{"id":174,"date":"2026-06-15T01:20:37","date_gmt":"2026-06-14T21:50:37","guid":{"rendered":"https:\/\/sciencio.ir\/?p=174"},"modified":"2026-06-15T01:20:37","modified_gmt":"2026-06-14T21:50:37","slug":"10-%d9%86%d9%85%d9%88%d8%af%d8%a7%d8%b1-%d9%85%db%8c%d9%86%da%a9%d9%88%d9%81%d8%b3%da%a9%db%8c","status":"publish","type":"post","link":"https:\/\/sciencio.ir\/?p=174","title":{"rendered":"10 \u0646\u0645\u0648\u062f\u0627\u0631 \u0645\u06cc\u0646\u06a9\u0648\u0641\u0633\u06a9\u06cc"},"content":{"rendered":"

\u0646\u0645\u0648\u062f\u0627\u0631 \u0645\u06cc\u0646\u06a9\u0648\u0641\u0633\u06a9\u06cc \u0627\u0628\u0632\u0627\u0631 \u0647\u0646\u062f\u0633\u06cc \u0628\u0631\u0627\u06cc \u062a\u0648\u0635\u06cc\u0641 \u0648 \u062d\u0644 \u0645\u0633\u0627\u0626\u0644 \u0646\u0633\u0628\u06cc\u062a \u0627\u0633\u062a. \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u067e\u06cc\u0634 \u062a\u0631 \u0628\u062d\u062b \u06a9\u0631\u062f\u06cc\u0645\u061b \u0628\u0631\u0627\u06cc \u0631\u0627\u062d\u062a\u06cc \u062f\u0631 \u062f\u0633\u062a\u06af\u0627\u0647 \u06cc\u06a9\u0627\u06cc\u06cc \u0642\u0631\u0627\u0631 \u0645\u06cc \u06af\u06cc\u0631\u06cc\u0645 \u06a9\u0647 $c=1$ \u0628\u0627\u0634\u062f. \u0628\u0647 \u0627\u06cc\u0646 \u0635\u0648\u0631\u062a \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645 \u0646\u0645\u0648\u062f\u0627\u0631\u06cc \u0637\u0631\u0627\u062d\u06cc \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0645\u062d\u0648\u0631 \u0639\u0645\u0648\u062f\u06cc \u0622\u0646 $t$ \u0648 \u0645\u062d\u0648\u0631 \u0627\u0641\u0642\u06cc \u0622\u0646 $x$ \u0628\u0627\u0634\u062f. \u0686\u0646\u06cc\u0646 \u0646\u0645\u0648\u062f\u0627\u0631\u06cc \u0628\u0647 \u06cc\u06a9 \u0628\u0639\u062f \u0641\u0636\u0627\u06cc\u06cc \u0628\u0627\u0644\u0627\u062a\u0631 \u0646\u06cc\u0632 \u0642\u0627\u0628\u0644 \u062a\u0639\u0645\u06cc\u0645 \u0627\u0633\u062a \u0648 \u06af\u0627\u0647\u0627 \u0627\u0632 \u0622\u0646 \u0646\u06cc\u0632 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n

1-10 \u0646\u0627\u0638\u0631 (\u0686\u0627\u0631\u0686\u0648\u0628) \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641<\/h3>\n

