Holographic principle

From Wikipedia, the free encyclopedia

String theory
Superstring theory
Theory
String theory
Superstrings
Bosonic string theory
M-theory (simplified)

Type I string · Type II string
Heterotic string
String field theory
Holographic principle
This box: view • talk • edit

The holographic principle is a speculative conjecture about quantum gravity theories, proposed by Gerard 't Hooft and improved and promoted by Leonard Susskind and John A. Wheeler, claiming that all of the information contained in a volume of space can be represented by information which lives in the boundary of that region. In other words, if you have an empty sphere, all of the events within can be explained by the arrangement of information on the surface of the sphere. In a larger sense, the theory suggests that the entire universe can be seen as a two-dimensional information structure "painted" on a boundary surface, and that the three dimensions we observe are illusory. The holographic principle also states that at most there is one degree of freedom (or 1 Boltzmann constant k unit of maximum entropy) for every four Planck areas in that theory, i.e. S\le A/4 in natural units.

Using theoretical arguments based on the holographic principle, many physicists suggest that 11-dimensional M-theory, which is described in many sectors by matrix string theory, in other sectors by perturbative string theory could ultimately form a complete theory of everything.[1][2]

Contents

[edit] 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".[3]

[edit] 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.

[edit] 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.

[edit] Reasons for the holographic principle

Black holes are maximal entropy objects [4], 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.[5]

According to the second law of thermodynamics, greater mass entails greater entropy. Because entropy is an extensive variable, being directly proportional to mass, which is proportional to volume (all else being equal, including the density of the mass), the holographic principle is counter-intuitive to many physicists, as it states that the maximal limit of entropy is directly proportional to the surface area of the region, not its volume.

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 isomorphic to the information "inscribed" on the spherical surface of its boundary [6].

[edit] Limit on information density

Entropy, if considered as information (see information entropy), can ultimately be measured in bits or nats. One nat corresponds to about 1.44 bits, and 1 nat corresponds to four Planck areas [6]. The total quantity of bits is related to the total degrees of freedom of matter/energy. The bits themselves would encode information about the states which that matter/energy is occupying.

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 fundamental particles. As the 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.

Some scientists may argue that the most rigorous realization of the holographic principle is the AdS/CFT correspondence by Juan Maldacena. However, J.D. Brown and Marc Henneaux[7] 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. The AdS/CFT correspondence of Maldacena on the other hand is also known as the Maldacena-Conjecture which is due to the fact that it still lacks a mathematical proof.

[edit] 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.


[edit] See also

[edit] References

General

  • Bousso, Raphael (2002). "The holographic principle". Reviews of Modern Physics 74: 825–874. arXiv:hep-th/0203101. 

Citations

  1. ^ Lloyd, Seth (2002-05-24). "Computational Capacity of the Universe". Physics Review Letters; American Physical Society 88 (23). doi:10.1103/PhysRevLett.88.237901. 
  2. ^ Davies, Paul. Multiverse Cosmological Models and the Anthropic Principle. CTNS. Retrieved on 2008-03-14.
  3. ^ Information in the Holographic Universe
  4. ^ Bekenstein, Jacob D. (January 1981 (Revision: August 25, 1980.)). "Universal upper bound on the entropy-to-energy ratio for bounded systems". Physical Review DD 23 (215). 
  5. ^ Majumdar, Parthasarathi (1998). "Black Hole Entropy and Quantum Gravity". arXiv: General Relativity and Quantum Cosmology. arXiv:gr-qc/9807045. 
  6. ^ a b Bekenstein, Jacob D. (August 2003). "Information in the Holographic Universe — Theoretical results about black holes suggest that the universe could be like a gigantic hologram". Scientific American: p. 59. 
  7. ^ 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

[edit] External links