{"id":992,"date":"2022-01-15T14:12:16","date_gmt":"2022-01-15T05:12:16","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=992"},"modified":"2022-06-21T16:53:57","modified_gmt":"2022-06-21T07:53:57","slug":"%e5%9b%ba%e6%9c%89%e6%99%82%e9%96%93%e3%82%92%e3%82%a2%e3%83%95%e3%82%a3%e3%83%b3%e3%83%91%e3%83%a9%e3%83%a1%e3%83%bc%e3%82%bf%e3%81%a8%e3%81%99%e3%82%8b%e6%b8%ac%e5%9c%b0%e7%b7%9a%e6%96%b9%e7%a8%8b","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%87%8d%e5%8a%9b%e5%a0%b4%e4%b8%ad%e3%81%ae%e3%83%86%e3%82%b9%e3%83%88%e7%b2%92%e5%ad%90%e3%81%ae%e9%81%8b%e5%8b%95\/%e5%9b%ba%e6%9c%89%e6%99%82%e9%96%93%e3%82%92%e3%82%a2%e3%83%95%e3%82%a3%e3%83%b3%e3%83%91%e3%83%a9%e3%83%a1%e3%83%bc%e3%82%bf%e3%81%a8%e3%81%99%e3%82%8b%e6%b8%ac%e5%9c%b0%e7%b7%9a%e6%96%b9%e7%a8%8b\/","title":{"rendered":"\u56fa\u6709\u6642\u9593\u3092\u30a2\u30d5\u30a3\u30f3\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u3059\u308b\u6e2c\u5730\u7dda\u65b9\u7a0b\u5f0f"},"content":{"rendered":"

\u91cd\u529b\u4ee5\u5916\u306e\u529b\u3092\u53d7\u3051\u305a\u306b\u904b\u52d5\u3059\u308b\u30c6\u30b9\u30c8\u7c92\u5b50\u306e\u7d4c\u8def\u306f\u6e2c\u5730\u7dda<\/strong><\/span>\u3067\u3042\u308a\uff0c\u56fa\u6709\u6642\u9593<\/strong><\/span> \\(\\tau\\) <\/strong><\/span>\u3092\u30a2\u30d5\u30a3\u30f3\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u3057\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u3051\u308b<\/strong><\/span>\u3053\u3068\u3092\u307e\u305a\u793a\u3057\u3066\u304a\u304f\u3002<\/p>\n

$$ \\frac{d\\boldsymbol{u}}{d\\tau} =\u00a0 \\frac{d}{d\\tau} \\left( \\frac{dx^{\\mu}}{d\\tau}\\,\\boldsymbol{e}_{\\mu}\\right) = \\boldsymbol{0}$$<\/p>\n

\u30a2\u30d5\u30a3\u30f3\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u5909\u63db<\/h3>\n

\u91cd\u529b\u4ee5\u5916\u306e\u529b\u3092\u53d7\u3051\u305a\u306b\u904b\u52d5\u3059\u308b\u30c6\u30b9\u30c8\u7c92\u5b50\u306e\u7d4c\u8def\u306f\u6e2c\u5730\u7dda<\/strong><\/span>\u3067\u3042\u308a\uff0c\u30a2\u30d5\u30a3\u30f3\u30d1\u30e9\u30e1\u30fc\u30bf<\/strong>\u3092 \\(v\\) \uff0c\u4e16\u754c\u7dda<\/strong><\/span>\u3092 \\(x^{\\mu}(v)\\)\uff0c\u63a5\u30d9\u30af\u30c8\u30eb<\/strong><\/span>\u3092 \\(\\boldsymbol{u}\\) \u3068\u66f8\u304f\u3068
\n$$ \\frac{d\\boldsymbol{u}}{dv} = \\frac{d}{dv} \\left( u^{\\mu}\\,\\boldsymbol{e}_{\\mu}\\right) = \\frac{d}{dv} \\left( \\frac{dx^{\\mu}}{dv}\\,\\boldsymbol{e}_{\\mu}\\right) = \\boldsymbol{0}$$<\/p>\n

\u3053\u308c\u304c\u30a2\u30d5\u30a3\u30f3\u30d1\u30e9\u30e1\u30fc\u30bf \\(v\\) \u3067\u30d1\u30e9\u30e1\u30c8\u30e9\u30a4\u30ba\u3055\u308c\u305f<\/strong>\u6e2c\u5730\u7dda\u65b9\u7a0b\u5f0f<\/strong><\/span>\u3067\u3042\u3063\u305f\u3002<\/p>\n