\u0646\u0627\u0638\u0631 $S$ \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f \u0628\u0627 \u0645\u062e\u062a\u0635\u0627\u062a $(t,x)$\u060c \u0645\u062d\u0648\u0631\u0647\u0627\u06cc \u0642\u0627\u0626\u0645 \u0631\u0627 \u062a\u0634\u06a9\u06cc\u0644 \u0645\u06cc \u062f\u0647\u0646\u062f. \u0645\u062d\u0648\u0631 \u0645\u06a9\u0627\u0646\u06cc \u0648 \u0632\u0645\u0627\u0646\u06cc \u0646\u0627\u0638\u0631\u0647\u0627\u06cc \u062f\u0644\u062e\u0648\u0627\u0647 \u062f\u06cc\u06af\u0631 \u0645\u0627\u0646\u0646\u062f $S’$ \u06cc\u0627 $S^{”}$ \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u0634\u06a9\u0644 \u0645\u062d\u0648\u0631\u0647\u0627\u06cc\u06cc \u0645\u0646\u062d\u0631\u0641 \u0634\u062f\u0647 \u0627\u0632 \u062f\u0648 \u0645\u062d\u0648\u0631 \u0642\u0627\u0626\u0645 \u0646\u0645\u0627\u06cc\u0634 \u062f\u0627\u062f. \u0627\u0644\u0628\u062a\u0647 \u0628\u0627\u0632\u0647\u0645 \u0642\u0627\u0628\u0644 \u0630\u06a9\u0631 \u0627\u0633\u062a \u06a9\u0647 \u0645\u0628\u062f\u0627\u0621 \u062a\u0645\u0627\u0645\u06cc \u0646\u0627\u0638\u0631\u0647\u0627 \u0631\u0627 \u06cc\u06a9\u0633\u0627\u0646 \u0641\u0631\u0636 \u0645\u06cc \u06a9\u0646\u06cc\u0645. \u062a\u0628\u062f\u06cc\u0644 \u0644\u0648\u0631\u0646\u062a\u0633 \u0645\u0639\u0627\u062f\u0644\u0647 \u0627\u06cc\u0646 \u0645\u062d\u0648\u0631\u0647\u0627 \u0631\u0627 \u062a\u0648\u0635\u06cc\u0641 \u0645\u06cc \u06a9\u0646\u062f. \u0645\u062d\u0648\u0631 $t’$ \u0631\u0627\u0628\u0637\u0647 $x’=0$ \u0648 \u0645\u062d\u0648\u0631 $x’$ \u0631\u0627\u0628\u0637\u0647 $t’=0$ \u0631\u0627 \u062a\u0648\u0635\u06cc\u0641 \u0645\u06cc \u06a9\u0646\u062f. \u0627\u0632 \u062a\u0628\u062f\u06cc\u0644 \u0644\u0648\u0631\u0646\u062a\u0633 \u062f\u0627\u0631\u06cc\u0645:<\/p>\n

$\\begin{equation} \\displaylines{ x\u2019=\\gamma (x-vt) \\\\ t\u2019= \\gamma(t-vx) } \\tag{10.1} \\label{eq:10.1} \\end{equation}$<\/p>\n

\u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0639\u0627\u0645\u0644 \u0644\u0648\u0631\u0646\u062a\u0633 $\\gamma = \\displaystyle{\\frac{1}{\\sqrt{1-v^2}}}$ \u0627\u0633\u062a \u0648 \u0686\u0648\u0646 $c=1$ \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u06cc\u0645 $0\\le |v| < 1$ . \u0628\u062f\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628 \u0645\u062d\u0648\u0631\u0647\u0627 \u0627\u0632 \u062a\u0633\u0627\u0648\u06cc \u062f\u0648 \u0631\u0627\u0628\u0637\u0647 ($\\ref{eq:10.1}$) \u0628\u0627 \u0635\u0641\u0631 \u0628\u062f\u0633\u062a \u0645\u06cc \u0622\u06cc\u062f:<\/p>\n

$\\begin{equation} \\displaylines{t’: x’=0 \\rightarrow x=vt \\\\ x’: t’=0 \\rightarrow t=vx } \\tag{10.2} \\label{eq:10.2} \\end{equation}$<\/p>\n

\u0628\u0627 \u062a\u0646\u0647\u0627 \u06a9\u0631\u062f\u0646 $t$ \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062d\u0648\u0631 \u0639\u0645\u0648\u062f\u06cc \u0646\u0645\u0648\u062f\u0627\u0631:<\/p>\n

$\\begin{equation} \\displaylines{t’: x’=0 \\rightarrow t=\\frac{1}{v}x \\\\ x’: t’=0 \\rightarrow t=vx } \\tag{10.3} \\label{eq:10.3} \\end{equation}$<\/p>\n

\u0628\u0647 \u0627\u06cc\u0646 \u0635\u0648\u0631\u062a \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u0631\u0627\u062d\u062a\u06cc \u0646\u0645\u0648\u062f\u0627\u0631 \u0645\u06cc\u0646\u06a9\u0648\u0641\u0633\u06a9\u06cc \u0631\u0627 \u0628\u0647 \u062a\u0635\u0648\u06cc\u0631 \u06a9\u0634\u06cc\u062f.<\/p>\n

