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 $I=2\pi \Delta \phi$ 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-Nordström 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.

published version

References in corpus (4)

• Entropic Accelerating Universe
• Sequestering the Standard Model Vacuum Energy
• Higher derivative corrections to black hole thermodynamics from supersymmetric matrix quantum mechanics
• Can Dark Matter Decay in Dark Energy?

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