﻿

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. It is a contentious subject since it violates a commonly assumed tenet of science&mdash;that information cannot be destroyed. [cite video | people = Stephen Hawking | title = The Hawking Paradox | publisher = Discovery, Inc. | location = Discovery Channel, The | date = 2006]

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).

On October 28, 2006, The Discovery Channel aired a show called "The Hawking Paradox”. The show explained Hawking's conclusion that one must look at the multiverse as a whole, and that information lost in black holes is saved in parallel universes where no black holes exist.

The equation

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

$S = frac\left\{c^\left\{3\right\}kA\right\}\left\{4 hbar G\right\}$

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.

ee also

*Cosmic censorship hypothesis
*Maxwell's Demon (in which information cannot be destroyed)

References

* [http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/info_loss.html Black Hole Information Loss Problem] , a USENET physics FAQ page
* " [http://xxx.lanl.gov/abs/hep-th/9209058 Do black holes destroy information?] ", John Preskill (1992), [http://xxx.lanl.gov/abs/hep-th/9209058 hep-th/9209058] . Discusses methods of attack on the problem, and their apparent shortcomings.
* [http://www.newscientist.com/news/news.jsp?id=ns99996193 Report] on Hawking's 2004 theory at New Scientist
* [http://www.nature.com/news/2004/040712/full/040712-12.html Report] on Hawking's 2004 theory at Nature
* Hawking, S. W. (July 2005), Information Loss in Black Holes, [http://arxiv.org/abs/hep-th/0507171 arxiv:hep-th/0507171] . Stephen Hawking's purported solution to the black hole unitarity paradox.
* [http://motls.blogspot.com/2005/07/hawking-and-unitarity.html Hawking and unitarity] : an up-to-date discussion of the information loss paradox and Stephen Hawking's role in it

Wikimedia Foundation. 2010.

Look at other dictionaries:

• Black hole — For other uses, see Black hole (disambiguation). Simulated view of a black hole (center) in front of the Large Magellanic Cloud. Note the gravitat …   Wikipedia

• Virtual black hole — In quantum gravity, a virtual black hole is a black hole which has a temporary existence as a result of a quantum fluctuation of spacetime. They are an example of quantum foam and are the gravitational analog of the virtual electron positron… …   Wikipedia

• Nonsingular black hole models — A nonsingular black hole model is a mathematical theory of black holes that avoids certain theoretical problems with the standard black hole model, including information loss and the unobservable nature of the black hole event horizon. Contents 1 …   Wikipedia

• Sonic black hole — A sonic black hole (sometimes called a dumb hole) is a phenomenon in which phonons (sound perturbations) are unable to escape from a fluid that is flowing more quickly than the local speed of sound. They are called sonic, or acoustic, black holes …   Wikipedia

• Micro black hole — MBH redirects here. For other uses see MBH (disambiguation) Micro black holes are tiny black holes, also called quantum mechanical black holes or mini black holes, for which quantum mechanical effects play an important role.[1] It is possible… …   Wikipedia

• Charged black hole — A charged black hole is a black hole that possesses electric charge. Since the electromagnetic repulsion in compressing an electrically charged mass is dramatically greater than the gravitational attraction (by about 40 orders of magnitude), it… …   Wikipedia

• Physical paradox — A physical paradox is an apparent contradiction in physical descriptions of the universe. While many physical paradoxes have accepted resolutions, others defy resolution and may indicate flaws in theory. In physics as in all of science,… …   Wikipedia

• Entropy in thermodynamics and information theory — There are close parallels between the mathematical expressions for the thermodynamic entropy, usually denoted by S , of a physical system in the statistical thermodynamics established by Ludwig Boltzmann and J. Willard Gibbs in the 1870s; and the …   Wikipedia

• Properties and features of black holes — According to the No Hair theorem a black hole has only three independent physical properties: mass, charge and angular momentum. [citation|last=Heusler |first=M. |year=1998 |title=Stationary Black Holes: Uniqueness and Beyond |journal=Living Rev …   Wikipedia

• Dumb hole — A dumb hole or mute hole is a theoretical sonic analog to a black hole, created in a region where the speed of flow in a fluid exceeds the speed of sound. The term was coined by William Unruh, who believes the sound waves radiated by a dumb hole… …   Wikipedia