In physics, the Bekenstein bound imposes a limit on the entropy S or information that can be contained within a three-dimensional volume. The bound was originally found by Jacob Bekenstein in the form Physics (from the Greek, (phúsis), nature and (phusiké), knowledge of nature) is the science concerned with the discovery and understanding of the fundamental laws which govern matter, energy, space, and time. ... Ice melting - classic example of entropy increasing[1] described in 1862 by Rudolf Clausius as an increase in the disgregation of the molecules of the body of ice. ... Information is the result of processing, manipulating and organizing data in a way that adds to the knowledge of the person receiving it. ... Jacob David Bekenstein (born May 1, 1947) is a physicist who has contributed to the foundation of black hole thermodynamics and to other aspects of the connections between information and gravitation. ...

,

where R is 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.

Applying this to the area A of the event horizon of a black hole, we find that since a black hole's radius and energy are both proportional to its mass, the limit to the entropy (and information) contained within a spherical volume is proportional to the area: This article or section is in need of attention from an expert on the subject. ... A black hole is an object predicted by general relativity,[1] with a gravitational field so powerful that even electromagnetic radiation (including light itself) cannot escape its pull. ...

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

Since a black hole has maximal entropy, this then imposes an upper limit for the amount of entropy that can be contained within any region. Gerard t' Hooft later generalized it to the form involving A/4. This is the holographic principle. The argument, in more detail, is that since the bound is known to hold for black holes on relatively firm model-independent grounds, it must hold more generally based on the second law of thermodynamics. If the bound was violated by a region of space that didn't contain a black hole, then mass could be brought into the region in order to form a black hole, resulting in a net decrease of entropy. If this argument is correct, then it is often taken to imply that spacetime is discrete, since continuous spacetime should be able hold an infinite amount of information within a finite volume. Gerard t Hooft at Harvard University Gerardus (Gerard) t Hooft [ut-hooft] (The prefix ’t is pronounced as ‘ut’ and stands for ‘het’) (born July 5, 1946) is a professor in theoretical physics at Utrecht University, The Netherlands. ... The holographic principle is a speculative conjecture about quantum gravity theories, proposed by Gerard t Hooft and improved and promoted by Leonard Susskind, claiming that all of the information contained in a volume of space can be represented by a theory that lives in the boundary of that region. ... The second law of thermodynamics is an expression of the universal law of increasing entropy. ...

Intuitively, the motivation for the Bekenstein bound is that, regardless of the existence of black holes in our universe, event horizons exist. An event horizon will be perceived by any observer who is in an accelerated frame of reference (which, by the equivalence principle, is equivalent to being in a gravitational field). When pairs of particles are produced at the horizon due to vacuum fluctuations, one comes to the observer, while the other moves out of the region of the universe observable to her. As seen by the observer, the horizon therefore radiates. All event horizons must look the same locally (except for differences due to the observer's own motion), since otherwise it would be possible for the observer to use the differences between them to obtain information about what was behind them. A horizon thus looks like a generic black-body radiator with a temperature . (In the special case where the horizon is that of a black hole, the radiation being described is that of black hole evaporation.) The entropy of the region behind the event horizon was taken there by the members of the particle pairs that went away from the observer rather than toward her. In relativity, the equivalence principle is applied to several related concepts dealing with gravitation and the uniformity of physical measurements in different frames of reference. ... As the temperature decreases, the peak of the black body radiation curve moves to lower intensities and longer wavelengths. ... In physics, Hawking radiation is thermal radiation emitted by black holes due to quantum effects. ...

See also

• Holographic Principle

The holographic principle is a speculative conjecture about quantum gravity theories, proposed by Gerard t Hooft and improved and promoted by Leonard Susskind, claiming that all of the information contained in a volume of space can be represented by a theory that lives in the boundary of that region. ...

References

• J. D. Bekenstein, "Generalized second law of thermodynamics in black hole physics", Phys. Rev. D 9, 3292 (1974).
• J. D. Bekenstein, "A universal upper bound on the entropy to energy ratio for bounded systems", Phys. Rev. D 23, 287 (1981).

Physical Review is one of the oldest and most-respected scientific journals publishing research on all aspects of physics. ... Physical Review is one of the oldest and most-respected scientific journals publishing research on all aspects of physics. ...

External links

• Home page of Gerard 't Hooft.
• Home page of Jacob Bekenstein.
• Generalized second law and the Bekenstein entropy bound in Gedankenexperiments with black holes