# Stephan Schlamminger

## The watt balance or a way to redefine the kilogram

### Motivation

The kilogram is currently defined as the mass of the international prototype of the kilogram, which is kept somewhere outside Paris. While this may be a practical definiton, it is philosphically not satisfying for two reasons:

(a) Lorentz symmetry says that the laws of physics are the same in all inertial systems. However, Paris is only accessible in a few inertial systems (think extraterrestrial intelligence).

(b) It is unclear how stable the mass of an artifact is over time.

A Watt balance is a device that allows a defintion of the kilogram by comparing (virtual) electrical power to (virtual) mechanical power. Electrical power can be expressed with the help of the Josephson effect and the Quantum hall effect as the product of two frequenies and Planck's constant (and unitless constants), (Js/s^{2}=W).

The Watt balance was first proposed by Brian Kibble in 1976 ( Kibble B P 1976, in Atomic Masses and Fundamental Constants vol 5 ed J H Sanders and A H Wapstra (New York: Plenum) pp 541–51). The basic principle of the Watt balance hinges on the symmetry of the Lorentz force of electrons in a a magnetic flux:

The Watt balance experiment is a procedures with two steps. In the first step, called the velocity mode, a piece of wire, of length l, is moved through a magnetic field, flux density, B, and ideally perpendicular to the wire and the motion. The ratio of induced voltage to the velocity is given by the geometry factor of the field and coil (lB).

In the second step, named weighing mode, the force acting on the wire transversed by the current I is compared to the force of a mass in the earths gravitational field.

Combining the result of both steps, we can find a value for the mass
Sounds easy, but the actual implementation is quite tricky. One has to bear in mind that some of the quantities are vectorial and these vectors need to be aligned right. In addition, these experiments shoot for a relative uncertainty of 10^{-8}.

04/30/11