{"id":328,"date":"2022-12-29T14:15:09","date_gmt":"2022-12-29T05:15:09","guid":{"rendered":"https:\/\/daba-no-heya.com\/?p=328"},"modified":"2024-04-27T08:09:33","modified_gmt":"2024-04-26T23:09:33","slug":"post-328","status":"publish","type":"post","link":"https:\/\/daba-no-heya.com\/?p=328","title":{"rendered":"\u30df\u30f3\u30b3\u30d5\u30b9\u30ad\u30fc\u8a08\u91cf"},"content":{"rendered":"\n

4\u6b21\u5143\u6642\u7a7a\u306e\u5ea7\u6a19\u3092$x^\\mu=(x^0,x^1,x^2,x^3)$\u3001\u5149\u901f\u5ea6\u3092$c$\u3068\u8868\u3059\u3053\u3068\u306b\u3057\u307e\u3059\u3002
\u3068\u3053\u308d\u3067\u3001\u7ba1\u7406\u4eba\u306e\u8a18\u61b6\u3067\u306f\u3001\u5b9a\u6570\u306f\u30a4\u30bf\u30ea\u30c3\u30af\u4f53\u306b\u3057\u306a\u3044\u3068\u7fd2\u3063\u305f\u6c17\u304c\u3057\u307e\u3059\u304c\u3001\u5165\u529b\u3059\u308b\u306e\u304c\u9762\u5012\u306a\u306e\u3067\u3001\u5b9a\u6570\u3082\u30a4\u30bf\u30ea\u30c3\u30af\u4f53\u3067\u8868\u8a18\u3057\u3066\u3057\u307e\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

$x_1^{\\;\\mu}=(ct_1,x_1,y_1,z_1)$\u3068$x_2^{\\;\\mu}=(ct_2,x_2,y_2,z_2)$\u306e\u9593\u306e\u5fae\u5c0f\u8ddd\u96e2$dx^\\mu$\u3092$dx^\\mu\\equiv x_2^{\\;\\mu}-x_1^{\\;\\mu}$\u3068\u5b9a\u7fa9\u3057\u307e\u3059\u3002
\u3053\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u5f0f\u3067\u8868\u3055\u308c\u308b\u91cf$ds$\u3092$x_1^{\\;\\mu}$\u3068$x_2^{\\;\\mu}$\u306e\u4e16\u754c\u9593\u9694<\/strong>(world interval)\u3068\u547c\u3073\u307e\u3059\u3002<\/p>\n\n\n\n

\n$$\nds^2=-(cdt)^2+dx^2+dy^2+dz^2=\\eta_{\\mu\\nu}dx^{\\mu}dx^{\\nu}\n$$\n<\/p>\n\n\n\n

\u5f0f\u306e\u4e2d\u306b\u4e0b\u4ed8\u304d\u306e\u6dfb\u5b57\u3068\u4e0a\u4ed8\u304d\u306e\u6dfb\u5b57\u304c\u4e21\u65b9\u73fe\u308c\u305f\u5834\u5408\u306b\u306f\u548c\u3092\u3068\u308a\u307e\u3059\u3002
\u3064\u307e\u308a\u3001<\/p>\n\n\n\n

$$\n\\eta_{\\mu\\nu}dx^{\\mu}dx^{\\nu}=\\sum_{\\mu,\\nu=0}^{3}\\eta_{\\mu\\nu}dx^{\\mu}dx^{\\nu}\n$$<\/p>\n\n\n\n

\u3092\u610f\u5473\u3057\u307e\u3059\u3002
\u3053\u306e\u3088\u3046\u306a\u8a18\u6cd5\u3092\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306e\u7e2e\u7d04\u8a18\u6cd5<\/strong>(Einstein summation notation)\u3068\u8a00\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

\u307e\u305f\u3001\u884c\u5217$\\eta_{\\mu\\nu}$<\/p>\n\n\n\n

$$\n\\eta_{\\mu\\nu}=\n\\begin{pmatrix}\n -1 & & & \\\\\n & 1 & & \\\\\n & & 1 & \\\\\n & & & 1\n\\end{pmatrix}\n$$<\/p>\n\n\n\n

\u3092\u30df\u30f3\u30b3\u30d5\u30b9\u30ad\u30fc\u8a08\u91cf<\/strong>(Minkowski metric)\u3068\u547c\u3073\u307e\u3059\u3002
\u884c\u5217\u8868\u793a\u304c\u7a7a\u767d\u306b\u306a\u3063\u3066\u3044\u308b\u90e8\u5206\u306f0\u3067\u3059\u3002<\/p>\n\n\n\n

\u8cc7\u6599\u306b\u3088\u3063\u3066\u306f\u3001<\/p>\n\n\n\n

$$\n\\begin{gather*}\n ds^2=(cdt)^2-dx^2-dy^2-dz^2=\\eta_{\\mu\\nu}dx^{\\mu}dx^{\\nu} \\\\\n \\eta_{\\mu\\nu}=\n \\begin{pmatrix}\n 1 & & & \\\\\n & -1 & & \\\\\n & & -1 & \\\\\n & & & -1\n \\end{pmatrix}\n\\end{gather*}\n$$<\/p>\n\n\n\n

\u3068\u5b9a\u7fa9\u3057\u3066\u3044\u308b\u3082\u306e\u3082\u3042\u308a\u307e\u3059\u3002
$ds^2=-(cdt)^2+dx^2+dy^2+dz^2$\u306e\u7b26\u53f7\u3065\u3051\u3092\u7a7a\u9593\u7684\u898f\u7d04\u3001$ds^2=(cdt)^2-dx^2-dy^2-dz^2$\u306e\u7b26\u53f7\u3065\u3051\u3092\u6642\u9593\u7684\u898f\u7d04\u3068\u547c\u3093\u3067\u533a\u5225\u3059\u308b\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002
\u4ee5\u964d\u3001\u7279\u306b\u3053\u3068\u308f\u308a\u304c\u306a\u3044\u9650\u308a\u3001\u524d\u8005\u306e\u7a7a\u9593\u7684\u898f\u7d04\u3092\u63a1\u7528\u3057\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

4\u6b21\u5143\u6642\u7a7a\u306e\u5ea7\u6a19\u3092$x^\\mu=(x^0,x^1,x^2,x^3)$\u3001\u5149\u901f\u5ea6\u3092$c$\u3068\u8868\u3059\u3053\u3068\u306b\u3057\u307e\u3059\u3002\u3068\u3053\u308d\u3067\u3001\u7ba1\u7406\u4eba\u306e\u8a18\u61b6\u3067\u306f\u3001\u5b9a\u6570\u306f\u30a4\u30bf\u30ea\u30c3\u30af\u4f53\u306b\u3057\u306a\u3044\u3068\u7fd2\u3063\u305f\u6c17\u304c\u3057\u307e\u3059\u304c\u3001\u5165\u529b\u3059\u308b\u306e\u304c\u9762\u5012\u306a\u306e\u3067\u3001\u5b9a\u6570\u3082\u30a4\u30bf\u30ea\u30c3\u30af […]<\/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-328","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\/328","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=328"}],"version-history":[{"count":7,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/328\/revisions"}],"predecessor-version":[{"id":1156,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/328\/revisions\/1156"}],"wp:attachment":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=328"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=328"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=328"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}