What Exactly is the Information Paradox?

What the information paradox is {\it not}

There still exist many confusions about the black hole information paradox and its resolution. We first give a precise formulation of the paradox, in four steps A-D. Then we examine several proposals for resolving the paradox. We note that in each case one of these four steps has been ignored, so that the proposal does not really target the essence of the paradox. Finally, we give a brief summary of the fuzzball construction and argue that it resolves the paradox in string theory. This resolution contains a deep lesson -- the phase space of quantum gravity is so large that the measure in the p…

What does the information paradox say about the universe?

The black hole information paradox is resolved in string theory by a radical change in the picture of the hole: black hole microstates are horizon sized quantum gravity objects called `fuzzballs' instead of vacuum regions with a central singularity. The requirement of causality implies that the quantum gravity wavefunctional $Ψ$ has an important component not present in the semiclassical picture: virtual fuzzballs. The large mass $M$ of the fuzzballs would suppress their virtual fluctuations, but this suppression is compensated by the large number -- $Exp[S_{bek}(M)]$ -- of possible fuzzballs.…

What can the information paradox tell us about the early Universe?

In recent years we have come to understand how the information paradox is resolved in string theory. The huge entropy $S_{bek}={A\over 4G}$ of black holes is realized by an explicit set of horizon sized `fuzzball' wavefunctions. The wavefunction of a collapsing shell spreads relatively quickly over this large phase space of states, invalidating the classical black hole geometry the shell would have created. We argue that a related effect may occur in the early Universe. When matter is crushed to high densities we can access a similarly large phase space of gravitational `fuzzball' solutions. W…

我们能从量子信息论中学到关于岛屿和状态悖论的什么？

What can we learn about islands and state paradox from quantum information theory?

本文从量子信息论出发，通过 qubit 模型对纠缠岛屿进行解释，将黑洞信息悖论与量子力学测量问题类比，指出即使信息丢失仍可实现 Page 曲线，并论证了该解释对体重建的必要性。

A Toy Model of the Information Paradox in Empty Space

A sharp version of the information paradox involves a seeming violation of the monogamy of entanglement during black hole evaporation. We construct an analogous paradox in empty anti-de Sitter space. In a local quantum field theory, Bell correlations between operators localized in mutually spacelike regions are monogamous. We show, through a controlled calculation, that this property can be violated by an order-1 factor in a theory of gravity. This example demonstrates that what appears to be a violation of the monogamy of entanglement may just be a subtle violation of locality in quantum grav…

探针、视界、炼狱、寓言、悖论？

Probes, purviews, purgatories, parable, paradox?

本文从信息论角度分析半经典引力中量子探针的视界、过度观测导致的高熵蒸发，以及随之而来的信息悖论解决。