Our kilogram is losing weight – can maths save the day?

LONDON: For more than 125 years, a single metal cylinder – kept under lock and key in Paris – has been used to define the precise weight of one kilogram. There was just one problem: over time, this scientifically sacred piece of platinum-iridium alloy was becoming lighter.

Scientists could not be sure why, but believed that the cylinder, kept in a vault at the International Bureau of Weights and Measures, was losing weight due to gas escaping from inside the high-grade metal. But, whatever the reason, they were left with the conundrum of redefining the kilogram using a more precise and reliable method.

Now, researchers believe they have succeeded in finding a viable mathematical constant to use as an alternative, and have achieved a minor breakthrough in the study of atoms – and very large numbers – in the process.

Scientists decided to replace the metal block, known as the international prototype kilogram, with a new definition based on Planck’s constant, which represents the size of the quanta in quantum physics.

However, to do this they needed to devise a way of estimating yet another constant, Avogadro’s number – a figure greater than the number of grains of sand in the world.

Now, Dr Giovanni Mana and his colleagues at Italy’s National Institute of Metrology Research in Turin have obtained what they believe to be the most accurate estimate of Avogadro’s number to date, which can now be used to quantify Planck’s constant and hence help to redefine the kilogram in purely mathematical terms.

In their study, published in the Journal of Physical and Chemical Reference Data, they estimated Avogadro’s number by “counting” the number of atoms in a kilogram sphere of pure silicon. They can make this estimate because pure silicon forms crystals composed of cubic cells each containing eight atoms of silicon.

In this way, it was possible to calculate the number of atoms in the sphere by examining the ratio between the total volume of the silicon sphere and the volume occupied by each silicon atom.

They made a similar estimate in 2011, with an uncertainty of 30 atoms per billion, but the latest estimate has an uncertainty of just 20 atoms.

This gave an estimate of Avogadro’s number of 6.02214082 (11) by 1023, where the brackets represent the uncertainty of the last two digits.

“Prior to redefining the kilogram, we must demonstrate that the new realisation is indistinguishable from the present one,” Mana said.

“Otherwise, when changing from the present definition to the new one, all users in science, industry and commerce must change the mass value of all the existing artefacts.”

The researchers believe that a more precise definition of Avogadro’s number strength- ens the definition of Planck’s constant – and finally leads science to a firmer mathematical definition of the measure.

The kilogram is one of the seven “base units” on which all other units of measurement in science are derived. The other six are the metre, second, ampere, kelvin, mole and candela, measuring, respectively, length, time, electric current, temperature, chemical amount and light intensity.

What makes the kilogram different is that it is the only international standard unit of measurement that is based on a physical object rather than a physical constant.

The metre, for instance, is no longer defined as the distance between two scratches on a metal bar, but on the distance travelled by light in a vacuum in 1/299792458 of a second. Physicists believe that redefining the kilogram with a physical constant can improve precision of electrical measurements fiftyfold. – The Independent