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Hole Argument
In general relativity, the hole argument is an apparent paradox that much troubled Albert Einstein while developing his famous field equations. Some philosophers of physics take the argument to raise a problem for '' manifold substantialism'', a doctrine that the manifold of events in spacetime is a "substance" which exists independently of the metric field defined on it or the matter within it. Other philosophers and physicists disagree with this interpretation, and view the argument as a confusion about gauge invariance and gauge fixing instead. Einstein's hole argument In a usual field equation, knowing the source of the field, and the boundary conditions, determines the field everywhere. For example, if we are given the current and charge density and appropriate boundary conditions, Maxwell's equations determine the electric and magnetic fields. They do not determine the vector potential though, because the vector potential depends on an arbitrary choice of gauge. Einstein n ...
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General Relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime. In particular, the ' is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of second order partial differential equations. Newton's law of universal gravitation, which describes classical gravity, can be seen as a prediction of general relativity for the almost flat spacetime geometry around stationary mass distributions. Some predictions of general relativity, however, are beyond Newton's law of universal gravitat ...
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John Stachel
John Stachel (; born 29 March 1928) is an American physicist and philosopher of science. Biography Stachel earned his PhD at Stevens Institute of Technology in Physics about a topic in General relativity in 1958. After holding different teaching positions at Lehigh University and the University of Pittsburgh, he went 1964 to Boston University where he was professor of physics until his emeritation. In 1977, Stachel became the first editor of the Einstein Papers Project, then at Boston University. The first two volumes (out of a projected twenty-five) of ''The Collected Papers of Albert Einstein'' were published during his tenure. He is head of the Boston University Center for Einstein Studies and, together with Don Howard, publishes the book series ''Einstein Studies''. Stachel also authored a text, entitled ''Einstein: From 'B' to 'Z'.'' In 2005 he delivered the British Academy The British Academy is the United Kingdom's national academy for the humanities and the soc ...
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Marcus Gaul
Marcus, Markus, Márkus or Mărcuș may refer to: * Marcus (name), a masculine given name * Marcus (praenomen), a Roman personal name Places * Marcus, a main belt asteroid, also known as (369088) Marcus 2008 GG44 * Mărcuş, a village in Dobârlău Commune, Covasna County, Romania * Marcus, Illinois, an unincorporated community * Marcus, Iowa, a city * Marcus, South Dakota, an unincorporated community * Marcus, Washington, a town * Marcus Island, Japan, also known as Minami-Tori-shima * Mărcuș River, Romania * Marcus Township, Cherokee County, Iowa Other uses * Markus, a beetle genus in family Cantharidae * ''Marcus'' (album), 2008 album by Marcus Miller * Marcus (comedian), finalist on ''Last Comic Standing'' season 6 * Marcus Amphitheater, Milwaukee, Wisconsin * Marcus Center, Milwaukee, Wisconsin * Marcus & Co., American jewelry retailer * Marcus by Goldman Sachs, an online bank * USS ''Marcus'' (DD-321), a US Navy destroyer (1919-1935) See also * Marcos (disambiguat ...
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Oxford University Press
Oxford University Press (OUP) is the university press of the University of Oxford. It is the largest university press in the world, and its printing history dates back to the 1480s. Having been officially granted the legal right to print books by decree in 1586, it is the second oldest university press after Cambridge University Press. It is a department of the University of Oxford and is governed by a group of 15 academics known as the Delegates of the Press, who are appointed by the vice-chancellor of the University of Oxford. The Delegates of the Press are led by the Secretary to the Delegates, who serves as OUP's chief executive and as its major representative on other university bodies. Oxford University Press has had a similar governance structure since the 17th century. The press is located on Walton Street, Oxford, opposite Somerville College, in the inner suburb of Jericho. For the last 500 years, OUP has primarily focused on the publication of pedagogical texts and ...
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Edward N
Edward is an English given name. It is derived from the Anglo-Saxon name ''Ēadweard'', composed of the elements '' ēad'' "wealth, fortune; prosperous" and '' weard'' "guardian, protector”. History The name Edward was very popular in Anglo-Saxon England, but the rule of the Norman and Plantagenet dynasties had effectively ended its use amongst the upper classes. The popularity of the name was revived when Henry III named his firstborn son, the future Edward I, as part of his efforts to promote a cult around Edward the Confessor, for whom Henry had a deep admiration. Variant forms The name has been adopted in the Iberian peninsula since the 15th century, due to Edward, King of Portugal, whose mother was English. The Spanish/Portuguese forms of the name are Eduardo and Duarte. Other variant forms include French Édouard, Italian Edoardo and Odoardo, German, Dutch, Czech and Romanian Eduard and Scandinavian Edvard. Short forms include Ed, Eddy, Eddie, Ted, Teddy and Ned ...
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The Principle Of Relativity (book)
In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference. For example, in the framework of special relativity the Maxwell equations have the same form in all inertial frames of reference. In the framework of general relativity the Maxwell equations or the Einstein field equations have the same form in arbitrary frames of reference. Several principles of relativity have been successfully applied throughout science, whether implicitly (as in Newtonian mechanics) or explicitly (as in Albert Einstein's special relativity and general relativity). Basic concepts Certain principles of relativity have been widely assumed in most scientific disciplines. One of the most widespread is the belief that any law of nature should be the same at all times; and scientific investigations generally assume that laws of nature are the same regardless of the person measuring them. These sorts ...
