A redefinition of SI base units is scheduled to come into force on 20 May 2019,^{[1]}^{[2]} the 144th anniversary of the Metre Convention. After the redefinition, the kilogram, ampere, kelvin, and mole will be defined by setting exact numerical values for the Planck constant (h), the elementary electric charge (e), the Boltzmann constant (k), and the Avogadro constant (N_{A}), 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 the wavelength of a spectral line of a krypton86 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 longterm 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.
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.
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 tenmillionth 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:
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]}
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 krypton86 radiation, replacing the preSI 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 caesium133 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]}
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).
Following the successful 1983 redefinition of the metre in terms of an exact numerical value for the speed of light, the BIPM's Consultative Committee for Units (CCU) recommended and the BIPM proposed that four further constants of nature should be defined to have exact values. These are:
These constants are described in the 2006 version of the SI manual but in that version, the latter three are defined as "constants to be obtained by experiment" rather than as "defining constants". The redefinition retains unchanged the numerical values associated with the following constants of nature:
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.
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.
Following the CCU proposal, the texts of the definitions of all of the base units were either refined or rewritten, changing the emphasis from explicitunit to explicitconstanttype definitions.^{[38]} Explicitunittype 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 explicitconstant 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 299792458 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.
The new definition of the second is effectively the same as the previous one, the only difference being that the conditions under which the definition applies are more rigorously defined.
The 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 will propagate to the metre.
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.
A consequence of this change is that the new definition of the kilogram is dependent on the definitions of the second and the metre.
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.
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 (μ_{0}) 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 (ε_{0}) had a fixed value, and from
that the impedance of free space (Z_{0}) 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 finestructure constant .^{[45]}
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.
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.
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.
One consequence of this change is that the current defined relationship between the mass of the ^{12}C atom, the dalton, the kilogram, and the Avogadro number will no longer be valid. One of the following must change:
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(^{12}C), is equal to 0.012 kg⋅mol^{−1} within a relative standard uncertainty equal to that of the recommended value of N_{A}h 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.
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.
All seven of the SI base units will be defined in terms of defined constants^{[Note 6]} and universal physical constants.^{[Note 7]}^{[47]} 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)^{[48]} 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.
Much of the work done by the CIPM is delegated to consultative committees. The CIPM Consultative Committee for Units (CCU) has made the proposed changes while other committees have examined the proposal in detail and have made recommendations regarding their acceptance by the CGPM in 2014. The consultative committees have laid down a number of criteria that must be met before they will support the CCU's proposal, including:
As of March 2011, the International Avogadro Coordination (IAC) group had obtained an uncertainty of 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}.^{[52]} 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".^{[53]}
As of the 2014 CODATArecommended 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.^{[54]}^{[55]}
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.^{[56]}
In 2010, Marcus Foster of the Commonwealth Scientific and Industrial Research Organisation (CSIRO) published a wideranging 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.^{[57]}
Concerns that the use of explicitconstant definitions of the unit being defined that are not related to an example of its quantity will have many adverse effects have been expressed.^{[58]} 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,^{[59]} 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.^{[60]} 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, currentcarrying 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]}
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 silicon28 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.^{[61]} 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 (N_{A}) 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".^{[57]}^{[62]}
The SI Brochure (8th edition) defines the dalton in terms of the mass of an atom of ^{12}C.^{[63]} 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 ^{12}C, with the effect that the link between the dalton and the kilogram will be broken.^{[64]}^{[65]}
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.^{[66]} This approval has since been given.^{[67]} 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 N_{A}=(g/Da) mol^{−1}, but that the unified atomic mass unit (m_{u}) retain its current definition based on the mass of ^{12}C, 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}.^{[68]} The draft of the ninth SI Brochure, however, defines both the dalton (Da) and the unified atomic mass unit (u) as exactly 1/12 of the mass of a free carbon12 atom and not in relation to the kilogram,^{[4]} with the effect that the above equation will be inexact.
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.^{[69]}^{[70]}
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.^{[57]}
is a set of instructions that allows the definition to be realised in practice at the highest level.
