  Gedanken experiments are used to explore properties of quantum vacuum energy
that are currently challenging to explore experimentally. A constant lateral
Casimir force is predicted to exist between two overlapping finite parallel
plates at 0 K, otherwise it would be possible to extract an arbitrary amount of
energy from the quantum vacuum. A rigid unpowered object cannot be accelerated
by the quantum vacuum because of the translational symmetry of space. By
considering systems in which vacuum energy and other forms of energy are
exchanged, we demonstrate that a change {\Delta}E in vacuum energy, whether
positive or negative with respect to the free field, corresponds to an
equivalent inertial mass and equivalent gravitational mass
{\Delta}M={\Delta}E/c^2. We consider the possibility of a gravitational shield,
and show that, if it exists, the energy to operate it would have to cancel the
net energy extracted from the gravitational field, otherwise we could extract
an arbitrary amount of energy from the field.
