Proposed redefinition of SI base units
- For a topical guide to this subject, see Outline of the metric system.
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 'General Conference on Weights and Measures', in 2014. The metric system was originally conceived as a system of measurement that was derivable from nature. When the metric system was first introduced in France in 1799 technical problems necessitated the use of artefacts as the prototype metre and kilogram. In 1960 the metre was redefined in terms of the speed of light, making it derivable from nature, but the kilogram has been defined by an artefact ever since its introduction. If the proposed redefinition is accepted, the metric system (SI) will, for the first time, be wholly derivable from nature.
The proposal can be summarised as follows:
- "There will still be the same seven base units (second, metre, kilogram, ampere, kelvin, mole, and candela). Of these, the kilogram, ampere, kelvin and mole will be redefined by choosing exact numerical values for the Planck constant, the elementary electric charge, the Boltzmann constant, and the Avogadro constant, respectively. The second, metre and candela are already defined by physical constants and it is only necessary to edit their present definitions. The new definitions will improve the SI without changing the size of any units, thus ensuring continuity with present measurements."
Further details are found in the draft chapter of the Ninth SI Units Brochure.
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 do not. The proposal before the CIPM seeks to remedy this by using the fundamental quantities of nature as the basis for deriving the base units. This will mean, amongst other things, that the prototype kilogram will cease to be used as the definitive replica of the kilogram. The second and the metre are already defined in such a manner.
A number of authors have published criticisms of the revised definitions — in particular that proposal had failed to address the impact of breaking the link between the mole, kilogram, the dalton, the Avogadro constant and Avogadro's number.
The basic structure of SI was developed over a period of about 170 years (1791 to 1960). Since 1960 technological advances have made it possible to address various weaknesses in SI, notably the dependence on an artefact to define the kilogram.
Development of SI 
During the early years of the French Revolution, the leaders of the French National Constituent Assembly decided to introduce a completely new system of measurement based on the principles of logic and natural phenomena. The resulting mètre des archives and kilogramme des archives were defined in terms of artefacts that were a "best attempt" at fulfilling these principles.
In 1875, by which time the use of the metric system had become widespread in Europe and in Latin America, twenty industrially developed nations 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 delegates 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 is the secretariat for the CIPM and the CGPM.
In 1889 the CGPM took delivery of 40 prototype metres and 40 prototype kilograms from the British firm Johnson Matthey. One of each of these was nominated by lot as the international prototypes, other copies were retained by the CGPM as working copies and the rest were distributed to member nations for use as their national prototypes. At regular intervals the national prototypes were compared with and recalibrated against the international prototype.
In 1921 the Convention of the Metre was revised and the mandate of the CGPM was extended to provide standards for all units of measure, not just mass and length. In the ensuing years the CGPM took on responsibility for providing standards of time, electric current, temperature, molar mass and luminosity.
The 9th CGPM (1948) instructed the CIPM "to make recommendations for a single practical system of units of measurement, suitable for adoption by all countries adhering to the Metre Convention". The recommendations based on this mandate were presented to the 11th CGPM (1960) where they were formally accepted and given the name "Système International d'Unités" and its abbreviation "SI".
Impetus for change 
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 artefact has been the kilogram. Over the years, drifts of up to 2×10−8 kilograms per annum in the national prototype kilograms relative to the international prototype kilogram have been detected. There was no way of determining whether the national prototypes were gaining mass or whether the IPK was losing mass. At the 21st meeting of the CGPM (1999), national laboratories were urged to investigate ways of breaking the link between the kilogram and a specific artefact. Newcastle University metrologist Peter Cumpson has since identified mercury vapour absorption or carbonaceous contamination as possible causes of this drift.
Independently of this drift having been identified, the Avogadro project and development of the Watt balance promised methods of indirectly measuring mass with a very high precision. These projects provided tools that would enable alternative means of redefining the kilogram.
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 kelvins and for temperatures above 1300 kelvins. 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 artefacts 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 presented a resolution for consideration at the 24th CGPM (17–21 October 2011) to agree the new definitions in principle, but not to implement them until the details have been finalised. This resolution was accepted by the conference, and in addition the CGPM moved the date of the 25th meeting forward from 2015 to 2014.
