{"id":3421,"date":"2022-03-24T17:50:08","date_gmt":"2022-03-24T17:50:08","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=3421"},"modified":"2022-03-24T13:42:48","modified_gmt":"2022-03-24T13:42:48","slug":"lorentzs-transformation","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/lorentzs-transformation\/","title":{"rendered":"\u09b2\u09b0\u09c7\u099e\u09cd\u099c-\u098f\u09b0 \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 (Lorentz’s transformation)"},"content":{"rendered":"

\u09b2\u09b0\u09c7\u099e\u09cd\u099c-\u098f\u09b0 \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 (Lorentz’s transformation)<\/strong><\/h2>\n

\u09af\u09c7 \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09df\u09cb\u0997\u09c7 \u09ac\u09bf\u09a6\u09cd\u09af\u09c1\u09ce \u099a\u09c1\u09ae\u09cd\u09ac\u0995\u09c0\u09af\u09bc \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u098f\u0995 \u099c\u09a1\u09bc \u0995\u09be\u09a0\u09be\u09ae\u09cb \u09a5\u09c7\u0995\u09c7 \u0985\u09a8\u09cd\u09af \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09a4\u09c7 \u09a8\u09bf\u09b2\u09c7 \u0985\u09ad\u09bf\u09a8\u09cd\u09a8\u09b0\u09c2\u09aa\u09c7 \u09aa\u09cd\u09b0\u0995\u09be\u09b6\u09bf\u09a4 \u09b9\u09af\u09bc \u09a4\u09be \u09b2\u09b0\u09c7\u099e\u09cd\u099c \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 (Lorentz’s transformation) \u09a8\u09be\u09ae\u09c7 \u09aa\u09b0\u09bf\u099a\u09bf\u09a4\u0964<\/span><\/p>\n

\u09b2\u09b0\u09c7\u099e\u09cd\u099c-\u098f\u09b0 \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 (Lorentz’s transformation) \u09ac\u09be \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a8\u09bf\u09ae\u09cd\u09a8\u09b2\u09bf\u0996\u09bf\u09a4 \u09a6\u09c1\u099f\u09bf \u09b8\u09cd\u09ac\u09c0\u0995\u09be\u09b0\u09cd\u09af\u09c7\u09b0 \u0993\u09aa\u09b0 \u09aa\u09cd\u09b0\u09a4\u09bf\u09b7\u09cd\u09a0\u09bf\u09a4\u0964<\/span><\/p>\n

\u09b8\u09cd\u09ac\u09c0\u0995\u09be\u09b0\u09cd\u09af (\u09e7): <\/b>\u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u09ac\u09bf\u09a6\u09cd\u09af\u09be\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u0997\u09c1\u09b2\u09cb \u09b8\u0995\u09b2 \u0985\u09ad\u09cd\u09af\u09a8\u09cd\u09a4\u09b0\u09c0\u09a3 \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09af\u09bc \u0985\u09ad\u09bf\u09a8\u09cd\u09a8 \u09a5\u09be\u0995\u09c7, \u09a4\u09ac\u09c7 \u0995\u09be\u09a0\u09be\u09ae\u09cb\u0997\u09c1\u09b2\u09cb\u0995\u09c7 \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0\u09c7\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u09b8\u09ae\u09ac\u09c7\u0997\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u09a5\u09be\u0995\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

