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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 Multiple time dimensions ： ウィキペディア英語版 Multiple time dimensions The possibility that there might be more than one dimension of time has occasionally been discussed in physics and philosophy. == Physics == Special relativity describes spacetime as a manifold whose metric tensor has a negative eigenvalue. This corresponds to the existence of a "time-like" direction. A metric with multiple negative eigenvalues would correspondingly imply ''several'' timelike directions, i.e. multiple time dimensions, but there is no consensus regarding the relationship of these extra "times" to time as conventionally understood. If thе special theory of relativity can be generalized for the case of ''k''-dimensional time (''t''1, ''t''2, ..., ''t''''k'') and ''n''-dimensional space (''x''''k''+1, ''x''''k''+2, ..., ''x''k''+n''), then the (''k''+''n'')-dimensional interval, being invariant, is given by the expression :(d''s''''k'',''n'')2 = (''c''d''t''1)2 + ... + (''c''d''t''''k'')2 − (d''x''''k''+1)2 − … − (d''x''''k''+''n'')2. The metric signature will be :$(\backslash underbrace\_,\backslash underbrace\_)$ (timelike sign convention) or :$(\backslash underbrace\_,\backslash underbrace\_)$ (spacelike sign convention). The transformations between the two inertial frames of reference ''K'' and ''K''′, which are in a standard configuration (i.e., transformations without translations and/or rotations of the space axis in the hyperplane of space and/or rotations of the time axis in the hyperplane of time), are given as follows:〔 〕 :$t\text{'}\_\; =\; \backslash sum\_^k\; \backslash left(\backslash delta\_\; t\_\backslash theta\; +\; \backslash frac\backslash beta^2\; \backslash zeta\; x\_,$ :$x\text{'}\_\; =\; -c^2\backslash beta^2\backslash zeta\backslash sum\_^k\; \backslash frac\; +\; \backslash zeta\; x\_,$ :$x\text{'}\_\backslash lambda\; =\; x\_\backslash lambda,$ where $\backslash mathbf\_1\; =\; (v\_1,\backslash underbrace\_),$ $\backslash mathbf\_2\; =\; (v\_2,\backslash underbrace\_),$ $\backslash mathbf\_k\; =\; (v\_k,\backslash underbrace\_)$ are the vectors of the velocities of ''K''′ against ''K'', defined accordingly in relation to the time dimensions ''t''1, ''t''2, ..., ''t''k; $\backslash beta\; =\; \backslash frac\}\};$ $\backslash zeta\; =\; \backslash frac\; =\; V\_$ and $\backslash frac\; =\; V\text{'}\_,$ where ''σ'' = 1, 2, ..., ''k''; ''η'' = ''k''+1, ''k''+2, ..., ''k''+''n''. The velocity-addition formula is then given by :$V\text{'}\_\; =\; \backslash frac^k\; \backslash frac\backslash beta^2\backslash left((\backslash zeta-1)\backslash sum\_^k\; \backslash frac,$ :$V\text{'}\_\; =\; \backslash frac\}\backslash beta^2\backslash left((\backslash zeta-1)\backslash sum\_^k\; \backslash frac,$ where ''σ'' = 1, 2, ..., ''k''; ''λ'' = ''k''+2, ''k''+3, ..., ''k''+''n''. For simplicity, let us consider only one spatial dimension ''x''3 and the two time dimensions ''x''1 and ''x''2. (E. g., ''x''1 = ''ct''1, ''x''2 = ''ct''2, ''x''3 = ''x''.) Let us assume that in point ''O'', having coordinates ''x''1 = 0, ''x''2 = 0, ''x''3 = 0, there has been an event ''E''. Let us further assume that a given interval of time $\backslash Delta\; T\; =\; \backslash sqrt\; \backslash geq\; 0$ has passed since the event ''E''. The causal region connected to the event ''E'' includes the lateral surface of the right circular cone , the lateral surface of the right circular cylinder and the inner region bounded by these surfaces, i.e., the causal region includes all points (''x''1, ''x''2, ''x''3), for which the conditions : or : or : are fulfilled.〔 〕 Theories with more than one dimension of time have sometimes been advanced in physics, whether as a serious description of reality or just as a curious possibility. Itzhak Bars's work on "two-time physics", inspired by the SO(10,2) symmetry of the extended supersymmetry structure of M-theory, is the most recent and systematic development of the concept (see also F-theory). Walter Craig and Steven Weinstein proved the existence of a well-posed initial value problem for the ultrahyperbolic equation (a wave equation in more than one time dimension). This showed that initial data on a mixed (spacelike and timelike) hypersurface obeying a particular nonlocal constraint evolves deterministically in the remaining time dimension. 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「Multiple time dimensions」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.