Black hole information paradox - AbsoluteAstronomy.com

The black hole information paradox results from the combination of quantum mechanics

Quantum mechanics

Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

and general relativity

General relativity

General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

. It suggests that physical information

Physical information

In physics, physical information refers generally to the information that is contained in a physical system. Its usage in quantum mechanics In physics, physical information refers generally to the information that is contained in a physical system. Its usage in quantum mechanics In physics,...

could disappear in a black hole

Black hole

A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

, allowing many physical states to evolve into 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. A postulate of quantum mechanics is that complete information about a system is encoded in its wave function, an abstract concept not present in classical physics. The evolution of the wave function is determined by a unitary operator

Unitary operator

In functional analysis, a branch of mathematics, a unitary operator is a bounded linear operator U : H → H on a Hilbert space H satisfyingU^*U=UU^*=I...

, and unitarity

Unitarity (physics)

In quantum physics, unitarity is a restriction on the allowed evolution of quantum systems that insures the sum of probabilities of all possible outcomes of any event is always 1....

implies that information is conserved in the quantum sense.

There are two main principles at work: quantum determinism, and reversibility

Reversibility

Reversibility can refer to:* Reversible dynamics, a mathematical dynamical system, or physical laws of motion, for which time-reversed dynamics are well defined* Reversible diffusion, an example of a reversible stochastic process...

. Quantum determinism means that given a present wave function, its future changes are uniquely determined by the evolution operator. Reversibility refers to the fact that the evolution operator has an inverse, meaning that the past wave functions are similarly unique. With quantum determinism, reversibility, and a conserved Liouville measure, the von Neumann entropy

Von Neumann entropy

In quantum statistical mechanics, von Neumann entropy, named after John von Neumann, is the extension of classical entropy concepts to the field of quantum mechanics....

ought to be conserved, if coarse graining is ignored.

Stephen Hawking

Stephen Hawking

Stephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...

presented rigorous theoretical arguments based on general relativity and thermodynamics

Black hole thermodynamics

In physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons...

which threatened to undermine these ideas about information conservation in the quantum realm

Quantum realm

Quantum realm is a term of art in physics referring to scales where quantum mechanical effects become important . Typically, this means distances of 100 nanometers or less. Not coincidentally, this is the same scale as nanotechnology....

. Several proposals have been put forth to resolve this paradox.

Hawking radiation

In 1975, Stephen Hawking and Jacob Bekenstein

Jacob Bekenstein

Jacob David Bekenstein is an Israeli theoretical physicist who has contributed to the foundation of black hole thermodynamics and to other aspects of the connections between information and gravitation.-Biography:...

showed that black holes should slowly radiate away energy, which poses a problem. From the no hair theorem

No hair theorem

The no-hair theorem postulates that all black hole solutions of the Einstein-Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three externally observable classical parameters: mass, electric charge, and angular momentum...

, one would expect the Hawking radiation

Hawking radiation

Hawking radiation is a thermal radiation with a black body spectrum predicted to be emitted by black holes due to quantum effects. It is named after the physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974, and sometimes also after the physicist Jacob Bekenstein...

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

Liouville's theorem (Hamiltonian)

In physics, Liouville's theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics...

and presents a physical paradox

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...

.

More precisely, if there is an entangled

Quantum entanglement

Quantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...

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

Partial trace

In linear algebra and functional analysis, the partial trace is a generalization of the trace. Whereas the trace is a scalar valued function on operators, the partial trace is an operator-valued function...

is taken over the interior of the black hole. But since everything within the interior of the black hole will hit the singularity

Gravitational singularity

A gravitational singularity or spacetime singularity is a location where the quantities that are used to measure the gravitational field become infinite in a way that does not depend on the coordinate system...

within a finite time, the part which is traced over partially might disappear completely from the physical system.

Hawking remained convinced that the equations of black hole thermodynamics together with the no-hair theorem led to the conclusion that quantum information may be destroyed. This annoyed many physicists, notably John Preskill

John Preskill

John Phillip Preskill is an American theoretical physicist and the Richard P. Feynman Professor of Theoretical Physics at the California Institute of Technology ....

, who in 1997 bet

Thorne-Hawking-Preskill bet

The Thorne–Hawking–Preskill bet refers to a public bet on the outcome of the black hole information paradox made in 1997 by physics theorists Kip Thorne, Stephen Hawking and John Preskill....

Hawking and Kip Thorne

Kip Thorne

Kip Stephen Thorne is an American theoretical physicist, known for his prolific contributions in gravitation physics and astrophysics and for having trained a generation of scientists...

that information was not lost in black holes. The implications Hawking had opined led to the Susskind-Hawking battle, where Leonard Susskind

Leonard Susskind

Leonard Susskind is the Felix Bloch Professor of Theoretical Physics at Stanford University. His research interests include string theory, quantum field theory, quantum statistical mechanics and quantum cosmology...

and Gerard 't Hooft publicly 'declared war' on Hawking's solution, with Susskind publishing a popular book about the debate in 2008 (The Black Hole War: My battle with Stephen Hawking to make the world safe for quantum mechanics, ISBN 9780316016407). The book carefully notes that the "war" was purely a scientific one, and that at a personal level, the participants remained friends. The solution to the problem that concluded the battle is the holographic principle

Holographic principle

The holographic principle is a property of quantum gravity and string theories which states that the description of a volume of space can be thought of as encoded on a boundary to the region—preferably a light-like boundary like a gravitational horizon...

