Proposed redefinition of SI base units

Background

The basic structure of SI was developed over a period of about 170 years (1791 to 1960). Since 1960 technological advances have made it possible to address various weaknesses in SI, notably the dependence on an artifact to define the kilogram.

Development of SI

During the early years of the French Revolution, the leaders of the French National Constituent Assembly decided to introduce a completely new system of measurement based on the principles of logic and natural phenomena. Specifically, 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 so that nobody would "own" the units, they could not be measured with sufficient convenience or precision for practical use. Instead copies were created in the form of the mètre des Archives and kilogramme des Archives which were a "best attempt" at fulfilling these principles.

In 1875, by which time the use of the metric system had become widespread in Europe and in Latin America, twenty industrially developed nations met for the Convention of the Metre. The result was 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. They were:

CGPM (General Conference on Weights and Measures / Conférence générale des poids et mesures)—The Conference meets every four to six years and consists of delegates of the nations who had signed the convention. It discusses and examines the arrangements required to ensure the propagation and improvement of the International System of Units and it endorses the results of new fundamental metrological determinations.

CIPM (International Committee for Weights and Measures / Comité international des poids et mesures)—The Committee consists of eighteen eminent scientists, each from a different country, nominated by the CGPM. The CIPM meets annually and is tasked to advise 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), amongst other things, advises the CIPM on matters concerning units of measurement.

BIPM (International Bureau for Weights and Measures / Bureau international des poids et mesures)—The Bureau provides safe keeping of the international prototype kilogram and metre, provides laboratory facilities for regular comparisons of the national prototypes with the international prototype and is the secretariat for the CIPM and the CGPM.

The first CGPM (1889) formally approved the use of 40 prototype metres and 40 prototype kilograms from the British firm Johnson Matthey as the standards mandated by the Convention of the Metre. One of each of these was nominated by lot as the international prototypes, other copies were retained by the CGPM 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. 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 electric current (1946), luminosity (1946), temperature (1948), time (1956) and molar mass (1971).

The 9th CGPM (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 "Système International d'Unités" and its abbreviation "SI".

Impetus for change

Changing the underlying principles behind the definition of the SI base units is not without precedent. The 11th CGPM (1960) defined the SI metre in terms of the wavelength of krypton-86 radiation, replacing the pre-SI metre bar. The 13th CGPM (1967) replaced the original definition of the second (which was based on a back-calculation of the Earth's rotation in the year 1900) with a definition based on the frequency of the radiation emitted between two hyperfine levels of the ground state of the caesium 133 atom. And 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.

Over the years, drifts of up to 6992200000000000000♠2×10⁻⁸ kilograms per annum in the national prototype kilograms relative to the international prototype kilogram have been detected. There was no way of determining whether the national prototypes were gaining mass or whether the IPK was losing mass. 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. Newcastle University metrologist Peter Cumpson has since identified mercury vapour absorption or carbonaceous contamination as possible causes of this drift.

Independently of this drift having been identified, the Avogadro project and development of the Watt balance promised methods of indirectly measuring mass with a very high precision. These projects provided tools that would 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 20 kelvins and for temperatures above 1300 kelvins. The committee was of the view that the Boltzmann constant provided a better basis for temperature measurement than did the triple point of water, as it overcame these difficulties.

At its 23rd meeting (2007), the GCPM 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). 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 that "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"; however, the CIPM presented a resolution for consideration at the 24th CGPM (17–21 October 2011) to agree the new definitions in principle, but not to implement them until the details have been finalised. This resolution was accepted by the conference, and in addition the CGPM moved the date of the 25th meeting forward from 2015 to 2014. At the 25th meeting (18–20 November 2014), it was found that "despite [the 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", thus postponing the revision to the next meeting in 2018.

Proposal

The BIPM's Consultative Committee for Units (CCU) proposed that, in addition to the speed of light, four further constants of nature should be defined to have exact values. Using the preliminary values from an unpublished draft of the 9th edition of the SI Brochure, the definitions would be:

The Planck constant h is exactly 6966662607004000000♠6.626070040×10⁻³⁴ joule-second (J·s).

The elementary charge e is exactly 6981160217662079999♠1.6021766208×10⁻¹⁹ coulomb (C).

The Boltzmann constant k is exactly 6977138064851999999♠1.38064852×10⁻²³ joule per kelvin (J·K⁻¹).

The Avogadro constant N_A is exactly 7023602214085700000♠6.022140857×10²³ reciprocal mole (mol⁻¹).

These constants were described in the 2006 version of the SI manual, but in that version the latter three were defined as "constants to be obtained by experiment" rather than as "defining constants".

