{"id":102201,"date":"2024-09-03T22:01:16","date_gmt":"2024-09-03T22:01:16","guid":{"rendered":"https:\/\/science-hub.click\/%E7%89%B9%E6%AE%8A%E7%9B%B8%E5%AF%BE%E6%80%A7%E7%90%86%E8%AB%96%E3%81%AE%E5%BD%A2%E5%BC%8F-%E5%AE%9A%E7%BE%A9\/"},"modified":"2024-09-03T22:01:16","modified_gmt":"2024-09-03T22:01:16","slug":"%E7%89%B9%E6%AE%8A%E7%9B%B8%E5%AF%BE%E6%80%A7%E7%90%86%E8%AB%96%E3%81%AE%E5%BD%A2%E5%BC%8F-%E5%AE%9A%E7%BE%A9","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=102201","title":{"rendered":"\u7279\u6b8a\u76f8\u5bfe\u6027\u7406\u8ad6\u306e\u5f62\u5f0f – \u5b9a\u7fa9"},"content":{"rendered":"

\u5c0e\u5165<\/h2>
<\/center><\/td><\/tr>
\u5149\u5b66<\/td><\/tr>
\u96fb\u78c1<\/td><\/tr>
\u91cf\u5b50\u7269\u7406\u5b66<\/td><\/tr>
\u71b1\u529b\u5b66<\/td><\/tr>
\u6d41\u4f53\u529b\u5b66<\/a><\/span><\/td><\/tr>
\u6a5f\u68b0\u5f0f<\/a><\/span><\/td><\/tr>
\u7279\u6b8a\u76f8\u5bfe\u6027\u7406\u8ad6<\/a><\/span><\/strong><\/td><\/tr>
\u30d6\u30e9\u30c3\u30af\u30db\u30fc\u30eb<\/a><\/span><\/td><\/tr>
\u30d9\u30af\u30c8\u30eb\u89e3\u6790<\/a><\/span><\/td><\/tr><\/table>
\n\"\u7279\u6b8a\u76f8\u5bfe\u6027\u7406\u8ad6\u306e\u5f62\u5f0f<\/figure>

\u8a55\u4fa1<\/h2>

\u6570\u5f0f\u306f\u3001\u56fa\u5b9a<\/i>\u6163\u6027\u7cfb (\u5730\u7403\u306a\u3069) \u5185\u306e\u30a4\u30d9\u30f3\u30c8\u306e\u5ea7\u6a19 ( t<\/i> , x<\/i> ) \u3068\u3001\u79fb\u52d5<\/i>\u7cfb (\u305f\u3068\u3048\u3070\u5730\u7403<\/a><\/span>) \u5185\u306e\u540c\u3058\u30a4\u30d9\u30f3\u30c8\u306e\u5ea7\u6a19 ( t’<\/i> , x’<\/i> ) \u306e\u9593\u306e\u901a\u904e\u3092\u78ba\u7acb\u3057\u307e\u3059\u3002\u30ed\u30b1\u30c3\u30c8<\/span>\u3001\u901f\u5ea6<\/a><\/span>v<\/i>\u3067x<\/i>\u8ef8\u306b\u6cbf\u3063\u3066\u79fb\u52d5\u3057\u307e\u3059\u3002<\/p>

\u6642\u9593<\/a><\/span>\u306e\u8d77\u6e90\u306f\u4e00\u81f4\u3059\u308b\u3068\u8003\u3048\u3089\u308c\u3066\u3044\u307e\u3059\u3002 <\/p>

$$ {t\\,=\\,t’\\,=\\,0} $$<\/div><\/dd><\/dl>

\u79c1\u305f\u3061\u306f\u30dd\u30fc\u30ba\u3092\u3068\u308a\u307e\u3059: <\/p>

$$ {\\beta \\,=\\,v\/c} $$<\/div><\/dd><\/dl>

\u7279\u6b8a\u76f8\u5bfe\u6027\u7406\u8ad6\u306e\u4e0d\u5909\u91cf<\/h2>

\u6b21\u306e\u91cf\u306f<\/a><\/span>\u5ea7\u6a19\u304c\u5909\u5316\u3057\u3066\u3082\u4e0d\u5909\u3067\u3059<\/p>

$$ {c^2\\tau^2\\,=\\,c^2t^2 – (x^2 + y^2 + z^2) = \\,c^2t’^2 – (x’^2 + y’^2 + z’^2)} $$<\/div><\/dd><\/dl>

