TheInfoList

OR:

In 2019, four of the seven
SI base unit The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which all ...
s specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artifacts such as the standard kilogram. Effective 20 May 2019, the 144th anniversary of the Metre Convention, the
kilogram The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially. ...
,
ampere The ampere (, ; symbol: A), often shortened to amp,SI supports only the use of symbols and deprecates the use of abbreviations for units. is the unit of electric current in the International System of Units (SI). One ampere is equal to elect ...
,
kelvin The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and ...
, and mole are now defined by setting exact numerical values, when expressed in SI units, for the
Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equiva ...
('), the elementary electric charge ('), the
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constan ...
(), and the Avogadro constant (), respectively. The
second The second (symbol: s) is the unit of time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds ...
,
metre The metre ( British spelling) or meter ( American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its pr ...
, and
candela The candela ( or ; symbol: cd) is the unit of luminous intensity in the International System of Units (SI). It measures luminous power per unit solid angle emitted by a light source in a particular direction. Luminous intensity is analogous to ...
physical constant A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature and have constant value in time. It is contrasted with a mathematical constant, ...
s. The four new definitions aimed to improve the SI without changing the value of any units, ensuring continuity with existing measurements. In November 2018, the 26th
General Conference on Weights and Measures The General Conference on Weights and Measures (GCWM; french: Conférence générale des poids et mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established i ...
(CGPM) unanimously approved these changes, The conference ran from 13–16 November and the vote on the redefinition was scheduled for the last day. Kazakhstan was absent and did not vote. which the
International Committee for Weights and Measures The General Conference on Weights and Measures (GCWM; french: Conférence générale des poids et mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established ...
(CIPM) had proposed earlier that year after determining that previously agreed conditions for the change had been met. These conditions were satisfied by a series of experiments that measured the constants to high accuracy relative to the old SI definitions, and were the culmination of decades of research. The previous major change of the metric system occurred in 1960 when the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...
(SI) was formally published. At this time the metre was redefined: the definition was changed from the prototype of the metre to a certain number of
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tr ...
s of a spectral line of a krypton-86 radiation, making it derivable from universal natural phenomena.The metre was redefined again in 1983 by fixing the value of the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit f ...
in vacuum. That definition went unaltered in 2019 and remains in effect today.
The kilogram remained defined by a physical prototype, leaving it the only artifact upon which the SI unit definitions depend. At this time the SI, as a coherent system, was constructed around seven '' base units'', powers of which were used to construct all other units. With the 2019 redefinition, the SI is constructed around seven defining ''constants'', allowing all units to be constructed directly from these constants. The designation of base units is retained but is no longer essential to define the SI units. The
metric system The metric system is a system of measurement that succeeded the decimalised system based on the metre that had been introduced in France in the 1790s. The historical development of these systems culminated in the definition of the Interna ...
was originally conceived as a system of measurement that was derivable from unchanging phenomena, but practical limitations necessitated the use of artifacts – the prototype of the metre and prototype of the kilogram – when the metric system was introduced in France in 1799. Although 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 as the
kelvin The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and ...
, 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 constant A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature and have constant value in time. It is contrasted with a mathematical constant, ...
s. 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 Dalton may refer to: Science * Dalton (crater), a lunar crater * Dalton (program), chemistry software * Dalton (unit) (Da), the atomic mass unit * John Dalton, chemist, physicist and meteorologist Entertainment * Dalton (Buffyverse), minor ...
The dalton is not defined in the formal proposal to be voted upon by the CGPM, only in the 9th edition of the ''SI Brochure''. and the definitions of the kilogram, the mole, and the Avogadro constant.