This is a truly major development, because these uncertainties are now sufficiently small that the adoption of the new SI by the 26th CGPM is expected.
In physics and chemistry, the atomic mass constant, m_{u}, is one twelfth of the mass of an unbound atom of carbon12 at rest and in its ground state. It serves to define the atomic mass unit and is, by definition, equal to 1 u. It is inverse of Avogadro constant (1/N_{A}) when expressed in grams (instead of SI unit kilogram). The CODATA recommended value is 1.660539040(20)×10^{−27} kg.
In practice, the atomic mass constant is determined from the electron rest mass m_{e} and the electron relative atomic mass A_{r}(e) (that is, the mass of the electron on a scale where ^{12}C = 12). The relative atomic mass of the electron can be measured in cyclotron experiments, while the rest mass of the electron can be derived from other physical constants.
where c is the speed of light, h is the Planck constant, α is the finestructure constant, and R_{∞} is the Rydberg constant.
The current (CODATA 2014) uncertainty in the value of the atomic mass constant – relative uncertainty 1.2×10^{−8} – is almost entirely due to the uncertainty in the value of the Planck constant in SI units. With the 2019 redefinition of SI base units, the relative uncertainty will improve to 4.7×10^{−10}, which will be almost entirely due to the uncertainty in the finestructure constant.
Atomic mass unitThe unified atomic mass unit or dalton (SI symbols: u, or Da; Deprecated/colloquial symbol: amu) is a standard unit of mass that quantifies mass on an atomic or molecular scale (atomic mass). One unified atomic mass unit is approximately the mass of one nucleon (either a single proton or neutron) and is numerically equivalent to 1 g/mol. It is defined as one twelfth of the mass of an unbound neutral atom of carbon12 in its nuclear and electronic ground state and at rest, and has a value of 1.660539040(20)×10−27 kg, or approximately 1.66 yoctograms. The CIPM has categorised it as a nonSI unit accepted for use with the SI, and whose value in SI units must be obtained experimentally.The atomic mass unit (amu) without the "unified" prefix is technically an obsolete unit based on oxygen, which was replaced in 1961. However, some nontechnical and preparatory sources continue to occasionally use the term amu but now define it in the same way as u (i.e., based on carbon12). In this sense, most uses of the terms atomic mass units and amu, today, actually refer to unified atomic mass unit. For standardization, a specific atomic nucleus (carbon12 vs. oxygen16) had to be chosen because the average mass of a nucleon depends on the count of the nucleons in the atomic nucleus due to mass defect. This is also why the mass of a proton or neutron by itself is more than (and not equal to) 1 u.
The atomic mass unit is not the unit of mass in the atomic units system, which is rather the electron rest mass (me).
Until the 2019 redefinition of SI base units, the number of daltons in a gram is exactly the Avogadro number by definition, or equivalently, a dalton is exactly equivalent to 1 gram/mol. Thereafter, these relationships will no longer be exact, but they will still be extremely accurate approximations.
Boltzmann constant
The Boltzmann constant (k_{B} or k) is a physical constant named after its discoverer, Ludwig Boltzmann, which relates the average relative kinetic energy of particles in a gas with the temperature of the gas and occurs in Planck's law of blackbody radiation and in Boltzmann's entropy formula.
It is the gas constant R divided by the Avogadro constant N_{A}:
The Boltzmann constant has the dimension energy divided by temperature, the same as entropy. As of 2017, its value in SI units is a measured quantity. The recommended value (as of 2015, with standard uncertainty in parentheses) is 1.38064852(79)×10^{−23} J/K.
Historically, measurements of the Boltzmann constant depended on the definition of the kelvin in terms of the triple point of water. However, in the redefinition of SI base units adopted at the 26th General Conference on Weights and Measures (CGPM) on 16 November 2018, the definition of the kelvin was changed to one based on a fixed, exact numerical value of the Boltzmann constant, similar to the way that the speed of light was given an exact numerical value at the 17th CGPM in 1983. The final value (based on the 2017 CODATA adjusted value of 1.38064903(51)×10^{−23} J/K) is 1.380649×10^{−23} J/K.
