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Proposed redeﬁnition of SI base units
For a topical guide to this subject, see Outline of the metric system.
K A scd kgmmol
Current (2013) SI System: Dependence of base unit deﬁnitions
on other base units (for example, the
metre
is deﬁned in terms of the distance traveled by light in a speciﬁc fraction of a
second
)Proposed SI System: Dependence of base unit deﬁnitions on physical constants with ﬁxed numerical values and on other baseunits that are derived from the same set of constants.
A committee of the International Committee for Weightsand Measures (CIPM) has proposed revised formal def-initions of the SI base units, which are being examinedby the CIPM and which may be considered by the 25th'General Conference on Weights and Measures’, in 2014.Themetricsystemwasoriginallyconceivedasasystemofmeasurement that was derivable from nature. When themetricsystemwasﬁrstintroducedinFrancein1799tech-nicalproblemsnecessitatedtheuseofartifactsasthepro-totype metre and kilogram. In 1960 the metre was rede-
ﬁned in terms of the wavelength of light from a speciﬁed
source, making it derivable from nature, but the kilogramhas been deﬁned by an artifact ever since its introduction.If the proposed redeﬁnition is accepted, the metric sys-tem (SI) will, for the ﬁrst time, be wholly derivable fromnature.The proposal can be summarised as follows:“There will still be the sameseven base units (second, metre,
kilogram, ampere, kelvin, mole,
and candela). Of these, the kilo-gram, ampere, kelvin and molewill be redeﬁned by choosing exactnumerical values for the Planckconstant, the elementary electriccharge, the Boltzmann constant,
and the Avogadro constant, re-spectively. The second, metreand candela are already deﬁned byphysical constants and it is onlynecessary to edit their presentdeﬁnitions. The new deﬁnitionswill improve the SI without chang-ing the size of any units, thusensuring continuity with presentmeasurements.”
[1]
Further details are found in the draft chapter of the
NinthSI Units Brochure
.
[2]
The last major overhaul of the metric system was in 1960when the International System of Units (SI) was formallypublished as a coherent set of units of measure. SI isstructured around seven base units that have apparently“arbitrary” deﬁnitions and another twenty units that arederived from these base units. Although the units them-selves form a coherent system, the deﬁnitions do not. Theproposal before the CIPM seeks to remedy this by usingthefundamentalquantitiesofnatureasthebasisforderiv-ing the base units. This will mean, amongst other things,that the prototype kilogram will cease to be used as
the
1
2
1 BACKGROUND
deﬁnitive replica of the kilogram. The second and themetre are already deﬁned in such a manner.A number of authors have published criticisms of the re-vised deﬁnitions — in particular that proposal had failedto address the impact of breaking the link between themole, kilogram, the dalton, the Avogadro constant and
Avogadro’s number.
1 Background
Main article: History of the metric systemThe basic structure of SI was developed over a periodof about 170 years (1791 to 1960). Since 1960 techno-logical advances have made it possible to address variousweaknesses in SI, notably the dependence on an artifactto deﬁne the kilogram.
1.1 Development of SI
DuringtheearlyyearsoftheFrenchRevolution, thelead-ers of the French National Constituent Assembly decidedto introduce a completely new system of measurementbased on the principles of logic and natural phenom-
ena. The resulting
mètre des archives
and
kilogramme des archives
were deﬁned in terms of artefacts that were a“best attempt” at fulﬁlling these principles.
[3]
In 1875, by which time the use of the metric systemhad become widespread in Europe and in Latin Amer-ica, twenty industrially developed nations met for theConvention of the Metre. The result was the signing ofthe Treaty of the Metre under which three bodies wereset up to take custody of the international prototype kilo-gramandmetreandtoregulatecomparisonswithnationalprototypes.
[4][5]
They were:
ã
CGPM (General Conference on Weights and Mea-sures /
Conférence générale des poids et mesures
)—The Conference meets every four to six years andconsists of delegates of the nations who had signedthe convention. It discusses and examines the ar-rangements required to ensure the propagation andimprovement of the International System of Unitsand it endorses the results of new fundamentalmetrological determinations.
ã
CIPM (International Committee for Weights andMeasures /
Comité international des poids et mesures
)—The Committee consists of eighteen em-inent scientists, each from a diﬀerent country, nom-inated by the CGPM. The CIPM meets annuallyand is tasked to advise the CGPM. The CIPM hasset up a number of sub-committees, each chargedwith a particular area of interest. One of these, theCCU (Consultative Committee for Units), amongstother things, advises the CIPM on matters concern-ing units of measurement.
[6]
ã
BIPM (International Bureau for Weights and Mea-sures /
Bureau international des poids et mesures
)—The Bureau provides safe keeping of the interna-tional prototype kilogram and metre, provides labo-ratory facilities for regular comparisons of the na-tional prototypes with the international prototypeand is the secretariat for the CIPM and the CGPM.The ﬁrst CGPM (1889) formally approved the use of40 prototype metres and 40 prototype kilograms fromthe British ﬁrm Johnson Matthey as the standards man-dated by the Convention of the Metre.
