{"id":10505,"date":"2025-07-15T15:19:39","date_gmt":"2025-07-15T06:19:39","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=10505"},"modified":"2025-07-21T10:16:31","modified_gmt":"2025-07-21T01:16:31","slug":"%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e5%be%ae%e5%88%86%e3%81%ae%e6%81%92%e7%ad%89%e5%bc%8f%e3%81%ae%e7%a9%8d%e5%88%86%e3%81%a8%e6%b7%b7%e4%b9%b1%e3%81%ae%e6%ad%a3%e3%81%97%e6%96%b9","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e5%be%ae%e5%88%86%e3%81%ae%e6%81%92%e7%ad%89%e5%bc%8f%e3%81%ae%e7%a9%8d%e5%88%86%e3%81%a8%e6%b7%b7%e4%b9%b1%e3%81%ae%e6%ad%a3%e3%81%97%e6%96%b9\/","title":{"rendered":"\u30d9\u30af\u30c8\u30eb\u5834\u306e\u5fae\u5206\u306e\u6052\u7b49\u5f0f\u306e\u7a4d\u5206\u3068\u6df7\u4e71\u306e\u6b63\u3057\u65b9"},"content":{"rendered":"<p>\u30d9\u30af\u30c8\u30eb\u5834\uff08\u542b\u30b9\u30ab\u30e9\u30fc\u5834\uff09\u306e2\u968e\u504f\u5fae\u5206\u306e\u6052\u7b49\u5f0f $\\nabla \\times (\\nabla\\psi) = \\boldsymbol{0}$ \u3068 $\\nabla\\cdot (\\nabla\\times \\boldsymbol{a}) = 0$ \u306e\u9762\u7a4d\u5206\u3084\u4f53\u7a4d\u7a4d\u5206\u306b\u3064\u3044\u3066\uff0c\u3042\u3089\u305f\u3081\u3066\u307e\u3068\u3081\u3066\u304a\u304f\u3002<\/p>\n<p><!--more--><\/p>\n<h3>$\\nabla \\times (\\nabla\\psi)$ \u306e\u9762\u7a4d\u5206<\/h3>\n<p>\u6052\u7b49\u5f0f $\\nabla \\times (\\nabla\\psi)=\\boldsymbol{0}$ \u306e\u5de6\u8fba\u3092\uff0c\u9589\u66f2\u7dda $C$ \u3092\u7e01\u3068\u3059\u308b\u4efb\u610f\u306e\u66f2\u9762 $S$ \u3067\u9762\u7a4d\u5206\u3059\u308b\u3068\uff0c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30b9\u30c8\u30fc\u30af\u30b9\u306e\u5b9a\u7406<\/strong><\/span>\u304b\u3089<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\iint_S \\bigl( \\nabla \\times (\\nabla\\psi)\\bigr)\\cdot\\boldsymbol{n}\\, dS<br \/>\n&amp;=&amp; \\oint_C\\ (\\nabla\\psi)\\cdot d\\boldsymbol{r} \\\\<br \/>\n&amp;=&amp; \\oint_C\\ d\\psi \\\\<br \/>\n&amp;=&amp; \\int_{\\boldsymbol{r}_1}^{\\boldsymbol{r}_1}\\ d\\psi \\\\<br \/>\n&amp;=&amp; \\bigl[ \\psi\\bigr]_{\\boldsymbol{r}_1}^{\\boldsymbol{r}_1} \\\\<br \/>\n&amp;=&amp; \\psi(\\boldsymbol{r}_1) -\\psi(\\boldsymbol{r}_1) \\\\<br \/>\n&amp;=&amp; 0<br \/>\n\\end{eqnarray}<\/p>\n<p>\u4e00\u65b9\uff0c\u6052\u7b49\u5f0f $\\nabla \\times (\\nabla\\psi)=\\boldsymbol{0}$ \u306e\u53f3\u8fba\u306e\u9762\u7a4d\u5206\u306f<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\iint_S \\boldsymbol{0}\\cdot\\boldsymbol{n}\\, dS<br \/>\n&amp;=&amp; 0<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3067\u3042\u308b\u304b\u3089\uff0c\u78ba\u304b\u306b\u5de6\u8fba\u306e\u9762\u7a4d\u5206\u3068\u53f3\u8fba\u306e\u9762\u7a4d\u5206\u304c\u7b49\u3057\u3044\u3053\u3068\u304c\u7c21\u5358\u306b\u308f\u304b\u308b\u3002\u3053\u306e\u5834\u5408\u306b\u306f\u4f55\u306e\u6df7\u4e71\u3082\u306a\u3044\u3002<\/p>\n<h3>$\\nabla\\cdot (\\nabla\\times \\boldsymbol{a}) $ \u306e\u4f53\u7a4d\u7a4d\u5206\uff1a\u6df7\u4e71\uff1f<\/h3>\n<p>\u6052\u7b49\u5f0f $\\nabla\\cdot (\\nabla\\times \\boldsymbol{a}) = 0$ \u306e\u5de6\u8fba\u3092\uff0c\u9589\u66f2\u9762 $S$ \u3067\u56f2\u307e\u308c\u305f\u4f53\u7a4d $V$ \u3067\u4f53\u7a4d\u7a4d\u5206\u3059\u308b\u3068\uff0c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30ac\u30a6\u30b9\u306e\u5b9a\u7406<\/strong><\/span>\u3068\uff0c\u3055\u3089\u306b<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30b9\u30c8\u30fc\u30af\u30b9\u306e\u5b9a\u7406<\/strong><\/span>\u304b\u3089\uff08\u5b57\u9762\u3060\u3051\u3092\u307f\u308b\u9650\u308a\u3067\u306f\uff09<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\iiint_V\\ \\nabla\\cdot (\\nabla\\times \\boldsymbol{a})\\ dV &amp;=&amp; \\iint_S\\ (\\nabla\\times \\boldsymbol{a})\\cdot\\boldsymbol{n}\\ dS \\qquad\\mbox{(\u30ac\u30a6\u30b9\u306e\u5b9a\u7406\u304b\u3089)}\\\\<br \/>\n&amp;=&amp; \\oint_C\\ \\boldsymbol{a}\\cdot d\\boldsymbol{r}\\qquad\\qquad\\qquad\\mbox{(\u30b9\u30c8\u30fc\u30af\u30b9\u306e\u5b9a\u7406\u304b\u3089\uff1f)}<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3068\u66f8\u3051\u308b\u3088\u3046\u306b\u601d\u3048\u308b\u3002\u4e00\u65b9\uff0c\u6052\u7b49\u5f0f $\\nabla\\cdot (\\nabla\\times \\boldsymbol{a}) = 0$ \u306e\u53f3\u8fba\u306e\u4f53\u7a4d\u6210\u5206\u306f\u76f4\u3061\u306b<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\iiint_V\\ 0\\\u00a0 dV &amp;=&amp; 0<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3067\u3042\u308b\u304b\u3089\uff0c\u4e00\u898b\uff0c\u4efb\u610f\u306e\u30d9\u30af\u30c8\u30eb\u5834 $\\boldsymbol{a}$ \u306b\u5bfe\u3057\u3066<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\oint_C\\ \\boldsymbol{a}\\cdot d\\boldsymbol{r} &amp;=&amp; 0<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3068\u306a\u3063\u3066\u3057\u307e\u3046\u3088\u3046\u306b\u898b\u3048\u308b\u3002\u3061\u3087\u3063\u3068\u6df7\u4e71\u3057\u305d\u3046\u3060\u3002\u3044\u3063\u305f\u3044\u3053\u308c\u306f\u6b63\u3057\u3044\u306e\u3067\u3042\u308d\u3046\u304b\uff1f<\/p>\n<h3>\u6df7\u4e71\u306e\u6b63\u3057\u65b9<\/h3>\n<p>\u4e0a\u8a18\u306e\u8a08\u7b97\u3067\u554f\u984c\u3068\u306a\u308b\u306e\u306f<span style=\"font-family: helvetica, arial, sans-serif; color: #ff0000;\"><strong>\u9589\u66f2\u9762 $S$ \u4e0a\u306e\u9762\u7a4d\u5206<\/strong><\/span>\u306b\u5bfe\u3057\u3066\uff08\u5b57\u9762\u3060\u3051\u3092\u307f\u3066\uff09<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30b9\u30c8\u30fc\u30af\u30b9\u306e\u5b9a\u7406<\/strong><\/span>\u3092\u4f7f\u3063\u3066\u5909\u5f62\u3059\u308b\u3068\u3053\u308d\u3067\u3042\u308b\u3002<\/p>\n<p>\u305d\u3082\u305d\u3082<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30b9\u30c8\u30fc\u30af\u30b9\u306e\u5b9a\u7406<\/strong><\/span>\u3068\u306f\uff0c<span style=\"font-family: helvetica, arial, sans-serif; color: #0000ff;\"><strong>\u9589\u66f2\u7dda $C$ \u3092\u5883\u754c\u30fb\u7e01\u3068\u3059\u308b\u958b\u66f2\u9762 $S$ \u4e0a\u306e\u9762\u7a4d\u5206<\/strong><\/span>\u306b\u3064\u3044\u3066\u9069\u7528\u3055\u308c\u308b\u3082\u306e\u3067\u3042\u3063\u305f\u306f\u305a\u3067\u3042\u308b\u3002\u3057\u304b\u3057\uff0c\u3044\u3063\u305f\u3093<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30ac\u30a6\u30b9\u306e\u5b9a\u7406<\/strong><\/span>\u3092\u4f7f\u3063\u3066\u4f53\u7a4d\u7a4d\u5206\u304b\u3089\u9762\u7a4d\u5206\u306b\u5909\u5f62\u3057\u305f\u3068\u304d\uff0c<span style=\"font-family: helvetica, arial, sans-serif; color: #ff0000;\"><strong>$S$ \u306f\u4f53\u7a4d $V$ \u3092\u56f2\u3080\u9589\u66f2\u9762<\/strong><\/span>\u3068\u306a\u3063\u3066\u3044\u308b\u3002<span style=\"font-family: helvetica, arial, sans-serif; color: #ff0000;\"><strong>\u9589\u66f2\u9762 $S$<\/strong><\/span>\u00a0\u3068\u306f\u5883\u754c\u30fb\u7e01\u304c\u306a\u3044\u306e\u3067\u3042\u308b\u304b\u3089\uff0c\u9589\u66f2\u9762 $S$ \u306e\u5883\u754c\u30fb\u7e01\u3068\u306a\u308b\u9589\u66f2\u7dda $C$ \u306f\u7121\u3044\u3002\u3042\u3048\u3066\u8a00\u3048\u3070\uff0c<span style=\"font-family: helvetica, arial, sans-serif; color: #ff0000;\"><strong>\u9589\u66f2\u9762 $S$<\/strong><\/span> \u306e\u5883\u754c\u30fb\u7e01\u3068\u306a\u308b $C$ \u306f\u9577\u3055\u30bc\u30ed\u306e\u9589\u66f2\u7dda\uff0c\u3068\u3067\u3082\u8a00\u3046\u3079\u304d\u304b\u3002<\/p>\n<p>\u3053\u306e\u3088\u3046\u306a\u6df7\u4e71\u3092\u907f\u3051\u308b\u305f\u3081\u306b\uff0c\u9762\u7a4d\u5206\u306e\u8868\u8a18\u3092\u533a\u5225\u3059\u308b\u3079\u304d\u3060\u3068\u3044\u3046\u306e\u304c\u79c1\u306e\u4e3b\u5f35\u3067\u3042\u308b\u3002<\/p>\n<p>\u4e00\u822c\u306b\uff0c\u9589\u66f2\u7dda $C$ \u3092\u7e01\u3068\u3059\u308b<span style=\"font-family: helvetica, arial, sans-serif;\"><strong><span style=\"color: #0000ff;\">\u958b\u66f2\u9762 $S$ \u4e0a\u306e\u9762\u7a4d\u5206<\/span><\/strong><\/span>\u306b\u3064\u3044\u3066\u306f\u901a\u5e38\u306e <span style=\"color: #0000ff;\">$\\displaystyle \\iint_S$<\/span> \u3092\u4f7f\u3063\u3066<\/p>\n<p>$${\\color{blue}\\iint_S}\\ \\boldsymbol{a}\\cdot\\boldsymbol{n}\\ dS$$<\/p>\n<p>\u306e\u3088\u3046\u306b\u66f8\u304f\u3002<span style=\"font-family: helvetica, arial, sans-serif;\"><strong><span style=\"color: #0000ff;\">\u958b\u66f2\u9762 $S$ \u4e0a\u306e\u9762\u7a4d\u5206<\/span><\/strong><\/span>\u306b\u3064\u3044\u3066\u306f\uff0c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30b9\u30c8\u30fc\u30af\u30b9\u306e\u5b9a\u7406<\/strong><\/span>\u304c\u6210\u308a\u7acb\u3061\uff0c<\/p>\n<p>$${\\color{blue}\\iint_{S}} \\ (\\nabla\\times \\boldsymbol{a})\\cdot \\boldsymbol{n}\\ dS = \\oint_{C}\\\u00a0 \\boldsymbol{a}\\cdot d\\boldsymbol{r}$$<\/p>\n<p>\u6b21\u306b\uff0c<span style=\"color: #ff0000; font-family: helvetica, arial, sans-serif;\"><strong>\u9589\u66f2\u9762 $S$ \u4e0a\u306e\u9762\u7a4d\u5206<\/strong><\/span>\u306f <span style=\"color: #ff0000;\">$\\displaystyle \\color{red}\\int\\!