{"id":338,"date":"2022-12-29T14:16:17","date_gmt":"2022-12-29T05:16:17","guid":{"rendered":"https:\/\/daba-no-heya.com\/?p=338"},"modified":"2026-02-15T15:06:15","modified_gmt":"2026-02-15T06:06:15","slug":"post-338","status":"publish","type":"post","link":"https:\/\/daba-no-heya.com\/?p=338","title":{"rendered":"\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db"},"content":{"rendered":"\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/daba-no-heya.com\/?p=338\/#%E6%85%A3%E6%80%A7%E7%B3%BB%E9%96%93%E3%81%AE%E5%BA%A7%E6%A8%99%E5%A4%89%E6%8F%9B\" >\u6163\u6027\u7cfb\u9593\u306e\u5ea7\u6a19\u5909\u63db<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/daba-no-heya.com\/?p=338\/#%E3%83%AD%E3%83%BC%E3%83%AC%E3%83%B3%E3%83%84%E5%A4%89%E6%8F%9B\" >\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/daba-no-heya.com\/?p=338\/#%E3%83%AD%E3%83%BC%E3%83%AC%E3%83%B3%E3%83%84%E5%8F%8E%E7%B8%AE\" >\u30ed\u30fc\u30ec\u30f3\u30c4\u53ce\u7e2e<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%85%A3%E6%80%A7%E7%B3%BB%E9%96%93%E3%81%AE%E5%BA%A7%E6%A8%99%E5%A4%89%E6%8F%9B\"><\/span>\u6163\u6027\u7cfb\u9593\u306e\u5ea7\u6a19\u5909\u63db<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u3042\u308b\u9759\u6b62\u7cfb$x^{\\mu}$\u306e\u539f\u70b9\u304b\u3089\u98db\u3070\u3057\u305f\u5149\u3092\u3001\u305d\u308c\u306b\u5bfe\u3057\u3066\u4e00\u5b9a\u901f\u5ea6$v^i (i=1,2,3)$\u3067\u904b\u52d5\u3059\u308b\u6163\u6027\u7cfb\u3067\u89b3\u6e2c\u3059\u308b\u3053\u3068\u3092\u8003\u3048\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u5149\u306e\u7d4c\u8def\u4e0a\u3067\u306f$ds^2=0$\u3068\u306a\u308a\u307e\u3059\u304c\u3001\u5149\u901f\u5ea6\u4e0d\u5909\u306e\u539f\u7406\u3088\u308a\u3001\u5225\u306e\u6163\u6027\u7cfb$x&#8217;^{\\mu}$\u306b\u79fb\u3063\u3066\u3082\u5149\u306e\u7d4c\u8def\u4e0a\u3067$ds&#8217;^2=0$\u3068\u306a\u308b\u3053\u3068\u304c\u8981\u8acb\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$\nds^2=0 \\Leftrightarrow ds&#8217;^2=-(cdt&#8217;)^2+dx&#8217;^2+dy&#8217;^2+dz&#8217;^2=0\n$$<\/p>\n\n\n\n<p>\u9759\u6b62\u7cfb$x^{\\mu}$\u3068\u6163\u6027\u7cfb$x&#8217;^{\\mu}$\u306e\u9593\u306e\u5ea7\u6a19\u5909\u63db\u306f\u3001$dx^{\\mu}=\\Lambda^{\\mu}_{\\;\\nu}(\\nu)dx&#8217;^{\\nu}$\u3068\u3044\u3046\u4e00\u6b21\u5909\u63db\u3067\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002<br>\u4e8c\u6b21\u4ee5\u4e0a\u306e\u9805\u304c\u3042\u308b\u3068\u305d\u306e\u7cfb\u306f\u52a0\u901f\u5ea6\u904b\u52d5\u3092\u3057\u3066\u3044\u308b\u3053\u3068\u306b\u306a\u3063\u3066\u3057\u307e\u3046\u306e\u3067\u3001\u4e00\u6b21\u5909\u63db\u306b\u306a\u308a\u307e\u3059\u3002<br>\u307e\u305f\u3001\u5149\u3092\u98db\u3070\u3057\u305f\u4f4d\u7f6e\u3068\u6642\u9593\u3092\u305d\u308c\u305e\u308c\u306e\u5ea7\u6a19\u7cfb\u306e\u539f\u70b9\u3068\u3059\u308b\u3053\u3068\u3067\u3001\u5b9a\u6570\u9805\u3082\u306a\u304f\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u3053\u3067\u3001$ds^2=0 \\Leftrightarrow ds&#8217;^2=0$\u3088\u308a\u3001$ds^2=Cds&#8217;^2$ \u3068\u3044\u3046\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002(\u8981\u691c\u8a3c)<br>\u3053\u3053\u3067\u767b\u5834\u3059\u308b\u5b9a\u6570$C$\u306b\u3064\u3044\u3066\u3001\u4ee5\u4e0b\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u3053\u3068\u304c\u8981\u8acb\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6642\u9593\u3068\u7a7a\u9593\u306e\u4e00\u69d8\u6027\u304b\u3089\u3001\u6642\u9593\u3068\u5ea7\u6a19\u306b\u4f9d\u5b58\u3057\u306a\u3044<\/li>\n\n\n\n<li>\u7a7a\u9593\u306e\u7b49\u65b9\u6027\u304b\u3089\u6163\u6027\u7cfb\u9593\u306e\u76f8\u5bfe\u901f\u5ea6\u306e\u65b9\u5411\u306b\u4f9d\u5b58\u3057\u306a\u3044<\/li>\n<\/ul>\n\n\n\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u5b9a\u6570\u306f\u6163\u6027\u7cfb\u306e\u901f\u5ea6\u306e\u7d76\u5bfe\u5024$|v|$\u306e\u307f\u306b\u4f9d\u5b58\u3059\u308b\u306e\u3067\u3001$C(|v|)$\u3068\u66f8\u304d\u8868\u3059\u3053\u3068\u306b\u3057\u307e\u3059\u3002<br>\u9006\u5909\u63db\u3092\u9069\u7528\u3057\u305f\u3068\u304d\u306b\u5143\u306e$ds^2$\u306b\u623b\u308b\u5fc5\u8981\u304c\u3042\u308b\u306e\u3067\u3001$C(|v|)C(|-v|)=C^2(|v|)=1$\u3088\u308a\u3001$C(|v|)=\\pm 1$\u3067\u3059\u304c\u3001$C(|v|)&gt;0$\u306a\u306e\u3067\u3001$C(|v|)=1$\u3068\u306a\u308a\u307e\u3059\u3002<br>$C(|v|)&gt;0$\u3067\u3042\u308b\u3053\u3068\u306f\u305d\u3093\u306a\u306b\u81ea\u660e\u3067\u306f\u306a\u3044\u3068\u601d\u3046\u306e\u3067\u3001\u304d\u3061\u3093\u3068\u3057\u305f\u8a3c\u660e\u304c\u5fc5\u8981\u3060\u3068\u601d\u3044\u307e\u3059\u3002<br>\u81ea\u5206\u306e\u7406\u89e3\u3068\u3057\u3066\u306f\u3001$C(|v|)=-1$\u3060\u3068\u5ea7\u6a19\u5909\u63db\u306b\u3088\u3063\u3066\u7a7a\u9593\u7684\u898f\u7d04\u3068\u6642\u9593\u7684\u898f\u7d04\u304c\u5165\u308c\u66ff\u308f\u3063\u3066\u3057\u307e\u3046\u306e\u3067\u3001$C(|v|)=1$\u3068\u3059\u308b\u306e\u304c\u81ea\u7136\u306a\u6d41\u308c\u306a\u306e\u3060\u3068\u601d\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4ee5\u4e0a\u3088\u308a\u3001$ds^2=ds&#8217;^2$\u3068\u3044\u3046\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%83%AD%E3%83%BC%E3%83%AC%E3%83%B3%E3%83%84%E5%A4%89%E6%8F%9B\"><\/span>\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u9759\u6b62\u7cfb$x^{\\mu}$\u3068\u6163\u6027\u7cfb$x&#8217;^{\\mu}$\u306e\u9593\u306e\u5ea7\u6a19\u5909\u63db\u304c$dx^{\\mu}=\\Lambda^{\\mu}_{\\;\\nu}(\\nu)dx&#8217;^{\\nu}$\u3068\u3044\u3046\u4e00\u6b21\u5909\u63db\u3067\u4e0e\u3048\u3089\u308c\u308b\u3053\u3068\u3092\u5148\u7a0b\u7d39\u4ecb\u3057\u307e\u3057\u305f\u3002<br>\u3053\u3053\u