On defining base units in terms of fundamental constants

Abstract

The definitions of the base units of the international system of units have been revised many times since the idea of such an international system was first conceived at the time of the French revolution. The objective today is to define all our units in terms of ‘invariants of nature’, i.e. by referencing our units to the fundamental constants of physics, or the properties of atoms, rather than the characteristics of our planet or of artefacts. This situation is reviewed, particularly in regard to finding a new definition of the kilogram to replace its present definition in terms of a prototype material artefact.

Acknowledgement

I am indebted to my colleagues who are the co-authors of reference [7] from whom I have learned so much of this subject. I am also indebted to Richard Davis at the BIPM, and to my colleague Catherine Deeley, for their comments on a first draft of this manuscript.

Dedication

This paper is offered in honour of Ben Widom, who is an inspiring scientist in the field of statistical mechanics and thermodynamics, an outstanding lecturer, and a valued friend.

Notes

Email: [email protected]

For small amplitude oscillations the period τ of a pendulum is given by the formula τ = 2π (l/g)^1/2, where l is the length of the pendulum and g is the local gravitational acceleration. Using SI units, this gives τ/s = 2π(l/m)^1/2 (g/m s⁻²)^−1/2, where (l/m) is the length of the pendulum expressed in metres and (g/m s⁻²) is the gravitational acceleration expressed in metres per second squared. Since π² is approximately equal to the gravitational acceleration in metres per second squared, a pendulum of length one metre has approximately a two second period. It would have exactly a 2 s period if g/(m s⁻²) were exactly equal to π².

To realize a definition is to make use of it to make a measurement.

The alloy is 90% platinum and 10% iridium. The International Kilogram is a cylinder about 39 mm high and 39 mm in diameter, and the metre is a stick with a tresca cross-section, an X with a central flat, and with two fine scratches at either end at right angles to its length between which the metre is measured.

The CIPM is the International Committee of Weights and Measures (Comité Interntaional des Poids et Mesures), which is responsible for running the BIPM between meetings of the CGPM, which occur only once every four years. The members of the CIPM are elected by the CGPM; they include representatives from many different countries, and the membership of the CIPM is rotated regularly.