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Equivalence Principle (geometric)
The equivalence principle is one of the corner-stones of gravitation theory. Different formulations of the equivalence principle are labeled ''weakest'', ''weak'', ''middle-strong'' and ''strong.'' All of these formulations are based on the empirical equality of inertial mass, gravitational active and passive charges. The ''weakest'' equivalence principle is restricted to the motion law of a probe point mass in a uniform gravitational field. Its localization is the ''weak'' equivalence principle that states the existence of a desired local inertial frame at a given world point. This is the case of equations depending on a gravitational field and its first order derivatives, e. g., the equations of mechanics of probe point masses, and the equations of electromagnetic and Dirac fermion fields. The ''middle-strong'' equivalence principle is concerned with any matter, except a gravitational field, while the ''strong'' one is applied to all physical laws. The above-mentioned varia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equivalence Principle
In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is the same as the ''pseudo-force'' experienced by an observer in a non-inertial (accelerated) frame of reference. Einstein's statement of the equality of inertial and gravitational mass Development of gravitational theory Something like the equivalence principle emerged in the early 17th century, when Galileo expressed experimentally that the acceleration of a test mass due to gravitation is independent of the amount of mass being accelerated. Johannes Kepler, using Galileo's discoveries, showed knowledge of the equivalence principle by accurately describing what would occur if the Moon were stopped in its orbit and dropped towards Earth. This can be deduced without knowing if or in what manner gravity decreases ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reduction Of The Structure Group
In differential geometry, a ''G''-structure on an ''n''-manifold ''M'', for a given structure group ''G'', is a principal ''G''- subbundle of the tangent frame bundle F''M'' (or GL(''M'')) of ''M''. The notion of ''G''-structures includes various classical structures that can be defined on manifolds, which in some cases are tensor fields. For example, for the orthogonal group, an O(''n'')-structure defines a Riemannian metric, and for the special linear group an SL(''n'',R)-structure is the same as a volume form. For the trivial group, an -structure consists of an absolute parallelism of the manifold. Generalising this idea to arbitrary principal bundles on topological spaces, one can ask if a principal G-bundle over a group G "comes from" a subgroup H of G. This is called reduction of the structure group (to H). Several structures on manifolds, such as a complex structure, a symplectic structure, or a Kähler structure, are ''G''-structures with an additional integrability c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravity
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong interaction, 1036 times weaker than the electromagnetic force and 1029 times weaker than the weak interaction. As a result, it has no significant influence at the level of subatomic particles. However, gravity is the most significant interaction between objects at the macroscopic scale, and it determines the motion of planets, stars, galaxies, and even light. On Earth, gravity gives weight to physical objects, and the Moon's gravity is responsible for sublunar tides in the oceans (the corresponding antipodal tide is caused by the inertia of the Earth and Moon orbiting one another). Gravity also has many important biological functions, helping to guide the growth of plants through the process of gravitropism and influencing the circ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sardanashvily
Gennadi Sardanashvily (russian: Генна́дий Алекса́ндрович Сарданашви́ли; March 13, 1950 – September 1, 2016) was a theoretical physicist, a principal research scientist of Moscow State University. Biography Gennadi Sardanashvily graduated from Moscow State University (MSU) in 1973, he was a Ph.D. student of the Department of Theoretical Physics ( MSU) in 1973–76, where he held a position in 1976. He attained his Ph.D. degree in physics and mathematics from MSU, in 1980, with Dmitri Ivanenko as his supervisor, and his D.Sc. degree in physics and mathematics from MSU, in 1998. Gennadi Sardanashvily was the founder and Managing Editor (2003 - 2013) of the International Journal of Geometric Methods in Modern Physics (IJGMMP). He was a member of Lepage Research Institute (Czech Republic). Research area Gennadi Sardanashvily research area is geometric method in classical and quantum mechanics and field theory, gravitation theory. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dmitri Ivanenko
Dmitri Dmitrievich Ivanenko (russian: Дми́трий Дми́триевич Иване́нко; July 29, 1904 – December 30, 1994) was a Ukrainian theoretical physicist who made great contributions to the physical science of the twentieth century, especially to nuclear physics, field theory, and gravitation theory. He worked in the Poltava Gravimetric Observatory of the Institute of Geophysics of NAS of Ukraine, was the head of the Theoretical Department Ukrainian Physico-Technical Institute in Kharkiv, Head of the Department of Theoretical Physics of the Kharkiv Institute of Mechanical Engineering. Professor of University of Kharkiv, Professor of Moscow State University (since 1943). Biography Dmitri Ivanenko was born on July 29, 1904 in Poltava, where he finished school, in 1920-1923 he studied at the Poltava Pedagogical Institute and began his creative path as a teacher of physics in middle school. Then D. D. Ivanenko studied at Kharkiv University, from which in 1923 he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steven Weinberg
Steven Weinberg (; May 3, 1933 – July 23, 2021) was an American theoretical physicist and Nobel laureate in physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interaction between elementary particles. He held the Josey Regental Chair in Science at the University of Texas at Austin, where he was a member of the Physics and Astronomy Departments. His research on elementary particles and physical cosmology was honored with numerous prizes and awards, including the 1979 Nobel Prize in physics and the 1991 National Medal of Science. In 2004, he received the Benjamin Franklin Medal of the American Philosophical Society, with a citation that said he was "considered by many to be the preeminent theoretical physicist alive in the world today." He was elected to the U.S. National Academy of Sciences, Britain's Royal Society, the American Philosophical Society, and the American Academy of Arts and Sciences. Weinb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reduction Of The Structure Group