\u09b8\u09cd\u09ac\u09c0\u0995\u09be\u09b0\u09cd\u09af (\u09e8):<\/b> \u09b6\u09c2\u09a8\u09cd\u09af\u09b8\u09cd\u09a5\u09be\u09a8\u09c7 \u0986\u09b2\u09cb\u09b0 \u09ac\u09c7\u0997 \u09b8\u09b0\u09cd\u09ac\u09a6\u09be \u09a7\u09cd\u09b0\u09c1\u09ac \u09a5\u09be\u0995\u09c7, \u098f\u099f\u09bf \u098f\u0995\u099f\u09bf \u0985\u09ad\u09cd\u09af\u09a8\u09cd\u09a4\u09b0\u09c0\u09a3 \u0995\u09be\u09a0\u09be\u09ae\u09cb \u09b9\u09a4\u09c7 \u0985\u09a8\u09cd\u09af\u099f\u09bf\u09a4\u09c7 \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0\u09bf\u09a4 \u09b9\u09b2\u09c7\u0993 \u09ae\u09be\u09a8 \u0985\u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09bf\u09a4 \u09a5\u09be\u0995\u09c7 \u098f\u09ac\u0982 \u0986\u09b2\u09cb\u09b0 \u098f\u0987 \u09ac\u09c7\u0997 c = 3 \\times 10^8 ms^{-1}<\/span><\/span>\u0964 \u098f\u0987 \u09ae\u09be\u09a8 \u09a6\u09b0\u09cd\u09b6\u0995\u09c7\u09b0 \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf \u09ac\u09be \u0997\u09a4\u09bf\u09b6\u09c0\u09b2\u09a4\u09be\u09b0 \u0993\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0 \u0995\u09b0\u09c7 \u09a8\u09be\u0964<\/span><\/p>\n

\u0989\u09aa\u09b0\u09cb\u0995\u09cd\u09a4 \u09b8\u09cd\u09ac\u09c0\u0995\u09be\u09b0\u09cd\u09af\u09c7\u09b0 \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf\u09a4\u09c7 \u09b2\u09b0\u09c7\u09a8\u09cd\u099c \u09a8\u09a4\u09c1\u09a8 \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u0986\u09ac\u09bf\u09b7\u09cd\u0995\u09be\u09b0 \u0995\u09b0\u09c7\u09a8 \u09af\u09be <\/span>\u09b2\u09b0\u09c7\u09a8\u09cd\u099c \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (Lorentz’s transformation equation ) <\/b>\u09a8\u09be\u09ae\u09c7 \u09aa\u09b0\u09bf\u099a\u09bf\u09a4\u0964 \u09a8\u09bf\u09ae\u09cd\u09a8\u09c7 \u09b2\u09b0\u09c7\u099e\u09cd\u099c\u09c7\u09b0 \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09b8\u09ae\u09c2\u09b9 \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09a8 \u0995\u09b0\u09be \u09b9\u09b2\u09cb\u0964<\/span><\/p>\n

\u09a7\u09b0\u09be \u09af\u09be\u0995 \u09a6\u09c1\u099f\u09bf \u0995\u09be\u09a0\u09be\u09ae\u09cb S \u098f\u09ac\u0982 S’-\u098f \u09a6\u09c1\u099c\u09a8 \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995 A \u098f\u09ac\u0982 A’ \u09b0\u09af\u09bc\u09c7\u099b\u09c7\u0964 S \u0995\u09be\u09a0\u09be\u09ae\u09cb \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u0995\u09be\u09a0\u09be\u09ae\u09cb S\u2019 \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 X \u0985\u0995\u09cd\u09b7 \u09ac\u09b0\u09be\u09ac\u09b0 \u03d1<\/span> \u09b8\u09ae\u09ac\u09c7\u0997\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2\u0964 \u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, \u0995\u09be\u09a0\u09be\u09ae\u09cb \u09a6\u09c1\u099f\u09bf t = 0 \u09b8\u09ae\u09af\u09bc\u09c7 \u098f\u0995\u0987 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8\u09c7 \u09b0\u09af\u09bc\u09c7\u099b\u09c7\u0964 \u098f \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u098f\u0995\u099f\u09bf \u0998\u099f\u09a8\u09be, \u09ae\u09a8\u09c7 \u0995\u09b0\u09be \u09af\u09be\u0995 \u098f\u0995\u099f\u09bf \u0986\u09b2\u09cb\u0995 \u09b8\u09cd\u09ab\u09c1\u09b2\u09bf\u0999\u09cd\u0997 (<\/span>pulse<\/span>) \u09a4\u09b0\u0999\u09cd\u0997\u09ae\u09c1\u0996 \u09b8\u09c3\u09b7\u09cd\u099f\u09bf \u0995\u09b0\u09be \u09b9\u09b2\u09cb\u0964 \u098f\u09ad\u09be\u09ac\u09c7 \u09b8\u09c3\u09b7\u09cd\u099f \u09a4\u09b0\u0999\u09cd\u0997\u09ae\u09c1\u0996 \u09b8\u09ae\u09af\u09bc\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8\u09c7\u09b0 \u09b8\u0999\u09cd\u0997\u09c7 \u09ac\u09b0\u09cd\u09a7\u09bf\u09a4 \u0997\u09cb\u09b2\u09c0\u09af\u09bc \u0986\u0995\u09be\u09b0\u09c7 \u09aa\u09cd\u09b0\u09b8\u09be\u09b0\u09bf\u09a4 \u09b9\u09a4\u09c7 \u09a5\u09be\u0995\u09ac\u09c7\u0964 t \u09b8\u09ae\u09af\u09bc \u09aa\u09b0\u09c7 \u09b8\u09cd\u09a5\u09bf\u09b0 \u0995\u09be\u09a0\u09be\u09ae\u09cb S-\u098f\u09b0 \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995 A \u09a6\u09c7\u0996\u09ac\u09c7 \u09af\u09c7 \u09a4\u09b0\u0999\u09cd\u0997\u09ae\u09c1\u0996 P \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09aa\u09cc\u0981\u099b\u09c7\u099b\u09c7\u0964 A \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995\u09c7\u09b0 \u09a8\u09bf\u0995\u099f P \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u09b9\u09ac\u09c7,\u00a0<\/span><\/p>\n

