2019 redefinition of the SI base units explained

In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artifacts such as the standard kilogram.[1] [2] Effective 20 May 2019, the 144th anniversary of the Metre Convention, the kilogram, ampere, kelvin, and mole are now defined by setting exact numerical values, when expressed in SI units, for the Planck constant (), the elementary electric charge (), the Boltzmann constant, and the Avogadro constant, respectively. The second, metre, and candela had previously been redefined using physical constants. The four new definitions aimed to improve the SI without changing the value of any units, ensuring continuity with existing measurements.[3] [4] In November 2018, the 26th General Conference on Weights and Measures (CGPM) unanimously approved these changes,[5] [6] which the International Committee for Weights and Measures (CIPM) had proposed earlier that year after determining that previously agreed conditions for the change had been met. These conditions were satisfied by a series of experiments that measured the constants to high accuracy relative to the old SI definitions, and were the culmination of decades of research.

The previous major change of the metric system occurred in 1960 when the International System of Units (SI) was formally published. At this time the metre was redefined: the definition was changed from the prototype of the metre to a certain number of wavelengths of a spectral line of a krypton-86 radiation, making it derivable from universal natural phenomena.[7] The kilogram remained defined by a physical prototype, leaving it the only artifact upon which the SI unit definitions depend. At this time the SI, as a coherent system, was constructed around seven base units, powers of which were used to construct all other units. With the 2019 redefinition, the SI is constructed around seven defining constants, allowing all units to be constructed directly from these constants. The designation of base units is retained but is no longer essential to define the SI units.

The metric system was originally conceived as a system of measurement that was derivable from unchanging phenomena,[8] but practical limitations necessitated the use of artifacts – the prototype of the metre and prototype of the kilogram – when the metric system was introduced in France in 1799. Although they were designed for long-term stability, the prototype kilogram and its secondary copies have shown small variations in mass relative to each other over time; they are not thought to be adequate for the increasing accuracy demanded by science, prompting a search for a suitable replacement. The definitions of some units were defined by measurements that are difficult to precisely realise in a laboratory, such as the kelvin, which was defined in terms of the triple point of water. With the 2019 redefinition, the SI became wholly derivable from natural phenomena with most units being based on fundamental physical constants.

A number of authors have published criticisms of the revised definitions; their criticisms include the premise that the proposal failed to address the impact of breaking the link between the definition of the dalton[9] and the definitions of the kilogram, the mole, and the Avogadro constant.

Background

See main article: History of the metric system. The basic structure of the SI was developed over about 170 years between 1791 and 1960. Since 1960, technological advances have made it possible to address weaknesses in the SI such as the dependence on a physical artifact 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 new system of measurement that was based on the principles of logic and natural phenomena. The metre was defined as one ten-millionth of the distance from the north pole to the equator and the kilogram as the mass of one thousandth of a cubic metre of pure water. Although these definitions were chosen to avoid ownership of the units, they could not be measured with sufficient convenience or precision to be of practical use. Instead, realisations were created in the form of the French: [[mètre des Archives]] and French: [[kilogramme des Archives]] which were a "best attempt" at fulfilling these principles.[10]

By 1875, use of the metric system had become widespread in Europe and in Latin America; that year, twenty industrially developed nations met for the Convention of the Metre, which led to the signing of the Treaty of the Metre, under which three bodies were set up to take custody of the international prototypes of the kilogram and the metre, and to regulate comparisons with national prototypes.[11] [12] They were:

The 1st CGPM (1889) formally approved the use of 40 prototype metres and 40 prototype kilograms made by the British firm Johnson Matthey as the standards mandated by the Convention of the Metre.[14] The prototypes Metre No. 6 and Kilogram KIII were designated as the international prototype of the metre and the kilogram, respectively; the CGPM retained other copies as working copies, and the rest were distributed to member states for use as their national prototypes. About once every 40 years, the national prototypes were compared with and recalibrated against the international prototype.[15]

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 electrical current (1946), luminosity (1946), temperature (1948), time (1956), and molar mass (1971). The 9th CGPM in 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".[16] The recommendations based on this mandate were presented to the 11th CGPM (1960), where they were formally accepted and given the name "French: Système International d'Unités" and its abbreviation "SI".[17]

Impetus for change

There is a precedent for changing the underlying principles behind the definition of the SI base units; the 11th CGPM (1960) defined the SI metre in terms of the wavelength of krypton-86 radiation, replacing the pre-SI metre bar, and the 13th CGPM (1967) replaced the original definition of the second, which was based on Earth's average rotation from 1750 to 1892,[18] with a definition based on the frequency of the radiation emitted or absorbed with a transition between two hyperfine levels of the ground state of the caesium-133 atom. The 17th CGPM (1983) replaced the 1960 definition of the metre with one based on the second by giving an exact definition of the speed of light in units of metres per second.

