<\/p>\n
\u5149\u901f<\/strong><\/span>\u3092\u4e00\u5b9a\u306b\u4fdd\u3064\u5ea7\u6a19\u5909\u63db\u3068\u3057\u3066\u5c0e\u5165\u3057\u305f\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db<\/strong><\/span>\u306f\uff0c<\/p>\n \u969b\u306e\u5fae\u5c0f\u5909\u4f4d \u3055\u3089\u306b\uff0c\u3044\u3063\u305f\u3093\u6210\u7acb\u3057\u305f\u3053\u306e\u4e0d\u5909\u6027\u306f\u00a0 \\(PQ\\)\u00a0 \u9593\u304c\u5149\u304c\u4f1d\u64ad\u3057\u305f\u5fae\u5c0f\u5909\u4f4d\u3067\u3042\u308b\u5fc5\u8981\u306f\u306a\u304f\u3066\u3082\u6210\u308a\u7acb\u3064\u3002\u3057\u305f\u304c\u3063\u3066\uff0c\u3053\u3053\u3067\u5b9a\u7fa9\u3055\u308c\u305f\u5fae\u5c0f\u5909\u4f4d\u00a0 \\( ds^2 \\)\u00a0 \u306f\u4f55\u304b\u7279\u5225\u306a\u4e0d\u5909\u6027\u3092\u3082\u3064\u3082\u306e\u3068\u3057\u3066\u3088\u304f\u73fe\u308c\u308b\u306e\u3067\u7dda\u7d20<\/strong><\/span>\u3068\u3044\u3046\u540d\u524d\u304c\u4ed8\u3051\u3089\u308c\u3066\u3044\u308b\u3002<\/p>\n \u307e\u3068\u3081\u308b\u3068\uff0c\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db<\/strong><\/span>\u3068\u306f\u7dda\u7d20<\/strong><\/span>$$ ds^2 = -c^2 dt^2 + dx^2 + dy^2 + dz^2 $$ \u4eca\u5f8c\uff0c\u5149\u901f<\/strong><\/span> \\( c \\) \u304c\u81f3\u308b\u6240\u306b\u73fe\u308c\u308b\u306e\u3067\uff0c\u7c21\u5358\u306e\u305f\u3081 \\( c = 1 \\) \u3068\u3044\u3046\u8868\u8a18\u3092\u3059\u308b\u3053\u3068\u304c\u3042\u308b\u3002\u3082\u3061\u308d\u3093\u5b9f\u969b\u306e\u7269\u7406\u91cf\u3092\u6570\u5024\u7684\u306b\u8a08\u7b97\u3059\u308b\u3068\u304d\u306b\u306f\uff0c\u3057\u3063\u304b\u308a\u3068 \\( c \\) \u306e\u5024\u3092\u5165\u308c\u306a\u3044\u3068\u3060\u3081\u3067\u3059\u3088\u3002<\/p>\n \u307e\u305f\uff0c4\u3064\u306e\u5ea7\u6a19 \\(t, x, y, z\\) \u3092\u8868\u3059\u306e\u306b\u4ee5\u4e0b\u306e\u3088\u3046\u306a4\u6b21\u5143\u306e\u6dfb\u5b57\u3067\u8868\u8a18\u3059\u308b\u3002 \u307e\u305f\uff0c\u6b21\u306e\u3088\u3046\u306a4\u884c4\u5217\u306e\u884c\u5217\u3092\u5b9a\u7fa9\u3059\u308b\u3002 \u3059\u308b\u3068\u7dda\u7d20\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u3051\u308b\u3002 \u5149\u901f\u4e0d\u5909\u306e\u539f\u7406\u3068\u306f\uff0c\u7dda\u7d20\u306e\u5f62\u304c\u5ea7\u6a19\u7cfb\u306b\u3088\u3089\u306a\u3044\u3053\u3068\uff0c\u3064\u307e\u308a<\/p>\n $$ds^2 = \\eta_{\\mu\\nu} dx^{\\mu} dx^{\\nu} = \\eta_{\\mu\\nu} \\,dx^{\\mu’} dx^{\\nu’}$$<\/p>\n \u3068\u3044\u3046\u3053\u3068\u3092\u610f\u5473\u3059\u308b\uff0e\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u3068\u306f\uff0c\u7dda\u7d20\u306b\u3042\u3089\u308f\u308c\u308b\u30df\u30f3\u30b3\u30d5\u30b9\u30ad\u30fc\u8a08\u91cf \\(\\eta_{\\mu\\nu}\\) \u3092\u4e0d\u5909\u306b\u4fdd\u3064\u5ea7\u6a19\u5909\u63db\u3067\u3042\u308a\uff0c\u5f53\u7136\u306a\u304c\u3089\u7279\u6b8a\u76f8\u5bfe\u8ad6\u7684\u72b6\u6cc1\u3067\u306e\u307f\u6709\u52b9\u3067\u3042\u308b\u3002<\/p>\n \u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u3092 $x^{\\mu}$ \u304b\u3089 $x^{\\mu’}$ \u3078\u306e\u5ea7\u6a19\u5909\u63db\u3068\u3057\u30664\u6b21\u5143\u6dfb\u5b57\u8868\u8a18\u3067\u66f8\u304f\u3068\uff0c<\/p>\n \\begin{eqnarray}\n
\n$$ ds^2 \\equiv -c^2 dt^2 + dx^2 + dy^2 + dz^2 $$
