The watt balance: determination of the Planck constant and redefinition of the kilogram
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Since 1889, the international prototype of the kilogram has served as the definition of the unit of mass in the International System of Units (SI). It is the last material artefact to define a base unit of the SI, and it influences several other base units. This situation is no longer acceptable in a time of ever-increasing measurement precision. It is therefore planned to redefine the unit of mass by fixing the numerical value of the Planck constant. At the same time three other base units,
... ther base units, the ampere, the kelvin and the mole, will be redefined. As a first step, the kilogram redefinition requires a highly accurate determination of the Planck constant in the present SI system, with a relative uncertainty of the order of 1 part in 10 8 . The most promising experiment for this purpose, and for the future realization of the kilogram, is the watt balance. It compares mechanical and electrical power and makes use of two macroscopic quantum effects, thus creating a relationship between a macroscopic mass and the Planck constant. In this paper, the operating principle of watt balance experiments is explained and the existing experiments are reviewed. An overview is given of all available experimental determinations of the Planck constant, and it is shown that further investigation is needed before the redefinition of the kilogram can take place. Independent of this requirement, a consensus has been reached on the form that future definitions of the SI base units will take. Every measurement in the world expressed using the kilogram unit is ultimately traceable to the international prototype of the kilogram at the BIPM. Most Member States of the Metre Convention hold national prototypes which are compared from time to time against the working standards of the BIPM, which are traceable to the international prototype. Although this system has worked quite well until now, and ensures uniform mass measurements throughout the world, unit definitions that can be realized anywhere are preferable. The international prototype as a material object could also be damaged, with obvious negative consequences for mass metrology. Three comparisons were carried out between the international prototype and the national prototypes, one in the 1880s, one in 1946 and one in 1989, and they show a trend towards larger mass values for most of the prototypes with respect to the international prototype, of approximately 50 mg over 100 years  . In relative terms, this corresponds to a change of 5 parts in 10 8 over 100 years. This observation might be interpreted as an indication that the international prototype loses mass. However, there is no clear explanation of the situation, because during the last century a more stable mass reference did not exist. It cannot be excluded that all prototypes show a common drift in addition to this relative drift, which cannot be detected by comparisons between the prototypes and which at present is completely unknown. The definitions of several other base units depend on the kilogram; this is the case for the ampere, the mole and the candela. Typical measurement uncertainties in chemistry and photometry are such that a possible slight drift of the kilogram, and consequently of the mole and the candela, would go unnoticed. Practical electrical metrology has since 1990 been based on the use of the Josephson effect and the quantum Hall effect, together with conventional values of the Josephson constant, K J-90 , and the von Klitzing constant, R K-90  . Conventional values have been chosen, because the reproducibility of both effects is better than the knowledge of the Josephson constant K J and von Klitzing constant R K in SI units. The use of conventional values allows us to benefit from the very high reproducibility of the Josephson effect (parts in 10 10 ) and the quantum Hall effect (parts in 10 9 ) but, strictly speaking, takes electrical metrology outside of the SI. Realizations of electrical units based directly on the SI definition of the ampere suffer from comparatively large uncertainties: the ampere can be realized with an ampere balance with an uncertainty of 4 parts in 10 6 , the volt balance allows realization of the volt to within 3 parts in 10 7  and the calculable capacitor realizes the farad to within 2 parts in 10 8  . The main shortcomings of the present SI system are the use of an artefact to define the unit of mass and the fact that the practical realization of electrical units is not based directly on the SI definition of the ampere but on conventional values for the Josephson and the quantum Hall effects. These are the main drivers for the planned redefinition of the kilogram and the ampere, which will remedy both problems. It is expected that the unit of thermodynamic temperature, the kelvin, and the unit of the amount of substance, the mole, will be redefined at the same time  .