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 artifacts as the prototype metre and kilogram. In 1960 the metre was redefined in terms of the wavelength of light from a specified source, making it derivable from nature, but the kilogram has been defined by an artifact 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."1
Further details are found in the draft chapter of the Ninth SI Units Brochure.2
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.
- 1 Background
- 2 The proposal
- 3 Impact on base unit definitions
- 4 Impact on reproducibility
- 5 Acceptance
- 6 Comment
- 7 See also
- 8 Notes
- 9 References
- 10 External links
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 artifact to define the kilogram.
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.3
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 take custody of the international prototype kilogram and metre and to regulate comparisons with national prototypes.45 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.6
- BIPM (International Bureau for Weights and Measures / Bureau international des poids et mesures)—The Bureau provides safe keeping of the international prototype kilogram and metre, provides laboratory facilities for regular comparisons of the national prototypes with the international prototype and is the secretariat for the CIPM and the CGPM.
The first CGPM (1889) formally approved the use of 40 prototype metres and 40 prototype kilograms from the British firm Johnson Matthey as the standards mandated by the Convention of the Metre.7 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.8 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 electric current (1946), luminosity (1946), temperature (1948), time (1956) and molar mass (1971).9
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".11 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".12
Changing the underlying principles behind the definition of the SI base units is not without precedent. The 13th CGPM (1967) replaced the original definition of the second (which was based on a back-calculation of the Earth's rotation in the year 1900) with a definition based on the frequency of the radiation emitted between two hyperfine levels of the ground state of the caesium 133 atom. Similarly, the 17th CGPM (1983) replaced the 1960 definition of the metreNote 2 with one where the metre is derived from the speed of light where the speed of light had been defined exactly in terms of metres per second.13
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.14 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.1516
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.17
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.18
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).19 At a meeting of the CCU held in Reading, United Kingdom, in September 2010, a resolution20 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.21 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.Note 3 For this reason the CIPM does not propose a revision of the SI at the present time";23 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.24 This resolution was accepted by the conference,25 and in addition the CGPM moved the date of the 25th meeting forward from 2015 to 2014.2627
- 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.2 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.
The CCU proposal recommended that the text of the definitions of all the base units be either refined or rewritten changing the emphasis from explicit-constant to explicit-unit type definitions.28 Explicit-unit type definitions define a unit in terms of a specific example of that unit—for example in 1324 Edward II defined the inch as being the length of three barleycorns29 and since 1889 the kilogram has been defined as being the mass of the International Prototype Kilogram. In explicit-unit definitions, a constant of nature is given a specified value and the definition of the unit emerges as a consequence. For example, in 1983, the speed of light was defined to be exactly 299,792,458 metres per second and as long as the second has already been defined, the length of the metre can be defined.
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 which is an artifact, not a constant of nature31 while the new definition relates it to the equivalent energy of a photon via the Planck 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.
Since the current definition contains a reference to force which has the dimensions MLT-2 it follows that in SI the kilogram, metre and second, the base units representing these dimensions, must be defined before the ampere can be defined. Other consequences of this definition are that in SI the value of vacuum permeability (μ0) is fixed at exactly 4π×10−7 H⋅m−1.32 Since the speed of light in vacuum (c) is also fixed, it follows from the relationship
that the vacuum permittivity (ε0) has a fixed value and from
One consequence of the proposed changes to the definition of the ampere is that the definition will no longer be dependent on the definitions of the kilogram and the metre, but will still be dependent on the definition of the second. In addition the vacuum permeability, vacuum permittivity and impedance of free space, which, in the current definition have exact values will, in the future, be subject to experimental error.34
The definition of the kelvin will undergo a fundamental change if the proposal is accepted. Rather than using the triple point of water 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.
For a physical interpretation of this new definition, consider an ideal gas concentrated such that the average volume per molecule is 1.38065X×10−23 m3. That is the volume of a cube with a side length of about 24 nm. The ratio of the gas's temperature and pressure would be defined exactly equal to 1 K/Pa.
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.