\\text {r} = \\text {c t}<\/span><\/span>\u00a0\u2026<\/span> \u2026<\/span> \u00a0 \u00a0 <\/span> \u00a0 \u00a0 (1)\u00a0<\/span><\/p>\n

\"Lorentz's-transformation\"<\/p>\n

\u0986\u09ac\u09be\u09b0, x^{2}+y^{2}+z^{2}=r^{2}<\/span><\/span><\/p>\n

\\therefore \\mathrm{r}^{2}=\\mathrm{x}^{2}+\\mathrm{y}^{2}+\\mathrm{z}^{2}=\\mathrm{c}^{2} \\mathrm{t}^{2}<\/span>\u00a0 \u00a0 \u00a0 \u00a0 <\/span>\u2026 \u00a0 \u00a0 \u00a0 \u2026\u00a0 \u00a0 \u00a0 (2)<\/span><\/p>\n

S\u2019 \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09b0 \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995\u09c7\u09b0 \u0995\u09be\u099b\u09c7 P \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u09b9\u09ac\u09c7,<\/span><\/p>\n

r^{\\prime}=\\mathrm{ct}^{\\prime}<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (3)<\/span><\/p>\n

S\u2019 \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7,<\/span><\/p>\n

r^{\\prime 2}=x^{\\prime 2}+y^{\\prime 2}+z^{\\prime 2}=c^{2} t^{\\prime 2}<\/span>\u00a0 \u00a0 \u00a0 \u00a0\u2026\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (4)<\/span><\/p>\n

\u098f\u0996\u09a8 \u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995\u09a4\u09be\u09b0 \u09ac\u09bf\u09b6\u09c7\u09b7 \u09a4\u09a4\u09cd\u09a4\u09cd\u09ac\u09c7\u09b0<\/a> \u09e7\u09ae \u09b8\u09cd\u09ac\u09c0\u0995\u09be\u09b0\u09cd\u09af \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u0989\u09ad\u09af\u09bc \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09af\u09bc \u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u09ac\u09bf\u099c\u09cd\u099e\u09be\u09a8\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0997\u09c1\u09b2\u09cb \u0985\u09ad\u09bf\u09a8\u09cd\u09a8 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

\u0985\u09b0\u09cd\u09a5\u09be\u09ce x^{2}+y^{2}+z^{2}-c^{2} t^{2}=x^{\\prime 2}+y^{\\prime 2}+z^{\\prime 2}-c^{2} t^{\\prime 2}<\/span><\/span>\u00a0<\/span>\u00a0\u00a0\u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026<\/span> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (5)<\/span><\/p>\n

