{"id":130,"date":"2022-01-05T10:57:52","date_gmt":"2022-01-05T01:57:52","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=130"},"modified":"2025-01-13T10:24:28","modified_gmt":"2025-01-13T01:24:28","slug":"%e5%85%89%e9%80%9f%e3%81%ae%e4%b8%8d%e5%a4%89%e6%80%a7%e3%81%a8%e3%83%ad%e3%83%bc%e3%83%ac%e3%83%b3%e3%83%84%e5%a4%89%e6%8f%9b","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%83%ad%e3%83%bc%e3%83%ac%e3%83%b3%e3%83%84%e5%a4%89%e6%8f%9b%e3%81%ab%e3%82%88%e3%82%89%e3%81%aa%e3%81%84%e7%9b%b8%e5%af%be%e8%ab%96%e3%81%ae%e7%90%86%e8%a7%a3\/%e5%85%89%e9%80%9f%e3%81%ae%e4%b8%8d%e5%a4%89%e6%80%a7%e3%81%a8%e3%83%ad%e3%83%bc%e3%83%ac%e3%83%b3%e3%83%84%e5%a4%89%e6%8f%9b\/","title":{"rendered":"\u5149\u901f\u306e\u4e0d\u5909\u6027"},"content":{"rendered":"<p><!--more--><\/p>\n<h3 id=\"yui_3_17_2_1_1641347818784_989\">\u5149\u306e\u901f\u3055\u3068\u306f<\/h3>\n<ul>\n<li>\u6642\u523b \\(t\\) \u306b\u70b9 \\(P (x, y, z)\\) \u304b\u3089\u51fa\u305f\u5149\u304c\uff0c<\/li>\n<li>\u6642\u523b \\(t+dt\\) \u306b\u8fd1\u508d\u306e\u70b9 \\(Q (x + dx, y + dy, z + dz) \\) \u306b\u5230\u9054\u3059\u308b\u3002<\/li>\n<\/ul>\n<p><span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u5149\u901f<\/strong><\/span>\u306f \\(c\\)\u00a0 \u3067\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u306f\uff0c<br \/>\n$$\\left(\\frac{dx}{dt}\\right)^2 + \\left(\\frac{dy}{dt}\\right)^2 + \\left(\\frac{dz}{dt}\\right)^2<br \/>\n= c^2 $$<br \/>\n\u4e21\u8fba\u306b \\(dt^2\\) \u3092\u304b\u3051\u3066\u6574\u7406\u3059\u308b\u3068<br \/>\n$$ -c^2 dt^2 + dx^2 + dy^2 + dz^2= 0$$<\/p>\n<p>\uff08\u9ad8\u6821\u306e\u6570\u5b66\u306e\u5148\u751f\u306f\uff0c\u5fae\u5206\u306f\u5206\u6570\u3067\u306f\u306a\u3044\uff01\u3068\u8a00\u3063\u305f\u304b\u3082\u3057\u308c\u306a\u3044\u304c\uff0c\u5927\u5b66\u3067\u306f\u5fae\u5206\u306f\u5206\u6570\u307f\u305f\u3044\u306a\u3082\u306e\u3060\u304b\u3089\uff0c\u3053\u3093\u306a\u5177\u5408\u306b\u300c\u5206\u6bcd\u3092\u306f\u3089\u3046\u300d\u3053\u3068\u304c\u3067\u304d\u308b\u3093\u3060\u3068\u6559\u3048\u308b\u3002\uff09<\/p>\n<p>\u3055\u3066\uff0c\u30c7\u30ab\u30eb\u30c8\u5ea7\u6a19\u7cfb \\(x, y, z\\) \u3067\u8868\u3055\u308c\u308b3\u6b21\u5143\u7a7a\u9593\u3068\u6642\u9593\u5ea7\u6a19 \\(t\\) \u3092\u307e\u3068\u3081\u30664\u6b21\u5143\u6642\u7a7a\u3068\u547c\u3076\u304c\uff0c\u4e0a\u8a18\u306f\uff0c\u3053\u306e\u6642\u7a7a\u3092 \\(t, x, y, z\\) \u3068\u3044\u3046\u5ea7\u6a19\u7cfb \\(S\\)\uff08\u7c21\u5358\u306e\u305f\u3081\u306b\u300c\\(S\\) \u7cfb\u300d\u3068\u3082\u66f8\u304f\uff09\u3067\u8868\u793a\u3057\u305f\u5834\u5408\u306e\u5f0f\u3067\u3042\u308b\u3002<\/p>\n<p>\u6b21\u306b\uff0c\\(S\\)\u7cfb\u306b\u5bfe\u3057\u3066\uff0c\\(+x\\) \u65b9\u5411\u306b\u901f\u3055 \\(V\\) \u3067\u904b\u52d5\u3059\u308b\u5225\u306e\u5ea7\u6a19\u7cfb\u3067\u3042\u308b \\(S&#8217;\\) \u7cfb\u3067\u8a18\u8ff0\u3057\u3066\u307f\u308b\u3068\uff0c<\/p>\n<ul>\n<li>\u6642\u523b \\(t&#8217;\\) \u306b\u70b9 \\(P (x&#8217;, y&#8217;,\u00a0 z&#8217;)\\) \u304b\u3089\u51fa\u305f\u5149\u304c\uff0c<\/li>\n<li>\u6642\u523b \\(t&#8217;+dt&#8217;\\) \u306b\u8fd1\u508d\u306e\u70b9 \\(Q (x&#8217; + dx&#8217;, y&#8217; + dy&#8217;, z&#8217; + dz&#8217;) \\) \u306b\u5230\u9054\u3059\u308b\u3002<\/li>\n<\/ul>\n<p>\\(S&#8217;\\) \u7cfb\u3067\u306e\u5149\u306e\u901f\u3055\u306f $$\\left(\\frac{dx&#8217;}{dt&#8217;}\\right)^2 + \\left(\\frac{dy&#8217;}{dt&#8217;}\\right)^2 + \\left(\\frac{dz&#8217;}{dt&#8217;}\\right)^2<br \/>\n= c^2 $$<br \/>\n\u3042\u308b\u3044\u306f\u6574\u7406\u3057\u3066\uff0c<br \/>\n$$ -c^2 dt&#8217;^2 + dx&#8217;^2 + dy&#8217;^2 + dz&#8217;^2= 0$$<br \/>\n\u3068\u306a\u308b\u3002\u5927\u4e8b\u306a\u3053\u3068\u306f\uff0c\\(S&#8217;\\) \u7cfb\u3067\u89b3\u6e2c\u3057\u3066\u3082\uff0c\u5149\u306e\u901f\u3055\u306f \\(c\\) \u3067\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u3002\u3053\u308c\u3092<\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: helvetica, arial, sans-serif; color: #ff0000;\"><strong>\u5149\u901f\u4e0d\u5909\u306e\u539f\u7406<\/strong><\/span><\/p>\n<p>\u3068\u547c\u3093\u3060\u308a\uff0c\u3042\u308b\u3044\u306f\u6587\u7ae0\u3068\u3057\u3066<\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: helvetica, arial, sans-serif;\"><strong><span style=\"color: #ff0000;\">\u5149\u306e\u901f\u3055\u306f\u5ea7\u6a19\u7cfb\u306b\u3088\u3089\u305a\u4e00\u5b9a\u3067\u3042\u308b<\/span><\/strong><\/span><\/p>\n<p>\u3068\u8a00\u3063\u305f\u308a\u3059\u308b\u3002<\/p>\n<h3>\u5ea7\u6a19\u7cfb\u306b\u3088\u3089\u305a\u5149\u901f\u306f\u4e00\u5b9a\u3067\u3042\u308b\u3068\u306f\uff1f<\/h3>\n<p>\\( S \\) \u7cfb \\( \\{t, x, y, z\\} \\) \u306b\u304a\u3044\u3066\u3082 \\(S&#8217; \\) \u7cfb \\( \\{t&#8217;, x&#8217;, y&#8217;, z&#8217;\\}\u00a0 \\) \u306b\u304a\u3044\u3066\u3082<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u5149\u901f\u306f\u4e00\u5b9a\u3067\u3042\u308b<\/strong><\/span>\uff0c\u3068\u3044\u3046\u3053\u3068\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u3051\u308b\u3002<\/p>\n<p>$$ -c^2 dt^2 + dx^2 + dy^2 + dz^2 =\u00a0 -c^2 dt&#8217;^2 + dx&#8217;^2 + dy&#8217;^2 + dz&#8217;^2 $$<\/p>\n<p>\u70b9 \\(P\\) \u304b\u3089\u8fd1\u508d\u306e\u70b9 \\(Q\\) \u307e\u3067\u5149\u304c\u4f1d\u64ad\u3059\u308b\u5834\u5408\u306e\u5fae\u5c0f\u5909\u4f4d\u306b\u3064\u3044\u3066\u306f\uff0c\u4e0a\u5f0f\u306e\u5de6\u8fba\u3082\u53f3\u8fba\u3082\u3069\u3061\u3089\u3082\u30bc\u30ed\u3068\u3044\u3046\u610f\u5473\u3067\u7b49\u53f7\u304c\u6210\u308a\u7acb\u3063\u3066\u3044\u308b\u3002<\/p>\n<h3>\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\uff1a\u5149\u901f\u3092\u4e00\u5b9a\u306b\u4fdd\u3064\u5ea7\u6a19\u5909\u63db<\/h3>\n<p>\u4e00\u822c\u306b<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u5ea7\u6a19\u5909\u63db<\/strong><\/span>\u3068\u306f2\u3064\u306e\u5ea7\u6a19\u7cfb \\( S\\{t, x, y, z \\} \\) \u3068 \\( S&#8217;\\{t&#8217;, x&#8217;, y&#8217;, z&#8217; \\} \\) \u306e\u5ea7\u6a19\u540c\u58eb\u3092\u95a2\u4fc2\u4ed8\u3051\u308b\u5f0f\u306e\u30bb\u30c3\u30c8\u3067\u3042\u308b\u3002\u300c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u5149\u306e\u901f\u3055\u306f\u5ea7\u6a19\u7cfb\u306b\u3088\u3089\u305a\u4e00\u5b9a\u3067\u3042\u308b<\/strong><\/span>\u300d\u3068\u3044\u3046\u7279\u6b8a\u76f8\u5bfe\u8ad6\u306e\u8981\u8acb\u3092\u6e80\u305f\u3059\u5ea7\u6a19\u5909\u63db\u306f<span style=\"color: #ff0000;\"><strong><span style=\"font-family: helvetica, arial, sans-serif;\">\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db<\/span><\/strong><\/span>\u3068\u547c\u3070\u308c\u308b\u3002<\/p>\n<p>\u5ea7\u6a19\u7cfb \\( S\\{t, x, y, z \\} \\) \u3068\uff0c\\(S\\) \u7cfb\u306b\u5bfe\u3057\u3066 \\(+x\\) \u65b9\u5411\u306b\u901f\u3055 \\(V\\) \u3067\u904b\u52d5\u3059\u308b\u5ea7\u6a19\u7cfb \\( S&#8217;\\{t&#8217;, x&#8217;, y&#8217;, z&#8217; \\} \\) \u306e\u9593\u306e<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db<\/strong><\/span>\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u3051\u308b\u3002\uff08\u5149\u901f \\(c\\) \u3092\u4f7f\u3063\u3066\uff0c\\(c t, \\ c t&#8217;\\) \u306a\u3069\u3068\u3057\u3066\u9577\u3055\u306e\u5358\u4f4d\u306b\u3042\u308f\u305b\u3066\u3044\u307e\u3059\u3002\uff09<\/p>\n<p>\\begin{eqnarray}<br \/>\nct&#8217; &amp;=&amp; \\frac{ct -\\frac{V}{c} x}{\\sqrt{1 -\\left(\\frac{V}{c}\\right)^2}}\\\\<br \/>\nx&#8217; &amp;=&amp; \\frac{x -\\frac{V}{c} c t}{\\sqrt{1 -\\left(\\frac{V}{c}\\right)^2}}\\\\<br \/>\ny&#8217; &amp;=&amp; y\\\\<br \/>\nz&#8217; &amp;=&amp; z<br \/>\n\\end{eqnarray}<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":0,"parent":71,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-130","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.0.1 - aioseo.com -->\n\t<meta name=\"description\" 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