\u305d\u3057\u3066\u9069\u5207\u306a\u6642\u9593<\/a><\/span>\u3092\u5b9a\u7fa9\u3057\u307e\u3059

$$ {\\,\\tau\\,.} $$<\/div><\/p>

\u89d2\u5ea6\u30d1\u30e9\u30e1\u30fc\u30bf<\/h2>

\u5f0f\u3092\u5358\u7d14\u5316\u3059\u308b\u306b\u306f\u3001\u6b21\u306e\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u89d2\u5ea6\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u5c0e\u5165\u3059\u308b\u3068\u4fbf\u5229\u3067\u3059\u3002 <\/p>

$$ {\\beta \\,=\\,\\tanh\\theta} $$<\/div>\u3069\u3061\u3089\u304b
$$ {\\theta \\,=\\, \\mathrm{atanh}\\beta} $$<\/div><\/dd><\/dl>

\u3053\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u8a18\u8ff0\u3067\u304d\u307e\u3059\u3002 <\/p>

$$ { \\gamma = (1 – \\beta^2)^{-1\/2} = (1 – \\tanh^2\\, \\theta)^{-1\/2} = \\cosh \\,\\theta } $$<\/div><\/dd>
$$ {\\beta\\gamma \\,=\\, \\beta (1 – \\beta^2)^{-1\/2} = \\tanh\\theta \\,\\cosh \\,\\theta = \\sinh\\,\\theta } $$<\/div><\/dd><\/dl>

\u6642\u9593\u306e\u9045\u308c<\/h2>

\u30ed\u30b1\u30c3\u30c8\u30af\u30ed\u30c3\u30af\u304c\u6301\u7d9a\u6642\u9593\u3092\u6e2c\u308b\u306a\u3089

$$ {\\Delta\\,t’} $$<\/div>\u3053\u306e\u30ed\u30b1\u30c3\u30c8\u5185\u3067\u767a\u751f\u3059\u308b 2 \u3064\u306e\u30a4\u30d9\u30f3\u30c8\u306e\u9593\u3001\u3057\u305f\u304c\u3063\u3066\u7a7a\u9593\u8ddd\u96e2\u306b\u3088\u3063\u3066\u5206\u96e2\u3055\u308c\u307e\u3059\u3002
$$ {\\Delta\\,x’=0} $$<\/div> \u3001\u5730\u7403\u306e\u56fa\u5b9a\u3055\u308c\u305f\u5b9f\u9a13\u5ba4\u3067\u6e2c\u5b9a\u3055\u308c\u305f\u6301\u7d9a\u6642\u9593\u306f\u3001 <\/p>
$$ {\\Delta t = \\Delta t’\\cosh\\,\\theta = \\gamma \\Delta t’ = \\frac{\\Delta t’}{\\sqrt{1 – (v^2\/c^2)}}\\,.} $$<\/div><\/dd><\/dl>

\u5916\u90e8\u30d9\u30f3\u30c1\u30de\u30fc\u30af\u3067\u6e2c\u5b9a\u3055\u308c\u305f\u671f\u9593\u306f\u3001\u5e38\u306b\u72ec\u81ea\u306e\u671f\u9593\u3088\u308a\u3082\u9577\u304f\u306a\u308a\u307e\u3059\u3002<\/p>

\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db<\/h2>
$$ { \\begin{cases}ct = \\gamma (ct’+ \\beta x’)\\\\ x = \\gamma (x’ + \\beta ct’)\\\\ y = y’\\\\ z = z’ \\end{cases} } $$<\/div><\/dd><\/dl>

\u3053\u308c\u306f\u884c\u5217\u5f62\u5f0f\u3067\u5f97\u3089\u308c\u307e\u3059 (\u8996\u899a\u5316\u304c\u5bb9\u6613\u306b\u306a\u308a\u307e\u3059)\u3002 <\/p>

$$ { \\begin{pmatrix} ct\\\\x\\\\y\\\\z \\end{pmatrix} = \\begin{pmatrix} \\gamma & \\beta\\gamma & 0 & 0\\\\ \\beta\\gamma & \\gamma & 0 & 0\\\\ 0 & 0 & 1 & 0\\\\ 0 & 0 & 0 & 1\\\\ \\end{pmatrix} \\begin{pmatrix} ct’\\\\x’\\\\y’\\\\z’ \\end{pmatrix} } $$<\/div><\/dd><\/dl>