\u098f\u0996\u09a8 Y \u098f\u09ac\u0982 Z \u0985\u0995\u09cd\u09b7 \u09ac\u09b0\u09be\u09ac\u09b0 \u0997\u09a4\u09bf \u09a8\u09be \u09a5\u09be\u0995\u09be\u09b0 \u0995\u09be\u09b0\u09a3\u09c7, y\u2019 = y \u098f\u09ac\u0982 z\u2019 = z \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

\u0985\u09a4\u098f\u09ac, \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (5) \u09a5\u09c7\u0995\u09c7,<\/span><\/p>\n

x^{2}-c^{2} t^{2}=x^{\\prime 2}-c^{2} t^{\\prime 2}<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>\u00a0<\/span>\u2026\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026\u00a0 \u00a0 \u00a0 (6)<\/span><\/p>\n

\u098f\u0996\u09a8 x \u098f\u09ac\u0982 x\u2019 \u098f\u09b0 \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a8\u09bf\u09ae\u09cd\u09a8\u09cb\u0995\u09cd\u09a4\u09ad\u09be\u09ac\u09c7 \u09b2\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc<\/span><\/p>\n

\\mathrm{X}^{\\prime}=\\mathrm{k}(\\mathrm{x}-\\vartheta \\mathrm{t})<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026 \u00a0 (7)<\/span><\/p>\n

\u098f\u0996\u09be\u09a8\u09c7 k \u09a7\u09cd\u09b0\u09c1\u09ac\u0995\u0964 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (7) \u098f\u09b0 \u09af\u09cc\u0995\u09cd\u09a4\u09bf\u0995\u09a4\u09be \u09b9\u09b2\u09cb \u098f\u0987 \u09af\u09c7 \u09b8\u09cd\u09ac\u09b2\u09cd\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u09ac\u09c7\u0997 (\\vartheta \\text { << c). }<\/span><\/span>-\u098f\u09b0 \u099c\u09a8\u09cd\u09af \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 \u0985\u09ac\u09b6\u09cd\u09af\u0987 \u0997\u09cd\u09af\u09be\u09b2\u09bf\u09b2\u09bf\u09af\u09bc \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0\u09c7\u09b0<\/a> \u09b0\u09c2\u09aa \u09a8\u09c7\u09ac\u09c7\u0964<\/span><\/p>\n

\u0985\u09a8\u09c1\u09b0\u09c2\u09aa\u09ad\u09be\u09ac\u09c7, \u09a7\u09b0\u09be \u09af\u09be\u09af\u09bc,<\/span><\/p>\n

\\mathrm{t}^{\\prime}=\\mathrm{a}(\\mathrm{t}-b x)<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026 \u00a0 (8)<\/span><\/p>\n

\u098f\u0996\u09be\u09a8\u09c7 a \u0993 b \u0989\u09ad\u09df\u0987 \u09a7\u09cd\u09b0\u09c1\u09ac\u0964<\/span><\/p>\n

\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (6)- \u098f x\u2019 \u098f\u09ac\u0982 t\u2019- \u098f\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09df\u09c7 \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09df,\u00a0<\/span><\/p>\n\\mathrm{x}^{2}-\\mathrm{c}^{2} \\mathrm{t}^{2}=\\mathrm{k}^{2}(\\mathrm{x}-\\vartheta \\mathrm{t})^{2}-\\mathrm{c}^{2} \\mathrm{a}^{2}(\\mathrm{t}-b x)^{2} <\/span>\n

\u09ac\u09be, \\mathrm{x}^{2}-\\mathrm{c}^{2} \\mathrm{t}^{2}=\\left(\\mathrm{k}^{2}-\\mathrm{a}^{2} \\mathrm{~b}^{2} \\mathrm{c}^{2}\\right) \\mathrm{x}^{2}-2\\left(\\mathrm{k}^{2} \\vartheta-\\mathrm{a}^{2} \\mathrm{bc}^{2}\\right) x \\mathrm{t}-\\left(a^{2}-\\frac{\\mathrm{k}^{2} \\vartheta^{2}}{\\mathrm{c}^{2}}\\right) \\mathrm{c}^{2} \\mathrm{t}^{2}<\/span><\/span>\u00a0 \u00a0 \u00a0<\/span>\u2026 \u00a0 <\/span>\u00a0\u00a0<\/span>(9)<\/span><\/p>\n

