Informational Singularities and the Completion of Gravity: Replica Wormholes, Indeterminism, and Cosmic Censorship

Abstract

Replica wormholes provide the first concrete evidence that quantum gravity can achieve informational completion-restoring a unique, coherent mapping from initial to final quantum states-without achieving geometric completion, the removal or resolution of curvature singularities. I make this distinction precise and use it to extend the framework of generalized indeterminism developed by Azhar and Namjoo into the quantum-gravitational regime. I introduce the concept of an informational singularity: a configuration in which a physical theory fails to provide an existent, unique, and coherent mapping from initial to final quantum states. This concept is logically independent of the geometric singularities of general relativity. The two notions can come apart in both directions: a geometrically smooth region (such as the asymptotic radiation zone in Hawking's calculation) can be informationally singular, while a region with a curvature singularity (such as the interior of an evaporating black hole described by the Page curve) can be informationally complete. I show that the island formula and replica wormhole construction realize informational completion while leaving the geometric singularity untouched, and I confront the ensemble interpretation of the gravitational path integral as a possible obstruction to single-theory completion. Finally, I propose a reformulation of strong cosmic censorship as Informational Cosmic Censorship: the principle that the full quantumgravitational theory provides a coherent state map for generic initial data, regardless of the geometric fate of Cauchy horizons. I argue that this reformulation captures Penrose's original predictability motivation more faithfully than the standard geometric formulation.