Thuyết Tương Đối Hẹp Và Rộng Của Albert Einstein

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Nh\u01b0\tch\u00fang\tta\t\u0111\u00e3\tnh\u1eafc\t\u0111\u1ebfn\tnhi\u1ec1u\tl\u1ea7n,\tc\u01a1\th\u1ecdc\tc\u1ed5\t\u0111i\u1ec3n\txu\u1ea5t\tph\u00e1t t\u1eeb\t \u0111\u1ecbnh\t lu\u1eadt\t sau\t \u0111\u00e2y:\t \u1ede\t \u0111\u1ee7\t xa\t c\u00e1c\t \u0111i\u1ec3m\t v\u1eadt\t ch\u1ea5t\t kh\u00e1c,\t c\u00e1c\t \u0111i\u1ec3m v\u1eadt\t ch\u1ea5t\t ti\u1ebfp\t t\u1ee5c\t chuy\u1ec3n\t \u0111\u1ed9ng\t th\u1eb3ng\t \u0111\u1ec1u\t hay\t \u00ec\t l\u1ea1i\t trong\t tr\u1ea1ng th\u00e1i\ty\u00ean\tt\u0129nh.\tCh\u00fang\tta\tc\u0169ng\tnhi\u1ec1u\tl\u1ea7n\tnh\u1ea5n\tm\u1ea1nh,\t\u0111\u1ecbnh\tlu\u1eadt\tc\u01a1 b\u1ea3n\t n\u00e0y\t ch\u1ec9\t c\u00f3\t th\u1ec3\t \u0111\u00fang\t cho\t c\u00e1c\t v\u1eadt\t th\u1ec3\t quy\t chi\u1ebfu\t K\t c\u00f3\t nh\u1eefng tr\u1ea1ng\t th\u00e1i\t chuy\u1ec3n\t \u0111\u1ed9ng\t \u0111\u1eb7c\t tr\u01b0ng\t nh\u1ea5t\t \u0111\u1ecbnh,\t v\u00e0\t ch\u00fang\t c\u00f3 chuy\u1ec3n\t \u0111\u1ed9ng\t t\u1ecbnh\t ti\u1ebfn\t \u0111\u1ec1u\t t\u01b0\u01a1ng\t \u0111\u1ed1i\t v\u1edbi\t nhau.\t \u0110\u1ed1i\t v\u1edbi\t c\u00e1c\t v\u1eadt th\u1ec3\t quy\t chi\u1ebfu\t K\u2019\t kh\u00e1c,\t \u0111\u1ecbnh\t l\u00fd\t kh\u00f4ng\t \u0111\u00fang.\t V\u00ec\t th\u1ebf,\t c\u1ea3\t trong\t c\u01a1 h\u1ecdc\tc\u1ed5\t\u0111i\u1ec3n\tl\u1eabn\tthuy\u1ebft\tt\u01b0\u01a1ng\t\u0111\u1ed1i\th\u1eb9p,\tng\u01b0\u1eddi\tta\tph\u00e2n\tbi\u1ec7t\tgi\u1eefa\tc\u00e1c v\u1eadt\t th\u1ec3\t quy\t chi\u1ebfu\t K\t m\u00e0\t \u0111\u1ed1i\t v\u1edbi\t ch\u00fang\t c\u00e1c\t \u0111\u1ecbnh\t lu\u1eadt\t t\u1ef1\t nhi\u00ean \u0111\u00fang,\tv\u00e0\tc\u00e1c\tv\u1eadt\tth\u1ec3\tquy\tchi\u1ebfu\tK'\tm\u00e0\t\u0111\u1ed1i\tv\u1edbi\tch\u00fang\tc\u00e1c\t\u0111\u1ecbnh\tlu\u1eadt t\u1ef1\tnhi\u00ean\tkh\u00f4ng\t\u0111\u00fang. Nh\u01b0ng\t kh\u00f4ng\t ai\t suy\t ngh\u0129\t nh\u1ea5t\t qu\u00e1n\t l\u1ea1i\t c\u00f3\t th\u1ec3\t th\u1ecfa\t m\u00e3n\t v\u1edbi t\u00ecnh\thu\u1ed1ng\tn\u00e0y.\tAnh\tta\th\u1ecfi:\t\\\"V\u00ec\tsao\tl\u1ea1i\tc\u00f3\tm\u1ed9t\ts\u1ed1\tc\u00e1c\tv\u1eadt\tth\u1ec3\tquy chi\u1ebfu\tnh\u1ea5t\t\u0111\u1ecbnh\t(hay\tc\u00e1c\ttr\u1ea1ng\tth\u00e1i\tchuy\u1ec3n\t\u0111\u1ed9ng\tc\u1ee7a\tch\u00fang)\tl\u1ea1i \u0111\u01b0\u1ee3c\t \u01b0u\t \u0111\u00e3i\t h\u01a1n\t c\u00e1c\t v\u1eadt\t th\u1ec3\t quy\t chi\u1ebfu\t kh\u00e1c\t (hay\t c\u00e1c\t tr\u1ea1ng\t th\u00e1i chuy\u1ec3n\t\u0111\u1ed9ng\tc\u1ee7a\tch\u00fang)?\t\u0110\u00e2u\tl\u00e0\tl\u00fd\tdo\tc\u1ee7a\ts\u1ef1\t\u01b0u\t\u0111\u00e3i\tn\u00e0y?\\\"\t\u0110\u1ec3\tl\u00e0m r\u00f5\t\u0111i\u1ec1u\tt\u00f4i\tmu\u1ed1n\tn\u00f3i\tv\u1edbi\tc\u00e2u\th\u1ecfi\tn\u00e0y,\txin\t\u0111\u01a1n\tc\u1eed\tm\u1ed9t\ts\u1ef1\tso\ts\u00e1nh. 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bao\tgi\u1edd\tbi\u1ebft\tl\u1eeda\tga\tl\u00e0\tg\u00ec.\tB\u1edfi\tv\u00ec\tt\u00f4i\tch\u1ec9\tc\u00f3\tth\u1ec3\tn\u00f3i,\tr\u1eb1ng\tc\u00e1i\tg\u00ec\tc\u00f3\t\u00e1nh s\u00e1ng\tm\u00e0u\txanh\tkia\tl\u00e0\tl\u00fd\tdo\tg\u00e2y\tra\ts\u1ef1\tph\u00e1t\tra\th\u01a1i\tn\u01b0\u1edbc,\thay\t\u00edt\tra\tc\u00f3 th\u1ec3\t g\u00e2y\t ra.\t Nh\u01b0ng\t n\u1ebfu\t t\u00f4i\t kh\u00f4ng\t th\u1ea5y\t c\u00e1i\t g\u00ec\t m\u00e0u\t xanh\t \u1edf\t c\u1ea3\t hai n\u1ed3i,\t v\u00e0\t n\u1ebfu\t ch\u1ec9\t th\u1ea5y\t m\u1ed9t\t c\u00e1i\t n\u1ed3i\t v\u1eabn\t ti\u1ebfp\t t\u1ee5c\t b\u1ed1c\t h\u01a1i,\t n\u1ed3i\t kia\t th\u00ec kh\u00f4ng,\tt\u00f4i\ts\u1ebd\tng\u1ea1c\tnhi\u00ean\tv\u00e0\tkh\u00f4ng\tth\u1ecfa\tm\u00e3n,\tcho\t\u0111\u1ebfn\tbao\tl\u00e2u\tt\u00f4i th\u1ea5y\t\u0111\u01b0\u1ee3c\tm\u1ed9t\tt\u00ecnh\thu\u1ed1ng\tn\u00e0o\t\u0111\u00f3\t\u0111\u1ec3\tc\u00f3\tth\u1ec3\tl\u1ea5y\t\u0111\u00f3\tquy\tv\u00e0o\ttr\u00e1ch nhi\u1ec7m\tc\u1ee7a\ts\u1ef1\tv\u1eadn\th\u00e0nh\tkh\u00e1c\tnhau\tc\u1ee7a\thai\tc\u00e1i\tn\u1ed3i.","M\u1ed9t\t c\u00e1ch\t t\u01b0\u01a1ng\t t\u1ef1,\t t\u00f4i\t \u0111i\t t\u00ecm\t trong\t c\u01a1\t h\u1ecdc\t c\u1ed5\t \u0111i\u1ec3n\t (v\u00e0\t trong thuy\u1ebft\tt\u01b0\u01a1ng\t\u0111\u1ed1i\th\u1eb9p),\tm\u1ed9t\tc\u00e1ch\tho\u00e0i\tc\u00f4ng,\tm\u1ed9t\tc\u00e1i\tg\u00ec\thi\u1ec7n\tth\u1ef1c \u0111\u1ec3\tc\u00f3\tth\u1ec3\tquy\tv\u1ec1\t\u0111\u00f3\ts\u1ef1\tv\u1eadn\th\u00e0nh\tkh\u00e1c\tbi\u1ec7t\tc\u1ee7a\tc\u00e1c\tv\u1eadt\tth\u1ec3\t\u0111\u1ed1i\tv\u1edbi c\u00e1c\th\u1ec7\tquy\tchi\u1ebfu\tK,\tK'.\tNewton\t \u0111\u00e3\t th\u1ea5y\t v\u1ea5n\t \u0111\u1ec1\t n\u00e0y,\t v\u00e0\t t\u00ecm\t c\u00e1ch l\u00e0m\tcho\tn\u00f3\tm\u1ea5t\thi\u1ec7u\tl\u1ef1c,\tnh\u01b0ng\tkh\u00f4ng\tth\u00e0nh\tc\u00f4ng.\tNg\u01b0\u1eddi\tnh\u1eadn th\u1ee9c\t n\u00f3\t r\u00f5\t nh\u1ea5t\t l\u00e0\t E.\t Mach,\t v\u00e0\t b\u1ea3n\t th\u00e2n\t \u00f4ng\t \u0111\u00e3\t \u0111\u00f2i\t h\u1ecfi\t c\u01a1\t h\u1ecdc ph\u1ea3i\t\u0111\u01b0\u1ee3c\t\u0111\u1eb7t\ttr\u00ean\tn\u1ec1n\tt\u1ea3ng\tm\u1edbi.\tNg\u01b0\u1eddi\tta\tch\u1ec9\tc\u00f3\tth\u1ec3\tlo\u1ea1i\tb\u1ecf\tv\u1ea5n \u0111\u1ec1\t n\u00e0y\t b\u1eb1ng\t m\u1ed9t\t l\u00fd\t thuy\u1ebft\t v\u1eadt\t l\u00fd\t ph\u00f9\t h\u1ee3p\t v\u1edbi\t nguy\u00ean\t l\u00fd\t t\u01b0\u01a1ng \u0111\u1ed1i\tr\u1ed9ng.\tB\u1edfi\tv\u00ec\tc\u00e1c\tph\u01b0\u01a1ng\ttr\u00ecnh\tc\u1ee7a\tm\u1ed9t\tl\u00fd\tthuy\u1ebft\tnh\u01b0\tth\u1ebf\t\u0111\u1ec1u c\u00f3\t hi\u1ec7u\t l\u1ef1c\t cho\t m\u1ecdi\t v\u1eadt\t th\u1ec3\t quy\t chi\u1ebfu,\t d\u00f9\t \u1edf\t tr\u1ea1ng\t th\u00e1i\t chuy\u1ec3n \u0111\u1ed9ng\tn\u00e0o\t\u0111i\tn\u1eefa.[53]","\u00a7\t22 V\u00e0i\tSuy\tDi\u1ec5n\tT\u1eeb\tNguy\u00ean\tL\u00fd\tT\u01b0\u01a1ng\t\u0110\u1ed1i\tR\u1ed9ng C\u00e1c\tsuy\tngh\u0129\t\u1edf\t\u00a7\t20\tcho\tth\u1ea5y,\tnguy\u00ean\tl\u00fd\tt\u01b0\u01a1ng\t\u0111\u1ed1i\tr\u1ed9ng\tt\u1ea1o\tcho ch\u00fang\t ta\t kh\u1ea3\t n\u0103ng\t suy\t di\u1ec5n\t c\u00e1c\t t\u00ednh\t ch\u1ea5t\t c\u1ee7a\t tr\u01b0\u1eddng\t h\u1ea5p\t d\u1eabn b\u1eb1ng\t con\t \u0111\u01b0\u1eddng\t thu\u1ea7n\t t\u00fay\t l\u00fd\t thuy\u1ebft.\t Th\u1ef1c\t v\u1eady,\t ch\u00fang\t ta\t gi\u1ea3 thi\u1ebft\t m\u1ed9t\t \\\"di\u1ec5n\t bi\u1ebfn\\\"\t kh\u00f4ng-th\u1eddi-gian\t c\u1ee7a\t m\u1ed9t\t hi\u1ec7n\t t\u01b0\u1ee3ng\t t\u1ef1 nhi\u00ean\t n\u00e0o\t \u0111\u00f3\t \u0111\u01b0\u1ee3c\t bi\u1ebft,\t c\u0169ng\t nh\u01b0\t bi\u1ebft\t n\u00f3\t di\u1ec5n\t ra\t th\u1ebf\t n\u00e0o\t trong mi\u1ec1n\tGalilei\t\u0111\u1ed1i\tv\u1edbi\tm\u1ed9t\tv\u1eadt\tth\u1ec3\tquy\tchi\u1ebfu\tGalilei\tK.\tL\u00fac\t\u0111\u00f3,\tb\u1eb1ng nh\u1eefng\tthao\tt\u00e1c\tthu\u1ea7n\tt\u00fay\tl\u00fd\tthuy\u1ebft,\tngh\u0129a\tl\u00e0\tb\u1eb1ng\tt\u00ednh\tto\u00e1n\t\u0111\u01a1n thu\u1ea7n,\t ng\u01b0\u1eddi\t ta\t c\u00f3\t th\u1ec3\t bi\u1ebft\t hi\u1ec7n\t t\u01b0\u1ee3ng\t t\u1ef1\t nhi\u00ean\t \u0111\u01b0\u1ee3c\t bi\u1ebft\t tr\u01b0\u1edbc n\u00e0y\t c\u00f3\t d\u1ea1ng\t nh\u01b0\t th\u1ebf\t n\u00e0o\t n\u1ebfu\t nh\u00ecn\t t\u1eeb\t m\u1ed9t\t v\u1eadt\t th\u1ec3\t quy\t chi\u1ebfu\t K\u2019 chuy\u1ec3n\t\u0111\u1ed9ng\tgia\tt\u1ed1c\t\u0111\u1ed1i\tv\u1edbi\tK.\tNh\u01b0ng\tv\u00ec\t\u0111\u1ed1i\tv\u1edbi\tv\u1eadt\tth\u1ec3\tquy\tchi\u1ebfu m\u1edbi\tK\u2019\tn\u00e0y\tc\u00f3\tm\u1ed9t\ttr\u01b0\u1eddng\th\u1ea5p\td\u1eabn\tt\u1ed3n\tt\u1ea1i,\tcho\tn\u00ean\tqua\tquan\ts\u00e1t, ch\u00fang\tta\tbi\u1ebft\ttr\u01b0\u1eddng\th\u1ea5p\td\u1eabn\t\u1ea3nh\th\u01b0\u1edfng\tth\u1ebf\tn\u00e0o\tl\u00ean\thi\u1ec7n\tt\u01b0\u1ee3ng \u0111ang\t\u0111\u01b0\u1ee3c\tnghi\u00ean\tc\u1ee9u. Ch\u1eb3ng\t h\u1ea1n\t ch\u00fang\t ta\t bi\u1ebft,\t m\u1ed9t\t v\u1eadt\t th\u1ec3,\t \u0111\u01b0\u1ee3c\t gi\u1ea3\t thi\u1ebft\t c\u00f3\t m\u1ed9t chuy\u1ec3n\t\u0111\u1ed9ng\tth\u1eb3ng\t\u0111\u1ec1u\t\u0111\u1ed1i\tv\u1edbi\tK\t(ph\u00f9\th\u1ee3p\tv\u1edbi\t\u0111\u1ecbnh\tlu\u1eadt\tGalilei), th\u00ec\ts\u1ebd\tth\u1ef1c\thi\u1ec7n\tm\u1ed9t\tchuy\u1ec3n\t\u0111\u1ed9ng\tgia\tt\u1ed1c\tv\u00e0\tcong,\tn\u00f3i\tchung,\t\u0111\u1ed1i v\u1edbi\tv\u1eadt\tth\u1ec3\tchuy\u1ec3n\t\u0111\u1ed9ng\tgia\tt\u1ed1c\tK'\t(h\u1ed9p).\tS\u1ef1\tgia\tt\u1ed1c\thay\tu\u1ed1n\tcong n\u00e0y\t t\u01b0\u01a1ng\t \u1ee9ng\t v\u1edbi\t \u1ea3nh\t h\u01b0\u1edfng\t c\u1ee7a\t tr\u01b0\u1eddng\t h\u1ea5p\t d\u1eabn\t \u0111ang\t ng\u1ef1\t tr\u1ecb \u0111\u1ed1i\t v\u1edbi\t K'\t l\u00ean\t v\u1eadt\t th\u1ec3\t chuy\u1ec3n\t \u0111\u1ed9ng.