The CCU also proposed that the numerical values associated with the following constants of nature be retained unchanged:

The speed of light c is exactly 7008299792458000000♠299792458 metres per second (m·s⁻¹).

The ground state hyperfine splitting frequency of the caesium-133 atom Δν(¹³³Cs)_hfs is exactly 7009919263177000000♠9192631770 hertz (Hz).

The luminous efficacy K_cd of monochromatic radiation of frequency 7014540000000000000♠540×10¹² Hz is exactly 7002683000000000000♠683 lumen per watt (lm·W⁻¹).

The seven definitions above are rewritten below after converting the derived units (joule, coulomb, hertz, lumen and watt) into the seven base units (second, metre, kilogram, ampere, kelvin, mole and candela), according to the updated draft of the 9th edition of the SI Brochure (2016). In the list that follows, the symbol sr stands for the dimensionless unit steradian.

Δν_Cs = Δν(¹³³Cs)_hfs = 7009919263177000000♠9192631770 s⁻¹

c = 7008299792458000000♠299792458 m·s⁻¹

h = 6966662607004000000♠6.626070040×10⁻³⁴ kg·m²·s⁻¹

e = 6981160217662079999♠1.6021766208×10⁻¹⁹ A·s

k = 6977138064851999999♠1.38064852×10⁻²³ kg·m²·K⁻¹·s⁻²

N_A = 7023602214085700000♠6.022140857×10²³ mol⁻¹

K_cd = 7002683000000000000♠683 cd·sr·s³·kg⁻¹·m⁻²

In addition the CCU proposed that

The international prototype kilogram be retired and that the current definition of the kilogram be abrogated,

The current definition of the ampere be abrogated,

The current definition of the kelvin be abrogated and

The current definition of the mole be revised.

These changes will have the effect of redefining the SI base units, though the definitions of the derived SI units will remain the same.

Impact on base unit definitions

The CCU proposal recommended that the text of the definitions of all the base units be 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 as being the length of three barleycorns and since 1889 the kilogram has been defined as being the mass of the International Prototype Kilogram. In explicit-constant definitions, a constant of nature is given a specified value and the definition of the unit emerges as a consequence. For example, in 1983, the speed of light was defined to be exactly 7008299792458000000♠299792458 metres per second and, since the second had been independently defined, the length of the metre could thus be derived.

The current (2008) and proposed (2016) definitions are given below.

Second

The proposed definition of the second is effectively the same as the current definition, the only difference being that the conditions under which the measurements are made are more rigorously defined.

Current definition: The second is the duration of 7009919263177000000♠9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. Proposed definition: The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency Δν_Cs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 7009919263177000000♠9192631770 when expressed in the unit Hz, which is equal to s⁻¹.

Metre

The proposed definition of the metre is effectively the same as the current definition, the only difference being that the additional rigour in the definition of the second will propagate to the metre.

Current definition: The metre is the length of the path travelled by light in vacuum during a time interval of 1/7008299792458000000♠299792458 of a second. Proposed definition: The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 7008299792458000000♠299792458 when expressed in the unit m·s⁻¹, where the second is defined in terms of the caesium frequency Δν_Cs.

Kilogram

The definition of the kilogram is undergoing a fundamental change—the current definition defines the kilogram as being the mass of the international prototype kilogram which is an artifact, not a constant of nature while the new definition relates it to the equivalent energy of a photon via the Planck constant.

Current definition: The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. Proposed definition: The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.626070040×10⁻³⁴ when expressed in the unit J s, which is equal to kg·m²·s⁻¹, where the metre and the second are defined in terms of c and Δν_Cs.

One consequence of this change is that the new definition makes the definition of the kilogram dependent on the definitions of the second and the metre.

Ampere

The definition of the ampere is undergoing a major overhaul—the current definition, which is difficult to realise with high precision in practice, is being replaced by a definition that is more intuitive and that is easier to realise.

Current 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 6993200000000000000♠2×10⁻⁷ newton per metre of length. Proposed definition: The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge e to be 1.6021766208×10⁻¹⁹ when expressed in the unit C, which is equal to A s, where the second is defined in terms of Δν_Cs.

Since the current definition contains a reference to force which has the dimensions MLT⁻² it follows that in SI the kilogram, metre and second, the base units representing these dimensions, must be defined before the ampere can be defined. Other consequences of this definition are that in SI the value of vacuum permeability (μ₀) is fixed at exactly 6993400000000000000♠4π×10⁻⁷ H·m⁻¹. Since the speed of light in vacuum (c) is also fixed, it follows from the relationship

c 2 = 1 μ 0 ε 0

that the vacuum permittivity (ε₀) has a fixed value and from

Z 0 = μ 0 ε 0

that the impedance of free space (Z₀) likewise has a fixed value.

