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

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.