\\!\\!\\!\\!\\!\\bigcirc\\!\\!\\!\\!\\!\\!\\int_{S}$<\/span> \u3092\u4f7f\u3063\u3066<\/p>\n<p>$${\\displaystyle \\color{red}\\int\\!\\!\\!\\!\\!\\!\\bigcirc\\!\\!\\!\\!\\!\\!\\int_{S}}\\ \\boldsymbol{a}\\cdot\\boldsymbol{n}\\ dS$$<\/p>\n<p>\u306e\u3088\u3046\u306b\u66f8\u304f\u3002<span style=\"font-family: helvetica, arial, sans-serif; color: #ff0000;\"><strong>\u9589\u66f2\u9762 $S$ \u4e0a\u306e\u9762\u7a4d\u5206<\/strong><\/span>\u306f<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30ac\u30a6\u30b9\u306e\u5b9a\u7406<\/strong><\/span>\u306b\u8868\u308c\uff0c<\/p>\n<p>$$\\iiint_V \\nabla\\cdot \\boldsymbol{a}\\, dV = {\\color{red}\\int\\!\\!\\!\\!\\!\\!\\bigcirc\\!\\!\\!\\!\\!\\!\\int_{S}}\\\u00a0 \\boldsymbol{a}\\cdot\\boldsymbol{n} \\ dS$$<\/p>\n<p><span style=\"font-family: helvetica, arial, sans-serif; color: #ff0000;\"><strong>\u9589\u66f2\u9762 $S$ <\/strong><\/span>\u306b\u306f\u5883\u754c\u30fb\u7e01\u304c\u5b58\u5728\u3057\u306a\u3044\u305f\u3081\uff0c\u7e01\u3068\u306a\u308b\u00a0\u9589\u66f2\u7dda $C$\u306e\u5b58\u5728\u3092\u524d\u63d0\u3068\u3059\u308b<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30b9\u30c8\u30fc\u30af\u30b9\u306e\u5b9a\u7406<\/strong><\/span>\u306f\u9069\u7528\u3067\u304d\u306a\u3044\u3002<\/p>\n<p>$$ {\\color{red}\\int\\!\\!\\!\\!\\!\\!\\bigcirc\\!\\!\\!\\!\\!\\!\\int_{S}} \\ (\\nabla\\times \\boldsymbol{a})\\cdot \\boldsymbol{n}\\ dS \\ {\\color{red}\\neq} \\oint_{C}\\\u00a0 \\boldsymbol{a}\\cdot d\\boldsymbol{r}$$<\/p>\n<p>\u5f37\u3044\u3066\u8a00\u3048\u3070\uff0c\u9577\u3055\u30bc\u30ed\u306e\u9589\u66f2\u7dda $C$ \u4e0a\u306e\u7dda\u7a4d\u5206\u3067\u3042\u308b\u304b\u3089\u30bc\u30ed\uff0c<\/p>\n<p>$$ {\\color{red}\\int\\!\\!\\!\\!\\!\\!\\bigcirc\\!\\!\\!\\!\\!\\!\\int_{S}} \\ (\\nabla\\times \\boldsymbol{a})\\cdot \\boldsymbol{n}\\ dS =0$$<\/p>\n<p>\u3068\u3067\u3082\u3059\u308c\u3070\u3088\u3044\u3060\u308d\u3046\u3002<\/p>\n<p>\u3053\u3046\u3059\u308b\u3068\uff0c$\\nabla\\cdot (\\nabla\\times \\boldsymbol{a}) $ \u306e\u4f53\u7a4d\u7a4d\u5206\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\uff0c<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\iiint_V\\ \\nabla\\cdot (\\nabla\\times \\boldsymbol{a})\\ dV<br \/>\n&amp;=&amp; {\\color{red}\\int\\!\\!\\!\\!\\!\\!\\bigcirc\\!\\!\\!\\!\\!\\!\\int_{S}}\\ (\\nabla\\times \\boldsymbol{a})\\cdot\\boldsymbol{n}\\ dS \\\\<br \/>\n&amp;=&amp; 0<br \/>\n\\end{eqnarray}<\/p>\n<p>\u6df7\u4e71\u306f\u7121\u304f\u306a\u308b\u3068\u601d\u3046\u306e\u3067\u3042\u308b\u304c\uff0c\u3044\u304b\u304c\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<h3>\u304a\u3055\u3089\u3044\u3068\u3057\u3066\u306e\u7df4\u7fd2\u554f\u984c<\/h3>\n<p>\u4ee5\u4e0a\u306e\u8a71\u3092\u7df4\u7fd2\u554f\u984c\u3068\u3057\u3066\u307e\u3068\u3081\u3066\u307f\u305f\u3002<\/p>\n<h4>1. \u52fe\u914d\u306e1\u5468\u7dda\u7a4d\u5206<\/h4>\n<p>\u4efb\u610f\u306e\u30b9\u30ab\u30e9\u30fc\u5834\uff08\u7a7a\u9593\u5ea7\u6a19\u306e\u95a2\u6570\u3067\u3042\u308b\u30b9\u30ab\u30e9\u30fc\u95a2\u6570\uff09 $\\psi(\\boldsymbol{r})$ \u306e\u52fe\u914d $\\nabla \\psi$ \u306b\u3064\u3044\u3066\uff0c\u4ee5\u4e0b\u3092\u793a\u305b\u3002<\/p>\n<p>$$\\oint_C\\ (\\nabla \\psi)\\cdot d\\boldsymbol{r} = 0$$<\/p>\n<p>\u3053\u3053\u3067 $C$ \u306f\u4efb\u610f\u306e\u9589\u66f2\u7dda\u3067\u3042\u308b\u3002<\/p>\n<h4>2. \u56de\u8ee2\u306e\u5782\u76f4\u6210\u5206\u306e\u9589\u66f2\u9762\u7a4d\u5206<\/h4>\n<p>\u4efb\u610f\u306e\u30d9\u30af\u30c8\u30eb\u5834\uff08\u5404\u6210\u5206\u304c\u7a7a\u9593\u5ea7\u6a19\u306e\u95a2\u6570\u3067\u3042\u308b\u30d9\u30af\u30c8\u30eb\uff09 $\\boldsymbol{a}$ \u306e\u56de\u8ee2 $\\nabla\\times\\boldsymbol{a}$ \u306b\u3064\u3044\u3066\uff0c\u4ee5\u4e0b\u3092\u793a\u305b\u3002<\/p>\n<p>$$\\iint_S\\ (\\nabla\\times\\boldsymbol{a})\\cdot\\boldsymbol{n}\\, dS = 0$$<\/p>\n<p>\u3053\u3053\u3067\uff0c$S$ \u306f\u4efb\u610f\u306e\u9589\u66f2\u9762\u3067\u3042\u308a\uff0c$\\boldsymbol{n}$ \u306f\u9589\u66f2\u9762 $S$ \u306b\u5782\u76f4\u306a\u5358\u306b\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308b\u3002<\/p>\n<h3>\u7df4\u7fd2\u554f\u984c\u306e\u89e3\u7b54\u4f8b<\/h3>\n<p>1. \u306b\u3064\u3044\u3066\u306f\uff0c\u30b9\u30c8\u30fc\u30af\u30b9\u306e\u5b9a\u7406\u3092\u4f7f\u3063\u3066\u9762\u7a4d\u5206\u306b\u3057\u3066&#8230;<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\oint_C\\ (\\nabla \\psi)\\cdot d\\boldsymbol{r} &amp;=&amp;<br \/>\n\\iint_S \\bigl( \\nabla \\times (\\nabla\\psi)\\bigr)\\cdot\\boldsymbol{n}\\, dS\\\\<br \/>\n&amp;=&amp; \\iint_S \\boldsymbol{0}\\cdot\\boldsymbol{n}\\, dS \\\\<br \/>\n&amp;=&amp; 0<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3053\u3053\u3067 $S$ \u306f\u9589\u66f2\u7dda $C$ \u3092\u5883\u754c\u3068\u3059\u308b\u66f2\u9762\u3067\u3042\u308a\uff0c\u30d9\u30af\u30c8\u30eb\u89e3\u6790\u306e\u6052\u7b49\u5f0f $\\nabla \\times (\\nabla\\psi) = \\boldsymbol{0}$ \u3092\u4f7f\u3063\u305f\u3002<\/p>\n<p>2. \u306b\u3064\u3044\u3066\u306f\uff0c\u601d\u308f\u305a\u30b9\u30c8\u30fc\u30af\u30b9\u306e\u5b9a\u7406\u3092\u4f7f\u3063\u3066&#8230;<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\iint_S\\ (\\nabla\\times\\boldsymbol{a})\\cdot\\boldsymbol{n}\\, dS &amp;=&amp;<br \/>\n\\oint_C \\ \\boldsymbol{a}\\cdot d\\boldsymbol{r} \\\\<br \/>\n&amp;=&amp; \\cdots<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3068\u3057\u3066\u3057\u307e\u3044\u305d\u3046\u3060\u304c\uff0c\u306f\u3066\uff0c\u9589\u66f2\u9762 $S$ \u306e\u5883\u754c\u3068\u306a\u308b $C$ \u306f\u3069\u3093\u306a\u9589\u66f2\u7dda\u3068\u306a\u308b\u3093\u3060\u308d\u3046\u304b\uff1f\u3068\u60a9\u3093\u3067\u3057\u307e\u3046\u306e\u3067\uff0c\u3053\u3053\u306f\u30ac\u30a6\u30b9\u306e\u5b9a\u7406\u3092\u4f7f\u3063\u3066\u4f53\u7a4d\u7a4d\u5206\u306b\u3057\u3066&#8230;<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\iint_S\\ (\\nabla\\times\\boldsymbol{a})\\cdot\\boldsymbol{n}\\, dS &amp;=&amp;<br \/>\n\\iiint_V\\ \\nabla\\cdot(\\nabla\\times\\boldsymbol{a})\\, dV \\\\<br \/>\n&amp;=&amp; 0<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3053\u3053\u3067 $V$ \u306f\u9589\u66f2\u9762 $S$ \u3067\u56f2\u307e\u308c\u305f\u9818\u57df\u306e\u4f53\u7a4d\u3067\u3042\u308a\uff0c\u30d9\u30af\u30c8\u30eb\u89e3\u6790\u306e\u6052\u7b49\u5f0f $\\nabla\\cdot(\\nabla\\times\\boldsymbol{a}) = 0$ \u3092\u4f7f\u3063\u305f\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u30d9\u30af\u30c8\u30eb\u5834\uff08\u542b\u30b9\u30ab\u30e9\u30fc\u5834\uff09\u306e2\u968e\u504f\u5fae\u5206\u306e\u6052\u7b49\u5f0f $\\nabla \\times (\\nabla\\psi) = \\boldsymbol{0}$ \u3068 $\\nabla\\cdot (\\nabla\\times \\boldsymbol{a}) = 0$ \u306e\u9762\u7a4d\u5206\u3084\u4f53\u7a4d\u7a4d\u5206\u306b\u3064\u3044\u3066\uff0c\u3042\u3089\u305f\u3081\u3066\u307e\u3068\u3081\u3066\u304a\u304f\u3002<\/p><p><a class=\"more-link btn\" href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e5%be%ae%e5%88%86%e3%81%ae%e6%81%92%e7%ad%89%e5%bc%8f%e3%81%ae%e7%a9%8d%e5%88%86%e3%81%a8%e6%b7%b7%e4%b9%b1%e3%81%ae%e6%ad%a3%e3%81%97%e6%96%b9\/\">\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"parent":2615,"menu_order":20,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-10505","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=\"\u30d9\u30af\u30c8\u30eb\u5834\uff08\u542b\u30b9\u30ab\u30e9\u30fc\u5834\uff09\u306e2\u968e\u504f\u5fae\u5206\u306e\u6052\u7b49\u5f0f $\\nabla \\times (\\nabla\\psi) = \\\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<link rel=\"canonical\" href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e5%be%ae%e5%88%86%e3%81%ae%e6%81%92%e7%ad%89%e5%bc%8f%e3%81%ae%e7%a9%8d%e5%88%86%e3%81%a8%e6%b7%b7%e4%b9%b1%e3%81%ae%e6%ad%a3%e3%81%97%e6%96%b9\/\" \/>\n\t<meta name=\"generator\" content=\"All in One SEO (AIOSEO) 4.9.10\" \/>\n\t\t<meta property=\"og:locale\" content=\"ja_JP\" \/>\n\t\t<meta