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arXiv:gr-qc/9305012 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Quantum mechanics, common sense, and the black hole information paradox

Ulf Danielsson, Marcelo Schiffer

Published Nov 15, 1993• 45 citations
arXivHTMLPDF

Abstract

The purpose of this paper is to analyze, in the light of information theory and with the arsenal of (elementary) quantum mechanics (EPR, correlations, copying machines, teleportation, mixing produced in subsystems owing to a trace operation, etc.) the scenarios available on the market to resolve the so-called black hole information paradox. We shall conclude that the only plausible ones are those where either the unitary evolution of quantum mechanics is given up, in which information leaks continuously in the course of black hole evaporation through nonlocal processes, or those in which the world is polluted by an infinite number of metastable remnants.

DOI
10.1103/physrevd.48.4779

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The purpose of this paper is to analyze, in the light of information theory and with the arsenal of (elementary) quantum mechanics (EPR, correlations, copying machines, teleportation, mixing produced in subsystems owing to a trace operation, etc.) the scenarios available on the market to resolve the so-called black hole information paradox. We shall conclude that the only plausible ones are those where either the unitary evolution of quantum mechanics is given up, in which information leaks continuously in the course of black hole evaporation through nonlocal processes, or those in which the world is polluted by an infinite number of metastable remnants.
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Can quantum-information theory shed light on black-hole evaporation? By entangling the in-fallen matter with an external system we show that the black-hole information paradox becomes more severe, even for cosmologically sized black holes. We rule out the possibility that the information about the in-fallen matter might hide in correlations between the Hawking radiation and the internal states of the black hole. As a consequence, either unitarity or Hawking's semiclassical predictions must break down. Any resolution of the black-hole information crisis must elucidate one of these possibilities.
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.
The black hole information paradox arises from an apparent conflict between the Hawk-ing black hole radiation and the fact that time evolution in quantum mechanics is unitary. The trouble is that while the former suggests that information of a system falling into a black hole disappears, the latter implies that information must be con-served. In this work we discuss the current divergence in views regarding the paradox, we evaluate the role that objective collapse theories could play in its resolution and we propose a link between spontaneous collapse events and microscopic virtual black holes. 1
We seek to examine the ontological aspects of the resolution of the black hole information paradox. Several concepts which are now central to our understanding of quantum mechanics arose from our resolution to this paradox, and these concepts point to the conservation of all information, even on a quantum level. If quantum information is conserved and can never be erased or destroyed, then this indicates that all information is at least theoretically, ultimately retrievable and knowable from the event horizon of the universe. Ontologically, this supports the contention that a repository of all information in the universe must therefore exist. Herein, we trace the steps in this contention and conclude with the argument that our understanding of the universe points to the existence of an omniscient entity.
We analyze a system consisting of an oscillator coupled to a field. With the field traced out as an environment, the oscillator loses coherence on a very short decoherence time scale; but, on a much longer relaxation time scale, it evolves predictably into a unique, pure (ground) state. This example of recoherence has interesting implications both for the interpretation of quantum theory and for the loss of information during black hole evaporation---the so-called black hole information paradox. We examine these implications by investigating the intermediate and final states of the quantum field, treated as an open system coupled to an unobserved oscillator.