Apart from the candela,Note 435 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 5 It should noted that in practice G can only be measured with a relative uncertainty of 10−4Note 6 which would have resulted in upper limit of the kilogram's reproducibility being 10−4 whereas the current international prototype kilogram can be measured with a relative uncertainty of 5 × 10−8.34 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)36 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.
|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|
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
|fine-structure constant||α||6.8 × 10−10||6.8 × 10−10||N/A|
|von Klitzing constant||RK||6.8 × 10−10||exact||h/e2|
|temperature of triple point of water||TTPW||exact||1.7 × 10−6||N/A|
|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.38 This approval has since been given.39 Following the proposal to redefine the mole by fixing the value of the Avogadro number, Brian Leonard of the University of Akron, writing in Metrologia proposed that the dalton (Da) be redefined as an SI derived unit exactly equal to (1/1000NA) kg; but that the unified atomic mass unit (mu) retain its current definition based on the mass of 12C, ceasing to be SI. This would result in the dalton and the atomic mass unit potentially differing from each other by a factor of the order of 10−9.40
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.4142
- 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.43
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 × 10−8.44
As of March 2013[update] the proposed redefinition is known as the "New SI",1 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".45
In 2010 Marcus Foster of the Commonwealth Scientific and Industrial Research Organisation published a wide-ranging critique of SI in which he raised numerous issues ranging from basic issues such as the absence of the symbol "Ω" from most Western keyboards to the abstract issues such as inadequate formalism in the metrological concepts on which SI is based. The changes proposed in the New SI only addressed issues regarding the definition of the base units including new definitions of the candela and the mole—units that Foster argued were not true base units. Other issues raised by Foster fell outside the scope of the proposal.46
Concerns have been expressed that the use of explicit-constant definitions of the unit being defined that are not related to an example of its quantity will have many adverse effects.47 Although this criticism applies to the proposed linking of the kilogram to the Planck constant via a route that requires a knowledge of both special relativity and quantum mechanics48 it does not apply to the proposed definition of the ampere which is closer to an example of its quantity than is the current definition.49 Some observers have welcomed the proposal to base the definition of electric current on the charge of the electron rather than the current definition of a force between two parallel current-carrying wires—since the nature of the electromagnetic interaction between two bodies at the quantum electrodynamics level is somewhat different from the nature at classical electrodynamic levels, it is considered inappropriate to use classical electrodynamics to define quantities that exist at quantum electrodynamic levels.34
When the scale of the divergence between the IPK and national kilogram prototypes was reported in 2005, a debate arose on how best to redefine the kilogram - should the kilogram be defined in terms of the mass of the silicon-28 atom or should it be determined using the watt balance? The mass of a silicon atom could be determined using the Avogadro project and using the Avogadro Number be linked directly to the kilogram.50
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 (NA) and Avogadro's number (NN).Note 7 This direct link has caused many to argue that the mole is not a true physical unit, but, in the words of the Swedish philosopher Johansson, the mole is a "scaling factor".4651
The SI Brochure (8th edition) implicitly defines the dalton as 0.001÷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.5253
Temperature is somewhat of an enigma - room temperature can be measured by means of expansion and contraction of a liquid in a thermometer, but high temperatures are often associated with a colour. Wojciech T. Chyla, approaching the structure of SI from a philosophical point of view in the Journal of the Polish Physical Society, argued that temperature is not a real base unit but is rather an average of the thermal energies of the individual particles that make up body concerned.34 He noted that in many theoretical papers, temperature is represented by the quantities Θ or β where
and kb is the Boltzmann constant.
Chyla acknowledged however that in the macroscopic world temperature plays the role of a base unit as much of the theory of thermodynamics is based on temperature. Foster,46 writing from the point of view of quality control argued that the introduction of the Boltzmann constant into the definition of temperature was an unnecessary complication.
The Consultative Committee for Thermometry, part of the International Committee for Weights and Measures publishes a mise en pratique (practical technique), last updated in 1990, for measuring temperature which, at very low and at very high temperatures, makes great use of linking energy to temperature via the Boltzmann constant.5455
Foster argued that "luminous intensity [the candela] is not a physical quantity, but a photobiological quantity that exists in human perception" thereby questioning whether or not the candela should be a base unit.46
- 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).
- Since the adoption of SI in 1960, the metre had been defined in terms of the wavelength of krypton 86 radiation.
