Jacob David Bekenstein
Regresar a Personajes Fundamentales
de la Informática Regresar a www.fgalindosoria.com fórmula
de Bekenstein-Hawking S =
Akc3 / 4Għ Black hole
entropy “Black hole
entropy is the entropy carried by a black hole. If black holes carried no
entropy, it would be possible to violate the second law of thermodynamics by
throwing mass into the black hole. The only way to satisfy the second law is
to admit that the black holes have entropy whose increase more than
compensates for the decrease of the entropy carried by the object that was
swallowed. Starting from theorems proved
by Stephen Hawking, Jacob
Bekenstein conjectured that the black hole entropy was proportional to
the area of its event horizon divided by the Planck area. Later,
Stephen Hawking showed that black holes emit thermal Hawking radiation corresponding to a certain
temperature (Hawking temperature). Using the thermodynamic
relationship between energy, temperature and entropy, Hawking was able to
confirm Bekenstein's conjecture and fix the constant of proportionality at
1/4:
where k
is Boltzmann's constant, and http://en.wikipedia.org/wiki/Black_hole_thermodynamics#Black_hole_entropy Jacob David
Bekenstein “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.
He was born in Mexico City, Mexico to Israeli Jewish settlers… …In 1972,
Bekenstein was the first to suggest that black holes should have a well-defined
entropy.
Bekenstein also formulated the generalized second law of thermodynamics, black hole thermodynamics, for systems
including black holes. Both contributions were affirmed when Stephen
Hawking proposed the existence of Hawking radiation two years later...”
(Wikipedia May 25, 2009) http://en.wikipedia.org/wiki/Jacob_Bekenstein Jacob
David Bekenstein “Jacob David Bekenstein (nacido el 1 de mayo de 1947 en la Ciudad de México) es un físico teórico que investiga la relación entre los agujeros negros, su entropía y su relación con la teoría de la información.” (Wikipedia, 29/viii/2010) http://es.wikipedia.org/wiki/Jacob_D._Bekenstein Bekenstein bound “In physics, the Bekenstein
bound is a conjectured limit on the entropy S or information
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, 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 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 G.” (Wikipedia May 25, 2009) http://en.wikipedia.org/wiki/Bekenstein_bound Black Holes and
Entropy Jacob D. Bekenstein, Phys. Rev. D 7, 2333 - 2346 (1973) Received 2 November 1972 “There are a number of similarities between black-hole physics and
thermodynamics. Most striking is the similarity in the behaviors of
black-hole area and of entropy: Both quantities tend to increase
irreversibly. In this paper we make this similarity the basis of a
thermodynamic approach to black-hole physics. After a brief review of the
elements of the theory of information, we discuss black-hole physics from the
point of view of information theory. We show that it is natural to introduce
the concept of black-hole entropy as the measure of information about a
black-hole interior which is inaccessible to an exterior observer.
