Archimedes Force on Casimir Apparatus

TL;DR

This paper investigates the gravitational behavior of a Casimir apparatus in a dense medium, deriving a general force expression and highlighting quantum corrections influenced by boundary conditions.

Contribution

It provides a new general expression for the Archimedes force on a Casimir apparatus in a gravitational field, including quantum corrections and boundary condition effects.

Findings

Universal volume-proportional term in the force

Quantum corrections depend on boundary conditions

Explicit formula for finite-sized apparatus in thermal bath

Abstract

We address a problem of Casimir apparatus in dense medium and weak gravitational field. The falling of the apparatus has to be governed by the equivalence principle, with proper account for contributions to the weight of the apparatus from its material part and from distorted quantum fields. We discuss general expression for the corresponding force in metric with cylindrical symmetry. By way of example we compute explicit expression for Archimedes force, acting on the Casimir apparatus of finite size, immersed into thermal bath of free scalar field. It is shown that besides universal term, proportional to the volume of the apparatus, there are non-universal quantum corrections, depending on the boundary conditions.