翻訳と辞書 Words near each other ・ Four-stroke engine ・ Four-stroke power valve system ・ Four-stroking ・ Four-tensor ・ Four-terminal sensing ・ Four-thousand footers ・ Four-thousander ・ Four-toed earless skink ・ Four-toed elephant shrew ・ Four-toed hedgehog ・ Four-toed jerboa ・ Four-toed rice tenrec ・ Four-toed salamander ・ Four-valued logic ・ Four-vector ・ Four-velocity ・ Four-vertex theorem ・ Four-wave mixing ・ Four-way valve ・ Four-wheel drive ・ Four-wheel drive in Formula One ・ Four-wire circuit ・ Four-wire terminating set ・ Four-year junior college ・ Four0ninE ・ Four11.com ・ FOUR40 ・ Four80East ・ Fouradi ・ Fourah Bay Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Four-velocity ： ウィキペディア英語版 Four-velocity In physics, in particular in special relativity and general relativity, a four-velocity is a four-vector in four-dimensional spacetime that represents the relativistic counterpart of velocity, which is a three-dimensional vector in space.〔Technically, the 4-vector should be thought of as residing in the tangent space of a point in spacetime, spacetime itself being modeled as a smooth manifold. This technical distinction is important in general relativity, but in special relativity, where spacetime is modeled as a vector space, the 4-vector can be thought of as residing in spacetime itself.〕 Physical events correspond to mathematical points in time and space, the set of all of them together forming a mathematical model of physical four-dimensional spacetime. The history of an object traces a curve in spacetime, called its world line. If the object is massive, so that its speed is less than the speed of light, the world line may be parametrized by the proper time of the object. The four-velocity is the rate of change of four-position with respect to the proper time along the curve. The velocity, in contrast, is the rate of change of the position in (three-dimensional) space of the object, as seen by an observer, with respect to the observer's time. The magnitude of an object's four-velocity (the quantity obtained by applying the metric tensor to the four-velocity and itself) is always equal to the square of ''c'', the speed of light. For an object at rest (with respect to the coordinate system) its four-velocity is parallel to the direction of the time coordinate. A four-velocity is thus the normalized future-directed timelike tangent vector to a world line, and is a contravariant vector. Though it is a vector, addition of two four-velocities does not yield a four-velocity: the space of four-velocities is not itself a vector space.〔The set of 4-vectors is a subset of the tangent space (which ''is'' a vector space) at an event. The label 4-vector stems from the behavior under Lorentz transformations, namely under which particular representation they transform.〕 == Velocity == The path of an object in three-dimensional space (in an inertial frame) may be expressed in terms of three spatial coordinate functions ''xi''(''t'') of time ''t'', where ''i'' is an index which takes values 1, 2, 3. The three coordinates form the 3d position vector, written as a column vector :$\backslash vec(t)\; =\; \backslash begin\; x^1(t)\; \backslash \backslash \; x^2(t)\; \backslash \backslash \; x^3(t)\; \backslash end\; \backslash ,.$ The components of the velocity $\}\; =\; \backslash beginu^1\; \backslash \backslash \; u^2\; \backslash \backslash \; u^3\backslash end\; =\; =$ \begin\tfrac \\ \tfrac \\ \tfrac\end. Each component is simply written :$u^i\; =$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Four-velocity」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.