Changes in the definitions of the basic units of SI (2018)

SI before reform

SI after reform

Changes in the definitions of the basic units of the International System of Units (SI) bind the basic SI units to fixed values of fundamental physical constants . As a result of the changes, the value of all units remained unchanged, however, the binding to material standards completely disappeared from the definitions. The changes were adopted in 2018 and entered into force in 2019.

Content

Content Changes

The international system of units , SI, includes 7 basic units of measurement - second , meter , kilogram , ampere , kelvin , mole , candela - and a number of derived units ^[1] .

Before the changes, the kilogram was defined as the mass of one specific standard - the international prototype of the kilogram. This definition had some drawbacks. Other basic units were not tied to specific artifacts, but some definitions were also inconvenient (and, moreover, they themselves relied on the definition of a kilogram) ^[2] .

The changes directly affect the definitions of kilogram, ampere, kelvin and mole: now these units are determined through fixed values of the elemental electric charge and the Planck , Boltzmann and Avogadro constants . The definitions of second, meter and candela have remained meaningful the same (apart from the fact that the definition of candela is based on the definition of a kilogram, which has changed), however, to maintain the stylistic unity of the definitions, all old definitions have been formally replaced. In addition, the fixed values of the Josephson constant K _J-90 and the von Klitzing constant R _K-90 ^[3] recommended for the implementation of volta and ohm are canceled.

The continuity of SI is observed: as a result of changes, the value of all units of measurement has not changed; the numerical value of the measurement results, expressed in old units, thus also did not change ^[4] (except for some electrical quantities, which will be discussed later). However, some quantities that were previously determined accurately have become experimentally determined. The masses of all kilogram standards dating back to the international kilogram prototype acquired an additional error of 10 μg, since the mass of the prototype itself is now equal to 1 kg with exactly this error ^[5] . The measured values and scales of voltages and resistances changed by a fraction of the order of 10 ⁻⁷ and 10 ⁻⁸ , respectively, however, this is not due to a change in the definitions of the basic units, but because previously fixed values of the Josephson and von Klitzing, not consistent with the rest of the SI ^[6] .

Although the international prototype of a kilogram no longer serves as a standard kilogram as a SI unit, it is still stored in the Bureau of Weights and Measures, as much as possible protected from external influences ^[7] .

New SI definition

The international system of units, SI, is a system of units in which ^[8] :

the frequency of hyperfine splitting of the ground state of the cesium-133 atom Δ ν _Cs is exactly equal to 9 192 631 770 Hz ;
the speed of light in vacuum c is exactly 299 792 458 m / s ;
Planck's constant ℎ is exactly equal to 6.626 070 15⋅10 ⁻³⁴ kg · m ² · s ⁻¹ ;
the elemental electric charge e is exactly 1.602 176 634⋅10 ⁻¹⁹ A · s;
the Boltzmann constant k is exactly 1.380 649⋅10 ⁻²³ J / K;
the Avogadro constant N _A is exactly 6.022 140 76⋅10 ²³ mol ⁻¹ ;
the luminous efficiency K _{cd of} monochromatic radiation with a frequency of 540-10 ¹² Hz is exactly 683 lm / W.

You can give this definition the form of a set of definitions of basic units ^[1] . This set of definitions is given in the article SI Basic Units § Basic Units .

Background, preparation and acceptance

The international system of units, SI, was adopted in 1960 and was supplemented and adjusted by the International Bureau of Weights and Measures (BIPM) in subsequent years. For more than 50 years, the SI definition of a kilogram has been preserved, which has been valid since 1889 (moreover, in the 19th century, a kilogram was also determined through a standard): 1 kilogram is the mass of the international prototype of a kilogram M _IPK . This created difficulties: both the prototype itself and its copies change mass over time due to contamination and wear; unambiguously establish the direction of change is possible only for copies relative to the prototype; in order to minimize changes in the mass of the prototype, its comparison with copies was extremely rare, and in the intervals between comparisons errors were accumulated due to changes in the mass of copies - and since there was no other way to reproduce a kilogram, all users of the standard kilogram (national metrological organizations) received a kilogram value with these mistakes. Suggestions to change the definition of a kilogram by fixing the value of some natural constant, like it was done with a meter, sounded long and regular, but only by the beginning of the XXI century the accuracy of experiments became sufficient to realize this idea ^[9] .

Communities of metrology specialists in various fields of science and technology have also supported the idea of change. The practical implementation of the units of voltage and resistance was based not on the definition of amperes, but on fixed values of the Josephson and von Klitzing constants; the rejection of these fixed values with the simultaneous fixing of e and бы would make units from the field of electricity and magnetism consistent with the rest of the SI. The temperature unit was determined by fixing the temperature of the triple point of water T _TPW , however, this temperature depends on the isotopic composition of the water and the impurities in it, and moreover, such a determination is poorly suited to very low and very high temperatures - redefining kelvin through fixation k solved these problems. Finally, since the concept of the quantity of a substance is not related to the mass of particles, it was proposed at the same time to change the definition of a mole by unlinking it from the mass of a carbon atom of 12 m ( ¹² C) and linking it to a fixed value of N _A ^[10] .

