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****************************************************** Information http://en.wikipedia.org/wiki/Information ¿Qué es la información? foro.migui, Noviembre 27, 2008 http://foro.migui.com/smf/index.php/topic,7840.0.html ************************************************** Information about information "We live in a golden age of information. Never has so much of it been available so easily to so many of us. Information is power, it's money and, given how much of our life is lived online, defines part of our reality. But what exactly is information? We tend to think of it as human made, but since we're all a result of our DNA sequence, perhaps we should think of humans as being made of information. We like to think of it as abstract, but there's no information without physical manifestation, be it in the neurons in our brains, the pages of a book, or the electrical circuits in a computer. We like to think of it as floating on top of reality like a cork on an ocean, but insights from quantum physics suggest that reality might itself be made up of it. Perhaps we do live in a matrix after all. Is there a universal language of information? Are there fundamental laws of information processing? Is the world made up of information? What is quantum information? Can information be destroyed?" http://plus.maths.org/content/informationaboutinformation ************************************************** Glosario de Carlos von der Becke información, infodinámica http://www.geocities.com/ohcop/informac.html ****************************************************** Information. As a property in physics http://en.wikipedia.org/wiki/Information#As_a_property_in_physics Physical information http://en.wikipedia.org/wiki/Physical_information Fisher information “In mathematical statistics and information theory, the Fisher information (denoted ) is the variance of the score. Its role in the asymptotic theory of maximumlikelihood estimation was emphasized by the statistician R.A. Fisher (following some initial results by F. Y. Edgeworth).” (Wikipedia May 25, 2009) http://en.wikipedia.org/wiki/Fisher_information#cite_note0 ****************************************************** Historia del Tiempo: Stephen Hawking http://www.librosmaravillosos.com/historiatiempo/ ****************************************************** Black Hole and Entropy "entropía de Boltzmann" Entropy “Entropy is a concept applied across physics, information theory, mathematics and other branches of science and engineering. The following definition is shared across all these fields: where S is the conventional symbol for entropy. The sum runs over all microstates consistent with the given macrostate and is the probability of the ith microstate. The constant of proportionality k depends on what units are chosen to measure S. When SI units are chosen, we have k = k_{B} = Boltzmann's constant = 1.38066×10^{−23} J K^{−1}. If units of bits are chosen, then k = 1/ln(2) so that . ” (Wikipedia May 31, 2009) http://en.wikipedia.org/wiki/Entropy Entropía (termodinámica) “En termodinámica, la entropía (simbolizada como S) es la magnitud física que mide la parte de la energía que no puede utilizarse para producir trabajo. Es una función de estado de carácter extensivo y su valor, en un sistema aislado, crece en el transcurso de un proceso que se dé de forma natural. La palabra entropía procede del griego (ἐντροπία) y significa evolución o transformación” (Wikipedia, 31 de Mayo del 2009) http://es.wikipedia.org/wiki/Entrop%C3%ADa_(termodin%C3%A1mica) ****************************************************** 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 welldefined 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 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) Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08540 Center for Relativity Theory, The University of Texas at Austin, Austin, Texas 78712 Received 2 November 1972 “There are a number of similarities between blackhole physics and thermodynamics. Most striking is the similarity in the behaviors of blackhole area and of entropy: Both quantities tend to increase irreversibly. In this paper we make this similarity the basis of a thermodynamic approach to blackhole physics. After a brief review of the elements of the theory of information, we discuss blackhole physics from the point of view of information theory. We show that it is natural to introduce the concept of blackhole entropy as the measure of information about a blackhole interior which is inaccessible to an exterior observer. Considerations of simplicity and consistency, and dimensional arguments indicate that the blackhole entropy is equal to the ratio of the blackhole 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 blackhole entropy derives from the following generalized version of the second law: When common entropy goes down a black hole, the common entropy in the blackhole exterior plus the blackhole 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 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 is the Planck length. The black hole entropy is proportional to its area A. The fact that the black hole entropy is also the maximal entropy that can be squeezed within a fixed volume was the main observation that led to the holographic principle. The subscript BH either stands for "black hole" or "BekensteinHawking".”(Wikipedia May 25, 2009) http://en.wikipedia.org/wiki/Black_hole_thermodynamics#Black_hole_entropy fórmula de BekensteinHawking S = Akc^{3}/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/BekensteinHawkingFormula.html http://scienceworld.wolfram.com/physics/hBar.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_ref0 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 stringtheory 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 lightlike 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…
(Wikipedia May 25, 2009) http://en.wikipedia.org/wiki/Holographic_principle#cite_note0 Information in the Holographic Universe Theoretical results about black holes suggest that the universe could be like a gigantic hologram. Jacob D. Bekenstein, Scientific American, August 2003 p. 59. http://www.sciam.com/article.cfm?articleid=000AF07248911F0A97AE80A84189EEDF. ****************************************************** Hiperdimensiones Sobre el vacío cuántico, una hipótesis fractal. 2008/05/13 http://labellateoria.blogspot.com/2008/05/sobreelvacocunticounahiptesis.html Diez dimensiones, supercuerdas y fractales 2008/08/30 http://labellateoria.blogspot.com/2008/08/diezdimensionessupercuerdasy.html ¿ Cómo se entiende lo de la dimensión fractal negativa? ( Una anomalía) La bella teoria, 2006/05/19 http://labellateoria.blogspot.com/2006/05/cmoseentiendelodelad_114802531438773700.html ****************************************************** Gravedad Cuántica de Bucles la Gravedad Cuántica de Bucles de Lee Smolin dandan  15 Abril, 2007 http://dandan.balearweb.net/post/32798 (Cambio en proceso a http://dandax.wordpress.com/) You are made of spacetime 12 August 2006 by Davide Castelvecchi and Valerie Jamieson Magazine issue 2564, http://www.newscientist.com/issue/2564 http://www.newscientist.com/article/mg19125645.800youaremadeofspacetime.html?full=true Tú estás hecho de espaciotiempo Escrito por Kanijo en Física, 13 de Abril de 2007 