IN A VAULT under a courtyard near Paris lies a small, shiny cylinder of precious metal – and a big scientific embarrassment. Once a year three people gather outside the vault, turn their three keys simultaneously, and open the door. They have come to check that the small, shiny cylinder is still there. Once satisfied that it is, they shut the door, say their farewells and depart – wondering how much longer science must endure this risible ritual.
It may only be 40 millimetres tall, but the cylinder kept under lock and key at the International Bureau of Weights and Measures (BIPM) at Sèvres in France is beyond price. For it is absolutely and utterly unique: the one object in all the Universe that has a mass of exactly 1 kilogram.
That is why teams of scientists around the world are hard at work trying to get rid of it. It is a liability. It is also inconvenient. Anyone who really wants to know how much a kilogram weighs has no choice but to travel to Sèvres and check out that cylinder in the vault. Sure, there are copies in various labs around the world, but they are just not the real thing.
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But what irritates scientists most about that shiny little cylinder is that it is really a millstone around their necks. After all, scientists are homing in on the fundamental nature of the Universe, using instruments of transcendent elegance. To do this, they collect data of stunning accuracy, expressed in terms of a beautifully consistent set of units – themselves defined in terms of fundamental constants. So, for example, the second is defined as 9,192,631,770 periods of a certain type of radiation emitted by atoms of caesium-133, not a smidgen more or less. The other base units such as the metre and the ampere are based on similarly elegant and fundamental physics (see “Measure up”).
But there is still one glaring exception: the kilogram. Despite years of effort to find an alternative, the precise definition of the unit of mass – that most basic and familiar property of matter – is still nothing more fundamental than the mass of that chunk of metal kept in a safe in Sèvres. Created in 1889 from an alloy of 90 per cent platinum and 10 per cent iridium, it might look beautiful. But to aficionados of elegant science, the international prototype of the kilogram is like a warthog at a fashion shoot.
Later this year experts in metrology, the science of measurement, will convene at the BIPM to compare notes on their efforts to get rid of that shiny metal cylinder. “In a way it is embarrassing,” admits Stuart Davidson of Britain’s National Physical Laboratory (NPL), which owns three of the 80 or so copies of the BIPM original. “It would look a lot better if it were a shiny box with lots of laser beams flying about.”
Along with his metrologist colleagues around the world, Davidson is keen to replace his duplicate kilogram with something more genuine and trustworthy. When they were made, the duplicate kilograms were as close to being perfect copies as was humanly possible. They differed from the mass of the Sèvres original by around 10 parts per billion at the most. The trouble is, they don’t stay that way. Every few decades, the copies are returned to BIPM for comparison with the real kilogram. Despite being made from corrosion-proof metal and kept in airtight covers, the mass of the copies changes – although quite why is far from clear.
The last weigh-in took place during the 1980s. Even after cleaning to remove surface contamination, some of the copies had mysteriously gained over 20 micrograms or 20 parts per billion compared with the original since they were last brought together in the 1940s. “The problem is they don’t gain weight at a standard rate,” says Davidson. And although each lab has its own mathematical model to describe how the mass changes over time, there is no real understanding of the cause.
These mass changes raise a deeper question about the international prototype itself. As it is made from the same alloy as the copies and kept in the same conditions, its mass too may change over time. Yet as its mass is, by definition, always exactly one kilogram, its mass must always be the same. It’s a paradox. And without some other independent definition of mass, there is only one way to resolve it: blame any changes found on the copies kept by everyone else.
It is all very unsatisfactory, says Davidson, but finding an alternative has proved frustratingly difficult. Dreaming up new ways of defining the kilogram is the easy part. The real challenge is finding ways of achieving the parts-per-billion accuracy required – anywhere and at any time.
The first scheme, known as the Avogadro project, has already been under development for three decades, even though the idea behind it is simplicity itself: you just define the kilogram as a fixed number of those most familiar building blocks, atoms. Chemists routinely measure out substances by the mole, which contains a fixed number of atoms. That number is a fundamental constant of nature known as the Avogadro constant, and is roughly 600,000 billion billion. So in theory, defining the kilogram is just a matter of bringing together a certain amount of a suitably stable substance whose atoms tot up to give 1 kilogram. Once the substance and amount have been decided, anyone wanting a perfect kilogram can make their own, and the silvery little cylinders can go into retirement.
Yet according to Davidson the devil is in the detail. If the Avogadro project is to be a suitable replacement for the chunk of metal, the number of atoms in a mole has to be pinned down more accurately than to a few tenths of parts per billion. And after more than 20 years of effort by many of the world’s leading metrology laboratories, that goal is far from being achieved.
It all seemed so simple once. The choice of the material was clear. Silicon was the obvious front-runner, as the microchip industry has spent huge sums of money on making the purest, perfect crystals of the stuff. Knowing the spacing between the atoms, researchers can work out the exact volume of silicon needed. As for the shape to choose to make the standard volume of silicon, a sphere seemed ideal. It can be polished to atomic-level smoothness, giving a precise radius and volume, and would have no sticky-out edges that might get chipped.
Samples of the silicon spheres needed for a kilogram standard were made at the German standards laboratory (PTB) in Braunschweig then turned into the world’s roundest objects by Michael Kenny and colleagues in Australia at the Commonwealth Scientific and Industrial Research Organisation in Lindfield, New South Wales. The polishing was successful to the point where the biggest irregularity of their surface was around 500 atoms high, equivalent to smoothing out the Earth until the tallest mountain is 10 metres high.