\t Tr\u01b0\u1eddng\t h\u1ea5p\t d\u1eabn\t b\u1eb1ng\t c\u00e1ch n\u00e0y\t\u1ea3nh\th\u01b0\u1edfng\tl\u00ean\tchuy\u1ec3n\t\u0111\u1ed9ng\tc\u1ee7a\tc\u00e1c\tv\u1eadt\tth\u1ec3,\t\u0111i\u1ec1u\t\u0111\u00f3\t\u0111\u00e3\t\u0111\u01b0\u1ee3c bi\u1ebft\t\u0111\u1ebfn,\tcho\tn\u00ean\ts\u1ef1\tsuy\tngh\u0129\tc\u1ee7a\tch\u00fang\tta\tkh\u00f4ng\tmang\tl\u1ea1i\tc\u00e1i\tg\u00ec m\u1edbi\tc\u01a1\tb\u1ea3n\tc\u1ea3. Tuy\tnhi\u00ean,\tch\u00fang\tta\t\u0111\u01b0\u1ee3c\tm\u1ed9t\tk\u1ebft\tqu\u1ea3\tm\u1edbi\tc\u00f3\tt\u1ea7m\tquan\ttr\u1ecdng c\u01a1\t b\u1ea3n\t khi\t \u00e1p\t d\u1ee5ng\t suy\t ngh\u0129\t t\u01b0\u01a1ng\t t\u1ef1\t l\u00ean\t m\u1ed9t\t tia\t s\u00e1ng.\t \u0110\u1ed1i\t v\u1edbi m\u1ed9t\t v\u1eadt\t th\u1ec3\t quy\t chi\u1ebfu\t Galilei\t K,\t tia\t s\u00e1ng\t truy\u1ec1n\t \u0111i\t theo\t \u0111\u01b0\u1eddng th\u1eb3ng\t v\u1edbi\t v\u1eadn\t t\u1ed1c\t c.\t Nh\u01b0ng\t \u0111\u1ed1i\t v\u1edbi\t c\u00e1i\t h\u1ed9p\t chuy\u1ec3n\t \u0111\u1ed9ng\t gia\t t\u1ed1c (v\u1eadt\t th\u1ec3\t quy\t chi\u1ebfu\t K\t \u2019),\t qu\u1ef9\t \u0111\u1ea1o\t c\u1ee7a\t c\u00f9ng\t tia\t s\u00e1ng\t kh\u00f4ng\t c\u00f2n\t l\u00e0 \u0111\u01b0\u1eddng\tth\u1eb3ng\tn\u1eefa,\tnh\u01b0\tc\u00f3\tth\u1ec3\td\u1ec5\td\u00e0ng\tsuy\tra.\tT\u1eeb\t\u0111\u00f3\tch\u00fang\tta\tk\u1ebft lu\u1eadn\tr\u1eb1ng,\tn\u00f3i\tchung,\ttrong\tc\u00e1c\ttr\u01b0\u1eddng\th\u1ea5p\td\u1eabn\tc\u00e1c\ttia\ts\u00e1ng\ttruy\u1ec1n \u0111i\t theo\t \u0111\u01b0\u1eddng\t cong.\t K\u1ebft\t qu\u1ea3\t n\u00e0y\t c\u00f3\t t\u1ea7m\t quan\t tr\u1ecdng\t theo\t hai ph\u01b0\u01a1ng\tdi\u1ec7n. Tr\u01b0\u1edbc\tti\u00ean,\tk\u1ebft\tqu\u1ea3\tn\u00e0y\tc\u00f3\tth\u1ec3\t\u0111\u01b0\u1ee3c\tso\ts\u00e1nh\tv\u1edbi\tth\u1ef1c\tti\u1ec5n.\tM\u1eb7c d\u00f9\tm\u1ed9t\ts\u1ef1\tnghi\u00ean\tc\u1ee9u\tchi\tti\u1ebft\tcho\tth\u1ea5y\t\u0111\u1ed9\tcong\tc\u1ee7a\tc\u00e1c\ttia\ts\u00e1ng, nh\u01b0\t\u0111\u01b0\u1ee3c\tcung\tc\u1ea5p\tb\u1edfi\tthuy\u1ebft\tt\u01b0\u01a1ng\t\u0111\u1ed1i\tr\u1ed9ng,\tch\u1ec9\tl\u00e0\tv\u00f4\tc\u00f9ng\tnh\u1ecf","\u0111\u1ed1i\t v\u1edbi\t c\u00e1c\t tr\u01b0\u1eddng\t h\u1ea5p\t d\u1eabn\t \u0111\u01b0\u1ee3c\t ch\u00fang\t ta\t bi\u1ebft\t trong\t kinh nghi\u1ec7m,\t th\u00ec\t n\u00f3\t l\u1ea1i\t c\u00f3\t tr\u1ecb\t s\u1ed1\t 1,7\t gi\u00e2y\t cung\t \u0111\u1ed1i\t v\u1edbi\t c\u00e1c\t tia\t s\u00e1ng\t \u0111i qua\t g\u1ea7n\t m\u1eb7t\t tr\u1eddi.\t \u0110\u1ed9\t cong\t n\u00e0y\t ph\u1ea3i\t \u0111\u01b0\u1ee3c\t bi\u1ec3u\t l\u1ed9\t b\u1eb1ng\t c\u00e1ch\t sau \u0111\u00e2y.\t Nh\u00ecn\t t\u1eeb\t m\u1eb7t\t \u0111\u1ea5t,\t c\u00e1c\t ng\u00f4i\t sao\t c\u1ed1\t \u0111\u1ecbnh\t xu\u1ea5t\t hi\u1ec7n\t g\u1ea7n\t m\u1eb7t tr\u1eddi,\t v\u00e0\t do\t \u0111\u00f3\t c\u00f3\t th\u1ec3\t quan\t s\u00e1t\t \u0111\u01b0\u1ee3c\t khi\t c\u00f3\t nh\u1eadt\t th\u1ef1c\t to\u00e0n\t ph\u1ea7n, ph\u1ea3i\thi\u1ec7n\tra\tl\u1ec7ch\tkh\u1ecfi\tm\u1eb7t\ttr\u1eddi\tv\u1edbi\t\u0111\u1ed9\tl\u1ec7ch\tb\u1eb1ng\t\u0111\u1ed9\tl\u1ec7ch\tn\u00f3i\ttr\u00ean, so\tv\u1edbi\tv\u1ecb\ttr\u00ed\tch\u00fang\tm\u00e0\tch\u00fang\tta\t\u0111\u00e3\tth\u1ea5y\ttr\u00ean\tb\u1ea7u\ttr\u1eddi\tkhi\tm\u1eb7t\ttr\u1eddi \u0111\u1ee9ng\t \u1edf\t m\u1ed9t\t v\u1ecb\t tr\u00ed\t kh\u00e1c.\t S\u1ef1\t ki\u1ec3m\t tra\t t\u00ednh\t \u0111\u00fang\t \u0111\u1eafn,\t hay\t kh\u00f4ng \u0111\u00fang\t \u0111\u1eafn,\t c\u1ee7a\t h\u1ec7\t lu\u1eadn\t n\u00e0y\t l\u00e0\t m\u1ed9t\t nhi\u1ec7m\t v\u1ee5\t c\u00f3\t t\u1ea7m\t quan\t tr\u1ecdng b\u1eadc\tnh\u1ea5t\tm\u00e0\tl\u1eddi\tgi\u1ea3i\t\u0111\u00e1p\ts\u1eafp\tt\u1edbi\tc\u1ee7a\tn\u00f3\tch\u00fang\tta\t\u0111\u01b0\u1ee3c\tquy\u1ec1n\tch\u1edd \u0111\u1ee3i\tt\u1eeb\tc\u00e1c\tnh\u00e0\tthi\u00ean\tv\u0103n\th\u1ecdc.[54] Th\u1ee9\t hai,\t h\u1ec7\t qu\u1ea3\t n\u00e0y\t l\u1ea1i\t ch\u1ee9ng\t minh\t r\u1eb1ng,\t theo\t thuy\u1ebft\t t\u01b0\u01a1ng \u0111\u1ed1i\t r\u1ed9ng,\t \u0111\u1ecbnh\t lu\u1eadt\t th\u01b0\u1eddng\t \u0111\u01b0\u1ee3c\t nh\u1eafc\t \u0111\u1ebfn\t v\u1ec1\t t\u00ednh\t h\u1eb1ng\t s\u1ed1\t c\u1ee7a v\u1eadn\t t\u1ed1c\t \u00e1nh\t s\u00e1ng,\t m\u1ed9t\t trong\t hai\t gi\u1ea3\t \u0111\u1ecbnh\t c\u01a1\t b\u1ea3n\t c\u1ee7a\t thuy\u1ebft t\u01b0\u01a1ng\t \u0111\u1ed1i\t h\u1eb9p,\t gi\u1edd\t kh\u00f4ng\t th\u1ec3\t y\u00eau\t s\u00e1ch\t c\u00f3\t hi\u1ec7u\t l\u1ef1c\t v\u00f4\t h\u1ea1n\t \u0111\u01b0\u1ee3c. Th\u1ef1c\t v\u1eady,\t m\u1ed9t\t s\u1ef1\t u\u1ed1n\t cong\t c\u1ee7a\t c\u00e1c\t tia\t s\u00e1ng\t ch\u1ec9\t c\u00f3\t th\u1ec3\t x\u1ea3y\t ra \u0111\u01b0\u1ee3c\t khi\t v\u1eadn\t t\u1ed1c\t \u00e1nh\t s\u00e1ng\t thay\t \u0111\u1ed5i\t theo\t v\u1ecb\t tr\u00ed.\t Ng\u01b0\u1eddi\t ta\t c\u00f3\t th\u1ec3 ngh\u0129\t qua\t h\u1ec7\t qu\u1ea3\t n\u00e0y,\t thuy\u1ebft\t t\u01b0\u01a1ng\t \u0111\u1ed1i\t h\u1eb9p,\t v\u00e0\t v\u1edbi\t n\u00f3\t thuy\u1ebft t\u01b0\u01a1ng\t \u0111\u1ed1i\t n\u00f3i\t chung,\t s\u1ebd\t b\u1ecb\t s\u1ee5p\t \u0111\u1ed5.\t Tuy\t nhi\u00ean\t \u0111i\u1ec1u\t n\u00e0y\t kh\u00f4ng \u0111\u00fang\ttr\u00ean\tth\u1ef1c\tt\u1ebf.\tNg\u01b0\u1eddi\tta\tch\u1ec9\tc\u00f3\tth\u1ec3\tk\u1ebft\tlu\u1eadn\t\u0111\u01b0\u1ee3c\tr\u1eb1ng\tthuy\u1ebft t\u01b0\u01a1ng\t\u0111\u1ed1i\th\u1eb9p\tkh\u00f4ng\tth\u1ec3\ty\u00eau\ts\u00e1ch\tm\u1ed9t\tmi\u1ec1n\thi\u1ec7u\tl\u1ef1c\tkh\u00f4ng\tgi\u1edbi h\u1ea1n;\t c\u00e1c\t k\u1ebft\t qu\u1ea3\t c\u1ee7a\t n\u00f3\t ch\u1ec9\t \u0111\u00fang\t trong\t ch\u1eebng\t m\u1ef1c\t ch\u00fang\t ta\t c\u00f3 th\u1ec3\tb\u1ecf\tqua\t\u0111\u01b0\u1ee3c\t\u1ea3nh\th\u01b0\u1edfng\tc\u1ee7a\tc\u00e1c\ttr\u01b0\u1eddng\th\u1ea5p\td\u1eabn\tt\u00e1c\td\u1ee5ng\tl\u00ean c\u00e1c\thi\u1ec7n\tt\u01b0\u1ee3ng\t(th\u00ed\td\u1ee5\tnh\u01b0\tl\u00ean\t\u00e1nh\ts\u00e1ng). V\u00ec\t c\u00e1c\t \u0111\u1ed1i\t th\u1ee7\t c\u1ee7a\t thuy\u1ebft\t t\u01b0\u01a1ng\t \u0111\u1ed1i\t th\u01b0\u1eddng\t cho\t r\u1eb1ng,\t thuy\u1ebft t\u01b0\u01a1ng\t\u0111\u1ed1i\th\u1eb9p\ts\u1ebd\tb\u1ecb\tthuy\u1ebft\tt\u01b0\u01a1ng\t\u0111\u1ed1i\tr\u1ed9ng\tl\u00e0m\t\u0111\u1ed5\tnh\u00e0o,\tt\u00f4i\tmu\u1ed1n l\u00e0m\t r\u00f5\t h\u01a1n\t t\u00ecnh\t hu\u1ed1ng\t th\u1eadt\t c\u1ee7a\t n\u00f3\t b\u1eb1ng\t m\u1ed9t\t s\u1ef1\t so\t s\u00e1nh.\t Tr\u01b0\u1edbc khi\t c\u00f3\t s\u1ef1\t xu\u1ea5t\t hi\u1ec7n\t c\u1ee7a\t \u0111i\u1ec7n\t \u0111\u1ed9ng\t l\u1ef1c\t h\u1ecdc\t th\u00ec\t c\u00e1c\t \u0111\u1ecbnh\t lu\u1eadt\t c\u1ee7a t\u0129nh\t \u0111i\u1ec7n\t h\u1ecdc\t \u0111\u01b0\u1ee3c\t xem\t nh\u01b0\t nh\u1eefng\t \u0111\u1ecbnh\t lu\u1eadt\t c\u1ee7a\t \u0111i\u1ec7n\t h\u1ecdc\t n\u00f3i chung.\tNg\u00e0y\tnay\tch\u00fang\tta\tbi\u1ebft\tr\u1eb1ng\tc\u00e1c\t\u0111i\u1ec7n\ttr\u01b0\u1eddng\t\u0111\u01b0\u1ee3c\tsuy\tra m\u1ed9t\t c\u00e1ch\t ch\u00ednh\t x\u00e1c\t t\u1eeb\t t\u0129nh\t \u0111i\u1ec7n\t h\u1ecdc\t ch\u1ec9\t trong\t tr\u01b0\u1eddng\t h\u1ee3p\t m\u00e0\t \u1edf \u0111\u00f3\t c\u00e1c\t kh\u1ed1i\t l\u01b0\u1ee3ng\t \u0111i\u1ec7n\t ho\u00e0n\t to\u00e0n\t \u0111\u1ee9ng\t y\u00ean\t v\u1edbi\t nhau\t v\u00e0\t v\u1edbi\t h\u1ec7 t\u1ecda\t \u0111\u1ed9,\t \u0111i\u1ec1u\t ch\u1eb3ng\t bao\t gi\u1edd\t \u0111\u01b0\u1ee3c\t th\u1ef1c\t hi\u1ec7n\t nghi\u00eam\t ng\u1eb7t\t c\u1ea3.\t C\u00f3 ph\u1ea3i\tv\u00ec\tth\u1ebf\tm\u00e0\tt\u0129nh\t\u0111i\u1ec7n\th\u1ecdc\tb\u1ecb\tc\u00e1c\tph\u01b0\u01a1ng\ttr\u00ecnh\ttr\u01b0\u1eddng\tMaxwell c\u1ee7a\t\u0111i\u1ec7n\t\u0111\u1ed9ng\tl\u1ef1c\th\u1ecdc\tl\u00e0m\t\u0111\u1ed5\tnh\u00e0o\tkh\u00f4ng?\tKh\u00f4ng\tch\u00fat\tn\u00e0o!\tT\u0129nh \u0111i\u1ec7n\t h\u1ecdc\t \u0111\u01b0\u1ee3c\t ch\u1ee9a\t \u0111\u1ef1ng\t trong\t \u0111i\u1ec7n\t \u0111\u1ed9ng\t l\u1ef1c\t h\u1ecdc\t nh\u01b0\t m\u1ed9t tr\u01b0\u1eddng\t h\u1ee3p\t t\u1edbi\t h\u1ea1n;\t c\u00e1c\t \u0111\u1ecbnh\t lu\u1eadt\t c\u1ee7a\t c\u00e1i\t sau\t tr\u1ef1c\t ti\u1ebfp\t d\u1eabn\t \u0111\u1ebfn c\u00e1c\t \u0111\u1ecbnh\t lu\u1eadt\t c\u1ee7a\t c\u00e1i\t tr\u01b0\u1edbc\t trong\t tr\u01b0\u1eddng\t h\u1ee3p\t c\u00e1c\t tr\u01b0\u1eddng\t kh\u00f4ng","bi\u1ebfn\tthi\u00ean\t\u0111\u1ed1i\tv\u1edbi\tth\u1eddi\tgian.\tKh\u00f4ng\tc\u00f3\ts\u1ed1\tm\u1ec7nh\tn\u00e0o\t\u0111\u1eb9p\th\u01a1n\tcho m\u1ed9t\t l\u00fd\t thuy\u1ebft\t v\u1eadt\t l\u00fd,\t khi\t ch\u00ednh\t n\u00f3\t ch\u1ec9\t ra\t con\t \u0111\u01b0\u1eddng\t \u0111i\t \u0111\u1ebfn\t thi\u1ebft l\u1eadp\tm\u1ed9t\tl\u00fd\tthuy\u1ebft\tr\u1ed9ng\tl\u1edbn\th\u01a1n,\t\u0111\u1ec3\tr\u1ed3i\tn\u00f3\ts\u1ed1ng\tti\u1ebfp\ttrong\t\u0111\u00f3\tnh\u01b0 m\u1ed9t\ttr\u01b0\u1eddng\th\u1ee3p\tt\u1edbi\th\u1ea1n. Trong\t th\u00ed\t d\u1ee5\t truy\u1ec1n\t \u00e1nh\t s\u00e1ng\t v\u1eeba\t \u0111\u01b0\u1ee3c\t \u0111\u1ec1\t c\u1eadp,\t ch\u00fang\t ta\t \u0111\u00e3 th\u1ea5y\tnguy\u00ean\tl\u00fd\tt\u01b0\u01a1ng\t\u0111\u1ed1i\tr\u1ed9ng\tl\u00e0m\tcho\tch\u00fang\tta\tc\u00f3\tkh\u1ea3\tn\u0103ng\tsuy di\u1ec5n\t \u0111\u01b0\u1ee3c\t b\u1eb1ng\t con\t \u0111\u01b0\u1eddng\t l\u00fd\t thuy\u1ebft\t \u1ea3nh\t h\u01b0\u1edfng\t c\u1ee7a\t tr\u01b0\u1eddng\t h\u1ea5p d\u1eabn\t l\u00ean\t di\u1ec5n\t bi\u1ebfn\t c\u1ee7a\t c\u00e1c\t hi\u1ec7n\t t\u01b0\u1ee3ng\t t\u1ef1\t nhi\u00ean\t m\u00e0\t c\u00e1c\t \u0111\u1ecbnh\t lu\u1eadt c\u1ee7a\t ch\u00fang\t \u0111\u00e3\t \u0111\u01b0\u1ee3c\t bi\u1ebft\t trong\t tr\u01b0\u1eddng\t h\u1ee3p\t tr\u01b0\u1eddng\t h\u1ea5p\t d\u1eabn\t v\u1eafng m\u1eb7t.