12. Scale-spanning units — a third unit category (R13)
The SI sorts its units into two categories — base (the kilogram, metre, second,
ampere, kelvin, candela, mole) and derived (everything built from them). Finkelstein
and Whitehead (Eur. J. Phys. 46 (2025) 035701) argue this two-way split is
insufficient. Of the seven base units, only four — the kilogram, metre, second, and
ampere — are genuinely dimensionally independent, each fixed by a natural constant
(h, c, Δν_Cs, e). The other three are not dimensionally independent of those
four: the kelvin has the dimension of energy (M·L²·T⁻², via the Boltzmann constant
k_B); the candela has the dimension of power (M·L²·T⁻³, via the luminous efficacy
K_cd); and the mole is a dimensionless number (via the Avogadro constant N_A). Yet
each is kept as a distinct, coherent unit because it carries a human-selected
coefficient — chosen for historical significance and a size that spans vast scales
without scientific notation (a temperature difference of 100 K, not 1.38 × 10⁻²¹ J per
degree of freedom). The authors propose a third category for them: scale-spanning
units.
R13 specifies that third category. Its point is the unit-layer twin of R1 (a kind is more than its dimension): whether a unit is scale-spanning is not a function of its dimension alone. ISO 80000-7 (the Light and radiation chapter) is where this lands on the standard — the candela and the mole appear there, and are handled by reduction, not by a new base generator.