Considerations of simplicity and consistency, and dimensional arguments
indicate that the black-hole entropy is equal to the ratio of the black-hole
area to the square of the Planck length times a dimensionless constant of
order unity. A different approach making use of the specific properties of
Kerr black holes and of concepts from information theory leads to the same
conclusion, and suggests a definite value for the constant. The physical
content of the concept of black-hole entropy derives from the following
generalized version of the second law: When common entropy goes down a black
hole, the common entropy in the black-hole exterior plus the black-hole
entropy never decreases. The validity of this version of the second law is
supported by an argument from information theory as well as by several examples.” (Abstract) http://prola.aps.org/abstract/PRD/v7/i8/p2333_1 fórmula de
Bekenstein-Hawking S = Akc3/4Għ http://foro.migui.com/phpbb/viewtopic.php?p=21850&sid=97badedd794728486288b8dbd82579c4 http://foro.migui.com/phpbb/viewtopic.php?t=1676&sid=d9c73bcc71714a1389819d31c82ab093 http://scienceworld.wolfram.com/physics/Bekenstein-HawkingFormula.html
http://scienceworld.wolfram.com/physics/h-Bar.html The Black Hole
Information Loss Problem Original by
Warren G. Anderson 1996., Usenet Physics
FAQ “In 1975
Hawking and Bekenstein made a remarkable connection between thermodynamics,
quantum mechanics and black holes, which predicted that black holes will
slowly radiate away. (see Relativity FAQ Hawking Radiation). It was soon realized that this
prediction created an information loss problem that has since become an
important issue in quantum gravity.” http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/info_loss.html 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 precisely the same state. This is a contentious
subject since it violates a commonly assumed tenet of science—that in
principle complete information about a physical system at one point in
time should determine its state at any other time.” (Wikipedia May 25, 2009) http://en.wikipedia.org/wiki/Black_hole_information_paradox#cite_ref-0 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. Much as the study of the
statistical mechanics of black body radiation led to the advent of the theory
of quantum mechanics, the effort to understand the
statistical mechanics of black holes has had a deep impact upon the
understanding of quantum gravity, leading to the formulation of
the holographic principle.” (Wikipedia May 25,
2009) http://en.wikipedia.org/wiki/Black_hole_thermodynamics 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.[1][2][3] 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
of the event horizon… 1. ^ Susskind, L., "The Black Hole War
- My Battle with Stephen Hawking to Make the World Safe for Quantum
Mechanics", Little, Brown and Company (2008) 2.
^ Lloyd, Seth (2002-05-24). "Computational Capacity
of the Universe". Physics Review Letters; American
Physical Society 88 (23): 237901. doi:. http://link.aps.org/abstract/PRL/v88/e237901. Retrieved on 2008-03-14. 3.
^ Davies, Paul. "Multiverse
Cosmological Models and the Anthropic Principle". CTNS. http://www.google.com/search?hl=en&lr=&as_qdr=all&q=holographic+everything+site%3Actnsstars.org. Retrieved on 2008-03-14.” (Wikipedia May
25, 2009) http://en.wikipedia.org/wiki/Holographic_principle#cite_note-0 Information in
the Holographic Universe. (A
fundamental Article, FGS May 31, 2009) Jacob David Bekenstein,
Scientific American, Volume 289, Number 2, August 2003 Theoretical
results about black holes suggest that the universe could be like a gigantic
hologram. http://www.sciam.com/article.cfm?articleid=000AF072-4891-1F0A-97AE80A84189EEDF. Information in
the Holographic Universe JACOB D.
BEKENSTEIN, Istanbul- August 10th 2003, http://gulizk.com Scientific
American, August 2003 http://www.sufizmveinsan.com/fizik/holographic.html La información en el universo holográfico (Inicio del artículo) Jacob D. Bekenstein,, Scientific American Latinpamerica,
año 2 N. 15, Octubre de 2003, pág. 38-45 En La información en el universo holográfico Bekenstein, Jacob D., Temas Investigación y Ciencia año 2006: 43 -Fronteras de la física Información y Entropía Guillermo Agudelo Murguía, José Guillermo Alcalá Rivero, Evolución y Ambiente (Comentarios al artículo La Información en el Universo Holográfico. Jacob D. Bekenstein. Scientific American Latinoamérica Año 2 No. 15 octubre de 2003) http://www.iieh.com/Informacion/articulos_informacion01.php Relación de la entropía con la Teoría de la información “Recientes estudios han podido establecer una relación
entre la entropía física y la entropía de la teoría de la información gracias a la
revisión de la física de los agujeros
negros. Según la nueva teoría de Jacob D. Bekenstein el bit de información
sería equivalente a una superficie de valor 1/4 del área de Planck. De hecho,
en presencia de agujeros negros la segunda ley de la termodinámica
sólo puede cumplirse si se introduce la entropía generalizada o suma de la
entropía convencional (Sconv) más un factor dependiente del
área total (A) de agujeros negros existente en el universo, del
siguiente modo: |
is
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