One consequence of the proposed changes to the definition of the ampere is that the definition will no longer be dependent on the definitions of the kilogram and the metre, but will still be dependent on the definition of the second. In addition the vacuum permeability, vacuum permittivity and impedance of free space, which, in the current definition have exact values will, in the future, be subject to experimental error.

Kelvin

The definition of the kelvin will undergo a fundamental change if the proposal is accepted. Rather than using the triple point of water to fix the temperature scale the proposal recommends that the energy equivalent as given by Boltzmann's equation be used.

Current definition: The kelvin, unit of thermodynamic temperature, is 1/273.16 of the thermodynamic temperature of the triple point of water. Proposed definition: The kelvin, symbol K, is the SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constant k to be 1.38064852×10⁻²³ when expressed in the unit J K⁻¹, which is equal to kg·m²·s⁻²·K⁻¹, where the kilogram, metre and second are defined in terms of h, c and Δν_Cs.

For a physical interpretation of this new definition, consider an ideal gas concentrated such that the average volume per molecule is 1.38064852×10⁻²³ m³. That is the volume of a cube with a side length of about 24 nm. The ratio of the gas's temperature and pressure would be defined exactly equal to 1 K/Pa.

One consequence of this change is that the new definition makes the definition of the kelvin depend on the definitions of the second, the metre, and the kilogram.

Mole

The current definition of the mole links it to the kilogram. The proposed definition will break that link by making a mole a specific number of entities of the substance in question.

Current definition: The mole is the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. Proposed definition: The mole, symbol mol, is the SI unit of amount of substance of a specified elementary entity, which may be an atom, molecule, ion, electron, any other particle or a specified group of such particles. It is defined by taking the fixed numerical value of the Avogadro constant N_A to be 6.022140857×10²³ when expressed in the unit mol⁻¹.

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

The mass of a ¹²C atom is exactly 12 dalton

The number of dalton in a gram is exactly the numerical value of the Avogadro constant

The draft SI brochure assumes the first will remain true, which would mean that the second will no longer be true. The molar mass constant, while still with great accuracy remaining equal to 1 g/mol, will no longer be exactly equal to that.

Candela

The proposed definition of the candela is effectively the same as the current definition, but has been rephrased.

Current definition: The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 7014540000000000000♠540×10¹² Hz and that has a radiant intensity in that direction of 1/683 watt per steradian. Proposed 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 7014540000000000000♠540×10¹² Hz, K_cd, to be 683 when expressed in the unit lm·W⁻¹, which is equal to cd·sr·W⁻¹, or cd·sr·kg⁻¹·m⁻²·s³, where the kilogram, metre and second are defined in terms of h, c and Δν_Cs.

Impact on reproducibility

Apart from the candela, all the base units will be defined in terms of universal physical constants, but without an explicit one-to-one correspondence between the constants and the base units. Thus six physical constants will be needed to define the six base units.

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. It should be noted that in practice G can only be measured with a relative uncertainty of the order of 10⁻⁵ which would have resulted in 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. The choice of physical constants was made 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.

Uncertainty of fundamental physical constants

Fundamental physical constants are often highly dependent upon each other. This implies that the best value of a fundamental physical constant, one with the least uncertainty, often can be determined by directly measuring other fundamental physical constants, from which the value can be calculated. The uncertainty in these constants is then determined from the uncertainty of the others by the propagation of uncertainty. Constants whose value is fixed, for determining the units in which they are expressed, don't have an uncertainty associated with them, so they do not account for any extra uncertainty in the value of the calculated constant. One of the reasons the SI unit system will be changed is that determination of values can often be greatly improved if expressed in these new units. This is due to the dependence of these values on physicals constants.

The following table catalogues the notable changes in determination of fundamental physical constants. The constants are expressed in direct measurements and fixed constants to minimize and determine the uncertainty. Some constants in that expression do not contribute significantly to the uncertainty, thus the only significant factors are noted. The value of the relative uncertainty by the data of CODATA of 2014 is given, and is expressed in the relative uncertainty of the significant factors, noted with u_r(constant). An approximately equals sign (≈) is used if an uncertainty is only approximated by the expression. This is due to unsignificant factors or rounding errors.

( c = speed of light, α = fine-structure constant, R ∞ = Rydberg constant.)

It should be noted that the relative atomic mass of the electron A_r(e) is measured relative to the mass of a carbon-12 atom (divided by 12). When the Avogadro constant is set in the new SI, atomic masses might be measured in dalton (by fixing the Avogadro constant), instead of atomic mass units (by fixing the mass of carbon-12), thus resulting in a difference between the values of the relative atomic mass and the atomic mass in units of dalton.

