Perfect mirrors and the self-accelerating box paradox

Abstract

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.

Do black holes radiate?

“…Clearly, this is a provocative result and one which needs to be investigated carefully. Recently, Marolf and Sorkin (2002) have argued that the result is unrealistic, and that a realistic treatment would require a quantization of the internal mirror modes (and does not seem to lead to self-acceleration).…”

Entropy bounds for charged and rotating systems

“…(8,16) to derive the bounds given in Eqs. (15,18), it was not really mandatory. We could obtain the same extensive bounds assuming only the BEB (1).…”

“…Later on, he has shown [15] that, if the box is not almost at the horizon, the typical wavelengths in the radiation are larger than the size of the box and, as a result, the derivation of the buoyant force from a fluid picture is incorrect. The question of whether the Bekenstein bound follows from the GSL via the Geroch process remains controversial (see [16,2,17,18]). However, as it was shown by Bousso [19] (see the following paragraphs), there is another link connecting the GSL with the Bekenstein bound.…”

Note on Bound States and the Bekenstein Bound

“…Such bounds were originally motivated by considerations of black hole thermodynamics [1,2,3,4]. Though this motivation has been criticized by various authors [7,8,9,10], the proposed bounds remain interesting topics of discussion and investigation.…”