2019 revision of the SI

{{Main|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 artefact to define the kilogram.

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 {{lang|fr|mètre des Archives}} and {{lang|fr|kilogramme des Archives}}, which were a "best attempt" at fulfilling these principles.{{cite book |title=The Measure of all Things – The Seven-Year-Odyssey that Transformed the World |author= Alder, Ken |year=2002 |publisher=Abacus |location=London |page=1|isbn = 978-0-349-11507-8}}

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.{{cite web |url=http://lamar.colostate.edu/~hillger/laws/metric-convention.html |title=Metric Convention of 1875 [English translation] |publisher=Office of the President of the United States |location=Washington, D.C. |year=1876 |url-status=dead |archive-url=https://web.archive.org/web/20050301093830/http://lamar.colostate.edu/~hillger/laws/metric-convention.html |archive-date=1 March 2005 }}

{{cite web |url=http://www.bipm.org/en/convention/ |title=The Metre Convention |location=Sèvres, France |publisher=International Bureau of Weights and Measures |access-date=21 June 2013 |archive-url=https://web.archive.org/web/20120926202046/http://www.bipm.org/en/convention/ |archive-date=26 September 2012 |url-status=live }} They were:

• CGPM (General Conference on Weights and Measures, {{lang|fr|Conférence générale des poids et mesures}}) – The Conference meets every four to six years and consists of delegates of the nations that 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, {{lang|fr|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 with advising the CGPM. The CIPM has set up a number of sub-committees, each charged with a particular area of interest. One of these, the Consultative Committee for Units (CCU), advises the CIPM on matters concerning units of measurement.{{cite web |url=http://www.bipm.org/en/committees/cipm/ |title=CIPM: International Committee for Weights and Measures |publisher=BIPM |location =Sèvres, France |access-date=3 October 2010 |archive-url=https://web.archive.org/web/20120924192125/http://www.bipm.org/en/committees/cipm/ |archive-date=24 September 2012 |url-status=live }}
• BIPM (International Bureau for Weights and Measures, {{lang|fr|Bureau international des poids et mesures}}) – The Bureau provides safe keeping of the international prototypes of the kilogram and the 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 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.{{cite web |url=http://www.bipm.org/en/CGPM/db/1/1/ |title=Resolution of the 1st meeting of the CGPM (1889) |location=Sèvres, France|access-date=21 June 2013 |publisher=International Bureau of Weights and Measures |archive-url=https://web.archive.org/web/20130521210811/http://www1.bipm.org/en/CGPM/db/1/1/ |archive-date=21 May 2013 |url-status=live }} 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.{{cite journal |last1 = Jabbour |first1 = Z.J. |last2 = Yaniv |first2 = S.L. |year = 2001 |title = The Kilogram and Measurements of Mass and Force |journal = Journal of Research of the National Institute of Standards and Technology |volume = 106 |issue = 1 |pages = 25–46 |url = http://nvl.nist.gov/pub/nistpubs/jres/106/1/j61jab.pdf |access-date = 28 March 2011 |doi = 10.6028/jres.106.003 |pmid = 27500016 |pmc = 4865288 |url-status = dead |archive-url = https://web.archive.org/web/20110604144310/http://nvl.nist.gov/pub/nistpubs/jres/106/1/j61jab.pdf |archive-date = 4 June 2011 |df = dmy-all}}

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).{{SIbrochure8th|pages=95, 97, 138–140}} 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".{{cite web |url = http://www.bipm.org/en/CGPM/db/9/6/ |title=Resolution 6 of the 9th meeting of the CGPM (1948): Proposal for establishing a practical system of units of measurement |access-date=23 March 2011 |archive-url=https://web.archive.org/web/20130514081152/http://www.bipm.org/en/CGPM/db/9/6/ |archive-date=14 May 2013 |url-status=live }} The recommendations based on this mandate were presented to the 11th CGPM (1960), where they were formally accepted and given the name "{{lang|fr|Système International d'Unités}}" and its abbreviation "SI".{{cite web |url=http://www.bipm.org/en/CGPM/db/11/12/ |location=Sèvres, France |title=Resolution 12 of the 11th meeting of the CGPM (1960): Système International d'Unités |access-date=23 March 2011 |archive-url=https://web.archive.org/web/20130514081801/http://www.bipm.org/en/CGPM/db/11/12/ |archive-date=14 May 2013 |url-status=live }}

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,

{{cite journal |first1 = F. R. |last1 = Stephenson |first2 = L. V. |last2 = Morrison |first3 = C. Y. |last3 = Hohenkerk |title = Measurement of the Earth's rotation: 720 BC to AD 2015 |journal = Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |date = December 2016 |volume = 472 |issue = 2196 |at = §4(a) |doi = 10.1098/rspa.2016.0404 |pmid = 28119545|pmc = 5247521|bibcode = 2016RSPSA.47260404S }} 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.{{SIBrochure8th |pages=112–116}}

File:Prototype mass drifts.jpg's sister copies: K32 and K8(41).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)._{{nbsp}} All mass changes are relative to the IPK.{{cite journal |title = The Third Periodic Verification of National Prototypes of the Kilogram (1988–1992) |first = G. |last = Girard |journal = Metrologia |volume = 31 |issue = 4 |year = 1994 |pages = 317–336 |doi = 10.1088/0026-1394/31/4/007 |bibcode = 1994Metro..31..317G|s2cid = 250743540 }}]]

