Holographic principle
Encyclopedia
The holographic principle is a property of quantum gravity
and string theories
which states that the description of a volume of space
can be thought of as encoded on a boundary
to the region—preferably a light-like boundary like a gravitational horizon
. First proposed by Gerard 't Hooft, it was given a precise string-theory interpretation by Leonard Susskind
who combined his ideas with previous ones of Gerard 't Hooft and Charles Thorn
. In fact, as pointed out by Raphael Bousso
, 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.
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, such that the three dimensions we observe are only an effective description at macroscopic scales and at low energies. Cosmological holography has not been made mathematically precise, partly because the cosmological horizon has a finite area and grows with time.
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 which 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.
is microscopically random, like a hot gas. A known configuration of classical fields has zero entropy: there is nothing random about electric
and magnetic field
s, or gravitational wave
s. Since black holes are exact solutions of Einstein's equations
, they were thought not to have any entropy either.
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 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.
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 gravitational; when there is too much energy the gas collapses into a black hole. Bekenstein used this to put an 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
.
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 law of entropy increase
, but at first, he did not take the analogy too seriously.
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:
Quantum gravity
Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...
and string theories
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...
which states that the description of a volume of space
Space
Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum...
can be thought of as encoded on a boundary
Boundary (topology)
In topology and mathematics in general, the boundary of a subset S of a topological space X is the set of points which can be approached both from S and from the outside of S. More precisely, it is the set of points in the closure of S, not belonging to the interior of S. An element of the boundary...
to the region—preferably a light-like boundary like a gravitational horizon
Apparent horizon
In general relativity, an apparent horizon is a surface that is the boundary between light rays that are directed outwards and moving outwards, and those directed outwards but moving inwards.Apparent horizons are not invariant properties of a spacetime...
. First proposed by Gerard 't Hooft, it was given a precise string-theory interpretation 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...
who combined his ideas with previous ones of Gerard 't Hooft and Charles Thorn
Charles Thorn
Charles Thorn is a Professor of Physics at University of Florida in Gainesville, Florida. He played an important role in the development of Dual Models and string theory. Among his contributions is the proof of the non-existence of ghosts in string theory. The Goddard–Thorn theorem is a...
. In fact, as pointed out by Raphael Bousso
Raphael Bousso
Rafael Bousso is a theoretical physicist and string theorist. Currently he is a professor at Department of Physics, UC Berkeley. He is known for the proposal of Bousso's holographic bound, also known as the covariant entropy bound.-Career:...
, 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.
In a larger and more speculative sense, the theory suggests that the entire universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...
can be seen as a two-dimensional
Dimension
In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...
information structure "painted" on the cosmological horizon, such that the three dimensions we observe are only an effective description at macroscopic scales and at low energies. Cosmological holography has not been made mathematically precise, partly because the cosmological horizon has a finite area and grows with time.
The holographic principle was inspired by black hole thermodynamics
Black hole thermodynamics
In physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons...
, which implies that the maximal entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
in any region scales with the radius squared, and not cubed as might be expected. In the case of a 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...
, the insight was that the informational content of all the objects which 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
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...
within the framework of string theory.
Black hole entropy
An object with entropyEntropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
is microscopically random, like a hot gas. A known configuration of classical fields has zero entropy: there is nothing random about electric
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
and magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
s, or gravitational wave
Gravitational wave
In physics, gravitational waves are theoretical ripples in the curvature of spacetime which propagates as a wave, traveling outward from the source. Predicted to exist by Albert Einstein in 1916 on the basis of his theory of general relativity, gravitational waves theoretically transport energy as...
s. Since black holes are exact solutions of Einstein's equations
Einstein field equations
The Einstein field equations or Einstein's equations are a set of ten equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy...
, they were thought not to have any entropy either.
But Jacob Bekenstein
Jacob Bekenstein
Jacob David Bekenstein is an Israeli theoretical physicist who has contributed to the foundation of black hole thermodynamics and to other aspects of the connections between information and gravitation.-Biography:...
noted that this leads to a violation of the second law of thermodynamics
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...
