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Sticky Bead Argument
In general relativity, the sticky bead argument is a simple thought experiment designed to show that gravitational radiation is indeed predicted by general relativity, and can have physical effects. These claims were not widely accepted prior to about 1955, but after the introduction of the bead argument, any remaining doubts soon disappeared from the research literature. The argument is often credited to Hermann Bondi, who popularized it, but it was originally proposed anonymously by Richard Feynman.Preskill, John and Kip S. Thorne. Foreword to ''Feynman Lectures On Gravitation''. Feynman et al. (Westview Press; 1st ed. (June 20, 2002) p. xxv–xxvLink PDF (page 17-18)/ref>DeWitt, Cecile M. (1957). Conference on the Role of Gravitation in Physics at the University of North Carolina, Chapel Hill, March 1957; WADC Technical Report 57-216 (Wright Air Development Center, Air Research and Development Command, United States Air Force, Wright Patterson Air Force Base, Ohio Description ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beck Vacuums
In general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically. According to the Einstein field equation, this means that the stress–energy tensor also vanishes identically, so that no matter or non-gravitational fields are present. These are distinct from the electrovacuum solutions, which take into account the electromagnetic field in addition to the gravitational field. Vacuum solutions are also distinct from the lambdavacuum solutions, where the only term in the stress–energy tensor is the cosmological constant term (and thus, the lambdavacuums can be taken as cosmological models). More generally, a vacuum region in a Lorentzian manifold is a region in which the Einstein tensor vanishes. Vacuum solutions are a special case of the more general exact solutions in general relativity. Equivalent conditions It is a mathematical fact that the Einstein tensor vanishes if and only if the Ricci tensor vanishes. This follows from ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bern
german: Berner(in)french: Bernois(e) it, bernese , neighboring_municipalities = Bremgarten bei Bern, Frauenkappelen, Ittigen, Kirchlindach, Köniz, Mühleberg, Muri bei Bern, Neuenegg, Ostermundigen, Wohlen bei Bern, Zollikofen , website = www.bern.ch Bern () or Berne; in other Swiss languages, gsw, Bärn ; frp, Bèrna ; it, Berna ; rm, Berna is the ''de facto'' capital of Switzerland, referred to as the "federal city" (in german: Bundesstadt, link=no, french: ville fédérale, link=no, it, città federale, link=no, and rm, citad federala, link=no). According to the Swiss constitution, the Swiss Confederation intentionally has no "capital", but Bern has governmental institutions such as the Federal Assembly and Federal Council. However, the Federal Supreme Court is in Lausanne, the Federal Criminal Court is in Bellinzona and the Federal Administrative Court and the Federal Patent Court are in St. Gallen, exemplifying the federal nature of the Confederation. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Special Relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The laws of physics are invariant (that is, identical) in all inertial frames of reference (that is, frames of reference with no acceleration). # The speed of light in vacuum is the same for all observers, regardless of the motion of the light source or the observer. Origins and significance Special relativity was originally proposed by Albert Einstein in a paper published on 26 September 1905 titled "On the Electrodynamics of Moving Bodies".Albert Einstein (1905)''Zur Elektrodynamik bewegter Körper'', ''Annalen der Physik'' 17: 891; English translatioOn the Electrodynamics of Moving Bodiesby George Barker Jeffery and Wilfrid Perrett (1923); Another English translation On the Electrodynamics of Moving Bodies by Megh Nad Saha (1920). The incompa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brinkmann Coordinates
Brinkmann coordinates are a particular coordinate system for a spacetime belonging to the family of pp-wave metrics. They are named for Hans Brinkmann. In terms of these coordinates, the metric tensor can be written as :ds^2 = H(u,x,y) du^2 + 2 du dv + dx^2 + dy^2 where \partial_, the coordinate vector field dual to the covector field dv, is a null vector field. Indeed, geometrically speaking, it is a null geodesic congruence with vanishing optical scalars. Physically speaking, it serves as the wave vector defining the direction of propagation for the pp-wave. The coordinate vector field \partial_ can be spacelike, null, or timelike at a given event in the spacetime, depending upon the sign of H(u,x,y) at that event. The coordinate vector fields \partial_, \partial_ are both spacelike vector fields. Each surface u=u_, v=v_ can be thought of as a wavefront. In discussions of exact solutions to the Einstein field equation, many authors fail to specify the intended ran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Caustic (mathematics)
In differential geometry, a caustic is the envelope of rays either reflected or refracted by a manifold. It is related to the concept of caustics in geometric optics. The ray's source may be a point (called the radiant) or parallel rays from a point at infinity, in which case a direction vector of the rays must be specified. More generally, especially as applied to symplectic geometry and singularity theory, a caustic is the critical value set of a Lagrangian mapping where is a Lagrangian immersion of a Lagrangian submanifold ''L'' into a symplectic manifold ''M'', and is a Lagrangian fibration of the symplectic manifold ''M''. The caustic is a subset of the Lagrangian fibration's base space ''B''. Explanation Concentration of light, especially sunlight, can burn. The word ''caustic'', in fact, comes from the Greek καυστός, burnt, via the Latin ''causticus'', burning. A common situation where caustics are visible is when light shines on a drinking glass. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational Plane Wave