Since their manufacture, drifts of up to kilograms (20 μg) per year in the national prototype kilograms relative to the international prototype of the kilogram (IPK) have been detected. There was no way of determining whether the national prototypes were gaining mass or whether the IPK was losing mass.[19] Newcastle University metrologist Peter Cumpson has since identified mercury vapour absorption or carbonaceous contamination as possible causes of this drift.[20] [21] 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 artifact.

Metrologists investigated several alternative approaches to redefining the kilogram based on fundamental physical constants. Among others, the Avogadro project and the development of the Kibble balance (known as the "watt balance" before 2016) promised methods of indirectly measuring mass with very high precision. These projects provided tools that enable alternative means of redefining the kilogram.[22]

A report published in 2007 by the Consultative Committee for Thermometry (CCT) to the CIPM noted that their current definition of temperature has proved to be unsatisfactory for temperatures below and for temperatures above . The committee took the view that the Boltzmann constant provided a better basis for temperature measurement than did the triple point of water because it overcame these difficulties.[23]

At its 23rd meeting (2007), the CGPM 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).[24] At a meeting of the CCU held in Reading, United Kingdom, in September 2010, a resolution[25] 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.[26] The CIPM meeting of October 2010 found "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".[27] The CIPM, however, presented a resolution for consideration at the 24th CGPM (17–21 October 2011) to agree to the new definitions in principle, but not to implement them until the details had been finalised.[28] This resolution was accepted by the conference,[29] and in addition the CGPM moved the date of the 25th meeting forward from 2015 to 2014.[30] [31] At the 25th meeting on 18 to 20 November 2014, it was found that "despite [progress in the necessary requirements] the data do not yet appear to be sufficiently robust for the CGPM to adopt the revised SI at its 25th meeting",[32] thus postponing the revision to the next meeting in 2018. Measurements accurate enough to meet the conditions were available in 2017 and the redefinition was adopted at the 26th CGPM (13–16 November 2018).

Defining constants

Following the successful 1983 redefinition of the metre in terms of an exact numerical value for the speed of light, the BIPM's Consultative Committee for Units (CCU) recommended and the BIPM proposed that four further constants of nature should be defined to have exact values. These are:[33]

The redefinition retains unchanged the numerical values associated with the following constants of nature:

The seven SI defining constants above, expressed in terms of derived units (joule, coulomb, hertz, lumen, and watt), are rewritten below in terms of the seven base units (second, metre, kilogram, ampere, kelvin, mole, and candela); the dimensionless unit steradian (symbol sr) is also used:

As part of the redefinition, the International Prototype of the Kilogram was retired and definitions of the kilogram, the ampere, and the kelvin were replaced. The definition of the mole was revised. These changes have the effect of redefining the SI base units, though the definitions of the SI derived units in terms of the base units remain the same.

Impact on base unit definitions

Following the CCU proposal, the texts of the definitions of all of the base units were either refined or rewritten, changing the emphasis from explicit-unit- to explicit-constant-type definitions.[34] 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 barleycorns,[35] and from 1889 to 2019 the kilogram was defined as the mass of the International Prototype of the Kilogram. In explicit-constant definitions, a constant of nature is given a specified value, and the definition of the unit emerges as a consequence; for example, in 2019, the speed of light was defined as exactly metres per second. The length of the metre could be derived because the second had been already independently defined. The previous and 2019 definitions are given below.

Second

The new definition of the second is effectively the same as the previous one, the only difference being that the conditions under which the definition applies are more rigorously defined.

The second may be expressed directly in terms of the defining constants:

1 s = .

Metre

The new definition of the metre is effectively the same as the previous one, the only difference being that the additional rigour in the definition of the second propagated to the metre.

The metre may be expressed directly in terms of the defining constants:

1 m = .

Kilogram

The definition of the kilogram fundamentally changed from an artifact (the International Prototype of the Kilogram) to a constant of nature.[37] Because the Planck constant relates photon energy to photon frequency, the new definition relates the kilogram to the mass equivalent of the energy of a photon at a specific frequency.

For illustration, an earlier proposed redefinition that is equivalent to this 2019 definition is: "The kilogram is the mass of a body at rest whose equivalent energy equals the energy of a collection of photons whose frequencies sum to [{{val|1.356392489652|e=50}}] hertz."[38]

The kilogram may be expressed directly in terms of the defining constants:

1 kg = .

Leading to

1 J⋅s =

1 J =

1 W =

1 N =

Ampere

The definition of the ampere underwent a major revision. The previous definition relied on infinite lengths that are impossible to realise:[39]

The alternative avoided that issue:

The ampere may be expressed directly in terms of the defining constants as:

1 A =

For illustration, this is equivalent to defining one coulomb to be an exact specified multiple of the elementary charge.

