# Maintaining weight

Planck’s constant is set to replace the metal cylinder that has served as an international reference for the kilogram since 1889

After debating for decades, physicists and other specialists in measurement, known as metrologists, are finalizing a new definition for the concept of kilogram, the base unit of mass in the International System of Units (SI). Starting in 2018, if things go as planned, the kilogram, currently used as a world standard in measuring the amount of matter in an object, will no longer be represented by a physical artifact: the International Prototype of the Kilogram, a cylinder made of a special alloy of iridium and platinum with a mass equal to that of one liter of distilled (very pure) water. Stored in a vault since 1889 under bell jars at the International Bureau of Weights and Measures (BIPM) in Sevres, France, this metal cylinder will no longer be tasked with defining the kilogram but will be replaced by a fundamental constant of nature, a value that at least in theory is universal and does not change over time. According to physicists, this change should democratize the ability to measure a kilogram precisely, since the measurement will no longer depend on a comparison with the metal cylinder in Sevres.

The invariant that will serve as the basis for defining the kilogram is Planck’s constant, proposed in 1900 by German physicist Max Planck (1858-1947). Represented by the letter *h*, this constant relates the energy of light particles, called photons, to the frequency at which they vibrate and is measured in units of energy (joules) multiplied by units of time (seconds). Planck’s constant describes several phenomena in the universe of elementary particles. Its value is an extremely small number—approximately 6.63×10^{-34} joules-second, a figure where 34 zeroes follow the decimal point—and it has been measured with increasing precision. While the value of a constant is fixed, its measured values change with the level of measurement precision. Since precision is never absolute, the absolute value of a constant cannot be known. To get around this obstacle, physicists and metrologists expect to arrive at a consensus value for Planck’s constant in July 2017.

The relation between this constant, which deals with phenomena in the subatomic world, and the mass equal to the mass of one liter of distilled water is not an obvious one. It arises from experiments proposed in the late 1950s to more precisely measure the value of an ampere, the unit that measures electrical current. A device later dubbed the watt balance was designed for the purpose of these experiments; it works by balancing two forces, like the scales once used to weigh food in a grocery store, with two plates suspended from the ends of a rod. The mass to be measured is placed on one side and counterweights of a known mass are placed on the other, until equilibrium is reached. A watt balance replaces the counterweight effect with a magnetic force.

In the mid-1970s, British physicist and metrologist Bryan Kibble, of the National Physical Laboratory (NPL), in Teddington, England, showed how the watt balance could be used to measure both the mass of an object as well as Planck’s constant with great accuracy. Later refined by the National Institute of Standards and Technology (NIST) in the United States, and renamed the Kibble balance in 2016, the device offers two modes of operation—and therein lies the secret of its precision.

The object whose mass is to be measured is first placed on one of the pans of the balance, which is immersed in the magnetic field of a large magnet. Gravity exerts the force called “weight” on this mass, lowering the pan. Since the pan is immersed in the magnet’s field, an electric current passing through a wire coil beneath the pan generates a magnetic force of the same intensity but in the opposite direction, offsetting the force-weight. This affords a precise measurement of the electric current that is balancing the pan perfectly; the current is proportional to weight and thus to mass. To reach equilibrium, the force-weight must be equal to the magnetic force, defined by a constant that is multiplied by the current. It is thus a matter of very precisely determining the value of the constant.

This is where Kibble’s genius comes into play. He realized that the value of this constant would not need to be known if another measurement were taken. In a second operation, the object is removed from the pan and the supporting wire is attached to a motor, which lifts the coil at a steady speed. The movement of the coil inside the magnetic field induces a voltage in the coil that is proportional to the velocity of displacement. This voltage is defined by displacement velocity divided by a constant—none other than the constant from the first stage of measurement. Since the current is proportional to the voltage, the constant can be mathematically eliminated from equations and the mass of the object then defined as a function of velocity. Equipment made of special materials that function as superconductors at extremely low temperatures is used to measure current and voltage, which are quantized in these materials, meaning that their values can only be multiples of Planck’s constant.

Various groups currently use the watt balance and this sequence of procedures to measure the value of Planck’s constant in terms of a previously known mass—in this case, the kilogram prototype and its copies, whose mass has been established with great precision. Once the measurements have reached an acceptable level of precision, the cylinder housed at Sevres and its working copies will become unnecessary to future calibrations. Although the mass of these cylinders is well known, the problem is that it is expected to keep changing. On the other hand, once the constant’s value has been precisely determined, the watt balance can be used to arrive at a very exact, time-constant measurement of the mass that corresponds precisely to one kilogram.

