{"id":204,"date":"2022-01-05T14:39:43","date_gmt":"2022-01-05T05:39:43","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=204"},"modified":"2023-07-13T15:32:06","modified_gmt":"2023-07-13T06:32:06","slug":"%e5%85%89%e3%81%ae%e3%83%89%e3%83%83%e3%83%97%e3%83%a9%e3%83%bc%e5%8a%b9%e6%9e%9c","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%83%ad%e3%83%bc%e3%83%ac%e3%83%b3%e3%83%84%e5%a4%89%e6%8f%9b%e3%81%ab%e3%82%88%e3%82%89%e3%81%aa%e3%81%84%e7%9b%b8%e5%af%be%e8%ab%96%e3%81%ae%e7%90%86%e8%a7%a3\/%e5%85%89%e3%81%ae%e3%83%89%e3%83%83%e3%83%97%e3%83%a9%e3%83%bc%e5%8a%b9%e6%9e%9c\/","title":{"rendered":"\u5149\u306e\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c"},"content":{"rendered":"<p>\u5149\u306e\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306f\uff0c\u4e16\u306b\u3042\u307e\u305f\u3042\u308b\u6a19\u6e96\u7684\u306a\u6559\u79d1\u66f8\u3067\u306f\uff0c\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u3092\u7528\u3044\u3066\u8aac\u660e\u3055\u308c\u308b\u306e\u3067\u3042\u3063\u305f\u3002\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u306b\u3082\u3068\u3065\u3044\u305f\u5149\u306e\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306e\u6a19\u6e96\u7684\u306a\u8aac\u660e\u306b\u3064\u3044\u3066\u306f\uff0c\u5225\u30da\u30fc\u30b8\u300c<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e8%b5%a4%e6%96%b9%e5%81%8f%e7%a7%bb%e3%81%ae%e7%b5%b1%e4%b8%80%e7%9a%84%e7%90%86%e8%a7%a3\/%e5%85%89%e3%81%ae%e3%83%89%e3%83%83%e3%83%97%e3%83%a9%e3%83%bc%e5%8a%b9%e6%9e%9c%e3%81%ae%e3%81%8a%e3%81%95%e3%82%89%e3%81%84\/\" target=\"_blank\" rel=\"noopener\">\u5149\u306e\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306e\u304a\u3055\u3089\u3044<\/a>\u300d\u306b\u307e\u3068\u3081\u3066\u3042\u308b\u3002<\/p>\n<p>\u3053\u3053\u3067\u306f\uff0c\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u306e\u65b9\u91dd\u300c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u306b\u3088\u3089\u306a\u3044\u7279\u6b8a\u76f8\u5bfe\u8ad6\u306e\u7d71\u4e00\u7684\u7406\u89e3<\/strong><\/span>\u300d\u306b\u5247\u3063\u3066\uff0c\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u3092\u4f7f\u308f\u305a\u306b\u5149\u306e\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306e\u8aac\u660e\u3092\u8a66\u307f\u308b\u3002<\/p>\n<p id=\"yui_3_17_2_1_1641360729261_1392\"><!--more--><\/p>\n<p>\u300c<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%83%ad%e3%83%bc%e3%83%ac%e3%83%b3%e3%83%84%e5%a4%89%e6%8f%9b%e3%81%ab%e3%82%88%e3%82%89%e3%81%aa%e3%81%84%e7%9b%b8%e5%af%be%e8%ab%96%e3%81%ae%e7%90%86%e8%a7%a3\/%e5%85%89%e3%81%ae4%e5%85%83%e3%83%99%e3%82%af%e3%83%88%e3%83%ab\/#4_boldsymbolk_31\" target=\"_blank\" rel=\"noopener\">\u5149\u306e4\u5143\u30d9\u30af\u30c8\u30eb<\/a>\u300d\u306e\u30da\u30fc\u30b8\u3067\u8ff0\u3079\u305f\u3088\u3046\u306b\uff0c\u5149\u306e\u4f1d\u64ad\u3092\u8868\u30594\u5143\u30d9\u30af\u30c8\u30eb \\(\\boldsymbol{k}\\) \u306f\uff0c4\u5143\u901f\u5ea6 \\(\\boldsymbol{u}\\) \u306e\u89b3\u6e2c\u8005 \\(A\\) \u304c\u89b3\u6e2c\u3059\u308b\u632f\u52d5\u6570 \\(\\omega\\) \u3068\u5149\u306e\u4f1d\u64ad\u65b9\u5411\u3092\u8868\u3059\u7a7a\u9593\u7684\u5358\u4f4d\u30d9\u30af\u30c8\u30eb \\( \\boldsymbol{\\gamma}\\) \u3092\u4f7f\u3063\u3066\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u3051\u308b\u306e\u3067\u3042\u3063\u305f\u3002$$ \\boldsymbol{k} = \\omega (\\boldsymbol{u} + \\boldsymbol{\\gamma}), \\quad\\omega \\equiv &#8211; \\boldsymbol{k} \\cdot\\boldsymbol{u} $$<\/p>\n<p id=\"yui_3_17_2_1_1641360729261_1393\">\u3053\u306e\u540c\u3058\u5149\uff0c\u3064\u307e\u308a\u540c\u3058 \\(\\boldsymbol{k}\\) \u3067\u8868\u3055\u308c\u308b\u5149\u3092\uff0c\u89b3\u6e2c\u8005 \\(A\\) \u306b\u5bfe\u3057\u3066\u901f\u5ea6 \\(V \\boldsymbol{e} \\) \u3067\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005 \\(B\\) \u304c\u6e2c\u5b9a\u3059\u308b\u3068\uff0c\u305d\u306e\u632f\u52d5\u6570 \\(\\bar{\\omega}\\) \u306f\uff0c\u89b3\u6e2c\u8005 \\(B\\) \u306e<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>4\u5143\u901f\u5ea6<\/strong><\/span> \\(\\bar{\\boldsymbol{u}}\\) \u3092\u4f7f\u3063\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u3051\u308b\u3002$$ \\bar{\\omega} = &#8211; \\boldsymbol{k}\\cdot \\bar{\\boldsymbol{u}}$$<br \/>\n\u305d\u3057\u3066\uff0c<br id=\"yui_3_17_2_1_1641360729261_1394\" \/>$$ \\boldsymbol{k} = \\bar{\\omega} (\\bar{\\boldsymbol{u}} + \\bar{\\boldsymbol{\\gamma}})$$<br \/>\n\u3068\u306a\u308a\uff0c\\(\\bar{\\boldsymbol{\\gamma}}\\)\u00a0 \u306f\u89b3\u6e2c\u8005 \\(B\\) \u304c\u89b3\u6e2c\u3059\u308b\u5149\u306e\u9032\u884c\u65b9\u5411\u3092\u8868\u3059\u7a7a\u9593\u7684\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308b\u3002<br \/>\n$$ \\bar{\\boldsymbol{\\gamma}}\\cdot\\bar{\\boldsymbol{u}} = 0, \\quad \\bar{\\boldsymbol{\\gamma}}\\cdot\\bar{\\boldsymbol{\\gamma}} = 1$$<\/p>\n<h4 id=\"yui_3_17_2_1_1641360729261_1395\"><\/h4>\n<h3 id=\"yui_3_17_2_1_1641360729261_1396\">\u00a0\\(A\\) \u3068\u3068\u3082\u306b\u9759\u6b62\u3057\u3066\u3044\u308b\u5149\u6e90\u304b\u3089\u306e\u5149\u3092\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005 \\(B\\) \u304c\u6e2c\u5b9a\u3059\u308b\u5834\u5408<\/h3>\n<p id=\"yui_3_17_2_1_1641360729261_1398\">\\(\\bar{\\omega}\\) \u3068 \\(\\omega\\) \u306e\u95a2\u4fc2\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3057\u3066\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<br id=\"yui_3_17_2_1_1641360729261_1399\" \/>\\begin{eqnarray}<br id=\"yui_3_17_2_1_1641360729261_1400\" \/>\\omega &amp;=&amp;\u00a0 &#8211; \\boldsymbol{k}\\cdot \\boldsymbol{u} \\\\<br id=\"yui_3_17_2_1_1641360729261_1401\" \/>&amp;=&amp; -\\bar{\\omega} (\\bar{\\boldsymbol{u}} + \\bar{\\boldsymbol{\\gamma}})\\cdot \\frac{1}{\\sqrt{1-V^2}} (\\bar{\\boldsymbol{u}} &#8211; V \\bar{\\boldsymbol{e}}) \\\\<br id=\"yui_3_17_2_1_1641360729261_1402\" \/>&amp;=&amp; \\bar{\\omega} \\frac{1+V \\bar{\\boldsymbol{\\gamma}}\\cdot \\bar{\\boldsymbol{e}}}{\\sqrt{1-V^2}}\\\\<br id=\"yui_3_17_2_1_1641360729261_1403\" \/>&amp;=&amp; \\bar{\\omega} \\frac{1+V \\cos\\bar{\\theta}}{\\sqrt{1-V^2}} <br id=\"yui_3_17_2_1_1641360729261_1404\" \/>\\end{eqnarray}<br id=\"yui_3_17_2_1_1641360729261_1405\" \/>\u3053\u3053\u3067\uff0c\\(\\bar{\\theta}\\) \u306f\u89b3\u6e2c\u8005 \\(B\\) \u304c\u89b3\u6e2c\u3059\u308b\uff0c\u9032\u884c\u65b9\u5411 \\(\\bar{\\boldsymbol{e}}\\) \u3068\u5149\u306e\u7a7a\u9593\u7684\u306a\u9032\u884c\u65b9\u5411 \\(\\bar{\\boldsymbol{\\gamma}}\\) \u3068\u306e\u306a\u3059\u89d2\u3067\u3042\u308a\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u4e0d\u5909\u306a4\u5143\u30b9\u30ab\u30e9\u30fc\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u3002<br id=\"yui_3_17_2_1_1641360729261_1406\" \/>$$ \\bar{\\boldsymbol{\\gamma}}\\cdot \\bar{\\boldsymbol{e}} \\equiv<br \/>\n\\sqrt{\\bar{\\boldsymbol{\\gamma}}\\cdot\\bar{\\boldsymbol{\\gamma}}}\\sqrt{\\bar{\\boldsymbol{e}}\\cdot\\bar{\\boldsymbol{e}}} \\cos\\bar{\\theta} = \\cos\\bar{\\theta}$$<br \/>\n$$ (\\because \\bar{\\boldsymbol{\\gamma}}\\cdot\\bar{\\boldsymbol{\\gamma}}= \\bar{\\boldsymbol{e}}\\cdot\\bar{\\boldsymbol{e}} =1)$$<br id=\"yui_3_17_2_1_1641360729261_1407\" \/>\u3053\u308c\u306f\uff0c2\u3064\u306e3\u6b21\u5143\u30d9\u30af\u30c8\u30eb \\(\\vec{a}, \\ \\vec{b}\\) \u306e\u5185\u7a4d\u304c\uff0c\\(\\vec{a}, \\ \\vec{b}\\) \u306e\u306a\u3059\u89d2 \\(\\theta\\) \u3092\u4f7f\u3063\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u3051\u308b\u3068\u3044\u3046\u3053\u3068\u3068\u5168\u304f\u540c\u3058\u95a2\u4fc2\u3067\u3042\u308b\u3002$$ \\vec{a}\\cdot\\vec{b}=|\\vec{a}||\\vec{b}| \\cos\\theta$$<\/p>\n<p id=\"yui_3_17_2_1_1641360729261_1409\">\u3057\u305f\u304c\u3063\u3066\uff0c\u3042\u3089\u305f\u3081\u3066\u5149\u6e90\u9759\u6b62\u7cfb\u3067\u306e\u632f\u52d5\u6570 \\(\\omega\\) \u3092 \\(\\omega_0\\) \uff0c\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u304c\u6e2c\u5b9a\u3059\u308b\u632f\u52d5\u6570 \\( \\bar{\\omega}\\) \u3092 \\(\\omega_{\\rm obs}\\) \u3068\u8868\u8a18\u3057\u76f4\u3059\u3068<br id=\"yui_3_17_2_1_1641360729261_1410\" \/>$$\\omega_{\\rm obs} = \\omega_0 \\frac{\\sqrt{1-V^2}}{1+V \\cos\\bar{\\theta}}$$<\/p>\n<h4 id=\"yui_3_17_2_1_1641360729261_1411\">\u89b3\u6e2c\u8005 \\(B\\) \u304c\u5149\u6e90\u304b\u3089\u9060\u3056\u304b\u308b\u5834\u5408<\/h4>\n<p id=\"yui_3_17_2_1_1641360729261_1412\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-629\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig20b-640x171.png\" alt=\"\" width=\"480\" height=\"128\" srcset=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig20b-640x171.png 640w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig20b-300x80.png 300w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig20b-1536x409.png 1536w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig20b-2048x546.png 2048w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig20b-750x200.png 750w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/p>\n<p>\\(\\bar{\\boldsymbol{\\gamma}}\\) \u3068 \\(\\bar{\\boldsymbol{e}}\\)\u00a0 \u306f\u540c\u3058\u5411\u304d\u306a\u306e\u3067 \\(\\bar{\\theta} = 0\\)\uff0c\u5f93\u3063\u3066 \\(\\cos\\bar{\\theta} = 1\\) \u3068\u306a\u308a\uff0c$$ \\omega_{\\rm obs}= \\omega_0 \\frac{\\sqrt{1-V^2}}{1+V } = \\omega_0 \\sqrt{\\frac{1-V}{1+V} }&lt; \\omega_0 $$<br \/>\n\u5149\u6e90\u304b\u3089\u9060\u3056\u304b\u308b\u89b3\u6e2c\u8005\u304c\u6e2c\u5b9a\u3059\u308b\u632f\u52d5\u6570\u306f\uff0c\u5149\u6e90\u9759\u6b62\u89b3\u6e2c\u8005\u306e\u305d\u308c\u3088\u308a\u3082\u5c0f\u3055\u304f\u306a\u308b\u3002\u632f\u52d5\u6570\u304c\u4e0b\u304c\u308b\uff0c\u3059\u306a\u308f\u3061\u6ce2\u9577\u304c\u4f38\u3073\u308b\u3002<\/p>\n<h4>\u89b3\u6e2c\u8005 \\(B\\) \u304c\u5149\u6e90\u306b\u8fd1\u3065\u304f\u5834\u5408<\/h4>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-630\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig21b-640x166.png\" alt=\"\" width=\"480\" height=\"125\" srcset=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig21b-640x166.png 640w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig21b-300x78.png 300w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig21b-1536x399.png 1536w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig21b-2048x532.png 2048w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig21b-750x195.png 750w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/p>\n<p>\\(\\bar{\\boldsymbol{\\gamma}}\\) \u3068 \\(\\bar{\\boldsymbol{e}}\\)\u00a0 \u306f\u53cd\u5bfe\u5411\u304d\u306a\u306e\u3067 \\(\\bar{\\theta} = \\pi\\)\uff0c\u5f93\u3063\u3066 \\(\\cos\\bar{\\theta} = -1\\) \u3068\u306a\u308a\uff0c$$ \\omega_{\\rm obs} = \\omega _0 \\frac{\\sqrt{1-V^2}}{1-V } = \\omega_0 \\sqrt{\\frac{1+V}{1-V} }&gt; \\omega_0 $$<br \/>\n\u5149\u6e90\u306b\u8fd1\u3065\u304f\u89b3\u6e2c\u8005\u304c\u6e2c\u5b9a\u3059\u308b\u632f\u52d5\u6570\u306f\uff0c\u5149\u6e90\u9759\u6b62\u89b3\u6e2c\u8005\u306e\u305d\u308c\u3088\u308a\u3082\u5927\u304d\u304f\u306a\u308b\u3002\u632f\u52d5\u6570\u304c\u4e0a\u304c\u308b\uff0c\u3059\u306a\u308f\u3061\u6ce2\u9577\u304c\u77ed\u304f\u306a\u308b\u3002<\/p>\n<h4>\u6a2a\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c<\/h4>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-631\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig22b-640x323.png\" alt=\"\" width=\"480\" height=\"243\" srcset=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig22b-640x323.png 640w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig22b-300x152.png 300w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig22b-1536x776.png 1536w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig22b-2048x1035.png 2048w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig22b-750x379.png 750w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/p>\n<p>\\(\\bar{\\boldsymbol{\\gamma}}\\) \u3068 \\(\\bar{\\boldsymbol{e}}\\)\u00a0 \u304c\u76f4\u4ea4\u3059\u308b\u5834\u5408\uff0c\\(\\bar{\\theta}=\\pi\/2\\)\uff0c\u5f93\u3063\u3066\\(\\cos\\bar{\\theta} = 0\\) \u3068\u306a\u308a\uff0c$$ \\omega_{\\rm obs} = \\omega_0 {\\sqrt{1-V^2}}\u00a0 &lt; \\omega_0$$ \u5149\u6e90\u306b\u5bfe\u3059\u308b\u89b3\u6e2c\u8005 \\(B\\) \u306e\u76f8\u5bfe\u901f\u5ea6\u306f\u3053\u306e\u77ac\u9593\u30bc\u30ed\uff08\u3059\u306a\u308f\u3061\u5149\u6e90\u306b\u5411\u304b\u3046\u3042\u308b\u3044\u306f\u96e2\u308c\u308b\u901f\u5ea6\u6210\u5206\u306f\u30bc\u30ed\uff09\u3067\u3042\u308b\u304c\uff0c\u632f\u52d5\u6570\u306e\u5909\u5316\u304c\u8d77\u3053\u308b\u3002\u7279\u6b8a\u76f8\u5bfe\u8ad6\u7279\u6709\u306e\u3053\u306e\u73fe\u8c61\u306f\u7279\u306b\u300c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u6a2a\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c<\/strong><\/span>\u300d\u3068\u547c\u3070\u308c\u308b\u3002<\/p>\n<p>&nbsp;<\/p>\n<h4><\/h4>\n<h3>\u00a0\\(B\\) \u3068\u3068\u3082\u306b\u904b\u52d5\u3057\u3066\u3044\u308b\u5149\u6e90\u304b\u3089\u306e\u5149\u3092\u9759\u6b62\u89b3\u6e2c\u8005 \\(A\\) \u304c\u6e2c\u5b9a\u3059\u308b\u5834\u5408<\/h3>\n<p>\\(\\bar{\\omega}\\) \u3068 \\(\\omega\\) \u306e\u95a2\u4fc2\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3057\u3066\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\bar{\\omega} &amp;=&amp;\u00a0 &#8211; \\boldsymbol{k} \\cdot\\bar{\\boldsymbol{u}} \\\\<br \/>\n&amp;=&amp; -\\omega (\\boldsymbol{u} + \\boldsymbol{\\gamma})\\cdot \\frac{1}{\\sqrt{1-V^2}} (\\boldsymbol{u} + V \\boldsymbol{e}) \\\\<br \/>\n&amp;=&amp; \\omega\\frac{1-V \\boldsymbol{\\gamma}\\cdot\\boldsymbol{e}}{\\sqrt{1-V^2}}\\\\<br \/>\n&amp;=&amp; \\omega \\frac{1-V \\cos\\theta}{\\sqrt{1-V^2}}<br \/>\n\\end{eqnarray}<br \/>\n\u3053\u3053\u3067\uff0c\\(\\theta\\) \u306f\u89b3\u6e2c\u8005 \\(A\\) \u304c\u6e2c\u5b9a\u3059\u308b\u5149\u6e90\u306e\u9032\u884c\u65b9\u5411 \\(\\boldsymbol{e}\\) \u3068\u5149\u306e\u7a7a\u9593\u7684\u306a\u9032\u884c\u65b9\u5411 \\(\\boldsymbol{\\gamma}\\) \u3068\u306e\u306a\u3059\u89d2\u3067\u3042\u308b\u3002\u3057\u305f\u304c\u3063\u3066\uff0c\u3042\u3089\u305f\u3081\u3066\u5149\u6e90\u9759\u6b62\u7cfb\u3067\u306e\u632f\u52d5\u6570 \\(\\bar{\\omega}\\) \u3092 \\(\\omega_0\\) \uff0c\u89b3\u6e2c\u8005 \\(A\\) \u304c\u6e2c\u5b9a\u3059\u308b\u632f\u52d5\u6570 \\( \\omega\\) \u3092 \\(\\omega_{\\rm obs}\\) \u3068\u8868\u8a18\u3057\u76f4\u3059\u3068<br \/>\n$$\\omega_{\\rm obs} = \\omega_0 \\frac{\\sqrt{1-V^2}}{1-V \\cos\\theta}$$<\/p>\n<h4>\u5149\u6e90\u304c\u89b3\u6e2c\u8005 \\(A\\) \u304b\u3089\u9060\u3056\u304b\u308b\u5834\u5408<\/h4>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-634\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig30b-1-640x168.png\" alt=\"\" width=\"480\" height=\"126\" srcset=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig30b-1-640x168.png 640w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig30b-1-300x79.png 300w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig30b-1-1536x403.png 1536w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig30b-1-2048x537.png 2048w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig30b-1-750x197.png 750w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/p>\n<p>\\(\\boldsymbol{e}\\) \u3068 \\(\\boldsymbol{\\gamma}\\) \u306f\u53cd\u5bfe\u5411\u304d\u306a\u306e\u3067\uff0c\\(\\theta=\\pi\\)\uff0c\u3057\u305f\u304c\u3063\u3066 \\(\\cos\\theta = -1\\) \u3068\u306a\u308a\uff0c<br \/>\n$$\\omega_{\\rm obs} = \\omega_0 \\frac{\\sqrt{1-V^2}}{1+V } = \\omega_0 \\sqrt{\\frac{1-V}{1+V}} &lt; \\omega_0$$<\/p>\n<p>&nbsp;<\/p>\n<h4>\u5149\u6e90\u304c\u89b3\u6e2c\u8005 \\(A\\) \u306b\u8fd1\u3065\u304f\u5834\u5408<\/h4>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-633\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig31b-640x166.png\" alt=\"\" width=\"480\" height=\"124\" srcset=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig31b-640x166.png 640w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig31b-300x78.png 300w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig31b-1536x398.png 