1 C =

Because the previous definition contains a reference to force, which has the dimensions MLT−2, it follows that in the previous SI the kilogram, metre, and second – the base units representing these dimensions – had to be defined before the ampere could be defined. Other consequences of the previous definition were that in SI the value of vacuum permeability was fixed at exactly H⋅m-1.[40]

\alpha

.[41] The CODATA 2018 value for the relative standard uncertainty of

\alpha

is [42]

The ampere definition leads to exact values for

1 V =

1 Wb =

1 Ω =

Kelvin

The definition of the kelvin underwent a fundamental change. Rather than using the triple point of water to fix the temperature scale, the new definition uses the energy equivalent as given by Boltzmann's equation.

The kelvin may be expressed directly in terms of the defining constants as:

1 K = .

Mole

The previous definition of the mole linked it to the kilogram. The revised definition breaks that link by making a mole a specific number of entities of the substance in question.

The mole may be expressed directly in terms of the defining constants as:

1 mol = .

One consequence of this change is that the previously defined relationship between the mass of the 12C atom, the dalton, the kilogram, and the Avogadro constant is no longer exact. One of the following had to change:

The wording of the 9th SI Brochure[44] implies that the first statement remains valid, which means the second is no longer exactly true. The molar mass constant, while still with great accuracy remaining, is no longer exactly equal to that. Appendix 2 to the 9th SI Brochure states that "the molar mass of carbon 12, M(12C), is equal to within a relative standard uncertainty equal to that of the recommended value of at the time this Resolution was adopted, namely, and that in the future its value will be determined experimentally",[45] [46] which makes no reference to the dalton and is consistent with either statement.

Candela

The new definition of the candela is effectively the same as the previous definition as dependent on other base units, with the result that the redefinition of the kilogram and the additional rigour in the definitions of the second and metre propagate to the candela.

The candela may be expressed directly in terms of the defining constants as:

1 cd = 

Impact on reproducibility

All seven of the SI base units are defined in terms of defined constants[47] and universal physical constants.[48] [49] Seven constants are needed to define the seven base units but there is not a direct correspondence between each specific base unit and a specific constant; except the second and the mole, more than one of the seven constants contributes to the definition of any given base unit.

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.[50] In practice, G can only be measured with a relative uncertainty of the order of 10−5,[51] which would have resulted in the upper limit of the kilogram's reproducibility being around 10−5 whereas the then-current international prototype of the kilogram can be measured with a reproducibility of 1.2 × 10−8.[52] The physical constants were chosen 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)[53] 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.

Acceptance

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 CGPM in 2014. The consultative committees have laid down a number of criteria that must be met before they will support the CCU's proposal, including:

As of March 2011, the International Avogadro Coordination (IAC) group had obtained an uncertainty of and NIST had obtained an uncertainty of in their measurements.[22] On 1 September 2012 the European Association of National Metrology Institutes (EURAMET) launched a formal project to reduce the relative difference between the Kibble balance and the silicon sphere approach to measuring the kilogram from to within .[57] the proposed redefinition is known as the "New SI"[3] but Mohr, in a paper following the CGPM proposal but predating the formal CCU proposal, suggested that because the proposed system makes use of atomic scale phenomena rather than macroscopic phenomena, it should be called the "Quantum SI System".[58]

As of the 2014 CODATA-recommended values of the fundamental physical constants published in 2016 using data collected until the end of 2014, all measurements met the CGPM's requirements, and the redefinition and the next CGPM quadrennial meeting in late 2018 could now proceed.[59] [60]

On 20 October 2017, the 106th meeting of the International Committee for Weights and Measures (CIPM) formally accepted a revised Draft Resolution A, calling for the redefinition of the SI, to be voted on at the 26th CGPM,[61] The same day, in response to the CIPM's endorsement of the final values, the CODATA Task Group on Fundamental Constants published its 2017 recommended values for the four constants with uncertainties and proposed numerical values for the redefinition without uncertainty. The vote, which was held on 16 November 2018 at the 26th GCPM, was unanimous; all attending national representatives voted in favour of the revised proposal.

The new definitions became effective on 20 May 2019.[62]

Concerns

In 2010, Marcus Foster of the Australian Commonwealth Scientific and Industrial Research Organisation (CSIRO) published a wide-ranging critique of the SI; he raised numerous issues ranging from basic issues such as the absence of the symbol "Ω" (omega, used for the ohm) from most Western computer keyboards to abstract issues such as inadequate formalism in the metrological concepts on which SI is based. The changes proposed in the new SI only addressed problems with the definition of the base units, including new definitions of the candela and the mole – units Foster argued are not true base units. Other issues raised by Foster fell outside the scope of the proposal.

