Holographic principle 14286 224733038 2008-07-10T04:43:35Z Likebox 4287880 rearrange + some string stuff {{String theory|cTopic=Theory}} {{redirect|Holographic Universe|the album|Holographic Universe (album)}} The '''holographic principle''' is a physical property of [[quantum gravity]] theories, proposed by [[Gerard 't Hooft]] and [[Leonard Susskind]]. It has been given precise mathematical form within string theory, largely as a result of Susskind's work. It has been widely recognized as a general principle of quantum gravity, which gives a consistent resolution to the [[black hole information paradox]]. The principle states that the description of a volume of space should be thought of as encoded on a boundary to the region, preferably a light-like boundary like a gravitational horizon. For a black hole, the principle states that the description of all the objects which will ever fall in is entirely contained in surface fluctuations. So far it has only been shown to be true within [[string theory]] and variants like [[M-theory]]. In a larger and more speculative sense, the theory suggests that the entire universe can be seen as a two-dimensional information structure "painted" on the [[cosmological horizon]], so that the three dimensions we observe are only an effective description at low energies. Cosmological holography has not yet been made mathematically precise, partly because the cosmological horizon has a finite area and grows with time. The holographic principle was sparked by the observation that there is at most one [[Degrees of freedom (physics and chemistry)|degree of freedom]] (or 1 [[Boltzmann constant]] ''k'' unit of maximum entropy) for every four [[Planck units|Planck area]]s in a gravitational horizon, i.e. <math>S\le A/4</math> in [[Units of measurement|natural units]], a consequence of the seminal work of [[Jacob Bekenstein]] and [[Stephen Hawking]] on the entropy and temperature of black holes. Since [[string theory]], or more generally [[M-theory]], is fundamentally built from entities which obey the [[holographic principle]], and since it is the only theory known to have this property, many physicists believe that these theories are the correct description of quantum gravity, that they are the [[theory of everything]].<ref> {{cite journal|title=Computational Capacity of the Universe|journal=Physics Review Letters; American Physical Society|date=2002-05-24|first=Seth|last=Lloyd|coauthors=|volume=88|issue=23|pages=237901|doi= 10.1103/PhysRevLett.88.237901|url=http://link.aps.org/abstract/PRL/v88/e237901|format=|accessdate=2008-03-14 }}</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> Unfortunately, no known solution of string theory has yet been found which describes the universe we inhabit, nor is it known if the structure of such a solution would be uniquely determined from the comparatively low-energy data accessible to experiments. ==Reasons for the holographic principle== Black holes are [[Principle of maximum entropy|maximal entropy]] objects <ref>{{cite journal | first = Jacob D. | last = Bekenstein | authorlink = Jacob Bekenstein | url = http://www.aeiveos.com/~bradbury/Authors/Computing/Bekenstein-JD/UUBotEtERfBS.html | title = Universal upper bound on the entropy-to-energy ratio for bounded systems | journal = Physical Review DD | volume = 23 | issue = 215 | year =January 1981 (Revision: August 25, 1980.) }}</ref>, and theoretical results of [[Black hole thermodynamics]] suggest that the [[Second law of thermodynamics]] is violated when matter crosses the event horizon of a [[Black hole]]. This conflict may be reconciled if black holes are accorded an [[entropy]] whose increase more than compensates for the entropy carried by the matter "swallowed", so '''Black hole entropy''' is the [[entropy]] of a [[black hole]]. [[Jacob Bekenstein]] posited that this black hole entropy is directly proportional to the area of the spherical [[event horizon]] divided by the [[Planck area]]. Later, [[Stephen Hawking]] was able to confirm Bekenstein's idea and showed that the constant of proportionality is 1/4.<ref>{{cite journal | first = Parthasarathi | last = Majumdar | title = Black Hole Entropy and Quantum Gravity | id = {{arxiv|archive=gr-qc|id=9807045}} | journal = arXiv: General Relativity and Quantum Cosmology | year = 1998}}</ref> The entropy of an object is the logarithm of the number of ways it can be configured microscopically, while leaving the macroscopic description unchanged. It is an [[extensive variable]], and in a clump of matter with constant density and temperature, it is directly proportional the volume. For this reason, black hole entropy is deeply puzzling--- it suggests that the number of states of a black hole is proportional to the area of the horizon, not the the volume in the interior.<ref name="sciam">{{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]] | year = August 2003 | pages = p. 59 }}</ref>. The mystery was further deepened when Hawking argued that the radiation which Black holes emit is not related in any way to the matter that they absorb. His contention was that the laws of quantum mechanics would have to be modified, so that a pure state described by a wavefunction could turn into a mixed state described by a density matrix. This is fundamentally incompatible with the fundamental laws of quantum mechanics, which require that states which are superpositions with probability amplitudes never become states which are probabilistic mixtures of different possibilities except in the case of measurements, which the black hole should not be performing. Troubled by this paradox, 'tHooft's analyzed the emission of [[Hawking radiation]] in more detail. He noted that when Hawking radiation escapes, the only universal way in which incoming particles can leave a signature is if they scatter the outgoing particles off their gravitational field. When a particle falls into a black hole, it is boosted relative to an outside observer, and its gravitational field assumes a universal form. 