. If one throws a hot gas with entropy into a black hole, once it crosses the 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
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
whose increase is greater than the entropy carried by the gas.
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 gravitational; when there is too much energy the gas collapses into a black hole. Bekenstein used this to put an upper bound
Bekenstein bound
In physics, the Bekenstein bound is an upper limit on the entropy S, or information I, that can be contained within a given finite region of space which has a finite amount of energy—or conversely, the maximum amount of information required to perfectly describe a given physical system down to the...
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
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...
.
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...
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
Black hole thermodynamics
In physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons...
, by analogy with the law of entropy increase
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...
, but at first, he did not take the analogy too seriously.
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:
-
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 balanceDetailed balanceThe principle of detailed balance is formulated for kinetic systems which are decomposed into elementary processes : At equilibrium, each elementary process should be equilibrated by its reverse process....
.
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 they doHawking radiationHawking 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...
, 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 unitsPlanck unitsIn physics, Planck units are physical units of measurement defined exclusively in terms of five universal physical constants listed below, in such a manner that these five physical constants take on the numerical value of 1 when expressed in terms of these units. Planck units elegantly simplify...
.
The entropy is proportional to the logarithm of the number of microstatesMicrostate (statistical mechanics)In statistical mechanics, a microstate is a specific microscopic configuration of a thermodynamic system that the system may occupy with a certain probability in the course of its thermal fluctuations...
, the ways a system can be configured microscopically while leaving the macroscopic description unchanged. Black hole entropy is deeply puzzling — it says that the logarithmLogarithmThe logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...
of the number of states of a black hole is proportional to the area of the horizon, not the volume in the interior.
Later, Raphael BoussoRaphael BoussoRafael Bousso is a theoretical physicist and string theorist. Currently he is a professor at Department of Physics, UC Berkeley. He is known for the proposal of Bousso's holographic bound, also known as the covariant entropy bound.-Career:...
came up with a covariant version of the boundBousso's holographic boundA simple generalization of the Black Hole entropy bound to generic systems is that, in quantum gravity, the maximum entropy which can be enclosed by a spatial boundary is given by a quarter of its surface area...
based upon null sheets.
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 only interact when they cross. It is implausible that the outgoing state would be completely determined by some tiny residual scattering.
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 matrixDensity matrixIn quantum mechanics, a density matrix is a self-adjoint positive-semidefinite matrix of trace one, that describes the statistical state of a quantum system...
. 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.
Troubled by this paradox, Gerard 't Hooft analyzed the emission of Hawking radiationHawking radiationHawking 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...
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 fieldGravitational fieldThe gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...
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 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 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. 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.
In 1995, Susskind, along with collaborators Tom BanksTom Banks (Physicist)Tom Banks is a theoretical physicist at University of California, Santa Cruz and a professor at Rutgers University. His work centers around string theory and its applications to high energy particle physics and cosmology. He received his Ph.D...
, Willy FischlerWilly FischlerWilly Fischler born in 1949 in Antwerpen, Belgium is a theoretical physicist and string theorist. He is currently the Jane and Roland Blumberg Centennial Professor of Physics at the University of Texas at Austin, where he is affiliated with the Weinberg theory group.Fischler is, among other things,...
, and Stephen ShenkerStephen ShenkerStephen Hart Shenker is an American theoretical physicist who works on string theory. He is a professor at Stanford University and former director of the Stanford Institute for Theoretical Physics. His brother Scott Shenker is a computer scientist...
, presented a formulation of the new M-theoryM-theoryIn theoretical physics, M-theory is an extension of string theory in which 11 dimensions are identified. Because the dimensionality exceeds that of superstring theories in 10 dimensions, proponents believe that the 11-dimensional theory unites all five string theories...
using a holographic description in terms of charged point black holes, the D0 branes of type IIA string theoryType II string theoryIn theoretical physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings. These account for two of the five consistent superstring theories in ten dimensions. Both theories have the maximal amount of supersymmetry — namely 32 supercharges...
