From computation to black holes and space-time foam

TL;DR

This paper establishes fundamental quantum and relativistic limits on the computational speed, memory, and precision of simple systems like black holes, linking these bounds to space-time fluctuations and the holographic principle.

Contribution

It derives universal bounds on computation and clock precision from quantum gravity principles and connects them to black hole physics and space-time fluctuations.

Findings

Black holes saturate the derived bounds, matching Hawking lifetime.

Space-time exhibits larger quantum fluctuations than previously thought.

These fluctuations could be detectable with current gravitational-wave detectors.

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 $\tilde{\nu}^2 I^{-1} \lsim t_P^{-2}$, 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.