Measuring inertial mass with Kibble balance

Abstract

A Kibble balance measures the $gravitational$ mass (weight) of a test mass with extreme precision by balancing the gravitational pull on the test mass against the electromagnetic lift force. The uncertainty in such mass measurement is currently ~$1\times 10^{-8} $. We show how the same Kibble balance can be used to measure the $inertial$ mass of a test mass, that too with potentially 50% better measurement uncertainty, i.e., ~$5\times 10^{-9} $. For measuring the inertial mass, the weight of the test mass and the assembly holding it is precisely balanced by a counterweight. The application of the known electromagnetic force accelerates the test mass. Measuring the velocity after a controlled elapsed time provides the acceleration and, consequently, the inertial mass of the accelerated assembly comprising the Kibble balance coil and the mass holding pan. Repeating the measurement with the test mass added to the assembly and taking the difference between the two measurements yields the inertial mass of the test mass. Thus, the extreme precision inertial and gravitational mass measurement of a test mass with a Kibble balance could provide a test of the equivalence principle. We discuss how the two masses are related to the Planck constant and other coupling constants and if the Kibble balance could be used to test the dynamic constants theories in Dirac cosmology.