{"id":347,"date":"2022-12-29T14:16:37","date_gmt":"2022-12-29T05:16:37","guid":{"rendered":"https:\/\/daba-no-heya.com\/?p=347"},"modified":"2024-04-27T08:33:51","modified_gmt":"2024-04-26T23:33:51","slug":"post-347","status":"publish","type":"post","link":"https:\/\/daba-no-heya.com\/?p=347","title":{"rendered":"\u56fa\u6709\u6642\u9593"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u3042\u308b\u7c92\u5b50\u304c\u904b\u52d5\u3059\u308b\u7d4c\u8def\u306e\u3053\u3068\u3092<strong>\u4e16\u754c\u7dda<\/strong>(world line)\u3068\u547c\u3073\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4eca\u3001\u4e16\u754c\u7dda\u3092$x^{\\mu}=x^{\\mu}(\\tau)=(ct(\\tau),x(\\tau),y(\\tau),z(\\tau))$\u3068\u6307\u5b9a\u3057\u307e\u3059\u3002<br>\u3053\u306e\u7c92\u5b50\u304c\u9759\u6b62\u3057\u3066\u898b\u3048\u308b\u6163\u6027\u7cfb$x&#8217;^{\\mu}=(c\\tau,x&#8217;,y&#8217;,z&#8217;)$\u306b\u79fb\u3063\u3066\u3053\u306e\u904b\u52d5\u3092\u89b3\u5bdf\u3059\u308b\u3068\u3001\u7c92\u5b50\u304c\u4e00\u70b9\u306b\u9759\u6b62\u3057\u3066\u898b\u3048\u308b\u306e\u3067\u3001$ds&#8217;^2=-(cd\\tau)^2+dx&#8217;^2+dy&#8217;^2+dz&#8217;^2=-(cd\\tau)^2$\u3088\u308a\u3001$cd\\tau=\\sqrt{-ds&#8217;^2}$\u3068\u306a\u308a\u307e\u3059\u3002<br>\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u8a08\u3089\u308c\u308b\u6642\u9593$\\tau$\u306e\u3053\u3068\u3092\u305d\u306e\u7c92\u5b50\u306e<strong>\u56fa\u6709\u6642\u9593<\/strong>(proper time)\u3068\u547c\u3073\u307e\u3059\u3002<br>\u56fa\u6709\u6642\u9593\u304c\u6700\u3082\u9577\u304f\u306a\u308b\u306e\u306f$-ds&#8217;^2$\u304c\u6700\u3082\u5927\u304d\u304f\u306a\u308b\u5834\u5408\u3001\u3059\u306a\u308f\u3061\u3001\u7c92\u5b50\u304c\u6163\u6027\u904b\u52d5\u3057\u3066\u3044\u3066$dx&#8217;,dy&#8217;,dz&#8217;=0$\u3068\u3067\u304d\u308b\u5834\u5408\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9759\u6b62\u7cfb\u3067\u3053\u306e\u7c92\u5b50\u3092\u898b\u305f\u3068\u304d\u306b$v^i=\\frac{dx^i}{dt} (i=1,2,3)$\u3067\u904b\u52d5\u3057\u3066\u3044\u308b\u3068\u3057\u307e\u3059\u3002<br>\u3053\u306e\u3068\u304d\u3001<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$\n\\begin{align*}\n    -(cd\\tau)^2&amp;=ds&#8217;^2 \\\\\n    &amp;=ds^2 \\\\\n    &amp;=-(cdt)^2+dx^2+dy^2+dz^2 \\\\\n    &amp;=-(cdt)^2(1-\\delta_{ij}\\frac{v^iv^j}{c^2})\n\\end{align*}\n$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$\nd\\tau=dt\\sqrt{1-\\frac{v^2}{c^2}}=\\frac{dt}{\\gamma}\n$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\gamma \\geq 1$\u306a\u306e\u3067\u3001\u56fa\u6709\u6642\u9593\u306f\u9759\u6b62\u7cfb\u3067\u8a08\u3063\u305f\u6642\u9593\u3088\u308a\u3082\u77ed\u304f\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u3042\u308b\u7c92\u5b50\u304c\u904b\u52d5\u3059\u308b\u7d4c\u8def\u306e\u3053\u3068\u3092\u4e16\u754c\u7dda(world line)\u3068\u547c\u3073\u307e\u3059\u3002 \u4eca\u3001\u4e16\u754c\u7dda\u3092$x^{\\mu}=x^{\\mu}(\\tau)=(ct(\\tau),x(\\tau),y(\\tau),z(\\tau))$\u3068\u6307\u5b9a\u3057\u307e\u3059\u3002\u3053\u306e [&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-347","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\/347","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=347"}],"version-history":[{"count":4,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/347\/revisions"}],"predecessor-version":[{"id":1163,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/347\/revisions\/1163"}],"wp:attachment":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=347"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=347"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=347"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}