Suppose, I am in an inertial frame of reference moving close to the speed of light. If I held a mirror in a direction of movement it would kick virtual particles from the vacuum into existence. Particles will draw some of the kinetic energy and I would feel a slight push on a mirror thus detecting movement in a certain direction, which I should not be able to do. Assumption that the only true inertial frame of reference is at rest with vacuum contradicts the statement that no privileged frame of reference exists. What is the logical error I made?
Well, I was reffering to dynamic Casimir effect experiment for particle production from vacuum arxiv.org/pdf/1105.4714.pdf. After reading it more carefully I realized that it has nothing to do with uniformly moving mirrors. The dynamic Casimir force arises as a result of Unruh radiation which is related to acceleration. Special relativity is saved :D :D