From computation to black holes and space-time foam

Abstract

We show that quantum mechanics and general relativity limit the speed $\tilde{\nu }$ of a simple computer (such as a black hole) and its memory space $I$ to ${\tilde{\nu }}^2{I}^{-1}\text{lsim}{t}_P^{-2}$, where $t_P$ is the Planck time. We also show that the life-time of a simple clock and its precision are similarly limited. These bounds and 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, and that space-time undergoes much larger quantum fluctuations than conventional wisdom claims -- almost within range of detection with modern gravitational-wave interferometers.

Comments: A misidentification of computer speeds is corrected. Our results for black hole computation now agree with those given by S. Lloyd. All other conclusions remain unchanged