\"v188854_3-10-1.jpg\"<\/p>\n

\u0634\u06a9\u0644 10-1\u060c \u0646\u0645\u0648\u062f\u0627\u0631 \u0645\u06cc\u0646\u06a9\u0648\u0641\u0633\u06a9\u06cc \u0633\u0647 \u0646\u0627\u0638\u0631\u060c \u0646\u0627\u0638\u0631 $S’:(t’,x’)$ \u0633\u0631\u0639\u062a\u06cc $0<v<1$ \u0646\u0633\u0628\u062a \u0628\u0647 \u0646\u0627\u0638\u0631 $S$ \u0648 \u0646\u0627\u0638\u0631 $S^{”}$ \u0633\u0631\u0639\u062a\u06cc $-1<v<0$ \u0646\u0633\u0628\u062a \u0628\u0647 \u0646\u0627\u0638\u0631 $S$ \u062f\u0627\u0631\u0627\u0633\u062a. \u0627\u0632 \u0622\u0646 \u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0633\u0631\u0639\u062a \u0646\u0648\u0631 \u062f\u0631 \u0647\u0645\u0647 \u062f\u0633\u062a\u06af\u0627\u0647 \u0647\u0627 \u06cc\u06a9\u0633\u0627\u0646 \u0627\u0633\u062a\u061b \u062f\u0631 \u0647\u0631 \u0646\u0627\u0638\u0631 $t=x$ \u060c $t=-x$ \u0648 \u062e\u0637\u0648\u0637 \u0645\u0648\u0627\u0632\u06cc \u0622\u0646 \u0645\u0633\u06cc\u0631 \u0646\u0648\u0631 \u062f\u0631 \u0641\u0636\u0627-\u0632\u0645\u0627\u0646 \u0631\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f.<\/p>\n

2-10 \u062e\u0637\u0648\u0637 \u0647\u0645\u0632\u0645\u0627\u0646\u06cc \u0648 \u0647\u0645 \u0645\u06a9\u0627\u0646\u06cc<\/h3>\n

\u0645\u0634\u0627\u0628\u0647 \u0645\u062e\u062a\u0635\u0627\u062a \u062f\u06a9\u0627\u0631\u062a\u06cc\u060c \u062e\u0637\u0648\u0637 \u0645\u0648\u0627\u0632\u06cc \u0628\u0627 \u0645\u062d\u0648\u0631 $t’$\u060c \u062e\u0637\u0648\u0637\u06cc \u0627\u0646\u062f \u06a9\u0647 \u062a\u0645\u0627\u0645\u06cc \u0631\u0648\u06cc\u062f\u0627\u062f\u0647\u0627\u06cc \u0622\u0646 \u0645\u06a9\u0627\u0646 \u06cc\u06a9\u0633\u0627\u0646\u06cc \u062f\u0627\u0631\u0646\u062f \u0648 \u0647\u0645 \u0645\u06a9\u0627\u0646<\/strong> \u062f\u0631\u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0647 \u0645\u06cc \u0634\u0648\u0646\u062f. \u062e\u0637\u0648\u0637\u00a0 \u0645\u0648\u0627\u0632\u06cc \u0628\u0627 \u0645\u062d\u0648\u0631 $x’$ \u0646\u06cc\u0632 \u0631\u0648\u06cc\u062f\u0627\u062f\u0647\u0627\u06cc \u0622\u0646 \u0632\u0645\u0627\u0646 \u06cc\u06a9\u0633\u0627\u0646 \u062f\u0627\u0631\u0646\u062f \u0648 \u0647\u0645\u0632\u0645\u0627\u0646<\/strong> \u0645\u062d\u0633\u0648\u0628 \u0645\u06cc \u0634\u0648\u0646\u062f. \u0628\u0647 \u0627\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628 \u0645\u062e\u062a\u0635\u0647 \u0645\u06a9\u0627\u0646\u06cc \u0648 \u0632\u0645\u0627\u0646\u06cc \u0631\u0648\u06cc\u062f\u0627\u062f \u062e\u0627\u0635 $A$\u060c \u062f\u0631 \u0686\u0627\u0631\u0686\u0648\u0628 $S’$ \u0628\u0627 \u062e\u0637 \u0647\u0645 \u0645\u06a9\u0627\u0646\u06cc \u0648 \u062e\u0637 \u0647\u0645\u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u062f\u0631 \u062a\u0642\u0627\u0637\u0639 \u0622\u0646 \u062f\u0648 \u0648\u0627\u0642\u0639 \u0634\u062f\u0647 \u0645\u0634\u062e\u0635 \u0645\u06cc \u0634\u0648\u062f.<\/p>\n

