How does Casimir energy fall?

Doubt continues to linger over the reality of quantum vacuum energy. There is some question whether fluctuating fields gravitate at all, or do so anomalously. Here we show that, for the simple case of parallel conducting plates, the associated Casimir energy gravitates just as required by the equivalence principle, and that therefore the inertial and gravitational masses of a system possessing Casimir energy $E_c$ are both $E_c/c^2$. This simple result disproves recent claims in the literature. We clarify some pitfalls in the calculation that can lead to spurious dependences on the coordinate system.

Figure 1

Relation between two Cartesian coordinate frames: one attached to the earth $(x,y,z)$, where $-z$ is the direction of gravity, and one attached to the parallel-plate Casimir apparatus $(\zeta ,\eta ,\chi )$, where $\zeta$ is in the direction normal to the plates. The parallel plates are indicated by the heavy lines parallel to the $\eta$ axis. The $x=\chi$ axis is perpendicular to the page.