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Redefining what is real (Image: Vladimir Godnik/Getty)

THE shiny metal machine would look at home in Doctor Who‘s Tardis. But rather than twisting space and time, it was built to master another elusive entity. The machine is a watt balance and, in simple terms, it weighs energy. Every few weeks, physicist Stephan Schlamminger and his team at the US National Institute of Standards and Technology (NIST) in Gaithersburg, Maryland, lift off the lid with a crane and tinker with its insides, adjusting a laser beam here and there, seeking perfect equilibrium. Their goal? To pin down mass.

NIST’s watt balance is part of a looming revolution. Along with several other super-precise devices around the world, the machine is helping to usher in a new order in the world of metrology, the science of measurement. It’s a world in need of a drastic shake up.

The International System of Units (SI) – the standard that underpins all measurements – is in a bit of a mess. In a bid to do away with out-dated definitions tied to the human world, metrologists are linking units such as the kilogram and ampere to universal constants and exact quantities of fundamental particles.

In doing so, metrologists are bumping up against the limits of our ability to probe the make-up of matter. But success will be worth it. When the revamp comes into play in 2018, the SI will have rigorous foundations for the first time in its history. “It will bring the physical world into sharper focus,” says Michael de Podesta, who specialises in temperature measurement at the National Physical Laboratory (NPL) in Teddington, UK.

Shaky foundations

The SI is built on seven “base units”, which underpin all others. But its temperature scale is pegged to a particular state of particular water that has to be scooped out of the middle of the ocean. Its unit of current, the ampere, is defined by an impossible experiment (see “Parallel lines“). Worst of all, its paragon of mass is a lump of platinum alloy that is constantly changing. And according to the SI, when the one true kilogram changes, so does our measurement of the mass of every particle in the universe. “Metrology is the foundation of all science,” says Schlamminger. “If you have broken foundations that is no good.”

“The unit of current, the ampere, is defined by an impossible experiment”

Units of measurement need to be the same for everyone, everywhere. “The point about the SI is it should be universal – whether you are doing particle physics in CERN or buying vegetables on the high street,” says Jonathan Williams, a colleague of de Podesta’s at NPL, who works on electrical standards.

But defining measurements is a thorny problem. Take the kilogram. The existing international prototype kilogram (IPK) is a cylinder of platinum-iridium alloy that was cast and polished to size in the 1870s as one of a set of about 40. Some of the copies are kept with the IPK in the International Bureau of Weights and Measures in Paris, France. Others are owned by standards laboratories around the world, and all are occasionally compared with one another. In 1949, metrologists found that the IPK and its companions had drifted apart by about 50 micrograms. Oops.

Endangered species

Every time the IPK is handled, there is a danger of introducing a new error. “You are afraid to touch it,” says de Podesta. Then there’s the small matter of the goats. In 1879 it was specified that the IPK was only to be cleaned with a chamois leather. Now, 150 years on, the chamois goat is an endangered species. “Getting hold of chamois leather is a problem,” says de Podesta.

What to do? Metrologist Ian Mills at the University of Reading in the UK served as president of the SI consultative committee for units for 17 years until 2014. “For the whole of my time we were worrying about how to define the kilogram,” he says. Thankfully, a solution is on the horizon – one that doesn’t involve goats.

Around the world, watt balances are bearing down on mass (Image: Jennifer Lauren Lee/NIST)

When it comes to redefining the kilogram, one option is to set it as a certain number of particular atoms. This is the aim of the international Avogadro Project. Its researchers have polished two 1-kilogram spheres of silicon-28 to exquisite precision – they claim they are the roundest objects in the world – which allows them to take extremely precise measurements of the diameter. In turn, this lets them calculate the spheres’ density, and thus the precise number of atoms within, thanks to the uniform nature of silicon’s crystalline structure.

Another option is to define the kilogram in terms of the Planck constant, as physicists Barry Taylor and Peter Mohr of NIST suggested in 1999. This number, written as h, is the constant of the quantum world. It relates the energy of any particle to its frequency of vibration: energy is h times frequency. And because energy is related to mass, so is h. It’s rather circuitous. But on the other hand, the Planck constant is a more fundamental aspect of reality than the mass of an atom.

In 2011, the Planck proposal won. The next step is to measure the Planck constant in terms of our existing kilogram. To do that, physicists have turned to the watt balance.

The machine has a weight on one side and an electromagnet on the other, and it balances gravitational forces (that is, weight) against electrical forces (that is, energy). So far, so simple. Where it gets fiddly is measuring the electrical force. To measure the voltage in the electromagnet, physicists use the Josephson effect: a superconducting flow of electrons oscillates at a frequency that is intimately linked to the voltage. Then, to measure the electromagnet’s resistance, they use the quantum Hall effect: sudden quantum jumps in resistance when a thin-film conductor is put in a strong magnetic field.

It’s hardly intuitive. There seems to be no easy way to say how the watt balance gives a kilogram in terms of h without delving into the quantum details. “We’ve been puzzling about it, but we don’t have an answer,” says Mills.