Explicit-unit and explicit-constant definitions

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.[63] Although this criticism applies to the linking of the kilogram to the Planck constant via a route that requires a knowledge of both special relativity and quantum mechanics,[64] it does not apply to the definition of the ampere, which is closer to an example of its quantity than is the previous definition.[65] Some observers have welcomed the change to base the definition of electric current on the charge of the electron rather than the previous definition of a force between two parallel, current-carrying wires; because the nature of the electromagnetic interaction between two bodies is somewhat different at the quantum electrodynamics level than at classical electrodynamic levels, it is considered inappropriate to use classical electrodynamics to define quantities that exist at quantum electrodynamic levels.[52]

Mass and the Avogadro constant

When the scale of the divergence between the IPK and national kilogram prototypes was reported in 2005, a debate began about whether the kilogram should be defined in terms of the mass of the silicon-28 atom or by using the Kibble balance. The mass of a silicon atom could be determined using the Avogadro project and using the Avogadro constant, it could be linked directly to the kilogram.[66] Concerns that the authors of the proposal had failed to address the impact of breaking the link between the mole, kilogram, dalton, and the Avogadro constant have also been expressed.[67] This direct link has caused many to argue that the mole is not a true physical unit but, according to the Swedish philosopher Johansson, a "scaling factor".[68]

The 8th edition of the SI Brochure defined the dalton in terms of the mass of an atom of 12C.[69] It defined the Avogadro constant in terms of this mass and the kilogram, making it determined by experiment. The redefinition fixes the Avogadro constant and the 9th SI Brochure retains the definition of dalton in terms of 12C, with the effect that the link between the dalton and the kilogram will be broken.[70] [71]

In 1993, the International Union of Pure and Applied Chemistry (IUPAC) approved the use of the dalton as an alternative to the unified atomic mass unit with the qualification that the CGPM had not given its approval.[72] This approval has since been given. Following the proposal to redefine the mole by fixing the value of the Avogadro constant, Brian Leonard of the University of Akron, writing in Metrologia, proposed that the dalton (Da) be redefined such that, but that the unified atomic mass unit retain its current definition based on the mass of 12C, ceasing to exactly equal the dalton. This would result in the dalton and the atomic mass unit potentially differing from each other with a relative uncertainty of the order of 10−10.[73] The 9th SI Brochure, however, defines both the dalton (Da) and the unified atomic mass unit (u) as exactly of the mass of a free carbon-12 atom and not in relation to the kilogram, with the effect that the above equation will be inexact.

Temperature

Different temperature ranges need different measurement methods. Room temperature can be measured by means of expansion and contraction of a liquid in a thermometer but high temperatures are often associated with colour of blackbody radiation. 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 an average of the thermal energies of the individual particles that comprise the body concerned.[52] He noted that in many theoretical papers, temperature is represented by the quantities or where

\Theta=kT;   \beta=

1
kT
and is the Boltzmann constant. Chyla acknowledged, however, that in the macroscopic world, temperature plays the role of a base unit because much of the theory of thermodynamics is based on temperature.[52]

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. At very low and at very high temperatures it often links energy to temperature via the Boltzmann constant.[74] [75]

Luminous intensity

Foster argued that "luminous intensity [the candela] is not a physical quantity, but a photobiological quantity that exists in human perception", questioning whether the candela should be a base unit.[76] Before the 1979 decision to define photometric units in terms of luminous flux (power) rather than luminous intensities of standard light sources, there was already doubt whether there should still be a separate base unit for photometry. Furthermore, there was unanimous agreement that the lumen was now more fundamental than the candela. However, for the sake of continuity the candela was kept as base unit.[77]

