2019 redefinition of

SI base units

The SI system after the 2019 redefinition:

Dependence of base unit definitions on physical
constants with fixed numerical values and on other
base units.
The SI system after 1983, but before the 2019
redefinition: Dependence of base unit definitions on
other base units (for example, the metre is defined as
the distance travelled by light in a specific fraction of
a second), with the constants of nature and artefacts
used to define them (such as the mass of the IPK for
the kilogram).

The 2019 redefinition of the SI base

units came into force on 20 May
2019,[1][2] the 144th anniversary of the
Metre Convention. After the redefinition,
the kilogram, ampere, kelvin, and mole
were defined by setting exact numerical
values for the Planck constant (h), the
elementary electric charge (e), the
Boltzmann constant (k), and the
Avogadro constant (NA), respectively.
The second, metre, and candela are
already defined by physical constants
and are subject to correction to their
present definitions. The new definitions
aim 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.[7]:23

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 metre to a
certain number of wavelengths of a
spectral line of a krypton-86
radiation,[Note 1] making it derivable from
universal natural phenomena. The
kilogram remained defined by a physical
prototype, leaving it the only artefact
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 are retained but are no longer
essential to define SI measures.

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 artefacts—the
prototype metre and prototype kilogram—
when the metric system was introduced
in France in 1799. Although it was
designed for long-term stability, the
masses of the prototype kilogram and its
secondary copies have shown small
variations 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 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[Note 2] and the definitions of
the kilogram, the mole, and the Avogadro
constant.

Background
The basic structure of SI was developed
over about 170 years between 1791 and
1960. Since 1960, technological
advances have made it possible to
address weaknesses in SI such as the
dependence on a physical artefact to
define the kilogram.

Development of SI

During the early years of the French

Revolution, the leaders of the French
National Constituent Assembly decided
to introduce a 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 mètre des Archives and kilogramme
des Archives which were a "best attempt"
at fulfilling these principles.[9]

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 prototype
kilogram and metre, and to regulate
comparisons with national
prototypes.[10][11] They were:

CGPM (General Conference on Weights

and Measures, Conférence générale des
poids et mesures) – The Conference
meets every four to six years and
consists of delegates of the nations
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, 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.[12]
BIPM (International Bureau for Weights
and Measures, Bureau international des
 poids et mesures) – The Bureau
provides safe keeping of the
international prototype kilogram and
metre, provides laboratory facilities for
regular comparisons of the national
prototypes with the international
prototype, and is the secretariat for the
CIPM and the CGPM.

The first CGPM (1889) formally approved

the use of 40 prototype metres and 40
prototype kilograms made by the British
firm Johnson Matthey as the standards
mandated by the Convention of the
Metre.[13] One of each of these was
nominated by lot as the international
prototypes, the CGMP retained other
copies as working copies, and the rest
were distributed to member nations for
use as their national prototypes. At
regular intervals the national prototypes
were compared with and recalibrated
against the international prototype.[14]

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).[15]
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
"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
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.[19]
 

Mass drift over time of national prototypes K21–K40,

plus two of the International Prototype Kilogram's
(IPK's) sister copies: K32 and K8(41).[Note 3] All mass
changes are relative to the IPK.[20]

Since their manufacture, drifts of up to

2 × 10−8 kilograms per year in the national
prototype kilograms relative to the
international prototype 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.[21] Newcastle
University metrologist Peter Cumpson
has since identified mercury vapour
absorption or carbonaceous
contamination as possible causes of this
drift.[22][23] 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.

Independently to the identification of this

drift, the Avogadro project and the
development of the Kibble balance, which
was 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.[24] 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
20 K and for temperatures above 1300 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.[25]

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).[26] At a meeting of the
CCU held in Reading, United Kingdom, in
September 2010, a resolution[27] 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.[28] The CIPM meeting of
October 2010 found "the conditions set
by the General Conference at its 23rd
meeting have not yet been fully
met.[Note 4] For this reason the CIPM does
not propose a revision of the SI at the
present time".[30] 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.[31] This
resolution was accepted by the
conference,[32] and in addition the CGPM
moved the date of the 25th meeting
forward from 2015 to 2014.[33][34] 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",[35] thus postponing the
revision to the next meeting in 2018.
Measurements accurate enough to meet
the conditions were available in 2017 and
the redefinition[36] was adopted at the
26th CGPM (13–16 November 2018).