# Background

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

## Development of SI

During the early years of the
French Revolution The French Revolution ( ) was a period of radical political and societal change in France that began with the Estates General of 1789 and ended with the formation of the French Consulate in November 1799. Many of its ideas are consider ...
, 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 ' and ' which were a "best attempt" at fulfilling these principles. By 1875, use of the metric system had become widespread in Europe and in
Latin America Latin America or * french: Amérique Latine, link=no * ht, Amerik Latin, link=no * pt, América Latina, link=no, name=a, sometimes referred to as LatAm is a large cultural region in the Americas where Romance languages — languages derived f ...
; that year, twenty industrially developed nations met for the Convention of the Metre, which led to the signing of the
Treaty of the Metre The Metre Convention (french: link=no, Convention du Mètre), also known as the Treaty of the Metre, is an international treaty that was signed in Paris on 20 May 1875 by representatives of 17 nations (Argentina, Austria-Hungary, Belgium, Brazi ...
, 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. They were: * CGPM (General Conference on Weights and Measures, ') – 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 The General Conference on Weights and Measures (GCWM; french: Conférence générale des poids et mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established i ...
(International Committee for Weights and Measures, ') – 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. *
BIPM The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an intergovernmental organisation, through which its 59 member-states act together on measurement standards in four areas: chemistry, ...
(International Bureau for Weights and Measures, ') – 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. 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. 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 In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in moles. The molar mass is a bulk, not molecular, ...
(1971). The 9th CGPM in 1948 instructed the CIPM "to make recommendations for a single practical system of units of measurement, suitable for adoption by all countries adhering to the Metre Convention". The recommendations based on this mandate were presented to the 11th CGPM (1960), where they were formally accepted and given the name "'" and its abbreviation "SI".

## 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 The second (symbol: s) is the unit of time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds ...
, which was based on Earth's average rotation from 1750 to 1892, with a definition based on the
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
of the radiation emitted or absorbed with a transition between two hyperfine levels of the ground state of the
caesium-133 Caesium (55Cs) has 40 known isotopes, making it, along with barium and mercury, one of the elements with the most isotopes. The atomic masses of these isotopes range from 112 to 151. Only one isotope, 133Cs, is stable. The longest-lived radioisot ...
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 The metre per second is the unit of both speed (a scalar quantity) and velocity (a vector quantity, which has direction and magnitude) in the International System of Units (SI), equal to the speed of a body covering a distance of one metre in ...
. Since their manufacture, drifts of up to kilograms/20 μg per year in the national prototype kilograms relative to the international prototype of the kilogram (IPK) have been detected. There was no way of determining whether the national prototypes were gaining mass or whether the IPK was losing mass. Newcastle University metrologist Peter Cumpson has since identified mercury vapour absorption or
carbon Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent—its atom making four electrons available to form covalent chemical bonds. It belongs to group 14 of the periodic table. Carbon makes up ...
aceous contamination as possible causes of this drift. At the 21st meeting of the CGPM (1999), national laboratories were urged to investigate ways of breaking the link between the kilogram and a specific artifact. Metrologists investigated several alternative approaches to redefining the kilogram based on fundamental physical constants. Among others, the Avogadro project and the development of the Kibble balance (known as the "watt balance" before 2016) promised methods of indirectly measuring mass with very high precision. These projects provided tools that enable alternative means of redefining the kilogram. A report published in 2007 by the Consultative Committee for Thermometry (CCT) to the CIPM noted that their current definition of temperature has proved to be unsatisfactory for temperatures below and for temperatures above . The committee took the view that the
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constan ...
provided a better basis for temperature measurement than did the triple point of water because it overcame these difficulties. At its 23rd meeting (2007), the CGPM mandated the CIPM to investigate the use of natural constants as the basis for all units of measure rather than the artifacts that were then in use. The following year this was endorsed by the International Union of Pure and Applied Physics (IUPAP). At a meeting of the CCU held in Reading, United Kingdom, in September 2010, a resolution 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. The CIPM meeting of October 2010 found "the conditions set by the General Conference at its 23rd meeting have not yet been fully met. For this reason the CIPM does not propose a revision of the SI at the present time". 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. This resolution was accepted by the conference, It was not expected to be adopted until some prerequisite conditions are met, and in any case not before 2014. See and in addition the CGPM moved the date of the 25th meeting forward from 2015 to 2014. At the 25th meeting on 18 to 20 November 2014, it was found that "despite rogress in the necessary requirementsthe data do not yet appear to be sufficiently robust for the CGPM to adopt the revised SI at its 25th meeting", 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).