property=\"og:site_name\" content=\"\u76f8\u5bfe\u8ad6\u306e\u7406\u89e3\u3068\u305d\u306e\u5468\u8fba -\" \/>\n\t\t<meta property=\"og:type\" content=\"article\" \/>\n\t\t<meta property=\"og:title\" content=\"\u30d9\u30af\u30c8\u30eb\u5834\u306e\u5fae\u5206\u306e\u6052\u7b49\u5f0f\u306e\u7a4d\u5206\u3068\u6df7\u4e71\u306e\u6b63\u3057\u65b9 - \u76f8\u5bfe\u8ad6\u306e\u7406\u89e3\u3068\u305d\u306e\u5468\u8fba\" \/>\n\t\t<meta property=\"og:description\" content=\"\u30d9\u30af\u30c8\u30eb\u5834\uff08\u542b\u30b9\u30ab\u30e9\u30fc\u5834\uff09\u306e2\u968e\u504f\u5fae\u5206\u306e\u6052\u7b49\u5f0f $\\nabla \\times (\\nabla\\psi) = \\\" \/>\n\t\t<meta property=\"og:url\" content=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e5%be%ae%e5%88%86%e3%81%ae%e6%81%92%e7%ad%89%e5%bc%8f%e3%81%ae%e7%a9%8d%e5%88%86%e3%81%a8%e6%b7%b7%e4%b9%b1%e3%81%ae%e6%ad%a3%e3%81%97%e6%96%b9\/\" \/>\n\t\t<meta property=\"article:published_time\" content=\"2025-07-15T06:19:39+00:00\" \/>\n\t\t<meta property=\"article:modified_time\" content=\"2025-07-21T01:16:31+00:00\" \/>\n\t\t<meta name=\"twitter:card\" content=\"summary\" \/>\n\t\t<meta name=\"twitter:title\" content=\"\u30d9\u30af\u30c8\u30eb\u5834\u306e\u5fae\u5206\u306e\u6052\u7b49\u5f0f\u306e\u7a4d\u5206\u3068\u6df7\u4e71\u306e\u6b63\u3057\u65b9 - \u76f8\u5bfe\u8ad6\u306e\u7406\u89e3\u3068\u305d\u306e\u5468\u8fba\" \/>\n\t\t<meta name=\"twitter:description\" content=\"\u30d9\u30af\u30c8\u30eb\u5834\uff08\u542b\u30b9\u30ab\u30e9\u30fc\u5834\uff09\u306e2\u968e\u504f\u5fae\u5206\u306e\u6052\u7b49\u5f0f $\\nabla \\times (\\nabla\\psi) = \\\" \/>\n\t\t<script type=\"application\/ld+json\" class=\"aioseo-schema\">\n\t\t\t{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/home.hirosaki-u.ac.jp\\\/relativity\\\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\\\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\\\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e5%be%ae%e5%88%86%e3%81%ae%e6%81%92%e7%ad%89%e5%bc%8f%e3%81%ae%e7%a9%8d%e5%88%86%e3%81%a8%e6%b7%b7%e4%b9%b1%e3%81%ae%e6%ad%a3%e3%81%97%e6%96%b9\\\/#breadcrumblist\",\"itemListElement\":[{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/home.hirosaki-u.ac.jp\\\/relativity#listItem\",\"position\":1,\"name\":\"\\u30db\\u30fc\\u30e0\",\"item\":\"https:\\\/\\\/home.hirosaki-u.ac.jp\\\/relativity\",\"nextItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/home.hirosaki-u.ac.jp\\\/relativity\\\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\\\/#listItem\",\"name\":\"\\u96fb\\u78c1\\u6c17\\u5b66 I\"}},{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/home.hirosaki-u.ac.jp\\\/relativity\\\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\\\/#listItem\",\"position\":2,\"name\":\"\\u96fb\\u78c1\\u6c17\\u5b66 I\",\"item\":\"https:\\\/\\\/home.hirosaki-u.ac.jp\\\/relativity\\\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\\\/\",\"nextItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/home.hirosaki-u.ac.jp\\\/relativity\\\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\\\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\\\/#listItem\",\"name\":\"\\u30d9\\u30af\\u30c8\\u30eb\\u5834\\u306e\\u7a4d\\u5206\"},\"previousItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/home.hirosaki-u.ac.jp\\\/relativity#listItem\",\"name\":\"\\u30db\\u30fc\\u30e0\"}},{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/home.hirosaki-u.ac.jp\\\/relativity\\\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\\\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\\\/#listItem\",\"position\":3,\"name\":\"\\u30d9\\u30af\\u30c8\\u30eb\\u5834\\u306e\\u7a4d\\u5206\",\"item\":\"https:\\\/\\\/home.hirosaki-u.ac.jp\\\/relativity\\\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\\\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\\\/\",\"nextItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/home.hirosaki-u.ac.jp\\\/relativity\\\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\\\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\\\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e5%be%ae%e5%88%86%e3%81%ae%e6%81%92%e7%ad%89%e5%bc%8f%e3%81%ae%e7%a9%8d%e5%88%86%e3%81%a8%e6%b7%b7%e4%b9%b1%e3%81%ae%e6%ad%a3%e3%81%97%e6%96%b9\\\/#listItem\",\"name\":\"\\u30d9\\u30af\\u30c8\\u30eb\\u5834\\u306e\\u5fae\\u5206\\u306e\\u6052\\u7b49\\u5f0f\\u306e\\u7a4d\\u5206\\u3068\\u6df7\\u4e71\\u306e\\u6b63\\u3057\\u65b9\"},\"previousItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/home.hirosaki-u.ac.jp\\\/relativity\\\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\\\/#listItem\",\"name\":\"\\u96fb\\u78c1\\u6c17\\u5b66 