Dalton

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 GCPM had not given its approval. This approval has since been given. Following the proposal to redefine the mole by fixing the value of Avogadro's number, Brian Leonard of the University of Akron, writing in Metrologia proposed that the dalton (Da) be redefined as an SI derived unit exactly equal to (1/1000N_A) kg; but that the unified atomic mass unit (m_u) retain its current definition based on the mass of ¹²C, ceasing to be SI. 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.

Acceptance

Much of the work done by the CIPM is delegated to consultative committees. The CIPM Consultative Committee for Units (CCU) has made the proposed changes while other committees have examined the proposal in detail and have made recommendations regarding their acceptance by the CGPM in 2014. The various consultative committees have laid down a number of criteria that must be met before they will support the CCU's proposal, including:

At least three separate experiments be carried out yielding values having a relative expanded (95%) uncertainty of no more than 6992500000000000000♠5×10⁻⁸ and at least one of these values should be better than 6992200000000000000♠2×10⁻⁸. Both the Watt balance and the Avogadro project should be included in the experiments and any differences between these be reconciled.

The relative uncertainty of Boltzmann constant derived from two fundamentally different methods such as acoustic gas thermometry and dielectric constant gas thermometry be better than one part in 10⁻⁶ and that these values be corroborated by other measurements.

As at March 2011, the International Avogadro Coordination (IAC) group had obtained an uncertainty of 6992300000000000000♠3.0×10⁻⁸ and NIST had obtained an uncertainty of 6992360000000000000♠3.6×10⁻⁸ in their measurements.

On 1 September 2012 the European Association of National Metrology Institutes (EURAMET) launched a formal project to reduce the relative difference between the watt-balance and the silicon sphere approach to measuring the kilogram from 6993170000000000000♠(17±5)×10⁻⁸ to within 6992200000000000000♠2×10⁻⁸.

As of March 2013 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 since the proposed system makes use of atomic scale 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 through the end of 2014), all measurements meet the CGPM's requirements and the way is clear to proceed with the redefinition and the next CGPM quadrennial meeting in late 2018.

Comment

In 2010 Marcus Foster of the Commonwealth Scientific and Industrial Research Organisation published a wide-ranging critique of SI in which he raised numerous issues ranging from basic issues such as the absence of the symbol "Ω" from most Western 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 issues regarding the definition of the base units including new definitions of the candela and the mole—units that Foster argued were 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 proposed 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 proposed definition of the ampere, which is closer to an example of its quantity than is the current definition. Some observers have welcomed the proposal to base the definition of electric current on the charge of the electron rather than the current definition of a force between two parallel current-carrying wires – since the nature of the electromagnetic interaction between two bodies at the quantum electrodynamics level is somewhat different from the nature 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

When the scale of the divergence between the IPK and national kilogram prototypes was reported in 2005, a debate arose on how best to redefine the kilogram – should the kilogram be defined in terms of the mass of the silicon-28 atom or should it be determined using the watt balance? The mass of a silicon atom could be determined using the Avogadro project and using Avogadro's number be linked directly to the kilogram.

Concern has also been expressed that the authors of the proposal had failed to address the impact of breaking the link between the mole, kilogram, the dalton (Da), the Avogadro constant (N_A) and Avogadro's number (N_N). This direct link has caused many to argue that the mole is not a true physical unit, but, in the words of the Swedish philosopher Johansson, the mole is a "scaling factor".

The SI Brochure (8th edition) implicitly defines the dalton as 0.001÷N_N kg where the value of N_N is determined by experiment. The proposal fixes N_A, so if the Avogadro constant and Avogadro's number are to be numerically identical, the dalton must be related to either the mass of a single carbon atom or to the kilogram—it cannot be related to both.

Temperature

Temperature is somewhat of an enigma – room temperature can be measured by means of expansion and contraction of a liquid in a thermometer, but high temperatures are often associated with a 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 rather an average of the thermal energies of the individual particles that make up the body concerned. He noted that in many theoretical papers, temperature is represented by the quantities Θ or β where

Θ = k b T ;       β = 1 k b T

and k_b is the Boltzmann constant.

Chyla acknowledged however that in the macroscopic world temperature plays the role of a base unit as much of the theory of thermodynamics is based on temperature. Foster, writing from the point of view of quality control argued that the introduction of the Boltzmann constant into the definition of temperature was an unnecessary complication.

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, makes great use of linking energy to temperature via the Boltzmann constant.

Luminous intensity

Foster argued that "luminous intensity [the candela] is not a physical quantity, but a photobiological quantity that exists in human perception", thereby questioning whether or not the candela should be a base unit.