Jacob David Bekenstein
Investigó
la relación entre los agujeros negros, su entropía
y su relación con la teoría de la información. ”...Si
preguntamos de qué se compone el mundo físico, se nos responderá que de
"materia y energía". Pero quien sepa algo de ingeniería, biología y
física nos citará también la información como elemento no menos
importante...” La
información en el universo holográfico (Inicio del artículo) Jacob
D. Bekenstein,, Scientific American Latinoamérica, año 2 N. 15, Octubre de
2003, pág. 38-45 Regresar
a Personajes Fundamentales
de la Informática Regresar a www.fgalindosoria.com fórmula de Bekenstein-Hawking S = Akc3 / 4Għ S entropía,
A área, k constante de Boltzmann, c velocidad de la luz, G constante de la gravitación, ħ=h/2π,
donde h es la constante de Planck. http://foro.migui.com/smf/index.php/topic,1676.0.html http://scienceworld.wolfram.com/physics/Bekenstein-HawkingFormula.html
http://scienceworld.wolfram.com/physics/h-Bar.html Black hole entropy Information in the Holographic
Universe 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 Bekenstein-Hawking entropy Scholarpedia 20140418 The Bekenstein-Hawking entropy or
black hole entropy is the amount of entropy
that must be assigned to a black
hole in order for it to comply with the laws of thermodynamics as they
are interpreted by observers external to that black
hole. This is particularly true for the first and second laws. Black hole
entropy is a concept with geometric root but with many physical consequences.
It ties together notions from gravitation, thermodynamics and quantum theory,
and is thus regarded as a window into the as yet mostly hidden world of quantum gravity. http://www.scholarpedia.org/article/Bekenstein-Hawking_entropy Jacob Bekenstein Wikipedia, 20140407 "Jacob David Bekenstein (Hebrew:
יעקב
בקנשטיין) (born May 1, 1947)
is Mexican-Israeli
theoretical physicist who has contributed
to the foundation of black hole thermodynamics and to other
aspects of the connections between information and gravitation. ...... Bekenstein was born in Mexico
City, Mexico.
He has been Arnow Professor of Astrophysics
at Ben-Gurion University and is now Polak Professor
of Theoretical Physics at the Hebrew University of Jerusalem. He
is a member of the Israel Academy of Sciences
and Humanities and of The World Jewish Academy of Sciences. ...... 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. Hawking had
initially opposed Bekenstein's idea.[2] Based on his black-hole thermodynamics work, Bekenstein
also demonstrated the Bekenstein bound: there is a maximum to the
amount of information that can potentially be stored in a given finite region
of space which has a finite amount of energy (which is similar to the holographic principle). ..... Wolf Prize in Physics in 2012. " 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 "....Uno de los resultados alentadores que se han
hallado en las investigaciones de la teoría de cuerdas es la derivación de la
fórmula de la entropía conocida como de Bekenstein-Hawking para los agujeros
negros, la cual se obtiene con la enumeración de los estados microscópicos de
las cuerdas que formarían un agujero negro. Esto ocurre si se admite que el
área del horizonte es análoga a la entropía, lo que implica que la gravedad
superficial tiene que ser igual a todos los puntos del horizonte de sucesos,
del mismo modo que es igual a la temperatura en todos los puntos de un cuerpo
con equilibrio térmico. Aunque exista claramente una semejanza entre entropía
y área del horizonte de sucesos, no aparece tan obvio el modo de identificar
el área con la entropía de un agujero negro. ¿Qué se puede entender por
entropía de un agujero negro? La afirmación la encontramos en los trabajos formulados en 1972 por Jacob D. Bekenstein de la Universidad del Neguev, en Israel. Dice así: cuando se crea un agujero negro por obra de un colapso gravitatorio, rápidamente entra en una situación estacionaria caracterizado sólo por tres parámetros: la masa, el momento angular y la carga eléctrica. Al margen de estas tres propiedades, el agujero negro no conserva ninguna otra de las características del objeto que se contrajo. Esta conclusión, conocida coloquialmente como el teorema «un agujero negro no tiene pelo», fue demostrada por esas formulaciones en colaboración con Stephen Hawking de la Universidad de Cambridge, Werner Israel de la Universidad de Alberta y David C. Robinson del King's College de Londres. El teorema de la carencia de pelo supone que durante la contracción gravitatoria se pierde una gran cantidad de información. .... un agujero negro de una masa, momento angular y carga eléctrica determinados podría haber surgido del colapso de cualquiera de las muchísimas configuraciones diferentes de la materia. .... El principio de incertidumbre de la mecánica cuántica implica, sin embargo, que una partícula de masa m se comporta como una onda de longitud h/mc, donde h es la constante de Planck (la pequeña cifra de 6,62 x 10-27 ergios por segundo) y c es la velocidad de la luz. Para que una nube de partículas sea capaz de contraerse hasta formar un agujero negro, parece necesario que esa longitud de onda tenga un tamaño inferior al del agujero negro así formado. Resulta por eso que el número de configuraciones susceptibles de formar un agujero negro de una masa, momento angular y carga eléctrica determinados, aunque muy grande, puede ser finito. Bekenstein afirmó que es posible interpretar el logaritmo de este número como la entropía de un agujero negro. El logaritmo del número sería una medida del volumen de información que se pierde irremediablemente durante el colapso a través de un horizonte de sucesos al surgir un agujero negro." © 2002 Javier de Lucas http://platea.pntic.mec.es/~jdelucas/18descubrimientosbekensteinhawking.htm
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: |
Regresar a Personajes Fundamentales de la Informática
Creación de la página Cd. de México, 25
de Mayo del 2009
Ultima actualización 8 de Abril del 2014
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