New SI Units Revised in 2018 and Effective Since 20th May 2019

The Watt balance at the US National Institute of Standards and Technology (NIST)
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The latest major revision for SI units proposed by International Committee for Weights and Measures (commonly known as CIPM for its French name Comite international des poids et mesuress) was approved by voting of member states in the 26th General Conference on Weights and Measures (commonly known as CGPM) held on November 16, 2018. It has now been decided that the SI would be based on the fixed numerical values of a set of seven defining constants from which the definitions of the seven base units of the SI would be deduced. New definitions of the SI Units come into effect from World Metrology Day of year 2019, that is, from May 20, 2019. (20th May is celebrated as World Metrology Day.)

After the revision in SI Units, there are still the same seven base units. (If you do not know what are the ‘base units’, follow this link for a more elimentry introduction to SI Units.) Of these, the kilogram, ampere, kelvin and mole are redefined by choosing exact numerical values for the Planck constant, the elementary electric charge, the Boltzmann constant, and the Avogadro constant, respectively. The second, metre and candela are already defined by physical constants and it is only necessary to edit their present definitions. The new definitions will improve the SI without changing the size of any units, thus ensuring continuity with present measurements.

The seven constants are chosen in such a way that any unit of the SI can be written either through a defining constant itself or through products or ratios of defining constants. These seven constants and their values are as follows. Note that the numerical values of these constants have no uncertainty.

  1. The unperturbed ground state hyperfine transition frequency of the caesium-133 atom, symbolized as \(\Delta \nu_{Cs}\), is \(9192631770\) \(Hz\).
  2. The speed of light in vacuum, symbolized as \(c\), is \(299792458\) \(m/s\).
  3. The Planck constant, symbolized as \(h\), is \(6.62607015 \times 10^{−34}\) \(Js\).
  4. The elementary charge, symbolized as \(e\), is \(1.602176634 \times 10^{−19}\) \(C\).
  5. The Boltzmann constant, symbolized as \(k\), is \(1.380649 \times 10^{−23}\) \(J/K\).
  6. The Avogadro constant, symbolized as \(N_A\), is \(6.02214076 \times 10^{23}\) \(mol^{−1}\).
  7. The luminous efficacy of monochromatic radiation of frequency \(540 \times 10^{12}\) \(Hz\), symbolized as \(K_{cd}\), is \(683\) \(lm/W\).

In above definitions, hertz (\(Hz\)), joule (\(J\)), coulomb (\(C\)), lumen (\(lm\)), and watt (\(W\)) are related, respectively, to the units second (\(s\)), metre (\(m\)), kilogram (\(kg\)), ampere (\(A\)), kelvin (\(K\)), mole (\(mol\)), and candela (\(cd\)) according to \(Hz = s^{–1}\), \(J = kg m^2 s^{–2}\), \(C = A s\), \(lm = cd m^2 m^{–2}\), and \(W = kg m^2 s^{–3}\).

Both the Planck constant \(h\) and the speed of light in vacuum \(c\) are properly described as fundamental. They determine quantum effects and space-time properties, respectively, and affect all particles and fields equally on all scales and in all environments.

The elementary charge \(e\) corresponds to a coupling strength of the electromagnetic force via the fine-structure constant \(\alpha = \frac{e^2}{2c \epsilon_0 h}\) where \(\epsilon_0\) is the vacuum electric permittivity or electric constant. Some theories predict a variation of \(\alpha\) over time. The experimental limits of the maximum possible variation in \(\alpha\) are so low, however, that any effect on foreseeable practical measurements can be ignored.

The Boltzmann constant \(k\) corresponds to a conversion factor between the quantities temperature (measured in kelvin) and energy (measured in joule), whereby the numerical value is obtained from historical specifications of the temperature scale. The temperature of a system scales with the thermal energy, but not necessarily with the internal energy of a system. In statistical physics, the Boltzmann constant connects the entropy \(S\) with the number \(\Omega\) of quantum-mechanically accessible states, \(S = k \ln \Omega\).

The caesium frequency \(\Delta \nu_{Cs}\), the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom, has the character of an atomic parameter, which may be affected by the environment, such as electromagnetic fields. However, the underlying transition is well understood, stable and a good choice as a reference transition under practical considerations.

The Avogadro constant \(N_A\) corresponds to a conversion factor between the quantity amount of substance (with unit mole) and the quantity for counting entities (with unit one, symbol 1). Thus it has the character of a constant of proportionality similar to the Boltzmann constant \(k\).

The luminous efficacy of monochromatic radiation of frequency \(540 \times 1012\) \(Hz\), \(K_{cd}\), is a technical constant that gives an exact numerical relationship between the purely physical characteristics of the radiant power stimulating the human eye (\(W\)) and its photobiological response defined by the luminous flux due to the spectral responsivity of a standard observer (\(lm\)) at a frequency of \(540 \times 1012\) hertz.