[7]
One of eachof these was nominated by lot as the international proto-types, other copies were retained by the CGPM as work-ing copies and the rest were distributed to member na-tionsforuseastheirnationalprototypes. Atregularinter-vals the national prototypes were compared with and re-calibrated against the international prototype.
[8]
In 1921the Convention of the Metre was revised and the man-date of the CGPM was extended to provide standardsfor all units of measure, not just mass and length. Inthe ensuing years the CGPM took on responsibility forprovidingstandardsofelectriccurrent(1946), luminosity
(1946), temperature (1948), time (1956) and molar mass
(1971).
[9]
MassdriftovertimeofnationalprototypesK21–K40, plustwoof the International Prototype Kilogram’s (IPK’s) sister copies : K32
and K8(41).
[Note 1]
All mass changes are relative to the IPK.
[10]
The 9th CGPM (1948) instructed the CIPM “to makerecommendations for a single practical system of units ofmeasurement, suitable for adoption by all countries ad-hering to the Metre Convention”.
[11]
The recommenda-tions based on this mandate were presented to the 11thCGPM (1960) where they were formally accepted andgiven the name
Système International d'Unités
and itsabbreviation “SI”.
[12]
1.2 Impetus for change
Changing the underlying principles behind the deﬁni-tion of the SI base units is not without precedent. The
313th CGPM (1967) replaced the srcinal deﬁnition ofthe second (which was based on a back-calculation of theEarth’s rotation in the year 1900) with a deﬁnition basedon the frequency of the radiation emitted between twohyperﬁne levels of the ground state of the caesium 133atom. Similarly, the 17th CGPM (1983) replaced the1960 deﬁnition of the metre
[Note 2]
with one where themetre is derived from the speed of light where the speedof light had been deﬁned exactly in terms of metres persecond.
[13]
Over the years, drifts of up to 2×10
−8
kilograms perannum in the national prototype kilograms relative tothe international prototype kilogram have been detected.There was no way of determining whether the nationalprototypesweregainingmassorwhethertheIPKwaslos-ing mass.
[14]
At the 21st meeting of the CGPM (1999),national laboratories were urged to investigate ways ofbreaking the link between the kilogram and a speciﬁcartefact. Newcastle University metrologist Peter Cump-son has since identiﬁed mercury vapour absorption orcarbonaceous contamination as possible causes of thisdrift.
[15][16]
Independently of this drift having been identiﬁed, theAvogadro project and development of the Watt balancepromised methods of indirectly measuring mass witha very high precision. These projects provided toolsthat would enable alternative means of redeﬁning thekilogram.
[17]
A report published in 2007 by the Consultative Commit-teeforThermometrytotheCIPMnotedthattheircurrentdeﬁnition of temperature has proved to be unsatisfactoryfor temperatures below 20 kelvins and for temperaturesabove 1300 kelvins. The committee was of the view thatthe Boltzmann constant provided a better basis for tem-perature measurement than did the triple point of water,as it overcame these diﬃculties.
[18]
At its 23rd meeting (2007), the GCPM mandated theCIPM to investigate the use of natural constants as thebasis for all units of measure rather than the artefacts thatwere then in use. The following year this was endorsedby the International Union of Pure and Applied Physics(IUPAP).
[19]
At a meeting of the CCU held in Reading,UnitedKingdom, inSeptember2010, aresolution
[20]
anddraftchangestotheSIbrochurethatweretobepresentedto the next meeting of the CIPM in October 2010 wereagreed to in principle.
[21]
The CIPM meeting of Octo-ber 2010 found that “the conditions set by the GeneralConference at its 23rd meeting have not yet been fullymet.
[Note 3]
For this reason the CIPM does not proposea revision of the SI at the present time ;
[23]
however, theCIPMpresentedaresolutionforconsiderationatthe24thCGPM (17–21 October 2011) to agree the new deﬁni-tions in principle, but not to implement them until thedetails have been ﬁnalised.
[24]
This resolution was ac-cepted by the conference,
[25]
and in addition the CGPMmoved the date of the 25th meeting forward from 2015to 2014.
[26][27]
2 The proposal
In this section, an “X” at the end of a number means one or more ﬁnal digits yet to be agreed upon
.In 2011 the CCU published a draft of the proposedchange in the form of an amendment that should be madetothe8theditionofthe
SIBrochure
.
[2]
Inittheyproposedthat in addition to the speed of light, four further con-stants of nature should be deﬁned to have exact values:
ã
The Planck constant
h
is exactly6.62606X×10
−34
joule second (J·s).
ã
The elementary charge
e
is exactly1.60217X× 10
−19
coulomb (C).
ã
The Boltzmann constant
k
is exactly1.38065X×10
−23
jouleperkelvin(J·K
−1
).