One could also get rid of the binding of the system of units to a specific electronic transition in a specific atom, fixing instead of it another fundamental constant - for example, the gravitational constant , as is done, for example, in the Planck system of units . However, the uncertainty of the measured value of the gravitational constant is too great for this ^[11] .

The changes in the form in which they were adopted go back to the 2006 proposal ^[4] . The basic principles of the reform and the requirements for the accuracy of measuring the values of the physical constants necessary for the reform were adopted at the General Conferences of Weights and Measures in 2011 and 2014. Specific values of physical constants were proposed in 2018 by the International Committee of Weights and Measures and adopted on November 16, 2018, when the XXVI General Conference of Weights and Measures unanimously voted for them ^[12] . The new SI definitions entered into force on May 20, 2019, the day of metrology ^[13] .

Kibble Scales at NIST

As part of the preparation of changes in 2014, an extraordinary comparison was made of the mass of the International kilogram prototype with its copies. Various scientific groups around the world have taken measurements of fundamental constants in order to reduce the error to the required level. The CODATA working group on fundamental constants collected this data in an extraordinary issue of the 2017 set of constant values, and based on these values, fixed values were chosen for the new SI ^[14] .

For each of the basic units in the new SI, recommended methods for the practical implementation of units are defined. So, for a kilogram, these are Kibble scales and X-ray crystal density analysis (XRCD) ^[15] .

The updated SI allows further changes. In particular, progress in the field of measuring the frequencies of electromagnetic waves and the design of atomic clocks allows us to expect that in about a decade a second will be redefined through the frequency of some other electronic transition ^[16] .

Weaknesses

Since the atomic mass unit is still determined through the mass of the carbon-12 atom, it ceased to be exactly 1 gram divided by the Avogadro number. Some authors criticize the new SI, pointing out that fixing the atomic mass unit instead of the Planck constant would solve this problem, and the arguments that led to the choice of the Planck constant in the 2000s lost their strength by the 2010s ^[17] .

The electric constant and magnetic constant in SI before the changes had exact values: $\varepsilon _{0}={\frac {1}{4\pi c^{2}}}\cdot 10^{7}$ ${\ displaystyle \ varepsilon _ {0} = {\ frac {1} {4 \ pi c ^ {2}}} \ cdot 10 ^ {7}}$ m / h and $\mu _{0}=4\pi \cdot 10^{-7}$ ${\ displaystyle \ mu _ {0} = 4 \ pi \ cdot 10 ^ {- 7}}$ GN / m After the reform, these equalities were not observed exactly, but up to nine significant figures, acquiring the same relative error as the fine structure constant $\alpha ={\frac {e^{2}}{2\varepsilon _{0}hc}}$ ${\ displaystyle \ alpha = {\ frac {e ^ {2}} {2 \ varepsilon _ {0} hc}}}$ . From this, in particular, it follows that the coefficients for the transfer between SI units and various variants of the GHS system are no longer accurate, fixed values, since they are expressed in terms of the magnetic constant. This could have been avoided if a non-elementary charge had been fixed $e$ ${\ displaystyle e}$ , and the previous value of the magnetic constant or, which is equivalent for fixed $h$ ${\ displaystyle h}$ and $c$ ${\ displaystyle c}$ Planck charge $e/{\sqrt {\alpha }}$ ${\ displaystyle e / {\ sqrt {\ alpha}}}$ . However, this option was rejected, since the previous implementation of the standards of quantities related to electricity and magnetism was based on fixed Josephson and von Klitzing constants, which is equivalent to fixing the Planck constant and elementary charge, so the transition to the new system was easier when fixing just the elementary charge ^{[ 18]} .