I\"}},{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/home.hirosaki-u.ac.jp\\\/relativity\\\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\\\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\\\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e5%be%ae%e5%88%86%e3%81%ae%e6%81%92%e7%ad%89%e5%bc%8f%e3%81%ae%e7%a9%8d%e5%88%86%e3%81%a8%e6%b7%b7%e4%b9%b1%e3%81%ae%e6%ad%a3%e3%81%97%e6%96%b9\\\/#listItem\",\"position\":4,\"name\":\"\\u30d9\\u30af\\u30c8\\u30eb\\u5834\\u306e\\u5fae\\u5206\\u306e\\u6052\\u7b49\\u5f0f\\u306e\\u7a4d\\u5206\\u3068\\u6df7\\u4e71\\u306e\\u6b63\\u3057\\u65b9\",\"previousItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/home.hirosaki-u.ac.jp\\\/relativity\\\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\\\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\\\/#listItem\",\"name\":\"\\u30d9\\u30af\\u30c8\\u30eb\\u5834\\u306e\\u7a4d\\u5206\"}}]},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/home.hirosaki-u.ac.jp\\\/relativity\\\/#organization\",\"name\":\"Understanding Theory of Relativity\",\"url\":\"https:\\\/\\\/home.hirosaki-u.ac.jp\\\/relativity\\\/\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/home.hirosaki-u.ac.jp\\\/relativity\\\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\\\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\\\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e5%be%ae%e5%88%86%e3%81%ae%e6%81%92%e7%ad%89%e5%bc%8f%e3%81%ae%e7%a9%8d%e5%88%86%e3%81%a8%e6%b7%b7%e4%b9%b1%e3%81%ae%e6%ad%a3%e3%81%97%e6%96%b9\\\/#webpage\",\"url\":\"https:\\\/\\\/home.hirosaki-u.ac.jp\\\/relativity\\\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\\\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\\\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e5%be%ae%e5%88%86%e3%81%ae%e6%81%92%e7%ad%89%e5%bc%8f%e3%81%ae%e7%a9%8d%e5%88%86%e3%81%a8%e6%b7%b7%e4%b9%b1%e3%81%ae%e6%ad%a3%e3%81%97%e6%96%b9\\\/\",\"name\":\"\\u30d9\\u30af\\u30c8\\u30eb\\u5834\\u306e\\u5fae\\u5206\\u306e\\u6052\\u7b49\\u5f0f\\u306e\\u7a4d\\u5206\\u3068\\u6df7\\u4e71\\u306e\\u6b63\\u3057\\u65b9 - \\u76f8\\u5bfe\\u8ad6\\u306e\\u7406\\u89e3\\u3068\\u305d\\u306e\\u5468\\u8fba\",\"description\":\"\\u30d9\\u30af\\u30c8\\u30eb\\u5834\\uff08\\u542b\\u30b9\\u30ab\\u30e9\\u30fc\\u5834\\uff09\\u306e2\\u968e\\u504f\\u5fae\\u5206\\u306e\\u6052\\u7b49\\u5f0f $\\\\nabla \\\\times (\\\\nabla\\\\psi) = \\\\\",\"inLanguage\":\"ja\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/home.hirosaki-u.ac.jp\\\/relativity\\\/#website\"},\"breadcrumb\":{\"@id\":\"https:\\\/\\\/home.hirosaki-u.ac.jp\\\/relativity\\\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\\\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\\\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e5%be%ae%e5%88%86%e3%81%ae%e6%81%92%e7%ad%89%e5%bc%8f%e3%81%ae%e7%a9%8d%e5%88%86%e3%81%a8%e6%b7%b7%e4%b9%b1%e3%81%ae%e6%ad%a3%e3%81%97%e6%96%b9\\\/#breadcrumblist\"},\"datePublished\":\"2025-07-15T15:19:39+09:00\",\"dateModified\":\"2025-07-21T10:16:31+09:00\"},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/home.hirosaki-u.ac.jp\\\/relativity\\\/#website\",\"url\":\"https:\\\/\\\/home.hirosaki-u.ac.jp\\\/relativity\\\/\",\"name\":\"\\u76f8\\u5bfe\\u8ad6\\u306e\\u7406\\u89e3\\u3068\\u305d\\u306e\\u5468\\u8fba\",\"inLanguage\":\"ja\",\"publisher\":{\"@id\":\"https:\\\/\\\/home.hirosaki-u.ac.jp\\\/relativity\\\/#organization\"}}]}\n\t\t<\/script>\n\t\t<!