CandelaThe candela ( or ; symbol: cd) is the base unit of luminous intensity in the International System of Units (SI); that is, luminous power per unit solid angle emitted by a point light source in a particular direction. Luminous intensity is analogous to radiant intensity, but instead of simply adding up the contributions of every wavelength of light in the source's spectrum, the contribution of each wavelength is weighted by the standard luminosity function (a model of the sensitivity of the human eye to different wavelengths). A common wax candle emits light with a luminous intensity of roughly one candela. If emission in some directions is blocked by an opaque barrier, the emission would still be approximately one candela in the directions that are not obscured.
The word candela is Latin for candle.
Conventional electrical unitA conventional electrical unit (or conventional unit where there is no risk of ambiguity) is a unit of measurement in the field of electricity which is based on the socalled "conventional values" of the Josephson constant and the von Klitzing constant agreed by the International Committee for Weights and Measures (CIPM) in 1988. These units are very similar in scale to their corresponding SI units, but are not identical because of their different definition. They are distinguished from the corresponding SI units by setting the symbol in italic typeface and adding a subscript "90" – e.g., the conventional volt has the symbol V90 – as they came into international use on 1 January 1990.
This system was developed to increase the precision of measurements: The Josephson and von Klitzing constants can be realized with great precision, repeatability and ease. The conventional electrical units have achieved acceptance as an international standard and are commonly used outside of the physics community in both engineering and industry.
The conventional electrical units are "quasinatural" in the sense that they are completely and exactly defined in terms of universal constants. They represent a significant step towards using "natural" fundamental physics for practical measurement purposes. However, the conventional electrical units are unlike other systems of natural units in that some physical constants are not set to unity but rather set to fixed numerical values that are very close to (but not precisely the same as) those in the SI system of units.
Several significant steps have been taken in the last half century to increase the precision and utility of measurement units:
In 1967, the thirteenth General Conference on Weights and Measures (CGPM) defined the second of atomic time in the International System of Units as the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium133 atom.
In 1983, the seventeenth CGPM redefined the metre in terms of the second and the speed of light, thus fixing the speed of light at exactly 299792458 m/s.
In 1988, the CIPM recommended adoption of conventional values for the Josephson constant as exactly KJ90 = 483597.9×109 Hz/V and for the von Klitzing constant as exactly RK90 = 25812.807 Ω as of 1 January 1990.
In 1991, the eighteenth CGPM noted the conventional values for the Josephson constant and the von Klitzing constant.
In 2000, the CIPM approved the use of the quantum Hall effect, with the value of RK90 to be used to establish a reference standard of resistance.
In 2018, the twentysixth CGPM resolved to abrogate the conventional values of the Josephson and von Klitzing constants with the 2019 redefinition of SI base units.
CoulombThe coulomb (symbol: C) is the International System of Units (SI) unit of electric charge. It is the charge (symbol: Q or q) transported by a constant current of one ampere in one second:
Thus, it is also the amount of excess charge on a capacitor of one farad charged to a potential difference of one volt:
The coulomb is equivalent to the charge of approximately 6.242×10^{18} (1.036×10^{−5} mol) protons, and −1 C is equivalent to the charge of approximately 6.242×10^{18} electrons.
A new definition, in terms of the elementary charge, will take effect on 20 May 2019. The new definition defines the elementary charge (the charge of the proton) as exactly 1.602176634×10^{−19} coulombs.
Elementary chargeThe elementary charge, usually denoted by e or sometimes qe, is the electric charge carried by a single proton or, equivalently, the magnitude of the electric charge carried by a single electron, which has charge −1 e. This elementary charge is a fundamental physical constant. To avoid confusion over its sign, e is sometimes called the elementary positive charge.
This charge has a measured value of approximately 1.6021766208(98)×10−19 C (coulombs). When the 2019 redefinition of SI base units takes effect on 20 May 2019, its value will be exactly 1.602176634×10−19 C by definition of the coulomb. In the centimetre–gram–second system of units (CGS), it is 4.80320425(10)×10−10 statcoulombs.Robert A. Millikan's oil drop experiment first measured the magnitude of the elementary charge in 1909.
