Gebruiker:Martinvl/New SI

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 noted that in practice G can only be measured with a relative uncertainty of 10⁻⁴ which would have resulted in upper limit of the kilogram's reproducibility being 10⁻⁴ whereas the current international prototype kilogram can be measured with a relative uncertainty of 5 × 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.

Physical constants used in the new definitions

The following table catalogues the changes in the relative uncertainty of the physical constants and of base units that are directly affected by the proposals:

Actual uncertainties are catalogued in the resolution

Relative uncertainty of various physical measurements and associated base units
Unit	Constant used as reference	Symbol	Current definitions (2006)	Proposed definitions (2006)	Current definitions (2017)	Proposed definitions (2017)
kg	Mass of International prototype kilogram	m(K)	exact	4.4 × 10−8	exact	1.0 × 10−8
	Planck constant	h	4.4 × 10−8	exact	1.0 × 10−8	exact
A	magnetic constant	μ0	exact	6.8 × 10−10	exact	2.3 × 10−10
	Elementary charge	e	2.2 × 10−8	exact	5.2 × 10−9	exact
K	Temperature of triple point of water	TTPW	exact	9.1 × 10−7	exact
	Boltzmann constant	k	9.1 × 10−7	exact	3.7 × 10−7	exact
mol	Molar mass 12C	M(12C)	exact	4.4 × 10−8	exact
	Avogadro constant	NA	4.4 × 10−8	exact	1.0 × 10−8	exact

Other physical constants

There are three categories of physical constants:

• The fundamental constants whose value is by definition fixed.
• Physical constants that are a function of the fundamental constants, for example the von Klitzing constant R_K = h/e². In this case, both e and h are fundamental constants, so the von Klitzing constant has an exact definition.
• Physical constants that were alternative candidates as fundamental constants. These have to be measured separately, but the fundamental constants are often used in calculating these constants.

Although there are potentially many thousands of constants in the latter two groups, those identified by Mills are listed below. Constants that are closely related have been grouped together.

CODATA reference

Relative uncertainty of various physical measurements						Relationship to basic constants of nature
Constant used as reference	Symbol	Current definitions (2006)	Proposed definitions (2006)	Current definitions (2017)	Proposed definitions (2017)
electron mass unified atomic mass unit or dalton carbon 12 atomic mass	me mu m(12C)	5.0 × 10−8 5.0 × 10−8 5.0 × 10−8	1.4 × 10−9 1.4 × 10−9 1.4 × 10−9	1.2 × 10−8 1.2 × 10−8 1.2 × 10−8	1.2 × 10−8 1.2 × 10−8 1.2 × 10−8	N/A
magnetic constant vacuum permittivity impedance of free space	μ0 ε0 Z0	exact exact exact	6.8 × 10−10 6.8 × 10−10 6.8 × 10−10	exact exact exact	2.3 × 10−10 2.3 × 10−10 2.3 × 10−10	$\mu _{0}\varepsilon _{0}={\frac {1}{c^{2}}};Z_{\rm {0}}=\mu _{0}c_{0}$
fine-structure constant	α	6.8 × 10−10	6.8 × 10−10	2.3 × 10−10	2.3 × 10−10	${\frac {1}{2\varepsilon _{0}}}{\frac {e^{2}}{hc}}$
von Klitzing constant	RK	6.8 × 10−10	exact	2.3 × 10−10	exact	${\frac {e^{2}}{h}},$
temperature of triple point of water	TTPW	exact	1.7 × 10−6	exact		N/A
Molar gas constant	R	1.7 × 10−6	exact	5.7 × 10−7	exact	$N_{\rm {A}}k_{\rm {B}},\,$
Stefan–Boltzmann constant	σ	3.6 × 10−6	exact	2.3 × 10−6	exact	${\frac {2\pi ^{5}k_{\rm {B}}^{4}}{15h^{3}c^{2}}}$
Faraday constant Josephson constant	F KJ	2.2 × 10−8 2.2 × 10−8	exact exact	6.2 × 10−9 6.2 × 10−9	exact exact	$F\,=\,eN_{A};K_{\rm {J}},={\frac {2e}{h}}$