cannot be part of the SI until one of their variables—the Planck constant—is a fixed value.

“It’s always grated on me that if I wanted to get my SI volt or my SI ohm, I had to go through the kilogram. I had to go through a mechanical unit to get my electrical units,” Newell says. “That seemed very 19th century, and it was.”

Now, the electrical units will be used to get the kilogram.

“People talk about, oh it’s the redefinition of the kilogram, but I think this actually misses an important point,” Schlamminger says. “We’re going to get these electrical units back into the SI.”

For All People, For All Time

There are more than a half-dozen Kibble balances around the world, and many countries from South America to Asia are building their own—because once scientists have one, they have the tool to access the kilogram and many other fundamental units and measures defined by nature. No longer will the kilogram be confined to a vault, where few have the privilege of ever accessing it, and everyone is so afraid to touch it that it is not used but once per half century.

“It means now, what we can do is spread the mode of determining mass around the world,” Robinson says.

For the scientists whose work this change affects, the new International System of Units is nothing short of a historic occasion.

“I’m still kind of worrying that this is all a dream, and tomorrow I wake up, and it’s not true,” Schlamminger says. “I think this is finishing the arc that people started thinking about before the French Revolution, and the idea was to have measurements for all times for all people.”

Lego Balance
Stephan Schlamminger explaining the Kibble balance with a working Lego model at the National Institute of Standards and Technology (NIST) in Gaithersburg, Maryland. (Jay Bennett)

“This has been one of the highlights of my life,” says Klaus von Klitzing of the Max Planck Institute, whose own constant will be cemented as a fixed value as a result of the new SI. “This is wonderful. We have the unification of these quantum units … with the new SI units, and therefore this is a wonderful situation.”

Such changes to our fundamental values to describe the universe do not come along often, and it is hard to imagine when one shall occur again. The meter was redefined in 1960 and then again in 1984.

The second was redefined in 1967. “Now that was quite a revolutionary change,” Davis says. “People for eternity had told time by the rotation of the Earth, and all of a sudden we changed to a vibration in an atom of cesium.”

Whether the redefinition of the second was a more fundamental change to human comprehension than the redefinition of the kilogram is not to say, but, like the second, the redefined kilogram is undoubtedly a notable moment in the advancement of our species.

“Getting rid of the last artifact … that’s the historic thing,” Davis says. “Measurement standards have been based on these artifacts, really, since anyone knows. Neolithic times excavations show standards—standard lengths, standard masses—that are little pieces of chert or rock or something. And so that’s how people have been doing it for millennia, and this is the last one.”

The SI will change again, though primarily as a matter of reducing already infinitesimal uncertainties, or switching to a different wavelength of light or chemical measure that is ever-so-slightly more precise. In the future, we may even add units to the SI for values that we have not yet thought to define. But we may never again do what we do now, to leave behind the understanding of our ancestors, and embrace a new system of measure.

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