\u89d2\u5ea6<\/a><\/span>\u03b8<\/i>\u306e\u53cc\u66f2\u7dda\u95a2\u6570\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u5e73\u9762\u56de\u8ee2\u306b\u3088\u3063\u3066\u5ea7\u6a19\u8ef8\u3092\u5909\u66f4\u3059\u308b\u305f\u3081\u306e\u516c\u5f0f\u306b\u985e\u4f3c\u3057\u305f\u5f0f\u304c\u5f97\u3089\u308c\u307e\u3059\u3002 <\/p>

$$ { \\begin{cases} ct= ct’\\cosh\\,\\theta + x’\\sinh\\,\\theta \\\\ x = ct’ \\sinh\\,\\theta + x’\\cosh\\,\\theta \\end{cases} } $$<\/div><\/dd><\/dl>

\u9006<\/a><\/span>\u65b9\u5411<\/a><\/span><\/p>

$$ { \\begin{cases}ct’ = \\gamma (ct – \\beta x)\\\\ x’ = \\gamma (x – \\beta ct )\\\\ y’ = y\\\\ z’ = z \\end{cases} } $$<\/div><\/dd><\/dl>

\u307e\u305f\u306f<\/p>

$$ { \\begin{cases} ct’= \\ ct\\cosh\\,\\theta – x\\sinh\\,\\theta \\\\ x’ = -ct \\sinh\\,\\theta + x\\cosh\\,\\theta \\end{cases} } $$<\/div><\/dd><\/dl>

\u901f\u5ea6\u306e\u5408\u6210\u6cd5\u5247<\/h2>

\u7832\u5f3e\u306f\u3001\u3053\u306e\u30ed\u30b1\u30c3\u30c8\u306e\u57fa\u6e96\u306b\u5bfe\u3057\u3066\u9032\u884c\u65b9\u5411\u306b\u901f\u5ea6w ‘<\/i>\u3067\u30ed\u30b1\u30c3\u30c8\u306b\u767a\u5c04\u3055\u308c\u307e\u3059\u3002\u5730\u7403\u306b\u5bfe\u3059\u308b\u7832\u5f3e\u306e\u901f\u5ea6w \u306f<\/i>\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ {w \\,=\\, \\frac{w’+v}{1 + (w’ v\/c^2)}\\,.} $$<\/div><\/dd><\/dl>

\u89d2\u5ea6\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u4f7f\u7528<\/p>

$$ {\\alpha’\\,=\\,\\mathrm{atanh}(w’\/c)} $$<\/div><\/dd>
$$ {\\alpha\\,=\\,\\mathrm{atanh}(w\/c)} $$<\/div><\/dd>
$$ {\\theta\\,=\\,\\mathrm{atanh}(v\/c)} $$<\/div><\/dd><\/dl>

\u79c1\u305f\u3061\u306b\u306f\u52a0\u7b97\u6cd5\u304c\u3042\u308a\u307e\u3059<\/p>

$$ {\\alpha\\,=\\,\\alpha’+\\theta} $$<\/div><\/dd><\/dl>
\n\"\u7279\u6b8a\u76f8\u5bfe\u6027\u7406\u8ad6\u306e\u5f62\u5f0f<\/figure>

\u9577\u3055\u306e\u53ce\u7e2e<\/h2>

\u30ed\u30b1\u30c3\u30c8\u304c\u305d\u308c\u81ea\u4f53\u306e\u57fa\u6e96\u7cfb\u3067\u9577\u3055<\/a><\/span>L’<\/i>\u3067\u3042\u308b\u5834\u5408\u3001\u5730\u7403\u4e0a\u306e 2 \u70b9\u9593\u306e\u8ddd\u96e2\u3067\u6e2c\u5b9a\u3057\u305f\u305d\u306e\u9577\u3055L \u306f<\/i>\u3001\u540c\u3058\u77ac\u9593<\/a><\/span>(\u5730\u7403\u4e0a) \u3067\u306e\u30ed\u30b1\u30c3\u30c8\u306e\u524d\u5f8c\u306e\u9577\u3055\u3068\u4e00\u81f4\u3057\u307e\u3059\u3002

$$ {\\Delta t\\,=\\,0} $$<\/div> \u3001\u306b\u3088\u3063\u3066\u4e0e\u3048\u3089\u308c\u307e\u3059<\/p>
$$ {L = L’\/\\gamma = L’ \\sqrt{1 – (v^2\/c^2)}\\,.} $$<\/div><\/dd><\/dl>