3067\u306f\u3001\u5ea7\u6a19\u5909\u63db\u3092\u884c\u3046\u4e00\u6b21\u5909\u63db\u306e\u5177\u4f53\u7684\u306a\u5f62\u3092\u5c0e\u51fa\u3057\u305f\u3044\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u7c21\u5358\u306e\u305f\u3081\u3001\u6642\u7a7a\u306e\u4e8c\u6b21\u5143\u90e8\u5206$(t,x)$\u3060\u3051\u306b\u6ce8\u76ee\u3059\u308b\u3053\u3068\u306b\u3057\u307e\u3059\u3002<br>\u307e\u305f\u3001\u30ed\u30fc\u30ec\u30f3\u30c4\u578b\u306e\u7dda\u7d20$-c^2dt^2+dx^2$\u306e\u4ee3\u308f\u308a\u306b\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u578b\u306e\u7dda\u7d20$dl^2 \\equiv d\\lambda^2+dx^2$\u3092\u8003\u3048\u307e\u3059\u3002<br>\u3053\u306e\u4e8c\u3064\u306e\u7dda\u7d20\u306f\u3001$d\\lambda=icdt$\u3068\u3044\u3046\u5909\u63db\u306b\u3088\u3063\u3066\u7d50\u3070\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u7dda\u7d20$dl^2$\u3092\u4e0d\u5909\u306b\u4fdd\u3064\u5909\u63db\u306f\u3001\u4e8c\u6b21\u5143\u5e73\u9762\u306e\u56de\u8ee2\u3068\u5e73\u884c\u79fb\u52d5\u306b\u9650\u3089\u308c\u307e\u3059\u3002<br>\u4e8c\u3064\u306e\u6163\u6027\u7cfb\u306e\u539f\u70b9\u304c\u540c\u3058\u3060\u3068\u4eee\u5b9a\u3057\u305f\u306e\u3067\u3001\u3053\u3053\u3067\u306f\u56de\u8ee2\u3060\u3051\u3092\u8003\u3048\u308b\u3053\u3068\u306b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$\n\\begin{gather*}\n    dx^{\\mu}=\\Lambda^{\\mu}_{\\;\\mu&#8217;}dx&#8217;^{\\mu&#8217;} \\\\\n    (dx^{\\mu})=\n    \\begin{pmatrix}\n        d\\lambda \\\\\n        dx\n    \\end{pmatrix}\n\\end{gather*}\n$$<\/p>\n\n\n\n<p>\u3068\u3059\u308b\u3068\u3001\u56de\u8ee2\u3092\u884c\u3046\u884c\u5217$\\Lambda^{\\mu}_{\\;\\mu&#8217;}$\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$\n(\\Lambda^{\\mu}_{\\;\\mu&#8217;})=\n\\begin{pmatrix}\n    \\cos\\theta &amp; \\sin\\theta \\\\\n    -\\sin\\theta &amp; \\cos\\theta\n\\end{pmatrix}\n$$<\/p>\n\n\n\n<p>\u3053\u308c\u3092\u30ed\u30fc\u30ec\u30f3\u30c4\u578b\u306e\u7dda\u7d20\u306b\u95a2\u3059\u308b\u5f0f\u306b\u76f4\u3059\u305f\u3081\u306b\u306f\u3001$d\\lambda=icdt$\u3001$\\theta=i\\psi$\u3068\u5909\u63db\u3057\u307e\u3059\u3002<br>\u3053\u306e\u3068\u304d\u3001$\\cos\\theta=\\cos(i\\psi)=\\cosh\\psi$\u3001$\\sin\\theta=\\sin(i\\psi)=i\\sinh\\psi$\u3068\u306a\u308b\u306e\u3067\u3001<\/p>\n\n\n\n<p>$$\n\\begin{gather*} \n(dx^{\\mu})= \n\\begin{pmatrix} \nicdt \\\\\ndx \n\\end{pmatrix} \\\\\n(\\Lambda^{\\mu}_{\\;\\mu\u2019})= \n\\begin{pmatrix} \n\\cosh\\psi &amp; i\\sinh\\psi \\\\\n-i\\sinh\\psi &amp; \\cosh\\psi \n\\end{pmatrix} \n\\end{gather*}\n$$<\/p>\n\n\n\n<p>\u5b9f\u969b\u306b$dx^{\\mu}=\\Lambda^{\\mu}_{\\;\\mu\u2019}dx\u2019^{\\mu\u2019}$\u3092\u8a08\u7b97\u3057\u3066\u307f\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u7c21\u7565\u5316\u3067\u304d\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$ \\begin{gather*} (dx^{\\mu})= \\begin{pmatrix} cdt \\\\ dx \\end{pmatrix} \\\\ (\\Lambda^{\\mu}_{\\;\\mu&#8217;})= \\begin{pmatrix} \\cosh\\psi &amp; \\sinh\\psi \\\\ \\sinh\\psi &amp; \\cosh\\psi \\end{pmatrix} \\end{gather*} $$<\/p>\n\n\n\n<p>$y$\u3001$z$\u65b9\u5411\u306e\u5ea7\u6a19\u306b\u306f\u5909\u63db\u306f\u767a\u751f\u3057\u306a\u3044\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3001<\/p>\n\n\n\n<p>$$ \\begin{gather*} (dx^{\\mu})= \\begin{pmatrix} cdt \\\\ dx \\\\ dy \\\\ dz \\end{pmatrix} \\\\ (\\Lambda^{\\mu}_{\\;\\mu&#8217;})= \\begin{pmatrix} \\cosh\\psi &amp; \\sinh\\psi &amp; &amp;\\\\ \\sinh\\psi &amp; \\cosh\\psi &amp; &amp; \\\\ &amp; &amp; 1 &amp; \\\\ &amp; &amp; &amp; 1 \\end{pmatrix} \\end{gather*} $$<\/p>\n\n\n\n<p>\u3053\u308c\u30924\u6b21\u5143\u30df\u30f3\u30b3\u30d5\u30b9\u30ad\u30fc\u7a7a\u9593\u306b\u304a\u3051\u308b<strong>\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db<\/strong>(Lorentz transformation)\u3068\u547c\u3073\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u306e$(t,x)$\u90e8\u5206\u306b\u6ce8\u76ee\u3059\u308b\u3068\u3001<\/p>\n\n\n\n<p>$$ \\left\\{ \\begin{aligned} cdt&amp;=\\cosh\\psi \\cdot cdt&#8217;+\\sinh\\psi \\cdot dx&#8217;\\\\ dx&amp;=\\sinh\\psi \\cdot cdt&#8217;+\\cosh\\psi \\cdot dx&#8217; \\end{aligned} \\right. $$<\/p>\n\n\n\n<p>\u6163\u6027\u7cfb\u3067\u9759\u6b62\u3057\u3066\u3044\u308b\u7c92\u5b50\u306e\u4e16\u754c\u7dda\u4e0a\u3067\u306f$dx&#8217;=0$\u304c\u6e80\u305f\u3055\u308c\u308b\u306e\u3067\u3001\u3053\u306e\u7c92\u5b50\u306e\u904b\u52d5\u3092\u9759\u6b62\u7cfb\u3067\u89b3\u6e2c\u3059\u308b\u3068\u3001\u305d\u306e\u4e16\u754c\u7dda\u4e0a\u3067\u306f\u3001<\/p>\n\n\n\n<p>$$ \\left\\{ \\begin{aligned} cdt&amp;=\\cosh\\psi \\cdot cdt&#8217; \\\\ dx&amp;=\\sinh\\psi \\cdot cdt&#8217; \\end{aligned} \\right. $$<\/p>\n\n\n\n<p>\u3088\u308a\u3001<\/p>\n\n\n\n<p>$$\nv \\equiv \\frac{dx}{dt}=c\\tanh\\psi\n$$<\/p>\n\n\n\n<p>$\\psi$\u306f\u9759\u6b62\u7cfb\u304b\u3089\u898b\u305f\u6163\u6027\u7cfb\u306e\u901f\u5ea6$v$\u306b\u5bfe\u5fdc\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u3053\u3067\u3001<\/p>\n\n\n\n<p>$$\n\\gamma \\equiv \\frac{1}{\\sqrt{1-(\\frac{v}{c})^2}}\n$$<\/p>\n\n\n\n<p>\u3068\u3059\u308b\u3068\u3001\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u306e\u5f0f\u306f\u3001<\/p>\n\n\n\n<p>$$\n(\\Lambda^{\\mu}_{\\;\\mu&#8217;})=\n\\begin{pmatrix}\n    \\gamma &amp; \\gamma\\frac{v}{c} &amp; &amp; \\\\\n    \\gamma\\frac{v}{c} &amp; \\gamma &amp; &amp; \\\\\n    &amp; &amp; 1 &amp; \\\\\n    &amp; &amp; &amp; 1\n\\end{pmatrix}\n$$<\/p>\n\n\n\n<p>\u3068\u8868\u305b\u307e\u3059\u3002<br>\u3053\u306e\u4fc2\u6570$\\gamma$\u3092<strong>\u30ed\u30fc\u30ec\u30f3\u30c4\u56e0\u5b50<\/strong>(Lorentz