QUANTUM FLUCTUATIONS OF VACUUM STRESS TENSORS AND SPACETIME CURVATURES

We analyze the quantum fluctuations of vacuum stress tensors and space time curvatures, using the framework of linear response theory which c onnects these fluctuations to dissipation mechanisms arising when stre ss tensors and spacetime metric are coupled. Vacuum fluctuations of sp acetime curvatures are shown to be a sum of two contributions at lowes t orders; the first one corresponds to vacuum gravitational waves and is restricted to light-like wavevectors and vanishing Einstein curvatu re, while the second one arises from gravity of vacuum stress tensors. From these fluctuations, we deduce noise spectra for geodesic deviati ons registered by probe fields which determine ultimate limits in leng th or time measurements. In particular, a relation between noise spect ra characterizing spacetime fluctuations and the number of massless ne utrino fields is obtained.