Black Hole Evaporation Entails an Objective Passage of Time

Abstract

Time's apparent passage has long been debated by philosophers, with no decisive argument for or against its objective existence. In this paper we show that introducing the issue of determinism gives the debate a new, empirical twist. We prove that any theory that states that the basic laws of physics are time-symmetric must be strictly deterministic. It is only determinism that enables time reversal, whether theoretical or experimental, of anyentropy-increasing process. A contradiction therefore arises between Hawking's argument that physical law is time-symmetric and his controversial claim that black-hole evaporation introduces a fundamental unpredictability into the physical world. The latter claim forcibly entails an intrinsic time-arrow independent of boundary conditions. A simulation of a simple system under time reversal shows how an intrinsic time arrow re-emerges, destroying the time reversal, when even the slightest failure of determinism occurs. This proof is then extended to the classical behavior of black holes. We conclude with pointing out the affinity between time's arrow and its apparent passage.