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| {{Redirect|Holographic Universe|the album|Holographic Universe (album)|the book by Michael Talbot|The Holographic Universe}}
| | Jeep Liberty Powertech employed engines are at present for sale online in three.7 and 2.4 sizes at the Got Engines web site. These original Chrysler builds can be purchased for a lowered cost.<br><br> |
| {{String theory|cTopic=Concepts}}
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| The '''holographic principle''' is a property of [[quantum gravity]] and [[string theory|string theories]] that states that the description of a volume of [[space]] can be thought of as encoded on a [[Boundary (topology)|boundary]] to the region—preferably a [[light-like]] boundary like a [[apparent horizon|gravitational horizon]]. First proposed by [[Gerard 't Hooft]], it was given a precise string-theory interpretation by [[Leonard Susskind]]<ref name=SusskindArXiv>{{cite journal |title=The World as a Hologram |last=Susskind |first=Leonard |doi=10.1063/1.531249 |year=1995 |journal=Journal of Mathematical Physics |volume=36 |issue=11 |pages=6377–6396|arxiv=hep-th/9409089 |bibcode = 1995JMP....36.6377S }}</ref> who combined his ideas with previous ones of 't Hooft and [[Charles Thorn]].<ref name=SusskindArXiv /><ref>Sakharov Conf on Physics, Moscow, (91):447-454</ref> As pointed out by [[Raphael Bousso]],<ref>{{cite journal |last=Bousso |first=Raphael |year=2002 |title=The Holographic Principle |journal=[[Reviews of Modern Physics]] |volume=74 |issue=3 |pages=825–874 |doi=10.1103/RevModPhys.74.825 |arxiv=hep-th/0203101 |bibcode=2002RvMP...74..825B}}</ref> Thorn observed in 1978 that string theory admits a lower-dimensional description in which gravity emerges from it in what would now be called a holographic way. | | The Powertech motor technology created by Chrysler for use in the Jeep and Dodge brands of cars can now be located in the utilized situation motor inventory at the http://www.gotengines.com website. Jeep Liberty Powertech utilized engines are now for sale in 3.7 and the two.four size this year.<br><br>This cross assistance format for Jeep motors will assist attain a split demographic of SUV and truck owners who favor Chrysler technologies in replacement engines. Going To [https://www.facebook.com/engines.for.sale http://www.gotengines.com] possibly provides lessons you could give to your girlfriend. Discover more on this partner article by clicking [http://www.pinterest.com/gotengines/ gotengines.com complaints]. Should people require to be taught new information about [https://www.facebook.com/engines.for.sale www.gotengines.com], there are lots of resources you might think about investigating. The 2.four I4 and 3.7 V6 [http://Www.thefreedictionary.com/motor+inventory motor inventory] now presented for public sale consists of a lowered level of pricing for consumers who decide to stick to by means of with a obtain.<br><br>"The Liberty is one particular of the sport utility vehicle brands that can be researched for replacement engines in our promoted warehouse inventory on our internet site," a Got Engines organization rep confirmed.<br><br>Since the three.7 displacement engine has been utilised in Dodge autos, owners of SUV or trucks in the Dodge division of Chrysler will have a new supply to obtain a very good situation motor to replace a defective one. All utilised Powertech engines that are shipped this year offer you a complete three-year parts warranty.<br><br>"We acquire motors for most American brands of vehicles and supply a private warranty coverage alternative that need to be activated before customers can reap the rewards of coverage," said the rep.<br><br>The Got Engines business has installed new speak to tools that support customers acquire answers to [http://Www.Questions.org/ questions] or information about motors in stock on the web. The connected database that now searches the organization warehouse for information is now linked with the front web page of the company web site.<br>About GotEngines.com<br><br>The GotEngines.com firm is currently selling replacement automobile motors at a discount price level that now aids shoppers find cost-effective replacement engines more than the Internet. The organization inventory is bought direct or offered by distinct suppliers. The GotEngines.com company is including a new group of service agents in its call center for this year to answer direct questions about mileage, pricing or other issues connected to employed automobile engines.<br><br>Study original article: http://www.prweb.com/releases/jeep-liberty/jeep-engines-sale-utilized/prweb11991352.htm.Got Engines<br>3740 Kori Rd <br>Jacksonville, FL 32257<br>http://www.gotengines.com<br><br>If you liked this posting and you would like to receive much more information relating to [http://clammycobweb1357.jimdo.com gap health insurance] kindly take a look at our own page. |
