From Computation to Black Holes and Space-Time Foam

We show that quantum mechanics and general relativity limit the speed $\nu$ of a simple computer (such as a black hole) and its memory space $I$ to $I{\nu }^2\lesssim t_P^{-2\mathrm{}}$, where $t_P$ is the Planck time. We also show that the lifetime 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.