Entropy and Gravitation: From Black Hole Computers to Dark Energy and Dark Matter

Abstract: We show that the concept of entropy and the dynamics of gravitation provide the linchpin in a unified scheme to understand the physics of black hole computers, space-time foam, dark energy, dark matter and the phenomenon of turbulence. We use three different methods to estimate the foaminess of space-time, which, in turn, provides a back-door way to derive the Bekenstein-Hawking formula for black hole entropy and the holographic principle. Generalizing the discussion for a static space-time region to the cosmos, we find a component of dark energy (resembling an effective positive cosmological constant of the correct magnitude) in the current epoch of the universe. The conjunction of entropy and gravitation is shown to give rise to a phenomenological model of dark matter, revealing the natural emergence, in galactic and cluster dynamics, of a critical acceleration parameter related to the cosmological constant; the resulting mass profiles are consistent with observations. Unlike ordinary matter, the quanta of the dark sector are shown to obey infinite statistics. This property of dark matter may lead to some non-particle phenomenology, and may explain why dark matter particles have not been detected in dark matter search experiments. We also show that there are deep similarities between the problem of "quantum gravity" (more specifically, the holographic space-time foam) and turbulence.