But it has been an uphill struggle from there. Despite having perhaps the single most-studied crystal structure of any element, silicon has still managed to spring a nasty surprise. In the mid-1990s, teams from Germany, Italy and Japan met to compare their estimates of the number of atoms in their silicon samples, and to their horror found that the Japanese sample was short of thousands of billions of atoms. Peering inside the silicon using X-rays, Richard Deslattes at the National Institute of Standards and Technology in Gaithersburg, Maryland, found out where they had gone wrong: the supposedly “perfect” silicon crystal was riddled with micrometre-sized voids, probably created by hydrogen gas bubbles trapped inside during manufacture. Their presence has introduced unwelcome uncertainty into attempts to create kilogram masses from silicon.
The pristine surface of the spheres also turned out to attract an atomic layer of oxide and various contaminants, affecting the mass and dimensions of the sphere. No one would usually fret about such subtle effects, but if silicon spheres are to replace the Sèvres kilogram, their properties will have to be replicated to astonishing accuracy.
Small wonder
Metrologists pride themselves on measuring the all-but-infinitesimal, but the Avogadro project is pushing their ingenuity to breaking point. Standard measuring techniques such as optical interferometry are fine down to a few thousand atomic diameters, but the project demands that the dimensions of the silicon sphere be determined a thousand times more precisely. Doing this requires ultra-stable laser light and extraordinary care. Even changes in the weather affect the measurements: atmospheric pressure affects the refractive index of the air through which the laser light passes, so the measurements have to be performed in a vacuum. And if the temperature changes by more than a few thousandths of a kelvin during measurements, the change in diameter of the sphere will exceed the uncertainty permitted if the sphere is to act as a reliable standard.
It is a metrological nightmare, but progress is being made. “At present the relative uncertainty is about 15o parts in a billion,” says Kenny. The goal now is to reduce the uncertainty to about 20 parts per billion. “This is feasible, but by no means easy,” he says. “It will take years of effort – and millions of dollars.”
All of which makes even supporters of the Avogadro project think there has to be a simpler way. Terry Quinn, director of the BIPM and the custodian of the Sèvres kilogram, shares the growing conviction of metrologists that the best candidate for replacing that little shiny cylinder in his vault lies in an entirely different approach: the Watt balance.
The basic idea, devised over 20 years ago by Bryan Kibble at the NPL, is to define the kilogram in terms of two things that metrologists can already measure very precisely: voltage and resistance. In essence, the Watt balance is an exquisitely sensitive set of scales, with the kilogram in one pan and an electromagnetic field tugging at the other. Defining the kilogram then becomes a matter of measuring the electromagnetic force needed to match the weight of the kilogram, and dividing the result by the acceleration due to gravity.
If only it were that simple. In practice, measuring the strength of the field is a tricky process that requires state-of-the-art quantum devices to reach the accuracy required. The outcome would be a definition of the kilogram in terms of the Planck constant, which links the electrical properties of the balance to the quantum processes used to measure them.
But as with the Avogadro project, turning this simple idea into a practical standard is proving to be a nightmare. The balance is besieged by a host of metrological demons, ranging from stray electromagnetic fields to the pull of the Moon. All the measurements have to be performed in a complete vacuum, screened from outside disturbances. After a decade of effort by metrology labs in Europe and the US, the accuracy of the Watt balance is now within a factor of 10 of the level needed to make it a replacement for the Sèvres kilogram. “It’s probably going to take another decade before it gets there,” says Quinn.
Although the Watt balance remains the leading contender for redefining the kilogram, few would describe it as the acme of elegance. As Quinn points out, it could all be so much easier if atoms weren’t so tiny, as then you wouldn’t need so many of them to make up a kilogram. That seems to rule out the idea of just counting the number of atoms needed to make a kilogram. Or does it?
In the early 1990s, Michael Glaeser at the PTB came up with a brilliantly simple idea: create a stream of atoms, collect them in a pot balanced on a set of scales, and see how long it takes to gather a kilogram’s worth.
Of course, in practice it is more complex than that, but not much. Glaeser’s original idea involved firing ions of an element such as gold through a series of magnets to form a tight beam of charged particles: in other words, an electric current. Counting the number of ions is then just a matter of letting this current flow for a while. A 10-milliamp current, for example, amounts to a flow of around 200 billion billion singly charged ions per hour. At that rate, it would take around six days to collect 10 grams of gold ions: enough to form the basis of a mass standard.
Glaeser and his colleagues are now trying to get his idea to work. So far, the biggest problem has been creating a large enough current: “We started with gold ions, but the current is only microamps,” says Glaeser. He now plans to replace the gold with bismuth, which evaporates more easily when it is heated to give much bigger currents. He has also had to find ways of slowing the ions as they approach the collector, to stop them bouncing straight back out like balls at a fairground attraction. It’s tricky, but far from impossible, and it is certainly elegant.
But is there a smarter way of defining the kilogram? Davidson at NPL certainly suspects so. “Ideally the definition would be as elegant as those of the metre and the second,” he says. “Maybe we have all been looking for too high-tech an answer. There could be something really obvious out there we’ve missed.”
It is a suspicion reflected in the plaintive final line of the NPL’s official website on this most vexing of metrological challenges: “Any better ideas on a postcard please.”