\t Nh\u01b0ng\t b\u00e0i\t to\u00e1n\t h\u1ea5p\t d\u1eabn\t nh\u1ea5t,\t m\u00e0\t thuy\u1ebft\t t\u01b0\u01a1ng\t \u0111\u1ed1i\t cung c\u1ea5p\t ch\u00eca\t kh\u00f3a\t cho\t l\u1eddi\t gi\u1ea3i\t c\u1ee7a\t n\u00f3,\t li\u00ean\t quan\t \u0111\u1ebfn\t vi\u1ec7c\t t\u00ecm\t ra\t c\u00e1c \u0111\u1ecbnh\tlu\u1eadt\tm\u00e0\tch\u00ednh\ttr\u01b0\u1eddng\th\u1ea5p\td\u1eabn\tth\u1ecfa\tm\u00e3n.\tT\u00ecnh\thu\u1ed1ng\t\u1edf\t\u0111\u00e2y l\u00e0\tnh\u01b0\tsau. Ch\u00fang\t ta\t bi\u1ebft\t nh\u1eefng\t mi\u1ec1n\t kh\u00f4ng-th\u1eddi-gian\t -\t m\u00e0\t v\u1edbi\t s\u1ef1\t ch\u1ecdn l\u1ef1a\t th\u00edch\t h\u1ee3p\t c\u1ee7a\t v\u1eadt\t th\u1ec3\t quy\t chi\u1ebfu\t -\t ch\u00fang\t v\u1eadn\t h\u00e0nh\t g\u1ea7n\t nh\u01b0 \\\"Galilei\\\",\tngh\u0129a\tl\u00e0\tc\u00e1c\tmi\u1ec1n\tm\u00e0\t\u1edf\t\u0111\u00f3\tc\u00e1c\ttr\u01b0\u1eddng\th\u1ea5p\td\u1eabn\tv\u1eafng\tm\u1eb7t. N\u1ebfu\t gi\u1edd\t ch\u00fang\t ta\t quy\t chi\u1ebfu\t m\u1ed9t\t mi\u1ec1n\t nh\u01b0\t th\u1ebf\t l\u00ean\t m\u1ed9t\t v\u1eadt\t th\u1ec3 quy\t chi\u1ebfu\t chuy\u1ec3n\t \u0111\u1ed9ng\t b\u1ea5t\t k\u1ef3\t K\u2019,\t th\u00ec\t \u0111\u1ed1i\t v\u1edbi\t K'\t ch\u00fang\t ta\t s\u1ebd\t c\u00f3 m\u1ed9t\ttr\u01b0\u1eddng\th\u1ea5p\td\u1eabn\tbi\u1ebfn\tthi\u00ean\ttheo\tth\u1eddi\tgian\tv\u00e0\tkh\u00f4ng\tgian[55]. T\u00ednh\t ch\u1ea5t\t c\u1ee7a\t tr\u01b0\u1eddng\t n\u00e0y\t d\u0129\t nhi\u00ean\t t\u00f9y\t thu\u1ed9c\t v\u00e0o\t chuy\u1ec3n\t \u0111\u1ed9ng \u0111\u00e3\t \u0111\u01b0\u1ee3c\t ch\u1ecdn\t l\u1ef1a\t cho\t K\u2019.\t Theo\t thuy\u1ebft\t t\u01b0\u01a1ng\t \u0111\u1ed1i\t r\u1ed9ng,\t \u0111\u1ecbnh\t lu\u1eadt ph\u1ed5\t qu\u00e1t\t c\u1ee7a\t tr\u01b0\u1eddng\t h\u1ea5p\t d\u1eabn\t ph\u1ea3i\t \u0111\u01b0\u1ee3c\t th\u1ecfa\t m\u00e3n\t cho\t t\u1ea5t\t c\u1ea3 tr\u01b0\u1eddng\t h\u1ea5p\t d\u1eabn\t \u0111\u01b0\u1ee3c\t t\u1ea1o\t ra\t b\u1eb1ng\t c\u00e1ch\t \u0111\u00f3.\t Tuy\t c\u0169ng\t kh\u00f4ng\t th\u1ec3 n\u00e0o\t t\u1ea1o\t ra\t \u0111\u01b0\u1ee3c\t t\u1ea5t\t c\u1ea3\t c\u00e1c\t tr\u01b0\u1eddng\t b\u1eb1ng\t c\u00e1ch\t \u0111\u00f3,\t nh\u01b0ng\t ng\u01b0\u1eddi\t ta v\u1eabn\tnu\u00f4i\thy\tv\u1ecdng\tr\u1eb1ng\tc\u00f3\tth\u1ec3\tt\u1eeb\tnh\u1eefng\ttr\u01b0\u1eddng\th\u1ea5p\td\u1eabn\tc\u00f3\td\u1ea1ng \u0111\u1eb7c\tbi\u1ec7t\tn\u00e0y\tm\u00e0\tsuy\tra\t\u0111\u01b0\u1ee3c\t\u0111\u1ecbnh\tlu\u1eadt\tph\u1ed5\tqu\u00e1t\tc\u1ee7a\th\u1ea5p\td\u1eabn.\tV\u00e0 ni\u1ec1m\t hy\t v\u1ecdng\t n\u00e0y\t \u0111\u00e3\t tr\u1edf\t th\u00e0nh\t s\u1ef1\t th\u1eadt\t m\u1ed9t\t c\u00e1ch\t \u0111\u1eb9p\t \u0111\u1ebd\t nh\u1ea5t! Nh\u01b0ng\t t\u1eeb\t ch\u1ed7\t th\u1ea5y\t \u0111\u01b0\u1ee3c\t r\u00f5\t r\u00e0ng\t m\u1ee5c\t ti\u00eau\t n\u00e0y\t \u0111\u1ebfn\t ch\u1ed7\t th\u1ef1c\t s\u1ef1 \u0111\u1ea1t\t\u0111\u01b0\u1ee3c\tn\u00f3,\tc\u00f2n\tc\u1ea7n\tph\u1ea3i\tv\u01b0\u1ee3t\tqua\tm\u1ed9t\tkh\u00f3\tkh\u0103n\tnghi\u00eam\ttr\u1ecdng m\u00e0\t t\u00f4i\t kh\u00f4ng\t \u0111\u01b0\u1ee3c\t ph\u00e9p\t gi\u1ea5u\t gi\u1ebfm\t b\u1ea1n\t \u0111\u1ecdc,\t b\u1edfi\t v\u00ec\t n\u00f3\t n\u1eb1m\t s\u00e2u trong\t b\u1ea3n\t ch\u1ea5t\t c\u1ee7a\t s\u1ef1\t vi\u1ec7c.\t Ch\u00fang\t ta\t tr\u01b0\u1edbc\t nh\u1ea5t\t c\u1ea7n\t m\u1ed9t\t s\u1ef1\t \u0111\u00e0o s\u00e2u\tm\u1ed9t\tl\u1ea7n\tn\u1eefa\tc\u00e1c\tkh\u00e1i\tni\u1ec7m\tc\u1ee7a\tcontinum\tkh\u00f4ng-th\u1eddi-gian.","\u00a7\t23 S\u1ef1\tV\u1eadn\tH\u00e0nh\tc\u1ee7a\t\u0110\u1ed3ng\tH\u1ed3\tv\u00e0\tThanh\t\u0110o\tTr\u00ean\tM\u1ed9t\tV\u1eadt\tTh\u1ec3\tQuy\tChi\u1ebfu\tQuay Cho\t\u0111\u1ebfn\tgi\u1edd\tt\u00f4i\t\u0111\u00e3\tc\u1ed1\t\u00fd\tkh\u00f4ng\tn\u00f3i\tv\u1ec1\ts\u1ef1\tl\u00fd\tgi\u1ea3i\tv\u1eadt\tl\u00fd\tc\u1ee7a\tc\u00e1c\ts\u1ed1 \u0111o\t kh\u00f4ng\t gian\t v\u00e0\t th\u1eddi\t gian\t trong\t tr\u01b0\u1eddng\t h\u1ee3p\t thuy\u1ebft\t t\u01b0\u01a1ng\t \u0111\u1ed1i r\u1ed9ng.\t Qua\t \u0111\u00f3\t t\u00f4i\t \u0111\u00e3\t l\u00e0m\t cho\t m\u00ecnh\t c\u00f3\t ph\u1ea7n\t m\u1eafc\t l\u1ed7i\t kh\u00f4ng\t c\u1ea9n th\u1eadn\t trong\t tr\u00ecnh\t b\u00e0y,\t \u0111i\u1ec1u\t m\u00e0\t ch\u00fang\t ta\t \u0111\u00e3\t bi\u1ebft\t trong\t ph\u1ea7n thuy\u1ebft\t t\u01b0\u01a1ng\t \u0111\u1ed1i\t h\u1eb9p,\t r\u1eb1ng\t n\u00f3\t kh\u00f4ng\t h\u1ec1\t nh\u1ecf\t hay\t c\u00f3\t th\u1ec3\t tha\t th\u1ee9 \u0111\u01b0\u1ee3c.\t B\u00e2y\t gi\u1edd\t \u0111\u00e3\t \u0111\u1ebfn\t l\u00fac\t ch\u00fang\t ta\t ph\u1ea3i\t l\u1ea5p\t l\u1ea1i\t c\u00e1i\t l\u1ed7\t h\u1ed5ng\t n\u00e0y; nh\u01b0ng\t t\u00f4i\t mu\u1ed1n\t n\u00f3i\t tr\u01b0\u1edbc\t c\u00f4ng\t vi\u1ec7c\t n\u00e0y\t \u0111\u00f2i\t h\u1ecfi\t kh\u00f4ng\t \u00edt\t ki\u00ean nh\u1eabn\tv\u00e0\tkh\u1ea3\tn\u0103ng\tt\u01b0\tduy\ttr\u1eebu\tt\u01b0\u1ee3ng\tc\u1ee7a\tb\u1ea1n\t\u0111\u1ecdc. Ch\u00fang\t ta\t l\u1ea1i\t xu\u1ea5t\t ph\u00e1t\t t\u1eeb\t nh\u1eefng\t tr\u01b0\u1eddng\t h\u1ee3p\t r\u1ea5t\t \u0111\u1eb7c\t th\u00f9\t \u0111\u00e3 th\u01b0\u1eddng\t\u0111\u01b0\u1ee3c\ts\u1eed\td\u1ee5ng.\tGi\u1ea3\tthi\u1ebft\tc\u00f3\tm\u1ed9t\tmi\u1ec1n\tkh\u00f4ng-th\u1eddi-gian\tsao cho\ttrong\t\u0111\u00f3\tch\u00fang\tta\tkh\u00f4ng\tc\u00f3\ttr\u01b0\u1eddng\th\u1ea5p\td\u1eabn\t\u0111\u1ed1i\tv\u1edbi\tm\u1ed9t\tv\u1eadt th\u1ec3\t quy\t chi\u1ebfu\t K,\t v\u1edbi\t m\u1ed9t\t tr\u1ea1ng\t th\u00e1i\t chuy\u1ec3n\t \u0111\u1ed9ng\t \u0111\u01b0\u1ee3c\t ch\u1ecdn th\u00edch\t h\u1ee3p.\t \u0110\u1ed1i\t v\u1edbi\t mi\u1ec1n\t xem\t x\u00e9t,\t K\t l\u00e0\t m\u1ed9t\t v\u1eadt\t th\u1ec3\t quy\t chi\u1ebfu Galilei,\t v\u00e0\t \u0111\u1ed1i\t v\u1edbi\t K\t c\u00e1c\t k\u1ebft\t qu\u1ea3\t c\u1ee7a\t thuy\u1ebft\t t\u01b0\u01a1ng\t \u0111\u1ed1i\t h\u1eb9p\t c\u00f3\t gi\u00e1 tr\u1ecb.\t Ch\u00fang\t ta\t quy\t chi\u1ebfu\t mi\u1ec1n\t n\u00e0y\t l\u00ean\t m\u1ed9t\t v\u1eadt\t th\u1ec3\t quy\t chi\u1ebfu\t th\u1ee9 hai\tK'\t c\u00f3\t chuy\u1ec3n\t \u0111\u1ed9ng\t quay\t \u0111\u1ec1u\t \u0111\u1ed1i\t v\u1edbi\t K.\t\u0110\u1ec3\tc\u1ed1\t \u0111\u1ecbnh\tsuy\t ngh\u0129, ch\u00fang\tta\th\u00e3y\tt\u01b0\u1edfng\tt\u01b0\u1ee3ng\tK\u2019\td\u01b0\u1edbi\td\u1ea1ng\tc\u1ee7a\tm\u1ed9t\t\u0111\u0129a\ttr\u00f2n\tph\u1eb3ng, quay\t \u0111\u1ec1u\t quanh\t t\u00e2m\t \u0111i\u1ec3m\t c\u1ee7a\t n\u00f3\t tr\u00ean\t m\u1eb7t\t ph\u1eb3ng.\t M\u1ed9t\t ng\u01b0\u1eddi quan\t s\u00e1t\t ng\u1ed3i\t tr\u00ean\t d\u0129a\t K'\t ngo\u00e0i\t t\u00e2m\t \u0111i\u1ec3m\t c\u1ee7a\t n\u00f3,\t c\u1ea3m\t nh\u1eadn\t m\u1ed9t l\u1ef1c\tt\u00e1c\td\u1ee5ng\txuy\u00ean\tt\u00e2m\th\u01b0\u1edbng\tra\tngo\u00e0i;\tl\u1ef1c\tn\u00e0y\t\u0111\u01b0\u1ee3c\tm\u1ed9t\tng\u01b0\u1eddi quan\t s\u00e1t\t \u0111\u1ee9ng\t y\u00ean\t \u0111\u1ed1i\t v\u1edbi\t v\u1eadt\t th\u1ec3\t quy\t chi\u1ebfu\t ban\t \u0111\u1ea7u\t K\t di\u1ec5n\t gi\u1ea3i l\u00e0\t m\u1ed9t\t t\u00e1c\t d\u1ee5ng\t qu\u00e1n\t t\u00ednh\t (l\u1ef1c\t ly\t t\u00e2m).\t Nh\u01b0ng\t ng\u01b0\u1eddi\t quan\t s\u00e1t ng\u1ed3i\t tr\u00ean\t \u0111\u0129a\t c\u00f3\t th\u1ec3\t cho\t r\u1eb1ng\t \u0111\u0129a\t anh\t ta\t l\u00e0\t v\u1eadt\t th\u1ec3\t \\\"\u0111\u1ee9ng\t y\u00ean\\\"; theo\t nguy\u00ean\t l\u00fd\t t\u01b0\u01a1ng\t \u0111\u1ed1i\t r\u1ed9ng,\t quan\t ni\u1ec7m\t c\u1ee7a\t anh\t ta\t l\u00e0\t ch\u00ednh \u0111\u00e1ng.\tAnh\tta\tdi\u1ec5n\tgi\u1ea3i\tl\u1ef1c\tt\u00e1c\td\u1ee5ng\tl\u00ean\tanh\tta,\thay\tn\u00f3i\tt\u1ed5ng\tqu\u00e1t, l\u00ean\tc\u00e1c\tv\u1eadt\tth\u1ec3\t\u0111\u1ee9ng\ty\u00ean\t\u0111\u1ed1i\tv\u1edbi\t\u0111\u0129a,\tl\u00e0\tt\u00e1c\td\u1ee5ng\tc\u1ee7a\tm\u1ed9t\ttr\u01b0\u1eddng h\u1ea5p\td\u1eabn.\tTuy\tnhi\u00ean\ts\u1ef1\tph\u00e2n\tb\u1ed1\tkh\u00f4ng\tgian\tc\u1ee7a\ttr\u1ecdng\ttr\u01b0\u1eddng\tn\u00e0y l\u00e0\t m\u1ed9t\t c\u00e1i\t g\u00ec\t kh\u00f4ng\t gi\u1ed1ng\t nh\u01b0\t h\u1ea5p\t d\u1eabn\t c\u1ee7a\t thuy\u1ebft\t Newton.