  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.
