Spacetime has a “thickness”

Abstract

Suppose we assume that (a) information about a black hole is encoded in its Hawking radiation and (b) causality is not violated to leading order in gently curved spacetime. Then, we argue that spacetime cannot just be described as a manifold with a shape; it must be given an additional attribute which we call “thickness.” This thickness characterizes the spread of the quantum gravity wave functional in superspace — the space of all three-geometries. Low energy particles travel on spacetime without noticing the thickness parameter, so they just see an effective manifold. Objects with energy large enough to create a horizon do note the finite thickness; this modifies the semiclassical evolution in such a way that we avoid horizon formation and the consequent violation of causality.