See also

Further reading

External links

Notes and References

  1. Web site: BIPM statement: Information for users about the proposed revision of the SI . 5 May 2018 . https://web.archive.org/web/20180121160000/https://www.bipm.org/utils/common/pdf/SI-statement.pdf . 21 January 2018 . live . dmy-all .
  2. Web site: Decision CIPM/105-13 (October 2016) . 31 August 2017 . https://web.archive.org/web/20170824095943/http://www.bipm.org/en/committees/cipm/meeting/105.html . 24 August 2017 . live . dmy-all .
  3. Web site: Michael . Kühne . Redefinition of the SI . Keynote address, ITS9 (Ninth International Temperature Symposium) . Los Angeles . 1 March 2012 . 22 March 2012 . NIST . https://web.archive.org/web/20130618064512/http://www.its9.org/symposium_program.html . 18 June 2013 . dead.
  4. Web site: 9th edition of the SI Brochure . BIPM . 2019 . 20 May 2019 . dmy-all.
  5. Historic Vote Ties Kilogram and Other Units to Natural Constants . NIST . 16 November 2018 . 16 November 2018 . https://web.archive.org/web/20181118014932/https://www.nist.gov/news-events/news/2018/11/historic-vote-ties-kilogram-and-other-units-natural-constants . 18 November 2018 . live . dmy-all .
  6. SIM XXII General Assembly . Montevideo, Uruguay . Highlights in the work of the BIPM in 2016 . http://www.sim-metrologia.org.br/docs/2016Presentations/ . 10 . Martin . Milton . 14 November 2016 . 13 January 2017 . https://web.archive.org/web/20170901031605/http://www.sim-metrologia.org.br/docs/2016Presentations/BIPM%202016.pdf#page=10 . 1 September 2017 . dead . dmy-all . The conference ran from 13–16 November and the vote on the redefinition was scheduled for the last day. Kazakhstan was absent and did not vote.
  7. The metre was redefined again in 1983 by fixing the value of the speed of light in vacuum. That definition went unaltered in 2019 and remains in effect today.
  8. Book: Crease, Robert P. . World in the Balance . 2011 . W. W. Norton & Company, Inc. . New York . 978-0-393-07298-3 . 83–84 . France: "Realities of Life and Labor".
  9. The dalton is not defined in the formal proposal to be voted upon by the CGPM, only in the 9th edition of the SI Brochure.
  10. Book: The Measure of all Things – The Seven-Year-Odyssey that Transformed the World . Alder, Ken . 2002 . Abacus . London . 1. 978-0-349-11507-8.
  11. Metric Convention of 1875 [English translation] ]. Office of the President of the United States . Washington, D.C. . 1876 . dead . https://web.archive.org/web/20050301093830/http://lamar.colostate.edu/~hillger/laws/metric-convention.html . 1 March 2005 .
  12. Web site: The Metre Convention . Sèvres, France . . 21 June 2013 . https://web.archive.org/web/20120926202046/http://www.bipm.org/en/convention/ . 26 September 2012 . live .
  13. Web site: CIPM: International Committee for Weights and Measures . . Sèvres, France . 3 October 2010 . https://web.archive.org/web/20120924192125/http://www.bipm.org/en/committees/cipm/ . 24 September 2012 . live .
  14. Web site: Resolution of the 1st meeting of the CGPM (1889) . Sèvres, France. 21 June 2013 . . https://web.archive.org/web/20130521210811/http://www1.bipm.org/en/CGPM/db/1/1/ . 21 May 2013 . live .
  15. Jabbour . Z.J. . Yaniv . S.L. . 2001 . The Kilogram and Measurements of Mass and Force . Journal of Research of the National Institute of Standards and Technology . 106 . 1 . 25–46 . 28 March 2011 . 10.6028/jres.106.003 . 27500016 . 4865288 . dead . https://web.archive.org/web/20110604144310/http://nvl.nist.gov/pub/nistpubs/jres/106/1/j61jab.pdf . 4 June 2011 . dmy-all.
  16. Web site: Resolution 6 of the 9th meeting of the CGPM (1948): Proposal for establishing a practical system of units of measurement . 23 March 2011 . https://web.archive.org/web/20130514081152/http://www.bipm.org/en/CGPM/db/9/6/ . 14 May 2013 . live .
  17. Web site: Resolution 12 of the 11th meeting of the CGPM (1960): Système International d'Unités . Sèvres, France . 23 March 2011 . https://web.archive.org/web/20130514081801/http://www.bipm.org/en/CGPM/db/11/12/ . 14 May 2013 . live .
  18. F. R. . Stephenson . L. V. . Morrison . C. Y. . Hohenkerk . Measurement of the Earth's rotation: 720 BC to AD 2015 . Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences . December 2016 . 472 . 2196 . §4(a) . 10.1098/rspa.2016.0404 . 28119545. 5247521. 2016RSPSA.47260404S .
  19. Web site: Recent progress in fundamental constants and the International System of Units . Peter, Mohr . Third Workshop on Precision Physics and Fundamental Physical Constant . 6 December 2010 . 2 January 2011 . https://web.archive.org/web/20110824105816/http://physics.vniim.ru/SI50/files/mohr.pdf . 24 August 2011 . dead . dmy-all .
  20. News: 7 January 2013 . The dirty secret of why you are not quite as heavy as you think . . London . Tom . Whipple . 23 March 2011 . 15 . https://web.archive.org/web/20130117041048/http://www.thetimes.co.uk/tto/science/physics/article3649580.ece . 17 January 2013 . live .
  21. Web site: The Kilogram Has Gained Weight . Tia . Ghose . LiveScience . 6 January 2013 . 23 March 2011 . https://web.archive.org/web/20130326085458/http://www.livescience.com/26017-kilogram-gained-weight.html . 26 March 2013 . live .
  22. Metrology in the balance . Robert P. . Crease . 28 June 2012 . Physics World . 24 . 3 . 39–45 . 22 March 2011. 2011PhyW...24c..39C . 10.1088/2058-7058/24/03/34 .
