The kilogram: inertial or gravitational mass?

TL;DR

This paper discusses the redefinition of the kilogram based on fixed fundamental constants, emphasizing that atom counting measures inertial mass directly and can test the equivalence principle.

Contribution

It clarifies that only atom counting directly measures inertial mass, providing a new perspective on testing the equivalence principle with the kilogram.

Findings

Atom counting measures inertial mass without assuming free fall universality.

Kibble balance measures gravitational mass, assuming equivalence principle.

Agreement between methods tests the equivalence principle.

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 $^{133}$Cs atom, 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. Therefore, the agreement between the two measures can be interpreted as a test of the equivalence principle.