A holographic bound on the total number of computations in the visible Universe

TL;DR

This paper explores the holographic principle to estimate the maximum number of computations the observable universe can perform, linking information, black hole physics, and cosmology.

Contribution

It introduces a holographic bound on total computations in the universe based on information encoding and black hole analogies, extending holographic concepts to cosmological scales.

Findings

The universe can perform up to 10^121 computations in the future.

Minimal screens encode at least four bits for particles with mass, charge, or angular momentum.

Holographic imaging relates information to detection probabilities and black hole properties.

Abstract

Information $I$ in holographic imaging of massive particles by star-like screens is shown to represent the probability of detection based on their propagator. Results are derived for screens in the shape of a plane, cube and sphere from unitarity in the exponentially small transition probability for a detection outside. We derive $I=2\pi \Delta\varphi$ in $\log2$ bits for the imaging of a particle by a spherical screen at a relative de Broglie phase $\Delta\varphi$. Encoding mass, charge, angular momentum or radiation requires at minimum four bits. Minimal screens at maximal information density hereby recover Reissner-Nordstr\"om and extremal Kerr black holes. Applied to the visible Universe, the Hubble flow of galaxies through the cosmological event horizon leaves $10^{121}$ computations in the future.