The Quantum Radiation from Mirrors Moving Sideways

Abstract

Radiation from moving mirrors, a pure quantum effect, is well understood for mirrors that advance or recede. Here the simplest complementary scenarios are explored, where the mirror is not displaced: half-spaces shifting parallel to their surface and spheres rotating around a diameter. Perfect mirrors do not then radiate at all; hence this preliminary study (for a scalar field) is confined to order (1−1/n2)2for media with a constant (nondispersive) refractive indexn≈1; and also to leading order in (mirror velocity ≡v)/c. The (photon-pair) emission probabilities, the radiative reaction force, and the radiated power are determined for a half-space with arbitraryv. For simple-harmonicvthe single-photon spectrum and angular distribution are given explicitly. The drag exerted on a fixed half-space by a moving one vanishes for constantv, although no reason from any symmetry is apparent. IfaΩ/c⪢1, then a sphere of radiusaoscillating harmonically at frequencyΩradiates power at the same rate per unit area of its surface as would a half-space with the same velocity; but ifaΩ/c⪡1, the power is less by a factor (aΩ/c)6, a measure of the difference between effectively infinite and finite-size mirrors. An appendix evaluates the finite-temperature reaction and drag forces at constantv. Remarkably, this drag on a fixed half-space is independent of its distance from the moving one.