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 for science since it violated a commonly assumed tenet of science—that information cannot be destroyed. Fig. ... General relativity (GR) [also called the general theory of relativity (GTR) and general relativity theory (GRT)] is the geometrical theory of gravitation published by Albert Einstein in 1915/16. ... Physical information refers generally to the information that is contained in a physical system. ... A black hole is an object with a gravitational field so powerful that no form of matter or radiation (including light) can escape once it is less than a certain distance from the center. ...

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. However, 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. Stephen William Hawking, CH, CBE, FRS, FRSA, (born 8 January 1942) is a British theoretical physicist. ... Jacob David Bekenstein (born May 1, 1947) is a physicist who has contributed to the foundation of black hole thermodynamics and to other aspects of the connections between information and gravitation. ... In astrophysics, the no-hair theorem states that black holes are completely characterized only by three externally observable parameters: mass, electrical charge, and angular momentum. ... In physics, Hawking radiation is thermal radiation thought to be emitted by black holes due to quantum effects. ... A quantum state is any possible state in which a quantum mechanical system can be. ... In mathematical physics, Liouvilles theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics. ... A physical paradox is an apparent contradiction relating to physical descriptions of the universe. ...

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 finite 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. It has been suggested that Quantum coherence be merged into this article or section. ... The term pure state refers to several related concepts in physics, particularly quantum mechanics and in functional analysis. ... In linear algebra and functional analysis, the partial trace is a generalization of the trace. ... A black hole is an object with a gravitational field so powerful that no form of matter or radiation (including light) can escape once it is less than a certain distance from the center. ...

However, Hawking was convinced 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. Thermodynamics (from the Greek θερμη, therme, meaning heat and δυναμις, dunamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... Two-dimensional analogy of space-time curvature described in General Relativity. ... Gravity is a force of attraction that acts between bodies that have mass. ... According to the Big Bang theory, the universe emerged from an extremely dense and hot state (singularity). ... Prof. ... A scientific wager is a wager whose outcome is settled by scientific method. ... Kip S. Thorne Professor Kip Stephen Thorne, Ph. ...

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 physics, the AdS/CFT correspondence is the equivalence between a string theory (or some other theory of quantum gravity like supergravity) defined on anti de Sitter space (AdS) (or the product of AdS with some closed manifold, orbifold, or noncommutative space), and a conformal field theory (CFT) defined on... This article is about Planck, the German physicist. ...

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. Basically, his argument assumes the unitarity of the AdS/CFT correspondence which implies that an AdS black hole which 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. For the science fiction film, see Event Horizon (film). ... In theoretical physics, an AdS black hole is a black hole solution of general relativity or its extensions which represents an isolated massive object, but with a nonzero cosmological constant. ... The word duality has a variety of different meanings in different contexts: In several spiritual, religious, and philosophical doctrines, duality refers to a two-fold division also called dualism. ... In theoretical physics, thermal quantum field theory is a set of methods to calculate physical observables at finite temperature. ... A conformal field theory is a quantum field theory (or statistical mechanics model) that is invariant under the conformal group. ... It has been suggested that Unitarity bound be merged into this article or section. ... A view of the playing field at Busch Memorial Stadium, St. ...

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 universe as a whole, and that information lost in black holes is saved in parallel universes where no black holes exist. October 28 is the 301st day of the year (302nd in leap years) in the Gregorian calendar, with 64 days remaining. ... For the Manfred Mann album, see 2006 (album). ... Discovery Channel is an American cable TV network, based in Silver Spring, MD, that has a variety of science programming, particularly documentaries and nature shows. ...

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, ħ ("h-bar") is the reduced Planck's Constant (or Dirac's Constant) and G is the gravitational constant. Ice melting - classic example of entropy increasing[1] described in 1862 by Rudolf Clausius as an increase in the disgregation of the molecules of the body of ice. ... A line showing the speed of light on a scale model of Earth and the Moon The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness. It is the speed of all electromagnetic radiation... The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ... A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ...

See also

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

This article or section is in need of attention from an expert on the subject. ... Maxwells demon is an 1867 thought experiment by the Scottish physicist James Clerk Maxwell, meant to raise questions about the possibility of violating the second law of thermodynamics. ...

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)