Casimir spring and compass: Stable levitation and alignment of compact objects

TL;DR

This paper explores a stable Casimir force setup with an object inside a dielectric cavity, analyzing stability and orientation dependence, revealing that force sign predicts stability but torque does not.

Contribution

It introduces a configuration for stable Casimir levitation and provides detailed calculations of force and torque dependencies on object position and orientation.

Findings

Force stability can be predicted by force sign.

Torque stability cannot be predicted solely by force sign.

The configuration enables stable levitation of objects.

Abstract

We investigate a stable Casimir force configuration consisting of an object contained inside a spherical or spheroidal cavity filled with a dielectric medium. The spring constant for displacements from the center of the cavity and the dependence of the energy on the relative orientations of the inner object and the cavity walls are computed. We find that the stability of the force equilibrium can be predicted based on the sign of the force, but the torque cannot be.