'tHooft showed that this field makes a dimple on the horizon of a black hole, and like a shadow, this dimple is an alternate description of the particle's location and mass. The nature of the dimple for a four-dimensional spherical uncharged black hole was reminiscent of the types of deformation on a string-theory world sheet which describe the emission and absorption of an asymptotic particle. This led 'tHooft to believe that some form of string theory could be derived from holographic considerations. This idea was expanded on by Leonard Susskind, who had also been developing holography largely independently. Susskind argued that the world-sheet theory of string theory was in fact a holographic description, because he could identify long string states with ordinary black hole states. This was a deep advance because it revealed that strings have a classical interpretation in terms of black holes--- and it suggested that any black-hole with appropriate properties would serve as a basis for a description of the theory of quantum gravity. In 1995, Susskind, along with collaborators [[Tom Banks]], [[Willy Fischler]], and [[Stephen Shenker]] found the first mathematically complete formulation of then new M-theory using a holographic description in terms of charged point black holes, the D0 branes of type IIA string theory. In 1997, [[Juan Maldacena]] gave the first holographic descriptions of a higher dimensional object, which resolved a long-standing problem of finding a string description which describes a [[gauge theory]]. The resolution to this problem not only impacted quantum gravity, but also led to advances in the study of [[quantum chromodynamics]] and has been corroborated to some extent by experiments on the quark gluon plasma. ==Limit on information density== 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. In a given volume, there is an upper limit to the density of information 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. The most rigorous realization of the holographic principle is the [[AdS/CFT]] correspondence by [[Juan Maldacena]]. However, J.D. Brown and [[Marc Henneaux]]<ref>J.D.Brown and M.Henneaux 1986 "Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity" Commun. Math. Phys. 104 207-226</ref> 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. ==High level summary== 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]], a collaborator of [[Albert Einstein]], which suggests scientists may ''"regard the physical world as made of information, with energy and matter as incidentals."'' Bekenstein quotes [[William Blake]] and questions whether the Holographic principle implies that seeing ''"the world in a grain of sand,"'' could be 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> ===Unexpected connection=== 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 DVDs, all rely on Shannon entropy. In [[Thermodynamics]] (the branch of physics dealing with heat) Entropy is popularly described as a measure of the "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 count of all the ways that the individual gas molecules could be distributed in the room, and all the ways they could be moving. ===Energy, matter and information equivalence=== 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''. 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. 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 spherical surface of its boundary <ref name="sciam">{{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]] | year = August 2003 | pages = p. 59 }}</ref>. ==Variations of the holographic principle== There are variations of the holographic known as the strong and weak holographic principles. '''The Strong Holographic Principle''' The strong holographic principle states that the information which an outside observer can derive from the surface of a black hole is directly proportional to the surface area of the event horizon. The "strong" version of the holographic principle states that an observer derives information from something through its surface which acts like a "screen" of sorts through which to view that information. However there is still a particle behind the screen projecting the information it holds onto the "screen" or surface. '''The Weak Holographic Principle''' The weak holographic principle states that all the information entering the event horizon of a black hole is encoded on the surface of the event horizon of that black hole and is proportional to the surface area of the event horizon. Unlike the "strong" version the weak holographic principle states that there is no particle behind the "screen" and that the physical processes of the universe can be wholly described by the "screens" or surfaces through which the information is observed. ==See also== * [[Black hole]] * [[AdS/CFT]] * [[Physical cosmology]] * [[Brane cosmology]] * [[Bekenstein Bound]] * [[String theory]] * [[Holographic paradigm]] ==References == ''General'' * {{cite journal | first = Raphael | last = Bousso | title = The holographic principle | journal = Reviews of Modern Physics | volume = 74 | year = 2002 | pages = 825–874 | id = {{arxiv|archive=hep-th|id=0203101}} | doi = 10.1103/RevModPhys.74.825 }} ''Citations'' <references /> ==External links== * [http://www.uctv.tv/search-details.asp?showID=11140 UC Berkeley's Raphael Bousso gives an introductory lecture on the holographic principle - Video.] * [http://community.livejournal.com/ref_sciam/1190.html ''Scientific American'' article on holographic principle by Jacob Bekenstein] [[Category:Theoretical physics]] [[Category:Black holes]] [[cs:Holografický princip]] [[de:Holografisches Prinzip]] [[es:Principio Holográfico]] [[fr:Principe holographique]] [[it:Principio olografico]] [[pt:Princípio holográfico]] [[ru:Голографический принцип]]