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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Four-acceleration ： ウィキペディア英語版 Four-acceleration In the theory of relativity, four-acceleration is a four-vector (vector in four-dimensional spacetime) that is analogous to classical acceleration (a three-dimensional vector). Four-acceleration has applications in areas such as the annihilation of antiprotons, resonance of strange particles and radiation of an accelerated charge. == Four-acceleration in inertial coordinates == In inertial coordinates in special relativity, four-acceleration is defined as the change in four-velocity over the particle's proper time: : $\backslash mathbf\; =\backslash frac=\backslash left(\backslash gamma\_u\backslash dot\backslash gamma\_u\; c,\backslash gamma\_u^2\backslash mathbf\; a+\backslash gamma\_u\backslash dot\backslash gamma\_u\backslash mathbf\; u\backslash right)$ =\left(\gamma_u^4\frac},\gamma_u^2\mathbf+\gamma_u^4\frac\right)}\mathbf\right), where : $\backslash mathbf\; a\; =$ and : $\backslash dot\backslash gamma\_u\; =\; \backslash frac\; \backslash gamma\_u^3\; =\; \backslash frac\; \backslash frac\backslash right)^\}$ and $\backslash gamma\_u$ is the Lorentz factor for the speed $u$. A dot above a variable indicates a derivative with respect to the coordinate time in a given reference frame, not the proper time $\backslash tau$. In an instantaneously co-moving inertial reference frame $\backslash mathbf\; u\; =\; 0$, $\backslash gamma\_u\; =\; 1$ and $\backslash dot\backslash gamma\_u\; =\; 0$, i.e. in such a reference frame : $\backslash mathbf\; =\backslash left(0,\; \backslash mathbf\; a\backslash right)$ Geometrically, four-acceleration is a curvature vector of a world line.〔 〕 Therefore, the magnitude of the four-acceleration (which is an invariant scalar) is equal to the proper acceleration that a moving particle "feels" moving along a world line. The world lines having constant magnitude of four-acceleration are Minkowski-circles i.e. hyperbolas (see ''hyperbolic motion'') The scalar product of a four-velocity and the corresponding four-acceleration is always 0. Even at relativistic speeds four-acceleration is related to the four-force such that : $F^\backslash mu\; =\; mA^\backslash mu$ where ''m'' is the invariant mass of a particle. When the four-force is zero one has gravitation acting alone, and the four-vector version of Newton's second law above reduces to the geodesic equation. A particle executing geodesic motion has zero value for each component of the acceleration four vector.This conforms to the fact that Gravity is not a force. The radial component four-acceleration of a body under free-fall,incidentally, is zero.This identifies the fact that the spatial part of four-acceleration is different from what we understand by acceleration in common day to day experience for example in the case of an apple falling from a tree. 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-acceleration」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.