\u30a2\u30d5\u30a3\u30f3\u30d1\u30e9\u30e1\u30fc\u30bf<\/strong><\/span> \\(v\\) \u306e\u304b\u308f\u308a\u306b<\/p>\n

$$ w = w(v), \\quad \\frac{d}{dv} = \\frac{dw}{dv} \\frac{d}{dw}$$ \u3067\u5b9a\u7fa9\u3055\u308c\u308b\u5225\u306e\u30d1\u30e9\u30e1\u30fc\u30bf \\(w\\) \u3092\u4f7f\u3046\u3068\uff0c<\/p>\n

\\begin{eqnarray}
\n\\frac{d}{dv} \\left( \\frac{dx^{\\mu}}{dv}\\,\\boldsymbol{e}_{\\mu}\\right) &=&
\n\\frac{dw}{dv} \\frac{d}{dw} \\left(\\frac{dw}{dv} \\frac{dx^{\\mu}}{dw}\\,\\boldsymbol{e}_{\\mu} \\right) \\\\
\n&=& \\left( \\frac{dw}{dv}\\right)^2 \\frac{d}{dw} \\left( \\frac{dx^{\\mu}}{dw}\\,\\boldsymbol{e}_{\\mu}\\right) + \\frac{dw}{dv}\\frac{d^2w}{dv^2}\\frac{dx^{\\mu}}{dw}\\,\\boldsymbol{e}_{\\mu} \\\\
\n&=& \\boldsymbol{0}
\n\\end{eqnarray}<\/p>\n

\u3057\u305f\u304c\u3063\u3066\uff0c\\(w\\) \u304c$$w = a v + b \\quad\\mbox{\uff08\\(a, b\\) \u306f\u5b9a\u6570\uff09}$$\u3068\u3044\u3046\u30a2\u30d5\u30a3\u30f3\u5909\u63db<\/strong><\/span>\u3067\u5909\u63db\u3055\u308c\u308b\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u3042\u308c\u3070\uff0c\\(\\displaystyle \\frac{d^2w}{dv^2} = 0\\) \u3060\u304b\u3089
\n$$ \\frac{d}{dw} \\left( \\frac{dx^{\\mu}}{dw}\\,\\boldsymbol{e}_{\\mu}\\right) = \\boldsymbol{0}$$
\n\u3064\u307e\u308a\uff0c\\(w\\) \u3082\u307e\u305f\uff0c\u3053\u306e\u6e2c\u5730\u7dda<\/strong><\/span>\u306e\u30a2\u30d5\u30a3\u30f3\u30d1\u30e9\u30e1\u30fc\u30bf<\/strong><\/span>\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n

\u56fa\u6709\u6642\u9593\u304c\u30a2\u30d5\u30a3\u30f3\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u3042\u308b\u3053\u3068<\/h3>\n

\u56fa\u6709\u6642\u9593<\/strong><\/span> \\(\\tau\\) \uff08\u306e\u5fae\u5c0f\u5909\u4f4d \\(d\\tau\\)\uff09\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u308b\u3002<\/p>\n

$$ds^2 = g_{\\mu\\nu} dx^{\\mu} dx^{\\nu} \\equiv – c^2 d\\tau^2$$<\/p>\n

\u4ee5\u4e0b\u3067\u306f \\(c = 1\\) \u3068\u3057\u3066\u8a71\u3092\u7d9a\u3051\u308b\u3002\u307e\u305a\u306f\u4e00\u822c\u306b \\(v\\) \u3092\u30a2\u30d5\u30a3\u30f3\u30d1\u30e9\u30e1\u30fc\u30bf<\/strong><\/span>\uff0c\u7c92\u5b50\u306e\u4e16\u754c\u7dda\u306e\u63a5\u30d9\u30af\u30c8\u30eb\u3092 \\(\\boldsymbol{u}\\) \u3068\u3059\u308b\u3068
\n$$ \\boldsymbol{u}\\cdot\\boldsymbol{u} = g_{\\mu\\nu} \\frac{dx^{\\mu}}{dv} \\frac{dx^{\\nu}}{dv} = – \\left( \\frac{d\\tau}{dv}\\right)^2 $$<\/p>\n

