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Relativity Of Simultaneity
In physics, the relativity of simultaneity is the concept that ''distant simultaneity'' – whether two spatially separated events occur at the same time – is not absolute, but depends on the observer's reference frame. This possibility was raised by mathematician Henri Poincaré in 1900, and thereafter became a central idea in the special theory of relativity. Description According to the special theory of relativity introduced by Albert Einstein, it is impossible to say in an ''absolute'' sense that two distinct events occur at the same time if those events are separated in space. If one reference frame assigns precisely the same time to two events that are at different points in space, a reference frame that is moving relative to the first will generally assign different times to the two events (the only exception being when motion is exactly perpendicular to the line connecting the locations of both events). For example, a car crash in London and another in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Kepler To Einstein
Johannes Kepler (27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws of planetary motion, and his books '' Astronomia nova'', ''Harmonice Mundi'', and ''Epitome Astronomiae Copernicanae'', influencing among others Isaac Newton, providing one of the foundations for his theory of universal gravitation. The variety and impact of his work made Kepler one of the founders and fathers of modern astronomy, the scientific method, natural and modern science. He has been described as the "father of science fiction" for his novel '' Somnium''. Kepler was a mathematics teacher at a seminary school in Graz, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to the astronomer Tycho Brahe in Prague, and eventually the imperial mathematician to Emperor Rudolf II and his two successors ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Max Jammer
Max Jammer (; born Moshe Jammer, ; 13 April 1915 – 18 December 2010), was an Israeli physicist and philosophy of physics, philosopher of physics. He was born in Berlin, Germany. He was Rector and Acting President at Bar-Ilan University from 1967 to 1977. Biography Jammer studied physics, philosophy and history of science, first at the University of Vienna, and then from 1935 at the Hebrew University of Jerusalem, where he received a PhD in experimental physics in 1942. He served in the British Army for the rest of the war. Jammer then returned to Hebrew University, where he lectured on the history and philosophy of science, before moving in 1952 to Harvard University. He subsequently became a lecturer there and a close colleague of Albert Einstein at Princeton University. He taught at Harvard, the University of Oklahoma, and Boston University, before in 1956 establishing the Department and becoming Professor of Physics at Bar-Ilan University in Israel. He was Rector and Actin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Bulletin Of The American Mathematical Society
The ''Bulletin of the American Mathematical Society'' is a quarterly mathematical journal published by the American Mathematical Society. Scope It publishes surveys on contemporary research topics, written at a level accessible to non-experts. It also publishes, by invitation only, book reviews and short ''Mathematical Perspectives'' articles. History It began as the ''Bulletin of the New York Mathematical Society'' and underwent a name change when the society became national. The Bulletin's function has changed over the years; its original function was to serve as a research journal for its members. Indexing The Bulletin is indexed in Mathematical Reviews, Science Citation Index, ISI Alerting Services, CompuMath Citation Index, and Current Contents/Physical, Chemical & Earth Sciences. See also *'' Journal of the American Mathematical Society'' *'' Memoirs of the American Mathematical Society'' *'' Notices of the American Mathematical Society'' *'' Proceedings of the Ame ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Robert Goldblatt
__NOTOC__ Robert Ian Goldblatt (born 1949) is a mathematical logician who is emeritus Professor in the School of Mathematics and Statistics at Victoria University, Wellington, New Zealand. His doctoral advisor was Max Cresswell. His most popular books are ''Logics of Time and Computation'' and ''Topoi: the Categorial Analysis of Logic''. He has also written a graduate level textbook on hyperreal numbers which is an introduction to nonstandard analysis. In 1987 he took "a trip on Einstein's train" to develop hyperbolic orthogonality, the geometry of relativity of simultaneity. He has been Coordinating Editor of The ''Journal of Symbolic Logic'' and a Managing Editor of '' Studia Logica''. He was elected Fellow and Councillor of the Royal Society of New Zealand, President of the New Zealand Mathematical Society, and represented New Zealand to the International Mathematical Union. In 2012 the Royal Society of New Zealand awarded him the Jones Medal for lifetime achievement i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
World Line
The world line (or worldline) of an object is the path that an object traces in 4-dimensional spacetime. It is an important concept of modern physics, and particularly theoretical physics. The concept of a "world line" is distinguished from concepts such as an "orbit" or a " trajectory" (e.g., a planet's ''orbit in space'' or the ''trajectory'' of a car on a road) by inclusion of the dimension ''time'', and typically encompasses a large area of spacetime wherein paths which are straight perceptually are rendered as curves in spacetime to show their (relatively) more absolute position states—to reveal the nature of special relativity or gravitational interactions. The idea of world lines was originated by physicists and was pioneered by Hermann Minkowski. The term is now used most often in the context of relativity theories (i.e., special relativity and general relativity). Usage in physics A world line of an object (generally approximated as a point in space, e.g., a p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Inertial Frame Of Reference