1536w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig31b-2048x530.png 2048w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig31b-750x194.png 750w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/p>\n<p>\\(\\boldsymbol{e}\\) \u3068 \\(\\boldsymbol{\\gamma}\\) \u306f\u540c\u3058\u5411\u304d\u306a\u306e\u3067\uff0c\\(\\theta=0\\)\uff0c\u3057\u305f\u304c\u3063\u3066 \\(\\cos\\theta = 1\\) \u3068\u306a\u308a\uff0c<br \/>\n$$\\omega_{\\rm obs} = \\omega_0 \\frac{\\sqrt{1-V^2}}{1-V } = \\omega_0 \\sqrt{\\frac{1+V}{1-V}} &gt; \\omega_0$$<\/p>\n<h4>\u6a2a\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c<\/h4>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-635\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig32b-640x395.png\" alt=\"\" width=\"480\" height=\"296\" srcset=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig32b-640x395.png 640w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig32b-300x185.png 300w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig32b-1536x948.png 1536w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig32b-750x463.png 750w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/fig32b.png 1916w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/p>\n<p>\\(\\boldsymbol{e}\\) \u3068 \\(\\boldsymbol{\\gamma}\\) \u304c\u76f4\u4ea4\u3059\u308b\u5834\u5408\uff0c\\(\\theta=\\pi\/2\\)\uff0c\u3057\u305f\u304c\u3063\u3066 \\(\\cos\\theta=0\\) \u3068\u306a\u308a\uff0c<br \/>\n$$\\omega_{\\rm obs} = \\omega_0\\sqrt{1-V^2} &lt; \\omega_0$$<\/p>\n<p>\u89b3\u6e2c\u8005 \\(A\\) \u306b\u5bfe\u3059\u308b\u5149\u6e90\u306e\u76f8\u5bfe\u901f\u5ea6\u306f\u3053\u306e\u77ac\u9593\u30bc\u30ed\uff08\u3059\u306a\u308f\u3061\uff0c\u89b3\u6e2c\u8005\u3078\u5411\u304b\u3046\u3042\u308b\u3044\u306f\u96e2\u308c\u308b\u901f\u5ea6\u6210\u5206\u306f\u30bc\u30ed\uff09\u3067\u3042\u308b\u304c\uff0c\u632f\u52d5\u6570\u306e\u5909\u5316\u304c\u8d77\u3053\u308b\u3002\u7279\u6b8a\u76f8\u5bfe\u8ad6\u7279\u6709\u306e\u3053\u306e\u73fe\u8c61\u306f\u7279\u306b\u300c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u6a2a\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c<\/strong><\/span>\u300d\u3068\u547c\u3070\u308c\u308b\u3002<\/p>\n<h3>\u88dc\u8db3\uff1a\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306f\u76f8\u5bfe\u901f\u5ea6\u306e\u307f\u3067\u6c7a\u307e\u308b\u304b\uff1f<\/h3>\n<p>\u4ee5\u4e0a\u306e\u3053\u3068\u304b\u3089\uff0c\u5149\u306e\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306f\u5149\u6e90\u304c\u52d5\u304f\u304b\uff0c\u89b3\u6e2c\u8005\u304c\u52d5\u304f\u304b\u304c\u554f\u984c\u306b\u306a\u308b\u306e\u3067\u306f\u306a\u304f\uff0c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u5149\u6e90\u3068\u89b3\u6e2c\u8005\u9593\u306e\u76f8\u5bfe\u901f\u5ea6 \\(V\\) \u306e\u307f\u306b\u3088\u3063\u3066\u6c7a\u307e\u308b<\/strong><\/span>\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n<p><a href=\"https:\/\/ja.wikipedia.org\/wiki\/%E3%83%89%E3%83%83%E3%83%97%E3%83%A9%E3%83%BC%E5%8A%B9%E6%9E%9C\" target=\"_blank\" rel=\"noopener\">Wikipedia \u306e\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306e\u9805<\/a>\u3067\u3082\uff0c\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306f\u300c\u6ce2\uff08\u97f3\u6ce2\u3084\u96fb\u78c1\u6ce2\u306a\u3069\uff09\u306e\u767a\u751f\u6e90\uff08\u97f3\u6e90\u30fb\u5149\u6e90\u306a\u3069\uff09\u3068\u89b3\u6e2c\u8005\u3068\u306e<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u76f8\u5bfe\u7684\u306a\u901f\u5ea6\u306e\u5b58\u5728<\/strong><\/span>\u306b\u3088\u3063\u3066\u3001\u6ce2\u306e\u5468\u6ce2\u6570\u304c\u7570\u306a\u3063\u3066\u89b3\u6e2c\u3055\u308c\u308b\u73fe\u8c61\u300d\u3067\u3042\u308b\u3068\u8aac\u660e\u3055\u308c\u3066\u3044\u308b\u3002<\/p>\n<p>\u3057\u304b\u3057\uff0c\u3053\u308c\u306f\u5149\u306b\u3064\u3044\u3066\u306f\u672c\u7a3f\u3067\u8ff0\u3079\u305f\u3088\u3046\u306b\u5f53\u3066\u306f\u307e\u308b\u304c\uff0c\u97f3\u306b\u3064\u3044\u3066\u306f\u5f53\u3066\u306f\u307e\u3089\u306a\u3044\u3002\u540c\u3058\u901f\u3055 \\(v\\) \u3067\u3042\u3063\u3066\u3082\uff0c\u97f3\u6e90\u304c\u52d5\u304f\u306e\u304b\uff0c\u89b3\u6e2c\u8005\u304c\u52d5\u304f\u306e\u304b\u3067\u7b54\u3048\u306f\u7570\u306a\u308b\u3053\u3068\u306b\u6ce8\u610f\u3002\u3057\u305f\u304c\u3063\u3066\u300c\u76f8\u5bfe\u901f\u5ea6\u300d\u3060\u3051\u3067\u6c7a\u307e\u308b\u306e\u3067\u306f\u306a\u3044\u3002\u4ee5\u4e0b\u306e Memo \u3082\u53c2\u7167\u3002<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/1842\/\" target=\"_blank\" rel=\"noopener\">\u97f3\u306e\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c<\/a><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>\u8ffd\u8a18\uff1a\u6a2a\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306b\u3064\u3044\u3066\u88dc\u8db3<\/h3>\n<p>\u4e0a\u3067\u8ff0\u3079\u305f\u3088\u3046\u306b\uff0c\u9759\u6b62\u89b3\u6e2c\u8005 \\(A\\) \u306b\u5bfe\u3059\u308b\u904b\u52d5\u5149\u6e90\u306e\u76f8\u5bfe\u901f\u5ea6\u304c\u30bc\u30ed\uff0c\u307e\u305f\u306f\u9759\u6b62\u5149\u6e90\u306b\u5bfe\u3059\u308b\u904b\u52d5\u89b3\u6e2c\u8005 \\(B\\) \u306e\u76f8\u5bfe\u901f\u5ea6\u304c\u30bc\u30ed\u306e\u77ac\u9593\u3067\u3042\u3063\u3066\u3082\uff0c\u632f\u52d5\u6570\u306e\u5909\u5316\u304c\u8d77\u3053\u308a\uff0c\u7279\u6b8a\u76f8\u5bfe\u8ad6\u7279\u6709\u306e\u3053\u306e\u73fe\u8c61\u306f\u7279\u306b\u300c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u6a2a\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c<\/strong><\/span>\u300d\u3068\u547c\u3070\u308c\u308b\u306e\u3067\u3042\u3063\u305f\u304c\uff0c\u601d\u3046\u3068\u3053\u308d\u3042\u3063\u3066\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u30da\u30fc\u30b8\u3082\u8ffd\u52a0\u3057\u3066\u66f8\u3044\u3066\u307f\u305f\u306e\u3067\uff0c\u53c2\u8003\u307e\u3067\u306b\u3002<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/3520\/\">\u6a2a\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u3092\u5225\u306e\u7acb\u5834\u304b\u3089\u307f\u308b\u3068\u300c\u771f\u6a2a\u300d\u3067\u306f\u306a\u3044\u3068\u3044\u3046\u8a71<\/a><\/li>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/6586\/\">\u6a2a\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u3068\u306f\u4f55\u304b\uff1f\u306b\u3064\u3044\u3066\u3082\u3046\u5c11\u3057<\/a><\/li>\n<\/ul>\n<p>\u306f\u3058\u3081\u306f\uff0c\u76f8\u5bfe\u901f\u5ea6\u304c\u30bc\u30ed