翻訳と辞書 Words near each other ・ Rinderhorn ・ Rinderkennzeichnungs- und Rindfleischetikettierungsüberwachungsaufgabenübertragungsgesetz ・ Rindermarktbrunnen ・ Rinderpest ・ Rindersbukta ・ Rindert Kromhout ・ Rindge ・ Rindge Co. v. County of Los Angeles ・ Rindge Dam ・ Rindge Towers ・ Rindge, New Hampshire ・ Rindgea ・ Rindgenaria ・ Rindheer ・ Rindi ・ Rindler coordinates ・ Rindler Creek ・ Rindo Majhi ・ Rindoon ・ Rindos ・ Rindos affair ・ Rindos v Hardwick ・ Rindr ・ Rindü ・ Rineceras ・ Rineen Ambush ・ Rinegg ・ Rineh ・ Rinehart ・ Rinehart & Company 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 Rindler coordinates ： ウィキペディア英語版 Rindler coordinates In relativistic physics, the Rindler coordinate chart is an important and useful coordinate chart representing part of flat spacetime, also called the Minkowski vacuum. The Rindler coordinate system or frame describes a uniformly accelerating frame of reference in Minkowski space. In special relativity, a uniformly accelerating particle undergoes hyperbolic motion. For each such particle a Rindler frame can be chosen in which it is at rest. The Rindler chart is named after Wolfgang Rindler who popularised its use, although it was already "well known" in 1935, according to a paper by Albert Einstein and Nathan Rosen.〔 See equation eqn 1 and footnote 1. They state that this metric is "well known" but provide no reference.〕 ==Relation to Cartesian chart== To obtain the Rindler chart, start with the Cartesian chart (an inertial frame) with the metric (''c''=1 is assumed) :$ds^2\; =\; -dT^2\; +\; dX^2\; +\; dY^2\; +\; dZ^2,\backslash ;\; \backslash forall\; T,\; X,\; Y,\; Z\; \backslash ,.$ In the region , which is often called the ''Rindler wedge'', if g represents the proper acceleration (along the hyperbola ''x''=1) of the Rindler observer whose proper time is defined to be equal to Rindler coordinate time (see below), the new chart is defined using the coordinate transformation :$t\; =\; \backslash frac\; \backslash operatorname\backslash left(\backslash frac\backslash right),\backslash ;\; x=\; \backslash sqrt,\backslash ;\; y\; =\; Y,\backslash ;\; z\; =\; Z\; \backslash ,.$ The inverse transformation is :$T\; =\; x\; \backslash ,\; \backslash sinh(gt),\; \backslash ;\; X\; =\; x\; \backslash ,\; \backslash cosh(gt),\; \backslash ;\; Y\; =\; y,\; \backslash ;\; Z\; =\; z\; \backslash ,.$ In the Rindler chart, the Minkowski line element becomes :$ds^2\; =\; -g^2\; x^2\; dt^2\; +\; dx^2\; +\; dy^2\; +\; dz^2,\; \backslash ;\; \backslash forall\; x>0,\; \backslash forall\; t,\; y,\; z\; \backslash ,.$ A ''Rindler observer'' is defined as an observer that is "at rest" in Rindler coordinates, i.e., maintaining constant ''x'', ''y'', ''z'' and only varying ''t'' as time passes. To maintain this world line, the observer must accelerate with a constant proper acceleration, with Rindler observers closer to x=0 (the Rindler horizon) having greater proper acceleration. All the Rindler observers are instantaneously at rest at time T=0 in the inertial frame, and at this time a Rindler observer with proper acceleration gi will be at position X = 1/gi (really X = c2/gi, but we assume units where c=1), which is also that observer's constant distance from the Rindler horizon in Rindler coordinates. If all Rindler observers set their clocks to zero at T=0, then when defining a Rindler coordinate system we have a choice of which Rindler observer's proper time will be equal to the coordinate time t in Rindler coordinates, and this observer's proper acceleration defines the value of g above (for other Rindler observers at different distances from the Rindler horizon, the coordinate time will equal some constant multiple of their own proper time).〔Koks, Don: ''Explorations in Mathematical Physics'' (2006), (pp. 240-252 )〕 It is a common convention to define the Rindler coordinate system so that the Rindler observer whose proper time matches coordinate time is the one who has proper acceleration g=1, so that g can be eliminated from the equations The above equation, :$t\; =\; \backslash frac\; \backslash operatorname\backslash left(\backslash frac\backslash right),\backslash ;\; x=\; \backslash sqrt,\backslash ;\; y\; =\; Y,\backslash ;\; z\; =\; Z$ has been simplified for c=1. The unsimplified equation is more convenient for finding the Rindler Horizon distance, given an acceleration g. :$\backslash begin$ t &= \frac \operatorname\left (\frac\right) \;\overset \approx\; \frac\\ X &\approx \frac \;\overset\approx\; \frac \end The remainder of the article will follow the convention of setting both g=1 and c=1, so units for X and x will be 1 unit = c^2/g = 1. Be mindful that setting g=1 light-second/second2 is very different from setting g=1 light-year/year^2. Even if we pick units where c=1, the magnitude of the proper acceleration g will depend on our choice of units: for example, if we use units of light-years for distance, (''X'' or ''x'') and years for time, (''T'' or ''t''), this would mean g = 1 light year/year2, equal to about 9.5 meters/second2, while if we use units of light-seconds for distance, (''X'' or ''x''), and seconds for time, (''T'' or ''t''), this would mean g = 1 light-second/second2, or 299792458 meters/second2). 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「Rindler coordinates」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.