- In particular the CIPM was to prepare a detailed mise en pratique for each the new definitions of the kilogram, ampere, kelvin and mole set by the 23rd CGPM22
- 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.
- 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 of the Avogadro constant and Avogadro's number are numerically the same, but while NA has the units of mole-1,NN is a pure number.
- Michael Kuehne (22 March 2012). "Redefinition of the SI". Keynote address, ITS9 (Ninth International Temperature Symposium). Los Angeles: NIST. Retrieved 2012-03-01.
- Ian Mills (27 September 2010). "Draft Chapter 2 for SI Brochure, following redefinitions of the base units". BIPM. Retrieved 2012-03-01.
- Alder, Ken (2002). The Measure of all Things - The Seven-Year-Odyssey that Transformed the World. London: Abacus. p. 1. ISBN 0349115079.
- Metric Convention of 1875 [English translation]. Washington, D.C.: Office of the President of the United States. 1876.
- "The Metre Convention". Sèvres, France: International Bureau of Weights and Measures. Retrieved 2013-06-21.
- "CIPM: International Committee for Weights and Measures". Sèvres, France: BIPM. Retrieved 2010-10-03.
- "Resolution of the 1st meeting of the CGPM (1889)". Sèvres, France: International Bureau of Weights and Measures. Retrieved 2013-06-21.
- Jabbour, Z.J.; Yaniv, S.L. (2001). "The Kilogram and Measurements of Mass and Force". J. Res. Natl. Inst. Stand. Technol. (National Institute of Standards and Technology (NIST) 106 (1): 25–46. Retrieved 2011-03-28.
- International Bureau of Weights and Measures (2006), The International System of Units (SI) (8th ed.), pp. 95, 97, 138–140, ISBN 92-822-2213-6
- G. Girard (1994). "The Third Periodic Verification of National Prototypes of the Kilogram (1988–1992)". Metrologia 31 (4): 317–336. Bibcode:1994Metro..31..317G. doi:10.1088/0026-1394/31/4/007.
- "Resolution 6 of the 9th meeting of the CGPM (1948): Proposal for establishing a practical system of units of measurement". Retrieved 2011-03-23.
- "Resolution 12 of the 11th meeting of the CGPM (1960): Système International d'Unités". Sèvres, France. Retrieved 2011-03-23.
- International Bureau of Weights and Measures (2006), The International System of Units (SI) (8th ed.), pp. 112–116, ISBN 92-822-2213-6
- Peter Mohr (6 December 2010). "Recent progress in fundamental constants and the International System of Units". Third Workshop on Precision Physics and Fundamental Physical Constants. Retrieved 2011-01-02.
- Whipple, Tom (7 January 2013). "The dirty secret of why you are not quite as heavy as you thinkhttp://www.livescience.com/26017-kilogram-gained-weight.html". The Times (London). p. 15. Retrieved 2011-03-23.
- Ghose, Tia (6 January 2013). "The Kilogram Has Gained Weight". LiveScience. Retrieved 2011-03-23.
- Crease, Robert P (22 March 2011). "Metrology in the balance". Physics World. Institute of Physics. Retrieved 2012-06-28.
- Fischer, J. et al (2 May 2007). "Report to the CIPM on the implications of changing the definition of the base unit kelvin". Retrieved 2011-01-02.
- "Resolution proposal submitted to the IUPAP Assembly by Commission C2 (SUNAMCO)". International Union of Pure and Applied Physics. 2008. Retrieved 2011-05-08.
- Ian Mills (29 September 2010). "On the possible future revision of the International System of Units, the SI". CCU. Retrieved 2011-01-01.
- Ian Mills (29 September 2010). "Draft Chapter 2 for SI Brochure, following redefinitions of the base units". CCU. Retrieved 2011-01-01.
- "Resolution 12 of the 23rd meeting of the CGPM (2007)". Sèvres, France: General Conference on Weights and Measures. Retrieved 2013-06-21.
- "Towards the "new SI"". International Bureau of Weights and Measures (BIPM). Retrieved 2011-02-20.
- "On the possible future revision of the International System of Units, the SI - Draft Resolution A". International Committee for Weights and Measures (CIPM). Retrieved 2011-07-14.
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