Faraday constantThe Faraday constant, denoted by the symbol F and sometimes stylized as ℱ, is named after Michael Faraday. In physics and chemistry, this constant represents the magnitude of electric charge per mole of electrons. It has the currently accepted value
This constant has a simple relation to two other physical constants:
where
N_{A} is the Avogadro constant (the ratio of the number of particles, N, which is unitless, to the amount of substance, n, in units of moles), and e is the elementary charge or the magnitude of the charge of an electron. This relation holds because the amount of charge of a mole of electrons is equal to the amount of charge in one electron multiplied by the number of electrons in a mole.
One common use of the Faraday constant is electrolysis. One can divide the amount of charge in coulombs by the Faraday constant in order to find the amount (in moles) of the element that has been oxidized.
The value of F was first determined by weighing the amount of silver deposited in an electrochemical reaction in which a measured current was passed for a measured time, and using Faraday's law of electrolysis. Research is continuing into more accurate ways of determining the interrelated constants F, N_{A}, and e.
Finestructure constantIn physics, the finestructure constant, also known as Sommerfeld's constant, commonly denoted by α (the Greek letter alpha), is a dimensionless physical constant characterizing the strength of the electromagnetic interaction between elementary charged particles. It is related to the elementary charge e, which characterizes the strength of the coupling of an elementary charged particle with the electromagnetic field, by the formula 4πε0ħcα = e2. As a dimensionless quantity, it has the same numerical value in all systems of units, which is approximately 1/137 . The inverse of α is 137.035999139(31).While there are multiple physical interpretations for α, it received its name from Arnold Sommerfeld introducing it (1916) in extending the Bohr model of the atom: α quantifies the gap in the fine structure of the spectral lines of the hydrogen atom, which had been precisely measured by Michelson and Morley.
Gas constantThe gas constant is also known as the molar, universal, or ideal gas constant, denoted by the symbol R or R and is equivalent to the Boltzmann constant, but expressed in units of energy per temperature increment per mole, i.e. the pressure–volume product, rather than energy per temperature increment per particle. The constant is also a combination of the constants from Boyle's law, Charles's law, Avogadro's law, and GayLussac's law. It is a physical constant that is featured in many fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation.
Physically, the gas constant is the constant of proportionality that happens to relate the energy scale in physics to the temperature scale, when a mole of particles at the stated temperature is being considered. Thus, the value of the gas constant ultimately derives from historical decisions and accidents in the setting of the energy and temperature scales, plus similar historical setting of the value of the molar scale used for the counting of particles. The last factor is not a consideration in the value of the Boltzmann constant, which does a similar job of equating linear energy and temperature scales.
The gas constant value is 8.3144598(48) J⋅mol^{−1}⋅K^{−1}. Following the 2019 redefinition of SI base units, which come into force on 20 May 2019, the value of the gas constant will change to be exactly 8.31446261815324 J⋅K^{−1}⋅mol^{−1}.
The two digits in parentheses are the uncertainty (standard deviation) in the last two digits of the value. The relative uncertainty is 5.7×10^{−7}. Some have suggested that it might be appropriate to name the symbol R the Regnault constant in honour of the French chemist Henri Victor Regnault, whose accurate experimental data were used to calculate the early value of the constant; however, the exact reason for the original representation of the constant by the letter R is elusive.
The gas constant occurs in the ideal gas law, as follows:
where P is the absolute pressure (SI unit pascals), V is the volume of gas (SI unit cubic metres), n is the amount of gas (SI unit moles), m is the mass (SI unit kilograms) contained in V, and T is the thermodynamic temperature (SI unit kelvins). R_{specific} is the molarweightspecific gas constant, discussed below. The gas constant is expressed in the same physical units as molar entropy and molar heat capacity.
Magnetic flux quantumThe magnetic flux, represented by the symbol Φ, threading some contour or loop is defined as the magnetic field B multiplied by the loop area S, i.e. Φ = B ⋅ S. Both B and S can be arbitrary and so is Φ. However, if one deals with the superconducting loop or a hole in a bulk superconductor, it turns out that the magnetic flux threading such a hole/loop is quantized.