In classical physics and special relativity, an inertial frame of reference (also called an inertial space or a Galilean reference frame) is a frame of reference in which objects exhibit inertia: they remain at rest or in uniform motion relative to the frame until acted upon by external forces. In such a frame, the laws of nature can be observed without the need to correct for acceleration. All frames of reference with zero acceleration are in a state of constant rectilinear motion (straight-line motion) with respect to one another. In such a frame, an object with zero net force acting on it, is perceived to move with a constant velocity, or, equivalently, Newton's laws of motion#Newton's first law, Newton's first law of motion holds. Such frames are known as inertial. Some physicists, like Isaac Newton, originally thought that one of these frames was absolute — the one approximated by the fixed stars. However, this is not required for the definition, and it is now known that t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Hyperbolic Orthogonality
In geometry, the relation of hyperbolic orthogonality between two lines separated by the asymptotes of a hyperbola is a concept used in special relativity to define simultaneous events. Two events will be simultaneous when they are on a line hyperbolically orthogonal to a particular timeline. This dependence on a certain timeline is determined by velocity, and is the basis for the relativity of simultaneity. Furthermore, keeping time and space axes hyperbolically orthogonal, as in Minkowski space, gives a constant result when measurements are taken of the speed of light. Geometry Two lines are hyperbolic orthogonal when they are reflections of each other over the asymptote of a given hyperbola. Two particular hyperbolas are frequently used in the plane: The relation of hyperbolic orthogonality actually applies to classes of parallel lines in the plane, where any particular line can represent the class. Thus, for a given hyperbola and asymptote ''A'', a pair of lines (''a'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Rapidity
In special relativity, the classical concept of velocity is converted to rapidity to accommodate the limit determined by the speed of light. Velocities must be combined by Einstein's velocity-addition formula. For low speeds, rapidity and velocity are almost exactly proportional but, for higher velocities, rapidity takes a larger value, with the rapidity of light being infinite. Mathematically, rapidity can be defined as the hyperbolic angle that differentiates two frames of reference in relative motion, each frame being associated with distance and time coordinates. Using the inverse hyperbolic function , the rapidity corresponding to velocity is where is the speed of light. For low speeds, by the small-angle approximation, is approximately . Since in relativity any velocity is constrained to the interval the ratio satisfies . The inverse hyperbolic tangent has the unit interval for its domain and the whole real line for its image; that is, the interval maps ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Velocity
Velocity is a measurement of speed in a certain direction of motion. It is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of physical objects. Velocity is a vector (geometry), vector Physical quantity, quantity, meaning that both magnitude and direction are needed to define it. The Scalar (physics), scalar absolute value (Magnitude (mathematics), magnitude) of velocity is called , being a coherent derived unit whose quantity is measured in the International System of Units, SI (metric system) as metres per second (m/s or m⋅s−1). For example, "5 metres per second" is a scalar, whereas "5 metres per second east" is a vector. If there is a change in speed, direction or both, then the object is said to be undergoing an ''acceleration''. Definition Average velocity The average velocity of an object over a period of time is its Displacement (geometry), change in position, \Delta s, divided by the duration of the period, \Delt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Minkowski Space
In physics, Minkowski space (or Minkowski spacetime) () is the main mathematical description of spacetime in the absence of gravitation. It combines inertial space and time manifolds into a four-dimensional model. The model helps show how a spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Mathematician Hermann Minkowski developed it from the work of Hendrik Lorentz, Henri Poincaré, and others said it "was grown on experimental physical grounds". Minkowski space is closely associated with Einstein's theories of special relativity and general relativity and is the most common mathematical structure by which special relativity is formalized. While the individual components in Euclidean space and time might differ due to length contraction and time dilation, in Minkowski spacetime, all frames of reference will agree on the total interval in spacetime between events.This makes spacetime distance an inva ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Space And Time
In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects, such as how different observers perceive ''where'' and ''when'' events occur. Until the turn of the 20th century, the assumption had been that the three-dimensional geometry of the universe (its description in terms of locations, shapes, distances, and directions) was distinct from time (the measurement of when events occur within the universe). However, space and time took on new meanings with the Lorentz transformation and special theory of relativity. In 1908, Hermann Minkowski presented a geometric interpretation of special relativity that fused time and the three spatial dimensions into a single four-dimensional continuum now known as Minkowski space. This interpretation proved vital to the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
