The kilogram: inertial or gravitational mass?

Abstract

With the redefinition of the international system of units, the value of the Planck constant was fixed, similarly to the values of the unperturbed ground state hyperfine transition frequency of the 133Cs atom and speed of light in vacuum. Theoretically and differently from the past, the kilogram is now explicitly defined as the unit of inertial mass. Experimentally, the kilogram is realized by atom count or the Kibble balance. We show that only the former method measures the inertial mass without assuming the universality of free fall. Under ordinary circumstances, the results obtained by the Kibble balance require the equivalence of inertial and gravitational mass. Therefore, the agreement between the two measures can be interpreted as a test of the equivalence principle.