Effects of stress tensor fluctuations upon focusing

We treat the gravitational effects of quantum stress tensor fluctuations. An operational approach is adopted in which these fluctuations produce fluctuations in the focusing of a bundle of geodesics. This can be calculated explicitly using the Raychaudhuri equation as a Langevin equation. The physical manifestation of these fluctuations are angular blurring and luminosity fluctuations of the images of distant sources. We give explicit results for the case of a scalar field on a flat background in a thermal state.

Figure 1

A source $S$ at a mean distance $s$ from an observer $O$ is displaced in direction $\psi$ by a distance $\rho$ from its average position $A$. The effect is to shift the apparent position of the source by an angle $\Delta \phi$.