, which was first proposed by 't Hooft but was given a precise string theory

String theory

String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...

interpretation by Susskind. With this, as the title of an article puts it, "Susskind quashes Hawking in quarrel over quantum quandary".

There are various ideas about how the paradox is solved. Since the 1997 proposal of the AdS/CFT correspondence

AdS/CFT correspondence

In physics, the AdS/CFT correspondence , sometimes called the Maldacena duality, is the conjectured equivalence between a string theory and gravity defined on one space, and a quantum field theory without gravity defined on the conformal boundary of this space, whose dimension is lower by one or more...

, 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 2004, Stephen Hawking published a paper and announced a theory that quantum perturbations of the event horizon

Event horizon

In general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. In layman's terms it is defined as "the point of no return" i.e. the point at which the gravitational pull becomes so great as to make escape impossible. The most common case...

could allow information to escape from a black hole, which would resolve the information paradox

Paradox

Similar to Circular reasoning, A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition...

. His argument assumes the unitarity of the AdS/CFT correspondence

AdS/CFT correspondence

which implies that an AdS black hole

AdS black hole

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 negative cosmological constant...

that is dual

AdS/CFT correspondence

to a thermal

Thermal quantum field theory

In theoretical physics, thermal quantum field theory or finite temperature field theory is a set of methods to calculate expectation values of physical observables of a quantum field theory at finite temperature....

conformal field theory

Conformal field theory

A conformal field theory is a quantum field theory that is invariant under conformal transformations...

. When announcing his result, Hawking also conceded the 1997 bet, paying Preskill with a baseball encyclopedia "from which information can be retrieved at will". However, Thorne remains unconvinced of Hawking's proof and declined to contribute to the award.

According to Roger Penrose

Roger Penrose

Sir Roger Penrose OM FRS is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College...

, loss of unitarity in quantum systems is not a problem: quantum measurements are by themselves already non-unitary. Penrose claims that quantum systems will in fact no longer evolve unitarily as soon as gravitation comes into play, precisely as in black holes. The Conformal Cyclic Cosmology

Conformal Cyclic Cosmology

The Conformal Cyclic Cosmology is a cosmological model in the framework of general relativity, advanced by the theoretical physicist Sir Roger Penrose. In CCC, the universe iterates through infinite cycles, with the future timelike infinity of each previous iteration being identified with the Big...

advocated by Penrose critically depends on the condition that information is in fact lost in black holes. This new cosmological model might in future be tested experimentally by detailed analysis of the cosmic microwave background radiation (CMB): if true the CMB should exhibit circular patterns with slightly lower or slightly higher temperatures. In November 2010, Penrose and V. G. Gurzadyan announced they had found evidence of such circular patterns, in data from the Wilkinson Microwave Anisotropy Probe

Wilkinson Microwave Anisotropy Probe

The Wilkinson Microwave Anisotropy Probe — also known as the Microwave Anisotropy Probe , and Explorer 80 — is a spacecraft which measures differences in the temperature of the Big Bang's remnant radiant heat — the Cosmic Microwave Background Radiation — across the full sky. Headed by Professor...

(WMAP) corroborated by data from the BOOMERanG experiment

BOOMERanG experiment

The BOOMERanG experiment measured the cosmic microwave background radiation of a part of the sky during three sub-orbital balloon flights. It was the first experiment to make large, high fidelity images of the CMB temperature anisotropies...

. The significance of the findings was subsequently debated by others.

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
Semiclassical gravity
Semiclassical gravity is the approximation to the theory of quantum gravity in which one treats matter fields as being quantum and the gravitational field as being classical....

.
Disadvantage: Violates unitarity, 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
Quantum gravity
Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...

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 violates the Bekenstein bound
Bekenstein bound
In physics, the Bekenstein bound is an upper limit on the entropy S, or information I, that can be contained within a given finite region of space which has a finite amount of energy—or conversely, the maximum amount of information required to perfectly describe a given physical system down to the...

.

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 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:

Advantage: Semiclassical gravity
Semiclassical gravity
Semiclassical gravity is the approximation to the theory of quantum gravity in which one treats matter fields as being quantum and the gravitational field as being classical....

is sufficient, i.e., the solution does not depend on details of (still not well understood) quantum gravity
Quantum gravity
Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...

.
Disadvantage: Contradicts the intuitive view of nature as an entity that evolves with time.

External links

Black Hole Information Loss Problem, a USENET physics FAQ page. Discusses methods of attack on the problem, and their apparent shortcomings.
Report on Hawking's 2004 theory at New Scientist
New Scientist
New Scientist is a weekly non-peer-reviewed English-language international science magazine, which since 1996 has also run a website, covering recent developments in science and technology for a general audience. Founded in 1956, it is published by Reed Business Information Ltd, a subsidiary of...
Report on Hawking's 2004 theory at Nature
Nature (journal)
Nature, first published on 4 November 1869, is ranked the world's most cited interdisciplinary scientific journal by the Science Edition of the 2010 Journal Citation Reports...
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)

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.

Hawking radiation

Main approaches to the solution of the paradox

See also

External links