<\/p>\n
\u5149\u901f<\/strong><\/span>\u306f \\(c\\)\u00a0 \u3067\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u306f\uff0c \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 \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 \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’\\) \u7cfb\u3067\u8a18\u8ff0\u3057\u3066\u307f\u308b\u3068\uff0c<\/p>\n \\(S’\\) \u7cfb\u3067\u306e\u5149\u306e\u901f\u3055\u306f $$\\left(\\frac{dx’}{dt’}\\right)^2 + \\left(\\frac{dy’}{dt’}\\right)^2 + \\left(\\frac{dz’}{dt’}\\right)^2 \u5149\u901f\u4e0d\u5909\u306e\u539f\u7406<\/strong><\/span><\/p>\n \u3068\u547c\u3093\u3060\u308a\uff0c\u3042\u308b\u3044\u306f\u6587\u7ae0\u3068\u3057\u3066<\/p>\n \u5149\u306e\u901f\u3055\u306f\u5ea7\u6a19\u7cfb\u306b\u3088\u3089\u305a\u4e00\u5b9a\u3067\u3042\u308b<\/span><\/strong><\/span><\/p>\n \u3068\u8a00\u3063\u305f\u308a\u3059\u308b\u3002<\/p>\n \\( S \\) \u7cfb \\( \\{t, x, y, z\\} \\) \u306b\u304a\u3044\u3066\u3082 \\(S’ \\) \u7cfb \\( \\{t’, x’, y’, z’\\}\u00a0 \\) \u306b\u304a\u3044\u3066\u3082\u5149\u901f\u306f\u4e00\u5b9a\u3067\u3042\u308b<\/strong><\/span>\uff0c\u3068\u3044\u3046\u3053\u3068\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u3051\u308b\u3002<\/p>\n $$ -c^2 dt^2 + dx^2 + dy^2 + dz^2 =\u00a0 -c^2 dt’^2 + dx’^2 + dy’^2 + dz’^2 $$<\/p>\n \u70b9 \\(P\\) \u304b\u3089\u8fd1\u508d\u306e\u70b9 \\(Q\\) \u307e\u3067\u5149\u304c\u4f1d\u64ad\u3059\u308b\u5834\u5408\u306e\u5fae\u5c0f\u5909\u4f4d\u306b\u3064\u3044\u3066\u306f\uff0c\u4e0a\u5f0f\u306e\u5de6\u8fba\u3082\u53f3\u8fba\u3082\u3069\u3061\u3089\u3082\u30bc\u30ed\u3068\u3044\u3046\u610f\u5473\u3067\u7b49\u53f7\u304c\u6210\u308a\u7acb\u3063\u3066\u3044\u308b\u3002<\/p>\n \u4e00\u822c\u306b\u5ea7\u6a19\u5909\u63db<\/strong><\/span>\u3068\u306f2\u3064\u306e\u5ea7\u6a19\u7cfb \\( S\\{t, x, y, z \\} \\) \u3068 \\( S’\\{t’, x’, y’, z’ \\} \\) \u306e\u5ea7\u6a19\u540c\u58eb\u3092\u95a2\u4fc2\u4ed8\u3051\u308b\u5f0f\u306e\u30bb\u30c3\u30c8\u3067\u3042\u308b\u3002\u300c\u5149\u306e\u901f\u3055\u306f\u5ea7\u6a19\u7cfb\u306b\u3088\u3089\u305a\u4e00\u5b9a\u3067\u3042\u308b<\/strong><\/span>\u300d\u3068\u3044\u3046\u7279\u6b8a\u76f8\u5bfe\u8ad6\u306e\u8981\u8acb\u3092\u6e80\u305f\u3059\u5ea7\u6a19\u5909\u63db\u306f\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db<\/span><\/strong><\/span>\u3068\u547c\u3070\u308c\u308b\u3002<\/p>\n \u5ea7\u6a19\u7cfb \\( S\\{t, x, y, z \\} \\) \u3068\uff0c\\(S\\) \u7cfb\u306b\u5bfe\u3057\u3066 \\(+x\\) \u65b9\u5411\u306b\u901f\u3055 \\(V\\) \u3067\u904b\u52d5\u3059\u308b\u5ea7\u6a19\u7cfb \\( S’\\{t’, x’, y’, z’ \\} \\) \u306e\u9593\u306e\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db<\/strong><\/span>\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u3051\u308b\u3002\uff08\u5149\u901f \\(c\\) \u3092\u4f7f\u3063\u3066\uff0c\\(c t, \\ c t’\\) \u306a\u3069\u3068\u3057\u3066\u9577\u3055\u306e\u5358\u4f4d\u306b\u3042\u308f\u305b\u3066\u3044\u307e\u3059\u3002\uff09<\/p>\n \\begin{eqnarray} 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\n$$\\left(\\frac{dx}{dt}\\right)^2 + \\left(\\frac{dy}{dt}\\right)^2 + \\left(\\frac{dz}{dt}\\right)^2
\n= c^2 $$
\n\u4e21\u8fba\u306b \\(dt^2\\) \u3092\u304b\u3051\u3066\u6574\u7406\u3059\u308b\u3068
\n$$ -c^2 dt^2 + dx^2 + dy^2 + dz^2= 0$$<\/p>\n\n
\n= c^2 $$
\n\u3042\u308b\u3044\u306f\u6574\u7406\u3057\u3066\uff0c
\n$$ -c^2 dt’^2 + dx’^2 + dy’^2 + dz’^2= 0$$
\n\u3068\u306a\u308b\u3002\u5927\u4e8b\u306a\u3053\u3068\u306f\uff0c\\(S’\\) \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\u5ea7\u6a19\u7cfb\u306b\u3088\u3089\u305a\u5149\u901f\u306f\u4e00\u5b9a\u3067\u3042\u308b\u3068\u306f\uff1f<\/h3>\n
\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\uff1a\u5149\u901f\u3092\u4e00\u5b9a\u306b\u4fdd\u3064\u5ea7\u6a19\u5909\u63db<\/h3>\n
\nct’ &=& \\frac{ct -\\frac{V}{c} x}{\\sqrt{1 -\\left(\\frac{V}{c}\\right)^2}}\\\\
\nx’ &=& \\frac{x -\\frac{V}{c} c t}{\\sqrt{1 -\\left(\\frac{V}{c}\\right)^2}}\\\\
\ny’ &=& y\\\\
\nz’ &=& z
\n\\end{eqnarray}<\/p>\n