Black hole information paradox

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The black hole information paradox results from the combination of quantum mechanics and general relativity. It suggests that physical information could "disappear" in a black hole, allowing many physical states to evolve into precisely the same state. This is a contentious subject since it violates a commonly assumed tenet of science—that in principle complete information about a physical system at one point in time should determine its state at any other time.^[1]

Contents 1 Hawking radiation 2 Main approaches to the solution of the paradox 3 The equation 4 See also 5 References 6 External links

[edit] Hawking radiation

In 1975, Stephen Hawking and Jacob Bekenstein showed that black holes should slowly radiate away energy, which poses a problem. From the no hair theorem, one would expect the Hawking radiation to be completely independent of the material entering the black hole. Nevertheless, if the material entering the black hole were a pure quantum state, the transformation of that state into the mixed state of Hawking radiation would destroy information about the original quantum state. This violates Liouville's theorem and presents a physical paradox.

More precisely, if there is an entangled pure state, and one part of the entangled system is thrown into the black hole while keeping the other part outside, the result is a mixed state after the partial trace is taken over the interior of the black hole. But since everything within the interior of the black hole will hit the singularity within a fixed time, the part which is traced over partially might "disappear", never to appear again. Of course, it is not really known what goes on at singularities once quantum effects are taken into account, which is why this theory is conjectural and controversial.

Hawking was convinced, however, because of the simple elegance of the resulting equation which "unified" thermodynamics, relativity, gravity, and Hawking's own work on the Big Bang. This annoyed many physicists, notably John Preskill, who in 1997 bet Hawking and Kip Thorne that information was not lost in black holes.

There are various ideas about how the paradox is solved. Since the 1997 proposal of the AdS/CFT correspondence, the predominant belief among physicists is that information is preserved and that Hawking radiation is not precisely thermal but receives quantum corrections. Other possibilities include the information being contained in a Planckian remnant left over at the end of Hawking radiation or a modification of the laws of quantum mechanics to allow for non-unitary time evolution.

In July 2005, Stephen Hawking published a paper and announced a theory that quantum perturbations of the event horizon could allow information to escape from a black hole, which would resolve the information paradox. His argument assumes the unitarity of the AdS/CFT correspondence which implies that an AdS black hole that is dual to a thermal conformal field theory, is unitary. When announcing his result, Hawking also conceded the 1997 bet, paying Preskill with a baseball encyclopedia (ISBN 1-894963-27-X) 'from which information can be retrieved at will'. However, Thorne remains unconvinced of Hawking's proof and declined to contribute to the award (see Thorne-Hawking-Preskill bet).

[edit] Main approaches to the solution of the paradox

Information is irretrievably lost:

• Advantage: Seems to be a direct consequence of relatively non-controversial calculation based on semiclassical gravity.
• Disadvantage: Violates unitarity (one of the basic principles of quantum mechanics), as well as energy conservation or causality.

Information gradually leaks out during the black-hole evaporation:

• Advantage: Intuitively appealing because it qualitatively resembles information recovery in a classical process of burning.
• Disadvantage: Requires a large deviation from classical and semiclassical gravity (which do not allow information to leak out from the black hole) even for macroscopic black holes for which classical and semiclassical approximations are expected to be good approximations.

Information suddenly escapes out during the final stage of black-hole evaporation:

• Advantage: A significant deviation from classical and semiclassical gravity is needed only in the regime in which the effects of quantum gravity are expected to dominate.
• Disadvantage: Just before the sudden escape of information, a very small black hole must be able to store an arbitrary amount of information, which badly violates the Bekenstein bound.

Information is stored in a Planck-sized remnant:

• Advantage: No mechanism for information escape is needed.
• Disadvantage: A very small object must be able to store an arbitrary amount of information, which badly violates the Bekenstein bound.

Information is stored in a massive remnant:

• Advantage: No mechanism for information escape is needed and a large amount of information does not need to be stored in a small object.
• Disadvantage: No appealing mechanism that could stop Hawking evaporation of a macroscopic black hole is known.

Information is stored in a baby universe that separates from our own universe:

• Advantage: No violation of known general principles of physics is needed.
• Disadvantage: It is difficult to find an appealing concrete theory that would predict such a scenario.

Information is encoded in the correlations between future and past:^[2][3]

• Advantage: Semiclassical gravity is sufficient, i.e., the solution does not depend on details of (still not well understood) quantum gravity.
• Disadvantage: Contradicts the intuitive view of nature as an entity that evolves with time.

[edit] The equation

The entropy of a black hole is given by the equation:

where S is the entropy, c is the speed of light, k is Boltzmann's constant, A is the surface area of the event horizon, ħ ("h-bar") is the reduced Planck's Constant (or Dirac's Constant) and G is the gravitational constant.

[edit] See also

• Bekenstein bound
• Black hole thermodynamics
• Cosmic censorship hypothesis
• Fuzzball (string theory)
• Holographic principle
• Maxwell's Demon (in which information cannot be destroyed)
• Susskind-Hawking battle

[edit] References

[edit] External links

• Black Hole Information Loss Problem, a USENET physics FAQ page
• "Do black holes destroy information?", John Preskill (1992), hep-th/9209058. Discusses methods of attack on the problem, and their apparent shortcomings.
• Report on Hawking's 2004 theory at New Scientist
• Report on Hawking's 2004 theory at Nature
• Hawking, S. W. (July 2005), Information Loss in Black Holes, arxiv:hep-th/0507171. Stephen Hawking's purported solution to the black hole unitarity paradox.
• Hawking and unitarity: an up-to-date discussion of the information loss paradox and Stephen Hawking's role in it
• The Hawking Paradox - BBC Horizon documentary (2005)

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