The constant gardeners

“HOW much does a kilogram weigh these days?” may sound an odd question. Does a kilogram not weigh just that, a kilogram? In fact, a kilogram is the mass of a cylindrical lump of platinum-iridium alloy that was cast in 1879 in Hatton Garden, the jewellery district of London, and then dispatched to the International Bureau of Weights and Measures (BIPM) in Sèvres, near Paris. It sits there still, nestled beneath three cheese-domelike bell jars in a safe that can be unlocked (though it rarely is) only by turning a set of three keys, each entrusted to a high-ranking BIPM dignitary.

Despite such precautions, the international prototype does not rest entirely unperturbed. On those occasions when it has been compared with some of its official copies, discrepancies of up to 69 micrograms—slightly smaller than a grain of sand—have been observed (see chart). Since there is no reason to believe that “the” kilogram is inherently more stable than any of its cousins, it is either shedding weight through wear and tear or putting it on through chemical processes such as those involved in cleaning the thing.

In a world increasingly dependent on precise measurements, metrologists think such inconstancy no longer cuts the mustard. On January 24th, therefore, they gathered at the Royal Society, in London, to discuss progress towards recasting the kilogram in terms of something less mercurial than a platinum-iridium alloy. And what better to do the job than the fundamental constants of nature which are, after all, by definition, constant?

The kilogram is the last bit of the International System of Units (SI) to be tied explicitly to an artefact. Once, the metre was too. It was the length of another platinum-iridium ingot stored in Sèvres. But the metre has been redefined twice since that ingot was deposited in 1889: first, in 1960, in terms of the wavelength of a particular sort of light; then, in 1983, as the path travelled by light in a vacuum in 1/299,792,458 of a second. Which, of course, raises the question of what a second is. Not, as you might think, a sixtieth of a sixtieth of a twenty-fourth of the period of the Earth's rotation. No. A second is the duration of 9,192,631,770 periods of a phenomenon called microwave transition in an atom of caesium-133. The remaining four basic SI units, the ampere (electricity), kelvin (temperature), mole (quantity of atoms, molecules or other particles) and candela (light), followed suit—though the ampere, candela and mole are linked to the kilogram, and so indirectly to the Sèvres prototype.

On a steady Planck

The reason why the kilogram has taken so long to ditch its historic deadweight is that Planck's constant (h), the most promising candidate for its remodelling, pertains to the subatomic scale. On that scale, strange things happen and particles start behaving like waves. Planck's constant is the number that links the energy of a particle with the frequency of its associated wave. It reflects the sizes of the quanta of quantum physics. A quantum is the minimum amount of a physical entity involved in a physical process. That is something very small indeed—many orders of magnitude smaller with respect to the kilogram than, say, a metre is compared with the distance travelled by light in a second. And that makes it rather difficult to measure.

The big cheese

The favoured way of measuring h in terms of mass employs a device called a watt balance. The mass is suspended from one arm of the balance. The other arm carries a wire coil attached to an electric circuit—in other words, an electromagnet. The coil is suspended in an external magnetic field and the current running through it adjusted so that the attraction between the two magnets balances the gravitational force on the suspended mass.

Then, the experiment is repeated without the suspended mass. Instead, the coil is pulled through the external magnetic field, which induces a voltage across it. By combining data from the two steps an equation linking mechanical power (dependent on mass) to electrical power (calculated by multiplying voltage by current) can be derived. Both types of power are balanced and expressed in watts, which explains the experiment's name. From that, through a complicated and rather tiresome procedure involving phenomena known as the Josephson effect and the quantum Hall effect, it is possible to express electrical power in terms of h—and so, to calculate h in terms of the balanced mass.

When the uncertainty of this calculation is reduced to about one part in 100m, which metrologists hope will happen over the next few years, the experiment will be performed with the Sèvres prototype—that is, with a mass of precisely one kilogram. The resulting reading for h will be fixed by fiat and, with it, the Planck-related definition of the kilogram. A kilogram will then be any mass which elicits a reading for Planck's constant on a watt balance that coincides with the now-fixed value.

All this sounds much more complicated than weighing from time to time a piece of metal stowed away in a vault. But unlike that, the watt-balance experiment can be performed by anyone at any time provided they possess the right equipment and expertise. This ensures that the new kilogram will be a truly universal and immutable standard, set in something much firmer than stone, or even platinum: the fundamental laws of nature.