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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 History of Lorentz transformations ： ウィキペディア英語版 History of Lorentz transformations The Lorentz transformations relate the space-time coordinates, which specify the position ''x'', ''y'', ''z'' and time ''t'' of an event, relative to a particular inertial frame of reference (the "rest system"), and the coordinates of the same event relative to another coordinate system moving in the positive ''x''-direction at a constant speed ''v'', relative to the rest system. It was devised as a theoretical transformation which makes the velocity of light invariant between different inertial frames. The coordinates of the event in this "moving system" are denoted ''x''′, ''y''′, ''z''′ and ''t''′. The rest system was sometimes identified with the luminiferous aether, the postulated medium for the propagation of light, and the moving system was commonly identified with the earth as it moved through this medium. Early approximations of the transformation were published by Voigt (1887) and Lorentz (1895). They were completed by Larmor (1897, 1900) and Lorentz (1899, 1904) and were brought into their modern form by Poincaré (1905), who gave the transformation the name of Lorentz. Eventually, Einstein (1905) showed in his development of special relativity that the transformations follow from the principle of relativity and the constant light speed alone, without requiring a mechanical aether, and are changing the traditional concepts of space and time. Subsequently, Minkowski used them to argue that space and time are inseparably connected as spacetime. In this article the historical notations are replaced with modern notations, with the Lorentz transformation, :$x^=\backslash gamma(x-vt),\backslash quad\; y^=y,\backslash quad\; z^=z,\backslash quad\; t^=\backslash gamma\backslash left(t-x\backslash frac\}$ ''v'' being the relative velocity of the two reference frames, and ''c'' the speed of light. == Sphere geometry in the 19th century == (詳細はTransformation by reciprocal radii within Möbius geometry, and the Transformation by reciprocal directions within Laguerre geometry.〔Kastrup (2008), section 2.3〕 Both can be seen as special cases of Lie sphere geometry. The connections of these transformations to Maxwell's equations and the laws of physics were discovered, however, only after 1905 when the Lorentz transformation was already derived in a different way by physicists. In several papers between 1847 and 1850 it was shown by Joseph Liouville〔 that the relation $\backslash lambda\backslash left(\backslash delta\; x^+\backslash delta\; y^+\backslash delta\; z^\backslash right)$ is invariant under the group of conformal transformations or the "Transformation by reciprocal radii" which transforms spheres into spheres. This theorem was extended to all dimensions by Sophus Lie (1871)〔 so that $\backslash lambda\backslash left(\backslash delta\; x\_^+\backslash dots+\backslash delta\; x\_^\backslash right)$ is invariant too.〔 In 1909, Harry Bateman and Ebenezer Cunningham showed that not only the quadratic form but also Maxwells equations are covariant with respect to conformal transformation, irrespective of the choice of $\backslash lambda$. This variant of conformal transformations were called spherical wave transformations by him.〔〔 However, this covariance is restricted to certain areas such as electrodynamics, whereas the totality of natural laws in inertial frames is covariant under the Lorentz group.〔 Albert Ribaucour (1870)〔 and in particular Edmond Laguerre (1880-1885)〔〔 employed another variant, namely the "transformation by reciprocal directions" or „Laguerre inversion/transformation“ which transforms spheres into spheres and planes into planes.〔 Laguerre explicitly wrote down the corresponding transformation formulas in 1882, with Gaston Darboux (1887) presenting them in respect to coordinates $x,\; y,\; z,\; R$ (''R'' being the radius):〔 :$\backslash begin$ x' & =x,\quad & z' & =\frac}z-\frac} producing the following relation: :$x^+y^+z^-R^=x^+y^+z^-R^$. Several authors showed the close relation to the Lorentz transformation (see Laguerre inversion and Lorentz transformation)〔〔 – by setting $R=t$, $c=1$, and $v=2k/\backslash left(1+k^\backslash right)$, it follows :$\backslash frac\}=\backslash sqrt,\backslash quad\backslash frac\{1-k^\{2\}\}=v\backslash gamma,$ thus the above transformation becomes similar to a Lorentz transformation with $z$ as direction of motion, except that the sign of $t\text{'}$ is reversed from $t-vz$ to $vz-t$: :$x\text{'}=x,\backslash quad\; y\text{'}=y,\backslash quad\; z\text{'}=\backslash gamma(z-vt),\backslash quad\; t\text{'}=\backslash gamma(vz-t)$ Furthermore, the group isomorphism between the Laguerre group and Lorentz group was pointed out by Élie Cartan, Henri Poincaré and others (see Laguerre group isomorphic to Lorentz group).〔〔Coolidge (1916), p. 370〕〔Klein & Blaschke (1926), p. 259〕 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「History of Lorentz transformations」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. 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