Solving information loss paradox via Euclidean path integral

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.

Is singularity resolution trivial?

“…As another example from recent works, in [25] it is stated as an "essential condition" for a solution to the "information loss paradox" that for an Euclidean gravitational path integral (EPI):…”

“…Here "information-losing history" means "the semi-classical history of an evaporating black hole in which the unitary evolution would be lost when the black hole has completely evaporated" [25], and from Figure 1 of that paper one might infer that an "information-losing history" is geodesically incomplete. The main idea of [25] is to understand information propagation of quantum black holes as tunneling processes in gravitational path integrals.…”

“…Here "information-losing history" means "the semi-classical history of an evaporating black hole in which the unitary evolution would be lost when the black hole has completely evaporated" [25], and from Figure 1 of that paper one might infer that an "information-losing history" is geodesically incomplete. The main idea of [25] is to understand information propagation of quantum black holes as tunneling processes in gravitational path integrals. It seems the main points of [25] depends on the presence of an information-preserving history h 2 rather than an information-losing history h 1 , and for reasons discussed in Section 4 I remain hopeful that the program of [25] to understand black hole information topics through gravitational tunneling will succeed.…”

Euclidean path integral, entanglement entropy, and quantum boundary conditions

“…As we have checked the existence of the tunneling channel toward a trivial geometry, i.e., the multi-history condition, we need to demonstrate the late-time dominance condition. In order to do this, we first observe the possible variety of the Euclidean time [5].…”

“…In this regards, to understand the physics in the common ground, we assume the following two contents [5].…”