In differential geometry, a ''G''-structure on an ''n''-manifold ''M'', for a given structure group ''G'', is a principal ''G''- subbundle of the tangent frame bundle F''M'' (or GL(''M'')) of ''M''. The notion of ''G''-structures includes various classical structures that can be defined on manifolds, which in some cases are tensor fields. For example, for the orthogonal group, an O(''n'')-structure defines a Riemannian metric, and for the special linear group an SL(''n'',R)-structure is the same as a volume form. For the trivial group, an -structure consists of an absolute parallelism of the manifold. Generalising this idea to arbitrary principal bundles on topological spaces, one can ask if a principal G-bundle over a group G "comes from" a subgroup H of G. This is called reduction of the structure group (to H). Several structures on manifolds, such as a complex structure, a symplectic structure, or a Kähler structure, are ''G''-structures with an additional integrability c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauge Gravitation Theory
In quantum field theory, gauge gravitation theory is the effort to extend Yang–Mills theory, which provides a universal description of the fundamental interactions, to describe gravity. ''Gauge gravitation theory'' should not be confused with the similarly-named gauge theory gravity, which is a formulation of (classical) gravitation in the language of geometric algebra. Nor should it be confused with Kaluza–Klein theory, where the gauge fields are used to describe particle fields, but not gravity itself. Overview The first gauge model of gravity was suggested by Ryoyu Utiyama (1916–1990) in 1956 just two years after birth of the gauge theory itself. However, the initial attempts to construct the gauge theory of gravity by analogy with the gauge models of internal symmetries encountered a problem of treating general covariant transformations and establishing the gauge status of a pseudo-Riemannian metric (a tetrad field). In order to overcome this drawback, representing tetr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equivalence Principle
In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is the same as the ''pseudo-force'' experienced by an observer in a non-inertial (accelerated) frame of reference. Einstein's statement of the equality of inertial and gravitational mass Development of gravitational theory Something like the equivalence principle emerged in the early 17th century, when Galileo expressed experimentally that the acceleration of a test mass due to gravitation is independent of the amount of mass being accelerated. Johannes Kepler, using Galileo's discoveries, showed knowledge of the equivalence principle by accurately describing what would occur if the Moon were stopped in its orbit and dropped towards Earth. This can be deduced without knowing if or in what manner gravity decreases ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Higgs Field (classical)
Spontaneous symmetry breaking, a vacuum Higgs field, and its associated fundamental particle the Higgs boson are quantum phenomena. A vacuum Higgs field is responsible for spontaneous symmetry breaking the gauge symmetries of fundamental interactions and provides the Higgs mechanism of generating mass of elementary particles. At the same time, classical gauge theory admits comprehensive geometric formulation where gauge fields are represented by connections on principal bundles. In this framework, spontaneous symmetry breaking is characterized as a reduction of the structure group G of a principal bundle P\to X to its closed subgroup H. By the well-known theorem, such a reduction takes place if and only if there exists a global section h of the quotient bundle P/G\to X. This section is treated as a classical Higgs field. A key point is that there exists a composite bundle P\to P/G\to X where P\to P/G is a principal bundle with the structure group H. Then matter fields, possess ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauge Gravitation Theory
In quantum field theory, gauge gravitation theory is the effort to extend Yang–Mills theory, which provides a universal description of the fundamental interactions, to describe gravity. ''Gauge gravitation theory'' should not be confused with the similarly-named gauge theory gravity, which is a formulation of (classical) gravitation in the language of geometric algebra. Nor should it be confused with Kaluza–Klein theory, where the gauge fields are used to describe particle fields, but not gravity itself. Overview The first gauge model of gravity was suggested by Ryoyu Utiyama (1916–1990) in 1956 just two years after birth of the gauge theory itself. However, the initial attempts to construct the gauge theory of gravity by analogy with the gauge models of internal symmetries encountered a problem of treating general covariant transformations and establishing the gauge status of a pseudo-Riemannian metric (a tetrad field). In order to overcome this drawback, representing tetr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudo-Riemannian Manifold
In differential geometry, a pseudo-Riemannian manifold, also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate. This is a generalization of a Riemannian manifold in which the requirement of positive-definiteness is relaxed. Every tangent space of a pseudo-Riemannian manifold is a pseudo-Euclidean vector space. A special case used in general relativity is a four-dimensional Lorentzian manifold for modeling spacetime, where tangent vectors can be classified as timelike, null, and spacelike. Introduction Manifolds In differential geometry, a differentiable manifold is a space which is locally similar to a Euclidean space. In an ''n''-dimensional Euclidean space any point can be specified by ''n'' real numbers. These are called the coordinates of the point. An ''n''-dimensional differentiable manifold is a generalisation of ''n''-dimensional Euclidean space. In a manifold it may only be possible to d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