\u3053\u308c\u3092 \\(v\\) \u3067\u5fae\u5206\u3057\u3066
\n$$\\frac{d}{dv} \\left( \\boldsymbol{u}\\cdot\\boldsymbol{u}\\right) = 2 \\boldsymbol{u}\\cdot\\frac{d\\boldsymbol{u}}{dv} = -2 \\frac{d\\tau}{dv} \\frac{d^2\\tau}{dv^2} $$<\/p>\n

\u6e2c\u5730\u7dda\u65b9\u7a0b\u5f0f<\/strong><\/span> \\(\\displaystyle \\frac{d\\boldsymbol{u}}{dv} = \\boldsymbol{0}\\) \u3088\u308a\uff0c
\n$$\\frac{d^2\\tau}{dv^2} = 0$$ \u3064\u307e\u308a\uff0c\u56fa\u6709\u6642\u9593<\/strong><\/span> \\(\\tau\\) \u3082\u307e\u305f\u30a2\u30d5\u30a3\u30f3\u5909\u63db\u306b\u3088\u3063\u3066\u95a2\u4fc2\u3065\u3051\u3089\u308c\u305f\u30a2\u30d5\u30a3\u30f3\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u3042\u308b<\/strong><\/span>\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n

\u3068\u3044\u3046\u308f\u3051\u3067\uff0c\u4eca\u5f8c\u306f\u30c6\u30b9\u30c8\u7c92\u5b50\u306e\u4e16\u754c\u7dda\u306e\u30a2\u30d5\u30a3\u30f3\u30d1\u30e9\u30e1\u30fc\u30bf<\/strong><\/span>\u3068\u3057\u3066\u306f\uff0c\u56fa\u6709\u6642\u9593<\/strong><\/span> \\(\\tau\\) \u3092\u4f7f\u3046\u3053\u3068\u306b\u3059\u308b\u3002<\/p>\n

\u56fa\u6709\u6642\u9593\u3092\u30a2\u30d5\u30a3\u30f3\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u3059\u308b\u6e2c\u5730\u7dda\u65b9\u7a0b\u5f0f<\/h3>\n

\u91cd\u529b\u4ee5\u5916\u306e\u529b\u3092\u53d7\u3051\u305a\u306b\u904b\u52d5\u3059\u308b\u30c6\u30b9\u30c8\u7c92\u5b50\u306e\u7d4c\u8def\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u56fa\u6709\u6642\u9593<\/strong><\/span> \\(\\tau\\) \u3092\u30a2\u30d5\u30a3\u30f3\u30d1\u30e9\u30e1\u30fc\u30bf<\/strong><\/span>\u3068\u3057\u305f\u6e2c\u5730\u7dda\u65b9\u7a0b\u5f0f<\/strong><\/span>\u3067\u8868\u3055\u308c\u308b\u3002<\/p>\n

$$ \\frac{d\\boldsymbol{u}}{d\\tau} = \\frac{d}{d\\tau} \\left( u^{\\mu}\\,\\boldsymbol{e}_{\\mu}\\right) = \\frac{d}{d\\tau} \\left( \\frac{dx^{\\mu}}{d\\tau}\\,\\boldsymbol{e}_{\\mu}\\right) = \\boldsymbol{0}$$<\/p>\n

\u5225\u30da\u30fc\u30b8\u300c\u6e2c\u5730\u7dda\u3068\u63a5\u7d9a\u4fc2\u6570\u30fb\u30af\u30ea\u30b9\u30c8\u30c3\u30d5\u30a7\u30eb\u8a18\u53f7<\/a>\u300d\u306b\u3042\u308b\u3088\u3046\u306b\uff0c\u6e2c\u5730\u7dda\u65b9\u7a0b\u5f0f\u3092\u6210\u5206\u3067\u66f8\u304f\u3068\uff0c\uff08\u30a2\u30d5\u30a3\u30f3\u30d1\u30e9\u30e1\u30fc\u30bf\u3092 \\(v\\) \u304b\u3089 \\(\\tau\\) \u306b\u3057\u3066\uff09<\/p>\n

\\begin{eqnarray}
\n\\frac{du^{\\mu}}{d\\tau} + \\varGamma^{\\mu}_{\\ \\ \\alpha\\beta} u^{\\alpha}u^{\\beta}
\n= 0
\n\\end{eqnarray}<\/p>\n

