How much does the SI, namely the proposed “New SI”, conform to principles of the Metre Treaty?

Abstract

The International System of Units (SI) was first adopted in 1960, as the more recent implementation of the Metre Treaty signed in 1875. Basic features of the original SI are that (a) seven units are chosen as “base units”, all the others being “derived units”, and (b) the definitions of the base units should not create interdependence. This way, the SI conforms to the basic principle of the Metre Treaty that each signatory country can realise its choice of primary national standards of the very definitions of the units without needing to resort to calibrations obtained from another country, and without obligation to have them realised for all the units. A mismatch already occurs to some extent with respect to the above features in the present definitions of SI base units. This contribution, strictly based on metrological considerations, illustrates how the present proposal concerning new definitions for the base units, called “New SI”, would extend the mismatch. In this frame, also the meaning is discussed of the concepts of hierarchy and traceability in metrology. By outlining some of the consequences, a discussion is stimulated related to the status of base unit, to the meaning of calibration at the level of the standards of the unit definitions, and to the interdependence of countries’ standards.

Appendix

The numerical values of the units deriving from the proposed new definitions using constants are shown in Table 3, where the asterisk indicates stipulated values: for this purpose, the CODATA 2010 adjusted values are used here as they are in [3]—but see [14] about problems in using CODATA values.

Table 3 Numerical values of the units reported in Table 2

The method of computation of the uncertainties in column 4 of Table 3 is not un-ambiguous, since c ₀ and Δν(¹³³Cs) are already stipulated at the present time.

The original uncertainties of c ₀ and Δν(¹³³Cs) at the moment of their stipulation are known: for c ₀ the datum of the Comité Consultatif pour la Définition du Mètre (CCDM, 1983) is indicated in [25]: c ₀ = (299 792 458.33 ± 0.6) m s⁻¹. The value Δν(¹³³Cs) = (9192 631 770 ± 20) s⁻¹ was drawn from [26]. Then, the usual propagation law of these uncertainties, and of those associated to h ({u(h)} = 29×10⁻⁴²), e ({u(e)} = 35×10⁻²⁸), k _B ({u(k _B)} = 13×10⁻³⁰) and N _A ({u(N _A)} = 27×10⁻³¹) [27], was used here to obtain the reported figures in the last column of Table 3.

The uncertain numerical values should be used as criteria for truncation of the stipulated numerical values [28].