Vacuum Fluctuations and Accelerated Frames

Abstract

Quantum fields carry energy and momentum and exert radiation pressure forces upon mirrors I. As known for a long time 2, a mirror immersed in thermal fields experiences a mean dissipative force proportional to its velocity as well as random force fluctuations. The dissipative and fluctuating forces are connected through fluctuation-dissipation relations 3, and they induce a Brownian motion for the mirror's position. The force fluctuations 4, the dissipative motional force 5 as well as the associated random motion 6 persist for mirrors immersed in vacuum fluctuations, that is at the zero temperature limit of thermal fluctuations. In a configuration with two mirrors, a mean force, the so-called Casimir force, appears between the two mirrors, which may be understood either as the consequence of the variation with distance of vacuum energy 7, or as the result of vacuum radiation pressure 8.9. Force fluctuations and motional forces have also been computed in this configuration 10. Now, the question arises whether or not these mechanical effects of vacuum obey the general laws of mechanics, and particularly the laws of relativity. For example, the laws of relativity require that the motional force vanishes for uniform motion in vacuum. The case of uniformly accelerated motion has to be carefully examined, since it is directly connected to the laws of inertia. A related question is whether or not vacuum fluctuations appear different after coordinate transformations to accelerated frames I I. For a perfect mirror moving in vacuum scalar fields in a two-dimensional (2D) space-time, the motional force is found to be proportional to the Abraham-Lorentz derivative, so that it vanishes for uniformly accelerated motion. In a linear approximation in a mirror's displacement oq, that is also in a non-relativistic approximation, the motional force may be simply written as the third-order time derivative of displacement: Fmot(t) = (tl/61tc 2) oq'''(t) This result corresponds to a motional susceptibility proportional to the third power of frequency in the spectral domain: Coherence and Quantum Optics VII Edited by Eberly, Mandel, and Wolf, Plenum Press, New York, 1996 153