Redefinition
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:

The Planck constant h is exactly

6.626 070 15 × 10−34 joule-second (J⋅s)
.
 The elementary charge e is exactly
1.602 176 634 × 10−19 coulomb (C).
The Boltzmann constant k is exactly
1.380 649 × 10−23 joule per kelvin (J⋅K−1)
.
The Avogadro constant NA is exactly
6.022 140 76 × 1023 reciprocal mole (mol−1)
.

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
redefinition retains unchanged the
numerical values associated with the
following constants of nature:
 The speed of light c is exactly
299 792 458 metres per second (m⋅s−1)
;
The ground state hyperfine structure
transition frequency of the caesium-
133 atom ΔνCs is exactly
9 192 631 770 hertz (Hz);
The luminous efficacy Kcd of
monochromatic radiation of frequency
540 × 1012 Hz (540 THz) – a frequency
of green colored light at approximately
the peak sensitivity of the human eye –
is exactly
683 lumens per watt (lm⋅W−1).

The seven definitions above are rewritten

below with the derived units joule,
coulomb, hertz, lumen, and watt)
expressed in terms of the seven base
units; second, metre, kilogram, ampere,
kelvin, mole, and candela, according to
the draft ninth SI Brochure.[4] In the list
that follows, the symbol sr stands for the
dimensionless unit steradian.

ΔνCs = Δν(133Cs)hfs = 9 192 631 770 s−1

c = 299 792 458 m⋅s−1
h = 6.626 070 15 × 10−34 kg⋅m2⋅s−1
e = 1.602 176 634 × 10−19 A⋅s
k = 1.380 649 × 10−23 kg⋅m2⋅K−1⋅s−2
NA = 6.022 140 76 × 1023 mol−1
Kcd = 683 cd⋅sr⋅s3⋅kg−1⋅m−2
As part of the redefinition, the
international prototype 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.[38]
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[39] and since 1889 the
kilogram has been defined as being the
mass of the International Prototype
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 1983, the speed of light was defined as
exactly 299 792 458 metres per second.
The length of the metre could be derived
because the second had been
independently defined. The previous[19]
(as of 2018) and 2019[4][37] 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.

Previous definition: The second is the

duration of 9 192 631 770 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 ΔνCs, the
unperturbed ground-state hyperfine
transition frequency of the caesium-
133 atom, to be 9 192 631 770 when
expressed in the unit Hz, which is equal
to s−1.

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.
 Previous definition: The metre is the
length of the path travelled by light in
vacuum during a time interval of
1
299 792 458 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 c to be
299 792 458 when expressed in the
unit m⋅s−1, where the second is defined
in terms of the caesium frequency
ΔνCs.

Kilogram
 

A Kibble balance, which is being used to measure the

Planck constant in terms of the international
prototype kilogram.[40]

The definition of the kilogram changed

fundamentally; the previous definition
defined the kilogram as the mass of the
international prototype kilogram, which is
an artefact rather than a constant of
nature.[41] The new definition relates the
kilogram to the equivalent mass of the
energy of a photon given its frequency,
via the Planck constant.
 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 h to be
6.626 070 15 × 10−34 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 c and
ΔνCs.

A consequence of this change is that the

new definition of the kilogram is
dependent on the definitions of the
second and the metre.

Ampere

The definition of the ampere underwent a

major revision. The previous definition,
which is difficult to realise with high
precision in practice, was replaced by a
definition that is more intuitive and easier
to realise.

Previous definition: The ampere is that

constant current which, if maintained
in two straight parallel conductors of
infinite length, of negligible circular
cross-section, and placed 1 m apart in
 vacuum, would produce between these
conductors a force equal to 2 × 10−7
newton per metre of length.
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 e to be
1.602 176 634 × 10−19 when expressed
in the unit C, which is equal to A⋅s,
where the second is defined in terms of
ΔνCs.

