Editing Holographic principle (section)

==Black hole information paradox==
{{Main|Black hole information paradox}}
Hawking's calculation suggested that the radiation which black holes emit is not related in any way to the matter that they absorb. The outgoing light rays start exactly at the edge of the black hole and spend a long time near the horizon, while the infalling matter only reaches the horizon much later. The infalling and outgoing mass/energy interact only when they cross. It is implausible that the outgoing state would be completely determined by some tiny residual scattering.{{citation needed|date=January 2019}}

Hawking interpreted this to mean that when black holes absorb some photons in a pure state described by a [[wave function]], they re-emit new [[photons]] in a thermal mixed state described by a [[density matrix]]. This would mean that quantum mechanics would have to be modified because, in quantum mechanics, states which are superpositions with probability amplitudes never become states which are probabilistic mixtures of different possibilities.<ref group=note>except in the case of measurements, which the black hole should not be performing</ref>

Troubled by this paradox, Gerard 't Hooft analyzed the emission of [[Hawking radiation]] in more detail.<ref>{{Cite book|url=https://books.google.com/books?id=ZE-yCQAAQBAJ&q=Troubled+by+this+paradox%2C+Gerard+%27t+Hooft+analyzed+the+emission+of+Hawking+radiation+in+more+detai&pg=PA100|title=The Cosmic Compendium: Black Holes|last=Anderson|first=Rupert W.|date=2015-03-31|publisher=Lulu.com|isbn=9781329024588|language=en}}{{self-published source|date=April 2020}}</ref>{{self-published inline|date=February 2020}} He noted that when Hawking radiation escapes, there is a way in which incoming particles can modify the outgoing particles. Their [[gravitational field]] would deform the horizon of the black hole, and the deformed horizon could produce different outgoing particles than the undeformed horizon. When a particle falls into a black hole, it is boosted relative to an outside observer, and its gravitational field assumes a universal form. 't Hooft showed that this field makes a logarithmic tent-pole shaped bump on the horizon of a black hole, and like a shadow, the bump is an alternative description of the particle's location and mass. For a four-dimensional spherical uncharged black hole, the deformation of the horizon is similar to the type of deformation which describes the emission and absorption of particles on a string-theory [[Worldsheet|world sheet]]. Since the deformations on the surface are the only imprint of the incoming particle, and since these deformations would have to completely determine the outgoing particles, 't Hooft believed that the correct description of the black hole would be by some form of string theory.

This idea was made more precise by Leonard Susskind, who had also been developing holography, largely independently. Susskind argued that the oscillation of the horizon of a black hole is a complete description{{refn|"Complete description" means all the ''primary'' qualities.  For example, [[John Locke]] (and before him [[Robert Boyle]]) determined these to be ''size, shape, motion, number, ''and'' solidity''. Such ''secondary quality'' information as ''color, aroma, taste ''and'' sound'',<ref>{{cite book|last=Dennett|first=Daniel|title=Consciousness Explained|date=1991|publisher=Back Bay Books|location=New York|isbn=978-0-316-18066-5|page=[https://archive.org/details/consciousnessexp00denn/page/371 371]|title-link=Consciousness Explained}}</ref> or internal quantum state is not information that is implied to be preserved in the surface fluctuations of the event horizon. (See however "path integral quantization")|group=note}} of both the infalling and outgoing matter, because the world-sheet theory of string theory was just such a holographic description. While short strings have zero entropy, he could identify long highly excited string states with ordinary black holes. This was a deep advance because it revealed that strings have a classical interpretation in terms of black holes.

This work showed that the black hole information paradox is resolved when quantum gravity is described in an unusual string-theoretic way assuming the string-theoretical description is complete, unambiguous and non-redundant.<ref>{{cite journal |last=Susskind |first=Leonard |date=February 2003 |title=The Anthropic landscape of string theory |journal=The Davis Meeting on Cosmic Inflation |page=26 |arxiv=hep-th/0302219 |bibcode=2003dmci.confE..26S}}</ref> The space-time in quantum gravity would emerge as an effective description of the theory of oscillations of a lower-dimensional black-hole horizon, and suggest that any black hole with appropriate properties, not just strings, would serve as a basis for a description of string theory.

In 1995, Susskind, along with collaborators [[Tom Banks (physicist)|Tom Banks]], [[Willy Fischler]], and [[Stephen Shenker]], presented a formulation of the new M-theory using a holographic description in terms of charged point black holes, the D0 [[Membrane (M-theory)|branes]] of [[Type II string theory|type IIA string theory]]. The matrix theory they proposed was first suggested as a description of two branes in [[eleven-dimensional supergravity]] by [[Bernard de Wit]], [[Jens Hoppe]], and [[Hermann Nicolai]]. The later authors reinterpreted the same matrix models as a description of the dynamics of point black holes in particular limits. Holography allowed them to conclude that the dynamics of these black holes give a complete [[non-perturbative]] formulation of [[M-theory]]. In 1997, [[Juan Maldacena]] gave the first holographic descriptions of a higher-dimensional object, the 3+1-dimensional [[Type II string theory|type IIB]] [[Membrane (M-theory)|membrane]], which resolved a long-standing problem of finding a string description which describes a [[gauge theory]]. These developments simultaneously explained how string theory is related to some forms of supersymmetric quantum field theories.