The (superconducting) magnetic flux quantum Φ0 = h/(2e) ≈ 2.067833831(13)×10−15 Wb is a combination of fundamental physical constants: the Planck constant h and the electron charge e. Its value is, therefore, the same for any superconductor.
The phenomenon of flux quantization was discovered experimentally by B. S. Deaver and W. M. Fairbank and, independently, by R. Doll and M. Näbauer, in 1961. The quantization of magnetic flux is closely related to the Little–Parks effect, but was predicted earlier by Fritz London in 1948 using a phenomenological model.
The inverse of the flux quantum, 1/Φ0, is called the Josephson constant, and is denoted KJ. It is the constant of proportionality of the Josephson effect, relating the potential difference across a Josephson junction to the frequency of the irradiation. The Josephson effect is very widely used to provide a standard for highprecision measurements of potential difference, which (since 1990) have been related to a fixed, conventional value of the Josephson constant, denoted KJ90. With the 2019 redefinition of SI base units, the Josephson constant will have an exact value of KJ = 483597.84841698... GHz⋅V−1, which will replace the conventional value KJ90.
MassMass is both a property of a physical body and a measure of its resistance to acceleration (a change in its state of motion) when a net force is applied. An object's mass also determines the strength of its gravitational attraction to other bodies.
The basic SI unit of mass is the kilogram (kg). In physics, mass is not the same as weight, even though mass is often determined by measuring the object's weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity, but it would still have the same mass. This is because weight is a force, while mass is the property that (along with gravity) determines the strength of this force.
Outline of the metric systemThe following outline is provided as an overview of and topical guide to the metric system – various loosely related systems of measurement that trace their origin to the decimal system of measurement introduced in France during the French Revolution.
Physical constantA 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, which has a fixed numerical value, but does not directly involve any physical measurement.
There are many physical constants in science, some of the most widely recognized being the speed of light in vacuum c, the gravitational constant G, the Planck constant h, the electric constant ε0, and the elementary charge e. Physical constants can take many dimensional forms: the speed of light signifies a maximum speed for any object and its dimension is length divided by time; while the finestructure constant α, which characterizes the strength of the electromagnetic interaction, is dimensionless.
The term fundamental physical constant is sometimes used to refer to universal but dimensioned physical constants such as those mentioned above. Increasingly, however, physicists reserve the use of the term fundamental physical constant for dimensionless physical constants, such as the finestructure constant α.
Physical constant in the sense under discussion in this article should not be confused with other quantities called "constants" that are assumed to be constant in a given context without the implication that they are fundamental, such as the "time constant" characteristic of a given system, or material constants, such as the Madelung constant, electrical resistivity, and heat capacity.
The International Bureau of Weights and Measures decided to redefine several SI base units as from 20 May 2019 by fixing the SI value of several physical constants, including the Planck constant, h, the elementary charge, e, the Boltzmann constant, kB, and the Avogadro constant, NA. The new fixed values are based on the best measurements of the constants based on the earlier definitions, including the kilogram, to ensure minimal impact. As a consequence, the uncertainty in the value of many physical constants when expressed in SI units will reduce substantially.
Planck constantThe Planck constant (denoted h, also called Planck's constant) is a physical constant that is the quantum of electromagnetic action, which relates the energy carried by a photon to its frequency. A photon's energy is equal to its frequency multiplied by the Planck constant. The Planck constant is of fundamental importance in quantum mechanics, and in metrology it is the basis for the definition of the kilogram.
At the end of the 19th century, physicists were unable to explain why the observed spectrum of black body radiation, which by then had been accurately measured, diverged significantly at higher frequencies from that predicted by existing theories. In 1900, Max Planck empirically derived a formula for the observed spectrum. He assumed that a hypothetical electrically charged oscillator in a cavity that contained black body radiation could only change its energy in a minimal increment, E, that was proportional to the frequency of its associated electromagnetic wave. He was able to calculate the proportionality constant, h, from the experimental measurements, and that constant is named in his honor. In 1905, the value E was associated by Albert Einstein with a "quantum" or minimal element of the energy of the electromagnetic wave itself. The light quantum behaved in some respects as an electrically neutral particle, as opposed to an electromagnetic wave. It was eventually called a photon. Max Planck received the 1918 Nobel Prize in Physics "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta".
