2019 revision of the SI

The seven SI base units and the interdependency of their current definitions

A committee of the International Committee for Weights and Measures (CIPM) has proposed revised formal definitions of the SI base units, which are being examined by the CIPM and which may be considered by the 25th CGPM, in 2015.

The last major overhaul of the metric system was in 1960 when the International System of Units (SI) was formally published as a coherent set of units of measure. SI is structured around seven base units that have apparently "arbitrary" definitions and another twenty units that are derived from these base units. Although the units themselves form a coherent system, the definitions themselves do not. The proposals before the CIPM seek to remedy this by using the fundamental quantities of nature as the basis for deriving the base units. This will mean, amongst other things, archiving the prototype kilogram. The second and the metre are already defined in such a manner.

There have been numerous criticisms of the revised definitions since their initial proposal, and it has been argued that the proposal for the new SI requires frank and open discussion before decisions are made.

Background to the proposal of new SI definitions

In 1875, twenty of the most industrially developed nations of the world met for the Convention of the Metre. The result was the signing of the Treaty of the Metre under which three bodies were set up to regulate units of measure that were to be used internationally. They were:

• CGPM (General Conference on Weights and Measures / Conférence Générale des Poids et Mesures) – The Conference meets every four to six years and consists of representatives of the nations who had signed the convention. It discusses and examines the arrangements required to ensure the propagation and improvement of the International System of Units and it endorses the results of new fundamental metrological determinations.
• CIPM (International Committee for Weights and Measures/Comité international des poids et mesures) The Committee consists of eighteen eminent scientists, each from a different country, nominated by the CGPM. The CIPM meets annually and is tasked to advise the CGPM. The CIPM has set up a number of sub-committees, each charged with a particular area of interest. One of these, the CCU (Consultative Committee for Units), amongst other things, advises the CIPM on matters concerning units of measurement.
• BIPM (International Bureau for Weights and Measures/Bureau international des poids et mesures) – The Bureau provides laboratory facilities and in the secretariat for the CIPM and the CGPM.

Since 1960, when the definition of the metre was linked to a particular wavelength of light rather than the international prototype metre, the only unit of measure that has been dependent on a particular artifact has been the kilogram. Over the years, small drifts which could be as high as 20×10⁻⁹ kilograms per annum in the mass of the international prototype kilogram have been detected. At the 21st meeting of the GCPM (1999), national laboratories were urged to investigate ways of breaking the link between the kilogram and a specific artifact.

A report published in 2007 by the Consultative Committee for Thermometry to the CIPM noted that their current definition of temperature has proved to be unsatisfactory for temperatures below 20 K and for temperatures above 1300 K. The committee was of the view that the Boltzmann constant provided a better basis for temperature measurement than did the triple point of water, as it overcame these difficulties.

At its 23rd meeting (2007), the GCPM mandated the CIPM to investigate the use of natural constants as the basis for all units of measure rather than the artifacts that were then in use. The following year this was endorsed by the International Union of Pure and Applied Physics (IUPAP). At a meeting of the CCU held in Reading, United Kingdom in September 2010, a resolution and draft changes to the SI brochure that were to be presented to the next meeting of the CIPM in October 2010 were agreed to in principle. The CIPM meeting of October 2010 found that "the conditions set by the General Conference at its 23rd meeting have not yet been fully met. For this reason the CIPM does not propose a revision of the SI at the present time"; however the CIPM has prepared a resolution for consideration at the 24th CGPM to agree to the new definitions in principle, but not to implement them until the details have been finalised.

The proposals

In this section, an "X" at the end of a number means that the final digit is yet to be agreed upon.

The CCU has proposed that in addition to the speed of light, four constants of nature be defined to have exact values:

• Planck's constant h is exactly 6.62606X×10⁻³⁴joule second (J·s).
• An elementary charge e is exactly 1.60217X× 10⁻¹⁹coulomb (C).
• Boltzmann constant k is exactly 1.38065X×10⁻²³joule per kelvin (J·K⁻¹).
• Avogadro constant N_A is exactly 6.02214X×10²³reciprocal mole (mol⁻¹).

