Black hole complementarity
Conjectured solution to the black hole information paradox.
Black hole complementarity is a proposed way out of the black hole information paradox, put forward by Leonard Susskind, Lárus Thorlacius, and Gerard 't Hooft.
Stephen Hawking had argued that once information crosses a black hole's event horizon, it is inevitably destroyed at the singularity, turning pure quantum states into mixed ones. Some physicists hoped a full theory of quantum gravity would preserve information through unitary time evolution. The problem is that information cannot leave the horizon without traveling faster than light, but in the complementarity proposal Hawking radiation is indeed the carrier of information via the stretched horizon. Nor can it simply bounce off the horizon, since locally the horizon is unremarkable.
The radical proposal is that information is both reflected at the horizon and passes through it, unable to escape—but no single observer can ever confirm both accounts at once. From the outside, infinite time dilation makes it appear to take forever for anything to reach the horizon. These external observers see a "stretched horizon," a hot, physical membrane hovering about a Planck length outside the event horizon. Infalling information heats this membrane, which then reradiates it as Hawking radiation, keeping the whole process unitary. For an infalling observer, however, nothing special happens at the horizon; both the observer and the information simply continue to the singularity. This does not mean two copies of the information exist—one inside and one outside—which would violate the no-cloning theorem. Instead, an observer can detect the information either at the horizon or inside, but never both. This is a quantum complementarity, like noncommuting observables: both stories are valid and do not contradict each other, preserving linearity in quantum mechanics.
An infalling observer sees the information's entry point localized on the event horizon. An external observer sees it spread uniformly over the entire stretched horizon before being re-radiated, perceiving the horizon as a dynamical membrane. For the infaller, information and entropy pass through without incident. For the external observer, the stretched horizon absorbs them, acting like a dissipative fluid with entropy, viscosity, and electrical conductivity—a picture known as the membrane paradigm.
- Proposed by
- Leonard Susskind, Lárus Thorlacius, Gerard 't Hooft
Lore & Background
Black hole complementarity was proposed by Leonard Susskind, Lárus Thorlacius, and Gerard 't Hooft as a radical resolution to the black hole information paradox. According to the paradox, Stephen Hawking suggested that information is lost in an evaporating black hole once it passes through the event horizon and is destroyed at the singularity, turning pure quantum states into mixed states. The complementarity proposal claims that information is both reflected at the event horizon and passes through it, with the catch that no observer can confirm both stories simultaneously.
For an external observer, infinite time dilation at the horizon makes it appear to take an infinite time to reach the horizon.
Reader's Guide
Black hole complementarity is significant as a conjectured resolution to the black hole information paradox, which challenges the unitarity of quantum mechanics in the presence of black holes. By proposing that information is both reflected at the event horizon and passes through it, with no observer able to confirm both stories, the conjecture attempts to reconcile general relativity and quantum mechanics without violating the no-cloning theorem. The concept of a stretched horizon, a hot membrane just outside the event horizon, provides a mechanism for information to be absorbed and reradiated as Hawking radiation, preserving unitarity for an external observer. The modern view emphasizes the stretched horizon as an incredibly fast quantum scrambler, with scrambling time logarithmic in entropy, implying non-local dynamics. This non-locality is supported by studies of the Sachdev-Ye-Kitaev model, which exhibits maximal quantum chaos. The conjecture remains a topic of debate, with suggestions that effective field theory near the horizon combined with monogamy of entanglement implies the existence of an AMPS 'firewall' of high-energy photons. Black hole complementarity thus represents a key attempt to understand information conservation in quantum gravity.
Did You Know?
- Black hole complementarity was proposed by Leonard Susskind, Lárus Thorlacius, John Uglum, and Gerard 't Hooft.
- The stretched horizon is a membrane about a Planck length outside the event horizon that is both physical and hot.
- According to conjectures by Hayden, Preskill, Sekino, and Susskind, black holes are the fastest scramblers in nature, with scrambling time t_s = (β/2π) log S.
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