. The Matrix theory they proposed was first suggested as a description of two branes in 11-dimensional supergravitySupergravityIn theoretical physics, supergravity is a field theory that combines the principles of supersymmetry and general relativity. Together, these imply that, in supergravity, the supersymmetry is a local symmetry...
by Bernard de WitBernard de WitBernard de Wit is a Dutch theoretical physicist specialized in supergravity and particle physics.Bernard de Wit studied theoretical physics at Utrecht University, where he got his PhD under supervision of Nobel Prize laureate Martinus Veltman in 1973...
, 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 IIBType II string theoryIn theoretical physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings. These account for two of the five consistent superstring theories in ten dimensions. Both theories have the maximal amount of supersymmetry — namely 32 supercharges...
membraneMembrane (M-Theory)In theoretical physics, a membrane, brane, or p-brane is a spatially extended mathematical concept that appears in string theory and related theories...
, which resolved a long-standing problem of finding a string description which describes a gauge theoryGauge theoryIn physics, gauge invariance is the property of a field theory in which different configurations of the underlying fundamental but unobservable fields result in identical observable quantities. A theory with such a property is called a gauge theory...
. These developments simultaneously explained how string theory is related to quantum chromodynamicsQuantum chromodynamicsIn theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of color-charged fermions...
, and afterwards holography gained wide acceptance.
Limit on information density
Entropy, if considered as information (see information entropyInformation entropyIn information theory, entropy is a measure of the uncertainty associated with a random variable. In this context, the term usually refers to the Shannon entropy, which quantifies the expected value of the information contained in a message, usually in units such as bits...
), is measured in bitBitA bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...
s. The total quantity of bits is related to the total degrees of freedomDegrees of freedom (physics and chemistry)A degree of freedom is an independent physical parameter, often called a dimension, in the formal description of the state of a physical system...
of matter/energy.
For a given energy in a given volume, there is an upper limit to the density of information (the Bekenstein boundBekenstein boundIn physics, the Bekenstein bound is an upper limit on the entropy S, or information I, that can be contained within a given finite region of space which has a finite amount of energy—or conversely, the maximum amount of information required to perfectly describe a given physical system down to the...
) 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 fundamental particlesElementary particleIn particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
. As the degrees of freedomDegrees of freedom (physics and chemistry)A degree of freedom is an independent physical parameter, often called a dimension, in the formal description of the state of a physical system...
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 HenneauxMarc HenneauxMarc Henneaux is a Belgian physicist and professor at the Universite Libre de Bruxelles . He studied physics at the ULB and obtained his PhD in 1980. Presently he serves as Director of the Service de Physique Théorique et Mathématique at the ULB and as the chair of the International Solvay...
had rigorously proved already in 1986, that the asymptotic symmetry of 2+1 dimensional gravity gives rise to a Virasoro algebraVirasoro algebraIn mathematics, the Virasoro algebra is a complex Lie algebra, given as a central extension of the complex polynomial vector fields on the circle, and is widely used in conformal field theory and string theory....
, 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 AmericanScientific AmericanScientific American is a popular science magazine. It is notable for its long history of presenting science monthly to an educated but not necessarily scientific public, through its careful attention to the clarity of its text as well as the quality of its specially commissioned color graphics...
magazine, Jacob BekensteinJacob BekensteinJacob David Bekenstein is an Israeli theoretical physicist who has contributed to the foundation of black hole thermodynamics and to other aspects of the connections between information and gravitation.-Biography:...
summarized a current trend started by John Archibald WheelerJohn Archibald WheelerJohn Archibald Wheeler was an American theoretical physicist who was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr in explaining the basic principles behind nuclear fission...
, which suggests scientists may "regard the physical world as made of informationInformationInformation in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...