[56] Nh\u01b0ng\tng\u01b0\u1eddi\tquan\ts\u00e1t\tkh\u00f4ng\tc\u1ea3m\tth\u1ea5y\tb\u1ed1i\tr\u1ed1i,\tv\u00ec\tanh\tta\ttin\tv\u00e0o thuy\u1ebft\tt\u01b0\u01a1ng\t\u0111\u1ed1i\tr\u1ed9ng;\tanh\tta\ttin\tm\u1ed9t\tc\u00e1ch\tch\u00ednh\t\u0111\u00e1ng,\tr\u1eb1ng\tm\u1ed9t \u0111\u1ecbnh\t lu\u1eadt\t h\u1ea5p\t d\u1eabn\t ph\u1ed5\t qu\u00e1t\t s\u1ebd\t \u0111\u01b0\u1ee3c\t t\u00ecm\t th\u1ea5y,\t kh\u00f4ng\t nh\u1eefng\t c\u00f3 kh\u1ea3\t n\u0103ng\t gi\u1ea3i\t th\u00edch\t ch\u00ednh\t x\u00e1c\t s\u1ef1\t v\u1eadn\t h\u00e0nh\t c\u1ee7a\t c\u00e1c\t tinh\t t\u00fa,\t m\u00e0 c\u00f2n\t gi\u1ea3i\t th\u00edch\t \u0111\u01b0\u1ee3c\t c\u1ea3\t tr\u01b0\u1eddng\t l\u1ef1c\t m\u00e0\t anh\t ta\t \u0111\u00e3\t c\u1ea3m\t nh\u1eadn\t tr\u00ean \u0111\u0129a.","Ng\u01b0\u1eddi\t quan\t s\u00e1t\t l\u00e0m\t c\u00e1c\t th\u00ed\t nghi\u1ec7m\t v\u1edbi\t \u0111\u1ed3ng\t h\u1ed3\t v\u00e0\t thanh\t \u0111o tr\u00ean\t \u0111\u0129a\t quay\t c\u1ee7a\t anh\t ta,\t v\u1edbi\t \u00fd\t \u0111\u1ecbnh,\t tr\u00ean\t c\u01a1\t s\u1edf\t c\u00e1c\t quan\t s\u00e1t\t c\u1ee7a m\u00ecnh,\tt\u00ecm\tth\u1ea5y\tc\u00e1c\t\u0111\u1ecbnh\tngh\u0129a\tch\u00ednh\tx\u00e1c\tcho\t\u00fd\tngh\u0129a\tc\u1ee7a\tc\u00e1c\ts\u1ed1 \u0111o\t th\u1eddi\t gian\t v\u00e0\t kh\u00f4ng\t gian\t \u0111\u1ed1i\t v\u1edbi\t \u0111\u0129a\t quay\t K'.\t Anh\t ta\t s\u1ebd\t thu ho\u1ea1ch\t\u0111\u01b0\u1ee3c\tnh\u1eefng\tkinh\tnghi\u1ec7m\tg\u00ec? \u0110\u1ec3\tb\u1eaft\t\u0111\u1ea7u,\tanh\tta\tl\u1ea5y\thai\t\u0111\u1ed3ng\th\u1ed3\tc\u1ea5u\tt\u1ea1o\tgi\u1ed1ng\tnhau,\t\u0111\u1eb7t\tm\u1ed9t c\u00e1i\t t\u1ea1i\t t\u00e2m\t \u0111i\u1ec3m\t c\u1ee7a\t \u0111\u0129a,\t c\u00e1i\t kia\t \u1edf\t v\u00f9ng\t bi\u00ean,\t c\u1ea3\t hai\t nh\u01b0\t v\u1eady\t s\u1ebd \u0111\u1ee9ng\t y\u00ean\t \u0111\u1ed1i\t v\u1edbi\t \u0111\u0129a\t quay.\t \u0110\u1ea7u\t ti\u00ean\t ch\u00fang\t ta\t h\u1ecfi,\t hai\t \u0111\u1ed3ng\t h\u1ed3 n\u00e0y\t c\u00f3\t ch\u1ea1y\t nhanh\t nh\u01b0\t nhau\t hay\t kh\u00f4ng\t nh\u00ecn\t t\u1eeb\t v\u1eadt\t th\u1ec3\t quy chi\u1ebfu\tGalilei\tkh\u00f4ng\tquay\tK.\tNh\u1eadn\tx\u00e9t\tt\u1eeb\t\u0111\u00e2y,\t\u0111\u1ed3ng\th\u1ed3\t\u1edf\tt\u00e2m\t\u0111i\u1ec3m kh\u00f4ng\t c\u00f3\t v\u1eadn\t t\u1ed1c,\t trong\t khi\t \u0111\u1ed3ng\t h\u1ed3\t \u1edf\t ngo\u1ea1i\t vi\t c\u00f3\t chuy\u1ec3n\t \u0111\u1ed9ng, h\u1ec7\tqu\u1ea3\tc\u1ee7a\tchuy\u1ec3n\t\u0111\u1ed9ng\tquay\t\u0111\u1ed1i\tv\u1edbi\tK.\t Theo\t k\u1ebft\t qu\u1ea3\t c\u1ee7a\t \u00a7\t 12, \u0111\u1ed3ng\t h\u1ed3\t th\u1ee9\t hai\t v\u00ec\t th\u1ebf\t lu\u00f4n\t lu\u00f4n\t ch\u1ea1y\t ch\u1eadm\t h\u01a1n\t \u0111\u1ed3ng\t h\u1ed3\t \u1edf\t t\u00e2m \u0111i\u1ec3m\t c\u1ee7a\t \u0111\u0129a\t quay,\t nh\u00ecn\t t\u1eeb\t K.\t Ng\u01b0\u1eddi\t quan\t s\u00e1t\t tr\u00ean\t \u0111\u0129a\t quay\t m\u00e0 ch\u00fang\t ta\t h\u00ecnh\t dung\t ng\u1ed3i\t t\u1ea1i\t t\u00e2m\t \u0111i\u1ec3m\t c\u1ee7a\t \u0111\u0129a\t quay,\t c\u1ea1nh\t c\u00e1i \u0111\u1ed3ng\t h\u1ed3\t \u1edf\t \u0111\u00f3,\t r\u00f5\t r\u00e0ng\t c\u0169ng\t ph\u1ea3i\t c\u00f3\t c\u00f9ng\t m\u1ed9t\t nh\u1eadn\t x\u00e9t\t nh\u01b0\t th\u1ebf. Do\t \u0111\u00f3,\t tr\u00ean\t \u0111\u0129a\t quay,\t v\u00e0\t t\u1ed5ng\t qu\u00e1t\t h\u01a1n\t trong\t m\u1ed7i\t tr\u01b0\u1eddng\t h\u1ea5p d\u1eabn,\t \u0111\u1ed3ng\t h\u1ed3\t s\u1ebd\t ch\u1ea1y\t nhanh\t h\u01a1n\t hay\t ch\u1eadm\t h\u01a1n\t t\u00f9y\t theo\t v\u1ecb\t tr\u00ed m\u00e0\t \u0111\u1ed3ng\t h\u1ed3\t \u0111\u01b0\u1ee3c\t \u0111\u1eb7t\t v\u00e0o\t (y\u00ean\t t\u0129nh).\t M\u1ed9t\t \u0111\u1ecbnh\t ngh\u0129a\t h\u1ee3p\t l\u00fd\t cho th\u1eddi\t gian\t v\u1edbi\t s\u1ef1\t gi\u00fap\t \u0111\u1ee1\t c\u1ee7a\t c\u00e1c\t \u0111\u1ed3ng\t h\u1ed3\t \u0111\u01b0\u1ee3c\t \u0111\u1eb7t\t y\u00ean\t t\u0129nh\t \u0111\u1ed1i v\u1edbi\tv\u1eadt\tth\u1ec3\tquy\tchi\u1ebfu\tnh\u01b0\tv\u1eady\tl\u00e0\tkh\u00f4ng\tth\u1ec3\tc\u00f3.\tM\u1ed9t\ts\u1ef1\tkh\u00f3\tkh\u0103n t\u01b0\u01a1ng\tt\u1ef1\tx\u1ea3y\tra\tn\u1ebfu\tch\u00fang\tta\tt\u00ecm\tc\u00e1ch\t\u00e1p\td\u1ee5ng\t\u1edf\t\u0111\u00e2y\tkh\u00e1i\tni\u1ec7m tr\u01b0\u1edbc\t \u0111\u00e2y\t c\u1ee7a\t ch\u00fang\t ta\t v\u1ec1\t t\u00ednh\t \u0111\u1ed3ng\t th\u1eddi.\t Nh\u01b0ng\t t\u00f4i\t kh\u00f4ng mu\u1ed1n\t\u0111i\ts\u00e2u\th\u01a1n. H\u01a1n\t n\u1eefa,\t \u1edf\t \u0111\u00e2y\t \u0111\u1ecbnh\t ngh\u0129a\t v\u1ec1\t t\u1ecda\t \u0111\u1ed9\t kh\u00f4ng\t gian\t tr\u01b0\u1edbc\t ti\u00ean c\u0169ng\t g\u1eb7p\t nh\u1eefng\t kh\u00f3\t kh\u0103n\t kh\u00f4ng\t v\u01b0\u1ee3t\t qua\t \u0111\u01b0\u1ee3c.\t Th\u1ef1c\t v\u1eady,\t n\u1ebfu ng\u01b0\u1eddi\tquan\ts\u00e1t\t\u0111ang\tchuy\u1ec3n\t\u0111\u1ed9ng\tc\u00f9ng\tv\u1edbi\t\u0111\u0129a\t\u0111\u1eb7t\tm\u1ed9t\tthanh\t\u0111o \u0111\u01a1n\tv\u1ecb\t(m\u1ed9t\tthanh\t\u0111o\tnh\u1ecf\t\u0111\u1ed1i\tv\u1edbi\t\u0111\u01b0\u1eddng\tk\u00ednh\t\u0111\u0129a)\tt\u1ea1i\tv\u00f2ng\tngo\u1ea1i vi\t c\u1ee7a\t \u0111\u0129a\t v\u00e0\t ti\u1ebfp\t tuy\u1ebfn\t v\u1edbi\t n\u00f3,\t th\u00ec\t thanh\t \u0111o\t n\u00e0y,\t quan\t s\u00e1t\t t\u1eeb\t h\u1ec7 t\u1ecda\t \u0111\u1ed9\t Galilei,\t ng\u1eafn\t h\u01a1n\t 1,\t b\u1edfi\t v\u00ec\t theo\t \u00a7\t 12\t c\u00e1c\t v\u1eadt\t th\u1ec3\t chuy\u1ec3n \u0111\u1ed9ng\t s\u1ebd\t ch\u1ecbu\t m\u1ed9t\t s\u1ef1\t thu\t ng\u1eafn\t theo\t h\u01b0\u1edbng\t chuy\u1ec3n\t \u0111\u1ed9ng.\t N\u1ebfu ng\u01b0\u1ee3c\t l\u1ea1i\t anh\t ta\t \u0111\u1eb7t\t thanh\t \u0111o\t d\u1ecdc\t theo\t \u0111\u01b0\u1eddng\t b\u00e1n\t k\u00ednh\t c\u1ee7a\t \u0111\u0129a, th\u00ec\t thanh\t \u0111o\t \u0111\u00f3,\t quan\t s\u00e1t\t t\u1eeb\t K,\t kh\u00f4ng\t ch\u1ecbu\t s\u1ef1\t thu\t ng\u1eafn.\t Do\t \u0111\u00f3 n\u1ebfu\t ng\u01b0\u1eddi\t quan\t s\u00e1t\t tr\u01b0\u1edbc\t h\u1ebft\t \u0111o\t chu\t vi\t c\u1ee7a\t \u0111\u0129a,\t sau\t \u0111\u00f3\t \u0111\u01b0\u1eddng k\u00ednh\t\u0111\u0129a\tb\u1eb1ng\tthanh\t\u0111o\tc\u1ee7a\tanh\tta,\tv\u00e0\tsau\t\u0111\u00f3\tchia\thai\tk\u1ebft\tqu\u1ea3\tcho nhau,\t anh\t ta\t s\u1ebd\t t\u00ecm\t th\u1ea5y\t t\u1ec9\t l\u1ec7\t kh\u00f4ng\t ph\u1ea3i\t l\u00e0\t con\t s\u1ed1\t quen\t thu\u1ed9c \u03c0=3,14...\t n\u1eefa,\t m\u00e0\t l\u00e0\t m\u1ed9t\t s\u1ed1\t l\u1edbn\t h\u01a1n,[57]\t trong\t khi\t tr\u00ean\t m\u1ed9t\t \u0111\u0129a \u0111\u1ee9ng\ty\u00ean\t\u0111\u1ed1i\tv\u1edbi\tK\tc\u00e1c\tph\u00e9p\tt\u00ednh\tn\u00e0y\td\u0129\tnhi\u00ean\tph\u1ea3i\tcho\tra\tch\u00ednh","x\u00e1c\t s\u1ed1\t \u03c0.\t Nh\u01b0\t v\u1eady\t \u0111i\u1ec1u\t n\u00e0y\t \u0111\u00e3\t ch\u1ee9ng\t minh\t r\u1eb1ng\t c\u00e1c\t \u0111\u1ecbnh\t l\u00fd\t c\u1ee7a h\u00ecnh\th\u1ecdc\tEuclid\ttr\u00ean\tm\u1ed9t\t\u0111\u0129a\tquay,\tv\u00e0\tdo\t\u0111\u00f3\tn\u00f3i\tchung\ttrong\tm\u1ed9t tr\u01b0\u1eddng\th\u1ea5p\td\u1eabn,\tkh\u00f4ng\tth\u1ec3\t\u0111\u00fang\tch\u00ednh\tx\u00e1c\tn\u1eefa,\t\u00edt\tra\tkhi\tng\u01b0\u1eddi\tta cho\t thanh\t \u0111o\t \u1edf\t m\u1ecdi\t v\u1ecb\t tr\u00ed\t v\u00e0\t m\u1ed7i\t h\u01b0\u1edbng\t \u0111\u1ed9\t d\u00e0i\t l\u00e0\t 1.\t Kh\u00e1i\t ni\u1ec7m \u0111\u01b0\u1eddng\tth\u1eb3ng\tc\u0169ng\tm\u1ea5t\t\u0111i\t\u00fd\tngh\u0129a\tc\u1ee7a\tn\u00f3.\tV\u00ec\tth\u1ebf\tch\u00fang\tta\tkh\u00f4ng c\u00f3\tkh\u1ea3\tn\u0103ng\t\u0111\u1ecbnh\tngh\u0129a\tm\u1ed9t\tc\u00e1ch\tch\u00ednh\tx\u00e1c\tc\u00e1c\tt\u1ecda\t\u0111\u1ed9\tx,\ty,\tz\t\u0111\u1ed1i v\u1edbi\t \u0111\u0129a\t quay\t theo\t ph\u01b0\u01a1ng\t ph\u00e1p\t \u0111\u00e3\t \u0111\u01b0\u1ee3c\t s\u1eed\t d\u1ee5ng\t trong\t thuy\u1ebft t\u01b0\u01a1ng\t \u0111\u1ed1i\t h\u1eb9p.\t V\u00e0\t bao\t l\u00e2u\t t\u1ecda\t \u0111\u1ed9\t v\u00e0\t th\u1eddi\t gian\t c\u1ee7a\t c\u00e1c\t s\u1ef1\t ki\u1ec7n kh\u00f4ng\t \u0111\u01b0\u1ee3c\t \u0111\u1ecbnh\t ngh\u0129a,\t c\u00e1c\t \u0111\u1ecbnh\t lu\u1eadt\t t\u1ef1\t nhi\u00ean\t trong\t \u0111\u00f3\t c\u00e1c\t t\u1ecda \u0111\u1ed9\tn\u00e0y\txu\u1ea5t\thi\u1ec7n,\tc\u0169ng\tkh\u00f4ng\tc\u00f3\t\u00fd\tngh\u0129a\tch\u00ednh\tx\u00e1c. Nh\u01b0\t v\u1eady,\t t\u1ea5t\t c\u1ea3\t nh\u1eefng\t suy\t ngh\u0129\t m\u00e0\t ch\u00fang\t ta\t \u0111\u00e3\t \u0111\u01b0a\t ra\t \u0111\u1ebfn nay\t v\u1ec1\t thuy\u1ebft\t t\u01b0\u01a1ng\t \u0111\u1ed1i\t r\u1ed9ng\t d\u01b0\u1eddng\t nh\u01b0\t \u0111\u00e3\t b\u1ecb\t \u0111\u1eb7t\t d\u1ea5u\t h\u1ecfi. Nh\u01b0ng\ts\u1ef1\tth\u1eadt,\tch\u00fang\tta\tc\u1ea7n\tm\u1ed9t\tcon\t\u0111\u01b0\u1eddng\tv\u00f2ng\ttinh\tt\u1ebf\th\u01a1n\t\u0111\u1ec3 \u00e1p\td\u1ee5ng\t\u0111\u01b0\u1ee3c\t\u0111\u1ecbnh\t\u0111\u1ec1\tc\u1ee7a\tthuy\u1ebft\tt\u01b0\u01a1ng\t\u0111\u1ed1i\tr\u1ed9ng\tm\u1ed9t\tc\u00e1ch\tch\u00ednh x\u00e1c.\t B\u1ea1n\t \u0111\u1ecdc\t s\u1ebd\t \u0111\u01b0\u1ee3c\t chu\u1ea9n\t b\u1ecb\t cho\t con\t \u0111\u01b0\u1eddng\t n\u00e0y\t b\u1eb1ng\t nh\u1eefng ch\u01b0\u01a1ng\tsau.","\u00a7\t24 Continum\tEuclid\tv\u00e0\tPhi-Euclid Tr\u01b0\u1edbc\t m\u1eb7t\t t\u00f4i\t l\u00e0\t b\u1ec1\t m\u1eb7t\t c\u1ee7a\t m\u1ed9t\t c\u00e1i\t b\u00e0n\t \u0111\u00e1\t c\u1ea9m\t th\u1ea1ch\t \u0111ang tr\u1ea3i\tra.