These constants were described in the 2006 version of the SI manual; the latter three were defined as "constants to be obtained by experiment".

It is proposed that the following constants of nature be retained unchanged:

• The speed of light c is exactly 299792458metres per second (m·s⁻¹).
• The ground state hyperfine splitting frequency of the caesium-133 atom Δν(¹³³Cs)_hfs is exactly 9192631770 hertz (Hz).
• The luminous efficacy K_cd of monochromatic radiation of frequency 540×10¹²Hz is exactly 683 lumen per watt (lm·W⁻¹).

The seven definitions above are rewritten below after converting the derived units (joule, coulomb, hertz, lumen and watt) into the seven base units (second, metre, kilogram, ampere, kelvin, mole and candela). In the list that follows, the symbol sr stands for the dimensionless unit steradian.

• Δν(¹³³Cs)_hfs = 9192631770s⁻¹
• c = 299792458s⁻¹·m
• h = 6.62606X×10⁻³⁴s⁻¹·m²·kg
• e = 1.60217X×10⁻¹⁹s·A
• k = 1.38065X×10⁻²³s⁻²·m²·kg·K⁻¹
• N_A = 6.02214X×10²³mol⁻¹
• K_cd = 683 s³·m⁻²·kg⁻¹·cd·sr

In addition the CCU has proposed that:

• The international prototype kilogram is retired and that the current definition of the kilogram is abrogated.
• The current definition of the ampere is abrogated.
• The current definition of the kelvin is abrogated.
• The current definition of the mole is revised.

These changes will have the effect of redefining the SI base units, though the definitions of the derived SI units will remain the same.

Proposed changes to the base units

It is proposed that the text of the definitions of all the base units be either refined or rewritten. The current (2008) and proposed (2011) definitions are given below. In many cases the final digit of any constant is yet to be agreed, so it has been represented by an "X"

Relations between proposed SI units definitions (in color) and with seven fundamental constants of nature (in grey) with fixed numerical values in the proposed system.

Second

The proposed definition is effectively the same as the current definition, the only difference being that the conditions under which the measurements are made will be tightened up.

Current definition: The second is the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.

Proposed definition: The second, s, is the unit of time; its magnitude is set by fixing the numerical value of the ground state hyperfine splitting frequency of the caesium-133 atom, at rest and at a temperature of 0 K, to be equal to exactly 9192631770 when it is expressed in the unit s⁻¹, which is equal to Hz.

Metre

The proposed definition is effectively the same as the current definition, the only difference being that the tightening up of the definition of the second will propagate to the metre

Current definition: The metre is the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second.

Proposed definition: The metre, m, is the unit of length; its magnitude is set by fixing the numerical value of the speed of light in vacuum to be equal to exactly 299792458 when it is expressed in the unit m·s⁻¹.

Kilogram

The definition of the kilogram is undergoing a fundamental change - the current definition defines the kilogram as being the mass of the international prototype kilogram, the new definition relates it to the equivalent energy of a photon via Planck's constant.

Current definition: The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.

Proposed definition: The kilogram, kg, is the unit of mass; its magnitude is set by fixing the numerical value of the Planck constant to be equal to exactly 6.62606X×10⁻³⁴ when it is expressed in the unit s⁻¹·m²·kg, which is equal to J·s.

One consequence of this change is that the new definition makes the definition of the kilogram dependent on the definitions of the second and the metre.

Ampere

The definition of the ampere is undergoing a major overhaul—the current definition, which is difficult to realise with high precision in practice, is being replaced by a definition which is more intuitive and which is easier to realise in practice.

Current definition: The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2×10⁻⁷ newton per metre of length.

Proposed definition: The ampere, A, is the unit of electric current; its magnitude is set by fixing the numerical value of the elementary charge to be equal to exactly 1.60217X×10⁻¹⁹ when it is expressed in the unit A·s, which is equal to C.

One consequence of this change is that the new definition of the Ampere will not be dependent on the definitions of the kilogram and the metre. In addition, by fixing the elementary charge to an exact value, the vacuum permeability, vacuum permittivity and impedance of free space, which are currently exact along with the speed of light, will all consequently carry experimental error.

