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Bekenstein bound
 
 
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In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, the Bekenstein bound is a conjectured limit on the entropy
Entropy

In many branches of science, entropy is a measure of the disorder of a system. The concept of entropy is particularly notable as it is applied across physics, information theory and mathematics....
 S or information
Information

Information as a Conveyed concept has a diversity of meanings, from everyday usage to technical settings. Generally speaking, the concept of information is closely related to notions of constraint, communication, control system, data, form, instruction, knowledge, Meaning , stimulation, pattern, perception, and knowledge representation....
 that can be contained within a region of space containing a known energy. It implies that information must be material, requiring finite size and energy. In Computer Science
Computer science

Computer science is the study of the theoretical foundations of information and computation, and of practical techniques for their implementation and application in computer systems....
, this implies that there is a maximum information processing rate and that Turing machines, with their (by definition) infinite memory tape, are physically impossible if they are to have a finite size and bounded energy. The bound was originally found by Jacob Bekenstein
Jacob Bekenstein

Jacob David Bekenstein is a physicist who has contributed to the foundation of black hole thermodynamics and to other aspects of the connections between physical information and gravitation....
 in the form

where R is loosely defined as the radius of the region, and E is the energy of the contained matter as measured when the matter is moved to an infinite distance, i.e., accounting for binding force potential energies.






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In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, the Bekenstein bound is a conjectured limit on the entropy
Entropy

In many branches of science, entropy is a measure of the disorder of a system. The concept of entropy is particularly notable as it is applied across physics, information theory and mathematics....
 S or information
Information

Information as a Conveyed concept has a diversity of meanings, from everyday usage to technical settings. Generally speaking, the concept of information is closely related to notions of constraint, communication, control system, data, form, instruction, knowledge, Meaning , stimulation, pattern, perception, and knowledge representation....
 that can be contained within a region of space containing a known energy. It implies that information must be material, requiring finite size and energy. In Computer Science
Computer science

Computer science is the study of the theoretical foundations of information and computation, and of practical techniques for their implementation and application in computer systems....
, this implies that there is a maximum information processing rate and that Turing machines, with their (by definition) infinite memory tape, are physically impossible if they are to have a finite size and bounded energy. The bound was originally found by Jacob Bekenstein
Jacob Bekenstein

Jacob David Bekenstein is a physicist who has contributed to the foundation of black hole thermodynamics and to other aspects of the connections between physical information and gravitation....
 in the form

where R is loosely defined as the radius of the region, and E is the energy of the contained matter as measured when the matter is moved to an infinite distance, i.e., accounting for binding force potential energies. Note that while gravity plays a significant role in its enforcement, the bound is independent of Newton's Constant
Gravitational constant

The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitation between objects with mass....
 .

Bekenstein derived the bound from heuristic arguments involving black holes. If a system exists that violates the bound, Bekenstein argued that it would be possible to violate the Second Law of Thermodynamics
Second law of thermodynamics

The second law of thermodynamics is an expression of the universal law of increasing entropy, stating that the entropy of an isolated system which is not in Thermodynamic equilibrium will tend to increase over time, approaching a maximum value at equilibrium....
 by lowering it into a black hole. However, no precise formulation of it is known, with the correct definitions of radius, energy and entropy all subject to debate. There is also considerable debate that any formulation of the bound exists.

Although the derivation of the bound is only valid for weakly gravitating systems, it happens that the Bekenstein-Hawking Entropy
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....
 of three-dimensional black holes exactly saturates the bound

where A is the two-dimensional area of the black hole's event horizon in units of the Planck area, .

The bound is closely associated with 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....
, the Holographic Principle
Holographic principle

The holographic principle is a property of quantum gravity theories which resolves the black hole information paradox within string theory. First proposed by Gerard 't Hooft, it was given a precise string-theory interpretation by Leonard Susskind....
 and the Covariant Entropy Bound of quantum gravity, and can be derived from a conjectured strong form of the latter. However, while the bound played an important role alongside their development, these topics are generally on firmer theoretical footing than the Bekenstein Bound, with more precise formulations and more consistent theoretical support.

See also

  • Holographic Principle
    Holographic principle

    The holographic principle is a property of quantum gravity theories which resolves the black hole information paradox within string theory. First proposed by Gerard 't Hooft, it was given a precise string-theory interpretation by Leonard Susskind....
  • 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....


External links

of Gerard 't Hooft
Gerardus 't Hooft

Gerardus 't Hooft is a professor in theoretical physics at Utrecht University, the Netherlands. He shared the 1999 Nobel Prize in Physics with Martinus J....
.