\tT\u00f4i\tc\u00f3\tth\u1ec3\t\u0111i\tt\u1eeb\tm\u1ed9t\t\u0111i\u1ec3m\tb\u1ea5t\tk\u1ef3\tc\u1ee7a\tb\u1ec1\tm\u1eb7t\t\u0111\u1ebfn\tm\u1ed9t\t\u0111i\u1ec3m b\u1ea5t\t k\u1ef3\t kh\u00e1c\t c\u1ee7a\t n\u00f3,\t b\u1eb1ng\t c\u00e1ch\t \u0111i\t li\u00ean\t t\u1ee5c\t t\u1eeb\t m\u1ed9t\t \u0111i\u1ec3m\t \u0111\u1ebfn\t \u0111i\u1ec3m \\\"l\u00e1ng\tgi\u1ec1ng\\\",\tv\u00e0\tti\u1ebfp\tt\u1ee5c\t\u0111i\tv\u1edbi\tm\u1ed9t\ts\u1ed1\t(l\u1edbn)\tl\u1ea7n,\thay\tn\u00f3i\tm\u1ed9t\tc\u00e1ch kh\u00e1c,\tb\u1eb1ng\tc\u00e1ch\tt\u00f4i\t\u0111i\tt\u1eeb\t\u0111i\u1ec3m\tn\u00e0y\t\u0111\u1ebfn\t\u0111i\u1ec3m\tkh\u00e1c\tm\u00e0\tkh\u00f4ng\tph\u1ea3i l\u00e0m\t nh\u1eefng\t \\\"b\u01b0\u1edbc\t nh\u1ea3y\\\".\t T\u00f4i\t ch\u1eafc\t \u0111\u1ed9c\t gi\u1ea3\t \u0111\u1ee7\t hi\u1ec3u\t c\u00e1c\t t\u1eeb\t \\\"l\u00e1ng gi\u1ec1ng\\\"\t hay\t \\\"b\u01b0\u1edbc\t nh\u1ea3y\\\"\t (n\u1ebfu\t anh\t ta\t kh\u00f4ng\t qu\u00e1\t kh\u00f3\t t\u00ednh).\t \u0110i\u1ec1u n\u00e0y\t \u0111\u01b0\u1ee3c\t ch\u00fang\t ta\t bi\u1ec3u\t th\u1ecb\t b\u1eb1ng\t c\u00e1ch\t n\u00f3i\t r\u1eb1ng\t b\u1ec1\t m\u1eb7t\t l\u00e0\t m\u1ed9t continum. Ch\u00fang\tta\th\u00e3y\tt\u01b0\u1edfng\tt\u01b0\u1ee3ng\tm\u1ed9t\ts\u1ed1\tl\u01b0\u1ee3ng\tl\u1edbn\tque\tcon\tc\u00f3\t\u0111\u1ed9\td\u00e0i b\u1eb1ng\t nhau\t \u0111\u01b0\u1ee3c\t s\u1ea3n\t xu\u1ea5t,\t chi\u1ec1u\t d\u00e0i\t c\u1ee7a\t ch\u00fang\t r\u1ea5t\t nh\u1ecf\t so\t v\u1edbi k\u00edch\t th\u01b0\u1edbc\t c\u1ee7a\t m\u1eb7t\t b\u00e0n.\t N\u1ebfu\t t\u00f4i\t b\u1ea3o\t chi\u1ec1u\t d\u00e0i\t c\u1ee7a\t ch\u00fang\t b\u1eb1ng nhau,\t\u0111i\u1ec1u\t\u0111\u00f3\tc\u00f3\tngh\u0129a\tr\u1eb1ng\tc\u00e1c\t\u0111\u1ea7u\tc\u1ee7a\tm\u1ed7i\thai\tque\tch\u1ed3ng\tkh\u00edt \u0111\u01b0\u1ee3c\t l\u00ean\t nhau\t (khi\t ch\u00fang\t ch\u1eadp\t l\u00ean\t nhau).\t B\u00e2y\t gi\u1edd\t ch\u00fang\t ta\t \u0111\u1eb7t b\u1ed1n\t trong\t c\u00e1c\t que\t con\t n\u00e0y\t l\u00ean\t m\u1eb7t\t b\u00e0n\t c\u1ea9m\t th\u1ea1ch\t th\u1ebf\t n\u00e0o\t \u0111\u1ec3 ch\u00fang\t l\u00e0m\t th\u00e0nh\t m\u1ed9t\t h\u00ecnh\t t\u1ee9\t gi\u00e1c\t c\u00f3\t c\u00e1c\t \u0111\u01b0\u1eddng\t ch\u00e9o\t d\u00e0i\t b\u1eb1ng nhau\t (h\u00ecnh\t vu\u00f4ng).\t \u0110\u1ec3\t b\u1ea3o\t \u0111\u1ea3m\t \u0111\u1eb3ng\t th\u1ee9c\t c\u1ee7a\t \u0111\u01b0\u1eddng\t ch\u00e9o, ch\u00fang\t ta\t c\u00f3\t th\u1ec3\t s\u1eed\t d\u1ee5ng\t m\u1ed9t\t que\t th\u1eed.\t C\u1ea1nh\t h\u00ecnh\t vu\u00f4ng\t n\u00e0y ch\u00fang\tta\t\u0111\u1eb7t\tc\u00e1c\th\u00ecnh\tvu\u00f4ng\tt\u01b0\u01a1ng\tt\u1ef1\tkh\u00e1c,\tm\u1ed7i\tc\u00e1i\tc\u1ee7a\tch\u00fang\tc\u00f3 chung\t v\u1edbi\t n\u00f3\t m\u1ed9t\t que\t con.\t R\u1ed3i\t l\u00e0m\t nh\u01b0\t th\u1ebf\t \u0111\u1ed1i\t v\u1edbi\t c\u00e1c\t h\u00ecnh vu\u00f4ng\t m\u1edbi,\t v.v.\t cho\t \u0111\u1ebfn\t khi\t cu\u1ed1i\t c\u00f9ng\t c\u1ea3\t m\u1eb7t\t b\u00e0n\t s\u1ebd\t \u0111\u01b0\u1ee3c\t ph\u1ee7 b\u1edfi\t c\u00e1c\t h\u00ecnh\t vu\u00f4ng.\t V\u1edbi\t s\u1ef1\t s\u1eafp\t x\u1ebfp\t n\u00e0y,\t m\u1ed7i\t m\u1ed9t\t c\u1ea1nh\t h\u00ecnh vu\u00f4ng\tb\u00ean\ttrong\tthu\u1ed9c\tv\u1ec1\thai\th\u00ecnh\tvu\u00f4ng,\tv\u00e0\tm\u1ed7i\t(\u0111i\u1ec3m)\tg\u00f3c\tc\u1ee7a h\u00ecnh\tvu\u00f4ng\tb\u00ean\ttrong\tthu\u1ed9c\tv\u1ec1\tb\u1ed1n\th\u00ecnh\tvu\u00f4ng. Th\u1eadt\tl\u00e0\tm\u1ed9t\t\u0111i\u1ec1u\tng\u1ea1c\tnhi\u00ean\t\u0111\u00edch\tth\u1ef1c\tkhi\tng\u01b0\u1eddi\tta\tc\u00f3\tth\u1ec3\tth\u1ef1c hi\u1ec7n\t c\u00f4ng\t vi\u1ec7c\t n\u00e0y\t m\u00e0\t kh\u00f4ng\t g\u1eb7p\t ph\u1ea3i\t kh\u00f3\t kh\u0103n\t l\u1edbn\t nh\u1ea5t\t n\u00e0o! Ng\u01b0\u1eddi\t ta\t ch\u1ec9\t c\u1ea7n\t ngh\u0129\t \u0111\u1ebfn\t \u0111i\u1ec1u\t sau\t \u0111\u00e2y.\t N\u1ebfu\t c\u1ee9\t ba\t h\u00ecnh\t vu\u00f4ng g\u1eb7p\t nhau\t t\u1ea1i\t m\u1ed9t\t g\u00f3c,\t th\u00ec\t hai\t c\u1ea1nh\t c\u1ee7a\t h\u00ecnh\t vu\u00f4ng\t th\u1ee9\t t\u01b0\t \u0111\u00e3 \u0111\u01b0\u1ee3c\t\u0111\u1eb7t\txu\u1ed1ng,\tv\u00e0\tdo\t\u0111\u00f3\thai\tc\u1ea1nh\tc\u00f2n\tl\u1ea1i\t\u0111\u00e3\t\u0111\u01b0\u1ee3c\tx\u00e1c\t\u0111\u1ecbnh\tho\u00e0n to\u00e0n.\t T\u00f4i\t kh\u00f4ng\t th\u1ec3\t \u0111i\u1ec1u\t ch\u1ec9nh\t h\u00ecnh\t t\u1ee9\t gi\u00e1c\t n\u1eefa\t \u0111\u1ec3\t l\u00e0m\t cho\t hai \u0111\u01b0\u1eddng\t ch\u00e9o\t b\u1eb1ng\t nhau.\t Ch\u00fang\t \u0111\u00e3\t b\u1eb1ng\t nhau,\t b\u1edfi\t \u0111\u00f3\t l\u00e0\t m\u1ed9t\t \u0111\u1eb7c \u00e2n\t c\u1ee7a\t m\u1eb7t\t b\u00e0n\t v\u00e0\t c\u1ee7a\t c\u00e1c\t que\t con\t m\u00e0\t t\u00f4i\t ch\u1ec9\t bi\u1ebft\t ng\u1ea1c\t nhi\u00ean trong\t s\u1ef1\t c\u00e1m\t \u01a1n!\t Ch\u00fang\t ta\t s\u1ebd\t ng\u1ea1c\t nhi\u00ean\t nhi\u1ec1u\t l\u1ea7n\t nh\u01b0\t th\u1ebf\t khi ch\u1ee9ng\tki\u1ebfn\ts\u1ef1\tx\u00e2y\td\u1ef1ng\t\u0111\u1ec1u\tk\u1ebft\tth\u00fac\tth\u00e0nh\tc\u00f4ng\tt\u1ed1t\t\u0111\u1eb9p.","N\u1ebfu\t th\u1ef1c\t s\u1ef1\t m\u1ecdi\t vi\u1ec7c\t di\u1ec5n\t ra\t m\u1ed9t\t c\u00e1ch\t tr\u00f4i\t ch\u1ea3y,\t th\u00ec\t t\u00f4i\t n\u00f3i r\u1eb1ng\t c\u00e1c\t \u0111i\u1ec3m\t c\u1ee7a\t m\u1eb7t\t b\u00e0n\t h\u1ee3p\t th\u00e0nh\t m\u1ed9t\t continum\t Euclid\t \u0111\u1ed1i v\u1edbi\tc\u00e1c\tque\tcon\t\u0111\u01b0\u1ee3c\ts\u1eed\td\u1ee5ng\tnh\u01b0\t\\\"kho\u1ea3ng\tc\u00e1ch\\\".\tB\u1eb1ng\tc\u00e1ch\tch\u1ecdn m\u1ed9t\t g\u00f3c\t c\u1ee7a\t m\u1ed9t\t h\u00ecnh\t vu\u00f4ng\t l\u00e0m\t \\\"\u0111i\u1ec3m\t g\u1ed1c\\\"\t ,\t t\u00f4i\t c\u00f3\t th\u1ec3\t \u0111\u1eb7c tr\u01b0ng\t m\u1ed7i\t m\u1ed9t\t g\u00f3c\t h\u00ecnh\t vu\u00f4ng\t kh\u00e1c\t \u0111\u1ed1i\t v\u1edbi\t \u0111i\u1ec3m\t g\u1ed1c\t b\u1eb1ng\t hai con\t s\u1ed1\t .\t T\u00f4i\t ch\u1ec9\t c\u1ea7n\t cho\t bi\u1ebft,\t t\u00f4i\t ph\u1ea3i\t \u0111i\t t\u1eeb\t \u0111i\u1ec3m\t g\u1ed1c\t qua\t bao nhi\u00eau\tque\tcon\tv\u1ec1\tph\u00eda\t\\\"ph\u1ea3i\\\"\tv\u00e0\tk\u1ebf\t\u0111\u00f3\tqua\tbao\tnhi\u00eau\tque\tcon\tl\u00ean ph\u00eda\t\\\"tr\u00ean\\\",\t\u0111\u1ec3\t\u0111i\t\u0111\u1ebfn\tg\u00f3c\th\u00ecnh\tvu\u00f4ng\t\u0111\u00e3\tn\u00f3i.\tHai\ts\u1ed1\tn\u00e0y\tch\u00ednh\tl\u00e0 c\u00e1c\t \\\"t\u1ecda\t \u0111\u1ed9\t Descartes\\\"\t c\u1ee7a\t g\u00f3c\t \u0111ang\t n\u00f3i\t \u0111\u1ed1i\t v\u1edbi\t \\\"h\u1ec7\t t\u1ecda\t \u0111\u1ed9 Descartes\\\"\t \u0111\u01b0\u1ee3c\t x\u00e1c\t \u0111\u1ecbnh\t b\u1eb1ng\t s\u1ef1\t s\u1eafp\t x\u1ebfp\t c\u1ee7a\t c\u00e1c\t que\t con\t \u0111\u00e3 \u0111\u01b0\u1ee3c\tth\u1ef1c\thi\u1ec7n. Tuy\t nhi\u00ean\t c\u0169ng\t c\u00f3\t nh\u1eefng\t tr\u01b0\u1eddng\t h\u1ee3p\t th\u00ed\t nghi\u1ec7m\t kh\u00f4ng th\u00e0nh\t c\u00f4ng,\t nh\u01b0\t ch\u00fang\t ta\t nh\u1eadn\t th\u1ea5y\t \u1edf\t s\u1ef1\t bi\u1ebfn\t th\u1ec3\t nh\u01b0\t sau\t c\u1ee7a th\u00ed\tnghi\u1ec7m\t\u00fd\tt\u01b0\u1edfng.\tCh\u00fang\tta\tgi\u1ea3\tthi\u1ebft\tc\u00e1c\tque\tcon\t\\\"gi\u00e3n\tn\u1edf\\\"\tt\u1ef7\tl\u1ec7 theo\t\u0111\u1ed9\tt\u0103ng\tc\u1ee7a\tnhi\u1ec7t\t\u0111\u1ed9. M\u1eb7t\t b\u00e0n\t \u0111\u01b0\u1ee3c\t \u0111un\t n\u00f3ng\t l\u00ean\t \u1edf\t gi\u1eefa,\t nh\u01b0ng\t \u1edf\t v\u00f9ng\t bi\u00ean\t th\u00ec kh\u00f4ng,\tn\u01a1i\t\u0111\u00f3\thai\ttrong\tb\u1ed1n\tque\tcon\tch\u00fang\tta\tv\u1eabn\tc\u00f2n\tc\u00f3\tth\u1ec3\t\u0111\u1eb7t tr\u00f9ng\t l\u00ean\t nhau\t t\u1ea1i\t m\u1ed7i\t \u0111i\u1ec3m\t c\u1ee7a\t b\u00e0n.\t Nh\u01b0ng\t vi\u1ec7c\t x\u00e2y\t d\u1ef1ng\t c\u00e1c h\u00ecnh\t vu\u00f4ng\t c\u1ee7a\t ch\u00fang\t ta\t \u1eaft\t ph\u1ea3i\t ch\u1ecbu\t s\u1ef1\t x\u00e1o\t tr\u1ed9n\t trong\t qu\u00e1 tr\u00ecnh\t\u0111un\tn\u00f3ng,\tb\u1edfi\tc\u00e1c\tque\tcon\tc\u1ee7a\tph\u1ea7n\ttrong\tm\u1eb7t\tb\u00e0n\tb\u1ecb\tgi\u00e3n n\u1edf,\tc\u00e1c\tque\tcon\tc\u1ee7a\tph\u1ea7n\tngo\u00e0i\tth\u00ec\tkh\u00f4ng. \u0110\u1ed1i\t v\u1edbi\t c\u00e1c\t que\t con\t c\u1ee7a\t ch\u00fang\t ta\t -\t \u0111\u01b0\u1ee3c\t \u0111\u1ecbnh\t ngh\u0129a\t nh\u01b0\t c\u00e1c kho\u1ea3ng\tc\u00e1ch\t\u0111\u01a1n\tv\u1ecb\t-\tth\u00ec\tm\u1eb7t\tb\u00e0n\tb\u00e2y\tgi\u1edd\tkh\u00f4ng\tc\u00f2n\tl\u00e0\tcontinum Euclid\tn\u1eefa,\tv\u00e0\tch\u00fang\tta\tc\u0169ng\tkh\u00f4ng\tc\u00f2n\tkh\u1ea3\tn\u0103ng\t\u0111\u1ecbnh\tngh\u0129a\tt\u1ecda \u0111\u1ed9\tDescartes\ttr\u1ef1c\tti\u1ebfp\tv\u1edbi\ts\u1ef1\tgi\u00fap\t\u0111\u1ee1\tc\u1ee7a\tch\u00fang\t\u0111\u01b0\u1ee3c,\tb\u1edfi\ts\u1ef1\tx\u00e2y d\u1ef1ng\t n\u00f3i\t tr\u00ean\t kh\u00f4ng\t th\u1ec3\t th\u1ef1c\t hi\u1ec7n\t \u0111\u01b0\u1ee3c\t n\u1eefa.