  23. Web site: Report to the CIPM on the implications of changing the definition of the base unit kelvin . Fischer . J. . 2 May 2007 . 2 January 2011 . etal . https://web.archive.org/web/20081123054012/http://www.bipm.org/wg/CCT/TG-SI/Allowed/Documents/Report_to_CIPM_2.pdf . 23 November 2008 . live .
  24. Web site: Resolution proposal submitted to the IUPAP Assembly by Commission C2 (SUNAMCO) . International Union of Pure and Applied Physics . 2008 . 6 September 2015 . https://web.archive.org/web/20160305121825/http://iupap.org/wp-content/uploads/2013/08/file_50095.pdf . 5 March 2016 . live .
  25. Web site: On the possible future revision of the International System of Units, the SI . Ian . Mills . CCU . 29 September 2010 . 1 January 2011 . https://web.archive.org/web/20120113075832/http://www.bipm.org/utils/en/pdf/24_CGPM_Convocation_Draft_Resolution_A.pdf . 13 January 2012 . live.
  26. Web site: Draft Chapter 2 for SI Brochure, following redefinitions of the base units . Ian . Mills . CCU . 29 September 2010 . 1 January 2011 . https://web.archive.org/web/20120316100258/http://www.bipm.org/utils/en/pdf/si_brochure_draft_ch2.pdf . 16 March 2012 . live .
  27. Web site: Towards the "new SI" . International Bureau of Weights and Measures (BIPM) . 20 February 2011 . https://web.archive.org/web/20110514140824/http://www.bipm.org/en/si/new_si/ . 14 May 2011 . live .
  28. Web site: On the possible future revision of the International System of Units, the SI – Draft Resolution A . International Committee for Weights and Measures (CIPM) . 14 July 2011 . https://web.archive.org/web/20110806053509/http://www.bipm.org/utils/common/pdf/24_CGPM_Convocation_Draft_Resolution_A.pdf . 6 August 2011 . live .
  29. It was not expected to be adopted until some prerequisite conditions are met, and in any case not before 2014. SeePossible changes to the international system of units . IUPAC Wire . 34 . 1 . January–February 2012.
  30. General Conference on Weights and Measures approves possible changes to the International System of Units, including redefinition of the kilogram. . . Sèvres, France . 23 October 2011 . 25 October 2011 . https://web.archive.org/web/20120209175127/http://www.bipm.org/utils/en/pdf/Press_release_resolution_1_CGPM.pdf . 9 February 2012 . live .
  31. Web site: Redefining the SI base units . Mohr, Peter . 2 November 2011 . NIST Newsletter . NIST . 1 March 2012 . https://web.archive.org/web/20160812012223/http://nist.gov/pml/newsletter/siredef.cfm . 12 August 2016 . live .
  32. Web site: Resolutions adopted by the CGPM at its 25th meeting (18–20 November 2014) . International Bureau for Weights and Measures . Sèvres, France . 21 November 2014 . 1 December 2014 . https://web.archive.org/web/20150325103457/http://www.bipm.org/utils/common/pdf/CGPM-2014/25th-CGPM-Resolutions.pdf . 25 March 2015 . live .
  33. These constants are described in the 2006 version of the SI manual but in that version, the latter three are defined as "constants to be obtained by experiment" rather than as "defining constants".
  34. Part II – Explicit-Constant Definitions for the Kilogram and for the Mole . Chemistry International . 33 . 5 . September–October 2011 . Mills, Ian . 0193-6484 . 12–15 . 28 June 2013 . https://web.archive.org/web/20170709120014/https://www.iupac.org/publications/ci/2011/3305/4_mills.html . 9 July 2017 . live .
  35. Book: Smoot's Ear – The Measure of Humanity . Travenor, Robert . 2007 . 978-0-300-14334-8 . 35–36 . .
  36. Although the phrase used here is more terse than in the previous definition, it still has the same meaning. This is made clear in the 9th SI Brochure, which almost immediately after the definition on p. 130 states: "The effect of this definition is that the second is equal to the duration of periods of the radiation corresponding to the transition between the two hyperfine levels of the unperturbed ground state of the 133Cs atom."
  37. The Current SI Seen From the Perspective of the Proposed New SI . Barry N . Taylor . Journal of Research of the National Institute of Standards and Technology . 116 . November–December 2011 . 797–80 . 6 . 10.6028/jres.116.022. 26989600 . 4551220 .
  38. On the redefinition of the kilogram . Barry N . Taylor . Peter J . Mohr . Metrologia . 1 . 36 . November 1999 . 63–64 . 10.1088/0026-1394/36/1/11 . 1999Metro..36...63T . 250823638 .
  39. Web site: 2018-05-15 . Ampere: Introduction . 2024-05-30 . NIST . en.
  40. Web site: Unit of electric current (ampere) . 7 September 2015 . Historical context of the SI . . https://web.archive.org/web/20130603235543/http://physics.nist.gov/cuu/Units/ampere.html . 3 June 2013 . live .
  41. Davis . Richard S. . Determining the value of the fine-structure constant from a current balance: getting acquainted with some upcoming changes to the SI . . 85 . 5 . 364–368 . 2017 . 10.1119/1.4976701 . 1610.02910. 2017AmJPh..85..364D . 119283799 .
  42. A note should be added on the definition of magnetic field unit (tesla). When the ampere was defined as the current that when flows in two long parallel wires separated by causes a force of on each other, there was also another definition: the magnetic field at the location of each of the wires in this configuration was defined to be . Namely is the intensity of the magnetic field B that causes a force of on a wire carrying a current of .The number was written also as μ0/2π. This arbitrary definition is what made μ0 to be exactly 4π H/m. Accordingly, the magnetic field near a wire carrying current is given by B = μ0I/2πr.

