Black hole complementarity is a conjectured solution to the black hole information paradox, proposed by

Leonard Susskind Leonard Susskind (; born June 16, 1940)his 60th birthday was celebrated with a special symposium at Stanford University.in Geoffrey West's introduction, he gives Suskind's current age as 74 and says his birthday was recent. is an American physicis ...

, Larus Thorlacius, and

Gerard 't Hooft Gerardus (Gerard) 't Hooft (; born July 5, 1946) is a Dutch theoretical physicist and professor at Utrecht University, the Netherlands. He shared the 1999 Nobel Prize in Physics with his thesis advisor Martinus J. G. Veltman "for elucidating th ...

Overview

Ever since Stephen Hawking suggested information is lost in an evaporating

black hole A black hole is a region of spacetime where gravity is so strong that nothing, including light or other electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts that a sufficiently compact mass can def ...

once it passes through the event horizon and is inevitably destroyed at the singularity, and that this can turn pure quantum states into mixed states, some physicists have wondered if a complete theory of

quantum gravity Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics; it deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vi ...

might be able to conserve information with a unitary

time evolution Time evolution is the change of state brought about by the passage of time, applicable to systems with internal state (also called ''stateful systems''). In this formulation, ''time'' is not required to be a continuous parameter, but may be disc ...

. But how can this be possible if information cannot escape the event horizon without traveling faster than light? This seems to rule out

Hawking radiation Hawking radiation is theoretical black body radiation that is theorized to be released outside a black hole's event horizon because of relativistic quantum effects. It is named after the physicist Stephen Hawking, who developed a theoretical a ...

as the carrier of the missing information. It also appears as if information cannot be "reflected" at the event horizon as there is nothing special about it locally.

proposed a radical resolution to this problem by claiming that the information is both reflected at the event horizon ''and'' passes through the event horizon and cannot escape, with the catch being no observer can confirm both stories simultaneously. According to an external observer, the infinite time dilation at the horizon itself makes it appear as if it takes an infinite amount of time to reach the horizon. He also postulated a stretched horizon, which is a

membrane A membrane is a selective barrier; it allows some things to pass through but stops others. Such things may be molecules, ions, or other small particles. Membranes can be generally classified into synthetic membranes and biological membranes. ...

hovering about a Planck length outside the event horizon and which is both physical and hot. According to the external observer, infalling information heats up the stretched horizon, which then reradiates it as Hawking radiation, with the entire evolution being unitary. However, according to an infalling observer, nothing special happens at the event horizon itself, and both the observer and the information will hit the singularity. This isn't to say there are two copies of the information lying about — one at or just outside the horizon, and the other inside the black hole — as that would violate the no-cloning theorem. Instead, an observer can only detect the information at the horizon itself, or inside, but never both simultaneously. Complementarity is a feature of the

quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...

of noncommuting observables, and Susskind proposed that both stories are complementary in the quantum sense, that there is no contradiction which also means no violation of linearity in quantum mechanics. An infalling observer will see the point of entry of the information as being localized on the event horizon, while an external observer will notice the information being spread out uniformly over the entire stretched horizon before being re-radiated, and perceives the event horizon as a dynamical membrane. To an infalling observer, information and

entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...

pass through the horizon with nothing of interest happening. To an external observer, the information and entropy is absorbed into the stretched horizon which acts like a dissipative fluid with entropy, viscosity and electrical conductivity. See the membrane paradigm for more details. The stretched horizon is conducting with surface charges which rapidly spread out logarithmically over the horizon. Recently, it appears that black hole complementarity combined with the monogamy of entanglement suggests the existence of an AMPS "

firewall Firewall may refer to: * Firewall (computing), a technological barrier designed to prevent unauthorized or unwanted communications between computer networks or hosts * Firewall (construction), a barrier inside a building, designed to limit the spre ...

", where high energy, short wavelength photons are present in the horizon, although this is still being hypothesised.

References

Quantum gravity {{relativity-stub