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| In a larger sense, the theory suggests that the entire [[universe]] can be seen as a [[dimension|two-dimensional]] information structure "painted" on the [[cosmological horizon]], such that the [[three dimensions]] we observe are an effective description only at [[macroscopic scale]]s and at [[high-energy physics|low energies]]. Cosmological holography has not been made mathematically precise, partly because the [[Observable universe#Particle horizon|cosmological horizon]] has a finite area and grows with time.<ref>{{cite journal|title=Computational Capacity of the Universe|date=2002-05-24|first=Seth|last=Lloyd|coauthors=|issue=23|page=237901|journal=[[Physical Review Letters]]|volume=88|doi= 10.1103/PhysRevLett.88.237901|pmid=12059399|bibcode=2002PhRvL..88w7901L|arxiv = quant-ph/0110141 }}</ref><ref>{{cite web|url=http://www.google.com/search?hl=en&lr=&as_qdr=all&q=holographic+everything+site%3Actnsstars.org |title=Multiverse Cosmological Models and the Anthropic Principle |accessdate=2008-03-14 |last=Davies |first=Paul |work=CTNS }}</ref>
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| The holographic principle was inspired by [[black hole thermodynamics]], which implies that the maximal [[entropy]] in any region scales with the radius ''squared'', and not cubed as might be expected. In the case of a [[black hole]], the insight was that the informational content of all the objects that have fallen into the hole can be entirely contained in surface fluctuations of the event horizon. The holographic principle resolves the [[black hole information paradox]] within the framework of string theory.<ref>Susskind, L., "The Black Hole War – My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics", Little, Brown and Company (2008)</ref>
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| ==Black hole entropy==
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| {{Main|Black hole thermodynamics}}
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| An object with [[entropy]] is microscopically random, like a hot gas. A known configuration of classical fields has zero entropy: there is nothing random about [[Electric field|electric]] and [[magnetic field]]s, or [[gravitational wave]]s. Since black holes are exact solutions of [[Einstein field equations|Einstein's equations]], they were thought not to have any entropy either.
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| But [[Jacob Bekenstein]] noted that this leads to a violation of the [[second law of thermodynamics]]. If one throws a hot gas with entropy into a black hole, once it crosses the [[event horizon]], the entropy would disappear. The random properties of the gas would no longer be seen once the black hole had absorbed the gas and settled down. The second law can only be salvaged if black holes are in fact random objects, with an enormous [[entropy]] whose increase is greater than the entropy carried by the gas.
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| Bekenstein argued that black holes are maximum entropy objects—that they have more entropy than anything else in the same volume. In a sphere of radius ''R'', the entropy in a relativistic gas increases as the energy increases. The only limit is [[gravitation]]al; when there is too much energy the gas collapses into a black hole. Bekenstein used this to put an [[Bekenstein bound|upper bound]] on the entropy in a region of space, and the bound was proportional to the area of the region. He concluded that the black hole entropy is directly proportional to the area of the [[event horizon]].<ref>{{cite journal |first=Jacob D. |last=Bekenstein |title=Universal upper bound on the entropy-to-energy ratio for bounded systems |journal=Physical Review D |volume=23 |issue=215 |pages=287–298 |date=January 1981 |doi=10.1103/PhysRevD.23.287 |bibcode = 1981PhRvD..23..287B }}</ref>
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| [[Stephen Hawking]] had shown earlier that the total horizon area of a collection of black holes always increases with time. The horizon is a boundary defined by lightlike [[geodesics]]; it is those light rays that are just barely unable to escape. If neighboring geodesics start moving toward each other they eventually collide, at which point their extension is inside the black hole. So the geodesics are always moving apart, and the number of geodesics which generate the boundary, the area of the horizon, always increases. Hawking's result was called the second law of [[black hole thermodynamics]], by analogy with the [[Second law of thermodynamics|law of entropy increase]], but at first, he did not take the analogy too seriously.
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| Hawking knew that if the horizon area were an actual entropy, black holes would have to radiate. When heat is added to a thermal system, the change in entropy is the increase in [[mass-energy]] divided by temperature:
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| ::<math>
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| {\rm d}S = \frac{{\rm d}M}{T}.
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| </math>
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| If black holes have a finite entropy, they should also have a finite temperature. In particular, they would come to equilibrium with a thermal gas of photons. This means that black holes would not only absorb photons, but they would also have to emit them in the right amount to maintain [[detailed balance]].
