Analogue of Null Geodesic in Quantum Spacetime

Abstract

In classical spacetime null geodesics give information on where free massless particles travel. In quantum spacetime where quantum indefiniteness renders spacetime fuzzy null geodesics as sharp trajectories cannot be retained. We propose a "tendency postulate" that gives information on where free massless objects tend to travel based exclusively on meaningful notions in quantum spacetime. It says that free massless objects tend to trace large quantum causal fluctuations. We implement the tendency postulate in concrete models of quantum spacetime that describe causal fluctuation. The tendency postulate supports the suggestion that information can leak out of black holes in a quantum spacetime without introducing superluminal signalling.