\t Nh\u01b0ng\t c\u0169ng\t c\u00f3 nh\u1eefng\t v\u1eadt\t kh\u00e1c\t kh\u00f4ng\t b\u1ecb\t \u1ea3nh\t h\u01b0\u1edfng\t b\u1edfi\t nhi\u1ec7t\t \u0111\u1ed9\t c\u1ee7a\t b\u00e0n\t m\u1ed9t c\u00e1ch\t t\u01b0\u01a1ng\t t\u1ef1\t nh\u01b0\t c\u00e1c\t que\t con\t (ho\u1eb7c\t kh\u00f4ng\t h\u1ec1\t b\u1ecb\t \u1ea3nh\t h\u01b0\u1edfng ch\u00fat\t n\u00e0o),\t n\u00ean,\t m\u1ed9t\t c\u00e1ch\t t\u1ef1\t nhi\u00ean,\t ta\t c\u00f3\t th\u1ec3\t v\u1eabn\t gi\u1eef\t quan\t \u0111i\u1ec3m, r\u1eb1ng\t m\u1eb7t\t b\u00e0n\t l\u00e0\t m\u1ed9t\t \\\"continum\t Euclid\\\";\t \u0111i\u1ec1u\t n\u00e0y\t c\u00f3\t th\u1ec3\t \u0111\u01b0\u1ee3c th\u1ef1c\thi\u1ec7n\tm\u1ed9t\tc\u00e1ch\tth\u1ecfa\t\u0111\u00e1ng\tb\u1eb1ng\tm\u1ed9t\tquy\t\u0111\u1ecbnh\ttinh\tt\u1ebf\th\u01a1n\tv\u1ec1 \u0111o\t\u0111\u1ea1c\thay\tso\ts\u00e1nh\tc\u00e1c\tkho\u1ea3ng\tc\u00e1ch. Nh\u01b0ng\t n\u1ebfu\t c\u00e1c\t que\t c\u1ee7a\t t\u1ea5t\t c\u1ea3\t m\u1ecdi\t lo\u1ea1i\t (ngh\u0129a\t l\u00e0\t m\u1ecdi\t lo\u1ea1i\t v\u1eadt ch\u1ea5t)\tv\u1eadn\th\u00e0nh\tc\u00f9ng\tm\u1ed9t\tc\u00e1ch\tnh\u1ea1y\tc\u1ea3m\t\u0111\u1ed1i\tv\u1edbi\tnhi\u1ec7t\t\u0111\u1ed9\ttr\u00ean\tm\u1eb7t b\u00e0n\t \u0111\u01b0\u1ee3c\t \u0111i\u1ec1u\t ch\u1ec9nh\t kh\u00e1c\t nhau,\t v\u00e0\t n\u1ebfu\t ch\u00fang\t ta\t kh\u00f4ng\t c\u00f3 ph\u01b0\u01a1ng\tti\u1ec7n\tn\u00e0o\tkh\u00e1c\t\u0111\u1ec3\tph\u00e1t\thi\u1ec7n\tt\u00e1c\td\u1ee5ng\tc\u1ee7a\tnhi\u1ec7t\t\u0111\u1ed9\th\u01a1n\tl\u00e0 s\u1ef1\t v\u1eadn\t h\u00e0nh\t h\u00ecnh\t h\u1ecdc\t c\u1ee7a\t c\u00e1c\t que\t con\t trong\t c\u00e1c\t th\u00ed\t nghi\u1ec7m","t\u01b0\u01a1ng\tt\u1ef1\tv\u1edbi\tth\u00ed\tnghi\u1ec7m\t\u0111\u00e3\t\u0111\u01b0\u1ee3c\tm\u00f4\tt\u1ea3\ttr\u00ean,\tth\u00ec\tc\u00f3\tl\u1ebd\tt\u1ed1t\th\u01a1n\tn\u1ebfu ch\u00fang\t ta\t quy\t \u0111\u1ecbnh\t kho\u1ea3ng\t c\u00e1ch\t c\u1ee7a\t hai\t \u0111i\u1ec3m\t tr\u00ean\t b\u00e0n\t l\u00e0\t 1,\t n\u1ebfu hai\t \u0111\u1ea7u\t c\u1ee7a\t m\u1ed9t\t trong\t c\u00e1c\t que\t con\t ch\u00fang\t ta\t c\u00f3\t th\u1ec3\t \u0111\u01b0\u1ee3c\t \u0111\u1eb7t tr\u00f9ng\t l\u00ean\t ch\u00fang;\t v\u00ec\t l\u00e0m\t sao\t ch\u00fang\t ta\t \u0111\u1ecbnh\t ngh\u0129a\t \u0111\u01b0\u1ee3c\t kho\u1ea3ng c\u00e1ch\tn\u1ebfu\tkh\u00f4ng\tb\u1eb1ng\tm\u1ed9t\ts\u1ef1\tt\u00f9y\tti\u1ec7n\tth\u00f4\tthi\u1ec3n\tnh\u01b0\tth\u1ebf?\tNh\u01b0ng nh\u01b0\tv\u1eady\tth\u00ec\tph\u01b0\u01a1ng\tph\u00e1p\tt\u1ecda\t\u0111\u1ed9\tDescartes\tph\u1ea3i\tb\u1ecb\tt\u1eeb\tb\u1ecf,\tv\u00e0\t\u0111\u01b0\u1ee3c thay\t th\u1ebf\t b\u1eb1ng\t m\u1ed9t\t ph\u01b0\u01a1ng\t ph\u00e1p\t kh\u00e1c\t kh\u00f4ng\t gi\u1ea3\t thi\u1ebft\t t\u00ednh\t hi\u1ec7u l\u1ef1c\t c\u1ee7a\t h\u00ecnh\t h\u1ecdc\t Euclid\t cho\t c\u00e1c\t v\u1eadt\t th\u1ec3\t r\u1eafn.[58]\t B\u1ea1n\t \u0111\u1ecdc\t nh\u1eadn\t ra r\u1eb1ng,\tt\u00ecnh\thu\u1ed1ng\t\u0111\u01b0\u1ee3c\tm\u00f4\tt\u1ea3\t\u1edf\t\u0111\u00e2y\tt\u01b0\u01a1ng\t\u1ee9ng\tv\u1edbi\tt\u00ecnh\thu\u1ed1ng\tn\u1ea3y sinh\tra\tb\u1edfi\t\u0111\u1ecbnh\t\u0111\u1ec1\tt\u01b0\u01a1ng\t\u0111\u1ed1i\tr\u1ed9ng\t(\u00a7\t23).","\u00a7\t25 T\u1ecda\t\u0110\u1ed9\tGauss Theo\tGauss,\tc\u00e1ch\tx\u1eed\tl\u00fd\tk\u1ebft\th\u1ee3p\th\u00ecnh\th\u1ecdc\tv\u00e0\tgi\u1ea3i\tt\u00edch\t\u0111\u1ed1i\tv\u1edbi\tb\u00e0i to\u00e1n\t \u0111\u1eb7t\t ra\t c\u00f3\t th\u1ec3\t \u0111\u1ea1t\t \u0111\u01b0\u1ee3c\t b\u1eb1ng\t c\u00e1ch\t th\u1ee9c\t nh\u01b0\t sau.\t Ch\u00fang\t ta t\u01b0\u1edfng\tt\u01b0\u1ee3ng\tc\u00f3\tm\u1ed9t\th\u1ec7\tth\u1ed1ng\tc\u00e1c\t\u0111\u01b0\u1eddng\tcong\tb\u1ea5t\tk\u1ef3\t(xem\t\u1ea2nh\t3) \u0111\u01b0\u1ee3c\tv\u1ebd\tl\u00ean\tm\u1eb7t\tb\u00e0n\tm\u00e0\tch\u00fang\tta\tg\u1ecdi\tl\u00e0\tnh\u1eefng\t\u0111\u01b0\u1eddng\tcong\tu,\tv\u00e0 \u0111\u01b0\u1ee3c\tt\u01b0\u1ee3ng\ttr\u01b0ng\tb\u1eb1ng\tm\u1ed9t\tcon\ts\u1ed1\tcho\tm\u1ed7i\tc\u00e1i. \u1ea2nh\t3 Trong\t \u1ea3nh\t nh\u1eefng\t \u0111\u01b0\u1eddng\t cong\t u\t =\t 1,\t u\t =\t 2,\t u\t =\t 3\t \u0111\u01b0\u1ee3c\t v\u1ebd\t l\u00ean. M\u1eb7t\tkh\u00e1c\th\u00e3y\tt\u01b0\u1edfng\tt\u01b0\u1ee3ng\tgi\u1eefa\thai\t\u0111\u01b0\u1eddng\tu\t=\t1\tv\u00e0\tu\t=\t2\tc\u00f3\tv\u00f4\ts\u1ed1 \u0111\u01b0\u1eddng\t cong\t \u0111\u01b0\u1ee3c\t v\u1ebd\t l\u00ean,\t ch\u00fang\t t\u01b0\u01a1ng\t \u1ee9ng\t v\u1edbi\t t\u1ea5t\t c\u1ea3\t c\u00e1c\t s\u1ed1\t th\u1ef1c n\u1eb1m\t gi\u1eefa\t 1\t v\u00e0\t 2.\t Nh\u01b0\t v\u1eady\t ch\u00fang\t ta\t c\u00f3\t m\u1ed9t\t h\u1ec7\t th\u1ed1ng\t c\u00e1c\t \u0111\u01b0\u1eddng cong\t u\t v\u00f4\t c\u00f9ng\t d\u00e0y\t \u0111\u1eb7c\t bao\t ph\u1ee7\t m\u1eb7t\t b\u00e0n.\t Kh\u00f4ng\t \u0111\u01b0\u1eddng\t u\t n\u00e0o \u0111\u01b0\u1ee3c\tph\u00e9p\tc\u1eaft\t\u0111\u01b0\u1eddng\tu\tkh\u00e1c,\tv\u00e0\tqua\tm\u1ed7i\t\u0111i\u1ec3m\tc\u1ee7a\tm\u1eb7t\tb\u00e0n\tch\u1ec9\tc\u00f3 m\u1ed9t\t\u0111\u01b0\u1eddng\tu\t\u0111\u01b0\u1ee3c\tph\u00e9p\t\u0111i\tqua\tth\u00f4i.\tM\u1ed7i\t\u0111i\u1ec3m\tc\u1ee7a\tb\u1ec1\tm\u1eb7t\tc\u1ee7a\tb\u00e0n do\t \u0111\u00f3\t t\u01b0\u01a1ng\t \u1ee9ng\t v\u1edbi\t m\u1ed9t\t tr\u1ecb\t s\u1ed1\t u\t ho\u00e0n\t to\u00e0n\t nh\u1ea5t\t \u0111\u1ecbnh.\t M\u1ed9t\t c\u00e1ch t\u01b0\u01a1ng\tt\u1ef1,\tch\u00fang\tta\tt\u01b0\u1edfng\tt\u01b0\u1ee3ng\tm\u1ed9t\th\u1ec7\tth\u1ed1ng\tc\u00e1c\t\u0111\u01b0\u1eddng\tcong\tv; \u0111\u01b0\u1ee3c\tv\u1ebd\tl\u00ean\tb\u1ec1\tm\u1eb7t,\tth\u1ecfa\tm\u00e3n\tc\u00f9ng\tnh\u1eefng\t\u0111i\u1ec1u\tki\u1ec7n\tnh\u01b0\tnh\u1eefng \u0111\u01b0\u1eddng\t cong\t u,\t \u0111\u01b0\u1ee3c\t \u0111\u00e1nh\t d\u1ea5u\t b\u1eb1ng\t c\u00e1c\t s\u1ed1\t m\u1ed9t\t c\u00e1ch\t t\u01b0\u01a1ng\t t\u1ef1,","nh\u01b0ng\t c\u0169ng\t c\u00f3\t d\u1ea1ng\t b\u1ea5t\t k\u1ef3.\t M\u1ed7i\t \u0111i\u1ec3m\t c\u1ee7a\t m\u1eb7t\t b\u00e0n\t nh\u01b0\t v\u1eady\t s\u1ebd t\u01b0\u01a1ng\t\u1ee9ng\tm\u1ed9t\ttr\u1ecb\ts\u1ed1\tv\tv\u00e0\tm\u1ed9t\ttr\u1ecb\ts\u1ed1\tv,\tv\u00e0\tch\u00fang\tta\tg\u1ecdi\thai\ts\u1ed1\tn\u00e0y l\u00e0\tt\u1ecda\t\u0111\u1ed9\tc\u1ee7a\tm\u1eb7t\tb\u00e0n\t(t\u1ecda\t\u0111\u1ed9\tGauss)\t.\t\u0110i\u1ec3m\tP\ttrong\th\u00ecnh\tv\u1ebd\tch\u1eb3ng h\u1ea1n\t c\u00f3\t t\u1ecda\t \u0111\u1ed9\t u\t =\t 3\t v\u00e0\t v\t =\t 1.\t Hai\t \u0111i\u1ec3m\t l\u00e2n\t c\u1eadn\t P\t v\u00e0\t P\u2019\t t\u01b0\u01a1ng\t \u1ee9ng v\u1edbi\tc\u00e1c\tt\u1ecda\t\u0111\u1ed9 P:\tu,\tv P\u2019:\tu\t+\tdu,\tv\t+\tdv trong\t \u0111\u00f3\t du\t v\u00e0\t dv\t c\u00f3\t ngh\u0129a\t l\u00e0\t nh\u1eefng\t s\u1ed1\t r\u1ea5t\t nh\u1ecf.\t M\u1ed9t\t c\u00e1ch t\u01b0\u01a1ng\tt\u1ef1,\tkho\u1ea3ng\tc\u00e1ch\t\u0111o\t\u0111\u01b0\u1ee3c\tv\u1edbi\tm\u1ed9t\tque\tcon\tc\u1ee7a\tP\tv\u00e0\tP'\tc\u0169ng l\u00e0\tm\u1ed9t\ts\u1ed1\tr\u1ea5t\tnh\u1ecf\tds.\tL\u00fac\t\u0111\u00f3\ttheo\tGauss\tch\u00fang\tta\tc\u00f3: ds\t2\t=\tg11du\t2\t+\t2g12dudv\t+\tg22\tdv\t2 trong\t\u0111\u00f3\tg11,\tgl2,\tg\t22\tl\u00e0\tnh\u1eefng\t\u0111\u1ea1i\tl\u01b0\u1ee3ng\tt\u00f9y\tthu\u1ed9c\tm\u1ed9t\tc\u00e1ch nh\u1ea5t\t\u0111\u1ecbnh\tv\u00e0o\tu\tv\u00e0\tv.\tC\u00e1c\t\u0111\u1ea1i\tl\u01b0\u1ee3ng\tg11,\tgl2\tv\u00e0\tg22\tx\u00e1c\t\u0111\u1ecbnh\tquan h\u1ec7\t c\u1ee7a\t c\u00e1c\t que\t \u0111o\t \u0111\u1ed1i\t v\u1edbi\t c\u00e1c\t \u0111\u01b0\u1eddng\t u\t v\u00e0\t \u0111\u01b0\u1eddng\t v,\t ngh\u0129a\t l\u00e0\t c\u0169ng \u0111\u1ed1i\t v\u1edbi\t b\u1ec1\t m\u1eb7t\t c\u1ee7a\t b\u00e0n.\t Trong\t tr\u01b0\u1eddng\t h\u1ee3p\t c\u00e1c\t \u0111i\u1ec3m\t c\u1ee7a\t b\u1ec1\t m\u1eb7t \u0111\u01b0\u1ee3c\txem\tx\u00e9t\tt\u1ea1o\tth\u00e0nh\tm\u1ed9t\tcontinum\tEuclid\t\u0111\u1ed1i\tv\u1edbi\tc\u00e1c\tque\t\u0111o con,\t v\u00e0\t c\u0169ng\t ch\u1ec9\t khi\t \u0111\u00f3,\t th\u00ec\t c\u00e1c\t \u0111\u01b0\u1eddng\t u\t v\u00e0\t \u0111\u01b0\u1eddng\t v\t c\u00f3\t th\u1ec3\t \u0111\u01b0\u1ee3c v\u1ebd\tv\u00e0\t\u0111\u01b0\u1ee3c\tmang\tc\u00e1c\ts\u1ed1\tsao\tcho\tch\u00fang\tta\tc\u00f3\tm\u1ed9t\tc\u00e1ch\t\u0111\u01a1n\tgi\u1ea3n ds\t2\t=\tdu\t2\t+\tdv\t2 L\u00fac\t \u0111\u00f3\t c\u00e1c\t \u0111\u01b0\u1eddng\t u\t v\u00e0\t \u0111\u01b0\u1eddng\t v\t l\u00e0\t nh\u1eefng\t \u0111\u01b0\u1eddng\t th\u1eb3ng\t theo ngh\u0129a\t c\u1ee7a\t h\u00ecnh\t h\u1ecdc\t Euclid,\t v\u00e0\t ch\u00fang\t th\u1eb3ng\t g\u00f3c\t nhau.\t \u1ede\t \u0111\u00e2y\t t\u1ecda \u0111\u1ed9\t Gauss\t \u0111\u01a1n\t gi\u1ea3n\t l\u00e0\t t\u1ecda\t \u0111\u1ed9\t Descartes.\t Ch\u00fang\t ta\t th\u1ea5y\t t\u1ecda\t \u0111\u1ed9 Gauss\t kh\u00f4ng\t g\u00ec\t kh\u00e1c\t h\u01a1n\t l\u00e0\t m\u1ed9t\t ph\u00e9p\t t\u01b0\u01a1ng\t \u1ee9ng\t c\u1ee7a\t c\u1ee9\t hai\t s\u1ed1 th\u00e0nh\t m\u1ed9t\t \u0111i\u1ec3m\t c\u1ee7a\t b\u1ec1\t m\u1eb7t\t \u0111ang\t xem\t x\u00e9t,\t sao\t cho\t c\u00e1c\t \u0111i\u1ec3m\t l\u00e2n c\u1eadn\t trong\t kh\u00f4ng\t gian\t t\u01b0\u01a1ng\t \u1ee9ng\t v\u1edbi\t nh\u1eefng\t tr\u1ecb\t s\u1ed1\t kh\u00e1c\t nhau\t r\u1ea5t \u00edt. Nh\u1eefng\t suy\t ngh\u0129\t n\u00e0y\t \u0111\u1ebfn\t nay\t \u0111\u00fang\t cho\t m\u1ed9t\t continum\t hai chi\u1ec1u.