factor)\u3068\u547c\u3073\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u3092\u9069\u7528\u3057\u305f\u5f8c\u306e\u5404\u6210\u5206\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$ \\left\\{ \\begin{aligned} cdt&amp;=\\gamma(cdt&#8217;+\\frac{v}{c}dx&#8217;) \\\\ dx&amp;=\\gamma(vdt&#8217;+dx&#8217;) \\\\ dy&amp;=dy&#8217; \\\\ dz&amp;=dz&#8217; \\end{aligned} \\right. $$<\/p>\n\n\n\n<p>$t=\\gamma(t&#8217;+\\frac{v}{c^2}x&#8217;)$\u306b\u6ce8\u76ee\u3059\u308b\u3068\u3001\u901f\u5ea6$v$\u306e\u6163\u6027\u7cfb\u3067\u9759\u6b62\u3057\u3066\u3044\u308b\u6642\u8a08\u304c$t&#8217;$\u79d2\u9032\u3080\u3068\u304d\u3001\u9759\u6b62\u7cfb\u306e\u6642\u8a08\u306f$t=\\gamma t&#8217;$\u79d2\u9032\u3080\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<br>$\\gamma \\geq 1$\u3088\u308a$t \\geq t&#8217;$\u3067\u3042\u308a\u3001\u9759\u6b62\u7cfb\u306e\u6642\u8a08\u306e\u65b9\u304c\u591a\u304f\u9032\u3080\u3001\u3059\u306a\u308f\u3061\u3001\u901f\u5ea6$v$\u3067\u904b\u52d5\u3057\u3066\u3044\u308b\u6163\u6027\u7cfb\u306e\u65b9\u304c\u6642\u9593\u306e\u6d41\u308c\u304c\u9045\u304f\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<br>\u3082\u3057\u30bf\u30a4\u30e0\u30de\u30b7\u30f3\u304c\u5b9f\u73fe\u53ef\u80fd\u3060\u3068\u3057\u305f\u3089\u3001\u3053\u306e\u3042\u305f\u308a\u304c\u4e00\u3064\u306e\u53ef\u80fd\u6027\u306b\u306a\u308a\u305d\u3046\u3067\u3059\u306d\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%83%AD%E3%83%BC%E3%83%AC%E3%83%B3%E3%83%84%E5%8F%8E%E7%B8%AE\"><\/span>\u30ed\u30fc\u30ec\u30f3\u30c4\u53ce\u7e2e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u306e\u5f0f\u304b\u3089\u3001<strong>\u30ed\u30fc\u30ec\u30f3\u30c4\u53ce\u7e2e<\/strong>(Lorentz contraction)\u3068\u3044\u3046\u9762\u767d\u3044\u73fe\u8c61\u304c\u5c0e\u304b\u308c\u307e\u3059\u3002<br>\u3053\u308c\u306f\u3001\u904b\u52d5\u3059\u308b\u6163\u6027\u7cfb\u306b\u3042\u308b\u68d2\u3092\u9759\u6b62\u7cfb\u304b\u3089\u89b3\u6e2c\u3059\u308b\u3068\u3001\u68d2\u306e\u9577\u3055\u304c\u7e2e\u3093\u3067\u898b\u3048\u308b\u3001\u3068\u3044\u3046\u73fe\u8c61\u3067\u3059\u3002<\/p>\n\n\n\n<p>$x$\u65b9\u5411\u306b\u4e00\u5b9a\u901f\u5ea6$v$\u3067\u904b\u52d5\u3059\u308b\u6163\u6027\u7cfb\u306b\u3042\u308b\u9577\u3055$L&#8217;$\u306e\u68d2\u306b\u3064\u3044\u3066\u3001\u305d\u306e\u9577\u3055\u3092\u9759\u6b62\u7cfb\u306e\u6642\u523b$t=0$\u3067\u8a08\u6e2c\u3059\u308b\u3053\u3068\u3092\u8003\u3048\u307e\u3059\u3002<br>\u6163\u6027\u7cfb\u306e\u6642\u523b$t&#8217;=0$\u306b\u304a\u3044\u3066\u68d2\u306e\u4e21\u7aef\u304c$(t&#8217;,x&#8217;)=(0,0),(0,L&#8217;)$\u306b\u3042\u308b\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u306e\u5f0f<\/p>\n\n\n\n<p>$$ \\left\\{ \\begin{aligned} t&amp;=\\gamma(t&#8217;+\\frac{v}{c^2}x&#8217;) \\\\ x&amp;=\\gamma(vt&#8217;+x&#8217;) \\end{aligned} \\right. $$<\/p>\n\n\n\n<p>\u3088\u308a\u3001\u9759\u6b62\u7cfb\u306b\u304a\u3051\u308b\u68d2\u306e\u4e21\u7aef\u306f$(t,x)=(0,0),(\\gamma\\frac{v}{c^2}L&#8217;,\\gamma L&#8217;)$\u306b\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u68d2\u306e\u53f3\u7aef\u306e\u4f4d\u7f6e\u3092\u6642\u523b$t=0$\u307e\u3067\u623b\u3059\u3068\u3001<\/p>\n\n\n\n<p>$$\n\\begin{align*}\n    x(t=0)&amp;=x-vt \\\\\n    &amp;=\\gamma L&#8217;-v\\gamma\\frac{v}{c^2}L&#8217; \\\\\n    &amp;=\\gamma(1-(\\frac{v}{c})^2)L&#8217; \\\\\n    &amp;=\\frac{L&#8217;}{\\gamma}\n\\end{align*}\n$$<\/p>\n\n\n\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u6642\u523b$t=0$\u3067\u68d2\u306e\u4e21\u7aef\u306e\u4f4d\u7f6e\u3092\u8aad\u307f\u53d6\u3063\u3066\u9577\u3055\u3092\u6e2c\u308b\u3068\u3001\u9759\u6b62\u6642\u306e\u9577\u3055$L&#8217;$\u306e$\\frac{1}{\\gamma}$\u500d\u306b\u7e2e\u3093\u3067\u898b\u3048\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u76f8\u5bfe\u6027\u7406\u8ad6\u306b\u304a\u3044\u3066\u306f\u3001\u3053\u308c\u306f\u5b9f\u969b\u306b\u68d2\u304c\u7e2e\u3093\u3067\u3044\u308b\u308f\u3051\u3067\u306f\u306a\u304f\u3001\u6163\u6027\u7cfb\u306b\u3088\u3063\u3066\u6e2c\u5b9a\u3057\u3066\u3044\u308b\u5834\u6240\u304c\u7570\u306a\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u8d77\u3053\u308b\u73fe\u8c61\u3067\u3042\u308b\u3068\u89e3\u91c8\u3055\u308c\u308b\u3089\u3057\u3044\u3067\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6163\u6027\u7cfb\u9593\u306e\u5ea7\u6a19\u5909\u63db \u3042\u308b\u9759\u6b62\u7cfb$x^{\\mu}$\u306e\u539f\u70b9\u304b\u3089\u98db\u3070\u3057\u305f\u5149\u3092\u3001\u305d\u308c\u306b\u5bfe\u3057\u3066\u4e00\u5b9a\u901f\u5ea6$v^i (i=1,2,3)$\u3067\u904b\u52d5\u3059\u308b\u6163\u6027\u7cfb\u3067\u89b3\u6e2c\u3059\u308b\u3053\u3068\u3092\u8003\u3048\u307e\u3059\u3002 \u5149\u306e\u7d4c\u8def\u4e0a\u3067\u306f$ds^2=0$\u3068\u306a\u308a\u307e\u3059\u304c\u3001\u5149\u901f\u5ea6\u4e0d\u5909 [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,10],"tags":[],"class_list":["post-338","post","type-post","status-publish","format-standard","hentry","category-9","category-10"],"_links":{"self":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/338","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=338"}],"version-history":[{"count":18,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/338\/revisions"}],"predecessor-version":[{"id":1679,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/338\/revisions\/1679"}],"wp:attachment":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=338"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=338"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=338"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}