ã
The Avogadro constant
N
A
is exactly6.02214X×10
23
reciprocal mole (mol
−1
).Theseconstantsweredescribedinthe2006versionoftheSI manual; the latter three were deﬁned as “constants tobe obtained by experiment”.The CCU also proposed that the numerical values asso-ciated with the following constants of nature be retainedunchanged:
ã
The speed of light
c
is exactly299792458metres per second (m·s
−1
).
ã
The ground state hyperﬁne splittingfrequency of the caesium
−
133 atom
Δ
ν
(
133
Cs)
is exactly 9192631770hertz (Hz).
ã
The luminous eﬃcacy
K
ofmonochromatic radiation of frequency540×10
12
Hz is exactly 683 lumen perwatt (lm·W
−1
).The seven deﬁnitions above are rewritten below af-ter converting the derived units (joule, coulomb, hertz,
lumen and watt) into the seven base units (second, metre,
kilogram, ampere, kelvin, mole and candela). In the listthat follows, the symbol sr stands for the dimensionlessunit steradian.
ã
Δ
ν
(
133
Cs) = 9192631770s
−1
ã
c
= 299792458s
−1
·m
ã
h
= 6.62606X×10
−34
s
−1
·m
2
·kg
ã
e
= 1.60217X×10
−19
s·A
4
3 IMPACT ON BASE UNIT DEFINITIONS
ã
k
= 1.38065X×10
−23
s
−2
·m
2
·kg·K
−1
ã
N
A = 6.02214X×10
23
mol
−1
ã
K
= 683 s
3
·m
−2
·kg
−1
·cd·srIn addition the CCU proposed that
ã
the international prototype kilogram beretired and that the current deﬁnition ofthe kilogram be abrogated,
ã
the current deﬁnition of the ampere beabrogated,
ã
the current deﬁnition of the kelvin be ab-rogated and
ã
the current deﬁnition of the mole be re-vised.These changes will have the eﬀect of redeﬁning the SIbase units, though the deﬁnitions of the derived SI unitswill remain the same.
3 Impact on base unit deﬁnitions
TheCCUproposalrecommendedthatthetextofthedef-initions of all the base units be either reﬁned or rewrit-ten changing the emphasis from explicit-unit to explicit-constant type deﬁnitions.
[28]
Explicit-unit type deﬁnitionsdeﬁne a unit in terms of a speciﬁc example of that unit—for example in 1324 Edward II deﬁned the inch as be-
ing the length of three barleycorns
[29]
and since 1889the kilogram has been deﬁned as being the mass of theInternational Prototype Kilogram. In explicit-constantdeﬁnitions, a constant of nature is given a speciﬁed valueand the deﬁnition of the unit emerges as a consequence.Forexample, in1983, thespeedoflightwasdeﬁnedtobeexactly 299,792,458 metres per second and as long as thesecond has already been deﬁned, the length of the metrecan be deﬁned.The current (2008)
[13]
and proposed (2011)
[21]
deﬁni-tions are given below. In many cases the ﬁnal digit of anyconstant is yet to be agreed, so it has been represented byan
X
3.1 Second
The proposed deﬁnition of the second is eﬀectively thesame as the current deﬁnition, the only diﬀerence be-ing thattheconditionsunderwhichthemeasurementsaremade are more rigorously deﬁned.
Current deﬁnition:
The second is the du-ration of 9192631770 periods of the radia-tion corresponding to the transition betweenthe two hyperﬁne levels of the ground state of
the caesium-133 atom.
Proposed deﬁnition:
The second, s, is theunit of time; its magnitude is set by ﬁxing thenumerical value of the ground state hyperﬁnesplitting frequency of the caesium-133 atom,at rest and at a temperature of 0 K, to be equalto exactly 9192631770 when it is expressed inthe unit s
−1
, which is equal to Hz.
3.2 Metre
The proposed deﬁnition of the metre is eﬀectively thesame as the current deﬁnition, the only diﬀerence beingthat the additional rigour in the deﬁnition of the secondwill propagate to the metre.
Currentdeﬁnition:
Themetreisthelengthofthe path travelled by light in vacuum during atime interval of 1/299792458 of a second.
Proposed deﬁnition:
The metre, m, is theunit of length; its magnitude is set by ﬁxing thenumerical value of the speed of light in vac-uum to be equal to exactly 299792458 when itis expressed in the unit m·s
−1
.
3.3 Kilogram
Thewattbalancewhichwillmeasuretheratioofthe Planckcon-
stant to the international prototype kilogram.
[30]
The deﬁnition of the kilogram is undergoing a fundamen-tal change - the current deﬁnition deﬁnes the kilogram asbeing the mass of the international prototype kilogramwhich is an artifact, not a constant of nature
[31]
whilethe new deﬁnition relates it to the equivalent energy ofa photon via the Planck constant.
Current deﬁnition:
The kilogram is the unitof mass; it is equal to the mass of the interna-tional prototype of the kilogram.

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