\t Nh\u01b0ng\t ph\u01b0\u01a1ng\t ph\u00e1p\t Gauss\t c\u0169ng\t \u00e1p\t d\u1ee5ng\t \u0111\u01b0\u1ee3c\t cho\t m\u1ed9t continum\t ba,\t b\u1ed1n,\t hay\t nhi\u1ec1u\t chi\u1ec1u.\t Ch\u1eb3ng\t h\u1ea1n\t v\u1edbi\t m\u1ed9t continum\tb\u1ed1n\tchi\u1ec1u,\tth\u00ec\tch\u00fang\tta\tc\u00f3\tth\u1ec3\tbi\u1ec3u\tth\u1ecb\tn\u00f3\tnh\u01b0\tsau.\tV\u1edbi m\u1ed7i\t\u0111i\u1ec3m\tc\u1ee7a\tcontinum\tch\u00fang\tta\tl\u00e0m\tt\u01b0\u01a1ng\t\u1ee9ng\tm\u1ed9t\tc\u00e1ch\tb\u1ea5t\tk\u1ef3 b\u1ed1n\ts\u1ed1\tx1,\tx2,\tx3\tv\u00e0\tx4\tm\u00e0\tch\u00fang\tta\tg\u1ecdi\tl\u00e0\t\\\"t\u1ecda\t\u0111\u1ed9\\\".\tC\u00e1c\t\u0111i\u1ec3m\tl\u00e2n c\u1eadn\tt\u01b0\u01a1ng\t\u1ee9ng\tv\u1edbi\tc\u00e1c\ttr\u1ecb\ts\u1ed1\tt\u1ecda\t\u0111\u1ed9\tl\u00e2n\tc\u1eadn.\tN\u1ebfu\thai\t\u0111i\u1ec3m\tl\u00e2n\tc\u1eadn P\tv\u00e0\tP\t\u2019\tt\u01b0\u01a1ng\t\u1ee9ng\tv\u1edbi\tm\u1ed9t\tkho\u1ea3ng\tc\u00e1ch\tds\tc\u00f3\tth\u1ec3\t\u0111o\t\u0111\u1ea1c\tv\u00e0\t\u0111\u01b0\u1ee3c","\u0111\u1ecbnh\tngh\u0129a\tr\u00f5\tv\u1ec1\tquan\t\u0111i\u1ec3m\tv\u1eadt\tl\u00fd,\tth\u00ec\tc\u00f4ng\tth\u1ee9c\tsau\t\u0111\u00e2y\ts\u1ebd\t\u0111\u00fang ds\t2\t=\tg11dx\t2\t+\t2g12dx1x\t2\t+...\t+\tg44dx4\t2 trong\t \u0111\u00f3\t c\u00e1c\t \u0111\u1ea1i\t l\u01b0\u1ee3ng\t g11,\t v.v.\t c\u00f3\t c\u00e1c\t tr\u1ecb\t s\u1ed1\t c\u00f3\t th\u1ec3\t bi\u1ebfn\t thi\u00ean theo\t v\u1ecb\t tr\u00ed\t trong\t continum.\t Ch\u1ec9\t trong\t tr\u01b0\u1eddng\t h\u1ee3p\t continum\t l\u00e0 m\u1ed9t\tcontinum\tEuclid,\tch\u00fang\tta\tc\u00f3\tth\u1ec3\tch\u1ecdn\tc\u00e1c\tt\u1ecda\t\u0111\u1ed9\tx1,\tx2,\tx3, x4\t t\u01b0\u01a1ng\t \u1ee9ng\t v\u1edbi\t c\u00e1c\t \u0111i\u1ec3m\t c\u1ee7a\t continum\t \u0111\u1ec3\t c\u00f3\t m\u1ed9t\t c\u00e1ch\t \u0111\u01a1n gi\u1ea3n ds\t2\t=\tdx\t2\t+\tdx2\t2\t+\tdx3\t2\t+\tdx4\t2 L\u00fac\t\u0111\u00f3\tc\u00e1c\tquan\th\u1ec7\ttrong\tcontinum\tb\u1ed1n\tchi\u1ec1u\tc\u0169ng\t\u0111\u00fang\tm\u1ed9t c\u00e1ch\t t\u01b0\u01a1ng\t t\u1ef1\t nh\u01b0\t c\u00e1c\t quan\t h\u1ec7\t \u0111\u00fang\t trong\t c\u00e1c\t ph\u00e9p\t \u0111o\t \u0111\u1ea1c\t ba chi\u1ec1u. Ph\u00e9p\tbi\u1ec3u\tth\u1ecb\tGauss\tcho\tds\t2\tch\u00fang\tta\tv\u1eeba\tth\u1ea5y\tth\u1ef1c\tra\tkh\u00f4ng ph\u1ea3i\t lu\u00f4n\t lu\u00f4n\t c\u00f3\t th\u1ec3\t th\u1ef1c\t hi\u1ec7n\t \u0111\u01b0\u1ee3c,\t m\u00e0\t ch\u1ec9\t c\u00f3\t th\u1ec3\t \u0111\u01b0\u1ee3c\t trong tr\u01b0\u1eddng\th\u1ee3p\tkhi\tcontinum\txem\tx\u00e9t\tc\u00f3\tt\u00ednh\tch\u1ea5t\tc\u00e1c\tmi\u1ec1n\t\u0111\u1ee7\tnh\u1ecf c\u1ee7a\tn\u00f3\tc\u00f3\tth\u1ec3\t\u0111\u01b0\u1ee3c\txem\tnh\u01b0\tnh\u1eefng\tcontinum\tEuclid.\t\u0110i\u1ec1u\t\u0111\u00f3\tr\u00f5 r\u00e0ng\t \u0111\u00fang\t trong\t tr\u01b0\u1eddng\t h\u1ee3p\t c\u1ee7a\t m\u1eb7t\t b\u00e0n\t c\u1ea9m\t th\u1ea1ch\t v\u00e0\t s\u1ef1\t bi\u1ebfn thi\u00ean\t c\u1ee5c\t b\u1ed9\t c\u1ee7a\t nhi\u1ec7t\t \u0111\u1ed9.\t B\u1edfi\t v\u00ec\t \u0111\u1ed1i\t v\u1edbi\t m\u1ed9t\t ph\u1ea7n\t nh\u1ecf\t c\u1ee7a\t b\u00e0n, nhi\u1ec7t\t \u0111\u1ed9\t \u0111\u01b0\u1ee3c\t xem\t nh\u01b0\t h\u1eb1ng\t s\u1ed1\t ,\t s\u1ef1\t v\u1eadn\t h\u00e0nh\t h\u00ecnh\t h\u1ecdc\t c\u1ee7a\t c\u00e1c que\t nh\u1ecf\t h\u1ea7u\t nh\u01b0\t l\u00e0\t s\u1ef1\t v\u1eadn\t h\u00e0nh\t theo\t c\u00e1c\t quy\t lu\u1eadt\t c\u1ee7a\t h\u00ecnh\t h\u1ecdc Euclid.\t C\u00e1c\t s\u1ef1\t b\u1ea5t\t nh\u1ea5t\t trong\t vi\u1ec7c\t x\u00e2y\t d\u1ef1ng\t h\u00ecnh\t vu\u00f4ng\t c\u1ee7a ch\u01b0\u01a1ng\ttr\u01b0\u1edbc\tch\u1ec9\thi\u1ec7n\tra,\tkhi\tvi\u1ec7c\tx\u00e2y\td\u1ef1ng\t\u0111\u01b0\u1ee3c\tn\u1edbi\tr\u1ed9ng\tra\tcho m\u1ed9t\tph\u1ea7n\t\u0111\u00e1ng\tk\u1ec3\tc\u1ee7a\tm\u1eb7t\tb\u00e0n. T\u00f3m\t t\u1eaft\t l\u1ea1i,\t ch\u00fang\t ta\t c\u00f3\t th\u1ec3\t n\u00f3i\t r\u1eb1ng:\t Gauss\t \u0111\u00e3\t ph\u00e1t\t minh\t ra m\u1ed9t\t ph\u01b0\u01a1ng\t ph\u00e1p\t cho\t vi\u1ec7c\t x\u1eed\t l\u00fd\t to\u00e1n\t h\u1ecdc\t c\u00e1c\t continum\t t\u1ed5ng qu\u00e1t,\ttrong\t\u0111\u00f3\tc\u00e1c\t\\\"quan\th\u1ec7\t\u0111\u1ed9\tl\u1edbn\\\"\t(\\\"kho\u1ea3ng\tc\u00e1ch\\\"\tc\u1ee7a\tc\u00e1c\t\u0111i\u1ec3m l\u00e2n\tc\u1eadn)\t\u0111\u01b0\u1ee3c\t\u0111\u1ecbnh\tngh\u0129a.\tM\u1ed7i\t\u0111i\u1ec3m\tc\u1ee7a\tcontinum\tt\u01b0\u01a1ng\t\u1ee9ng\tv\u1edbi nhi\u1ec1u\t s\u1ed1\t (t\u1ecda\t \u0111\u1ed9\t Gauss)\t nh\u01b0\t s\u1ed1\t chi\u1ec1u\t c\u1ee7a\t continum.\t Ph\u00e9p\t t\u01b0\u01a1ng \u1ee9ng\t n\u00e0y\t \u0111\u01b0\u1ee3c\t th\u1ef1c\t hi\u1ec7n\t sao\t cho\t t\u00ednh\t duy\t nh\u1ea5t\t c\u1ee7a\t n\u00f3\t \u0111\u01b0\u1ee3c\t b\u1ea3o \u0111\u1ea3m,\t v\u00e0\t t\u01b0\u01a1ng\t \u1ee9ng\t v\u1edbi\t nh\u1eefng\t \u0111i\u1ec3m\t l\u00e2n\t c\u1eadn\t l\u00e0\t nh\u1eefng\t s\u1ed1\t kh\u00e1c nhau\tv\u00f4\tc\u00f9ng\tnh\u1ecf.\tH\u1ec7\tt\u1ecda\t\u0111\u1ed9\tGauss\tl\u00e0\tm\u1ed9t\ts\u1ef1\tt\u1ed5ng\tqu\u00e1t\th\u00f3a\tl\u00f4g\u00edc c\u1ee7a\th\u1ec7\tt\u1ecda\t\u0111\u1ed9\tDescartes.\tN\u00f3\tc\u0169ng\t\u0111\u01b0\u1ee3c\t\u00e1p\td\u1ee5ng\tl\u00ean\tc\u00e1c\tcontinum phi-Euclid,\tnh\u01b0ng\tch\u1ec9\tc\u00f3\tth\u1ec3\t\u0111\u01b0\u1ee3c\tkhi\t\u0111\u1ed1i\tv\u1edbi\t\u0111\u1ed9\t\u0111o\t\u0111\u00e3\t\u0111\u01b0\u1ee3c\t\u0111\u1ecbnh ngh\u0129a\t (\\\"kho\u1ea3ng\t c\u00e1ch\\\"),\t c\u00e1c\t ph\u1ea7n\t nh\u1ecf\t c\u1ee7a\t continum\t v\u1eadn\t h\u00e0nh c\u00e0ng\t gi\u1ed1ng\t Euclid\t -\t v\u1edbi\t s\u1ef1\t x\u1ea5p\t x\u1ec9\t c\u00e0ng\t l\u1edbn\t -\t n\u1ebfu\t ph\u1ea7n\t \u0111\u01b0\u1ee3c\t xem x\u00e9t\tc\u1ee7a\tcontinum\tc\u00e0ng\tnh\u1ecf.","","\u00a7\t26 Continum\tKh\u00f4ng-th\u1eddi-gian\tc\u1ee7a\tThuy\u1ebft\tT\u01b0\u01a1ng\t\u0110\u1ed1i\tH\u1eb9p\tL\u00e0\tEuclid Gi\u1edd\t \u0111\u00e2y\t ch\u00fang\t ta\t c\u00f3\t \u0111\u1ea7y\t \u0111\u1ee7\t \u0111i\u1ec1u\t ki\u1ec7n\t \u0111\u1ec3\t bi\u1ec3u\t th\u1ecb\t m\u1ed9t\t c\u00e1ch ch\u00ednh\t x\u00e1c\t h\u01a1n\t \u00fd\t t\u01b0\u1edfng\t c\u1ee7a\t Minkowski\t \u0111\u00e3\t \u0111\u01b0\u1ee3c\t ph\u00e1c\t h\u1ecda\t trong\t \u00a7 17.\tTheo\tthuy\u1ebft\tt\u01b0\u01a1ng\t\u0111\u1ed1i\th\u1eb9p,\t\u0111\u1ec3\tbi\u1ec3u\tth\u1ecb\tcontinum\tkh\u00f4ng-th\u1eddi- gian\t b\u1ed1n\t chi\u1ec1u,\t m\u1ed9t\t s\u1ed1\t h\u1ec7\t t\u1ecda\t \u0111\u1ed9\t nh\u1ea5t\t \u0111\u1ecbnh\t \u0111\u01b0\u1ee3c\t \u01b0u\t \u0111\u00e3i\t m\u00e0 ch\u00fang\tta\t\u0111\u00e3\tg\u1ecdi\tl\u00e0\t\\\"h\u1ec7\tt\u1ecda\t\u0111\u1ed9\tGalilei\\\".\t\u0110\u1ed1i\tv\u1edbi\th\u1ec7\tn\u00e0y,\tch\u00fang\tta\tc\u00f3 b\u1ed1n\tt\u1ecda\t\u0111\u1ed9\tx,\ty,\tz,\tt\t\u0111\u00e3\t\u0111\u01b0\u1ee3c\tx\u00e1c\t\u0111\u1ecbnh\tv\u1ec1\tv\u1eadt\tl\u00fd\tm\u1ed9t\tc\u00e1ch\t\u0111\u01a1n\tgi\u1ea3n; ch\u00fang\tx\u00e1c\t\u0111\u1ecbnh\tm\u1ed9t\ts\u1ef1\tki\u1ec7n\t-\thay\tn\u00f3i\tm\u1ed9t\tc\u00e1ch\tkh\u00e1c\t-\tm\u1ed9t\t\u0111i\u1ec3m c\u1ee7a\t continum\t b\u1ed1n\t chi\u1ec1u,\t nh\u01b0\t \u0111\u00e3\t tr\u00ecnh\t b\u00e0y\t chi\t ti\u1ebft\t trong\t ph\u1ea7n th\u1ee9\tnh\u1ea5t\tc\u1ee7a\tquy\u1ec3n\ts\u00e1ch.\t\u0110\u1ed1i\tv\u1edbi\ts\u1ef1\tchuy\u1ec3n\t\u0111\u1ed5i\tt\u1eeb\tm\u1ed9t\th\u1ec7\tGalilei sang\t m\u1ed9t\t h\u1ec7\t kh\u00e1c\t c\u00f3\t chuy\u1ec3n\t \u0111\u1ed9ng\t \u0111\u1ec1u\t \u0111\u1ed1i\t v\u1edbi\t h\u1ec7\t th\u1ee9\t nh\u1ea5t,\t c\u00e1c ph\u01b0\u01a1ng\ttr\u00ecnh\tc\u1ee7a\tph\u00e9p\tbi\u1ebfn\t\u0111\u1ed5i\tLorentz\tc\u00f3\thi\u1ec7u\tl\u1ef1c.\tC\u00e1c\tph\u01b0\u01a1ng tr\u00ecnh\tn\u00e0y\tl\u00e0m\tth\u00e0nh\tc\u01a1\ts\u1edf\tdi\u1ec5n\td\u1ecbch\tc\u00e1c\th\u1ec7\tqu\u1ea3\tc\u1ee7a\tthuy\u1ebft\tt\u01b0\u01a1ng \u0111\u1ed1i\t h\u1eb9p,\t v\u00e0\t b\u1ea3n\t th\u00e2n\t ch\u00fang\t kh\u00f4ng\t g\u00ec\t kh\u00e1c\t h\u01a1n\t l\u00e0\t s\u1ef1\t bi\u1ec3u\t hi\u1ec7n t\u00ednh\t hi\u1ec7u\t l\u1ef1c\t ph\u1ed5\t qu\u00e1t\t c\u1ee7a\t \u0111\u1ecbnh\t lu\u1eadt\t truy\u1ec1n\t \u00e1nh\t s\u00e1ng\t cho\t t\u1ea5t\t c\u1ea3 c\u00e1c\th\u1ec7\tquy\tchi\u1ebfu\tGalilei. Minkowski\t\u0111\u00e3\tt\u00ecm\tth\u1ea5y\tc\u00e1c\tph\u00e9p\tbi\u1ebfn\t\u0111\u1ed5i\tLorentz\tth\u1ecfa\tm\u00e3n\tc\u00e1c \u0111i\u1ec1u\t ki\u1ec7n\t \u0111\u01a1n\t gi\u1ea3n\t sau\t \u0111\u00e2y.