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## ux̉FDphbNXvx󂵂Ă݂悤iTj

<<   쐬 F 2016/12/08 00:01   >>

 wikipediaBell's spaceship paradox̖̑܂B [Analysis][Rotating disc]̕łB [Rotating discF]~]============================================= Bell's spaceship paradox is not about preserving the rest length between objects (as in Born rigidity), but about preserving the distance in an inertial frame relative to which the objects are in motion, for which the Ehrenfest paradox is an example. Historically, Albert Einstein had already recognized in the course of his development of general relativity, that the circumference of a rotating disc is measured to be larger in the corotating frame than the one measured in an inertial frame. Einstein explained in 1916. "We suppose that the circumference and diameter of a circle have been measured with a standard measuring rod infinitely small compared with the radius, and that we have the quotient of the two results. If this experiment were performed with measuring rods at rest relatively to the Galilean system K, the quotient would be . With measuring rods at rest relatively to K, the quotient would be greater than . This is readily understood if we envisage the whole process of measuring from the "stationary" system K, and take into consideration that the measuring rods applied to the periphery undergoes a Lorentz contraction, while the ones applied along the radius do not. Hence Euclidean geometry does not apply to K." x̉FD̃phbNX́ÅԂ̐Î~ۂƂł͂Ȃi{̂悤ɁjÂĂ銵n̋ۑ邱ƂɊւ̂ŁAG[tFXg=phbNX͈łB jIɁAAo[gEACV^ĆA]~Ղ̉~nő肳ꂽ̂]n傫肳ĂƂƂAʑΐ_̔WߒɂĂłɔFĂBACV^C1916NɐB u~̉~ƒáAaƔrĖɏW_ő肳AX2̌ʂ̏LƉ肷B̎KCnK 'ɑ΂đΓIɐÎ~_{ꍇA̓΂ƂȂB_Kɑ΂đΓIɐÎ~ƁA̓΂傫ȂB́A"Œ"n K '瑪肷SvZXz肵AӂɓKpꂽ_[ck󂯂邱ƂlƗeՂɗ邪AaɉēKp̂͂ł͂ȂB ă[Nbh􉽊wKɂ͓KpȂBv As pointed out more precisely by Einstein in 1919, the relation is given $U= \gamma U_{0}$ $\110dpi U$ being the circumference in the corotating frame, $\110dpi U_{0}$ in the laboratory frame, $\110dpi \gamma$ is the Lorentz factor@ $\110dpi 1/\sqrt{1-v^{2}/c^{2}}$ . Therefore, it's impossible to bring a disc from the state of rest into rotation in a Born rigid manner. Instead, stresses arise during the phase of accelerated rotation, until the disc enters the state of uniform rotation. 1919NɃACV^CɂĂ萳mɎwEĂ悤ɁA֌W͗^ĂB $U= \gamma U_{0}$ $\110dpi U$͉]n̉~A$\110dpi U_{0}$ ͎n̉~A$\110dpi \gamma$ ̓[cq $\110dpi 1/\sqrt{1-v^{2}/c^{2}}$ łB ̂߁AÎ~Ԃ̉~Ղ{̏Ԃŉ]邱Ƃ͕s\łBɁA~Ղψȉ]ԂɂȂ܂ŁAꂽ]̒iK̊Ԃɉ͂B ========================================================================== ŁAlȃphbNXłEhrenfest paradoxɂĊȒPɐĂ܂AɂĂ͌Ō@艺邱Ƃɂ܂傤B ͂̕ӂŁBB

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