The good news is that it provides very accurate measurements. The best yet is by the Canadian National Research Council in Ottawa. With a machine originally built at NPL, researchers there narrowed down the uncertainty of h to less than 20 parts in a billion. is aiming to beat this with its new balance – as are teams in France, Switzerland, New Zealand and South Korea.

And it turns out that there is a role for the Avogadro Project’s silicon spheres as well. The mass of a silicon atom can be compared with the mass of an electron using a device called a mass spectrometer. In turn, the mass of the electron can be linked to the energy of light emitted by atoms – again as a multiple of h. So you can also build a Planck kilogram by counting silicon atoms.

For many years, results from the two approaches disagreed. Researchers with the Avogadro Project guessed that it might be to do with impurities in their spheres, so they started again from scratch.

First, silicon-28 was isolated at the Central Design Bureau for Machine Building in St Petersburg, Russia. Then, at the German National Metrology Institute (PTB) in Berlin, this was turned into a single crystal, which was cut up and polished into two almost perfect spheres at the Australian Center for Precision Optics in Lindfield, New South Wales. Back at PTB, scientists used lasers to measure the diameter of the sphere in all directions, analysed the remaining impurities and fired in X-rays to find the spacing between atoms.

In 2011, the group found that their atom-counting method agreed with the watt balance – with experimental uncertainties of only 30 parts in a billion. Last year, after discovering a hint of metallic contamination in the surface and etching it off, they got that down to 20 parts per billion. “The watt balance comes out of physics, the Avogadro Project from chemistry,” says Schlamminger. “That the two agree so closely is very powerful.”

The Avogadro Project is now stepping up a gear: researchers are preparing two spheres of even purer silicon-28, with four more on order. As well as mechanical polishing, the PTB team will use a beam of ions to make the surfaces even smoother. “We will be able to remove all the mountains,” says Horst Bettin, head of the Avogadro group at PTB. The biggest of these mountains are 100 nanometres high. The new spheres should have peaks of no more than 5 to 10 nm.

If all goes to plan, these results will define the new kilogram. What’s more, they will also be used to redefine the mole – another base unit – by tying it to the Avogadro constant.

That leaves the kelvin. One kelvin, the SI unit of temperature, is currently defined as 1/273.16 of 0.01 °C – the temperature of the triple point of pure water, at which ice, liquid and vapour can coexist. In other words, 0.01 °C is 273.16 kelvin. But like the kilogram and its chamois leather, it all hangs on something surprisingly arbitrary. In 2005, the definition was updated to specify how to obtain pure water: you take a boat to the middle of the ocean, scoop a sample from the surface and distil it. “This is what happens when you have a unit that isn’t abstract,” says de Podesta.

So the kelvin will soon leave water behind and evolve into an entity of pure energy. Temperature is a measure of how fast the particles in an object are moving around – how much kinetic energy they have – and the two are linked by the Boltzmann constant, which is about 1.38 × 10^-23 joules per kelvin. This allows the kelvin to be defined as an unchanging fraction of a joule. And a joule is derived from the kilogram, metre and second. With those pegged to constants, the kelvin will be too.

But it all hangs on knowing the precise value of the Boltzmann constant. To measure it, de Podesta’s team have used a singing wisp of gas: measuring the speed of sound in argon at the triple point of water gives you Boltzmann’s constant. In 2013, they thought they had this number down to less than one part per million – good enough for the new definition.

The wrong argon

Then they hit a snag. To do the calculation you need to know the average mass of the atoms. On Earth, most argon is in the form of argon-40, with a trace of argon-36. The team had diligently compared the balance of these isotopes in their sample against what they thought was the balance in the atmosphere. “But it turns out people disagree about the isotope ratio in the atmosphere,” says de Podesta. So now they are redoing the experiment using pure isotopes. These are insanely expensive, he says. Argon-36 is £4000 per gram. “You open a valve at the wrong time and – pff – it’s gone.” The expense has paid off, however. “I think we’ve made the most accurate temperature measurements in human history,” says de Podesta.

With everything set to meet the long-held goal of nailing all our units of measurement to nature, will that be the end of the metrology business? Hardly. For a start, you can’t weigh out a kilogram of apples with just a definition. So there will still be standard kilogram lumps sent out to industry – but they will now be calibrated against watt balances and silicon spheres. And PTB is working on a plan to make much cheaper standard spheres out of natural unpurified silicon, then comparing their density with the pure silicon spheres simply by weighing the two in and out of water, as Archimedes is said to have done to test the purity of a golden crown. Similar kit will need to be developed for the other units.

And we can’t rule out the definitions changing again. We have chosen what seem to be the most accessible constants today, says Williams. “In 100 years, there might be different ones.” He also says that within a decade, the second may be pegged to a new generation of atomic clocks, more accurate than today’s caesium-based ones.

We are marking out reality with more precision than ever before. What will there be to show for it? “It is like having work done on the foundations of a house,” says de Podesta. “It’s time consuming and expensive and in the end the house looks the same. But you have confidence that it will not subside.”

Leader “The mismeasure of metrology“

This article appeared in print under the headline “The measure of things”