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 (μ0) was fixed at
exactly 4π × 10−7 H⋅m−1.[42] Because the
speed of light in vacuum (c) is also fixed,
it followed from the relationship

that the vacuum permittivity (ε0) had a

fixed value, and from

 
that the impedance of free space (Z0)
likewise had a fixed value.[43]

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 of the vacuum
permeability, vacuum permittivity, and
impedance of free space, which were
exact before the redefinition, will be
subject to experimental error after the
redefinition.[44] For example, the
numerical value of the vacuum
permeability will have a relative
uncertainty equal to that of the
experimental value of the fine-structure
constant   .[45] The CODATA 2018 value
for the relative standard uncertainty of  
is 1.5 × 10−10.[46]

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.

Previous definition: The kelvin, unit of

1
thermodynamic temperature, is 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 k to be 1.380 649 × 10−23
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 h, c and ΔνCs.

One consequence of this change is that

the new definition of the kelvin depends
on the definitions of the second, the
metre, and the kilogram.
Mole

A near-perfect sphere of ultra-pure silicon – part of

the Avogadro project, an International Avogadro
Coordination project to determine the Avogadro
number[40]

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:[7]:22 The mole, symbol
mol, is the SI unit of amount of
substance. One mole contains exactly
6.022 140 76 × 1023 elementary
entities. This number is the fixed
numerical value of the Avogadro
constant, NA, when expressed in the
unit mol−1 and is called the Avogadro
 number.[7][47] The amount of
substance, symbol 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.

One consequence of this change is that

the current defined relationship between
the mass of the 12C atom, the dalton, the
kilogram, and the Avogadro number will
no longer be valid. One of the following
must change:

The mass of a 12C atom is exactly 12

dalton.
 The number of dalton in a gram is
exactly the numerical value of the
Avogadro number: (i.e.,
1 g/Da=1 mol ⋅ NA).

The wording of the ninth SI

Brochure[4][Note 5] implies that the first
statement remains valid, which means
the second is no longer true. The molar
mass constant, while still with great
accuracy remaining 1 g/mol, is no longer
exactly equal to that. Draft Resolution A,
which was voted on at the 26th CGPM,
only stated that "the molar mass of
carbon 12, M(12C), is equal to
0.012 kg⋅mol−1 within a relative standard
uncertainty equal to that of the
recommended value of NAh at the time
this Resolution was adopted, namely
4.5 × 10−10, and that in the future its value
will be determined experimentally", 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, the only difference being that
the additional rigour in the definition of
the second and metre will 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 540 × 1012 Hz
and that has a radiant intensity in that
1
direction of 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 540 × 1012 Hz,
Kcd, 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 h, c and ΔνCs.

Impact on reproducibility
All seven of the SI base units will be
defined in terms of defined
constants[Note 6] and universal physical
constants.[Note 7][48] 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.[Note 8] In practice, G can only be
measured with a relative uncertainty of
the order of 10−5,[Note 9] which would have
resulted in the upper limit of the
kilogram's reproducibility being around
10−5 whereas the current international
prototype kilogram can be measured with
a reproducibility of 1.2 × 10−8.[44] 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)[49] 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:

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 5 × 10−8
must be carried out and at least one of
these values should be better than
2 × 10−8. Both the Kibble balance and
the Avogadro project should be
included in the experiments and any
 differences between these must be
reconciled.[50][51]
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.[52]

As of March 2011, the International

Avogadro Coordination (IAC) group had
obtained an uncertainty of 3.0 × 10−8 and
NIST had obtained an uncertainty of
3.6 × 10−8 in their measurements.[24] 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 (17 ± 5) × 10−8 to within
2 × 10−8.[53] As of March 2013 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".[54]
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.[55][56]

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,[7]:17–23 The
same day, in response to the CIPM's
endorsement of the final values,[7]: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.[37] 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 will become effective
on 20 May 2019.[57]

Concerns
In 2010, Marcus Foster of the
Commonwealth Scientific and Industrial
Research Organisation (CSIRO) published
a wide-ranging critique of SI; he raised
numerous issues ranging from basic
issues such as the absence of the
symbol "Ω" (Omega) from most Western
computer keyboards to the abstract
issues such as inadequate formalism in
the metrological concepts on which SI is
based. The changes proposed in the New
SI only addressed 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.[58]

