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A little over 20 years ago, Mike Moldover played a tune through a sphere of argon gas and became something of a rock star in the exacting field of metrology. The way those notes reverberated enabled him and his colleagues to determine the value of the Boltzmann constant — the relationship between the average kinetic energy of molecules and temperature — better than anyone ever before. Moldover was sufficiently confident of the result to put a bold promise into his paper: "if by any chance our value is shown to be in error by more than 10 parts in 106, we are prepared to eat the apparatus" (M. R. Moldover et al. J. Res. Natl Bur. Stand. 93, 85–144; 1988). No one expects Moldover to have to swallow his argon anytime soon.

Moldover, who worked at the US National Institute of Standards and Technology in Gaithersburg, Maryland, and his colleagues determined the value of the Boltzmann constant (kB) as being 1.3806513 × 10−23 joules per kelvin with an uncertainty of just 1.8 parts per million (p.p.m.). A generation later, that result continues to inspire others. "Scientists are sort of in awe of Mike," says Michael de Podesta of the National Physical Laboratory in Teddington, UK. Today, de Podesta is racing others around the world to whittle down the error in Moldover's experiment to just 1 p.p.m. and at the same time confirm his result. Once the constant has been measured to that level of accuracy, an international committee plans to set it in stone, and use it to fundamentally shift the definition of the unit of temperature. "It's the hope that once this is settled, the world will stop worrying about thermometry," says Moldover.

The worry does not, admittedly, keep many people awake at night, nor is it of immediate practical importance. But it does have a certain philosophical heft. Today, the SI unit of thermodynamic temperature, the kelvin, is defined in terms of absolute zero and the triple point of water (the temperature and pressure at which water exists as a solid, liquid and gas in equilibrium), which is fixed at 273.16 K. This was done for historical reasons that were logical at the time. But to metrologists, the definition is inelegant, illogical and downright irritating.

The kelvin is ripe for redefining. Richard Davis

"It's a slightly bonkers way to do it," says de Podesta. According to the metrological code of ethics, it is bad form to grant special status to any single physical object, such as water. Worse, 'water' needs to be qualified further: at present, it is defined as 'Vienna standard mean ocean water', a recipe that prescribes the fractions of hydrogen and oxygen isotopes to at least seven decimal places. Finally, it makes no sense for researchers studying the chilly climes of low-temperature physics or the blazing heat of stars to have their measurements of temperature rely, even theoretically, on comparison to a random piece of ice. "The kelvin is ripe for redefining," says Richard Davis, one of Moldover's former colleagues, who works at the International Bureau of Weights and Measures (BIPM) in Sèvres, France.

The BIPM, which is in charge of such things as units, aims to fix this unconscionable situation by 2011. The Boltzmann constant, which is currently a measured value with some uncertainty, will be declared a set number (letting it live up to its name of 'constant') and the kelvin will be redefined as something like the change in thermodynamic temperature that results in a change of mean translational kinetic energy of 1.38065XX × 10−23 joules — the current work will fill in the Xs.

Sound science

The change represents a metrological sleight of hand. Whatever uncertainty existed in the measure of the Boltzmann constant will be wiped clean by definition, and transferred to uncertainty in the measure of temperature. These new temperature uncertainties are so tiny that they certainly won't cause panic in any lab — most researchers won't even notice them. Instead the redefinition will open the door for improved accuracy at the far ends of the temperature spectrum. More than that, it frees the kelvin from an unsteady connection to water and rests it on the intellectually firmer foundations of a physical constant. As such, the move mirrors what metrologists are doing with all the units of measurement.

In the case of the kelvin, the technique of choice for determining kB is called acoustic thermometry, and it relies on being able to precisely determine the speed of sound in a gas-filled sphere at a fixed temperature. From this the Boltzmann constant falls out of the equations relating the kinetic energy (E) to the thermal energy of the gas (E = 1/2mv2 = 3/2kBT, in which m is the mass of one atom, v is the average speed of the atoms — which is proportional to the speed of sound in the gas — and T is the temperature). The speed of sound can be measured by analysing the frequency of the sound waves that resonate within the sphere. The good news is that experimentalists can measure the frequency with great precision; de Podesta has a rubidium clock in his lab that's accurate to 1 part in 1013. The bad news is that to analyse the resonances accurately, the volume of the container must be known with great precision. Moldover did this in his groundbreaking 1988 experiment by first filling his 3-litre sphere with mercury and weighing it. (He promised in his paper to eat this, too, should his result be proved wrong).

Michael de Podesta and his team is trying to lessen the error margin in measuring the Boltzmann constant. Credit: A. Heume

The volume issue remains the hardest problem to crack. Filling the spheres with a liquid and weighing them is still a possible solution. But there is a more elegant method, the details of which have just been worked out by one of Moldover's original colleagues, James Mehl, professor emeritus at the University of Delaware in Newark. The idea is to fit the sphere with tiny antennas to measure the resonance of microwaves in the cavity, then use this measurement to determine the sphere's volume. The researchers will deliberately use a lopsided sphere, such as one with three axes of slightly different lengths, to avoid the complicated pattern of overlapping resonances that results from using a sphere approaching, but not reaching, perfection.