Since their manufacture, drifts of up to {{val|2|e=-8}} 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.{{cite web |url=http://physics.vniim.ru/SI50/files/mohr.pdf |author=Peter, Mohr |title=Recent progress in fundamental constants and the International System of Units |work=Third Workshop on Precision Physics and Fundamental Physical Constant |date=6 December 2010 |access-date=2 January 2011 |archive-url=https://web.archive.org/web/20110824105816/http://physics.vniim.ru/SI50/files/mohr.pdf |archive-date=24 August 2011 |url-status=dead |df=dmy-all }} Newcastle University metrologist Peter Cumpson has since identified mercury vapour absorption or carbonaceous contamination as possible causes of this drift.{{cite news |date=7 January 2013 |url=https://www.thetimes.com/uk/science/article/the-dirty-secret-of-why-you-are-not-quite-as-heavy-as-you-think-hzhrqpmhsl0 |newspaper= The Times |location=London |title =The dirty secret of why you are not quite as heavy as you think |first1=Tom |last1=Whipple |access-date=23 March 2011 |page=15 |archive-url=https://web.archive.org/web/20130117041048/http://www.thetimes.co.uk/tto/science/physics/article3649580.ece |archive-date=17 January 2013 |url-status=live }}{{cite web |url=http://www.livescience.com/26017-kilogram-gained-weight.html |title=The Kilogram Has Gained Weight |first1=Tia |last1=Ghose |publisher=LiveScience |date=6 January 2013 |access-date=23 March 2011 |archive-url=https://web.archive.org/web/20130326085458/http://www.livescience.com/26017-kilogram-gained-weight.html |archive-date=26 March 2013 |url-status=live }} 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.

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.{{cite journal |url=http://physicsworld.com/cws/article/indepth/2011/mar/22/metrology-in-the-balance |title=Metrology in the balance |first1=Robert P. |last1=Crease |access-date=28 June 2012 |journal=Physics World |volume=24 |issue=3 |pages=39–45 |date=22 March 2011|bibcode=2011PhyW...24c..39C |doi=10.1088/2058-7058/24/03/34 |url-access=subscription }}

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 {{val|20|u=K}} and for temperatures above {{val|1300|u=K}}. 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.{{cite web |url=http://www.bipm.org/wg/CCT/TG-SI/Allowed/Documents/Report_to_CIPM_2.pdf |title=Report to the CIPM on the implications of changing the definition of the base unit kelvin |last=Fischer |first=J. |date=2 May 2007 |access-date=2 January 2011 |display-authors=etal |archive-url=https://web.archive.org/web/20081123054012/http://www.bipm.org/wg/CCT/TG-SI/Allowed/Documents/Report_to_CIPM_2.pdf |archive-date=23 November 2008 |url-status=live }}

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 artefacts that were then in use. The following year this was endorsed by the International Union of Pure and Applied Physics (IUPAP).{{cite web |url=http://iupap.org/wp-content/uploads/2013/08/file_50095.pdf |title=Resolution proposal submitted to the IUPAP Assembly by Commission C2 (SUNAMCO) |publisher=International Union of Pure and Applied Physics |year=2008 |access-date=6 September 2015 |archive-url=https://web.archive.org/web/20160305121825/http://iupap.org/wp-content/uploads/2013/08/file_50095.pdf |archive-date=5 March 2016 |url-status=live }} At a meeting of the CCU held in Reading, United Kingdom, in September 2010, a resolution{{cite web |url=http://www.bipm.org/utils/en/pdf/24_CGPM_Convocation_Draft_Resolution_A.pdf |title=On the possible future revision of the International System of Units, the SI |first=Ian |last=Mills |publisher=CCU |date=29 September 2010 |access-date=1 January 2011 |archive-url=https://web.archive.org/web/20120113075832/http://www.bipm.org/utils/en/pdf/24_CGPM_Convocation_Draft_Resolution_A.pdf |archive-date=13 January 2012 |url-status=live}} 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.{{cite web |url=http://www.bipm.org/utils/en/pdf/si_brochure_draft_ch2.pdf |title=Draft Chapter 2 for SI Brochure, following redefinitions of the base units |first=Ian |last=Mills |publisher=CCU |date=29 September 2010 |access-date=1 January 2011 |archive-url=https://web.archive.org/web/20120316100258/http://www.bipm.org/utils/en/pdf/si_brochure_draft_ch2.pdf |archive-date=16 March 2012 |url-status=live }} The CIPM meeting of October 2010 found "the conditions set by the General Conference at its 23rd meeting have not yet been fully met.{{#tag:ref|In particular the CIPM was to prepare a detailed mise en pratique for each of the new definitions of the kilogram, ampere, kelvin and mole set by the 23rd CGPM.{{cite web |url=http://www.bipm.org/en/CGPM/db/23/12 |title=Resolution 12 of the 23rd meeting of the CGPM (2007) |location=Sèvres, France |publisher=General Conference on Weights and Measures |access-date=2013-06-21 |archive-url=https://web.archive.org/web/20130421103428/http://www.bipm.org/en/CGPM/db/23/12/ |archive-date=21 April 2013 |url-status=live |df=dmy-all }}|group=Note}} For this reason the CIPM does not propose a revision of the SI at the present time".{{cite web |url=http://www.bipm.org/en/si/new_si/ |title=Towards the "new SI" |publisher=International Bureau of Weights and Measures (BIPM) |access-date=20 February 2011 |archive-url=https://web.archive.org/web/20110514140824/http://www.bipm.org/en/si/new_si/ |archive-date=14 May 2011 |url-status=live }} 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.{{cite web |url=http://www.bipm.org/utils/common/pdf/24_CGPM_Convocation_Draft_Resolution_A.pdf |title=On the possible future revision of the International System of Units, the SI – Draft Resolution A |publisher=International Committee for Weights and Measures (CIPM) |access-date=14 July 2011 |archive-url=https://web.archive.org/web/20110806053509/http://www.bipm.org/utils/common/pdf/24_CGPM_Convocation_Draft_Resolution_A.pdf |archive-date=6 August 2011 |url-status=live }} This resolution was accepted by the conference,{{Citation |title=24th meeting of the General Conference on Weights and Measures |contribution=Resolution 1: On the possible future revision of the International System of Units, the SI |contribution-url=http://www.bipm.org/utils/en/pdf/24_CGPM_Resolution_1.pdf |publisher=International Bureau for Weights and Measures |location=Sèvres, France |date=21 October 2011 |mode=cs1}} It was not expected to be adopted until some prerequisite conditions are met, and in any case not before 2014. See{{cite journal |title=Possible changes to the international system of units |journal=IUPAC Wire |volume=34 |issue=1 |date=January–February 2012}} and in addition the CGPM moved the date of the 25th meeting forward from 2015 to 2014.{{cite press release |url=http://www.bipm.org/utils/en/pdf/Press_release_resolution_1_CGPM.pdf |title=General Conference on Weights and Measures approves possible changes to the International System of Units, including redefinition of the kilogram. |publisher=General Conference on Weights and Measures |location=Sèvres, France |date=23 October 2011 |access-date=25 October 2011 |archive-url=https://web.archive.org/web/20120209175127/http://www.bipm.org/utils/en/pdf/Press_release_resolution_1_CGPM.pdf |archive-date=9 February 2012 |url-status=live }}{{cite web |title=Redefining the SI base units |author=Mohr, Peter |date=2 November 2011 |work=NIST Newsletter |url=https://www.nist.gov/pml/newsletter/siredef.cfm |publisher=NIST |access-date=1 March 2012 |archive-url=https://web.archive.org/web/20160812012223/http://nist.gov/pml/newsletter/siredef.cfm |archive-date=12 August 2016 |url-status=live }} 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",{{cite web |title=Resolutions adopted by the CGPM at its 25th meeting (18–20 November 2014) |url=http://www.bipm.org/utils/common/pdf/CGPM-2014/25th-CGPM-Resolutions.pdf |publisher=International Bureau for Weights and Measures |location=Sèvres, France |date=21 November 2014 |access-date=1 December 2014 |archive-url=https://web.archive.org/web/20150325103457/http://www.bipm.org/utils/common/pdf/CGPM-2014/25th-CGPM-Resolutions.pdf |archive-date=25 March 2015 |url-status=live }} 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).