Since energy and mass are equivalent, the Planck constant also relates mass to frequency. By 2017, the Planck constant had been measured with sufficient accuracy in terms of the SI base units, that it was central to replacing the metal cylinder, called the International Prototype of the Kilogram (IPK), that had defined the kilogram since 1889. The new definition was unanimously approved at the General Conference on Weights and Measures (CGPM) on 16 November 2018 as part of the 2019 redefinition of SI base units. For this new definition of the kilogram, the Planck constant, as defined by the ISO standard, was set to 6.62607015×10−34 J⋅s exactly. The kilogram was the last SI base unit to be redefined by a fundamental physical property to replace a physical artefact.
SI base unitNote: In May 2019, the technical definition of the SI base units will change: see 2019 redefinition of SI base units
The International System of Units (SI = Systeme Internationale) defines seven units of measure as a basic set from which all other SI units can be derived. The SI base units and their physical quantities are the second for time, the metre for measurement of length, the kilogram for mass, the ampere for electric current, the kelvin for temperature, the mole for amount of substance, and the candela for luminous intensity.
The SI base units form a set of mutually independent dimensions as required by dimensional analysis commonly employed in science and technology.
The names and symbols of SI base units are written in lowercase, except the symbols of those named after a person, which are written with an initial capital letter. For example, the metre (US English: meter) has the symbol m, but the kelvin has symbol K, because it is named after Lord Kelvin and the ampere with symbol A is named after AndréMarie Ampère.
Several other units, such as the litre (US English: liter), are formally not part of the SI, but are accepted for use with SI.
Timevariation of fundamental constantsThe term physical constant expresses the notion of a physical quantity subject to experimental measurement which is independent of the time or location of the experiment. The constancy (immutability) of any "physical constant" is thus subject to experimental verification.
Paul Dirac in 1937 speculated that physical constants such as the gravitational constant or the finestructure constant might be subject to change over time in proportion of the age of the universe.
Experiments conducted since then have put upper bounds on their timedependence. This concerns the fine structure constant, the gravitational constant and the protontoelectron mass ratio specifically, for all of which there are ongoing efforts to improve tests on their timedependence.The immutability of these fundamental constants is an important cornerstone of the laws of physics as currently known; the postulate of the timeindependence of physical laws is tied to that of the conservation of energy (Noether theorem), so that the discovery of any variation would imply the discovery of a previously unknown law of force.In a more philosophical context, the conclusion that these quantities are constant raises the question of why they have the specific value they do in what appears to be a "finetuned Universe", while their being variable would mean that their known values are merely an accident of the current time at which we happen to measure them.
Triple pointIn thermodynamics, the triple point of a substance is the temperature and pressure at which the three phases (gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium. It is that temperature and pressure at which the sublimation curve, fusion curve and the vaporisation curve meet. For example, the triple point of mercury occurs at a temperature of −38.83440 °C and a pressure of 0.2 mPa.
In addition to the triple point for solid, liquid, and gas phases, a triple point may involve more than one solid phase, for substances with multiple polymorphs. Helium4 is a special case that presents a triple point involving two different fluid phases (lambda point).The triple point of water was used to define the kelvin, the base unit of thermodynamic temperature in the International System of Units (SI). The value of the triple point of water was fixed by definition, rather than measured, but that changed with the 2019 redefinition of SI base units. The triple points of several substances are used to define points in the ITS90 international temperature scale, ranging from the triple point of hydrogen (13.8033 K) to the triple point of water (273.16 K, 0.01 °C, or 32.018 °F).
The term "triple point" was coined in 1873 by James Thomson, brother of Lord Kelvin.
World Metrology DayWorld Metrology Day is an event occurring on the 20th of May celebrating the International System of Units. The date is the anniversary of the signing of the Metre Convention in 1875 . Metrology is the study of measurement.
The World Metrology Day project is currently realized jointly by the BIPM and the OIML.
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