Gedanken experiments with Casimir forces, vacuum energy, and gravity

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.