\u5730\u7403\u4e0a\u3067\u6e2c\u5b9a\u3055\u308c\u305f\u9577\u3055\u306f\u30ed\u30b1\u30c3\u30c8\u81ea\u4f53\u306e\u9577\u3055\u3088\u308a\u3082\u77ed\u3044\u3067\u3059\u3002<\/p>

\u904b\u52d5\u30a8\u30cd\u30eb\u30ae\u30fc<\/h2>

\u7c92\u5b50\u306e\u904b\u52d5\u30a8\u30cd\u30eb\u30ae\u30fc<\/a><\/span>\u306f\u3001 <\/p>

$$ { K\\, = E – m c^2 \\,=\\,m c^2\\left( \\frac{1}{\\sqrt{1 – (v^2\/c^2)}} – 1\\right)\\,.} $$<\/div><\/dd><\/dl>

\u306e\u305f\u3081\u306b

$$ {v\\ll c} $$<\/div><\/p>
$$ {K\\,= \\,(1\/2) m v^2\\,} $$<\/div><\/dd><\/dl>

\u305d\u3057\u3066\u306e\u305f\u3081\u306b

$$ {v\\simeq c} $$<\/div><\/p>
$$ {K \\simeq E \\simeq pc = \\frac{mc^2}{\\sqrt{2(1-\\beta)}}\\equiv \\frac{mc^2}{\\sqrt{2[1-(v\/c)]}}\\,.} $$<\/div><\/dd><\/dl>

\u30a8\u30cd\u30eb\u30ae\u30fc\u904b\u52d5\u91cf\u30af\u30ef\u30c9\u30ea\u30d9\u30af\u30bf\u30fc<\/h2>
$$ { \\begin{cases} p_t=E\/c = mc \\ dt\/d\\tau\\\\ p_x = m\\ dx\/d\\tau\\\\ p_y =m\\ dy\/d\\tau\\\\ p_z=m\\ dz\/d\\tau\\,. \\end{cases}} $$<\/div><\/dd><\/dl>

\u3068\u3057\u3066<\/p>

$$ {dt\/d\\tau\\,=\\,\\gamma \\equiv (1-\\beta^2)^{-1\/2}\\,,} $$<\/div><\/dd><\/dl>

\u6211\u3005\u306f\u6301\u3063\u3066\u3044\u307e\u3059<\/p>

$$ {E \\,=\\,\\gamma mc^2} $$<\/div><\/dd>
$$ {p \\equiv (p_x^2 + p_y^2 + p_z^2)^{1\/2} = m\\gamma\\beta c= m v \/\\sqrt{1 – (v^2\/c^2)}} $$<\/div><\/dd><\/dl>

\u4f4e\u901f\u6642

$$ {v\\,\\ll\\,c} $$<\/div><\/p>
$$ {E \\,=\\, mc^2 + (1\/2) m v^2\\,.} $$<\/div><\/dd><\/dl>

\u79c1\u305f\u3061\u306f\u307e\u3060\u95a2\u4fc2\u3092\u6301\u3063\u3066\u3044\u307e\u3059<\/p>

$$ {p\\,=\\,\\beta E\/c\\,.} $$<\/div><\/dd><\/dl>

\u6b21\u306e\u91cf\u306f\u57fa\u6e96\u304c\u5909\u5316\u3057\u3066\u3082\u4e0d\u5909\u3067\u3059<\/p>

$$ {E^2 – p^2c^2\\,=\\,m^2c^4} $$<\/div><\/dd><\/dl>

\u5149\u5b50<\/a><\/span>\u306e\u5834\u5408\u3001 m<\/i> = 0 \u3067\u3042\u308a\u3001 <\/p>

