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Black Hole Information Paradox
The black hole information paradox is a paradox 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 semiclassical approach of quantum field theory in curved spacetime to such systems and found that an isolated black hole would emit a form of radiation (now called Hawking radiation in his honor). He also argued that the detailed form of the radiation would be independent of the initial state of the black hole, and 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Black Hole - Messier 87 Crop Max Res
Black is a color that results from the absence or complete absorption of visible light. It is an achromatic color, without chroma, like white and grey. It is often used symbolically or figuratively to represent darkness.Eva Heller, ''Psychologie de la couleur – effets et symboliques'', pp. 105–26. Black and white have often been used to describe opposites such as good and evil, the Dark Ages versus the Age of Enlightenment, and night versus day. Since the Middle Ages, black has been the symbolic color of solemnity and authority, and for this reason it is still commonly worn by judges and magistrates. Black was one of the first colors used by artists in Neolithic cave paintings. It was used in ancient Egypt and Greece as the color of the underworld. In the Roman Empire, it became the color of mourning, and over the centuries it was frequently associated with death, evil, witches, and magic. In the 14th century, it was worn by royalty, clergy, judges, and government of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wave Function
In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi (letter), psi, respectively). Wave functions are complex number, complex-valued. For example, a wave function might assign a complex number to each point in a region of space. The Born rule provides the means to turn these complex probability amplitudes into actual probabilities. In one common form, it says that the squared modulus of a wave function that depends upon position is the probability density function, probability density of measurement in quantum mechanics, measuring a particle as being at a given place. The integral of a wavefunction's squared modulus over all the system's degrees of freedom must be equal to 1, a condition called ''normalization''. Since the wave function is complex-valued, only its relative phase and relative magnitud ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacob Bekenstein
Jacob David Bekenstein (; May 1, 1947 – August 16, 2015) was a Mexican-born American-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. Early life and education 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 and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermodynamics
Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of thermodynamics, which convey a quantitative description using measurable macroscopic physical quantity, physical quantities but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to various topics in science and engineering, especially physical chemistry, biochemistry, chemical engineering, and mechanical engineering, as well as other complex fields such as meteorology. Historically, thermodynamics developed out of a desire to increase the thermodynamic efficiency, efficiency of early steam engines, particularly through the work of French physicist Nicolas Léonard Sadi Carnot, Sadi Carnot (1824) who believed that engine efficiency was the key that could help France win ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Irreversible Process
In thermodynamics, an irreversible process is a thermodynamic processes, process that cannot be undone. All complex natural processes are irreversible, although a phase transition at the coexistence temperature (e.g. melting of ice cubes in water) is well approximated as reversible. A change in the thermodynamic state of a system and all of its surroundings cannot be precisely restored to its initial state by infinitesimal changes in some property of the system without expenditure of energy. A system that undergoes an irreversible process may still be capable of returning to its initial state. Because entropy is a state function, the change in entropy of the system is the same whether the process is reversible or irreversible. However, the impossibility occurs in restoring the Environment (systems), environment to its own initial conditions. An irreversible process increases the total entropy of the system and its surroundings. The second law of thermodynamics can be used to dete ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bijection
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between two sets such that each element of the second set (the codomain) is the image of exactly one element of the first set (the domain). Equivalently, a bijection is a relation between two sets such that each element of either set is paired with exactly one element of the other set. A function is bijective if it is invertible; that is, a function f:X\to Y is bijective if and only if there is a function g:Y\to X, the ''inverse'' of , such that each of the two ways for composing the two functions produces an identity function: g(f(x)) = x for each x in X and f(g(y)) = y for each y in Y. For example, the ''multiplication by two'' defines a bijection from the integers to the even numbers, which has the ''division by two'' as its inverse function. A function is bijective if and only if it is both injective (or ''one-to-one'')—meaning that each element in the codomain is mappe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Reversibility
In mathematics and physics, time-reversibility is the property (mathematics), property of a process whose governing rules remain unchanged when the direction of its sequence of actions is reversed. A deterministic process is time-reversible if the time-reversed process satisfies the same dynamic equation (other), dynamic equations as the original process; in other words, the equations are invariant (mathematics), invariant or symmetrical under a change in the Sign (mathematics), sign of time. A stochastic process is reversible if the statistical properties of the process are the same as the statistical properties for time-reversed data from the same process. Mathematics In mathematics, a dynamical system is time-reversible if the forward evolution is one-to-one function, one-to-one, so that for every state there exists a transformation (an Involution (mathematics), involution) π which gives a one-to-one mapping between the time-reversed evolution of any one state and t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Determinism
Determinism is the Metaphysics, metaphysical view that all events within the universe (or multiverse) can occur only in one possible way. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping motives and considerations. Like Eternalism (philosophy of time), eternalism, determinism focuses on particular events rather than the future as a concept. Determinism is often contrasted with free will, although some philosophers claim that the two are compatibilism, compatible. A more extreme antonym of determinism is indeterminism, or the view that events are not deterministically caused but rather occur due to random chance. Historically, debates about determinism have involved many philosophical positions and given rise to multiple varieties or interpretations of determinism. One topic of debate concerns the scope of determined systems. Some philosophers have maintained that the entire universe is a single determinate system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schrödinger Equation
The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after Erwin Schrödinger, an Austrian physicist, who postulated the equation in 1925 and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933. Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in classical mechanics. Given a set of known initial conditions, Newton's second law makes a mathematical prediction as to what path a given physical system will take over time. The Schrödinger equation gives the evolution over time of the wave function, the quantum-mechanical characterization of an isolated physical system. The equation was postulated by Schrödinger based on a postulate of Louis de Broglie that all matter has an associated matter wave. The equati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Gravity
Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics. It deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vicinity of black holes or similar compact astrophysical objects, as well as in the early stages of the universe moments after the Big Bang. Three of the four fundamental forces of nature are described within the framework of quantum mechanics and quantum field theory: the Electromagnetism, electromagnetic interaction, the Strong interaction, strong force, and the Weak interaction, weak force; this leaves gravity as the only interaction that has not been fully accommodated. The current understanding of gravity is based on Albert Einstein's general theory of relativity, which incorporates his theory of special relativity and deeply modifies the understanding of concepts like time and space. Although general relativity is highly regarded for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Von Neumann Entropy
In physics, the von Neumann entropy, named after John von Neumann, is a measure of the statistical uncertainty within a description of a quantum system. It extends the concept of Gibbs entropy from classical statistical mechanics to quantum statistical mechanics, and it is the quantum counterpart of the Shannon entropy from classical information theory. For a quantum-mechanical system described by a density matrix , the von Neumann entropy is S = - \operatorname(\rho \ln \rho), where \operatorname denotes the trace and \operatorname denotes the matrix version of the natural logarithm. If the density matrix is written in a basis of its eigenvectors , 1\rangle, , 2\rangle, , 3\rangle, \dots as \rho = \sum_j \eta_j \left, j \right\rang \left\lang j \ , then the von Neumann entropy is merely S = -\sum_j \eta_j \ln \eta_j . In this form, ''S'' can be seen as the Shannon entropy of the eigenvalues, reinterpreted as probabilities. The von Neumann entropy and quantities based upon i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
