From computation to black holes and space-time foam

In principle, black holes can serve as clocks and computers. Here we show that, according to the laws of quantum mechanics and gravitation, both the speed $\nu$ with which a simple computer (such as a black hole) can process information and the amount of information $I$ that it can process are limited by the input power. In particular, their product is bounded by a universal constant given by $I \nu^2 \lsim t_P^{-2}$, where $t_P$ is the Planck time. As a prelude, we show that the maximum time that a simple clock remains accurate is limited by the precision of the clock. All these bounds (including the holographic bound) originate from the same physics that governs the quantum fluctuations of space-time. We further show that these physical bounds are realized for black holes, yielding the correct Hawking black hole lifetime. This study also strongly suggests that space-time undergoes much larger quantum fluctuations than conventional wisdom claims --- large enough to be detected with modern gravitational-wave interferometers through future refinements.