\n\u3092\u4e0d\u5909\u306b\u4fdd\u3064\u5909\u63db\u3067\u3042\u308b\u3002\uff08\u5149\u306e\u5834\u5408\u306f $ds^2 = 0$\uff09<\/p>\n
\n\u3092\u4e0d\u5909\u306b\u4fdd\u3064\u5ea7\u6a19\u5909\u63db\u3067\u3042\u308b\uff01\u3068\u3044\u3046\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n4\u6b21\u5143\u306e\u6dfb\u5b57\u8868\u8a18<\/h3>\n
\n\\begin{eqnarray}
\nx^0 &\\equiv& ct\u00a0 \\\\
\nx^1 &\\equiv& x\\\\
\nx^2 &\\equiv& y\\\\
\nx^3 &\\equiv& z
\n\\end{eqnarray}
\n\u307e\u305f\uff0c\u6dfb\u5b57\u306b \\( \\mu, \\nu, \\dots\\) \u306a\u3069\u306e\u30ae\u30ea\u30b7\u30a2\u6587\u5b57\u3092\u4f7f\u3046\u5834\u5408\uff0c\u3053\u308c\u3089\u306f \\( 0\\) \u304b\u3089 \\(3\\) \u307e\u3067\u306e\u5168\u3066\u306e\u6570\u5024\u3092\u3068\u308b\u3068\u3059\u308b\u3002\u3064\u307e\u308a\uff0c\\( x^{\\mu} \\) \u3068\u66f8\u304f\u3068\uff0c\\( \\mu \\) \u306f\\( 0\\) \u304b\u3089 \\(3\\) \u307e\u3067\u306e\u3069\u308c\u3067\u3082\u3068\u308c\u308b\u306e\u3067\uff0c
\n\\begin{eqnarray}
\nx^{\\mu} &=&\u00a0 (x^0, x^1, x^2, x^3)\\\\
\n&=& ( c t, x, y, z)
\n\\end{eqnarray}
\n\u306e4\u3064\u306e\u5ea7\u6a19\u3092\u4e00\u6319\u306b\u8868\u3059\u3002\u5ea7\u6a19\u306e\u5fae\u5c0f\u5909\u4f4d\u306b\u3064\u3044\u3066\u3082\u540c\u69d8\u3067\uff0c
\n\\begin{eqnarray}
\ndx^{\\mu} &=& (dx^0, dx^1,d x^2, dx^3)\\\\
\n&=& ( c dt, dx, dy, dz)
\n\\end{eqnarray}<\/p>\n
\n\\begin{eqnarray}
\n\\eta_{\\mu\\nu} &\\equiv&
\n\\left(\u00a0 \\begin{array}{cccc}
\n\\eta_{00} & \\eta_{01} & \\eta_{02} & \\eta_{03} \\\\
\n\\eta_{10} & \\eta_{11} & \\eta_{12} & \\eta_{13} \\\\
\n\\eta_{20} & \\eta_{21} & \\eta_{22} & \\eta_{23} \\\\
\n\\eta_{30} & \\eta_{31} & \\eta_{32} & \\eta_{33}
\n\\end{array} \\right) \\\\ \\ \\\\
\n&=&
\n\\left(\\begin{array}{cccc}
\n-1 & 0 & 0 & 0 \\\\
\n0 & 1 & 0 & 0 \\\\
\n0 &0 & 1 & 0 \\\\
\n0 & 0 & 0 & 1
\n\\end{array}\\right)
\n\\end{eqnarray}<\/p>\n
\n\\begin{eqnarray}
\nds^2 &=& \\sum_{\\mu=0}^{3} \\sum_{\\nu=0}^{3} \\eta_{\\mu\\nu} dx^{\\mu} dx^{\\nu} \\\\ \\ \\\\
\n&\\equiv& \\eta_{\\mu\\nu} dx^{\\mu} dx^{\\nu}
\n\\end{eqnarray}
\n\u6700\u5f8c\u304c\u5927\u4e8b\u3067\uff0c\u4e0a\u4e0b\u6dfb\u5b57\u306b\u540c\u3058\u30ae\u30ea\u30b7\u30a2\u6587\u5b57\u304c\u3042\u308b\u5834\u5408\u306f<\/strong><\/span><\/span> \\(\\displaystyle\\sum\\) <\/strong><\/span>\u306e\u8a18\u53f7\u304c\u66f8\u3044\u3066\u3044\u306a\u304f\u3066\u3082\u81ea\u52d5\u7684\u306b \\(0\\) \u304b\u3089\\(3\\) \u307e\u3067\u306e\u548c\u3092\u3068\u308b<\/strong><\/span><\/span><\/span>\u3053\u3068\u306b\u3059\u308b\u3002\u3053\u308c\u3092\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306e\u898f\u7d04<\/strong><\/span>\u3068\u547c\u3093\u3067\u3044\u307e\u3059\u3002\u3053\u306e\u304a\u304b\u3052\u3067\u305a\u3044\u3076\u3093\u3068\u3059\u3063\u304d\u308a\u3057\u305f\u8868\u8a18\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n
\nx^{0\u2019} &=& \\frac{x^0 -\\frac{V}{c} x^1}{\\sqrt{1 -\\left(\\frac{V}{c}\\right)^2}}\\\\
\nx^{1\u2019} &=& \\frac{x^1 -\\frac{V}{c} x^0}{\\sqrt{1 -\\left(\\frac{V}{c}\\right)^2}}\\\\
\nx^{2\u2019} &=& x^2\\\\
\nx^{3\u2019} &=& x^3
\n\\end{eqnarray}<\/p>\n\u30d9\u30af\u30c8\u30eb\u306e\u8868\u8a18<\/h3>\n