\u306e\u77ac\u9593\u306b\u300c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u6a2a\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c<\/strong><\/span>\u300d\u3068\u3057\u3066\u89b3\u6e2c\u3055\u308c\u305f\u5149\u306f\uff0c\u3044\u3064\u767a\u5c04\u3055\u308c\u305f\u5149\u306a\u306e\u304b\uff0c\u3072\u3087\u3063\u3068\u3057\u3066\uff08\u305f\u3076\u3093\uff09\u76f8\u5bfe\u901f\u5ea6\u304c\u3042\u308b\u6642\u306b\u767a\u5c04\u3055\u308c\u305f\u5149\u3067\u3057\u3087\uff1f\u3068\u3044\u3046\u7591\u3044\u3067\u8abf\u3079\u3066\u307f\u305f\u306e\u304c\uff0c\u300c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u5149\u884c\u5dee<\/strong><\/span>\u300d\u3068\u3044\u3046\u73fe\u8c61\u3082\u8003\u3048\u308b\u5fc5\u8981\u304c\u3042\u308b\u3088\u306d\uff0c\u3068\u3044\u3046\u8a71\u306b\u306a\u3063\u305f\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5149\u306e\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306f\uff0c\u4e16\u306b\u3042\u307e\u305f\u3042\u308b\u6a19\u6e96\u7684\u306a\u6559\u79d1\u66f8\u3067\u306f\uff0c\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u3092\u7528\u3044\u3066\u8aac\u660e\u3055\u308c\u308b\u306e\u3067\u3042\u3063\u305f\u3002\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u306b\u3082\u3068\u3065\u3044\u305f\u5149\u306e\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306e\u6a19\u6e96\u7684\u306a\u8aac\u660e\u306b\u3064\u3044\u3066\u306f\uff0c\u5225\u30da\u30fc\u30b8\u300c\u5149\u306e\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306e\u304a\u3055\u3089\u3044\u300d\u306b\u307e\u3068\u3081\u3066\u3042\u308b\u3002<\/p>\n<p>\u3053\u3053\u3067\u306f\uff0c\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u306e\u65b9\u91dd\u300c\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u306b\u3088\u3089\u306a\u3044\u7279\u6b8a\u76f8\u5bfe\u8ad6\u306e\u7d71\u4e00\u7684\u7406\u89e3\u300d\u306b\u5247\u3063\u3066\uff0c\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u3092\u4f7f\u308f\u305a\u306b\u5149\u306e\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306e\u8aac\u660e\u3092\u8a66\u307f\u308b\u3002<\/p><p><a class=\"more-link btn\" href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%83%ad%e3%83%bc%e3%83%ac%e3%83%b3%e3%83%84%e5%a4%89%e6%8f%9b%e3%81%ab%e3%82%88%e3%82%89%e3%81%aa%e3%81%84%e7%9b%b8%e5%af%be%e8%ab%96%e3%81%ae%e7%90%86%e8%a7%a3\/%e5%85%89%e3%81%ae%e3%83%89%e3%83%83%e3%83%97%e3%83%a9%e3%83%bc%e5%8a%b9%e6%9e%9c\/\">\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n<p id=\"yui_3_17_2_1_1641360729261_1392\">\n","protected":false},"author":2,"featured_media":0,"parent":71,"menu_order":11,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-204","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\/204","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=204"}],"version-history":[{"count":21,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/204\/revisions"}],"predecessor-version":[{"id":6664,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/204\/revisions\/6664"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/71"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=204"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}