    Now, with the new definition of the ampere, the definition of the tesla is also affected. More specifically, the definition relying on the force of a magnetic field on a wire carrying current is maintained (F = I⋅B⋅l) while, as mentioned above, μ0 can no longer be exactly 4π H/m and has to be measured experimentally.

    The value of the vacuum permittivity is also affected accordingly. The Maxwell equations will 'see to it' that the electrostatic force between two point charges will be F = 1/(4πε0)(q1q2)/r2.

  43. Web site: Redefining the Mole . NIST . 24 October 2018 . 23 October 2018 . https://web.archive.org/web/20181024074533/https://www.nist.gov/si-redefinition/redefining-mole . 24 October 2018 . live .
  44. A footnote in Table 8 on non-SI units states: "The dalton (Da) and the unified atomic mass unit (u) are alternative names (and symbols) for the same unit, equal to 1/12 of the mass of a free carbon 12 atom, at rest and in its ground state."
  45. Web site: Resolutions adopted. November 2018. Bureau international des poids et mesures. dead. https://web.archive.org/web/20200204124652/https://www.bipm.org/utils/common/pdf/CGPM-2018/26th-CGPM-Resolutions.pdf. 4 February 2020. 2020-02-04.
  46. Book: Nawrocki, Waldemar. Introduction to Quantum Metrology: The Revised SI System and Quantum Standards. 2019-05-30. Springer. 978-3-030-19677-6. 54. en.
  47. Though the three quantities temperature, luminous intensity and amount of substance may be regarded from a fundamental physical perspective as derived quantities, these are perceptually independent quantities and have conversion constants defined that relate the historically defined units to the underlying physics.
  48. The definition of the candela is atypical within the base units; translating physical measurements of spectral intensity into units of candela also requires a model of the response of the human eye to different wavelengths of light known as the luminosity function and denoted by V(λ), a function that is determined by the International Commission on Illumination (CIE).
  49. Book: Principles covering Photometry . Conférence général des poids et mesures (CGPM) . Sevres . Wyszecki, G. . Blevin, W.R. . Kessler, K.G. . Mielenz, K.D. . 1983 . 23 April 2012 . https://web.archive.org/web/20081011204957/http://www.bipm.org/utils/en/pdf/Monographie1983-1.pdf . 11 October 2008 . live .
  50. 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. When fundamental constants as relations between these three units are set, the units can be deduced from a combination of these constants; for example, as a linear combination of Planck units.
  51. 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
  52. Evolution of the International Metric System of Units SI . Chyla, W.T. . December 2011 . Acta Physica Polonica A . 6 . 120 . 998–1011 . 10.12693/APhysPolA.120.998 . 2011AcPPA.120..998C . free .
  53. Web site: What is a mise en pratique? . . 2011 . is a set of instructions that allows the definition to be realised in practice at the highest level. . 6 September 2015 . https://web.archive.org/web/20150922051552/http://www.bipm.org/en/measurement-units/new-si/mise-en-pratique.html . 22 September 2015 . live .
  54. Web site: Recommendations of the Consultative Committee for Mass and Related Quantities to the International Committee for Weights and Measures. . 12th Meeting of the CCM . 26 March 2010 . Bureau International des Poids et Mesures . Sèvres . 27 June 2012 . https://web.archive.org/web/20130514081750/http://www.bipm.org/utils/common/pdf/CCM12.pdf#page=23 . 14 May 2013 . dead .
  55. Web site: Recommendations of the Consultative Committee for Amount of Substance: Metrology in Chemistry to the International Committee for Weights and Measures. . 16th Meeting of the CCQM . 15–16 April 2010 . Bureau International des Poids et Mesures . Sèvres . 27 June 2012 . https://web.archive.org/web/20130514072057/http://www.bipm.org/utils/common/pdf/CCQM16.pdf#page=40 . 14 May 2013 . dead .
  56. Web site: Recommendations of the Consultative Committee for Thermometry to the International Committee for Weights and Measures. . 25th Meeting of the Consultative Committee for Thermometry . 6–7 May 2010 . Bureau International des Poids et Mesures . Sèvres . 27 June 2012 . https://web.archive.org/web/20130514064646/http://www.bipm.org/utils/common/pdf/CCT25.pdf#page=53 . 14 May 2013 . dead .