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| Time independent solutions to field equations don't emit radiation, because a time independent background conserves energy. Based on this principle, Hawking set out to show that black holes do not radiate. But, to his surprise, a careful analysis convinced him that [[Hawking radiation|they do]], and in just the right way to come to equilibrium with a gas at a finite temperature. Hawking's calculation fixed the constant of proportionality at 1/4; the entropy of a black hole is one quarter its horizon area in [[Planck units]].<ref>{{cite journal | first = Parthasarathi | last = Majumdar | title = Black Hole Entropy and Quantum Gravity | arxiv = gr-qc/9807045 | journal = ArXiv: General Relativity and Quantum Cosmology | year = 1998|bibcode = 1999InJPB..73..147M | volume = 73 | pages = 147 }}</ref>
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| The entropy is proportional to the logarithm of the number of [[microstate (statistical mechanics)|microstates]], the ways a system can be configured microscopically while leaving the macroscopic description unchanged. Black hole entropy is deeply puzzling — it says that the [[logarithm]] of the number of states of a black hole is proportional to the area of the horizon, not the volume in the interior.<ref name="sciam2003">{{cite journal | first = Jacob D. | last = Bekenstein | authorlink = Jacob Bekenstein | url = http://www.sciam.com/article.cfm?articleid=000AF072-4891-1F0A-97AE80A84189EEDF | title = Information in the Holographic Universe — Theoretical results about black holes suggest that the universe could be like a gigantic hologram | journal = [[Scientific American]] |date=August 2003 | pages = p. 59 }}</ref> | |
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| Later, [[Raphael Bousso]] came up with a [[Bousso's holographic bound|covariant version of the bound]] based upon null sheets.
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| ==Black hole information paradox==
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| {{Main|Black hole information paradox}}
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| 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 only interact when they cross. It is implausible that the outgoing state would be completely determined by some tiny residual scattering.
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| 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>
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| Troubled by this paradox, [[Gerard 't Hooft]] analyzed the emission of [[Hawking radiation]] in more detail. 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 alternate 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 [[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.
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| 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]]|year=1991|publisher=Back Bay Books|location=New York|isbn=0-316-18066-1|page=371}}</ref> or internal quantum state is not information that is implied to be preserved in the surface fluctuations of the event horizon.|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.
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| This work showed that the black hole information paradox is resolved when quantum gravity is described in an unusual string-theoretic way. The space-time in quantum gravity should emerge as an effective description of the theory of oscillations of a lower-dimensional black-hole horizon. This suggested that any black hole with appropriate properties, not just strings, would serve as a basis for a description of string theory.
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| 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)|brane]]s of [[Type II string theory|type IIA string theory]]. The Matrix theory they proposed was first suggested as a description of two branes in 11-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 [[quantum chromodynamics]].
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| ==Limit on information density==
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| Entropy, if considered as information (see [[information entropy]]), is measured in [[bit]]s. The total quantity of bits is related to the total [[Degrees of freedom (physics and chemistry)|degrees of freedom]] of matter/energy.
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| For a given energy in a given volume, there is an upper limit to the density of information (the [[Bekenstein bound]]) about the whereabouts of all the particles which compose matter in that volume, suggesting that matter itself cannot be subdivided infinitely many times and there must be an ultimate level of [[elementary particle|fundamental particles]]. As the [[degrees of freedom (physics and chemistry)|degrees of freedom]] of a particle are the product of all the degrees of freedom of its sub-particles, were a particle to have infinite subdivisions into lower-level particles, then the degrees of freedom of the original particle must be infinite, violating the maximal limit of entropy density. The holographic principle thus implies that the subdivisions must stop at some level, and that the fundamental particle is a bit (1 or 0) of information.
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| The most rigorous realization of the holographic principle is the [[AdS/CFT]] correspondence by [[Juan Maldacena]].
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| However, J.D. Brown and [[Marc Henneaux]] had rigorously proved already in 1986, that the asymptotic symmetry of 2+1 dimensional gravity gives rise to a [[Virasoro algebra]], whose corresponding quantum theory is a 2 dimensional conformal field theory.<ref>{{Cite journal |first=J. D. |last=Brown |lastauthoramp=yes |first2=M. |last2=Henneaux |year=1986 |title=Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity |journal=Communications in Mathematical Physics |volume=104 |issue=2 |pages=207–226 |doi=10.1007/BF01211590 |postscript=<!--None--> |bibcode = 1986CMaPh.104..207B }}.</ref>
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| ==High-level summary==
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| The physical universe is widely seen to be composed of "matter" and "energy". In his 2003 article published in [[Scientific American]] magazine, [[Jacob Bekenstein]] summarized a current trend started by [[John Archibald Wheeler]], which suggests scientists may ''"regard the physical world as made of [[information]], with energy and matter as incidentals."'' Bekenstein asks "Could we, as [[William Blake]] memorably penned, 'see a world in a grain of sand,' or is that idea no more than '[[poetic license]],'"<ref>[http://www.sciamdigital.com/index.cfm?fa=Products.ViewIssuePreview&ARTICLEID_CHAR=0E90201A-2B35-221B-6BBEB44296C90AAD Information in the Holographic Universe<!-- Bot generated title -->]</ref> referring to the holographic principle. | |
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| ===Unexpected connection===
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| Bekenstein's topical overview "A Tale of Two Entropies" describes potentially profound implications of Wheeler's trend, in part by noting a previously unexpected connection between the world of [[information theory]] and classical physics. This connection was first described shortly after the seminal 1948 papers of American applied mathematician [[Claude E. Shannon]] introduced today's most widely used measure of information content, now known as [[Shannon entropy]]. As an objective measure of the quantity of information, Shannon entropy has been enormously useful, as the design of all modern communications and data storage devices, from cellular phones to [[modems]] to hard disk drives and [[DVD]]s, rely on Shannon entropy.