{{hatnote|The numerical values adopted by the CGPM{{cite web |title=Draft Resolution A "On the revision of the International System of units (SI)" to be submitted to the CGPM at its 26th meeting (2018) |url=https://www.bipm.org/utils/en/pdf/CGPM/Draft-Resolution-A-EN.pdf |access-date=5 May 2018 |archive-url=https://web.archive.org/web/20180429025229/https://www.bipm.org/utils/en/pdf/CGPM/Draft-Resolution-A-EN.pdf |archive-date=29 April 2018 |url-status=live }} are identical to the published CODATA 2017 values.{{cite journal |title=The CODATA 2017 Values of h, e, k, and N_A for the Revision of the SI |last1=Newell |first1=David B. |last2=Cabiati |first2=F. |last3=Fischer |first3=J. |last4=Fujii |first4=K. |last5=Karshenboim |first5=S. G. |last6=Margolis |first6=H. S. |last7=de Mirandés |first7=E. |last8=Mohr |first8=P. J. |last9=Nez |first9=F. | last10=Pachucki |first10=K. |last11=Quinn |first11=T. J. |last12=Taylor |first12=B. N. |last13=Wang |first13=M. |last14=Wood |first14=B. M. |last15=Zhang |first15=Z. |collaboration=CODATA Task Group on Fundamental Constants |doi=10.1088/1681-7575/aa950a |doi-access=free |journal=Metrologia |volume=55 |issue=1 |pages=L13 |date=20 October 2017 |bibcode=2018Metro..55L..13N }}}}

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: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".

• The Planck constant {{Mvar|h}} is exactly {{val|6.62607015|e=-34|u=joule-second (J⋅s)}}.
• The elementary charge {{Mvar|e}} is exactly {{val|1.602176634|e=-19|u=coulomb (C)}}.
• The Boltzmann constant {{Mvar|k}} is exactly {{val|1.380649|e=-23|u=joule per kelvin (J⋅K⁻¹)}}.
• The Avogadro constant {{Math|N_A}} is exactly {{val|6.02214076|e=23|u=reciprocal mole (mol⁻¹)}}.

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

• The speed of light {{Math|c}} is exactly {{val|299792458|u=metres per second (m⋅s⁻¹)}};
• The ground state hyperfine structure transition frequency of the caesium-133 atom {{math|Δν_Cs}} is exactly {{val|9192631770|u=hertz (Hz)}};
• The luminous efficacy of monochromatic radiation of frequency {{val|5.40|e=14|u=Hz}} ({{val|540|u=THz}}) – a frequency of green-colored light at approximately the peak sensitivity of the human eye – {{Math|K_cd}} (where the subscript "cd" is the symbol for candela) is exactly {{val|683|u=lumens per watt (lm⋅W⁻¹)}}.

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);{{r|Brochure9_2019}} the dimensionless unit steradian (symbol sr) is also used:

• {{math|h}} = {{val|6.62607015|e=-34|u=kg⋅m²⋅s⁻¹}}
• {{math|e}} = {{val|1.602176634|e=-19|u=A⋅s}}
• {{math|k}} = {{val|1.380649|e=-23|u=kg⋅m²⋅K⁻¹⋅s⁻²}}
• {{math|N_A}} = {{val|6.02214076|e=23|u=mol⁻¹}}
• {{math|c}} = {{val|299792458|u=m⋅s⁻¹}}
• {{math|Δν_Cs}} = {{math|Δν(¹³³Cs)_hfs}} = {{val|9192631770|u=s⁻¹}}
• {{math|K_cd}} = {{val|683|u=cd⋅sr⋅s³⋅kg⁻¹⋅m⁻²}}

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.