Kelvin

The definition of the kelvin will undergo a fundamental change if the proposals are accepted. Rather than using points where water changes state to fix the temperature scale the proposal recommends that the energy equivalent as given by Boltzmann's equation be used.

Current definition: The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.

Proposed definition: The kelvin, K, is the unit of thermodynamic temperature; its magnitude is set by fixing the numerical value of the Boltzmann constant to be equal to exactly 1.38065X×10⁻²³ when it is expressed in the unit s⁻²·m²·kg K⁻¹, which is equal to J·K⁻¹.

One consequence of this change is that the new definition makes the definition of the kelvin depend on the definitions of the second, the metre, and the kilogram.

Mole

The current definition of the mole links it to the kilogram. The proposed definition will break that link by making a mole a specific number of entities of the substance in question.

Current definition: The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

Proposed definition: The mole, mol, is the unit of amount of substance of a specified elementary entity, which may be an atom, molecule, ion, electron, any other particle or a specified group of such particles; its magnitude is set by fixing the numerical value of the Avogadro constant to be equal to exactly 6.02214X×10²³ when it is expressed in the unit mol⁻¹.

One consequence of this change is that the current defined relationship between the mass of the ¹²C atom, the dalton, the kilogram, and Avogadro's number will no longer be valid. One of the following must change:

• the mass of ¹²C, which would no longer be exactly 12 dalton
• the mass of the dalton itself. This would change the numerical masses of all atoms except ¹²C
• the number of ¹²C atoms in 12 grams or 0.012 kilogram, which is currently N_A by definition.

Candela

The proposed definition is effectively the same as the current definition, but rephrased.

Current definition: The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×10¹² Hz and that has a radiant intensity in that direction of 1/683 watt per steradian.

Proposed definition: The candela, cd, is the unit of luminous intensity in a given direction; its magnitude is set by fixing the numerical value of the luminous efficacy of monochromatic radiation of frequency 540×10¹² Hz to be equal to exactly 683 when it is expressed in the unit s³·m⁻²·kg⁻¹·cd·sr, or cd·sr·W⁻¹, which is equal to lm·W⁻¹.

Impact on reproducibility

Overall the changes in the definitions will give an improvement in the uncertainty of the reproduction of the base units using the standard mise en pratique (practical technique).

The following table catalogues the improvements:

Relative uncertainty of various physical measurements
Unit	Constant used as reference	Symbol	Current definitions	Proposed definitions
kg	Mass of International prototype kilogram	m(K)	exact	5.0 × 10−8
	Planck constant	h	5.0 × 10−8	exact
A	magnetic constant	μ0	exact	6.9 × 10−10
	Elementary charge	e	2.5 × 10−8	exact
K	Temperature of triple point of water	TTPW	exact	1.7 × 10−6
	Boltzmann constant	k	1.7 × 10−6	exact
mol	Molar mass 12C	M(12C)	exact	1.4 × 10−9
	Avogadro constant	NA	1.4 × 10−9	exact

The relative uncertainty in measuring the second will remain at 1×10⁻¹⁴ and that for the metre will remain at 2.5×10⁻⁸.

Criticisms of the proposed new SI definitions

Price has argued that the new proposal will:

• cause confusion because the new explicit-constant definitions do not relate a unit to an example of its quantity
• risk damage to the enterprise of science because the circular definition of units will render it impossible to detect any future change in fundamental constants
• cause economic damage due to increased transaction costs and barriers to international trade

Leonard has argued that "the fundamental concept of the mole requires the number of entities comprising one mole, i.e. Avogadro's number, to be exactly equal to the gram-to-dalton mass ratio" and that the proposal breaks this compatibility condition by defining the kilogram, dalton and mole independently.

Pavese has argued that a number of issues need to be better understood before the definitions are changed. The issues include the count nature and the value of the Avogadro number; the loss of the concept of base unit; the possibility of checking future changes in the 'fundamental constants', and the shift to the unit of the experimental uncertainty.

See also

• International Vocabulary of Metrology
• International System of Units
• Physical constant
• SI base unit

External links

• The New SI: Units of measurement based on fundamental constants