In general relativity, a gravitational plane wave is a special class of a vacuum pp-wave spacetime, and may be defined in terms of Brinkmann coordinates by ds^2= (u)(x^2-y^2)+2b(u)xyu^2+2dudv+dx^2+dy^2 Here, a(u), b(u) can be any smooth functions; they control the waveform of the two possible polarization modes of gravitational radiation. In this context, these two modes are usually called the plus mode and cross mode, respectively. See also *vacuum solution (general relativity) In general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically. According to the Einstein field equation, this means that the stress–energy tensor also vanishes identically, so that no matter or non ... {{relativity-stub Exact solutions in general relativity ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Caltech
The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasionally referred to as "CIT", most notably in its alma mater, but this is uncommon. is a private university, private research university in Pasadena, California. Caltech is ranked among the best and most selective academic institutions in the world, and with an enrollment of approximately 2400 students (acceptance rate of only 5.7%), it is one of the world's most selective universities. The university is known for its strength in science and engineering, and is among a small group of Institute of Technology (United States), institutes of technology in the United States which is primarily devoted to the instruction of pure and applied sciences. The institution was founded as a preparatory and vocational school by Amos G. Throop in 1891 and began ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Field Theory
A classical field theory is a physical theory that predicts how one or more physical fields interact with matter through field equations, without considering effects of quantization; theories that incorporate quantum mechanics are called quantum field theories. In most contexts, 'classical field theory' is specifically intended to describe electromagnetism and gravitation, two of the fundamental forces of nature. A physical field can be thought of as the assignment of a physical quantity at each point of space and time. For example, in a weather forecast, the wind velocity during a day over a country is described by assigning a vector to each point in space. Each vector represents the direction of the movement of air at that point, so the set of all wind vectors in an area at a given point in time constitutes a vector field. As the day progresses, the directions in which the vectors point change as the directions of the wind change. The first field theories, Newtonian gravitat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton University
Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest institution of higher education in the United States and one of the nine colonial colleges chartered before the American Revolution. It is one of the highest-ranked universities in the world. The institution moved to Newark, New Jersey, Newark in 1747, and then to the current site nine years later. It officially became a university in 1896 and was subsequently renamed Princeton University. It is a member of the Ivy League. The university is governed by the Trustees of Princeton University and has an endowment of $37.7 billion, the largest List of colleges and universities in the United States by endowment, endowment per student in the United States. Princeton provides undergraduate education, undergraduate and graduate education, graduate in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leopold Infeld
Leopold Infeld (20 August 1898 – 15 January 1968) was a Polish physicist who worked mainly in Poland and Canada (1938–1950). He was a Rockefeller fellow at Cambridge University (1933–1934) and a member of the Polish Academy of Sciences. Early life Leopold Infeld was born into a family of Polish Jews in Kraków, then part of the Austro-Hungarian Empire (it rejoined an independent Poland in 1918). He studied physics at Kraków's Jagiellonian University and from 1920 in Berlin, where he had engaged Albert Einstein's help to gain admission to the University of Berlin. He obtained a doctorate in 1921. In 1933 he left for England, then for the United States and Canada after the death of his second wife, Halina. Work Infeld was interested in the theory of relativity. He was awarded a doctorate at the Jagiellonian University(1921), worked as an assistant and a docent at the University of Lwów (1930–1933) and then as a professor at the University of Toronto between 1939 and 1950 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of The Franklin Institute
The Franklin Institute is a science museum and the center of science education and research in Philadelphia, Pennsylvania. It is named after the American scientist and statesman Benjamin Franklin. It houses the Benjamin Franklin National Memorial. Founded in 1824, the Franklin Institute is one of the oldest centers of science education and development in the United States. Its chief astronomer is Derrick Pitts. History On February 5, 1824, Samuel Vaughan Merrick and William H. Keating founded the Franklin Institute of the State of Pennsylvania for the Promotion of the Mechanic Arts. Begun in 1825, the institute was an important force in the professionalization of American science and technology through the nineteenth century, beginning with early investigations into steam engines and water power. In addition to conducting scientific inquiry, it fostered research and education by running schools, publishing the influential ''Journal of The Franklin Institute'', sponsoring exhib ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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