New Definitions of the Basic SI units

Earlier SI Units were categorised into Base Units and Derived Units. Seven Base Units were defined and Derived Units were constructed as products of powers of the Base Units. However, since 20th June, 2019, as decided in 26th CGPM on November 16, 2018, SI Units are now defined by fixing numerical values of seven defining constants as mentioned above. (For a brief history of SI Units, follow this link.) Defining SI Units by defining seven constants has the effect that this categorisation of SI Units into the Base and the Derived units is, in principle, not needed, since all units – Base as well as Derived – may be constructed directly from the defining constants. Nevertheless, the concept of Base and Derived units is maintained, not only because it is useful and historically well established, but also because it is necessary to maintain consistency with existing systems wherein both Base and Derived units have been used.

The second

The second, symbol \(s\), is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency \(\Delta \nu_{Cs}\), the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9192631770 when expressed in the unit \(Hz\), which is equal to \(s^{−1}\).

This definition implies the exact relation \(\Delta \nu_{Cs} = 9192631770\) \(Hz\). Inverting this relation gives an expression for the unit second in terms of the defining constant \(\Delta \nu_{Cs}\):

\[1 Hz = \frac{\Delta \nu_{Cs}}{9192631770}\]

or

\[1 s = \frac{9192631770}{\Delta \nu_{Cs}}\]

The effect of this definition is that the second is equal to the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the unperturbed ground state of the Cs-133 atom.

The metre

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 299792458 when expressed in the unit \(m s^{−1}\), where the second is defined in terms of the caesium frequency \(\Delta \nu_{Cs}\).

This definition implies the exact relation \(c = 299792458\) \(ms^{−1}\). Inverting this relation gives an exact expression for the metre in terms of the defining constants \(c\) and \(\Delta \nu_{Cs}\):

\[1m = (\frac{c}{299792458})s\]

or

\[1m = (\frac{9192631770}{299792458})(\frac{c}{\Delta \nu_{Cs}}) \]

or

\[1m \approx 30.663319 (\frac{c}{\Delta \nu_{Cs}})\]

The effect of this definition is that one metre is the length of the path travelled by light in vacuum during a time interval with a duration of \(1/299792458\) of a second.

The kilogram

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 \(6.62607015 \times 10^{−34}\) when expressed in the unit \(Js\), which is equal to \(kg m^2 s^{−1}\), where the metre and the second are defined in terms of \(c\) and \(\Delta \nu_{Cs}\).

This definition implies the exact relation \(h = 6.62607015 \times 10^{−34}\) \(kg m^2 s^{−1}\). Inverting this relation gives an exact expression for the kilogram in terms of the three defining constants \(h\), \(\Delta \nu_{Cs}\), and \(c\):

\[1 kg = (\frac{h}{6.62607015 \times 10^{-34}}) m^{-2} s\]

which is equal to

\[1 kg = (\frac{299792458^2}{(6.62607015 \times 10^{-34}) (9192631770)}) (\frac{h \Delta \nu_{Cs}}{c^2})\]

or

\[1 kg \approx 1 . 4755214 \times 10^{40} (\frac{h \Delta \nu_{Cs}}{c^2})\]

The effect of this definition is that we can define mass expressed in terms of the Planck constant h.

The previous definition of the kilogram fixed the value of the mass of the international prototype of the kilogram to be equal to one kilogram exactly and the value of the Planck constant \(h\) had to be determined by experiment. The present definition fixes the numerical value of \(h\) exactly and the mass of the prototype has now to be determined by experiment.

The number chosen for the numerical value of the Planck constant in this definition is such that at the time of its adoption, the kilogram was equal to the mass of the international prototype with a relative standard uncertainty of \(1 \times 10^{−8}\), which was the standard uncertainty of the combined best estimates of the value of the Planck constant at that time.

The ampere

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 \(1.602176634) \times 10^{−19}\) when expressed in the unit \(C\), which is equal to \(A s\), where the second is defined in terms of \(\Delta \nu_{Cs}\).

This definition implies the exact relation \(e = 1.602176634 \times 10^{−19}\) \(A s\). Inverting this relation gives an exact expression for the unit ampere in terms of the defining constants \(e\) and \(\Delta \mu_{Cs}\):

\[1A = (\frac{e}{1.602176634 \times 10^{-19}}) s^{-1}\]

which is equal to

\[1A = (\frac{1}{(9192631770) (1.602176634 \times 10^{−19})}) \Delta \mu_{Cs} e \]

or

\[1A \approx (6.789687 \times 10^8) \Delta \mu_{Cs} e\]

The effect of this definition is that one ampere is the electric current corresponding to the flow of \(1/(1.602176634 \times 10^{−19})\) elementary charges per second.

The previous definition of the ampere was based on the force between two current carrying conductors and had the effect of fixing the value of the vacuum magnetic permeability \(\mu_0\) (also known as the magnetic constant) to be exactly \(4\pi \times 10^{-7}\) \(H m^{−1}\) or \(4\pi \times 10^{-7}\) \(N A^{−2}\), where \(H\) and \(N\) denote the coherent derived units henry and newton, respectively. The new definition of the ampere fixes the value of \(e\) instead of \(\mu_0\). As a result, \(\mu_0\) must be determined experimentally.