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Philosophy Of Space And Time
Philosophy of space and time is the branch of philosophy concerned with the issues surrounding the ontology and epistemology of space and time. While such ideas have been central to philosophy from its inception, the philosophy of space and time was both an inspiration for and a central aspect of early analytic philosophy. The subject focuses on a number of basic issues, including whether time and space exist independently of the mind, whether they exist independently of one another, what accounts for time's apparently unidirectional flow, whether times other than the present moment exist, and questions about the nature of identity (particularly the nature of identity over time). Ancient and medieval views The earliest recorded philosophy of time was expounded by the ancient Egyptian thinker Ptahhotep (c. 2650–2600 BC) who said: The ''Vedas'', the earliest texts on Indian philosophy and Hindu philosophy, dating back to the late 2nd millennium BC, describe ancient Hindu cosmol ...
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Erich Kretschmann
Erich Justus Kretschmann (14 July 1887 – 1973) was a German physicist. (Gebhardt gives a list of Kretschmann's publications.) Life Kretschmann was born in Berlin. He obtained his PhD at Berlin University in 1914 with his dissertation entitled "''Eine Theorie der Schwerkraft im Rahmen der ursprünglichen Einsteinschen Relativitätstheorie''" (A theory of gravity in the framework of the original Einstein theory of relativity). His advisors were Max Planck and Heinrich Rubens. After working as a Gymnasium (school) teacher, he became Privatdozent for theoretical physics at the University of Königsberg in 1920, where he eventually became professor extraordinarius in 1926. From 1946 until 1952, Kretschmann was professor for theoretical physics and director of the institute for theoretical physics at the University of Halle-Wittenberg. Work In his 1915 papers, he introduced the Kretschmann scalar. In his 1915 papers he also introduced, though not in name, the point coincidence ar ...
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AdS/CFT
In theoretical physics, the anti-de Sitter/conformal field theory correspondence, sometimes called Maldacena duality or gauge/gravity duality, is a conjectured relationship between two kinds of physical theories. On one side are anti-de Sitter spaces (AdS) which are used in theories of quantum gravity, formulated in terms of string theory or M-theory. On the other side of the correspondence are conformal field theories (CFT) which are quantum field theories, including theories similar to the Yang–Mills theories that describe elementary particles. The duality represents a major advance in the understanding of string theory and quantum gravity.de Haro et al. 2013, p. 2 This is because it provides a non-perturbative formulation of string theory with certain boundary conditions and because it is the most successful realization of the holographic principle, an idea in quantum gravity originally proposed by Gerard 't Hooft and promoted by Leonard Susskind. It also provides a pow ...
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String Theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string. In string theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries the gravitational force. Thus, string theory is a theory of quantum gravity. String theory is a broad and varied subject that attempts to address a number of deep questions of fundamental physics. String theory has contributed a number of advances to mathematical physics, which have been applied to a variety of problems in black hole physics, early universe cosmology, nuclear physics, and conde ...
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Spin Foam
In physics, the topological structure of spinfoam or spin foam consists of two-dimensional faces representing a configuration required by functional integration to obtain a Feynman's path integral description of quantum gravity. These structures are employed in loop quantum gravity as a version of quantum foam. In loop quantum gravity The covariant formulation of loop quantum gravity provides the best formulation of the dynamics of the theory of quantum gravity – a quantum field theory where the invariance under diffeomorphisms of general relativity applies. The resulting path integral represents a sum over all the possible configurations of spin foam. Spin network A spin network is a one-dimensional graph, together with labels on its vertices and edges which encode aspects of a spatial geometry. A spin network is defined as a diagram like the Feynman diagram which makes a basis of connections between the elements of a differentiable manifold for the Hilbert spaces d ...
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Thomas Thiemann
Thomas may refer to: People * List of people with given name Thomas * Thomas (name) * Thomas (surname) * Saint Thomas (other) * Thomas Aquinas (1225–1274) Italian Dominican friar, philosopher, and Doctor of the Church * Thomas the Apostle * Thomas (bishop of the East Angles) (fl. 640s–650s), medieval Bishop of the East Angles * Thomas (Archdeacon of Barnstaple) (fl. 1203), Archdeacon of Barnstaple * Thomas, Count of Perche (1195–1217), Count of Perche * Thomas (bishop of Finland) (1248), first known Bishop of Finland * Thomas, Earl of Mar (1330–1377), 14th-century Earl, Aberdeen, Scotland Geography Places in the United States * Thomas, Illinois * Thomas, Indiana * Thomas, Oklahoma * Thomas, Oregon * Thomas, South Dakota * Thomas, Virginia * Thomas, Washington * Thomas, West Virginia * Thomas County (other) * Thomas Township (other) Elsewhere * Thomas Glacier (Greenland) Arts, entertainment, and media * ''Thomas'' (Burton novel) 1969 nove ...
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