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.{{cite journal |url=http://www.iupac.org/publications/ci/2011/3305/4_mills.html |journal=Chemistry International |volume=33 |number=5 |date=September–October 2011 |title=Part II – Explicit-Constant Definitions for the Kilogram and for the Mole |author=Mills, Ian |issn=0193-6484 |pages=12–15 |access-date=28 June 2013 |archive-url=https://web.archive.org/web/20170709120014/https://www.iupac.org/publications/ci/2011/3305/4_mills.html |archive-date=9 July 2017 |url-status=live }} 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,{{cite book |title=Smoot's Ear – The Measure of Humanity |author=Travenor, Robert |year=2007 |isbn=978-0-300-14334-8 |pages=[https://archive.org/details/smootsearmeasure0000tave/page/35 35–36] |publisher=Yale University Press |url=https://archive.org/details/smootsearmeasure0000tave/page/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 {{val|299792458}} metres per second. The length of the metre could be derived because the second had been already independently defined. The previous{{r|BaseDefs}} and 2019{{r|Brochure9_2019|codata_2017}} definitions are given below.

{{see also|Caesium standard}}

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.

• Previous definition: The second is the duration of {{val|9192631770}} periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.
• 2019 definition: The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency, {{math|Δν_Cs}}, the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom,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 {{val|9192631770}} periods of the radiation corresponding to the transition between the two hyperfine levels of the unperturbed ground state of the ¹³³Cs atom." to be {{val|9192631770}} when expressed in the unit Hz, which is equal to s⁻¹.

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

: 1 s = {{math|{{sfrac|{{val|9192631770}}|Δν_Cs}}}}.

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.

• Previous definition: The metre is the length of the path travelled by light in vacuum during a time interval of {{sfrac|{{val|299792458}}}} of a second.
• 2019 definition: The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum {{mvar|c}} to be {{val|299792458}} when expressed in the unit m⋅s⁻¹, where the second is defined in terms of the caesium frequency {{math|Δν_Cs}}.

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

: 1 m = {{math|{{sfrac|{{val|9192631770}}|{{val|299792458}}}}{{sfrac|c|Δν_Cs}}}}.

File:Watt balance, large view.jpg, which was used to measure the Planck constant in terms of the international prototype of the kilogram.{{cite web |url=http://www.bipm.org/en/scientific/elec/watt_balance/ |title=The BIPM watt balance |publisher=International Bureau of Weights and Measures |access-date=28 March 2013 |year=2012 |archive-url=https://web.archive.org/web/20130421095804/http://www.bipm.org/en/scientific/elec/watt_balance/ |archive-date=21 April 2013 |url-status=live }}]]

The definition of the kilogram fundamentally changed from an artefact (the International Prototype of the Kilogram) to a constant of nature.{{cite journal |title=The Current SI Seen From the Perspective of the Proposed New SI |first1=Barry N |last1=Taylor |journal=Journal of Research of the National Institute of Standards and Technology |volume=116 |date=November–December 2011 |pages=797–80 | issue=6 | doi=10.6028/jres.116.022|pmid=26989600 |pmc=4551220 }} 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.

• Previous definition: The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.
• 2019 definition: The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant {{mvar|h}} to be {{val|6.62607015|e=-34}} when expressed in the unit J⋅s, which is equal to kg⋅m²⋅s⁻¹, where the metre and the second are defined in terms of {{mvar|c}} and {{math|Δν_Cs}}.

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."{{cite journal |title=On the redefinition of the kilogram |first1=Barry N |last1=Taylor |first2=Peter J |last2=Mohr |journal=Metrologia |number=1 |volume=36 |date=November 1999 |pages=63–64 |doi=10.1088/0026-1394/36/1/11 |bibcode=1999Metro..36...63T |s2cid=250823638 }}

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

: 1 kg = {{math|{{sfrac|({{val|299792458}}){{sup|2}}|({{val|6.62607015|e=-34}})({{val|9192631770}})}}{{sfrac|{{gaps|h|Δν_Cs}}|c{{sup|2}}}}}}.

Leading to

: 1 J⋅s = {{math|{{sfrac|h|{{val|6.62607015|e=-34}}}}}}

: 1 J = {{math|{{sfrac|{{gaps|h|Δν_Cs}}|({{val|6.62607015|e=-34}})({{val|9192631770}})}}}}

: 1 W = {{math|{{sfrac|{{gaps|h|(Δν_Cs)²}}|({{val|6.62607015|e=-34}})({{val|9192631770}})²}}}}

:1 N = {{math|{{gaps|{{sfrac|{{val|299792458}}|({{val|6.62607015|e=-34}})({{val|9192631770}})²}}|{{sfrac|{{gaps|h|(Δν_Cs)²}}|c}}}}}}

The definition of the ampere underwent a major revision. The previous definition relied on infinite lengths that are impossible to realise:{{Cite web |date=2018-05-15 |title=Ampere: Introduction |url=https://www.nist.gov/si-redefinition/ampere-introduction |access-date=2024-05-30 |website=NIST |language=en}}

• Previous definition: The ampere is that constant current that, 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 {{val|2|e=-7}} newton per metre of length.

The alternative avoided that issue:

• 2019 definition: The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge {{mvar|e}} to be {{val|1.602176634|e=-19}} when expressed in the unit C, which is equal to A⋅s, where the second is defined in terms of {{math|Δν_Cs}}.