Explicit-unit and explicit-

constant definitions
Concerns 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 have been expressed.[59] Although
this criticism applies to the proposed
linking of the kilogram to the Planck
constant h via a route that requires a
knowledge of both special relativity and
quantum mechanics,[60] it does not apply
to the proposed definition of the ampere,
which is closer to an example of its
quantity than is the current definition.[61]
Some observers have welcomed the
proposal to base the definition of electric
current on the charge of the electron
rather than the current definition of a
force between two parallel, current-
carrying wires; 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.[44]

Mass and the Avogadro

constant

When the scale of the divergence

between the IPK and national kilogram
prototypes was reported in 2005, a
debate about whether the kilogram
should be defined in terms of the mass of
the silicon-28 atom or by using the Kibble
balance began. The mass of a silicon
atom could be determined using the
Avogadro project and using the Avogadro
number, it could be linked directly to the
kilogram.[62] 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 (NA) have also been
expressed.[Note 10] 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".[58][63]
The SI Brochure (8th edition) defines the
dalton in terms of the mass of an atom of
12C.[64] It defines the Avogadro constant
in terms of this mass and the kilogram,
making it determined by experiment. The
proposal fixes the Avogadro constant and
the draft of the Ninth SI Brochure[4]
retains the definition of dalton in terms of
12C, with the effect that the link between
the dalton and the kilogram will be
broken.[65][66]

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.[67] This approval has since
been given.[68] 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 NA=(g/Da) mol−1,
but that the unified atomic mass unit
(mu) retain its current definition based on
the mass of 12C, ceasing to exactly equal
to 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.[69] The draft of the ninth SI
Brochure, however, defines both the
dalton (Da) and the unified atomic mass
 1
unit (u) as exactly 12 of the mass of a
free carbon-12 atom and not in relation to
the kilogram,[4] with the effect that the
above equation will be inexact.

Temperature

Temperature is somewhat of an enigma;

room temperature can be measured by
means of expansion and contraction of a
liquid in a thermometer but high
temperatures are often associated with
colour. Wojciech T. Chyla, approaching
the structure of SI from a philosophical
point of view in the Journal of the Polish
Physical Society, argued that temperature
is not a real base unit but is an average of
the thermal energies of the individual
particles that comprise the body
concerned.[44] He noted that in many
theoretical papers, temperature is
represented by the quantities Θ or β
where

and 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.[44]

The Consultative Committee for

Thermometry, part of the International
Committee for Weights and Measures,
publishes a mise en pratique (practical
technique), last updated in 1990, for
measuring temperature which, at very low
and at very high temperatures, often links
energy to temperature via the Boltzmann
constant.[70][71]

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.[58]
See also
International System of Units – a
system of units of measurement for
base and derived physical quantities
International Vocabulary of Metrology
Physical constant – Universal and
unchanging physical quantity
SI base unit
2005-2019 definitions of the SI base
units

Notes
1. The metre was redefined again in
1983 by fixing the value of the speed
of light. That definition will remain in
effect after 2019.
2. The dalton is not defined in the
formal proposal to be voted upon by
the CGPM, only in the (draft) Ninth SI
Brochure.
3. 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). 
4. 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[29]
5. 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."
6. 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.
7. 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).
8. 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.
9. The following terms are defined in
International vocabulary of metrology
– Basic and general concepts and
associated terms Archived 17
March 2017 at the Wayback Machine:
measurement reproducibility –
definition 2.25
standard measurement
uncertainty – definition 2.30
relative standard measurement
uncertainty – definition 2.32
10. The two quantities of the Avogadro
constant NA and the Avogadro
number NN are numerically identical
but while NA has the unit mol−1, NN is
a pure number.

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Further reading
International Bureau of Weights and
Measures (5 February 2018), SI
Brochure: The International System of
Units (SI) (PDF) (Draft) (9th ed.)
International Bureau of Weights and
Measures (BIPM) (10 August 2017).
 "Input data for the special CODATA-
2017 adjustment" . Metrologia
(Updated ed.). Retrieved 14 August
2017.

External links
BIPM website on the New SI , including
a FAQ page .

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