\\left.\\begin{array}{c}\n\n\\mathrm{k}^{2}-\\mathrm{a}^{2} \\mathrm{~b}^{2} \\mathrm{c}^{2}=1 \\\\\n\n\\mathrm{k}^{2} \\vartheta-\\mathrm{a}^{2} \\mathrm{bc}^{2}=0 \\\\\n\na^{2}-\\frac{\\mathrm{k}^{2} \\vartheta^{2}}{\\mathrm{c}^{2}}=1\n\n\\end{array}\\right\\}<\/span>\u00a0 \u00a0 \u00a0\u2026 \u00a0 <\/span>\u00a0\u00a0<\/span>(10)<\/span><\/p>\n

\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (10) \u09b8\u09ae\u09be\u09a7\u09be\u09a8 \u0995\u09b0\u09c7, \u0986\u09ae\u09b0\u09be \u09aa\u09be\u0987,\u00a0<\/span><\/p>\n

\\mathrm{k}=\\mathrm{a}=\\frac{1}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}}<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026 \u00a0 \u00a0 \u00a0 (11)<\/span><\/p>\n

\u098f\u09ac\u0982 \\mathbf{b}=\\frac{\\vartheta}{c^{2}}<\/span><\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026 \u00a0 \u00a0 \u00a0 \u00a0 (12)<\/span><\/p>\n

\u098f\u0996\u09a8, \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (7) \u0993 (8)\u2013\u098f k, a \u098f\u09ac\u0982 b-\u098f\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09df\u09c7 \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09ac\u09c7,\u00a0<\/span><\/p>\n\\begin{array}{l}\n\n\\mathrm{x}^{\\prime}=\\frac{\\mathrm{X}-\\vartheta \\mathrm{t}}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}} \\\\\n\n\\text {\u098f\u09ac\u0982} \\mathrm{t}^{\\prime}=\\frac{\\mathrm{t}-\\vartheta x \/ c^{2}}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}}\n\n\\end{array}<\/span>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 S\u2019 \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995\u0997\u09c1\u09b2\u09cb S \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995\u09c7\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u09b2\u09c7\u0996\u09be \u09af\u09be\u09df,\u00a0\u00a0<\/span><\/p>\n

x^{\\prime}=\\frac{x-\\vartheta t}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}}<\/span> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (13)<\/span><\/p>\n

\\mathrm{y}^{\\prime}=\\mathrm{y}<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (14)\u00a0<\/span><\/p>\n

\\mathrm{z}^{\\prime}=\\mathrm{z}<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (15)<\/span><\/p>\n

\u098f\u09ac\u0982 \\mathrm{t}^{\\prime}=\\frac{\\mathrm{t}-\\vartheta x \/ c^{2}}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}}<\/span><\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (16)<\/span><\/p>\n

\u098f\u0987 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0997\u09c1\u09b2\u09cb\u0987 \u09b2\u09b0\u09c7\u099e\u09cd\u099c-\u098f\u09b0 \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3(Lorentz’s transformation) \u09a8\u09be\u09ae\u09c7 \u09aa\u09b0\u09bf\u099a\u09bf\u09a4\u0964 1930 \u09b8\u09be\u09b2\u09c7 \u098f\u0987\u099a \u098f \u09b2\u09b0\u09c7\u099e\u09cd\u099c \u098f\u09b0 \u099a\u09cc\u09ae\u09cd\u09ac\u0995 \u09a4\u09a4\u09cd\u09a4\u09cd\u09ac\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af \u09a6\u09bf\u09af\u09bc\u09c7 \u098f\u0987 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0997\u09c1\u09b2\u09bf \u09aa\u09cd\u09b0\u09a4\u09bf\u09b7\u09cd\u09a0\u09bf\u09a4 \u09b9\u09af\u09bc\u09c7\u099b\u09bf\u09b2 \u09ac\u09b2\u09c7 \u098f\u09a6\u09c7\u09b0\u0995\u09c7 \u09b2\u09b0\u09c7\u099e\u09cd\u099c \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 (Lorentz’s transformation)\u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964<\/b><\/p>\n

