Solving information loss paradox via Euclidean path integral

TL;DR

This paper proposes a novel approach using Euclidean path integrals with branching histories to address the black hole information loss paradox, recovering the Page curve and suggesting potential entropy bound violations.

Contribution

It introduces a new framework allowing for multiple histories in Euclidean path integrals, explaining the Page curve shift and unitarity preservation in black hole evaporation.

Findings

Reproduces the Page curve with a late-time shift

Suggests possible violation of entropy bounds

Provides a new perspective on black hole information paradox

Abstract

The information loss paradox associated with black hole Hawking evaporation is an unresolved problem in modern theoretical physics. In this paper, we revisit the entanglement entropy via the Euclidean path integral (EPI) of the quantum state and allow for the branching of semi-classical histories along the Lorentzian evolution. We posit that there exist at least two histories that contribute to EPI, where one is an information-losing history while the other is information-preserving. At early times, the former dominates EPI, while at late times the latter becomes dominant. By so doing we recover the essence of the Page curve and thus the unitarity, albeit with the turning point, i.e., the Page time, much shifted toward the late time. One implication of this modified Page curve is that the entropy bound may thus be violated. We comment on the similarity and difference between our approach and that of the replica wormholes and the island conjecture.