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| In [[thermodynamics]] (the branch of physics dealing with heat), entropy is popularly described as a measure of the "[[Order and disorder (physics)|disorder]]" in a physical system of matter and energy. In 1877 Austrian physicist [[Ludwig Boltzmann]] described it more precisely in terms of the ''number of distinct microscopic states'' that the particles composing a macroscopic "chunk" of matter could be in while still ''looking'' like the same macroscopic "chunk". As an example, for the air in a room, its thermodynamic entropy would equal the logarithm of the count of all the ways that the individual gas molecules could be distributed in the room, and all the ways they could be moving.
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| ===Energy, matter, and information equivalence===
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| Shannon's efforts to find a way to quantify the information contained in, for example, an e-mail message, led him unexpectedly to a formula with the same form as [[Boltzmann's entropy formula|Boltzmann's]]. In an article in the August 2003 issue of Scientific American titled "Information in the Holographic Universe", Bekenstein summarizes that ''"Thermodynamic entropy and Shannon entropy are conceptually equivalent: the number of arrangements that are counted by Boltzmann entropy reflects the amount of Shannon information one would need to implement any particular arrangement..."'' of matter and energy. The only salient difference between the thermodynamic entropy of physics and the Shannon's entropy of information is in the units of measure; the former is expressed in units of energy divided by temperature, the latter in ''essentially dimensionless'' "bits" of information, and so the difference is merely a matter of convention.
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| The holographic principle states that the entropy of ''ordinary mass'' (not just black holes) is also proportional to surface area and not volume; that volume itself is illusory and the universe is really a [[hologram]] which is [[isomorphism|isomorphic]] to the information "inscribed" on the surface of its boundary.<ref name="sciam2003"/>
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| ===Recent work===
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| [[Nature_(journal)|Nature]] <ref>Simulations back up theory that Universe is a hologram, December 2013 , http://www.nature.com/news/simulations-back-up-theory-that-universe-is-a-hologram-1.14328</ref> presents two papers <ref>Quantum Near Horizon Geometry of Black 0-Brane, Yoshifumi Hyakutake, http://arxiv.org/abs/1311.7526</ref> <ref>Holographic description of quantum black hole on a computer, Masanori Hanada, Yoshifumi Hyakutake, Goro Ishiki, Jun Nishimura, http://arxiv.org/abs/1311.5607</ref> authored by Yoshifumi Hyakutake that bring computational evidence that Maldacena’s conjecture is true. One paper computes the internal energy of a black hole, the position of its event horizon, its entropy and other properties based on the predictions of [[string theory]] and the effects of [[virtual particle|virtual particles]]. The other paper calculates the internal energy of the corresponding lower-dimensional cosmos with no gravity. The two simulations match. These papers have received positive appreciation from [[Juan Maldacena|Maldacena]] himself and [[Leonard Susskind]], one of the founders of string theory. The papers do not suggest that the universe we actually live in is a hologram and are not an actual proof of Maldacena's conjecture for all cases but a demonstration that the conjecture works for a particular theoretical case. The situation they examine is a hypothetical universe, not a universe necessarily like ours. The new work is a mathematical test that verifies the AdS/CFT correspondence for a particular situation.<ref>New work gives credence to theory of universe as a hologram, http://phys.org/news/2013-12-credence-theory-universe-hologram.html</ref>
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| ==Claimed experimental tests==
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| The [[Fermilab]] physicist [[Craig Hogan]] claims that the holographic principle would imply quantum fluctuations in spatial position<ref>{{Cite journal |last=Hogan |first=Craig J. |year=2008 |title=Measurement of quantum fluctuations in geometry |journal=[[Physical Review D]] |volume=77 |issue=10 |pages=104031 |doi=10.1103/PhysRevD.77.104031 |arxiv=0712.3419 |postscript=<!--None--> |bibcode = 2008PhRvD..77j4031H }}.</ref> that would lead to apparent background noise or "holographic noise" measurable at gravitational wave detectors, in particular [[GEO 600]].<ref>{{Cite news |last=Chown|first=Marcus|title=Our world may be a giant hologram|newspaper=NewScientist|date=15 January 2009|url=http://www.newscientist.com/article/mg20126911.300|accessdate=2010-04-19}}</ref> However these claims have not been widely accepted, or cited, among quantum gravity researchers and appear to be in direct conflict with string theory calculations.<ref>"Consequently, he ends up with inequalities of the type... Except that one may look at the actual equations of Matrix theory and see that none of these commutators is nonzero... The last displayed inequality above obviously can't be a consequence of quantum gravity because it doesn't depend on G at all! However, in the G→0 limit, one must reproduce non-gravitational physics in the flat Euclidean background spacetime. Hogan's rules don't have the right limit so they can't be right." – [[Lubos Motl]], [http://motls.blogspot.com/2012/02/hogans-holographic-noise-doesnt-exist.html Hogan's holographic noise doesn't exist], Feb 7, 2012</ref>
