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 On the future revision of the SI

At its 25th meeting (November 2014) the CGPM adopted a Resolution on the future revision of the International System of Units. This Resolution built on the CGPM's previous Resolution (2011), which took note of the CIPM's intention to propose a revision of the SI and set out a detailed road-map towards the future changes.

 In the "New SI" four of the SI base units – namely the kilogram, the ampere, the kelvin and the mole – will be redefined in terms of constants; the new definitions will be based on fixed numerical values of the Planck constant (h), the elementary charge (e), the Boltzmann constant (kB), and the Avogadro constant (NA), respectively. Further, the definitions of all seven base units of the SI will also be uniformly expressed using the explicit-constant formulation, and specific mises en pratique will be drawn up to explain the realization of the definitions of each of the base units in a practical way.

In the "New SI" all units are defined in terms of a set of seven reference constants, to be known as the "defining constants of the SI", namely the caesium hyperfine splitting frequency, the speed of light in vacuum, the Planck constant, the elementary charge (i.e. the charge on a proton), the Boltzmann constant, the Avogadro constant, and the luminous efficacy of a specified monochromatic source.

This results in a simpler and more fundamental definition of the entire SI, and dispenses with the last of the definitions based on a material artefact – the international prototype of the kilogram.

In brief, the (new) SI will be the system of units in which:

• the ground state hyperfine splitting frequency of the caesium 133 atom (133Cs)hfs is exactly 9 192 631 770 hertz,

• the speed of light in vacuum c is exactly 299 792 458 metre per second,

• the Planck constant h is exactly 6.626 06X x 10–34 joule second,

• the elementary charge e is exactly 1.602 17X x 10–19 coulomb,

• the Boltzmann constant kB is exactly 1.380 6X x 10–23 joule per kelvin,

• the Avogadro constant NA is exactly 6.022 14X x 1023 reciprocal mole,

• the luminous efficacy Kcd of monochromatic radiation of frequency 540 x 1012 Hz is exactly 683 lumen per watt,

where

• the hertz, joule, coulomb, lumen, and watt, with unit symbols Hz, J, C, lm, and W, respectively, are related to the units second, metre, kilogram, ampere, kelvin, mole, and candela, with unit symbols s, m, kg, A, K, mol, and cd, respectively, according to Hz = s–1, J = m2 kg s–2, C = s A, lm = cd m2 m–2 = cd sr, and W = m2 kg s–3,

• the symbol X represents one or more additional digits to be added to the numerical values of h, e, kB, and NA, using values based on the most recent CODATA adjustment.

The SI may alternatively be defined by statements that explicitly define seven individual base units: the second, metre, kilogram, ampere, kelvin, mole, and candela. These correspond to the seven base quantities time, length, mass, electric current, thermodynamic temperature, amount of substance, and luminous intensity. All other units are then obtained as products of powers of the seven base units, which involve no numerical factors; these are called coherent derived units.

For full details the reader is referred to the formal texts of the adopted Resolutions:

 Resolution 1 of the CGPM (2014): On the future revision of the International System of Units, the SI Resolution 1 of the CGPM (2011): On the possible future revision of the International System of Units, the SI Resolution 12 of the CGPM (2007): On the possible redefinition of certain base units of the International System of Units (SI)

The revision of the SI will ensure that the SI continues to meet the needs of science, technology, and commerce in the 21st century.

Of the seven base units of the SI, only the kilogram is still defined in terms of a material artefact, namely the international prototype kept at the BIPM. The major disadvantage of the present definition of the kilogram is that it refers to the mass of the artefact which, by its very nature, we know cannot be absolutely stable.

The results of comparisons between the official copies and the international prototype show some divergence with time. The graph opposite shows changes of about 5 parts in 108, equivalent to 50 µg, in the mass of the standards since their first calibration more than 100 years ago. Note that this graph shows only the relative changes from the mass of the international prototype (corresponding to the zero value of the y-axis). The drift in the mass of the international prototype itself since 1889 cannot be shown but it must certainly be present. The rate of change of its mass can be determined only by absolute experiments which up to now are of insufficiently high precision.

Unknown changes in the mass unit also influence the electrical units, because the definition of the ampere is related to the kilogram. Similarly, the definitions of the mole and candela also depend on the kilogram.

At its 21st meeting (1999) the CGPM therefore recommended in its Resolution 7 that efforts continue to refine experiments linking the unit of mass to fundamental constants with a view to a future "quantum-based" redefinition of the kilogram. Any new definition would need to be consistent within some parts in 108 with the present definition to ensure continuity of mass values.

When the definition of the kilogram is based on an invariant of nature instead of a material artefact, it will be possible to realize the SI unit of mass at any place, at any time and by anyone (see also What is a mise en pratique?). Resolution 1 (2011) also highlights the following advantages:

 The uncertainties of all SI electrical units realized directly or indirectly by means of the Josephson and quantum Hall effects together with the SI values of the Josephson and von Klitzing constants KJ and RK would be significantly reduced if the kilogram were redefined so as to be linked to an exact numerical value of h, and if the ampere were to be redefined so as to be linked to an exact numerical value of the elementary charge e. The kelvin is currently defined in terms of an intrinsic property of water that, while being an invariant of nature, in practice depends on the purity and isotopic composition of the water used. The kelvin would be better defined if it were linked to an exact numerical value of the Boltzmann constant kB. Redefining the mole so that it is linked to an exact numerical value of the Avogadro constant NA would have the consequence that it is no longer dependent on the definition of the kilogram even when the kilogram is defined so that it is linked to an exact numerical value of h. This would thereby emphasize the distinction between the quantities "amount of substance" and "mass". The uncertainties of the values of many other important fundamental constants and energy conversion factors would be eliminated or greatly reduced if h, e, kB and NA had exact numerical values when expressed in SI units.

The following road-map sets out the likely timescale to redefinition of the units in 2018:

An important date to note is the closing date for the publication of new data to be considered by the CODATA Task Group on Fundamental Constants for the special adjustment of the fundamental constants in preparation for the redefinition. New results for inclusion in this adjustment must be accepted for publication by 1 July 2017.

In order to encourage communication, awareness and debate on the future revision of the SI, access is given here to the following key document, which is currently at consultation stage with the national metrology institutes and the CIPM:

 [dated 10 November 2016]

The CIPM Consultative Committees are preparing draft mises en pratique for the future new definitions of the units:

CCEM:
 [Draft #1, CCEM/09-05]
CCM:
 [version 9.0, CCM/15-02A]
CCQM:
 [CCQM/16-04]
CCT:
 [CCT/TEMP-10]

Of course, none of these documents can be finalized until the redefinitions are decided.