Resolving information loss paradox with Euclidean path integral

TL;DR

This paper proposes a novel Euclidean path integral approach with branching histories to resolve the black hole information loss paradox, recovering the Page curve and maintaining unitarity, but with shifted Page time and potential entropy bound violations.

Contribution

It introduces a new framework allowing for branching histories in Euclidean path integrals, providing a fresh perspective on unitarity and the Page curve in black hole evaporation.

Findings

Reproduces the Page curve with late-time dominance of information-preserving histories.

Suggests the entropy bound may be violated due to shifted Page time.

Provides a comparison with string-based islands and replica wormholes.

Abstract

The information loss paradox remains unresolved ever since Hawking's seminal discovery of black hole evaporation. In this essay, we revisit the entanglement entropy via Euclidean path integral (EPI) and allow for the branching of semi-classical histories during the Lorentzian evolution. We posit that there exist two histories that contribute to EPI, where one is information-losing that dominates at early times, while the other is information-preserving that dominates at late times. By so doing we recover the Page curve and preserve the unitarity, albeit with the Page time shifted significantly towards the late time. One implication is that the entropy bound may thus be violated. We compare our approach with string-based islands and replica wormholes concepts.