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

: 1 A = {{math|{{sfrac|{{gaps|e|Δν_Cs}}|({{val|1.602176634|e=-19}})({{val|9192631770}})}}}}

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

: 1 C = {{math|{{sfrac|e|{{val|1.602176634|e=-19}}}}}}

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 ({{math|μ₀}}) was fixed at exactly {{val|4|end=π|e=-7}} H⋅m⁻¹.{{cite web |url=http://physics.nist.gov/cuu/Units/ampere.html |title=Unit of electric current (ampere) |access-date=7 September 2015 |work=Historical context of the SI |publisher=NIST |archive-url=https://web.archive.org/web/20130603235543/http://physics.nist.gov/cuu/Units/ampere.html |archive-date=3 June 2013 |url-status=live }}

A consequence of the revised definition is that the ampere no longer depends on the definitions of the kilogram and the metre; it does, however, still depend on the definition of the second. In addition, the numerical values when expressed in SI units of the vacuum permeability, vacuum permittivity, and impedance of free space, which were exact before the redefinition, are subject to experimental error after the redefinition. For example, the numerical value of the vacuum permeability has a relative uncertainty equal to that of the experimental value of the fine-structure constant $\backslash alpha$.{{cite journal |last=Davis |first=Richard S. |title=Determining the value of the fine-structure constant from a current balance: getting acquainted with some upcoming changes to the SI |journal=American Journal of Physics |volume=85 |number=5 |pages=364–368 |year=2017 |doi=10.1119/1.4976701 |arxiv=1610.02910|bibcode=2017AmJPh..85..364D |s2cid=119283799 }} The CODATA 2018 value for the relative standard uncertainty of $\backslash alpha$ is {{physconst|alpha|runc=yes|after=.}}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 {{val|1|u=m}} causes a force of {{val|2|e=-7|u=N/m}} 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 {{val|2|e=-7|u=T}}. Namely {{val|1|u=T}} is the intensity of the magnetic field B that causes a force of {{val|1|u=N/m}} on a wire carrying a current of {{val|1|u=A}}.

The number {{val|2|e=-7}} was written also as μ₀/2π. This arbitrary definition is what made μ₀ to be exactly 4π{{e|-7}} 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{{e|-7}} H/m and has to be measured experimentally.

The value of the vacuum permittivity {{nowrap|1=ε₀ = 1/(μ₀c²)}} 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.

The ampere definition leads to exact values for

: 1 V = {{math|{{gaps|{{sfrac|{{val|1.602176634|e=-19}}|({{val|6.62607015|e=-34}})({{val|9192631770}})}}|{{sfrac|{{gaps|h|Δν_Cs}}|e}}}}}}

: 1 Wb = {{math|{{gaps|{{sfrac|{{val|1.602176634|e=-19}}|{{val|6.62607015|e=-34}}}}|{{sfrac|h|e}}}}}}

: 1 Ω = {{math|{{gaps|{{sfrac|({{val|1.602176634|e=-19}})²|{{val|6.62607015|e=-34}}}}|{{sfrac|h|e²}}}}}}

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.

• Previous definition: The kelvin, unit of thermodynamic temperature, is {{sfrac|273.16}} of the thermodynamic temperature of the triple point of water.
• 2019 definition: The kelvin, symbol K, is the SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constant {{mvar|k}} to be {{val|1.380649|e=-23}} when expressed in the unit J⋅K⁻¹, which is equal to kg⋅m²⋅s⁻²⋅K⁻¹, where the kilogram, metre and second are defined in terms of {{mvar|h}}, {{mvar|c}} and {{math|Δν_Cs}}.

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

: 1 K = {{math|{{sfrac|{{val|1.380649|e=-23}}|({{val|6.62607015|e=-34}})({{val|9192631770}})}}{{sfrac|{{gaps|h|Δν_Cs}}|k}}}}.

File:Silicon sphere for Avogadro project.jpg, an International Avogadro Coordination project to determine the Avogadro constant]]

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.

• Previous 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.
• 2019 definition:{{r|cipm_106|p=22}} The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly {{val|6.02214076|e=23}} elementary entities. This number is the fixed numerical value of the Avogadro constant, {{math|N_A}}, when expressed in the unit mol⁻¹ and is called the Avogadro number.{{cite web |title=Redefining the Mole |url=https://www.nist.gov/si-redefinition/redefining-mole |website=NIST |access-date=24 October 2018 |date=23 October 2018 |archive-url=https://web.archive.org/web/20181024074533/https://www.nist.gov/si-redefinition/redefining-mole |archive-date=24 October 2018 |url-status=live }} The amount of substance, symbol {{math|n}}, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles.

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

: 1 mol = {{math|{{sfrac|{{val|6.02214076|e=23}}|N{{sub|A}}}}}}.

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 mass of a ¹²C atom, unbound and in its electronic and nuclear ground states, is exactly 12 dalton.
• The number of dalton in a gram is exactly the numerical value of the Avogadro constant: (i.e., {{nowrap|1=1 g/Da = 1 mol ⋅ {{math|N_A}}}}).

The wording of the 9th SI Brochure{{r|Brochure9_2019}}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." 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 {{val|1|u=g/mol}}, 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 {{val|0.012|u=kg.mol-1}} within a relative standard uncertainty equal to that of the recommended value of {{math|N_Ah}} at the time this Resolution was adopted, namely {{val|4.5|e=-10}}, and that in the future its value will be determined experimentally",{{Cite web|url=https://www.bipm.org/utils/common/pdf/CGPM-2018/26th-CGPM-Resolutions.pdf|title=Resolutions adopted|date=November 2018|website=Bureau international des poids et mesures|url-status=dead|archive-url=https://web.archive.org/web/20200204124652/https://www.bipm.org/utils/common/pdf/CGPM-2018/26th-CGPM-Resolutions.pdf|archive-date=4 February 2020|access-date=2020-02-04}}{{Cite book|url=https://books.google.com/books?id=yOmaDwAAQBAJ&pg=PA54|title=Introduction to Quantum Metrology: The Revised SI System and Quantum Standards|last=Nawrocki|first=Waldemar|date=2019-05-30|publisher=Springer|isbn=978-3-030-19677-6|pages=54|language=en}} which makes no reference to the dalton and is consistent with either statement.

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.

