- Black hole information paradox
The black hole information paradox results from the combination of
quantum mechanicsand general relativity. It suggests that physical informationcould "disappear" in a black hole. It is a contentious subject since it violates a commonly assumed tenet of science—that information cannot be destroyed. [cite video | people = Stephen Hawking | title = The Hawking Paradox | publisher = Discovery, Inc. | location = Discovery Channel, The | date = 2006]
Stephen Hawkingand Jacob Bekensteinshowed that black holes should slowly radiate away energy, which poses a problem. From the no hair theoremone would expect the Hawking radiationto 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 traceis 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 Thornethat 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 horizoncould allow information to escape from a black hole, which would resolve the information paradox. His argument assumes the unitarity of the AdS/CFT correspondencewhich implies that an AdS black holethat is dual to a thermal conformal field theory, is unitary. When announcing his result, Hawking also conceded the 1997 bet, paying Preskill with a baseballencyclopedia (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).
October 28, 2006, The Discovery Channelaired a show called "The Hawking Paradox”. The show explained Hawking's conclusion that one must look at the multiverseas a whole, and that information lost in black holes is saved in parallel universes where no black holes exist.
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.
Cosmic censorship hypothesis
Maxwell's Demon(in which information cannot be destroyed)
* [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
* [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
* [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
* [http://video.google.com/videoplay?docid=8205975042597389275 The Hawking Paradox - BBC Horizon documentary (2005)]
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