-- All in One SEO -->\n\n","aioseo_head_json":{"title":"\u30d9\u30af\u30c8\u30eb\u5834\u306e\u5fae\u5206\u306e\u6052\u7b49\u5f0f\u306e\u7a4d\u5206\u3068\u6df7\u4e71\u306e\u6b63\u3057\u65b9 - \u76f8\u5bfe\u8ad6\u306e\u7406\u89e3\u3068\u305d\u306e\u5468\u8fba","description":"\u30d9\u30af\u30c8\u30eb\u5834\uff08\u542b\u30b9\u30ab\u30e9\u30fc\u5834\uff09\u306e2\u968e\u504f\u5fae\u5206\u306e\u6052\u7b49\u5f0f $\\nabla \\times (\\nabla\\psi) = \\","canonical_url":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e5%be%ae%e5%88%86%e3%81%ae%e6%81%92%e7%ad%89%e5%bc%8f%e3%81%ae%e7%a9%8d%e5%88%86%e3%81%a8%e6%b7%b7%e4%b9%b1%e3%81%ae%e6%ad%a3%e3%81%97%e6%96%b9\/","robots":"max-image-preview:large","keywords":"","webmasterTools":{"miscellaneous":""},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"BreadcrumbList","@id":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e5%be%ae%e5%88%86%e3%81%ae%e6%81%92%e7%ad%89%e5%bc%8f%e3%81%ae%e7%a9%8d%e5%88%86%e3%81%a8%e6%b7%b7%e4%b9%b1%e3%81%ae%e6%ad%a3%e3%81%97%e6%96%b9\/#breadcrumblist","itemListElement":[{"@type":"ListItem","@id":"https:\/\/home.hirosaki-u.ac.jp\/relativity#listItem","position":1,"name":"\u30db\u30fc\u30e0","item":"https:\/\/home.hirosaki-u.ac.jp\/relativity","nextItem":{"@type":"ListItem","@id":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/#listItem","name":"\u96fb\u78c1\u6c17\u5b66 I"}},{"@type":"ListItem","@id":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/#listItem","position":2,"name":"\u96fb\u78c1\u6c17\u5b66 I","item":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/","nextItem":{"@type":"ListItem","@id":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\/#listItem","name":"\u30d9\u30af\u30c8\u30eb\u5834\u306e\u7a4d\u5206"},"previousItem":{"@type":"ListItem","@id":"https:\/\/home.hirosaki-u.ac.jp\/relativity#listItem","name":"\u30db\u30fc\u30e0"}},{"@type":"ListItem","@id":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\/#listItem","position":3,"name":"\u30d9\u30af\u30c8\u30eb\u5834\u306e\u7a4d\u5206","item":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\/","nextItem":{"@type":"ListItem","@id":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e5%be%ae%e5%88%86%e3%81%ae%e6%81%92%e7%ad%89%e5%bc%8f%e3%81%ae%e7%a9%8d%e5%88%86%e3%81%a8%e6%b7%b7%e4%b9%b1%e3%81%ae%e6%ad%a3%e3%81%97%e6%96%b9\/#listItem","name":"\u30d9\u30af\u30c8\u30eb\u5834\u306e\u5fae\u5206\u306e\u6052\u7b49\u5f0f\u306e\u7a4d\u5206\u3068\u6df7\u4e71\u306e\u6b63\u3057\u65b9"},"previousItem":{"@type":"ListItem","@id":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/#listItem","name":"\u96fb\u78c1\u6c17\u5b66 I"}},{"@type":"ListItem","@id":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e5%be%ae%e5%88%86%e3%81%ae%e6%81%92%e7%ad%89%e5%bc%8f%e3%81%ae%e7%a9%8d%e5%88%86%e3%81%a8%e6%b7%b7%e4%b9%b1%e3%81%ae%e6%ad%a3%e3%81%97%e6%96%b9\/#listItem","position":4,"name":"\u30d9\u30af\u30c8\u30eb\u5834\u306e\u5fae\u5206\u306e\u6052\u7b49\u5f0f\u306e\u7a4d\u5206\u3068\u6df7\u4e71\u306e\u6b63\u3057\u65b9","previousItem":{"@type":"ListItem","@id":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\/#listItem","name":"\u30d9\u30af\u30c8\u30eb\u5834\u306e\u7a4d\u5206"}}]},{"@type":"Organization","@id":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/#organization","name":"Understanding Theory of Relativity","url":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/"},{"@type":"WebPage","@id":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e5%be%ae%e5%88%86%e3%81%ae%e6%81%92%e7%ad%89%e5%bc%8f%e3%81%ae%e7%a9%8d%e5%88%86%e3%81%a8%e6%b7%b7%e4%b9%b1%e3%81%ae%e6%ad%a3%e3%81%97%e6%96%b9\/#webpage","url":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e5%be%ae%e5%88%86%e3%81%ae%e6%81%92%e7%ad%89%e5%bc%8f%e3%81%ae%e7%a9%8d%e5%88%86%e3%81%a8%e6%b7%b7%e4%b9%b1%e3%81%ae%e6%ad%a3%e3%81%97%e6%96%b9\/","name":"\u30d9\u30af\u30c8\u30eb\u5834\u306e\u5fae\u5206\u306e\u6052\u7b49\u5f0f\u306e\u7a4d\u5206\u3068\u6df7\u4e71\u306e\u6b63\u3057\u65b9 - \u76f8\u5bfe\u8ad6\u306e\u7406\u89e3\u3068\u305d\u306e\u5468\u8fba","description":"\u30d9\u30af\u30c8\u30eb\u5834\uff08\u542b\u30b9\u30ab\u30e9\u30fc\u5834\uff09\u306e2\u968e\u504f\u5fae\u5206\u306e\u6052\u7b49\u5f0f $\\nabla \\times (\\nabla\\psi) = \\","inLanguage":"ja","isPartOf":{"@id":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/#website"},"breadcrumb":{"@id":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e5%be%ae%e5%88%86%e3%81%ae%e6%81%92%e7%ad%89%e5%bc%8f%e3%81%ae%e7%a9%8d%e5%88%86%e3%81%a8%e6%b7%b7%e4%b9%b1%e3%81%ae%e6%ad%a3%e3%81%97%e6%96%b9\/#breadcrumblist"},"datePublished":"2025-07-15T15:19:39+09:00","dateModified":"2025-07-21T10:16:31+09:00"},{"@type":"WebSite","@id":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/#website","url":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/","name":"\u76f8\u5bfe\u8ad6\u306e\u7406\u89e3\u3068\u305d\u306e\u5468\u8fba","inLanguage":"ja","publisher":{"@id":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/#organization"}}]},"og:locale":"ja_JP","og:site_name":"\u76f8\u5bfe\u8ad6\u306e\u7406\u89e3\u3068\u305d\u306e\u5468\u8fba -","og:type":"article","og:title":"\u30d9\u30af\u30c8\u30eb\u5834\u306e\u5fae\u5206\u306e\u6052\u7b49\u5f0f\u306e\u7a4d\u5206\u3068\u6df7\u4e71\u306e\u6b63\u3057\u65b9 - \u76f8\u5bfe\u8ad6\u306e\u7406\u89e3\u3068\u305d\u306e\u5468\u8fba","og:description":"\u30d9\u30af\u30c8\u30eb\u5834\uff08\u542b\u30b9\u30ab\u30e9\u30fc\u5834\uff09\u306e2\u968e\u504f\u5fae\u5206\u306e\u6052\u7b49\u5f0f $\\nabla \\times (\\nabla\\psi) = \\","og:url":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e5%be%ae%e5%88%86%e3%81%ae%e6%81%92%e7%ad%89%e5%bc%8f%e3%81%ae%e7%a9%8d%e5%88%86%e3%81%a8%e6%b7%b7%e4%b9%b1%e3%81%ae%e6%ad%a3%e3%81%97%e6%96%b9\/","article:published_time":"2025-07-15T06:19:39+00:00","article:modified_time":"2025-07-21T01:16:31+00:00","twitter:card":"summary","twitter:title":"\u30d9\u30af\u30c8\u30eb\u5834\u306e\u5fae\u5206\u306e\u6052\u7b49\u5f0f\u306e\u7a4d\u5206\u3068\u6df7\u4e71\u306e\u6b63\u3057\u65b9 - \u76f8\u5bfe\u8ad6\u306e\u7406\u89e3\u3068\u305d\u306e\u5468\u8fba","twitter:description":"\u30d9\u30af\u30c8\u30eb\u5834\uff08\u542b\u30b9\u30ab\u30e9\u30fc\u5834\uff09\u306e2\u968e\u504f\u5fae\u5206\u306e\u6052\u7b49\u5f0f $\\nabla \\times (\\nabla\\psi) = \\"},"aioseo_meta_data":{"post_id":"10505","title":null,"description":null,"keywords":null,"keyphrases":{"focus":{"keyphrase":"","score":0,"analysis":{"keyphraseInTitle":{"score":0,"maxScore":9,"error":1}}},"additional":[]},"primary_term":null,"canonical_url":null,"og_title":null,"og_description":null,"og_object_type":"default","og_image_type":"default","og_image_url":null,"og_image_width":null,"og_image_height":null,"og_image_custom_url":null,"og_image_custom_fields":null,"og_video":"","og_custom_url":null,"og_article_section":null,"og_article_tags":null,"twitter_use_og":false,"twitter_card":"default","twitter_image_type":"default","twitter_image_url":null,"twitter_image_custom_url":null,"twitter_image_custom_fields":null,"twitter_title":null,"twitter_description":null,"schema":{"blockGraphs":[],"customGraphs":[],"default":{"data":{"Article":[],"Course":[],"Dataset":[],"FAQPage":[],"Movie":[],"Person":[],"Product":[],"ProductReview":[],"Car":[],"Recipe":[],"Service":[],"SoftwareApplication":[],"WebPage":[]},"graphName":"WebPage","isEnabled":true},"graphs":[]},"schema_type":"default","schema_type_options":null,"pillar_content":false,"robots_default":true,"robots_noindex":false,"robots_noarchive":false,"robots_nosnippet":false,"robots_nofollow":false,"robots_noimageindex":false,"robots_noodp":false,"robots_notranslate":false,"robots_max_snippet":"-1","robots_max_videopreview":"-1","robots_max_imagepreview":"large","priority":null,"frequency":"default","local_seo":null,"breadcrumb_settings":null,"limit_modified_date":false,"ai":null,"created":"2025-07-15 05:02:23","updated":"2025-07-21 01:16:31","seo_analyzer_scan_date":null},"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/10505","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\/33"}],"replies":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/comments?post=10505"}],"version-history":[{"count":43,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/10505\/revisions"}],"predecessor-version":[{"id":10556,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/10505\/revisions\/10556"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2615"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=10505"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}