The proposal 
- In this section, an "X" at the end of a number means one or more final digits yet to be agreed upon.
In 2011 the CCU published a draft of the proposed change in the form of an amendment that should be made to the 8th edition of the SI Brochure. In it they proposed that in addition to the speed of light, four further constants of nature should be defined to have exact values:
These constants were described in the 2006 version of the SI manual; the latter three were defined as "constants to be obtained by experiment".
The CCU also proposed that the numerical values associated with 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 Kcd 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
- NA = 6.02214X×1023mol−1
- Kcd = 683 s3•m−2•kg−1•cd•sr
In addition the CCU proposed that
These changes will have the effect of redefining the SI base units, though the definitions of the derived SI units will remain the same.
Impact on base unit definitions 
The CCU proposal recommended 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"
The proposed definition of the second is effectively the same as the current definition, the only difference being that the conditions under which the measurements are made are more rigorously defined.
- 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.
The proposed definition of the metre is effectively the same as the current definition, the only difference being that the additional rigour in 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.
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.
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 that is more intuitive and that is easier to realise.
- 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.
The definition of the kelvin will undergo a fundamental change if the proposal is 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.
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 that 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 a 12C atom is exactly 12 dalton
- the number of dalton in a gram is exactly the numerical value of Avogadro's constant
The draft SI brochure assumes the first will remain true, which would mean that the second will no longer be true. The molar mass constant, while still with great accuracy remaining equal to 1 g/mol, will no longer be exactly equal to that.
The proposed definition of the candela is effectively the same as the current definition, but has been 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 
Apart from the candela,[Note 2] all the base units will be defined in terms of universal physical constants, but without an explicit one-to-one correspondence between the constants and the base units. Thus six physical constants will be needed to define the six base units.
When the New SI was first designed, there were more than six suitable physical constants from which the designers could choose. For example, once length and time had been established, the universal gravitational constant G could, from a dimensional point of view, be used to define mass.[Note 3] In practice G is an unsuitable physical constant[Note 4] as it can only be measured with a relative uncertainty of 10−4[Note 5] which would have resulted in upper limit of the kilogram's reproducibility being 10−4 — the current international prototype kilogram can be measured with a relative uncertainty of 5 × 10−8. The choice of physical constants was made on the basis of minimal uncertainty associated with measuring the constant and the degree of independence of the constant in respect of other constants that were being used. Although the BIPM has developed a standard mise en pratique (practical technique) for each type of measurement, the mise en pratique used to make the measurement is not part of the measurement's definition — it is merely an assurance that the measurement can be done without exceeding the specified maximum uncertainty.
Physical constants used in the new definitions 
|Relative uncertainty of various physical measurements and associated base units|
|Unit||Constant used as reference||Symbol||Current definitions||Proposed definitions|
|kg||Mass of International prototype kilogram||m(K)||exact||4.4 × 10−8|
|Planck constant||h||4.4 × 10−8||exact|
|A||magnetic constant||μ0||exact||6.8 × 10−10|
|Elementary charge||e||2.2 × 10−8||exact|
|K||Temperature of triple point of water||TTPW||exact||9.1 × 10−7|
|Boltzmann constant||k||9.1 × 10−7||exact|
|mol||Molar mass 12C||M(12C)||exact||4.4 × 10−8|
|Avogadro constant||NA||4.4 × 10−8||exact|
Other physical constants 
There are three categories of physical constants:
- The fundamental constants whose value is by definition fixed.
- Physical constants that are a function of the fundamental constants, for example the von Klitzing constant RK = h/e2. In this case, both e and h are fundamental constants, so the von Klitzing constant has an exact definition.
