I don't see your point. But to make things clearer, I know pretty well SR, let's say. And I know the answer to my question. I mean, I have two plates that attract each other and I put something that prevent them to schrink down. In the laboratory frame, the system is at equilibrium, and will stay so. And of course, the fact that someone is moving very fast wrt the lab, won't change anything to this.
My question, then, is simply: how the moving guy describes this system? You see, we more oftenly use SR as only a kinematical theory, whereas it also describes dynamics. And in my thought experiment there is dynamics because there are forces involved. So again, how it comes that the moving guy indeed sees a system at equilibrium with the distance between plates reduced by a factor gamma, whereas we (naively) expect the various forces in this system to be boosted by various powers of gamma? (for Casimir, gamma^4). I guess the answer lies in the transformation law of 4-forces, but... i would appreciate some hints!