Framework-local SI units, the vacuum constants and the exact/measured status of their values

Adopt the SI system of units for this framework, with the following quantity table and conventions; every symbol is a quantity of this framework and the laboratory structure is that of Laboratory geometry: a restricted inertial chart, its spatial slices and fixed-time fields.

(a) [Coordinates and constants] $x^0=ct$ and each spatial coordinate $x^i$ carries the metre (m); the time coordinate $t$ carries the second (s); the conversion constant $c>0$ carries m s${}^{-1}$ and has the exact SI defining value $c=299792458\mathrm{m}{\mathrm{s}}^{-1}$; the elementary charge $e$ has the exact SI defining value $e=1.602176634\times {10}^{-19}\mathrm{C}$, and this item does not assert that physical charge is quantised; the magnetic constant ${\mu }_0>0$ carries N A${}^{-2}$ and is measured, so no exact numerical value of ${\mu }_0$ is asserted. The pre-2019 SI fixed the historical nominal ${\mu }_{0,\mathrm{n}\mathrm{o}\mathrm{m}}:=4\pi \times {10}^{-7}\mathrm{H}{\mathrm{m}}^{-1}=4\pi \times {10}^{-7}\mathrm{N}{\mathrm{A}}^{-2}$ exactly; since the revised SI took effect on 20 May 2019, ${\mu }_0$ is experimentally determined. The SI brochure quotes the nominal ${\mu }_{0,\mathrm{n}\mathrm{o}\mathrm{m}}$ as the estimate at the 2019 adoption with relative standard uncertainty $2.3\times {10}^{-10}$; this is historical estimate and uncertainty context, not an exact equality for the actual ${\mu }_0$ or a current measured value. The electric constant is defined within the framework by

${\epsilon }_0:=({\mu }_0{c}^2{)}^{-1}$

in F m${}^{-1}$, consistent with the exact SI relation ${\epsilon }_0{\mu }_0=1\mathrm{/}{c}^2$, so that $c^2{\epsilon }_0{\mu }_0=1$ and ${\epsilon }_0$ inherits the relative standard uncertainty of ${\mu }_0$.

(b) [Electromagnetic quantities] Charge $q$ carries the coulomb (C); the charge density $\rho$ of the framework's source definition carries C m${}^{-3}$ and the current density $J$ carries A m${}^{-2}$, so that the four-current components $(c\rho ,J)$ carry A m${}^{-2}$; the electric field $E$ carries V m${}^{-1}$; the magnetic field $B$ carries the tesla (T), where $1\mathrm{T}=1\mathrm{N}{\mathrm{A}}^{-1}{\mathrm{m}}^{-1}$; the scalar potential $\phi$ carries V and the vector potential $A$ carries T m, so that the four-potential components $(\phi \mathrm{/}c,A)$ carry T m; the components of the electromagnetic two-form of the framework's tensor definition carry T; a force carries the newton (N), $1\mathrm{N}=1\mathrm{k}\mathrm{g}\mathrm{m}{\mathrm{s}}^{-2}$.

(c) [Mechanical quantities] A rest mass parameter $m$ carries the kilogram (kg) and a four-momentum $P=mU$ of the relativistic particle model carries kg m s${}^{-1}$; field energy density carries J m${}^{-3}$, energy flux W m${}^{-2}$, so that $1\mathrm{W}=1\mathrm{J}{\mathrm{s}}^{-1}=1\mathrm{V}\mathrm{A}$.

(d) [Bookkeeping only] The unit of a quantity records the adopted system of units; it does not show that a quantity is primitive in this or any other framework, it contains no measurement, and it does not identify a quantity with a similarly named quantity of another framework. The exact defining values of $c$ and $e$ fix numerical conventions of the SI; they do not by themselves identify $c$ with the vacuum propagation constant of ideal light, which is the physical adoption of the framework's Minkowski postulate.