# 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 The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equiva ...
is exactly . * The
elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
is exactly . * The
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constan ...
is exactly . * The Avogadro constant is exactly . 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 is exactly ; * The ground state hyperfine structure transition frequency of the caesium-133 atom is exactly ; * The luminous efficacy of monochromatic radiation of frequency () – a frequency of green-colored light at approximately the peak sensitivity of the human eye – is exactly . The seven definitions above are rewritten below with the derived units (
joule The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applied ...
,
coulomb The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI). In the present version of the SI it is equal to the electric charge delivered by a 1 ampere constant current in 1 second and to elementary char ...
,
hertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that one he ...
, lumen, and
watt The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James Wa ...
) expressed in terms of the seven base units: second, metre, kilogram, ampere, kelvin, mole, and candela, according to the 9th SI Brochure. In the list that follows, the symbol sr stands for the dimensionless unit
steradian The steradian (symbol: sr) or square radian is the unit of solid angle in the International System of Units (SI). It is used in three-dimensional geometry, and is analogous to the radian, which quantifies planar angles. Whereas an angle in radia ...
. * = = * = * = * = * = * = * = As part of the redefinition, the
International Prototype of the Kilogram The International Prototype of the Kilogram (referred to by metrologists as the IPK or Le Grand K; sometimes called the '' ur-kilogram,'' or ''urkilogram,'' particularly by German-language authors writing in English) is an object that was used t ...
was retired and definitions of the kilogram, the
ampere The ampere (, ; symbol: A), often shortened to amp,SI supports only the use of symbols and deprecates the use of abbreviations for units. is the unit of electric current in the International System of Units (SI). One ampere is equal to elect ...
, 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. 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 Measuring tape with inches The inch (symbol: in or ″) is a unit of length in the British imperial and the United States customary systems of measurement. It is equal to yard or of a foot. Derived from the Roman uncia ("twelfth") ...
as being the length of three barleycorns 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 1983, the speed of light was defined as exactly metres per second. The length of the metre could be derived because the second had been already independently defined. The previous and 2019 definitions are given below.

## Second

The new definition of the
second The second (symbol: s) is the unit of time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds ...
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 periods of the radiation corresponding to the transition between the two hyperfine levels of the
ground state The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. I ...
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, , the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom, to be 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 = .

## Metre

The new definition of the
metre The metre ( British spelling) or meter ( American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its pr ...
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 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 to be when expressed in the unit m⋅s−1, where the second is defined in terms of the caesium frequency . The metre may be expressed directly in terms of the defining constants: : 1 m = .

## Kilogram

The definition of the
kilogram The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially. ...
changed fundamentally; the previous definition defined the kilogram as the mass of the
International Prototype of the Kilogram The International Prototype of the Kilogram (referred to by metrologists as the IPK or Le Grand K; sometimes called the '' ur-kilogram,'' or ''urkilogram,'' particularly by German-language authors writing in English) is an object that was used t ...
, which is an artifact rather than a constant of nature. The new definition relates the kilogram to, amongst things, the equivalent mass of the energy of a
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...
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 The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equiva ...
to be 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 and . 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 [] hertz."'' The kilogram may be expressed directly in terms of the defining constants: : 1 kg = . Leading to : 1 J⋅s = : 1 J = :1 W = :1 N =

## Ampere

The definition of the
ampere The ampere (, ; symbol: A), often shortened to amp,SI supports only the use of symbols and deprecates the use of abbreviations for units. is the unit of electric current in the International System of Units (SI). One ampere is equal to elect ...
underwent a major revision. The previous definition, which is difficult to realise with high precision in practice, was replaced by a definition that is 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 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 The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
to be when expressed in the unit C, which is equal to A⋅s, where the second is defined in terms of . The ampere may be expressed directly in terms of the defining constants as: : 1 A = For illustration, this is equivalent to defining one
coulomb The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI). In the present version of the SI it is equal to the electric charge delivered by a 1 ampere constant current in 1 second and to elementary char ...
to be an exact specified multiple of the elementary charge. : 1 C = Because the previous definition contains a reference to
force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as ...
, which has the
dimension In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordi ...
s 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 The vacuum magnetic permeability (variously ''vacuum permeability'', ''permeability of free space'', ''permeability of vacuum''), also known as the magnetic constant, is the magnetic permeability in a classical vacuum. It is a physical constant, ...
() was fixed at exactly . Because the speed of light in vacuum () is also fixed, it followed from the relationship $c^2=\frac$ that the vacuum permittivity () had a fixed value, and from $Z_0=\sqrt ,$ that the impedance of free space () likewise had a fixed value. 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 $\alpha$. The CODATA 2018 value for the relative standard uncertainty of $\alpha$ is A note should be added on the definition of magnetic field unit (tesla). When the ampere was defined as the current that when flows in two long parallel wires separated by causes a force of on each other, there was also another definition: the magnetic field at the location of each of the wires in this configuration was defined to be . Namely is the intensity of the magnetic field B that causes a force of on a wire carrying a current of . The number was written also as ''μ''0/2''π''. This arbitrary definition is what made ''μ''0 to be exactly 4''π'' H/m. Accordingly, the magnetic field near a wire carrying current is given by B = ''μ''0''I''/2''πr''. 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, ''μ''0 can no longer be exactly 4''π'' H/m and has to be measured experimentally. The value of the vacuum permittivity is also affected accordingly. The Maxwell equations will 'see to it' that the electrostatic force between two point charges will be ''F'' = 1/(4''πε''0)(''q''1''q''2)/''r''2. The ampere definition leads to exact values for :1 V = :1 Wb = :1 Ω =

