The Planck constant of action and the Kibble balance

Abstract

It has been shown previously (P. R. Bunker and Per Jensen, J. Quant. Spectrosc. Radiat. Transf., 243 (2020) 106835) that if we choose angles to have dimension, we have to distinguish between the Planck constant $h$, having the dimension of $\mathrm{action}{\mathrm{angle}}^{-1}$, and the Planck constant of action $h_A$, having the dimension of $\mathrm{action}$. In the present paper, we show that a further implication that results from choosing angles to have dimension is that the Kibble balance equation relating the mass weighed to the Planck constant has to involve both of the distinct fundamental constants $h$ and $h_A$. We derive that new equation here and show how it compares to the equation that is obtained if one chooses angles to be dimensionless as required in SI.