\u3042\u308b\u3044\u306f\uff0c\\(\\displaystyle u^{\\mu} = \\frac{dx^{\\mu}}{d\\tau}\\) \u3092\u4f7f\u3063\u3066\uff0c<\/p>\n

\\begin{eqnarray}
\n\\frac{d^2 x^{\\mu}}{d\\tau^2} + \\varGamma^{\\mu}_{\\ \\ \\alpha\\beta} \\frac{d x^{\\alpha}}{d\\tau} \\frac{d x^{\\beta}}{d\\tau}
\n= 0
\n\\end{eqnarray}<\/p>\n

\u4e16\u306e\u4e2d\u306e\u6559\u79d1\u66f8\u3067\u306f\uff0c\u6e2c\u5730\u7dda\u65b9\u7a0b\u5f0f\u306f\u56fa\u6709\u6642\u9593 \\(\\tau\\) \u6c7a\u3081\u6253\u3061\u3067\u4e0a\u8a18\u306e\u3088\u3046\u306b\u306a\u308b\u3068\u3044\u3046\u8aac\u660e\u3092\u3057\uff0c\u3057\u304b\u3057\u5149\u306e\u5834\u5408\u306f \\(d\\tau = 0\\) \u3060\u304b\u3089\u5225\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\uff08\u3053\u308c\u3092\u30a2\u30d5\u30a3\u30f3\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u547c\u3076\uff09\uff0c\u305f\u3068\u3048\u3070 \\(v\\) \u3068\u304b\u3092\u4f7f\u3063\u3066\u6e2c\u5730\u7dda\u65b9\u7a0b\u5f0f\u3092\u66f8\u304f\uff0c\u306a\u3069\u3068\u3044\u3046\u30b7\u30e7\u30fc\u30c8\u30ab\u30c3\u30c8\u306a\u8aac\u660e\u304c\u306a\u3055\u308c\u308b\u3053\u3068\u304c\u591a\u3044\u3002\u672c\u7a3f\u3067\u306e\u7acb\u5834\u306f\u305d\u3046\u3067\u306f\u306a\u304f\u3066\uff0c\u3059\u3079\u304b\u3089\u304f\u6e2c\u5730\u7dda\u65b9\u7a0b\u5f0f\u3068\u3044\u3046\u3082\u306e\u306f\uff0c\u30c6\u30b9\u30c8\u7c92\u5b50\u306b\u3064\u3044\u3066\u3067\u3042\u308c\u5149\u306b\u3064\u3044\u3066\u3067\u3042\u308c\uff0c\u30a2\u30d5\u30a3\u30f3\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u4f7f\u3063\u3066\u66f8\u304b\u308c\u308b\u3093\u3067\u3059\u3088\uff0c\u7279\u306b\u30c6\u30b9\u30c8\u7c92\u5b50\u306e\u5834\u5408\u306f\u56fa\u6709\u6642\u9593\u3092\u30a2\u30d5\u30a3\u30f3\u30d1\u30e9\u30e1\u30fc\u30bf\u306b\u3068\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3088\uff0c\u3068\u3044\u3046\u7acb\u5834\u3067\u66f8\u3044\u3066\u307f\u307e\u3057\u305f\u3002\u30a2\u30d5\u30a3\u30f3\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u306a\u3044\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u306f\u6e2c\u5730\u7dda\u65b9\u7a0b\u5f0f\u306f\u3069\u306e\u3088\u3046\u306a\u5f62\u306b\u306a\u308b\u304b\uff0c\u3068\u3044\u3046\u7df4\u7fd2\u554f\u984c\u3082\u5927\u5b66\u9662\u306e\u6388\u696d\u3067\u306f\u51fa\u3057\u305f\u308a\u3057\u307e\u3059\u3002<\/p>\n

\u5171\u5909\u6210\u5206\u306b\u5bfe\u3059\u308b\u6e2c\u5730\u7dda\u65b9\u7a0b\u5f0f<\/h3>\n