\"q13122_3-10-2.jpg\"<\/p>\n

\u0634\u06a9\u0644 10-2\u060c \u062e\u0637\u0648\u0637 \u0645\u0648\u0627\u0632\u06cc \u0645\u062d\u0648\u0631 \u0645\u06a9\u0627\u0646\u06cc\u060c \u062e\u0637\u0648\u0637 \u0647\u0645\u0632\u0645\u0627\u0646\u06cc (\u0645\u062b\u0644\u0627 $t’=1,2,3,…$) \u0648 \u062e\u0637\u0648\u0637 \u0645\u0648\u0627\u0632\u06cc \u0645\u062d\u0648\u0631 \u0632\u0645\u0627\u0646\u06cc\u060c \u062e\u0637\u0648\u0637 \u0647\u0645 \u0645\u06a9\u0627\u0646\u06cc (\u0645\u062b\u0644\u0627 $x’=1,2,3,…$) \u0627\u0633\u062a. \u0645\u062e\u062a\u0635\u0627\u062a \u0631\u0648\u06cc\u062f\u0627\u062f $A$ \u062f\u0631 \u0647\u0631 \u0646\u0627\u0638\u0631 \u0628\u0647 \u0648\u0633\u06cc\u0644\u0647 \u062a\u0628\u062f\u06cc\u0644 \u0644\u0648\u0631\u0646\u062a\u0633 \u0642\u0627\u0628\u0644 \u062a\u0628\u062f\u06cc\u0644 \u0627\u0633\u062a.<\/p>\n

\u0628\u0627\u06cc\u062f \u062f\u0642\u062a \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u062f\u0631 \u062a\u0628\u062f\u06cc\u0644 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0631\u0648\u06cc \u0645\u062d\u0648\u0631 \u0647\u0627\u06cc \u0645\u062a\u0639\u0627\u0645\u062f \u0648 \u063a\u06cc\u0631\u0645\u062a\u0639\u0627\u0645\u062f \u062f\u06cc\u06af\u0631 \u0642\u0636\u06cc\u0647 \u0641\u06cc\u062b\u0627\u063a\u0648\u0631\u062b \u0628\u0631\u0642\u0631\u0627\u0631 \u0646\u06cc\u0633\u062a. \u0686\u0648\u0646 \u0641\u0636\u0627-\u0632\u0645\u0627\u0646 \u0645\u06cc\u0646\u06a9\u0648\u0641\u0633\u06a9\u06cc \u0628\u0627 \u0641\u0636\u0627\u06cc \u0627\u0642\u0644\u06cc\u062f\u0633\u06cc \u0645\u062a\u0641\u0627\u0648\u062a \u0627\u0633\u062a. \u062f\u0631 \u0641\u0636\u0627\u06cc \u0627\u0642\u0644\u06cc\u062f\u0633\u06cc \u06a9\u0645\u06cc\u062a \u0637\u0648\u0644 $\\Delta l^2=\\Delta x^2+\\Delta y^2+\\Delta z^2$\u00a0\u06a9\u0645\u06cc\u062a\u06cc \u0646\u0627\u0648\u0631\u062f\u0627 \u06cc\u0627 \u0628\u062f\u0648\u0646 \u062a\u063a\u06cc\u06cc\u0631 \u062a\u062d\u062a \u062a\u0628\u062f\u06cc\u0644\u0627\u062a \u0645\u062e\u062a\u0635\u0627\u062a \u0627\u0633\u062a. \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u0628\u0627 \u0627\u0636\u0627\u0641\u0647 \u0634\u062f\u0646 \u0645\u062e\u062a\u0635\u0647 \u0632\u0645\u0627\u0646\u06cc\u060c \u062f\u0631 \u0641\u0636\u0627-\u0632\u0645\u0627\u0646 \u0686\u0647\u0627\u0631\u0628\u0639\u062f\u06cc \u0645\u06cc\u0646\u06a9\u0648\u0641\u0633\u06a9\u06cc \u0686\u0646\u06cc\u0646 \u0686\u06cc\u0632\u06cc \u0628\u0631\u0642\u0631\u0627\u0631 \u0646\u06cc\u0633\u062a \u0648 \u0637\u0648\u0644 \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u062a\u062d\u062a \u062a\u0628\u062f\u06cc\u0644 \u0644\u0648\u0631\u0646\u062a\u0633 \u062a\u063a\u06cc\u06cc\u0631 \u06a9\u0646\u062f.<\/p>\n

3-10 \u0637\u0648\u0644 \u0641\u0636\u0627-\u0632\u0645\u0627\u0646\u06cc<\/h3>\n

\u0645\u0639\u0627\u062f\u0644 \u0637\u0648\u0644 \u0646\u0627\u0648\u0631\u062f\u0627\u06cc \u0627\u0642\u0644\u06cc\u062f\u0633\u06cc\u060c \u06a9\u0645\u06cc\u062a \u0637\u0648\u0644 \u0641\u0636\u0627-\u0632\u0645\u0627\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0628\u0647 \u0634\u06a9\u0644 \u0632\u06cc\u0631 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc \u0634\u0648\u062f (\u0627\u06cc\u0646\u062c\u0627 \u062f\u0648\u0628\u0627\u0631\u0647 $c$ \u0631\u0627 \u0628\u0631\u0627\u06cc \u062f\u0631\u06a9 \u0628\u0647\u062a\u0631 \u0628\u0627 \u0646\u0645\u0627\u062f \u062e\u0648\u062f \u0630\u06a9\u0631 \u0645\u06cc \u06a9\u0646\u06cc\u0645):<\/p>\n

