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arXiv:1408.3062 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Nonparadoxical loss of information in black hole evaporation in a quantum collapse model

Sujoy K. Modak, L. Ortíz, Igor Peña, Daniel Sudarsky

Published Jun 2, 2015• 72 citations
arXivHTMLPDF

Abstract

We consider a novel approach to address the black hole information paradox. The idea is based on adapting, to the situation at hand, the modified versions of quantum theory involving spontaneous stochastic dynamical collapse of quantum states, which have been considered in attempts to deal with shortcomings of the standard Copenhagen interpretation of quantum mechanics, in particular, the issue known as ``the measurement problem.'' The new basic hypothesis is that the modified quantum behavior is enhanced in the region of high curvature so that the information encoded in the initial quantum state of the matter fields is rapidly erased as the black hole singularity is approached. We show that in this manner the complete evaporation of the black hole via Hawking radiation can be understood as involving no paradox. Calculations are performed using a modified version of quantum theory known as ``continuous spontaneous localization'' (CSL), which was originally developed in the context of many-particle nonrelativistic quantum mechanics. We use a version of CSL tailored to quantum field theory and applied in the context of the two -dimensional Callan-Giddings-Harvey-Strominger model. Although the role of quantum gravity in this picture is restricted to the resolution of the singularity, related studies suggest that there might be further connections.

DOI
10.1103/physrevd.91.124009

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We consider a novel approach to address the black hole information paradox. The idea is based on adapting, to the situation at hand, the modified versions of quantum theory involving spontaneous stochastic dynamical collapse of quantum states, which have been considered in attempts to deal with shortcomings of the standard Copenhagen interpretation of quantum mechanics, in particular, the issue known as the measurement problem.'' The new basic hypothesis is that the modified quantum behavior is enhanced in the region of high curvature so that the information encoded in the initial quantum state of the matter fields is rapidly erased as the black hole singularity is approached. We show that in this manner the complete evaporation of the black hole via Hawking radiation can be understood as involving no paradox. Calculations are performed using a modified version of quantum theory known as continuous spontaneous localization'' (CSL), which was originally developed in the context of many-particle nonrelativistic quantum mechanics. We use a version of CSL tailored to quantum field theory and applied in the context of the two -dimensional Callan-Giddings-Harvey-Strominger model. Although the role of quantum gravity in this picture is restricted to the resolution of the singularity, related studies suggest that there might be further connections.
We consider the black hole information problem within the context of collapse theories in a scheme that allows the incorporation of the backreaction to the Hawking radiation. We explore the issue in a setting of the two dimensional version of black hole evaporation known as the Russo-Susskind-Thorlacius model. We summarize the general ideas based on the semiclassical version of Einstein’s equations and then discuss specific modifications that are required in the context of collapse theories when applied to this model.
We study a proposal for the resolution of the black hole information puzzle within the context of modified versions of quantum theory involving spontaneous reduction of the quantum state. The theories of this kind, which were developed in order to address the so-called measurement problem in quantum theory have, in the past, been framed in a nonrelativistic setting and in that form they were previously applied to the black hole information problem. Here, and for the first time, we show in a simple toy model, a treatment of the problem within a fully relativistic setting. We also discuss the issues that the present analysis leaves as open problems to be dealt with in future refinements of the present approach.
Suppose a black hole forms from a pure quantum state ∣ψ⟩\ketψ∣ψ⟩. The black hole information loss paradox arises from semiclassical arguments suggesting that, even in a closed system, the process of black hole formation and evaporation evolves a pure state into a mixed state. Resolution to the paradox typically demands violation of quantum mechanics or relativity in domains where they should hold. Instead, I propose that in a complete theory of quantum gravity, any region U\mathcal{U}U that could collapse into a black hole should already be described by a mixed state, thus bypassing the paradox entirely. To that end, I present a model in which the universe is in a quantum error-corrected state, such that any local black hole appears mixed and encodes no information locally.
Stephen Hawking's discovery of black hole evaporation has the remarkable consequence that information is destroyed by a black hole, which can only be accommodated by modifying the laws of quantum mechanics. Different attempts to evade the information loss paradox were subsequently suggested, apparently without a satisfactory resolution of the paradox. On the other hand, attempting to include nonunitarity in quantum mechanics might lead to laws predicting observable consequences such as nonlocality or violation of energy–momentum conservation; but it may be possible to circumvent these obstacles. Recent developments seem to require a different view on quantum gravity and suggest that ideas about locality in physics and Hawking's semiclassical approximation are misleading. An accurate description may show unitary evolution and no information loss after all.
The black hole information paradox originates from the thermal character of Hawking radiation, which appears to erase information about the collapsing matter. However, thermality constrains only observables defined at a single time and leaves the structure of temporal quantum correlations largely unexplored. Here we show that multi-time quantum-field correlations provide a concrete mechanism for the survival of pre-collapse information in black hole evaporation. Using a two-dimensional model of gravitational collapse and evaporation, we demonstrate that late-time multi-time correlations are not fully reproduced by the Unruh vacuum. In particular, they contain a contribution that depends explicitly on parameters characterizing the pre-collapse state, despite the thermal character of the asymptotic radiation. Our results identify measurable multi-time correlations as carriers of information in Hawking radiation and suggest that formulations of the black hole information paradox based solely on single-time observables are incomplete.
Abstract In 1974 Steven Hawking showed that black holes emit thermal radiation, which eventually causes them to evaporate. The problem of the fate of information in this process is known as the “black hole information paradox”. Two main types of resolution postulate either a fundamental loss of information in Nature — hence the breakdown of quantum mechanics — or some sort of new physics, e.g. quantum gravity, which guarantee the global preservation of unitarity. Here we explore the second possibility with the help of recent developments in continuous-variable quantum information. Concretely, we employ the solution to the Gaussian quantum marginal problem to show that the thermality of all individual Hawking modes is consistent with a global pure state of the radiation. Surprisingly, we find out that the mods of radiation of an astrophysical black hole are thermal until the very last burst. In contrast, the single-mode thermality of Hawking radiation originating from microscopic black holes, expected to evaporate through several quanta, is not excluded, though there are constraints on modes' frequencies. Our result paves the way towards a systematic study of multi-mode correlations in Hawking radiation.