• Previous definition: The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency {{val|540|e=12|u=Hz}} and that has a radiant intensity in that direction of {{sfrac|683}} watt per steradian.
• 2019 definition: The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency {{val|540|e=12|u=Hz}}, {{math|K_cd}}, to be 683 when expressed in the unit lm⋅W⁻¹, which is equal to cd⋅sr⋅W⁻¹, or cd⋅sr⋅kg⁻¹⋅m⁻²⋅s³, where the kilogram, metre and second are defined in terms of {{mvar|h}}, {{mvar|c}} and {{math|Δν_Cs}}.

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

:1 cd = {{math|{{gaps|{{sfrac|{{gaps|K_cd|h|(Δν_Cs)²}}|683⋅({{val|6.62607015|e=-34}})({{val|9192631770}})²}}}}}}

All seven of the SI base units are defined in terms of defined constantsThough 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. and universal physical constants.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).{{cite book |url= http://www.bipm.org/utils/en/pdf/Monographie1983-1.pdf |title=Principles covering Photometry |publisher=Conférence général des poids et mesures (CGPM) |location=Sevres |author1=Wyszecki, G. |author2=Blevin, W.R. |author3=Kessler, K.G. |author4=Mielenz, K.D. |year=1983 |access-date=23 April 2012 |archive-url=https://web.archive.org/web/20081011204957/http://www.bipm.org/utils/en/pdf/Monographie1983-1.pdf |archive-date=11 October 2008 |url-status=live }} 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.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. In practice, G can only be measured with a relative uncertainty of the order of 10⁻⁵,

The following terms are defined in [http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2012.pdf International vocabulary of metrology – Basic and general concepts and associated terms] {{Webarchive|url=https://web.archive.org/web/20170317223139/http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2012.pdf |date=17 March 2017 }}:

• measurement reproducibility – definition 2.25
• standard measurement uncertainty – definition 2.30
• relative standard measurement uncertainty – definition 2.32

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.

{{cite journal |title=Evolution of the International Metric System of Units SI |author=Chyla, W.T. |date=December 2011 |journal=Acta Physica Polonica A |number=6 |volume=120 |pages=998–1011 |doi=10.12693/APhysPolA.120.998 |bibcode=2011AcPPA.120..998C |doi-access=free }} 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)

{{cite web |url=http://www.bipm.org/en/measurement-units/new-si/mise-en-pratique.html |title=What is a mise en pratique? |publisher=BIPM |year=2011 |quote=is a set of instructions that allows the definition to be realised in practice at the highest level. |access-date=6 September 2015 |archive-url=https://web.archive.org/web/20150922051552/http://www.bipm.org/en/measurement-units/new-si/mise-en-pratique.html |archive-date=22 September 2015 |url-status=live }} 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.

{{See also|CODATA 2018}}

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:

• For the redefinition of the kilogram, at least three separate experiments yielding values for the Planck constant having a relative expanded (95%) uncertainty of no more than {{val|5|e=-8}} must be carried out and at least one of these values should be better than {{val|2|e=-8}}. Both the Kibble balance and the Avogadro project should be included in the experiments and any differences between these must be reconciled.{{cite web |url=http://www.bipm.org/utils/common/pdf/CCM12.pdf#page=23 |title=Recommendations of the Consultative Committee for Mass and Related Quantities to the International Committee for Weights and Measures. |work=12th Meeting of the CCM |date=26 March 2010 |publisher=Bureau International des Poids et Mesures |location=Sèvres |access-date=27 June 2012 |archive-url=https://web.archive.org/web/20130514081750/http://www.bipm.org/utils/common/pdf/CCM12.pdf#page=23 |archive-date=14 May 2013 |url-status=dead }}{{cite web |url=http://www.bipm.org/utils/common/pdf/CCQM16.pdf#page=40 |title=Recommendations of the Consultative Committee for Amount of Substance: Metrology in Chemistry to the International Committee for Weights and Measures. |work=16th Meeting of the CCQM |date=15–16 April 2010 |publisher=Bureau International des Poids et Mesures |location=Sèvres |access-date=27 June 2012 |archive-url=https://web.archive.org/web/20130514072057/http://www.bipm.org/utils/common/pdf/CCQM16.pdf#page=40 |archive-date=14 May 2013 |url-status=dead }}
• For the redefinition of the kelvin, the relative uncertainty of the Boltzmann constant derived from two fundamentally different methods such as acoustic gas thermometry and dielectric constant gas thermometry must be better than 10⁻⁶, and these values must be corroborated by other measurements.{{cite web |url=http://www.bipm.org/utils/common/pdf/CCT25.pdf#page=53 |title=Recommendations of the Consultative Committee for Thermometry to the International Committee for Weights and Measures. |work=25th Meeting of the Consultative Committee for Thermometry |date=6–7 May 2010 |publisher=Bureau International des Poids et Mesures |location=Sèvres |access-date=27 June 2012 |archive-url=https://web.archive.org/web/20130514064646/http://www.bipm.org/utils/common/pdf/CCT25.pdf#page=53 |archive-date=14 May 2013 |url-status=dead }}

As of March 2011, the International Avogadro Coordination (IAC) group had obtained an uncertainty of {{val|3.0|e=-8}} and NIST had obtained an uncertainty of {{val|3.6|e=-8}} in their measurements. 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 {{val|17|5|e=-8}} to within {{val|2|e=-8}}.{{cite web |url=http://www.inrim.it/luc/know/index.htm |title=kilogram NOW – Realization of the awaited definition of the kilogram |publisher=European Association of National Metrology Institutes |access-date=8 October 2012 |archive-url=https://web.archive.org/web/20160304084349/http://www.inrim.it/luc/know/index.htm |archive-date=4 March 2016 |url-status=live }} {{As of|2013|3}} 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 because the proposed system makes use of atomic scale phenomena rather than macroscopic phenomena, it should be called the "Quantum SI System".

