Perfect mirrors and the self-accelerating box paradox

We consider the question raised by Unruh and Wald of whether mirrored boxes can self-accelerate in flat spacetime (the “self-accelerating box paradox”). From the point of view of the box, which perceives the acceleration as an impressed gravitational field, this is equivalent to asking whether the box can be supported by the buoyant force arising from its immersion in a perceived bath of thermal (Unruh) radiation. The perfect mirrors we study are of the type that rely on light internal degrees of freedom which adjust to and reflect impinging radiation. We suggest that a minimum of one internal mirror degree of freedom is required for each bulk field degree of freedom reflected. A short calculation then shows that such mirrors necessarily absorb enough heat from the thermal bath that their increased mass prevents them from floating on the thermal radiation. For this type of mirror the paradox is therefore resolved. We also observe that this failure of boxes to “float” invalidates one of the assumptions going into the Unruh-Wald analysis of entropy balances involving boxes lowered adiabatically toward black holes. Nevertheless, their broad argument can be maintained until the box reaches a new regime in which box-antibox pairs dominate over massless fields as contributions to thermal radiation.