Universal Limits on Computation

Abstract

The physical limits to computation have been under active scrutiny over the past decade or two, as theoretical investigations of the possible impact of quantum mechanical processes on computing have begun to make contact with realizable experimental configurations. We demonstrate here that the observed acceleration of the Universe can produce a universal limit on the total amount of information that can be stored and processed in the future, putting an ultimate limit on future technology for any civilization, including a time-limit on Moore's Law. The limits we derive are stringent, and include the possibilities that the computing performed is either distributed or local. A careful consideration of the effect of horizons on information processing is necessary for this analysis, which suggests that the total amount of information that can be processed by any observer is significantly less than the Hawking-Bekenstein entropy associated with the existence of an event horizon in an accelerating universe.Comment: 3 pages including eps figure, submitted to Phys. Rev. Lett; several typos corrected, several references added, and a short discussion of w <-1 adde