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Bousso's Holographic Bound
The Bousso bound captures a fundamental relation between quantum information and the geometry of space and time. It appears to be an imprint of a unified theory that combines quantum mechanics with Einstein's general relativity. The study of black hole thermodynamics and the information paradox led to the idea of the holographic principle: the entropy of matter and radiation in a spatial region cannot exceed the Bekenstein–Hawking entropy of the boundary of the region, which is proportional to the boundary area. However, this "spacelike" entropy bound fails in cosmology; for example, it does not hold true in our universe. Raphael Bousso showed that the spacelike entropy bound is violated more broadly in many dynamical settings. For example, the entropy of a collapsing star, once inside a black hole, will eventually exceed its surface area. Due to relativistic length contraction, even ordinary thermodynamic systems can be enclosed in an arbitrarily small area. To preserve the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. As the study of the statistical mechanics of black-body radiation led to the development 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. Overview The second law of thermodynamics requires that black holes have entropy. If black holes carried no entropy, it would be possible to violate the second law by throwing mass into the black hole. The increase of the entropy of the black hole more than compensates for the decrease of the entropy carried by the object that was swallowed. In 1972, Jacob Bekenstein conjectured that black holes should have an entropy, where by the same year, he proposed no-hair theorems. In 1973 Bekenstein suggested \frac\approx 0 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Black Hole Information Paradox
The black hole information paradox is a puzzle that appears when the predictions of quantum mechanics and general relativity are combined. The theory of general relativity predicts the existence of black holes that are regions of spacetime from which nothing — not even light — can escape. In the 1970s, Stephen Hawking applied the rules of quantum mechanics to such systems and found that an isolated black hole would emit a form of radiation called Hawking radiation. Hawking also argued that the detailed form of the radiation would be independent of the initial state of the black hole and would depend only on its mass, electric charge and angular momentum. The information paradox appears when one considers a process in which a black hole is formed through a physical process and then evaporates away entirely through Hawking radiation. Hawking's calculation suggests that the final state of radiation would retain information only about the total mass, electric charge and angular m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Holographic Principle
The holographic principle is an axiom in string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region — such as a light-like boundary like a gravitational horizon. First proposed by Gerard 't Hooft, it was given a precise string-theory interpretation by Leonard Susskind, who combined his ideas with previous ones of 't Hooft and Charles Thorn. Leonard Susskind said, “The three-dimensional world of ordinary experience––the universe filled with galaxies, stars, planets, houses, boulders, and people––is a hologram, an image of reality coded on a distant two-dimensional surface." As pointed out by Raphael Bousso, Thorn observed in 1978 that string theory admits a lower-dimensional description in which gravity emerges from it in what would now be called a holographic way. The prime example of holography is the AdS/CFT correspondence. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacob Bekenstein
Jacob David Bekenstein ( he, יעקב בקנשטיין; May 1, 1947 – August 16, 2015) was an American and Israeli theoretical physicist who made fundamental contributions to the foundation of black hole thermodynamics and to other aspects of the connections between information and gravitation. Biography Jacob Bekenstein was born in Mexico City to Joseph and Esther (''née'' Vladaslavotsky), Polish Jews who immigrated to Mexico. He moved to the United States during his early life, gaining U.S. citizenship in 1968. He was also a citizen of Israel. Bekenstein attended the Polytechnic Institute of Brooklyn, now known as the New York University Tandon School of Engineering, obtaining both an undergraduate degree and a Master of Science degree in 1969. He went on to receive a Doctor of Philosophy degree from Princeton University, working under the direction of John Archibald Wheeler, in 1972. Bekenstein had three children with his wife, Bilha. All three children, Yehonadav, Uriya ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, sociology, weather science, climate change, and information systems including the transmission of information in telecommunication. The thermodynamic concept was referred to by Scottish scientist and engineer William Rankine in 1850 with the names ''thermodynamic function'' and ''heat-potential''. In 1865, German physicist Rudolf Clausius, one of the leading founders of the field of thermodynamics, defined it as the quotient of an infinitesimal amount of hea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Raphael Bousso
