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# Fixing the SI System Permanently

By: Suad Čobo

The International System of Units (SI – French: Système Internationale (d'Unités)) is the modern form of the metric system and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, which are the second, metre, kilogram, ampere, kelvin, mole, candela, and a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system also specifies names for 22 derived units, such as lumen and watt, for other common physical quantities.

A replica of the International Prototype Kilogram on display at Cité des Sciences et de l'Industrie (Photo: Wikimedia Commons) [1]

The base units are currently defined in terms of constants of nature, such as the speed of light in a vacuum and the charge of an electron, which can be observed and measured with great accuracy; however, they were not always defined with these constants. In this article we will be looking back on how some base units, particularly the kilogram, have been defined for 130 years.

In 1889, the first meeting of the General Conference on Weights and Measures (CGPM) was held in Sèvres, France (south-west of Paris). The International Prototype Kilogram (IPK), a cylinder made of platinum-iridium, was selected alongside the International Prototype Metre, an X-cross-section bar also made from platinum-iridium and manufactured by the British firm Johnson Matthey. Working copies of both artifacts were also selected by lot and other copies were distributed to member nations. The prototypes and working copies were deposited at the International Bureau of Weights and Measures (Bureau international des poids et mesures - BIPM) in Sèvres. Before the decision of CGPM, the kilogram was originally defined as the mass of a liter of water, which was a simple definition but hard to replicate precisely.

Although efforts were made to maintain it, evidence accumulated that the mass of the International Prototype Kilogram had been changing; the IPK had diverged from its replicas by approximately 50 micrograms since its manufacture late in the 19th century. This led to several competing efforts to develop measurement technology precise enough to allow replacing the kilogram artifact with a definition based directly on physical fundamental constants. This culminated in 2018 with a redefinition of the kilogram in terms of Planck’s constant, which relates the energy of one quantum of electromagnetic radiation to the frequency of that radiation. As a result of this redefinition, the kilogram is now defined in terms of the second and the metre, replacing the IPK as primary standard. The new definition was approved by the CGPM on 16 November 2018. Physical standard masses such as the IPK and its replicas still serve as secondary standards.

New Definition

The 26th CGPM meeting was held from 13-16th November 2018. During this meeting, the kilogram, ampere, kelvin and mole were redefined with the new permanently fixed values of Planck’s constant (h), elementary charge (e), Boltzmann constant (k) and Avogadro constant (NA), respectively. The second, metre, and candela were already defined by physical constants and were subject to correction to their definitions. This decision is effective from the 144th anniversary of the Metre Convention on 20th May, 2019.

Due to the changing nature of previously mentioned constants, 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:

• The Planck constant h=6.626 070 15*1034 Js (joule-second)

• the elementary charge e=1.602 176 634*10-34 C (coulomb)

• the Boltzmann constant k=1.380 649*10-23 J*k-1 (joule per kelvin)

• the Avogadro constant NA=6.022 140 76*1023 mol-1

• the speed of light c = 299 792 458 m*s-1 (meters per second)

• The ground state hyperfine structure transition frequency of the 133CS atom ΔνCs =9 192 631 770 Hz (hertz)

As part of the redefinition, the IPK was retired and the definitions of the kilogram, ampere and kelvin were replaced and 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.

These redefinitions do not have a big practical impact on everyday life, but they do make the SI system permanently defined, instead of changing the definitions by themselves.

# References

[1] Japs88. (2012, 05 29). File:Prototype_kilogram_replica.JPG. Retrieved from Wikimedia Commons: https://commons.wikimedia.org/wiki/File:Prototype_kilogram_replica.JPG

[2] 2019 redefinition of the SI base units. (n.d.). Retrieved from Wikipedia (English): https://en.wikipedia.org/wiki/2019_redefinition_of_the_SI_base_units

[3] Convocation de la Conférence générale des poids et mesures (26e réunion) / Convocation of the General Conference on Weights and Measures (26th meeting). (2018, 11 13-16). Retrieved from Bureau international des poids et mesures / International Bureau of Weights and Measures (BIPM): https://www.bipm.org/utils/en/pdf/CGPM/Convocation-2018.pdf

[4] General Conference on Weights and Measures. (n.d.). Retrieved from Wikipedia (English): https://en.wikipedia.org/wiki/General_Conference_on_Weights_and_Measures

[5] Kilogram. (n.d.). Retrieved from Wikipedia (English): https://en.wikipedia.org/wiki/Kilogram

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