Considerations on future redefinitions of the kilogram, the mole and of other units

Abstract

The definitions of some units of the Système International are likely to be revised as early as 2011 by basing them on fixed values of fundamental constants of nature, provided experimental realizations are demonstrated with sufficiently small uncertainties. As regards the kilogram, experiments aiming at linking it to the Planck constant and the atomic mass constant are under way in several laboratories. The other units likely to be redefined are the ampere, the kelvin and the mole. We discuss the advantages and disadvantages of different alternatives for revised definitions of the kilogram and the mole. From physical considerations, metrological consequences and ease of understanding, a definition of the kilogram based on the mass of a particle, such as an atom or the electron, is favoured. One of the proposed definitions fixes the value of the Planck constant through the Compton frequency of a material, though unphysical, particle. Finally, a redefinition of the mole, the counting unit of the amount-of-substance, is proposed which fixes the Avogadro constant as a dimensionless number.

A sorites paradox in the conventional definition of amount of substance

“…Several authors have commented on the confusion and difficulty, especially for students, surrounding the current definition of the mole [3,[18][19][20][21][22][23]. This is perhaps understandable, when the current definition of the mole and the conventional definition of amount of substance are centred around a number of elementary entities, presumably to be determined.…”

“…Some authors have attempted to resolve this paradox by saying that amount of substance is (or should be) a quantity of dimension 1 [2,3]: several reasons why this approach is unsatisfactory have been discussed elsewhere [4]. This paper explains why amount of substance, as that term is generally understood, must be a continuous quantity.…”

“…Problems with differentiation can be resolved by taking a separate physical quantity which is both continuous and proportional to amount of substance: for example, chemical potential can also be defined by (3), and this is closer to Gibbs' original definition [7]. 3 µ = M(∂G/∂m) T,p (3) The many problems caused by ignoring the separate quantity dimension of amount of substance are discussed elsewhere [4]. For the purposes of this discussion, it is sufficient to note that the mass of a given chemical substance is just as discrete at the microscopic scale as the number of entities.…”

“…3 Gibbs originally defined chemical potential as an extensive quantity, i.e. without multiplying by the molar mass in (3).…”

Evolution of the International Metric System of Units SI

“…Therefore, elementary particles are better suited than atoms to become reference entities when defining units of measurement. The New SI definition of the ampere in terms of the elementary charge e can be considered one example of such a new approach; definition of the kilogram in terms of the mass of an elementary particle (the free electron) has also been proposed [21].…”