**Counting atoms**

The search for new criteria for defining the kilogram began in the 1980s, when a problem was detected with the metal cylinder at Sevres: the kilogram used as a world standard was losing mass, possibly when it was handled during cleaning or through evaporation of its component material. Measurements taken over the course of the last century have also shown that the mass of its copies around the world has varied, with some gaining and others losing millionths of one gram. Even such a tiny variation is unwelcome in a base unit. If it is to serve as a basis for comparison, the standard defining this unit must be quantified as precisely as possible and hold steady over time.

In 2011, the General Conference on Weights and Measures (CGPM), an international organization with 51 member nations, including Brazil, officially recognized the limits of the standard kilogram and decided that the unit of mass should be redefined in terms of “invariants of nature,” whose measurement has become increasingly more precise. A panel of CGPM experts decided that the unit of mass should be determined in terms of Planck’s constant. But it recommended that the value of the constant first be defined on the basis of three more precise measurements, obtained using at least two different methods, and the results of these measurements, derived from distinct approaches, should agree at a level of uncertainty below a pre-determined value.

The first of these methods is to define the value of Planck’s constant by counting the number of atoms in a 1-kilogram sphere of pure silicon. Counting the sphere’s atoms makes it possible to arrive at the value of the Avogadro constant, which indicates the number of particles in a determined mass; this enables later calculation of the value of Planck’s constant. Researchers with the International Avogadro Project counted the atoms in these extraordinary spheres—there are only two in the world, carefully hand-crafted at a cost of $3.2 million each—and were thus able to measure the value of the Avogadro constant, and consequently of Planck’s, with an uncertainty of 30 parts per billion. This level of precision amounts to measuring a 100-meter-long city block within micrometers.

The other way of measuring Planck’s constant relies on the watt balance. Working with one of NIST’s most recent versions of the balance—called NIST-4, in operation since 2015—physicist Stephan Schlamminger and his team measured Planck’s constant with an uncertainty of 34 parts per billion. This result, published in 2016 in the journal *Review of Scientific Instruments*, shows that the fourth-generation watt balance is accurate enough to be used to redefine the kilogram. More recently, researchers at Canada’s National Research Council (NRC) employed the watt balance conceptualized by Kibble in the 1970s to arrive at a lower uncertainty: 9 parts per billion. These and other groups have until July 2017 to submit their findings to the CGPM, which will define the value to be used in calculating the kilogram.

“The value of Planck’s constant is already more than precise enough to be used in the new definition of the kilogram,” says physicist Vanderlei Bagnato, a professor at the São Carlos Institute of Physics (IFSC), of the University of São Paulo (USP). Bagnato chairs the commission on fundamental constants of the International Union of Pure and Applied Physics (IUPAP), one of the institutions that is collaborating in redefining the kilogram. IUPAP is set to discuss the matter at its annual meeting, to be held for the first time in São Paulo, in October 2017. “We no longer have to depend on an artifact like the metal cylinder in Sevres,” Bagnato says.

**The old-fashioned way**

The kilogram is the last of the seven main SI base units still calculated on the basis of a physical artifact (the others have been measured in terms of fundamental constants of nature for years). This change, which may go into effect in 2018, should make calibration more reliable, obviously something of great value to physics—since the field uses the kilogram in defining 20 other units of measure—as well as to international trade. In theory, calibrating the value of the kilogram should also become a more accessible procedure. Any laboratory that is technologically equipped to produce a decidedly precise watt balance will be able to measure the mass of objects exactly, thus eliminating the need for access to the artifact stored in France.

The new way of measuring the kilogram will have no impact on people’s daily lives. “Nothing will change in the lives of people going to bakeries, shops, supermarkets, or airports,” says physicist Humberto Brandi, full professor emeritus at the Federal University of Rio de Janeiro (UFRJ) and director of scientific metrology at Brazil’s National Institute of Metrology, Quality, and Technology (Inmetro). “This change will be of benefit in the international trade of high-tech manufactured and healthcare goods.” By helping set standards for international trade, especially the high-tech area, scientific metrology plays a valuable role in areas like quality control of exports and imports.

*Scientific articles*

HADDAD, D. *et al.* Invited article: A precise instrument to determine the Planck constant, and the future kilogram. **Review of Scientific Instruments**. V. 87, 061301. 2016.

MANA, G. *et al.* The correlation of the NA measurements by counting 28Si atoms. **Journal of Physical and Chemical Reference Data**. V. 44, 031209. 2015.

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