The watt balance: determination of the Planck constant and redefinition of the kilogram

Abstract

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, 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.

Adapting the International System of Units to the twenty-first century

“…Although defining the kilogram by fixing the value of the Planck constant is conceptually more complex than, for example, defining the kilogram in terms of the mass of the electron or a specified atom, the other advantages of fixing the value of the Planck constant make this the preferable definition. See also the paper by Bordé [13], as well as those of Becker & Bettin [14], Stock [15] and Davis [16] in this issue.…”

The Precise Determination of Mass through the Oscillations of a Very High-Q Electromechanical System

“…Therefore, a simple experimental relation between mass and the Planck constant is obtained from this experiment (see [4] for a related discussion for the Watt Balance Method), provided Q is very large. The entire setup and theoretical analysis is considerably simpler than the Watt Balance Method adopted in recent attempts for the determination of the new standard for the kilogram [3,4].…”

“…The present investigation is motivated by a particular (long-standing) Metrology problem, namely the determination of a new international standard for the kilogram in terms of an experimental expression involving well defined standardized parameters like the electronic charge and Planck's constant. The current stage of such efforts has been described for instance in [3,4]. Our objective hereafter is to show that a relatively simple electromechanical system, in a single experiment, and adopting Equation (4) as the definition of mass might be able to produce an extremely precise measure for the mass of an object.…”

“…Equation (3) states that the total energy contained in the system is given by the work done upon the system by the force F along the range of oscillation. By taking the time derivative of Equation (2) we obtain the velocity of the oscillating load, and realize that Equation (3) can be rewritten in the concise form…”

Gravity without Newton's Gravitational Constant and No Knowledge of Mass Size

“…In that case, we need to know the Planck constant in addition to the speed of light. The Planck constant can be measured independent of any knowledge of the Newton gravitational constant, using the Kibble balance, for example; see [21][22][23]. The main point is that we do not need to know the Newton gravitational constant to find the Planck mass.…”