  57. Web site: kilogram NOW – Realization of the awaited definition of the kilogram . . 8 October 2012 . https://web.archive.org/web/20160304084349/http://www.inrim.it/luc/know/index.htm . 4 March 2016 . live .
  58. Book: Advances in Quantum Chemistry . The Quantum SI: A Possible New International System of Units . 2008 . Mohr, Peter J. . 53 . 34 . 978-0-12-373925-4 . Academic Press . 2 April 2012 . 10.1016/s0065-3276(07)53003-0 . 2008AdQC...53...27M.
  59. Universe's Constants Now Known with Sufficient Certainty to Completely Redefine the International System of Units . 31 December 2016 . . 22 November 2016 . https://web.archive.org/web/20170101003042/https://www.nist.gov/news-events/news/2016/11/universes-constants-now-known-sufficient-certainty-completely-redefine . 1 January 2017 . live .
  60. CODATA recommended values of the fundamental physical constants: 2014 . . 88 . 3 . 035009–1–73 . 26 September 2016 . Mohr, Peter J. . Newell, David B. . Taylor, Barry N. . 10.1103/RevModPhys.88.035009 . This is a truly major development, because these uncertainties are now sufficiently small that the adoption of the new SI by the 26th CGPM is expected. . 1507.07956 . 2016RvMP...88c5009M . 1115862 .
  61. Proceedings of the 106th meeting . International Committee for Weights and Measures . 16–20 October 2017 . https://www.bipm.org/en/committees/cipm/meeting/106.html . Sèvres . 27 January 2018 . https://web.archive.org/web/20180127202612/https://www.bipm.org/utils/en/pdf/CIPM/CIPM2017-EN.pdf?page=23 . 27 January 2018 . live .
  62. Web site: It's official: We're redefining the kilogram . Emily . Conover . 16 November 2018 . 16 November 2018 . . https://web.archive.org/web/20181116171854/https://www.sciencenews.org/article/official-redefining-kilogram-units-measurement . 16 November 2018 . live .
  63. A sceptic's review of the New SI . Price, Gary . 2011 . Accreditation and Quality Assurance . 16 . 3 . 121–132 . 10.1007/s00769-010-0738-x. 110127259 .
  64. Part I – From the Current "Kilogram Problem" to a Proposed Definition . Chemistry International . 33 . 5 . September–October 2011 . Censullo, Albert C. . 0193-6484 . 9–12 . 28 June 2013 . https://web.archive.org/web/20170709120014/https://www.iupac.org/publications/ci/2011/3305/4_mills.html . 9 July 2017 . live .
  65. The Background and Implications of the "New SI" for Analytical Chemists . Journal of the Association of Public Analysts (Online) . 2013 . 41 2 . 28–44 . D Thorburn . Burns . EH . Korte . 25 June 2013 . https://web.archive.org/web/20160306125346/http://www.apajournal.org.uk/2013_0028-0044.pdf . 6 March 2016 . live .
  66. Proposed change to the definition of the kilogram: Consequences for legal metrology . OIML Bulletin. LII . 4 . October 2011 . Richard . Davis . 28 June 2013 . https://web.archive.org/web/20150327081726/http://kcdb.bipm.org/NL/16/OIML_Davis_2011.pdf . 27 March 2015 . live .
  67. The two quantities of the Avogadro constant and the Avogadro number are numerically identical but while has the unit mol−1, is a pure number.
  68. The Mole is Not an Ordinary Measurement Unit . Ingvar . Johansson . Accreditation and Quality Assurance . 16 . 2011 . 16 . 467–470 . 10.1007/s00769-011-0804-z. 121496106 .
  69. http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf SI Brochure (8th edition)
  70. Comments on recent proposals for redefining the mole and kilogram . B.P. . Leonard . 2010 . 47 . 3 . L5–L8 . . 10.1088/0026-1394/47/3/L01 . 2010Metro..47L...5L . 118098528 .
  71. Some reflections on the proposed redefinition of the unit for the amount of substance and of other SI units . Pavese . Franco . 2011 . Accreditation and Quality Assurance . 16 . 3 . 161–165 . 10.1007/s00769-010-0700-y . 121598605 .
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  73. Why the dalton should be redefined exactly in terms of the kilogram . Leonard, Brian Phillip . May 2012 . Metrologia . 49 . 4 . 487–491 . 10.1088/0026-1394/49/4/487 . 2012Metro..49..487L . 55717564 .
  74. Web site: Mise en pratique for the definition of the kelvin . 2011 . Consultative Committee for Thermometry (CCT), International Committee for Weights and Measures (CIPM) . Sèvres, France . 25 June 2013 . https://web.archive.org/web/20130508191638/http://www1.bipm.org/utils/en/pdf/MeP_K.pdf . 8 May 2013 . live .
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  77. Procès-verbaux du Comité International des Poids et Mesures, 66th Meeting . The International Temperature Scale of 1990 (ITS-90) . 1977. 1 September 2019 . 14, 143 . fr .

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