## Kelvin

The definition of the
kelvin The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and ...
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 Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics. Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic wo ...
, is 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 The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constan ...
to be 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 , and . The kelvin may be expressed directly in terms of the defining constants as: : 1 K = .

## Mole

The previous definition of the mole linked it to the kilogram. The revised definition breaks that link by making a mole a specific number of entities of the substance in question. *Previous definition: The mole is the
amount of substance In chemistry, the amount of substance ''n'' in a given sample of matter is defined as the quantity or number of discrete atomic-scale particles in it divided by the Avogadro constant ''N''A. The particles or entities may be molecules, atoms, ions, ...
of a system that contains as many elementary entities as there are
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, ...
s in 0.012 kilogram of
carbon-12 Carbon-12 (12C) is the most abundant of the two stable isotopes of carbon (carbon-13 being the other), amounting to 98.93% of element carbon on Earth; its abundance is due to the triple-alpha process by which it is created in stars. Carbon-12 is ...
. When the mole is used, the elementary entities must be specified and may be atoms,
molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...
s,
ion An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by convent ...
s,
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kno ...
s, other particles, or specified groups of such particles. *2019 definition: The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly elementary entities. This number is the fixed numerical value of the Avogadro constant, , when expressed in the unit mol−1 and is called the Avogadro number. The amount of substance, symbol , 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 = . One consequence of this change is that the previously defined relationship between the mass of the 12C atom, the
dalton Dalton may refer to: Science * Dalton (crater), a lunar crater * Dalton (program), chemistry software * Dalton (unit) (Da), the atomic mass unit * John Dalton, chemist, physicist and meteorologist Entertainment * Dalton (Buffyverse), minor ...
, the kilogram, and the Avogadro constant is no longer valid. One of the following had to 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 constant: (i.e., ). The wording of the 9th SI BrochureA 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 true. The molar mass constant, while still with great accuracy remaining , is no longer exactly equal to that. Appendix 2 to the 9th SI Brochure states that "the molar mass of carbon 12, ''M''(12C), is equal to within a relative standard uncertainty equal to that of the recommended value of at the time this Resolution was adopted, namely , and that in the future its value will be determined experimentally", which makes no reference to the dalton and is consistent with either statement.

## Candela

The new definition of the
candela The candela ( or ; symbol: cd) is the unit of luminous intensity in the International System of Units (SI). It measures luminous power per unit solid angle emitted by a light source in a particular direction. Luminous intensity is analogous to ...
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 photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle, based on the luminosity function, a standardized model of the sensitivity of the human eye ...
, in a given direction, of a source that emits
monochromatic radiation {{Short description, Electromagnetic radiation with a single constant frequency In physics, monochromatic radiation is electromagnetic radiation with a single constant frequency. When that frequency is part of the visible spectrum (or near it) the ...
of frequency and that has a radiant intensity in that direction of watt per
steradian The steradian (symbol: sr) or square radian is the unit of solid angle in the International System of Units (SI). It is used in three-dimensional geometry, and is analogous to the radian, which quantifies planar angles. Whereas an angle in radia ...
. *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 , , 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 , and . :1 cd =