- Physical constants that were alternative candidates as fundamental constants. These have to be measured separately, but the fundamental constants are often used in calculating these constants.
|Relative uncertainty of various physical measurements||Relationship to
|Constant used as reference||Symbol||Current definitions||Proposed definitions|
unified atomic mass unit or dalton
carbon 12 atomic mass
|5.0 × 10−8
5.0 × 10−8
5.0 × 10−8
|1.4 × 10−9
1.4 × 10−9
1.4 × 10−9
impedance of free space
|6.8 × 10−10
6.8 × 10−10
6.8 × 10−10
|Hall effect constant||α||6.8 × 10−10||6.8 × 10−10||-|
|von Klitzing constant||RK||6.8 × 10−10||exact||h/e2|
|temperature of triple point of water||TTPW||exact||1.7 × 10−6||-|
|Molar gas constant||R||1.7 × 10−6||exact||NAk|
|Stefan–Boltzmann constant||σ||3.6 × 10−6||exact||2π5k4/15h3c2|
|2.2 × 10−8
2.2 × 10−8
In 1993, the International Union of Pure and Applied Chemistry approved the use of the dalton as an alternative to the unified atomic mass unit with the qualification that the GCPM had not given its approval. This approval has since been given. Following the proposal to redefine the mole by fixing the value of the Avogadro number, Leonard has proposed that the dalton (Da) be redefined as being 0.001/NA kg exactly but that the unified atomic mass unit (mu) retain its current definition based on the mass of 12C. This would result in the dalton and the atomic mass unit having different meanings and potentially differing from each other by a factor of the order of 10−9.
Much of the work done by the CIPM is delegated to consultative committees. The CIPM Consultative Committee for Units (CCU) has made the proposed changes while other committees have examined the proposal in detail and have made recommendations regarding their acceptance by the GCPM in 2014. The various consultative committees have laid down a number of criteria that must be met before they will support the CCU's proposal including
- At least three separate experiments be carried out yielding values having a relative standard uncertainty of no more than 5 × 10−8 and at least one of these values should be better than 2 × 10−8. Both the Watt balance and the Avogadro project should be included in the experiments and any differences between these be reconciled.
- The relative uncertainty of Boltzmann constant derived from two fundamentally different methods such as acoustic gas thermometry and dielectric constant gas thermometry be better than one part in 10−6 and that these values be corroborated by other measurements.
On 1 September 2012 the European Association of National Metrology Institutes (Euramet) launched a formal project to reduce the relative difference between the watt-balance and the silicon sphere approach to measuring the kilogram from 17 ± 5 × 10−8 to within 2 × 10−8.
As of March 2013[update] the proposed redefinition is known as the "New SI", but Mohr, in a paper following the CGPM proposal but predating the formal CCU proposal, suggested that since the proposed system makes use of atomic scale phenomena rather than macroscopic phenomena, it should be called the "Quantum SI System".
Concern has been expressed that the proposals will cause confusion because the new explicit-constant definitions do not relate a unit to an example of its quantity and have urged that the implications of the proposal be examined more deeply before irreversible decisions are made.
Concern has also been expressed that the authors of the proposal had failed to address the impact of breaking the link between the mole, kilogram, the dalton (Da), the Avogadro constant and Avogadro's number (NN).[Note 6] The SI Brochure (8th edition) implicitly makes the following definition:
- 1 Da = mass of one 12C atom = 0.12÷NN kg
- where the value of NN is determined by experiment.
The proposal fixes NA, so if the Avogadro constant and Avogadro's number are to be numerically identical, the dalton must be related to either the mass of a single carbon atom or to the kilogram — it cannot be related to both.
See also 
- BIPM website on the New SI, including a FAQ page.
- The New SI: Units of measurement based on fundamental constants
- Prototype No. 8(41) was accidentally stamped with the number 41, but its accessories carry the proper number 8. Since there is no prototype marked 8, this prototype is referred to as 8(41).
- Measurement of the candela also requires a knowledge of the response of the human eye to different wavelengths of light known as the (luminosity function) and denoted by V(λ), a function computed by the International Commission on Illumination (CIE) to different wavelengths of light.
- The dimensions of G are L3M−1T−2, so once standards have been established for length and for time, mass can in theory be deduced from G.
- G was chosen by Wikipedia editors for purposes of illustration only
- The following terms are defined in International vocabulary of metrology – Basic and general concepts and associated terms:
- measurement reproducibility - definition 2.25
- standard measurement uncertainty - definition 2.30
- relative standard measurement uncertainty - definition 2.32
- The two quantities are numerically the same, but while NA has the units of mole-1,NN is a pure number.
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