$\\begin{equation} \\Delta s^2=-c^2 \\Delta t^2 +\\Delta x^2+\\Delta y^2+\\Delta z^2\u00a0 \\tag{10.4} \\label{eq:10.4} \\end{equation}$<\/p>\n

\u0646\u0627\u0648\u0631\u062f\u0627\u06cc\u06cc \u0637\u0648\u0644 \u0628\u0627\u0644\u0627 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0627\u0632 \u062c\u0627\u06cc\u06af\u0630\u0627\u0631\u06cc \u062a\u0628\u062f\u06cc\u0644 \u0644\u0648\u0631\u0646\u062a\u0633 \u0627\u062b\u0628\u0627\u062a \u0646\u0645\u0648\u062f:<\/p>\n

$\\begin{equation} \\displaylines{ -c^2 \\Delta t’^2 +\\Delta x’^2+\\Delta y’^2+\\Delta z’^2 = \\\\ -c^2 \\gamma^2 (\\frac{v^2}{c^4}\\Delta x^2 + \\Delta t^2 -2\\frac{v}{c^2}\\Delta x \\Delta t) + \\gamma^2 (\\Delta x^2 + v^2\\Delta t^2 -2v\\Delta x \\Delta t)\u00a0 + \\Delta y^2 + \\Delta z^2 = \\\\ c^2\\Delta t^2 (-\\gamma^2+\\gamma^2\\frac{\u00a0v^2}{c^2})+\\Delta x^2 (\\gamma^2-\\gamma^2 \\frac{v^2}{c^2})+ \\Delta y^2 + \\Delta z^2\u00a0 \u00a0\\tag{10.5} \\label{eq:10.5}} \\end{equation}$<\/p>\n

\u06a9\u0647 \u062f\u0631 \u0631\u0627\u0628\u0637\u0647 \u0628\u0627\u0644\u0627 \u0627\u0632 \u062a\u0639\u0631\u06cc\u0641 \u0639\u0627\u0645\u0644 \u0644\u0648\u0631\u0646\u062a\u0633 \u062f\u0627\u0631\u06cc\u0645 $\\gamma^2-\\gamma^2 \\frac{v^2}{c^2}=1$ \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646:<\/p>\n

$\\begin{equation} -c^2 \\Delta t’^2 +\\Delta x’^2+\\Delta y’^2+\\Delta z’^2 = -c^2 \\Delta t^2 +\\Delta x^2+\\Delta y^2+\\Delta z^2 \u00a0\\tag{10.6} \\label{eq:10.6} \\end{equation}$<\/p>\n

\u06a9\u0645\u06cc\u062a \u0628\u0627\u0644\u0627 \u0637\u0648\u0644 \u0641\u0636\u0627-\u0632\u0645\u0627\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0646\u0627\u0648\u0631\u062f\u0627 \u062a\u062d\u062a \u062a\u0628\u062f\u06cc\u0644\u0627\u062a \u0644\u0648\u0631\u0646\u062a\u0633 \u0645\u06cc \u0628\u0627\u0634\u062f. \u0627\u06cc\u0646 \u06a9\u0645\u06cc\u062a \u0628\u0647 \u0634\u06a9\u0644 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644\u06cc \u0646\u06cc\u0632 \u062d\u0627\u0626\u0632 \u0627\u0647\u0645\u06cc\u062a \u0627\u0633\u062a \u0648 \u0627\u0644\u0645\u0627\u0646 \u062e\u0637 \u0641\u0636\u0627\u06cc \u0645\u06cc\u0646\u06a9\u0648\u0641\u0633\u06a9\u06cc<\/strong> \u0646\u0627\u0645 \u062f\u0627\u0631\u062f:<\/p>\n

$\\begin{equation} d s^2=-c^2 d t^2 +d x^2+d y^2+d z^2\u00a0 \\tag{10.7} \\label{eq:10.7} \\end{equation}$<\/p>\n\n\n\n\n
\n

\u062a\u0645\u0631\u06cc\u0646\u0627\u062a<\/h3>\n<\/td>\n<\/tr>\n

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 <\/p>\n","protected":false},"excerpt":{"rendered":"

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