Raphael Bousso () (born 1971) is a theoretical physicist and cosmologist. He is a professor at the Berkeley Center for Theoretical Physics in the Department of Physics, UC Berkeley. He is known for the Bousso bound on the information content of the universe. With Joseph Polchinski, Bousso proposed the string theory landscape as a solution to the cosmological constant problem. Life and career Bousso was born in Haifa, Israel, the son of late scientisDino Bousso He grew up near Augsburg, Germany, where he studied physics from 1990 until 1993. Bousso earned his Ph.D. at Cambridge University in 1997; his doctoral advisor was Stephen Hawking. Bousso did postdoctoral research at Stanford University until 2000, and at the Kavli Institute for Theoretical Physics in Santa Barbara until 2002. In 2002/03, Bousso was a fellow at the Harvard University physics department and the Radcliffe Institute for Advanced Study. Since 2002, he has been a professor in the physics department at the Uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trapped Surface
Closed trapped surfaces are a concept used in black hole solutions of general relativity which describe the inner region of an event horizon. Roger Penrose defined the notion of closed trapped surfaces in 1965. A trapped surface is one where light is not moving away from the black hole. The boundary of the union of all trapped surfaces around a black hole is called an apparent horizon. A related term trapped null surface is often used interchangeably. However, when discussing causal horizons, trapped null surfaces are defined as only null vector fields giving rise to null surfaces. But marginally trapped surfaces may be spacelike, timelike or null. Definition They are spacelike surfaces (topological spheres, tubes, etc.) with restricted bounds, their area tending to decrease locally along any possible future direction and with a dual definition with respect to the past. The trapped surface is a spacelike surface of co-dimension 2, in a Lorentzian spacetime. It follows that any n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trapped Surface
Closed trapped surfaces are a concept used in black hole solutions of general relativity which describe the inner region of an event horizon. Roger Penrose defined the notion of closed trapped surfaces in 1965. A trapped surface is one where light is not moving away from the black hole. The boundary of the union of all trapped surfaces around a black hole is called an apparent horizon. A related term trapped null surface is often used interchangeably. However, when discussing causal horizons, trapped null surfaces are defined as only null vector fields giving rise to null surfaces. But marginally trapped surfaces may be spacelike, timelike or null. Definition They are spacelike surfaces (topological spheres, tubes, etc.) with restricted bounds, their area tending to decrease locally along any possible future direction and with a dual definition with respect to the past. The trapped surface is a spacelike surface of co-dimension 2, in a Lorentzian spacetime. It follows that any n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bekenstein Bound
In physics, the Bekenstein bound (named after Jacob Bekenstein) is an upper limit on the thermodynamic entropy ''S'', or Shannon entropy ''H'', that can be contained within a given finite region of space which has a finite amount of energy—or conversely, the maximal amount of information required to perfectly describe a given physical system down to the quantum level. It implies that the information of a physical system, or the information necessary to perfectly describe that system, must be finite if the region of space and the energy are finite. In computer science this implies that non-finite models such as Turing machines are not realizable as finite devices. Equations The universal form of the bound was originally found by Jacob Bekenstein in 1981 as the inequality : S \leq \frac, where ''S'' is the entropy, ''k'' is the Boltzmann constant, ''R'' is the radius of a sphere that can enclose the given system, ''E'' is the total mass–energy including any rest masses, ''ħ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Model
The Standard Model of particle physics is the theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists worldwide, with the current formulation being finalized in the mid-1970s upon experimental confirmation of the existence of quarks. Since then, proof of the top quark (1995), the tau neutrino (2000), and the Higgs boson (2012) have added further credence to the Standard Model. In addition, the Standard Model has predicted various properties of weak neutral currents and the W and Z bosons with great accuracy. Although the Standard Model is believed to be theoretically self-consistent and has demonstrated huge successes in providing experimental predictions, it leaves some physics beyond the standard m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