{{cite book |journal=Advances in Quantum Chemistry |url=https://books.google.com/books?id=Wsk36wNstDEC&q=si+definitions+boltzmann+planck&pg=PA34 |year=2008 |title=The Quantum SI: A Possible New International System of Units |author=Mohr, Peter J. |volume=53 |page=34 |isbn=978-0-12-373925-4 |publisher=Academic Press |access-date=2 April 2012 |doi=10.1016/s0065-3276(07)53003-0 |bibcode=2008AdQC...53...27M}}

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.{{cite press release |title=Universe's Constants Now Known with Sufficient Certainty to Completely Redefine the International System of Units |url=https://www.nist.gov/news-events/news/2016/11/universes-constants-now-known-sufficient-certainty-completely-redefine |access-date=31 December 2016 |publisher=NIST |date=22 November 2016 |archive-url=https://web.archive.org/web/20170101003042/https://www.nist.gov/news-events/news/2016/11/universes-constants-now-known-sufficient-certainty-completely-redefine |archive-date=1 January 2017 |url-status=live }}{{cite journal |title=CODATA recommended values of the fundamental physical constants: 2014 |journal=Reviews of Modern Physics |volume=88 |issue=3 |pages=035009–1–73 |date=26 September 2016 |author=Mohr, Peter J. |author2= Newell, David B. |author3=Taylor, Barry N. |doi=10.1103/RevModPhys.88.035009 |quote=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. |arxiv=1507.07956 |bibcode=2016RvMP...88c5009M |s2cid=1115862 }}

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,{{cite conference |title=Proceedings of the 106th meeting |conference=International Committee for Weights and Measures |date=16–20 October 2017 |url=https://www.bipm.org/utils/en/pdf/CIPM/CIPM2017-EN.pdf?page=23 |conference-url=https://www.bipm.org/en/committees/cipm/meeting/106.html |location=Sèvres |access-date=27 January 2018 |archive-url=https://web.archive.org/web/20180127202612/https://www.bipm.org/utils/en/pdf/CIPM/CIPM2017-EN.pdf?page=23 |archive-date=27 January 2018 |url-status=live }}{{Rp|17–23}} The same day, in response to the CIPM's endorsement of the final values,{{r|cipm_106|p=22}} 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.{{r|codata_2017}} 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.{{cite web |url=https://www.sciencenews.org/article/official-redefining-kilogram-units-measurement |title=It's official: We're redefining the kilogram |first=Emily |last=Conover |date=16 November 2018 |access-date=16 November 2018 |work=Science News |archive-url=https://web.archive.org/web/20181116171854/https://www.sciencenews.org/article/official-redefining-kilogram-units-measurement |archive-date=16 November 2018 |url-status=live }}

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.

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.{{cite journal |title=A sceptic's review of the New SI |author=Price, Gary |year=2011 |journal=Accreditation and Quality Assurance |volume=16 |issue=3 |pages=121–132 |doi=10.1007/s00769-010-0738-x|s2cid=110127259 }} Although this criticism applies to the linking of the kilogram to the Planck constant {{math|h}} via a route that requires a knowledge of both special relativity and quantum mechanics,{{cite journal |url=http://www.iupac.org/publications/ci/2011/3305/4_mills.html |journal=Chemistry International |volume=33 |number=5 |date=September–October 2011 |title=Part I – From the Current "Kilogram Problem" to a Proposed Definition |author=Censullo, Albert C. |issn=0193-6484 |pages=9–12 |access-date=28 June 2013 |archive-url=https://web.archive.org/web/20170709120014/https://www.iupac.org/publications/ci/2011/3305/4_mills.html |archive-date=9 July 2017 |url-status=live }} it does not apply to the definition of the ampere, which is closer to an example of its quantity than is the previous definition.{{cite journal |url=http://www.apajournal.org.uk/2013_0028-0044.pdf |journal=Journal of the Association of Public Analysts (Online) |year=2013 |number=41 2 |pages=28–44 |title=The Background and Implications of the "New SI" for Analytical Chemists |first1=D Thorburn |last1=Burns |first2=EH |last2=Korte |access-date=25 June 2013 |archive-url=https://web.archive.org/web/20160306125346/http://www.apajournal.org.uk/2013_0028-0044.pdf |archive-date=6 March 2016 |url-status=live }} 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.

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. If the mass of a silicon atom were to be determined by the Avogadro project using the Avogadro constant, it could be linked directly to the kilogram.{{cite journal |url=http://kcdb.bipm.org/NL/16/OIML_Davis_2011.pdf |journal=OIML Bulletin|volume=LII |number=4 |date=October 2011 |title=Proposed change to the definition of the kilogram: Consequences for legal metrology |first1=Richard |last1=Davis |access-date=28 June 2013 |archive-url=https://web.archive.org/web/20150327081726/http://kcdb.bipm.org/NL/16/OIML_Davis_2011.pdf |archive-date=27 March 2015 |url-status=live }} 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 ({{math|N_A}}) have also been expressed.The two quantities of the Avogadro constant {{math|N_A}} and the Avogadro number {{math|N_N}} are numerically identical but while {{math|N_A}} has the unit mol⁻¹, {{math|N_N}} is a pure number. 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".{{cite journal |title=The Mole is Not an Ordinary Measurement Unit |first1=Ingvar |last1=Johansson |journal=Accreditation and Quality Assurance |volume=16 |year=2011 |number=16 |pages=467–470 |doi=10.1007/s00769-011-0804-z|s2cid=121496106 }}

