Using Casimir force as a thruster

Question

In quantum mechanics, there is a phenomenon called the 'Casimir effect'. As two metal plates have a very small distance, the plates work as a potential well, causing limited wave function between the plates while outside doesn't. As a result, two plates have a attraction force. (In some case it could be repulsive but that another story.) In this case we can assume that the plate works as infinite potential. But what if one of the plates are not infinite potential wall? Would sum of Casimir force be non-zero quantity?

For example, let's assume that potential is as follows.

$V(x<0)=0$

$V(0<x<a)=\infty$

$V(a<x<b)=0$

$V(b<x<c)=V_0$

$V(c<x)=0$

What happens?

Answer 1

When the plates (say 1 metal, and the other a dielectric ) are stationary, and the field is in the ground state the forces must be equal, by conservation of momentum. It is worth noting however that when one plate is moved with respect to the other then there will be radiation coming through the dielectric plate. This would result in unequal forces on the plates, but it takes energy to move the plates. Once the plates become stationary, the field in the vicinity of the plates returns to the ground state and the forces become equal.