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| Analyses in 2011 of measurements of gamma ray burst [[GRB 041219A]] in 2004 by the [[INTEGRAL]] space observatory launched in 2002 by the [[European Space Agency]] shows that Craig Hogan's noise is absent down to a scale of 10<sup>−48</sup> meters, as opposed to scale of 10<sup>−35</sup> meters predicted by Hogan, and the scale of 10<sup>−16</sup> meters found in measurements of the [[GEO 600]] instrument.<ref>{{cite web|url=http://www.esa.int/Our_Activities/Space_Science/Integral_challenges_physics_beyond_Einstein|title=Integral challenges physics beyond Einstein|date=30 June 2011|publisher=[[European Space Agency]]|accessdate=3 February 2013}}</ref> Searches for Hogan's effect continue as of 2012.<ref>{{cite news|url=http://www.scientificamerican.com/article.cfm?id=is-space-digital|title=Is Space Digital?:|last=Moyer|first=Michael|date=17 January 2012|work=[[Scientific American]]|accessdate=3 February 2013}}</ref>
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| [[Jacob Bekenstein]] also claims to have found a way to test the holographic principle with a simple tabletop photon experiment.<ref>{{cite news|url=http://www.nature.com/news/single-photon-could-detect-quantum-scale-black-holes-1.11871|title=Single photon could detect quantum-scale black holes|last=Cowen|first=Ron|date=22 November 2012|work=[[Nature (journal)|Nature]]|accessdate=3 February 2013}}</ref>
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| ==See also==
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| * [[Bekenstein bound]]
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| * [[Bousso's holographic bound]]
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| * [[Brane cosmology]]
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| * [[Entropic gravity]]
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| * [[Implicate and explicate order according to David Bohm]]
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| * [[Margolus–Levitin theorem]]
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| * [[Physical cosmology]]
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| * [[Quantum foam]]
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| * [[Simulated reality]]
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| ==Notes==
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| {{reflist|group=note}}
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| ==References==
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| ;General
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| * {{cite journal
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| | first = Raphael | last = Bousso | title = The holographic principle
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| | journal = Reviews of Modern Physics
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| | volume = 74
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| | year = 2002
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| | pages = 825–874
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| | arxiv = hep-th/0203101
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| | doi = 10.1103/RevModPhys.74.825
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| | bibcode=2002RvMP...74..825B
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| | issue = 3}}
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| *{{Cite journal |last='t Hooft |first=Gerard |year=1993 |title=Dimensional Reduction in Quantum Gravity |work=|arxiv=gr-qc/9310026 |postscript=<!--None--> |bibcode = 1993gr.qc....10026T |pages=10026 }}. 't Hooft's original paper.
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| ;Citations
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| {{Reflist|colwidth=30em}}
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| ==External links==
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| * [http://www.uctv.tv/search-details.asp?showID=11140 UC Berkeley's Raphael Bousso gives an introductory lecture on the holographic principle - Video.]
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| * [http://community.livejournal.com/ref_sciam/1190.html ''Scientific American'' article on holographic principle by Jacob Bekenstein]
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| {{Black holes}}
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| {{quantum gravity}}
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| {{Use dmy dates|date=July 2011}}
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| {{DEFAULTSORT:Holographic Principle}}
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| [[Category:Theoretical physics]]
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| [[Category:Black holes]]
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| [[Category:Quantum information science]]
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| [[Category:Holography]]
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