Notes

↑ ¹ ² SI Brochure, 2019 , p. 18-23, 130-135.
↑ Stock et al, 2019 , pp. 3-4.
↑ SI Brochure, 2019 , p. 92-94, 197-199.
↑ ¹ ² Stock et al, 2019 , p. 2.
↑ Note on the impact of the redefinition of the kilogram on BIPM mass calibration uncertainties (neopr.) . Bipm . Date of treatment June 9, 2019.
↑ CCEM Guidelines for Implementation of the 'Revised SI' (neopr.) . Bipm . Date of treatment June 9, 2019.
↑ FAQs: Frequently Asked Questions about the revision of the SI (neopr.) . Bipm . Date of treatment June 12, 2019.
↑ SI Brochure, 2019 , p. 15-16, 127-128.
↑ Stock et al, 2019 , pp. 1-2.
↑ Stock et al, 2019 , pp. 2–3.
↑ C. Rothleitner and S. Schlamminger. Invited Review Article: Measurements of the Newtonian constant of gravitation, G // Review of Scientific Instruments. - 2017 .-- Vol. 88. - P. 111101. - DOI : 10.1063 / 1.4994619 .
↑ Resolution 1 of the 26th CGPM (2018) (neopr.) . Bipm . Circulation date May 22, 2019.
↑ The International System of Units - making measurements fundamentally better (neopr.) . Bipm . Circulation date May 22, 2019.
↑ Stock et al, 2019 , pp. 3-10.
↑ Practical realizations of the definitions of some important units (neopr.) . Bipm . Date of treatment June 10, 2019.
↑ Fritz Riehle, Patrick Gill, Felicitas Arias and Lennart Robertsson. The CIPM list of recommended frequency standard values: guidelines and procedures // Metrologia. - 2018 .-- Vol. 55. - P. 188. - DOI : 10.1088 / 1681-7575 / aaa302 .
↑ Bronnikov K.A., Ivashchuk V.D., Kalinin M.I., Melnikov V.N., Khrushchev V.V. On the choice of fixed fundamental constants for new definitions of SI units // Measuring technique. - 2016. - No. 8. - S. 11-15.
↑ Ronald B. Goldfarb. The Permeability of Vacuum and the Revised International System of Units // IEEE Magnetics Letters. - Vol. 8.- DOI : 10.1109 / LMAG.2017.2777782 .

Literature

Le Système international d'unités (SI) / The International System of Units (SI) . - 9th ed. - BIPM, 2019 .-- ISBN 978-92-822-2272-0 .
Input data for the special CODATA-2017 adjustment (unspecified) . The appeal date is May 31, 2019. is a special issue of the journal Metrologia dedicated to obtaining the values of the constants on which the changes are based.
- Michael Stock, Richard Davis, Estefanía de Mirandés and Martin JT Milton. The revision of the SI — the result of three decades of progress in metrology // Metrologia. - 2019 .-- Vol. 56, No. 022001. - DOI : 10.1088 / 1681-7575 / ab0013 .

[units-1] ¹ ² SI Brochure, 2019 , p. 18-23, 130-135.

[_18912eaf42adcb4d-2] Stock et al, 2019 , pp. 3-4.

[_1346770f830ecad3-3] SI Brochure, 2019 , p. 92-94, 197-199.

[_01c677b38fa56267-4] ¹ ² Stock et al, 2019 , p. 2.

[5] Note on the impact of the redefinition of the kilogram on BIPM mass calibration uncertainties (neopr.) . Bipm . Date of treatment June 9, 2019.

[6] CCEM Guidelines for Implementation of the 'Revised SI' (neopr.) . Bipm . Date of treatment June 9, 2019.

[faq-7] FAQs: Frequently Asked Questions about the revision of the SI (neopr.) . Bipm . Date of treatment June 12, 2019.

[_0335b1acb164fdbf-8] SI Brochure, 2019 , p. 15-16, 127-128.

[_2401fe988500c745-9] Stock et al, 2019 , pp. 1-2.

[_2c8a40ba1da15837-10] Stock et al, 2019 , pp. 2–3.

[11] C. Rothleitner and S. Schlamminger. Invited Review Article: Measurements of the Newtonian constant of gravitation, G // Review of Scientific Instruments. - 2017 .-- Vol. 88. - P. 111101. - DOI : 10.1063 / 1.4994619 .

[Resolution2018-12] Resolution 1 of the 26th CGPM (2018) (neopr.) . Bipm . Circulation date May 22, 2019.

[13] The International System of Units - making measurements fundamentally better (neopr.) . Bipm . Circulation date May 22, 2019.

[_6c7d9bce4d506b68-14] Stock et al, 2019 , pp. 3-10.

[15] Practical realizations of the definitions of some important units (neopr.) . Bipm . Date of treatment June 10, 2019.

[16] Fritz Riehle, Patrick Gill, Felicitas Arias and Lennart Robertsson. The CIPM list of recommended frequency standard values: guidelines and procedures // Metrologia. - 2018 .-- Vol. 55. - P. 188. - DOI : 10.1088 / 1681-7575 / aaa302 .

[17] Bronnikov K.A., Ivashchuk V.D., Kalinin M.I., Melnikov V.N., Khrushchev V.V. On the choice of fixed fundamental constants for new definitions of SI units // Measuring technique. - 2016. - No. 8. - S. 11-15.

[18] Ronald B. Goldfarb. The Permeability of Vacuum and the Revised International System of Units // IEEE Magnetics Letters. - Vol. 8.- DOI : 10.1109 / LMAG.2017.2777782 .