Black hole complementarity
Encyclopedia
Black hole complementarity is a conjectured solution to the black hole information paradox
, proposed by Leonard Susskind
and Gerard 't Hooft.
Ever since Stephen Hawking
suggested information is lost in evaporating black hole
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
might be able to conserve information with a unitary time evolution. But how can this be possible if information can't escape the event horizon without traveling faster than light? This seems to rule out Hawking radiation
as the carrier of the missing information. It also appears as if information can't be "reflected" at the event horizon as there is nothing special about it locally.
Leonard Susskind
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 can't 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
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 of noncommuting observables, and Susskind proposed that both stories are complementarity in the quantum sense.
Interestingly enough, 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.
To an infalling observer, information and entropy passes through the horizon with nothing strange 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 over the horizon.
Global symmetries don't exist in quantum gravity
. Baryon number is violated, but only at very small scales, and the proton has a very long lifetime. But with a short enough time resolution, the proton oscillates between different baryon numbers and the time warping near the horizon magnifies that. Alternatively, the hot temperatures of the stretched horizon cause the proton to decay. But an infalling observer never has time to see the proton decay.
Black hole information paradox
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, allowing many physical states to evolve into the same state...
, proposed by 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.
Ever since 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...
suggested information is lost in evaporating 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...
once it passes through 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...
and is inevitably destroyed at 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...
and that this can turn pure quantum states into mixed states, some physicists have wondered if a complete theory 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...
might be able to conserve information with a unitary time evolution. But how can this be possible if information can't escape the event horizon without traveling faster than light? This seems to rule out 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...
as the carrier of the missing information. It also appears as if information can't be "reflected" at the event horizon as there is nothing special about it locally.
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...
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 can't 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
Membrane paradigm
In black hole theory, the black hole membrane paradigm is a useful "toy model" method or "engineering approach" for visualising and calculating the effects predicted by quantum mechanics for the exterior physics of black holes, without using quantum-mechanical principles or calculations...
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
No cloning theorem
The no-cloning theorem is a result of quantum mechanics that forbids the creation of identical copies of an arbitrary unknown quantum state. It was stated by Wootters, Zurek, and Dieks in 1982, and has profound implications in quantum computing and related fields.The state of one system can be...
. 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 of noncommuting observables, and Susskind proposed that both stories are complementarity in the quantum sense.
Interestingly enough, 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.
To an infalling observer, information and entropy passes through the horizon with nothing strange 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
Membrane paradigm
In black hole theory, the black hole membrane paradigm is a useful "toy model" method or "engineering approach" for visualising and calculating the effects predicted by quantum mechanics for the exterior physics of black holes, without using quantum-mechanical principles or calculations...
for more details. The stretched horizon is conducting with surface charges which rapidly spread out over the horizon.
Global symmetries don't exist in 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...
. Baryon number is violated, but only at very small scales, and the proton has a very long lifetime. But with a short enough time resolution, the proton oscillates between different baryon numbers and the time warping near the horizon magnifies that. Alternatively, the hot temperatures of the stretched horizon cause the proton to decay. But an infalling observer never has time to see the proton decay.
See also
- Black hole information paradoxBlack hole information paradoxThe 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, allowing many physical states to evolve into the same state...
- Membrane paradigmMembrane paradigmIn black hole theory, the black hole membrane paradigm is a useful "toy model" method or "engineering approach" for visualising and calculating the effects predicted by quantum mechanics for the exterior physics of black holes, without using quantum-mechanical principles or calculations...