\u09aa\u09c1\u09a8\u0983 \u09af\u09a6\u09bf \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09b0 \u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995 \u09ac\u09c7\u0997 \u03d1\u00a0<\/span> \u0986\u09b2\u09cb\u0995\u09c7\u09b0 \u09ac\u09c7\u0997\u09c7\u09b0 \u09a4\u09c1\u09b2\u09a8\u09be\u09af\u09bc \u0996\u09c1\u09ac\u0987 \u099b\u09cb\u099f \u09b9\u09af\u09bc, \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u03d1 \u226a c, <\/span>\u00a0\u09a4\u09be\u09b9\u09b2\u09c7 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (13) \u098f\u09ac\u0982 (16) \u09a8\u09bf\u09ae\u09cd\u09a8\u09b0\u09c2\u09aa\u09c7 \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 \u09b9\u09ac\u09c7<\/span><\/p>\n\\mathrm{x}^{\\prime}=\\frac{\\mathrm{x}-\\vartheta \\mathrm{t}}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}}<\/span>\n=\\mathrm{x}-\\vartheta \\mathrm{t} \\quad\\left[\\because \\vartheta^{2} \/ c^{2} \\ll 1\\right]<\/span>\n

\u098f\u09ac\u0982 \\mathrm{t}^{\\prime}=\\mathrm{t}-\\vartheta x \/ c^{2}<\/span><\/span><\/p>\n

\u098f\u0997\u09c1\u09b2\u09cb \u0997\u09cd\u09af\u09be\u09b2\u09bf\u09b2\u09bf\u0993\u09b0 \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09ae\u09be\u09a4\u09cd\u09b0\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u0993\u09aa\u09b0\u09c7\u09b0 \u0986\u09b2\u09cb\u099a\u09a8\u09be \u09a5\u09c7\u0995\u09c7 \u098f\u099f\u09be \u09b8\u09cd\u09aa\u09b7\u09cd\u099f \u09af\u09c7 \u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995 \u09ac\u09c7\u0997 \u0986\u09b2\u09cb\u0995\u09c7\u09b0 \u09ac\u09c7\u0997\u09c7\u09b0 \u09ae\u09be\u09a8\u09c7\u09b0 \u0995\u09be\u099b\u09be\u0995\u09be\u099b\u09bf \u09a8\u09be \u09b9\u09b2\u09c7 \u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995\u09a4\u09be\u09b0 \u09ac\u09bf\u09b6\u09c7\u09b7 \u09a4\u09a4\u09cd\u09a4\u09cd\u09ac \u09b9\u09a4\u09c7 \u09aa\u09cd\u09b0\u09be\u09aa\u09cd\u09a4 \u09ab\u09b2\u09be\u09ab\u09b2 \u09aa\u09b0\u09bf\u09ae\u09be\u09aa\u09af\u09cb\u0997\u09cd\u09af \u09b9\u09ac\u09c7 \u09a8\u09be\u0964 \u09b8\u09c7\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09b8\u09a8\u09be\u09a4\u09a8 \u09a7\u09be\u09b0\u09a3\u09be\u0987 \u09ac\u09b2\u09ac\u09ce \u09a5\u09be\u0995\u09ac\u09c7\u0964 \u09af\u0996\u09a8 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09a6\u09cd\u09b0\u09c1\u09a4\u09bf \u0986\u09b2\u09cb\u09b0 \u09a6\u09cd\u09b0\u09c1\u09a4\u09bf\u09b0 \u0995\u09be\u099b\u09be\u0995\u09be\u099b\u09bf \u0995\u0996\u09a8\u0987 \u09b2\u09b0\u09c7\u099e\u09cd\u099c \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 \u09aa\u09cd\u09b0\u09df\u09cb\u0997 \u0995\u09b0\u09be \u09b9\u09af\u09bc\u0964<\/span><\/p>\n

\u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09b2\u09b0\u09c7\u099e\u09cd\u099c \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 (<\/b>Inverse Lorentz’s transformation<\/b>)<\/b><\/h2>\n