\u307e\u305f\uff0c\u5b9f\u969b\u306e\u8a08\u7b97\u306e\u969b\u306b\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3057\u3066\uff0c\u4fdd\u5b58\u91cf\u304c\u308f\u304b\u308a\u3084\u3059\u3044\u3088\u3046\u306b\u5909\u5f62\u3057\u305f\u6e2c\u5730\u7dda\u65b9\u7a0b\u5f0f\u3092\u4f7f\u3046\u3053\u3068\u304c\u4fbf\u5229\u306a\u5834\u5408\u304c\u3042\u308b\u3002<\/p>\n

\u6e2c\u5730\u7dda\u65b9\u7a0b\u5f0f<\/strong><\/span>\u3068\u57fa\u672c\u30d9\u30af\u30c8\u30eb<\/strong><\/span> \\(\\boldsymbol{e}_{\\nu} \\) \u3068\u306e\u5185\u7a4d\u3092\u3068\u3063\u3066<\/p>\n

\\begin{eqnarray}
\n0 = \\boldsymbol{e}_{\\nu}\\cdot \\frac{d\\boldsymbol{u}}{d\\tau} &=&
\n\\frac{d}{d\\tau} \\left( \\boldsymbol{u}\\cdot\\boldsymbol{e}_{\\nu} \\right) –
\n\\boldsymbol{u}\\cdot\\boldsymbol{e}_{\\nu, \\lambda}\\frac{dx^{\\lambda}}{d\\tau} \\\\
\n&=& \\frac{d}{d\\tau} \\left( u^{\\mu} \\boldsymbol{e}_{\\mu}\\cdot\\boldsymbol{e}_{\\nu} \\right) – \\boldsymbol{e}_{\\mu}\\cdot \\boldsymbol{e}_{\\lambda, \\nu} u^{\\mu} u^{\\lambda} \\\\
\n&=& \\frac{d}{d\\tau} \\left( g_{\\nu\\mu} u^{\\mu}\u00a0 \\right) – \\frac{1}{2} g_{\\mu\\lambda, \\nu} u^{\\mu} u^{\\lambda}
\n\\end{eqnarray}<\/p>\n

\\( u_{\\nu} \\equiv g_{\\nu\\mu} u^{\\mu} \\) \u3068\u3059\u308b\u3068\uff0c \u300c\u5171\u5909\u6210\u5206<\/strong><\/span>\u300d\\(u_{\\nu} \\) \uff08\u6b74\u53f2\u7684\u306b\u306f\u4e0a\u4ed8\u6dfb\u5b57\u6210\u5206<\/strong><\/span> \\(u^{\\mu}\\) \u3092\u53cd\u5909\u6210\u5206<\/strong><\/span>\u3068\u304b\u53cd\u5909\u30d9\u30af\u30c8\u30eb<\/strong><\/span>\u306a\u3069\u3068\u547c\u3073\uff0c\u4e0b\u4ed8\u6dfb\u5b57\u6210\u5206<\/strong><\/span> \\(u_{\\mu}\\) \u3092\u5171\u5909\u6210\u5206<\/strong><\/span>\u3068\u304b\u5171\u5909\u30d9\u30af\u30c8\u30eb<\/strong><\/span>\u306a\u3069\u3068\u547c\u3093\u3067\u3044\u305f\uff09\u306b\u5bfe\u3059\u308b\u6e2c\u5730\u7dda\u65b9\u7a0b\u5f0f<\/strong><\/span>\u306f\uff08\u6dfb\u5b57\u3092\u66f8\u304d\u63db\u3048\u3066\uff09<\/p>\n

$$\\frac{d u_{\\mu}}{d\\tau} = \\frac{1}{2} g_{\\alpha\\beta, \\mu} u^{\\alpha} u^{\\beta}$$ \u3068\u306a\u308b\u3002<\/p>\n

\u3053\u306e\u3053\u3068\u304b\u3089\uff0c\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u306e\u6210\u5206 \\(g_{\\alpha\\beta} \\) \u304c\u3042\u308b\u7279\u5b9a\u306e\u5ea7\u6a19 \\(x^{\\mu} \\) \u4f9d\u5b58\u6027\u3092\u3082\u305f\u306a\u3044\u5834\u5408\u306f\uff0c\u305f\u3060\u3061\u306b
\n$$\\displaystyle g_{\\alpha\\beta, \\mu} = 0\\quad\\Rightarrow\\quad \\frac{d u_{\\mu}}{d\\tau} = 0 \\quad\\Rightarrow\\quad u_{\\mu} = \\mbox{const.} $$
\n\u3068\u306a\u308a\u4e0b\u4ed8\u6dfb\u5b57\u306e \\(u_{\\mu} \\) \u6210\u5206\u304c\u4fdd\u5b58\u91cf\u3068\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n