, with energy and matter as incidentals." Bekenstein quotes William BlakeWilliam BlakeWilliam Blake was an English poet, painter, and printmaker. Largely unrecognised during his lifetime, Blake is now considered a seminal figure in the history of both the poetry and visual arts of the Romantic Age...
and asks whether the holographic principle implies that seeing "the world in a grain of sandAuguries of InnocenceAuguries of Innocence is a poem from one of William Blake's notebooks now known as The Pickering Manuscript. It is assumed to have been written in 1803, but was not published until 1863 in the companion volume to Alexander Gilchrist's biography of William Blake. The poem contains a series of...
," could be more than "poetic license".
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 theoryInformation theoryInformation theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...
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 DVDDVDA DVD is an optical disc storage media format, invented and developed by Philips, Sony, Toshiba, and Panasonic in 1995. DVDs offer higher storage capacity than Compact Discs while having the same dimensions....
s, rely on Shannon entropy.
In thermodynamicsThermodynamicsThermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
(the branch of physics dealing with heat), entropy is popularly described as a measure of the "disorderDisorderDisorder may refer to :* Chaos, unpredictability and in the metaphysical sense, it is the opposite of law and order* Civil disorder, one or more forms of disturbance caused by a group of people...
" in a physical system of matter and energy. In 1877 Austrian physicist Ludwig BoltzmannLudwig BoltzmannLudwig Eduard Boltzmann was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics...
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.
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'sBoltzmann's entropy formulaIn statistical thermodynamics, Boltzmann's equation is a probability equation relating the entropy S of an ideal gas to the quantity W, which is the number of microstates corresponding to a given macrostate:...
. 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 isomorphicIsomorphismIn abstract algebra, an isomorphism is a mapping between objects that shows a relationship between two properties or operations. If there exists an isomorphism between two structures, the two structures are said to be isomorphic. In a certain sense, isomorphic structures are...
to the information "inscribed" on the surface of its boundary.
Claimed experimental test at gravitational wave detectors
The FermilabFermilabFermi National Accelerator Laboratory , located just outside Batavia, Illinois, near Chicago, is a US Department of Energy national laboratory specializing in high-energy particle physics...
physicist Craig HoganCraig HoganCraig Hogan is a Professor of Astronomy and Physics at the University of Chicago and he is the director of the Fermilab Center for Particle Astrophysics....
claims that the holographic principle may imply quantum fluctuations in spatial position that would lead to apparent background noise or holographic noise measurable at gravitational wave detectors, in particular GEO 600GEO 600GEO 600 is a gravitational wave detector located near Sarstedt, Germany. This instrument, and its sister interferometric detectors, when operational, are some of the most sensitive gravitational wave detectors ever designed...
.
See also
- Bekenstein boundBekenstein boundIn physics, the Bekenstein bound is an upper limit on the entropy S, or information I, that can be contained within a given finite region of space which has a finite amount of energy—or conversely, the maximum amount of information required to perfectly describe a given physical system down to the...
- Bousso's holographic boundBousso's holographic boundA simple generalization of the Black Hole entropy bound to generic systems is that, in quantum gravity, the maximum entropy which can be enclosed by a spatial boundary is given by a quarter of its surface area...
- Brane cosmologyBrane cosmologyBrane cosmology refers to several theories in particle physics and cosmology motivated by, but not exclusively derived from, superstring theory and M-theory.-Brane and bulk:...
- Entropic gravity
- Margolus–Levitin theorem
- Physical cosmologyPhysical cosmologyPhysical cosmology, as a branch of astronomy, is the study of the largest-scale structures and dynamics of the universe and is concerned with fundamental questions about its formation and evolution. For most of human history, it was a branch of metaphysics and religion...
- Implicate and explicate order according to David BohmImplicate and explicate order according to David BohmAccording to David Bohm's theory, implicate and explicate orders are characterised by:-David Bohm's challenges to some generally prevailing views:...
External links
- Bekenstein bound