\u0986\u09ae\u09b0\u09be \u09af\u09a6\u09bf S’ \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09b0 \u09aa\u09b0\u09bf\u09ae\u09be\u09aa\u0995\u09c7 S \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09b0 \u09aa\u09b0\u09bf\u09ae\u09be\u09aa\u09c7 \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0\u09bf\u09a4 \u0995\u09b0\u09a4\u09c7 \u099a\u09be\u0987 \u09a4\u09be\u09b9\u09b2\u09c7 <\/span> \u098f\u09b0 \u09b8\u09cd\u09a5\u09b2\u09c7 <\/span>–<\/span> \u09ac\u09b8\u09be\u09a4\u09c7 \u09b9\u09ac\u09c7 \u098f\u09ac\u0982 x\u2019, y\u2019, z\u2019, t\u2019 \u098f\u09ac\u0982 x, y, z, t \u0995\u09c7 \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09ac\u09bf\u09a8\u09bf\u09ae\u09af\u09bc \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964 \u098f\u09ad\u09be\u09ac\u09c7 \u09af\u09c7 \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc \u09a4\u09be \u09b9\u09b2\u09cb \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09b2\u09b0\u09c7\u099e\u09cd\u099c \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 (Inverse Lorentz transformation)\u0964<\/span><\/p>\n

\u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09b2\u09b0\u09c7\u099e\u09cd\u099c \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0997\u09c1\u09b2\u09cb (Lorentz’s transformation) \u09b9\u09b2\u09cb,<\/span><\/p>\n

x=\\frac{x^{\\prime}+\\vartheta \\dagger^{\\prime}}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}}<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [17(a)]<\/span><\/p>\n

y=y^{\\prime}<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [18(a)]<\/span><\/p>\n

z=z^{\\prime}<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [19(a)]<\/span><\/p>\n

\\mathrm{t}=\\frac{\\mathrm{t}^{\\prime}+\\vartheta x^{\\prime} \/ c^{2}}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}}\n\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [20(a)]<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

\u09b2\u09b0\u09c7\u099e\u09cd\u099c-\u098f\u09b0 \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 (Lorentz’s transformation) \u09af\u09c7 \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09df\u09cb\u0997\u09c7 \u09ac\u09bf\u09a6\u09cd\u09af\u09c1\u09ce \u099a\u09c1\u09ae\u09cd\u09ac\u0995\u09c0\u09af\u09bc \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u098f\u0995 \u099c\u09a1\u09bc \u0995\u09be\u09a0\u09be\u09ae\u09cb \u09a5\u09c7\u0995\u09c7 \u0985\u09a8\u09cd\u09af \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09a4\u09c7 \u09a8\u09bf\u09b2\u09c7 \u0985\u09ad\u09bf\u09a8\u09cd\u09a8\u09b0\u09c2\u09aa\u09c7 \u09aa\u09cd\u09b0\u0995\u09be\u09b6\u09bf\u09a4 \u09b9\u09af\u09bc \u09a4\u09be \u09b2\u09b0\u09c7\u099e\u09cd\u099c \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 (Lorentz’s transformation) \u09a8\u09be\u09ae\u09c7 \u09aa\u09b0\u09bf\u099a\u09bf\u09a4\u0964 \u09b2\u09b0\u09c7\u099e\u09cd\u099c-\u098f\u09b0 \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 (Lorentz’s transformation) \u09ac\u09be \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a8\u09bf\u09ae\u09cd\u09a8\u09b2\u09bf\u0996\u09bf\u09a4 \u09a6\u09c1\u099f\u09bf \u09b8\u09cd\u09ac\u09c0\u0995\u09be\u09b0\u09cd\u09af\u09c7\u09b0 \u0993\u09aa\u09b0<\/p>\n

Read More<\/a><\/p>\n","protected":false},"author":56,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[4252,3029,50,51],"tags":[2402,2400,2401],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/3421"}],"collection":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/users\/56"}],"replies":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/comments?post=3421"}],"version-history":[{"count":11,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/3421\/revisions"}],"predecessor-version":[{"id":5208,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/3421\/revisions\/5208"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=3421"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=3421"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=3421"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}