An observer's perspective of the Unruh and Hawking effects—Using coherent signals to extract information from a black hole

Abstract

The Unruh effect is one of the first calculations that explain what one would see when transiting between an inertial reference frame in its quantum field vacuum state and a non-inertial (specifically, uniformly accelerating) reference frame. The inertial reference frame's vacuum state would not correspond to the vacuum state of the non-inertial frame. The observer in the non-inertial frame would see radiation, with a corresponding Bose distribution and a temperature proportional to the acceleration. In this paper, I compute the response of this non-inertial observer to a single frequency mode in the inertial frame and deduce that, indeed, the cumulative distribution (over the observer's proper time) of frequencies observed by the accelerating observer would be the Bose distribution with a temperature proportional to the acceleration. The conclusion is that the Unruh effect (and the related Hawking effect) is generic, in that it would appear with any incoming incoherent state and the Bose distribution is obtained as a consequence of the non-inertial frame's motion, rather than some special property of the quantum vacuum. As a consequence of the analysis of a coherent set of signals, I show how to extract information from the spectrum that an accelerated observer would see (as well as from the radiation from a black hole).