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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 Ehrenfest paradox ： ウィキペディア英語版 Ehrenfest paradox The Ehrenfest paradox concerns the rotation of a "rigid" disc in the theory of relativity. In its original formulation as presented by Paul Ehrenfest 1909 in relation to the concept of Born rigidity within special relativity,〔 it discusses an ideally rigid cylinder that is made to rotate about its axis of symmetry.〔, (Extract of page 363 )〕 The radius ''R'' as seen in the laboratory frame is always perpendicular to its motion and should therefore be equal to its value R0 when stationary. However, the circumference (''2πR'') should appear Lorentz-contracted to a smaller value than at rest, by the usual factor γ. This leads to the contradiction that R=R0 ''and'' R0.〔 The paradox has been deepened further by Albert Einstein, who showed that since measuring rods aligned along the periphery and moving with it should appear contracted, more would fit around the circumference, which would thus measure greater than 2πR. This indicates that geometry is non-Euclidean for rotating observers, and was important for Einstein's development of general relativity.〔 Any rigid object made from real materials that is rotating with a transverse velocity close to the speed of sound in the material must exceed the point of rupture due to centrifugal force, because centrifugal pressure can not exceed the shear modulus of material. where $c\_s$ is speed of sound, $\backslash rho$ is density and $G$ is shear modulus. Therefore, when considering velocities close to the speed of light, it is only a thought experiment. Neutron-degenerate matter allows velocities close to speed of light, because e.g. the speed of neutron-star oscillations is relativistic; however; these bodies cannot strictly be said to be "rigid" (per Born rigidity). ==Essence of the paradox== Imagine a disk of radius R rotating with constant angular velocity $\backslash omega$. The reference frame is fixed to the stationary center of the disk. Then the magnitude of the relative velocity of any point in the circumference of the disk is $\backslash omega\; R$. So the circumference will undergo Lorentz contraction by a factor of $\backslash sqrt$. However, since the radius is perpendicular to the direction of motion, it will not undergo any contraction. So $\backslash frac\}=\backslash frac\; =\; \backslash pi\; \backslash sqrt$. This is paradoxical, since in accordance with Euclidean geometry, it should be exactly equal to $\backslash pi$. 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「Ehrenfest paradox」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.