{"id":1211,"date":"2022-01-19T12:41:32","date_gmt":"2022-01-19T03:41:32","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=1211"},"modified":"2024-07-08T12:23:29","modified_gmt":"2024-07-08T03:23:29","slug":"%e5%8b%95%e5%be%84%e6%96%b9%e5%90%91%e3%81%ab%e8%87%aa%e7%94%b1%e8%90%bd%e4%b8%8b%e3%81%99%e3%82%8b%e6%99%82%e8%a8%88%e3%81%ae%e9%80%b2%e3%81%bf%e6%96%b9","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%e6%99%82%e9%96%93%e3%81%ae%e9%80%b2%e3%81%bf%e6%96%b9\/%e5%8b%95%e5%be%84%e6%96%b9%e5%90%91%e3%81%ab%e8%87%aa%e7%94%b1%e8%90%bd%e4%b8%8b%e3%81%99%e3%82%8b%e6%99%82%e8%a8%88%e3%81%ae%e9%80%b2%e3%81%bf%e6%96%b9\/","title":{"rendered":"\u52d5\u5f84\u65b9\u5411\u306b\u81ea\u7531\u843d\u4e0b\u3059\u308b\u89b3\u6e2c\u8005\u306e\u6642\u9593\u306e\u9032\u307f\u65b9"},"content":{"rendered":"<p><!--more--><\/p>\n<p><span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30b7\u30e5\u30d0\u30eb\u30c4\u30b7\u30eb\u30c8\u6642\u7a7a<\/strong><\/span>\u306b\u304a\u3044\u3066\uff0c<\/p>\n<ul>\n<li>\\(r = r_i\\) \u306b\u9759\u6b62\u3057\u3066\u3044\u308b\u6642\u8a08\u306e\u9032\u307f\u3092 \\(\\varDelta \\tau_i\\)<\/li>\n<li>\\(r = r_i\\) \u304b\u3089\u521d\u901f\u5ea6\u30bc\u30ed\u3067\u52d5\u5f84\u65b9\u5411\u306b\u81ea\u7531\u843d\u4e0b\u904b\u52d5\u3057\u3066\u3044\u308b\u6642\u8a08\u306e\uff0c\u52d5\u5f84\u5ea7\u6a19 \\(r (&lt; r_i)\\) \u306b\u304a\u3051\u308b\u9032\u307f\u3092 \\(\\varDelta \\bar{\\tau}\\)<\/li>\n<li>\u52d5\u5f84\u5ea7\u6a19 \\(r (&lt; r_i)\\)\u306b\u9759\u6b62\u3057\u3066\u3044\u308b\u6642\u8a08\u306e\u9032\u307f\u3092 \\(\\varDelta \\tau\\)<\/li>\n<\/ul>\n<p>\u3068\u3059\u308b\u3002<\/p>\n<p>\u3053\u306e\u3068\u304d\uff0c \\(r = r_i\\) \u304b\u3089<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u81ea\u7531\u843d\u4e0b\u3057\u3066\u3044\u304f\u6642\u8a08\u306e\u9032\u307f<\/strong><\/span> \\(\\varDelta \\bar{\\tau}\\) \u3068\uff0c \\(r = r_i\\) \u306b<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u9759\u6b62\u3057\u7d9a\u3051\u3066\u3044\u308b\u6642\u8a08\u306e\u9032\u307f<\/strong><\/span> \\(\\varDelta \\tau_i\\) \u306e\u6bd4 \\(\\displaystyle \\frac{\\varDelta \\bar{\\tau}}{\\varDelta \\tau_i}\\) \u306f\u3069\u3046\u306a\u308b\u304b\uff0c\u3068\u3044\u3046\u8a71\u3002<\/p>\n<h3>\u7570\u306a\u308b\u5730\u70b9\u306b\u9759\u6b62\u3057\u3066\u3044\u308b\u6642\u8a08\u306e\u9032\u307f\u306e\u6bd4<\/h3>\n<p>\u307e\u305a\uff0c \u7570\u306a\u308b\u5730\u70b9\u306b\u9759\u6b62\u3057\u3066\u3044\u308b\u6642\u8a08\u306e\u9032\u307f\u65b9\u306e\u6bd4\u306f\uff0c<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%87%8d%e5%8a%9b%e5%a0%b4%e4%b8%ad%e3%81%ae%e6%99%82%e9%96%93%e3%81%ae%e9%80%b2%e3%81%bf%e6%96%b9\/%e9%87%8d%e5%8a%9b%e5%a0%b4%e4%b8%ad%e3%81%ae%e7%95%b0%e3%81%aa%e3%82%8b%e5%9c%b0%e7%82%b9%e3%81%a7%e3%81%ae%e6%99%82%e9%96%93%e3%81%ae%e9%80%b2%e3%81%bf%e6%96%b9\/#i-2\">\u65e2\u306b\u8aac\u660e\u3057\u305f\u3088\u3046\u306b<\/a><\/p>\n<p>$$\\frac{\\varDelta \\tau}{\\varDelta \\tau_i} = \\frac{\\sqrt{1 &#8211; \\frac{r_g}{r}}}{\\sqrt{1 &#8211; \\frac{r_g}{r_i}}} $$<\/p>\n<h3>\u30ed\u30fc\u30ec\u30f3\u30c4\u56e0\u5b50<\/h3>\n<p>\u6b21\u306b\uff0c\u540c\u3058\u52d5\u5f84\u5ea7\u6a19 \\(r\\) \u306b\u9759\u6b62\u3057\u3066\u3044\u308b\u6642\u8a08\u306e\u9032\u307f \\(\\Delta t\\) \u3068\uff0c\u901f\u3055 \\(V\\) \u3067\u904b\u52d5\u3057\u3066\u3044\u308b\u6642\u8a08\u306e\u9032\u307f \\(\\Delta \\bar{t}\\) \u306f\uff0c\u7279\u6b8a\u76f8\u5bfe\u8ad6\u306e\u5834\u5408\u3068\u540c\u69d8\u306b\u4e00\u822c\u76f8\u5bfe\u8ad6\u7684\u72b6\u6cc1\u4e0b\u306b\u304a\u3044\u3066\u3082\uff0c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30ed\u30fc\u30ec\u30f3\u30c4\u56e0\u5b50<\/strong><\/span>\u306e\u9006\u6570\u3067\u3042\u308b \\(\\sqrt{1 &#8211; V^2}\\) \u3060\u3051\u7570\u306a\u308b\u306f\u305a\u3067\u3042\u308b\u3002\uff08\\(c = 1\\)\uff09<\/p>\n<p><a href=\"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%8b%95%e5%be%84%e6%96%b9%e5%90%91%e3%81%ae%e8%87%aa%e7%94%b1%e8%90%bd%e4%b8%8b%e9%81%8b%e5%8b%95\/#4\">\u9759\u6b62\u89b3\u6e2c\u8005\u304b\u3089\u307f\u305f\uff0c\u52d5\u5f84\u65b9\u5411\u306b\u81ea\u7531\u843d\u4e0b\u3059\u308b\u89b3\u6e2c\u8005\u306b\u95a2\u3059\u308b<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30ed\u30fc\u30ec\u30f3\u30c4\u56e0\u5b50<\/strong><\/span> \\(\\gamma\\) \u306f<\/a><\/p>\n<p>$$\\gamma\\equiv \\frac{1}{\\sqrt{1-V^2}} = \\frac{\\sqrt{1 &#8211; \\frac{r_g}{r_i}}}{\\sqrt{1 &#8211; \\frac{r_g}{r}}}$$<\/p>\n<p>\u3067\u3042\u3063\u305f\u304b\u3089\uff0c<\/p>\n<p>$$ \\frac{\\varDelta \\bar{\\tau}} {\\varDelta \\tau} = \\sqrt{1 &#8211; V^2} = \\frac{\\sqrt{1 &#8211; \\frac{r_g}{r}}}{\\sqrt{1 &#8211; \\frac{r_g}{r_i}}}$$<\/p>\n<h3>\u9759\u6b62\u89b3\u6e2c\u8005\u304b\u3089\u307f\u305f\u81ea\u7531\u843d\u4e0b\u3059\u308b\u6642\u8a08\u306e\u9032\u307f<\/h3>\n<p>\u3068\u3044\u3046\u3053\u3068\u3067\uff0c\u6700\u7d42\u7684\u306b\u306f<\/p>\n<p>$$ \\frac{\\varDelta \\bar{\\tau}}{\\varDelta \\tau_i} = \\frac{\\varDelta \\tau}{\\varDelta \\tau_i} \\frac{\\varDelta \\bar{\\tau}} {\\varDelta \\tau} = \\frac{\\sqrt{1 &#8211; \\frac{r_g}{r}}}{\\sqrt{1 &#8211; \\frac{r_g}{r_i}}} \\frac{\\sqrt{1 &#8211; \\frac{r_g}{r}}}{\\sqrt{1 &#8211; \\frac{r_g}{r_i}}}<br \/>\n= \\frac{1 &#8211; \\frac{r_g}{r}}{1 &#8211; \\frac{r_g}{r_i}}$$<\/p>\n<p>\\(r = r_i \\gg r_g\\) \u306b\u9759\u6b62\u3057\u3066\u3044\u308b\u89b3\u6e2c\u8005\u304b\u3089\u307f\u3066\u3044\u308b\u3068\uff0c\u81ea\u7531\u843d\u4e0b\u3059\u308b\u6642\u8a08\u304c \\(r \\rightarrow r_g\\) \u3068 \\(r_g\\) \u306b\u8fd1\u3065\u304f\u306b\u3064\u308c\u3066\uff0c\u6642\u8a08\u306e\u9032\u307f \\(\\varDelta \\bar{\\tau}\\) \u306f\u3060\u3093\u3060\u3093\u5c0f\u3055\u304f\u30fb\u3086\u3063\u304f\u308a\u306b\u306a\u308a \\(\\Delta \\bar{\\tau} \\rightarrow 0\\) \u3068\u306a\u3063\u3066\u3044\u304f\u3002<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":0,"parent":103,"menu_order":4,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-1211","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.10 - aioseo.com -->\n\t<meta name=\"description\" content=\"\u30b7\u30e5\u30d0\u30eb\u30c4\u30b7\u30eb\u30c8\u6642\u7a7a\u306b\u304a\u3044\u3066\uff0c \\(r = r_i\\) \u306b\u9759\u6b62\u3057\u3066\u3044\u308b\u6642\u8a08\u306e\u9032\u307f\u3092 \\(\\varDelta \\\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<link rel=\"canonical\" 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