The 8th edition of the SI Brochure defined the dalton in terms of the mass of an atom of ¹²C.http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf SI Brochure (8th edition) 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{{r|Brochure9_2019}} retains the definition of dalton in terms of ¹²C, with the effect that the link between the dalton and the kilogram will be broken.{{cite journal |title=Comments on recent proposals for redefining the mole and kilogram |first=B.P. |last=Leonard |year=2010 |volume=47 |issue=3 |pages=L5–L8 |journal=Metrologia |doi=10.1088/0026-1394/47/3/L01 |bibcode=2010Metro..47L...5L |s2cid=118098528 }}{{cite journal |title=Some reflections on the proposed redefinition of the unit for the amount of substance and of other SI units |last1=Pavese |first1= Franco |year=2011 |journal=Accreditation and Quality Assurance |volume=16 |issue=3 |pages=161–165 |doi=10.1007/s00769-010-0700-y |s2cid=121598605 }}

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.{{cite book |title=Quantities, Units and Symbols in Physical Chemistry International Union of Pure and Applied Chemistry; Physical Chemistry Division |publisher=International Union of Pure and Applied Chemistry, Blackwell Science Ltd |edition=2nd |year=1993 |author1=Mills, Ian |author2=Cvitaš, Tomislav |author3=Homann, Klaus |author4=Kallay, Nikola |author5=Kuchitsu, Kozo |isbn=978-0-632-03583-0 |url-access=registration |url=https://archive.org/details/quantitiesunitss0000unse }} This approval has since been given.{{SIBrochure8th|pages=114, 115}} 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 {{nowrap|1={{math|N_A}} = (g/Da) mol{{sup|−1}}}}, but that the unified atomic mass unit ({{math|m_u}}) 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.{{cite journal |url=https://www.researchgate.net/publication/231073122 |title=Why the dalton should be redefined exactly in terms of the kilogram |author=Leonard, Brian Phillip |date=May 2012 |journal=Metrologia |volume=49 |issue=4 |pages=487–491 |doi=10.1088/0026-1394/49/4/487 |bibcode=2012Metro..49..487L |s2cid=55717564 }} The 9th SI Brochure, however, defines both the dalton (Da) and the unified atomic mass unit (u) as exactly {{sfrac|1|12}} of the mass of a free carbon-12 atom and not in relation to the kilogram,{{r|Brochure9_2019}} with the effect that the above equation will be inexact.

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. He noted that in many theoretical papers, temperature is represented by the quantities {{math|Θ}} or {{math|β}} where

$$\backslash Theta=k\; T;\; \backslash quad\; \backslash beta\; =\; \backslash frac\{1\}\{k\; T\}$$

and {{math|k}} 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.

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.{{cite web |title=Mise en pratique for the definition of the kelvin |year=2011 |url=http://www.bipm.org/utils/en/pdf/MeP_K.pdf |publisher=Consultative Committee for Thermometry (CCT), International Committee for Weights and Measures (CIPM) |location=Sèvres, France |access-date=25 June 2013 |archive-url=https://web.archive.org/web/20130508191638/http://www1.bipm.org/utils/en/pdf/MeP_K.pdf |archive-date=8 May 2013 |url-status=live }}{{cite journal |journal=Procès-verbaux du Comité International des Poids et Mesures, 78th Meeting |url=http://www.bipm.org/utils/en/pdf/ITS-90.pdf |title=The International Temperature Scale of 1990 (ITS-90) |year=1989 |author=Consultative Committee for Thermometry (CCT) |access-date=25 June 2013 |archive-url=https://web.archive.org/web/20130623020049/http://www.bipm.org/utils/en/pdf/ITS-90.pdf |archive-date=23 June 2013 |url-status=live }}

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.{{cite journal |url = http://publications.csiro.au/rpr/download?pid=csiro:EP11794&dsid=DS4 |author = Foster, Marcus P |journal = Metrologia |volume = 47 |pages = R41–R51 |number = 6 |date = 5 October 2010 |access-date = 24 June 2013 |doi = 10.1088/0026-1394/47/6/R01 |title = The next 50 years of the SI: a review of the opportunities for the e-Science age |bibcode = 2010Metro..47R..41F |s2cid = 117711734 |archive-url = https://web.archive.org/web/20160306004745/https://publications.csiro.au/rpr/download?pid=csiro:EP11794&dsid=DS4 |archive-date = 6 March 2016 |url-status = live |url-access = subscription }} 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.{{cite journal |journal=Procès-verbaux du Comité International des Poids et Mesures, 66th Meeting |url=http://www.bipm.org/utils/common/pdf/CIPM-PV-OCR/CIPM1977.pdf |title=The International Temperature Scale of 1990 (ITS-90) |year=1977|access-date=1 September 2019 |pages=14, 143 |language=fr }}

• {{annotated link|International System of Units}}
• {{annotated link|International Vocabulary of Metrology}}
• {{annotated link|Physical constant}}
• {{annotated link|SI base unit}}
• {{annotated link|2005–2019 definitions of the SI base units}}
• {{annotated link|Non-SI units mentioned in the SI}} – changes associated with the 2019 redefinition

{{Reflist|60em|group="Note"}}

{{reflist}}

• [https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf The International System of Units] (9th ed.), International Bureau of Weights and Measures, 2019, ISBN 978-92-822-2272-0
• {{cite web

|work=Metrologia

|author=International Bureau of Weights and Measures (BIPM)

|title=Input data for the special CODATA-2017 adjustment

|edition=Updated

|date=10 August 2017

|url=http://iopscience.iop.org/journal/0026-1394/page/CODATA-2017_adjustment

|access-date = 14 August 2017

}}

• [http://www.bipm.org/en/si/new_si/ BIPM website on the New SI], including a [http://www.bipm.org/en/si/new_si/faqs.html FAQ page].
• [https://www.nist.gov/si-redefinition/turning-point-humanity-redefining-worlds-measurement-system A Turning Point for Humanity: Redefining the World’s Measurement System] by NIST
• [https://www.bbc.co.uk/programmes/m000znw3 Measuring Mass: The Last Artefact] – BBC Four

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