Casimir apparatuses in a weak gravitational field

TL;DR

This paper reviews recent theoretical work on the behavior of Casimir apparatuses in Earth's weak gravitational field, showing that Casimir energy gravitates and predicting a tiny upward force on the apparatus.

Contribution

It provides a comprehensive assessment of the covariant conservation of energy-momentum and the finite Casimir energy in weak gravity, extending results to electromagnetic fields and first-order gravity effects.

Findings

Casimir energy is shown to gravitate, producing a tiny upward force.

Energy-momentum tensor remains covariantly conserved in weak gravity.

Finite Casimir energy and pressure are obtained under conformal coupling.

Abstract

We review and assess a part of the recent work on Casimir apparatuses in the weak gravitational field of the Earth. For a free, real massless scalar field subject to Dirichlet or Neumann boundary conditions on the parallel plates, the resulting regularized and renormalized energy-momentum tensor is covariantly conserved, while the trace anomaly vanishes if the massless field is conformally coupled to gravity. Conformal coupling also ensures a finite Casimir energy and finite values of the pressure upon parallel plates. These results have been extended to an electromagnetic field subject to perfect conductor (hence idealized) boundary conditions on parallel plates, by various authors. The regularized and renormalized energy-momentum tensor has been evaluated up to second order in the gravity acceleration. In both the scalar and the electromagnetic case, studied to first order in the gravity acceleration, the theory predicts a tiny force in the upwards direction acting on the apparatus. This effect is conceptually very interesting, since it means that Casimir energy is indeed expected to gravitate, although the magnitude of the expected force makes it necessary to overcome very severe signal-modulation problems.