\u4ee5\u4e0a\u306e\u3053\u3068\u304b\u3089\u308f\u304b\u308b\u3088\u3046\u306b\uff0c\u3053\u306e\u300c\u5171\u5909\u6210\u5206\u300d\u306b\u5bfe\u3059\u308b\u6e2c\u5730\u7dda\u65b9\u7a0b\u5f0f\u306f\uff0c\u89e3\u6790\u529b\u5b66\u306b\u304a\u3051\u308b\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u65b9\u7a0b\u5f0f\u306b\u76f8\u5f53\u3057\uff0c\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb \\(g_{\\alpha\\beta} \\) \uff0c\u3057\u305f\u304c\u3063\u3066\u30e9\u30b0\u30e9\u30f3\u30b8\u30a2\u30f3\u304c\u7279\u5b9a\u306e\u5ea7\u6a19 \\(x^{\\mu} \\) \u4f9d\u5b58\u6027\u3092\u3082\u305f\u306a\u3044\u5834\u5408\u306f\uff0c \\(x^{\\mu} \\) \u306f\u5faa\u74b0\u5ea7\u6a19\u3068\u547c\u3070\u308c\uff0c\u3053\u306e\u5faa\u74b0\u5ea7\u6a19\u306b\u5171\u5f79\u306a\u4e00\u822c\u5316\u904b\u52d5\u91cf\u3067\u3042\u308b \\(u_{\\mu} \\) \u304c\u4fdd\u5b58\u3059\u308b\u3068\u3044\u3046\u3053\u3068\u3092\u8868\u3057\u3066\u3044\u308b\u3002\uff08\u89e3\u6790\u529b\u5b66\u3092\u5b66\u3093\u3060\u5b66\u751f\u3055\u3093\u306b\u306f\uff0c\u3053\u306e\u3088\u3046\u306a\u8aac\u660e\u304c\u30a6\u30b1\u308b\u304b\u3082\u3057\u308c\u306a\u3044\u304c\uff0c\u3046\u3061\u306e\u5b66\u79d1\u306f\u7269\u7406\u5b66\u79d1\u3067\u306f\u306a\u3044\u306e\u3067\u89e3\u6790\u529b\u5b66\u306e\u6388\u696d\u304c\u306a\u304f\uff0c\u30e9\u30b0\u30e9\u30f3\u30b8\u30a2\u30f3\u3042\u308a\u304d\u306e\u8aac\u660e\u306f\u5c01\u5370\u3002\uff09<\/p>\n

4\u5143\u901f\u5ea6<\/h3>\n

\u56fa\u6709\u6642\u9593<\/strong><\/span> \\(\\tau\\) \u3092\u30a2\u30d5\u30a3\u30f3\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u3059\u308b\u30c6\u30b9\u30c8\u7c92\u5b50\u306e\u4e16\u754c\u7dda<\/strong><\/span> \\(x^{\\mu}(\\tau)\\) \u306e\u63a5\u30d9\u30af\u30c8\u30eb
\n$$\\displaystyle\u00a0 \\boldsymbol{u} = \\frac{dx^{\\mu}}{d\\tau} \\, \\boldsymbol{e}_{\\mu} $$
\n\u30924\u5143\u901f\u5ea6<\/strong><\/span>\u3068\u547c\u3076\u30024\u5143\u901f\u5ea6<\/strong><\/span>\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u898f\u683c\u5316\u3055\u308c\u3066\u3044\u308b\u3002<\/p>\n

$$ \\boldsymbol{u}\\cdot\\boldsymbol{u} = g_{\\mu\\nu} \\frac{dx^{\\mu}}{d\\tau} \\frac{dx^{\\nu}}{d\\tau} = \\frac{ds^2}{d\\tau^2} = -c^2 (=-1\\quad \\because c = 1)$$<\/p>\n