$$ {E\\,=\\,pc} $$<\/div><\/dd><\/dl>

\u30c9\u30c3\u30d7\u30e9\u30fc\u30fb\u30d5\u30a3\u30be\u30fc\u52b9\u679c<\/h2>
\n\"\"<\/figure>
\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c<\/div><\/div><\/div>

$$ {\\nu\\,} $$<\/div>\u5730\u7403\u4e0a\u3067\u53d7\u4fe1\u3055\u308c\u308b\u5468\u6ce2\u6570\u3067\u3059\u3002
$$ {\\nu’\\,} $$<\/div>\u97f3\u6e90\u304b\u3089\u767a\u305b\u3089\u308c\u308b\u5468\u6ce2\u6570\u3001
$$ {\\theta’\\,} $$<\/div>\u3053\u306e\u30bd\u30fc\u30b9\u306e\u53c2\u7167\u7cfb\u3067\u5149\u5b50\u304cOx<\/i>\u8ef8\u3068\u306a\u3059\u89d2\u5ea6\u3001
$$ {\\theta\\,} $$<\/div>\u5730\u7403\u57fa\u6e96\u7cfb\u306b\u304a\u3051\u308bOx<\/i>\u8ef8\u3068\u306e\u89d2\u5ea6\u3001
$$ {v\\,} $$<\/div>\u5730\u7403\u306b\u5bfe\u3059\u308b\u30bd\u30fc\u30b9\u306e\u901f\u5ea6\u3068
$$ {v_r\\equiv v\\cos\\theta’} $$<\/div>\u534a\u5f84\u65b9\u5411\u306e\u901f\u5ea6\u306f<\/p>
$$ {\\nu\\,=\\,\\gamma\\,(1 + \\beta\\cos\\theta’) \\nu’\\equiv \\frac{1 + (v_r\/c)}{\\sqrt{1 – (v^2\/c^2)}}\\,\\nu’} $$<\/div><\/dd><\/dl>

\u4f4e\u901f\u6642

$$ {v\\ll c} $$<\/div><\/p>
$$ {\\frac{\\Delta\\nu}{\\nu} \\equiv \\frac{\\nu – \\nu’}{\\nu’} \\simeq \\frac{\\nu – \\nu’}{\\nu} = \\frac{v_r}{c}\\,.} $$<\/div><\/dd><\/dl>

\u661f\u304c<\/a><\/span>\u9060\u3056\u304b\u308b\u3068\u3001 v<\/i>\u306f\u6b63\u3001 cos\u03b8’<\/span>\u306f\u8ca0\u3001

$$ {v_r\\,=\\,v\\cos\\theta’} $$<\/div>\u306f\u8ca0\u3067\u3042\u308b\u305f\u3081\u3001\u5468\u6ce2\u6570\u306f\u6e1b\u5c11\u3057\u307e\u3059<\/b>(\u6ce2\u9577<\/a><\/span>\u304c\u5897\u52a0\u3059\u308b\u3068\u3001\u3053\u308c\u304c\u8d64\u65b9\u504f\u79fb\u306b\u306a\u308a\u307e\u3059)\u3002<\/p>

\u5149\u53ce\u5dee\u73fe\u8c61\uff1a <\/p>

$$ {\\begin{cases}\\cos\\theta = (\\beta + \\cos\\theta’)\/(1 + \\beta\\cos\\theta’)\\\\ \\sin\\theta = \\gamma^{-1}\\sin\\theta’\/(1+\\beta\\cos\\theta’) \\end{cases}} $$<\/div><\/dd><\/dl><\/div>

\u53c2\u8003\u8cc7\u6599<\/h2>
  1. \u0627\u0633\u062a\u0645\u0627\u0631\u0629 \u2013 arabe<\/a><\/li>
  2. Formulari \u2013 catalan<\/a><\/li>
  3. Formul\u00e1\u0159 \u2013 tch\u00e8que<\/a><\/li>
  4. Blanket \u2013 danois<\/a><\/li>
  5. Formular \u2013 allemand<\/a><\/li>
  6. Form (document) \u2013 anglais<\/a><\/li><\/ol><\/div>\n
    \n

    \n \u7279\u6b8a\u76f8\u5bfe\u6027\u7406\u8ad6\u306e\u5f62\u5f0f – \u5b9a\u7fa9\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n
    \n \n
    \n
    \n