# Impact on reproducibility

All seven of the SI base units will be 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 A luminous efficiency function or luminosity function represents the average spectral sensitivity of human visual perception of light. It is based on subjective judgements of which of a pair of different-colored lights is brighter, to describe ...
and denoted by ''V''(''λ''), a function that is determined by the
International Commission on Illumination The International Commission on Illumination (usually abbreviated CIE for its French name, Commission internationale de l'éclairage) is the international authority on light, illumination, colour, and colour spaces. It was established in 1913 a ...
(CIE).
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 The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in th ...
''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 i
''International vocabulary of metrology – Basic and general concepts and associated terms''
: *measurement reproducibility – definition 2.25 *standard measurement uncertainty – definition 2.30 *relative standard measurement uncertainty – definition 2.32
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. 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) 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 The General Conference on Weights and Measures (GCWM; french: Conférence générale des poids et mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established i ...
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 must be carried out and at least one of these values should be better than . Both the Kibble balance and the Avogadro project should be included in the experiments and any differences between these must be reconciled. * 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. As of March 2011, the International Avogadro Coordination (IAC) group had obtained an uncertainty of and
NIST The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sc ...
had obtained an uncertainty of 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 to within . 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 Atomic spacing refers to the distance between the nuclei of atoms in a material. This space is extremely large compared to the size of the atomic nucleus, and is related to the chemical bonds which bind atoms together. In solid materials, the ato ...
phenomena rather than macroscopic phenomena, it should be called the "Quantum SI System". 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. 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, The same day, in response to the CIPM's endorsement of the final values, the CODATA Task Group on Fundamental Constants published its 2017 recommended values for the four constants with uncertainties and proposed numerical values for the redefinition without uncertainty. The vote, which was held on 16 November 2018 at the 26th GCPM, was unanimous; all attending national representatives voted in favour of the revised proposal. The new definitions became effective on 20 May 2019.

# Concerns

In 2010, Marcus Foster of the 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, 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 The candela ( or ; symbol: cd) is the unit of luminous intensity in the International System of Units (SI). It measures luminous power per unit solid angle emitted by a light source in a particular direction. Luminous intensity is analogous to ...
and the mole – units Foster argued are not true base units. Other issues raised by Foster fell outside the scope of the proposal.

## Explicit-unit and explicit-constant definitions

Concerns have been expressed that the use of explicit-constant definitions of the unit being defined that are not related to an example of its quantity will have many adverse effects. Although this criticism applies to the linking of the kilogram to the Planck constant via a route that requires a knowledge of both special relativity and quantum mechanics, it does not apply to the definition of the ampere, which is closer to an example of its quantity than is the previous definition. 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.

## Mass and the Avogadro constant

International Union of Pure and Applied Chemistry The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...
(IUPAC) approved the use of the dalton as an alternative to the
unified atomic mass unit The dalton or unified atomic mass unit (symbols: Da or u) is a non-SI unit of mass widely used in physics and chemistry. It is defined as of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at r ...
with the qualification that the CGPM had not given its approval. This approval has since been given. Following the proposal to redefine the mole by fixing the value of the Avogadro constant, Brian Leonard of the University of Akron, writing in ''
Metrologia ''Metrologia'' is a bimonthly journal dealing with the scientific aspects of metrology. It has been running since 1965 and has been published by the International Bureau of Weights and Measures since 1991. Since 2003 the journal has been published ...
'', proposed that the dalton (Da) be redefined such that , but that the unified atomic mass unit () retain its current definition based on the mass of 12C, ceasing to exactly equal the dalton. This would result in the dalton and the atomic mass unit potentially differing from each other with a relative uncertainty of the order of 10−10. The 9th SI Brochure, however, defines both the dalton (Da) and the unified atomic mass unit (u) as exactly of the mass of a free carbon-12 atom and not in relation to the kilogram, with the effect that the above equation will be inexact.

## Temperature

Different temperature ranges need different measurement methods. Room temperature can be measured by means of expansion and contraction of a liquid in a thermometer but high temperatures are often associated with colour of
blackbody radiation Black-body radiation is the thermal electromagnetic radiation within, or surrounding, a body in thermodynamic equilibrium with its environment, emitted by a black body (an idealized opaque, non-reflective body). It has a specific, continuous spect ...
. 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 or where $\Theta=k T; \quad \beta = \frac$ and is the Boltzmann constant. Chyla acknowledged, however, that in the macroscopic world, temperature plays the role of a base unit because much of the theory of
thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of t ...
is based on temperature. The Consultative Committee for Thermometry, part of the
International Committee for Weights and Measures The General Conference on Weights and Measures (GCWM; french: Conférence générale des poids et mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established ...
, 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.

## Luminous intensity

Foster argued that "luminous intensity he candelais not a
physical quantity A physical quantity is a physical property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a ' Numerical value ' and a ' Unit '. For exam ...
, but a photobiological quantity that exists in human perception", questioning whether the candela should be a base unit. 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.

* * * * * * – changes associated with the 2019 redefinition

* *