\u53c2\u8003\uff1a\u30c6\u30b9\u30c8\u7c92\u5b50\u3068\u306f<\/h3>\n

\u3061\u306a\u307f\u306b\uff0c\u30c6\u30b9\u30c8\u7c92\u5b50<\/strong><\/span>\u3068\u306f\u8cea\u91cf\u306f\u6301\u3064\u304c\uff0c\u305d\u306e\u8cea\u91cf\u304c\u4f5c\u308b\u3042\u3089\u305f\u306a\u91cd\u529b\u5834\u306f\u7121\u8996\u3067\u304d\u308b\u3088\u3046\u306a\u72b6\u6cc1\u3092\u3055\u3059\u3002\uff08\u91cd\u529b\u6e90\u304b\u3089\u306e\u300c\u4f5c\u7528\u300d\u306f\u53d7\u3051\u308b\u304c\uff0c\u300c\u53cd\u4f5c\u7528\u300d\u306f\u53ca\u307c\u3055\u306a\u3044\uff0c\u3068\u3044\u3046\u7406\u89e3\u3067\u3082\u3088\u3044\u3002\uff09
\n\u91cd\u529b\u6e90\u3068\u306a\u308b\u5929\u4f53\uff08\u8cea\u70b9\uff09\u304c1\u4f53\u306e\u307f\u306e\u5834\u5408\uff0c\u3053\u308c\u306f\u30cb\u30e5\u30fc\u30c8\u30f3\u529b\u5b66\u3067\u306f1\u4f53\u554f\u984c<\/strong><\/span>\u3068\u547c\u3070\u308c\u308b\u72b6\u6cc1\u3067\uff0c\u30c6\u30b9\u30c8\u7c92\u5b50\u306e\u904b\u52d5\u306f\u4e00\u822c\u7684\u306b\uff08\u6955\u5186\u8ecc\u9053\u306a\u3069\u3068\u3057\u3066\uff09\u89e3\u6790\u7684\u306b\u89e3\u3051\u3066\u3057\u307e\u3046\u3002<\/p>\n

\u307e\u305f\uff0c\u30cb\u30e5\u30fc\u30c8\u30f3\u529b\u5b66\u3067\u306f2\u3064\u306e\u5929\u4f53\uff08\u8cea\u70b9\uff09\u304c\u4e92\u3044\u306b\u91cd\u529b\u3092\u53ca\u307c\u3057\u5408\u3063\u3066\u904b\u52d5\u3059\u308b2\u4f53\u554f\u984c<\/strong>\u30821\u4f53\u554f\u984c\u306b\u5e30\u7740\u3057\u3066\u53b3\u5bc6\u306b\u89e3\u3051\u308b<\/strong><\/span>\u304c\uff0c3\u4f53\u554f\u984c\uff08\u4ee5\u4e0a\uff09\u306f\uff08\u7279\u6b8a\u306a\u5834\u5408\u3092\u9664\u304d\uff09\u4e00\u822c\u306b\u306f\u89e3\u6790\u7684\u306b\u89e3\u3051\u306a\u3044\u3002<\/p>\n

\u76f8\u5bfe\u8ad6\u306b\u304a\u3044\u3066\u306f\uff0c2\u4f53\u554f\u984c<\/strong><\/span>\u306f\u3082\u3061\u308d\u3093\u306e\u3053\u3068\uff0c1\u4f53\u554f\u984c<\/strong><\/span>\u3055\u3048\u3082\uff08\u5186\u8ecc\u9053<\/strong><\/span>\u3084\u52d5\u5f84\u65b9\u5411\u306e\u81ea\u7531\u843d\u4e0b<\/strong><\/span>\u7b49\u306e\u7279\u6b8a\u306a\u5834\u5408\u3092\u9664\u304d\uff09\u4e00\u822c\u306b\u306f\u89e3\u6790\u7684\u306a\u53b3\u5bc6\u89e3\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u306a\u3044\u306e\u3067\uff0c\u5149\u306e\u7d4c\u8def\u306e\u5834\u5408\u3068\u540c\u69d8\u306b\uff0c\u4f55\u3089\u304b\u306e\u8fd1\u4f3c\u7684\u624b\u6cd5\u306b\u3088\u308b\u8fd1\u4f3c\u89e3\u3092\u6c42\u3081\u308b\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

\n","protected":false},"author":2,"featured_media":0,"parent":85,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-992","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/992","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/comments?post=992"}],"version-history":[{"count":21,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/992\/revisions"}],"predecessor-version":[{"id":3054,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/992\/revisions\/3054"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/85"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=992"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}