Casimir–Lifshitz Frictional Heating in a System of Parallel Metallic Plates

Abstract

The Casimir–Lifshitz force of friction between neutral bodies in relative motion, along with the drag effect, causes their heating. This paper considers this frictional heating in a system of two metal plates within the framework of fluctuation electromagnetic theory. Analytical expressions for the friction force in the limiting cases of low (zero) temperature and low and high speeds, as well as general expressions describing the kinetics of heating, have been obtained. It is shown that the combination of low temperatures (T < 10 K) and velocities of 10–103 m/s provides the most favorable conditions when measuring the Casimir–Lifshitz friction force from heat measurements. In particular, the friction force of two coaxial disks of gold 10 cm in diameter and 500 nm in thickness, one of which rotates at a frequency of 10–103 rps (revolutions per second), can be measured using the heating effect of 1–2 K in less than 1 min. A possible experimental layout is discussed.