"It needs to be very exactly not a sphere," says de Podesta. To reach that kind of precision, he uses the same manufacturers that are involved in producing the mirrors for the future James Webb Space Telescope.

The effort to best Moldover has inspired a friendly race between three main laboratories: the National Physical Laboratory, the National Institute of Metrological Research in Turin, Italy, and France's equivalent national lab outside Paris. All three are using acoustic thermometry — although with slightly different apparatus — to determine kB. Every aspect of their work requires extreme care. "You buy a very pure gas, which isn't pure enough. So you purify it more," says Roberto Gavioso from the institute in Italy, explaining just one technical detail from a long, long list. One or all of the labs should hit 1 p.p.m. by the end of 2009 or 2010. "I'm cheering for these guys," says Moldover who, now 69, has passed on the Boltzmann torch.

At the same time, the German National Metrology Institute in Berlin, heads an alternative approach. Bernd Fellmuth's kit consists of a pressure chamber surrounded by a cubic metre of water to keep the temperature constant. A set of capacitors inside the chamber measures the capacitance before and after helium is inserted, which allows the team to calculate kB using a different set of equations from those used by the acoustic thermometry group. A difficulty here, however, is how to measure the pressure to the required accuracy; currently that's only possible to about 4 p.p.m., and an entire team is required to reach that point. The group hopes to begin experiments in January 2010 that could get the accuracy down to 1 or 2 p.p.m. by the end of that year. Moldover calls that an optimistic target, but it would be good to have a check for the acoustic work in time for 2011, he says.

Once the results are in, the decision goes to an international vote. Each of the 53 nations that are members of the BIPM supplies delegates to the General Conference on Weights and Measures, which will make the final decision. This high-level conference meets once every four years — the next being in 2011.

A lump of metal serves as the kilogram standard. Credit: BIPM/ Getty Images

Why the rush to this finish line for the kelvin? It is all the kilogram's fault. The kilogram is the last remaining quantity that is defined by a single, physical object — a lump of platinum and iridium, dubbed Le Grand K, that is held in a BIPM vault on the outskirts of Paris. This has the curious effect that the value of one kilogram, although meant to be constant, almost certainly changes as atoms are added to or brushed off the surface of Le Grand K. No one knows exactly how unstable this value is, of course, as there is no fundamental standard with which to compare it. This is hardly firm bedrock on which to rest all measurements of mass.

To solve this problem, various research teams have been seeking to redefine the kilogram on the basis of a universal quality. The most intuitive technique involves making a perfect sphere of silicon-28, such that the number of atoms within the sphere can be precisely determined. Thus a kilogram could be redefined as the mass of a set number of silicon atoms, although in practice this would be almost impossible to achieve because making a perfect enough sphere is tremendously difficult to do.

A more practical method involves a 'watt balance', which measures the electromagnetic force required to counterbalance a kilogram under Earth's gravity. The equations describing that electrical force involve Planck's constant, a fundamental parameter of quantum physics. Right now, like the Boltzmann constant, Planck's constant must be measured, but if it were given a set value, the kilogram could be redefined on the basis of that number. To accomplish this feat, metrologists are trying to determine Planck's constant with an uncertainty of less than the instability thought to be associated with Le Grand K. That outdated object, having been used as a standard to set the value of the Planck constant, could then be retired.

Both methods are being actively pursued, as checks to one another, and researchers are keen to change the definition of a kilogram as soon as possible as it will stop the 'drift' in its value.

As work on the kilogram progresses, metrologists have resolved to tie up all their other loose ends. In 2005, they decided to reconsider the kelvin, the kilogram, the ampere and the mole — four of the seven 'base quantities' — the other three being the metre, the second and the candela. These four all have definitional deficiencies and are ripe for updating. The redefinition of the ampere and the mole is linked to the work on the kilogram. But the kelvin stands alone.

So thermometry specialists press on with their efforts to tidy up their corner of the metrological universe, even though this work will make little immediate difference to the world. To keep science and industry on an even keel, nothing will change initially except the definition (see 'A temperature for the masses').

That lack of impact might provoke existential stress for some scientists. "Sometimes I feel a bit guilty because maybe I should be helping starving children or something," says de Podesta. But he says he feels deeply that it really matters that there are people worrying about tiny fractions of a kelvin and about laying a foundation of truth in thermometry. One day, someone will need accurate and precise thermodynamic temperature readings, and having a fixed value for kB will help them. "I'm doing a small thing," says de Podesta. "But I do think it's a good thing for the world."

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