Since the vacuum electric permittivity \(\varepsilon_0\) (also known as the electric constant) is equal to \(\frac{1}{\mu_0 c^2}\), it is affected by the same relative standard uncertainty as \(\mu_0\) since \(c\) is exactly known. At the time of adopting the present definition of the ampere, \(\mu_0\) was equal to \(4\pi \times 10^{-7}\) \(H m^{−1}\) with a relative standard uncertainty of \(2.3 \times 10^{−10}\).

The kelvin

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 \(1.380649 \times 10^{−23}\) when expressed in the unit \(J K^{−1}\), which is equal to \(kg m^2 s^{−2} K^{−1}\), where the kilogram, metre and second are defined in terms of \(h\), \(c\), and \(\Delta \mu_{Cs}\).

This definition implies the exact relation \(k = 1.380649 \times 10^{−23}\) \(kg m^2 s^{−2} K^{−1}\). Inverting this relation gives an exact expression for the kelvin in terms of the defining constants \(k\), \(h\) and \(\Delta \mu_{Cs}\):

\[1K = (\frac{1.380649 \times 10^{-23}}{k}) kg m^2 s^{-2}\]

which is equal to

\[1K = \frac{1.380649 \times 10^{−23}}{(6.62607015 \times 10^{-34})(9192631770)} \frac{\Delta \mu_{Cs} h}{k}\]

or

\[1K \approx 2.2666653 \frac{\Delta \mu_{Cs} h}{k}\]

The effect of this definition is that one kelvin is equal to the change of thermodynamic temperature that results in a change of thermal energy \(kT\) by \(1.380649 \times 10^{−23}\) \(J\).

The previous definition of the kelvin set the temperature of the triple point of water, \(T_{TPW}\), to be exactly \(273.16\) \(K\). Due to the fact that the present definition of the kelvin fixes the numerical value of \(k\) instead of \(T_{TPW}\), the latter must now be determined experimentally. At the time of adopting the present definition, \(T_{TPW}\) was equal to \(273.16\) \(K\) with a relative standard uncertainty of \(3.7 \times 10^{−7}\) based on measurements of \(k\) made prior to the redefinition.

The mole

The mole, symbol \(mol\), is the SI unit of amount of substance. One mole contains exactly \(6.02214076 \times 10^{23}\) elementary entities. This number is the fixed numerical value of the Avogadro constant, \(N_A\), when expressed in the unit \(mol^{−1}\) and is called the Avogadro number.

The amount of substance, symbol \(n\), of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles.

This definition implies the exact relation \(N_A = 6.02214076 \times 10^{23}\) \(mol^{−1}\). Inverting this relation gives an exact expression for the mole in terms of the defining constant \(N_A\):

\[1 mol = (\frac{6.02214076 \times 10^{23}}{N_A})\]

The effect of this definition is that the mole is the amount of substance of a system that contains \(6.02214076 \times 10^{23}\) specified elementary entities.

The previous definition of the mole fixed the value of the molar mass of carbon 12, \(M(^{12}C)\), to be exactly \(0.012\) \(kg/mol\). According to the present definition \(M(^{12}C)\) is no longer known exactly and must be determined experimentally. The value chosen for \(N_A\) is such that at the time of adopting the present definition of the mole, \(M(^{12}C)\) was equal to \(0.012\) \(kg/mol\) with a relative standard uncertainty of \(4.5 \times 10^{−10}\).

The candela

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 \(540 \times 10^{12}\) \(Hz\), \(K_{cd}\), to be \(683\) when expressed in the unit \(lm W^{-1}\), which is equal to \(cd sr W^{−1}\), or \(cd sr kg^{-1} m^{-2} s^3\), where the kilogram, metre, and second are defined in terms of \(h\), \(c\), and \(\Delta \mu_{Cs}\).

This definition implies the exact relation \(K_{cd} = 683\) \(cd sr kg^{−1} m^{−2} s^3\) for monochromatic radiation of frequency \( \nu = 540 \times 10^{12}\) \(Hz\). Inverting this relation gives an exact expression for the candela in terms of the defining constants \(K_{cd}\), \(h\) and \(\Delta \mu_{Cs}\):

\[1 cd = \frac{K_{cd}}{683} kg m^2 s^{-3} sr^{-1}\]

which is equal to

\[1cd = \frac{1}{(6.62607015 \times 10^{-34})(9192631770)^2(683)} (\Delta \mu_{Cs})^2 h K_{cd}\]

or

\[1cd \approx 2.614830 \times 10^{10} (\Delta \mu_{Cs})^2 h K_{cd}\]

The effect of this definition is that one candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency \(540 \times 10^{12}\) \(Hz\) and has a radiant intensity in that direction of \(1/683\) \(W/sr\).

Note: The steradian, \(sr\), is a unit for solid angle. One steradian is the solid angle subtended at the centre of a sphere by an area of the surface that is equal to the squared radius. Like the radian, the steradian was formerly an SI supplementary unit.

Attribution: Featured Photo by Richard Steiner (The original uploader was Greg L at English Wikipedia.) [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons



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A Brief History of SI Units and CGPM

Nations which traded and exchanged scientific ideas with each other had started realizing the importance and necessity of standardisation of weights and […]

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