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

摘要

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 phi in log 2 bits for the imaging of a particle by a spherical screen at a relative de Broglie phase Delta phi Encoding mass, charge, angular momentum or radiation requires at minimum four bits. Minimal screens at maximal information density hereby recover Reissner-Nordstrom 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.