Tunneling between multiple histories as a solution to the information loss paradox

TL;DR

This paper proposes a novel approach to the black hole information loss paradox by considering multiple histories in the Euclidean path integral, leading to a modified Page curve and potential entropy bound violations.

Contribution

It introduces the concept of tunneling between multiple histories in the EPI framework to explain unitarity and the Page curve in black hole evaporation.

Findings

Recovered the Page curve with a shifted Page time.

Suggested the entropy bound may be violated.

Compared approach with replica wormholes and islands.

Abstract

The information loss paradox associated with black hole Hawking evaporation is an unresolved problem in modern theoretical physics. In a recent brief essay, we revisited the the evolution of the black hole 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 posited 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 recovered 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. In this full-length paper, we fill in the details of our arguments and calculations to strengthen our notion. 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 islands conjectures.