\t Ch\u00fang\t ta\t x\u00e9t\t hai\t s\u1ef1\t ki\u1ec7n\t l\u00e2n\t c\u1eadn nhau\tm\u00e0\tv\u1ecb\ttr\u00ed\tt\u01b0\u01a1ng\t\u0111\u1ed1i\ttrong\tcontinum\tb\u1ed1n\tchi\u1ec1u\t\u0111\u01b0\u1ee3c\tcho\tb\u1edfi c\u00e1c\t hi\u1ec7u\t s\u1ed1\t t\u1ecda\t \u0111\u1ed9\t kh\u00f4ng\t gian\t dx,\tdy,\tdz\t v\u00e0\t hi\u1ec7u\t s\u1ed1\t th\u1eddi\t gian\t dt \u0111\u1ed1i\tv\u1edbi\tm\u1ed9t\tv\u1eadt\tth\u1ec3\tquy\tchi\u1ebfu\tGalilei\tK.\t\u0110\u1ed1i\tv\u1edbi\tm\u1ed9t\th\u1ec7\tGalilei\tth\u1ee9 hai,\t c\u00e1c\t hi\u1ec7u\t s\u1ed1\t t\u01b0\u01a1ng\t t\u1ef1\t cho\t hai\t s\u1ef1\t ki\u1ec7n\t n\u00e0y\t l\u00e0\t dx\u2019,\t dy\u2019,\t dz\u2019,\t dt\u2019. L\u00fac\t\u0111\u00f3\tch\u00fang\tta\tlu\u00f4n\tlu\u00f4n\tc\u00f3\tm\u1ed1i\tli\u00ean\th\u1ec7\tgi\u1eefa\tch\u00fang: dx\t2\t+\tdy\t2\t+\tdz\t2\t-\tc\t2\tdt\t2\t=\tdx\u2019\t2\t+\tdy\t\u00ed2\t+\tdz\u2019\t2\tc\t2\tdt\u2019\t2 M\u1ed1i\t li\u00ean\t h\u1ec7\t n\u00e0y\t l\u00e0\t h\u1ec7\t qu\u1ea3\t t\u1eeb\t t\u00ednh\t hi\u1ec7u\t l\u1ef1c\t c\u1ee7a\t ph\u00e9p\t bi\u1ebfn\t \u0111\u1ed5i Lorentz.\tCh\u00fang\tta\tc\u00f3\tth\u1ec3\tph\u00e1t\tbi\u1ec3u\t\u0111i\u1ec1u\tn\u00e0y\tnh\u01b0\tsau:\t\u0110\u1ea1i\tl\u01b0\u1ee3ng ds\t2\t=\tdx\t2\t+\tdy\t2\t+\tdz\t2\t-\tc\t2\tdt\t2 thu\u1ed9c\tv\u1ec1\thai\t\u0111i\u1ec3m\tl\u00e2n\tc\u1eadn\tc\u1ee7a\tcontinum\tkh\u00f4ng-th\u1eddi-gian\tb\u1ed1n chi\u1ec1u\t lu\u00f4n\t lu\u00f4n\t c\u00f3\t c\u00f9ng\t tr\u1ecb\t s\u1ed1\t \u0111\u1ed1i\t v\u1edbi\t t\u1ea5t\t c\u1ea3\t v\u1eadt\t th\u1ec3\t quy\t chi\u1ebfu (Galilei)\t\u0111\u01b0\u1ee3c\t\u01b0u\t\u0111\u00e3i.\tN\u1ebfu\tthay\tth\u1ebf\tx,\ty,\tz,\t \tb\u1eb1ng\tx1,\tx2,\tx3, x4\tch\u00fang\tta\tc\u0169ng\t\u0111\u01b0\u1ee3c\tk\u1ebft\tqu\u1ea3,\tr\u1eb1ng\t\u0111\u1ea1i\tl\u01b0\u1ee3ng ds\t2\t=\tdx1\t2\t+\tdx2\t2\t+\tdx3\t2\t+\tdx4\t2","l\u00e0\t\u0111\u1ed9c\tl\u1eadp\tv\u1edbi\ts\u1ef1\tch\u1ecdn\tl\u1ef1a\tc\u1ee7a\tv\u1eadt\tth\u1ec3\tquy\tchi\u1ebfu.\tCh\u00fang\tta\tg\u1ecdi \u0111\u1ea1i\t l\u01b0\u1ee3ng\t ds\t l\u00e0\t \\\"kho\u1ea3ng\t c\u00e1ch\\\"\t c\u1ee7a\t hai\t s\u1ef1\t ki\u1ec7n,\t hay\t hai\t \u0111i\u1ec3m\t b\u1ed1n chi\u1ec1u. Nh\u01b0\tth\u1ebf,\tn\u1ebfu\tch\u1ecdn\tbi\u1ebfn\ts\u1ed1\t\u1ea3o\tct\tthay\tv\u00ec\tbi\u1ebfn\ts\u1ed1\tth\u1ef1c\tt,\tch\u00fang\tta c\u00f3\t th\u1ec3\t quan\t ni\u1ec7m\t continum\t kh\u00f4ng-th\u1eddi-gian,\t ph\u00f9\t h\u1ee3p\t v\u1edbi thuy\u1ebft\tt\u01b0\u01a1ng\t\u0111\u1ed1i\th\u1eb9p,\tnh\u01b0\tm\u1ed9t\tcontinum\tb\u1ed1n\tchi\u1ec1u\tEuclid,\ttheo nh\u01b0\tnh\u1eefng\ttr\u00ecnh\tb\u00e0y\tc\u1ee7a\tch\u01b0\u01a1ng\ttr\u01b0\u1edbc.","\u00a7\t27 Continum\tKh\u00f4ng-th\u1eddi-gian\tc\u1ee7a\tThuy\u1ebft\tT\u01b0\u01a1ng\t\u0110\u1ed1i\tR\u1ed9ng\tL\u00e0\tPhi-Euclid Trong\t ph\u1ea7n\t th\u1ee9\t nh\u1ea5t\t c\u1ee7a\t cu\u1ed1n\t s\u00e1ch\t nh\u1ecf\t n\u00e0y\t ch\u00fang\t ta\t \u0111\u00e3\t c\u00f3 th\u1ec3\ts\u1eed\td\u1ee5ng\tc\u00e1c\tt\u1ecda\t\u0111\u1ed9\tkh\u00f4ng-th\u1eddi-gian.\tCh\u00fang\tcho\tph\u00e9p\tm\u1ed9t\ts\u1ef1 di\u1ec5n\t gi\u1ea3i\t v\u1eadt\t l\u00fd\t h\u1ecdc\t tr\u1ef1c\t ti\u1ebfp\t v\u00e0\t \u0111\u01a1n\t gi\u1ea3n,\t v\u00e0\t theo\t \u00a7\t 26,\t c\u00f3\t th\u1ec3 \u0111\u01b0\u1ee3c\t xem\t nh\u01b0\t t\u1ecda\t \u0111\u1ed9\t Descartes\t b\u1ed1n\t chi\u1ec1u.\t \u0110i\u1ec1u\t \u0111\u00f3\t c\u00f3\t th\u1ec3\t \u0111\u01b0\u1ee3c, tr\u00ean\tc\u01a1\ts\u1edf\t\u0111\u1ecbnh\tlu\u1eadt\tv\u1ec1\tt\u00ednh\th\u1eb1ng\ts\u1ed1\tc\u1ee7a\tv\u1eadn\tt\u1ed1c\t\u00e1nh\ts\u00e1ng.\tNh\u01b0ng theo\t \u00a7\t 21,\t thuy\u1ebft\t t\u01b0\u01a1ng\t \u0111\u1ed1i\t r\u1ed9ng\t l\u1ea1i\t kh\u00f4ng\t th\u1ec3\t gi\u1eef\t v\u1eefng\t \u0111\u01b0\u1ee3c \u0111\u1ecbnh\tlu\u1eadt\tn\u00e0y.\tNg\u01b0\u1ee3c\tl\u1ea1i,\tth\u1ef1c\tt\u1ebf\tch\u00fang\tta\t\u0111\u00e3\t\u0111i\t\u0111\u1ebfn\tk\u1ebft\tqu\u1ea3,\ttheo thuy\u1ebft\t sau\t v\u1eadn\t t\u1ed1c\t \u00e1nh\t s\u00e1ng\t ph\u1ea3i\t lu\u00f4n\t l\u1ec7\t thu\u1ed9c\t v\u00e0o\t c\u00e1c\t t\u1ecda\t \u0111\u1ed9, khi\tc\u00f3\tm\u1ed9t\ttr\u01b0\u1eddng\th\u1ea5p\td\u1eabn\tt\u1ed3n\tt\u1ea1i.\tH\u01a1n\tn\u1eefa,\t\u1edf\tm\u1ed9t\tth\u00ed\td\u1ee5\t\u0111\u1eb7c\tbi\u1ec7t trong\t \u00a7\t 23,\t ch\u00fang\t ta\t c\u00f2n\t t\u00ecm\t th\u1ea5y\t s\u1ef1\t hi\u1ec7n\t di\u1ec7n\t c\u1ee7a\t m\u1ed9t\t tr\u01b0\u1eddng h\u1ea5p\td\u1eabn\tl\u00e0m\tcho\t\u0111\u1ecbnh\tngh\u0129a\tv\u1ec1\tt\u1ecda\t\u0111\u1ed9\tv\u00e0\tth\u1eddi\tgian\tv\u00f4\tngh\u0129a,\t\u0111i\u1ec1u m\u00e0\tv\u1edbi\tthuy\u1ebft\tt\u01b0\u01a1ng\t\u0111\u1ed1i\th\u1eb9p\t\u0111\u00e3\tth\u00e0nh\tc\u00f4ng. 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Tuy\tnhi\u00ean\tc\u00e1c\tsuy\tngh\u0129\tc\u1ee7a\t\u00a7\t25\tv\u00e0\t\u00a7\t26\tch\u1ec9\tcho\tch\u00fang\tta\tcon \u0111\u01b0\u1eddng\t kh\u1eafc\t ph\u1ee5c\t kh\u00f3\t kh\u0103n\t n\u00e0y.\t Ch\u00fang\t ta\t quy\t chi\u1ebfu\t continum kh\u00f4ng-th\u1eddi-gian\tb\u1ed1n\tchi\u1ec1u\tm\u1ed9t\tc\u00e1ch\tb\u1ea5t\tk\u1ef3\tl\u00ean\tc\u00e1c\tt\u1ecda\t\u0111\u1ed9\tGauss. V\u1edbi\t m\u1ed7i\t \u0111i\u1ec3m\t (s\u1ef1\t ki\u1ec7n)\t c\u1ee7a\t continum\t ch\u00fang\t ta\t l\u00e0m\t t\u01b0\u01a1ng\t \u1ee9ng b\u1ed1n\ts\u1ed1\tx1,\tx2,\tx3,\tx4\t(t\u1ecda\t\u0111\u1ed9),\ttr\u01b0\u1edbc\tti\u00ean\tkh\u00f4ng\tc\u00f3\t\u00fd\tngh\u0129a\tv\u1eadt\tl\u00fd tr\u1ef1c\t ti\u1ebfp\t n\u00e0o\t c\u1ea3,\t m\u00e0\t ch\u1ec9\t \u0111\u1ec3\t \u0111\u00e1nh\t s\u1ed1\t c\u00e1c\t \u0111i\u1ec3m\t c\u1ee7a\t continum\t m\u1ed9t c\u00e1ch\tn\u00e0o\t\u0111\u00f3,\tv\u00e0\tt\u00f9y\tti\u1ec7n.\tCh\u00fang\tta\tc\u0169ng\tkh\u00f4ng\tc\u1ea7n\tph\u1ea3i\thi\u1ec3u\tx1, x2,\tx3\tl\u00e0\tc\u00e1c\tt\u1ecda\t\u0111\u1ed9\t\\\"kh\u00f4ng\tgian\\\",\tv\u00e0\tx4\tl\u00e0\tt\u1ecda\t\u0111\u1ed9\t\\\"th\u1eddi\tgian\\\". 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Tr\u01b0\u1edbc\t \u0111\u00e2y\t khi\t m\u00f4\t t\u1ea3\t chuy\u1ec3n\t \u0111\u1ed9ng\t c\u1ee7a\t m\u1ed9t\t \u0111i\u1ec3m\t v\u1eadt\t ch\u1ea5t\t \u0111\u1ed1i v\u1edbi\tm\u1ed9t\tv\u1eadt\tth\u1ec3\tquy\tchi\u1ebfu,\tch\u00fang\tta\tkh\u00f4ng\tx\u00e1c\tnh\u1eadn\tg\u00ec\tkh\u00e1c\th\u01a1n l\u00e0\tnh\u1eefng\ts\u1ef1\tg\u1eb7p\tg\u1ee1\tc\u1ee7a\t\u0111i\u1ec3m\tn\u00e0y\tv\u1edbi\tnh\u1eefng\t\u0111i\u1ec3m\tnh\u1ea5t\t\u0111\u1ecbnh\tc\u1ee7a v\u1eadt\t th\u1ec3\t quy\t chi\u1ebfu.\t C\u00e1c\t x\u00e1c\t nh\u1eadn\t th\u1eddi\t gian\t li\u00ean\t quan\t c\u0169ng\t \u0111\u01b0\u1ee3c quy\t v\u1ec1\t x\u00e1c\t nh\u1eadn\t c\u00e1c\t s\u1ef1\t g\u1eb7p\t g\u1ee1\t c\u1ee7a\t v\u1eadt\t th\u1ec3\t v\u1edbi\t c\u00e1c\t \u0111\u1ed3ng\t h\u1ed3,\t k\u1ebft h\u1ee3p\t v\u1edbi\t x\u00e1c\t nh\u1eadn\t s\u1ef1\t g\u1eb7p\t g\u1ee1\t c\u1ee7a\t kim\t \u0111\u1ed3ng\t h\u1ed3\t v\u1edbi\t c\u00e1c\t \u0111i\u1ec3m\t nh\u1ea5t \u0111\u1ecbnh\t c\u1ee7a\t c\u00e1c\t m\u1eb7t\t s\u1ed1\t \u0111\u1ed3ng\t h\u1ed3.\t N\u00f3\t kh\u00f4ng\t g\u00ec\t kh\u00e1c\t h\u01a1n\t \u0111\u1ed1i\t v\u1edbi\t c\u00e1c \u0111o\t \u0111\u1ea1c\t kh\u00f4ng\t gian\t b\u1eb1ng\t thanh\t \u0111o,\t nh\u01b0\t m\u1ed9t\t v\u00e0i\t suy\t ngh\u0129\t cho th\u1ea5y. M\u1ed9t\tc\u00e1ch\tt\u1ed5ng\tqu\u00e1t\tch\u00fang\tta\tc\u00f3:\tM\u1ed7i\ts\u1ef1\tm\u00f4\tt\u1ea3\tv\u1eadt\tl\u00fd\t\u0111\u01b0\u1ee3c\tquy v\u1ec1\t m\u1ed9t\t s\u1ed1\t c\u00e1c\t m\u1ec7nh\t \u0111\u1ec1,\t m\u00e0\t m\u1ed7i\t m\u1ec7nh\t \u0111\u1ec1\t trong\t \u0111\u00f3\t quy\t v\u1ec1\t s\u1ef1 tr\u00f9ng\th\u1ee3p\tc\u1ee7a\thai\ts\u1ef1\tki\u1ec7n\tA\tv\u00e0\tB.\tM\u1ed7i\tm\u1ec7nh\t\u0111\u1ec1\tnh\u01b0\tth\u1ebf\t\u0111\u01b0\u1ee3c\tbi\u1ec3u th\u1ecb\ttrong\tt\u1ecda\t\u0111\u1ed9\tGauss\tb\u1eb1ng\ts\u1ef1\ttr\u00f9ng\tnhau\tc\u1ee7a\tb\u1ed1n\tt\u1ecda\t\u0111\u1ed9\tx1,\tx2, x3,\tx4.\tS\u1ef1\tm\u00f4\tt\u1ea3\tcontinum\tkh\u00f4ng-th\u1eddi-gian\tb\u1eb1ng\tt\u1ecda\t\u0111\u1ed9\tGauss\tdo","\u0111\u00f3\t th\u1ef1c\t s\u1ef1\t thay\t th\u1ebf\t ho\u00e0n\t to\u00e0n\t s\u1ef1\t m\u00f4\t t\u1ea3\t b\u1eb1ng\t m\u1ed9t\t v\u1eadt\t th\u1ec3\t quy chi\u1ebfu,\tm\u00e0\tkh\u00f4ng\tph\u1ea3i\tch\u1ecbu\tthi\u1ec7t\tth\u00f2i\tt\u1eeb\tnh\u1eefng\tkhuy\u1ebft\t\u0111i\u1ec3m\tc\u1ee7a ph\u01b0\u01a1ng\tph\u00e1p\tm\u00f4\tt\u1ea3\tsau;\tn\u00f3\tkh\u00f4ng\tb\u1ecb\tg\u1eafn\tli\u1ec1n\tv\u1edbi\tt\u00ednh\tch\u1ea5t\tEuclid c\u1ee7a\tcontinum\tc\u1ea7n\t\u0111\u01b0\u1ee3c\tbi\u1ebfu\tdi\u1ec5n.","\u00a7\t28 S\u1ef1\tDi\u1ec5n\tT\u1ea3\tCh\u00ednh\tX\u00e1c\tc\u1ee7a\tNguy\u00ean\tL\u00fd\tT\u01b0\u01a1ng\t\u0110\u1ed1i\tR\u1ed9ng B\u00e2y\tgi\u1edd\tch\u00fang\tta\tc\u00f3\tkh\u1ea3\tn\u0103ng\tthay\tth\u1ebf\ts\u1ef1\tbi\u1ec3u\tth\u1ecb\tt\u1ea1m\tth\u1eddi\tc\u1ee7a nguy\u00ean\tl\u00fd\tt\u01b0\u01a1ng\t\u0111\u1ed1i\tr\u1ed9ng\t\u0111\u00e3\t\u0111\u01b0\u1ee3c\ttr\u00ecnh\tb\u00e0y\ttrong\t\u00a7\t18\tb\u1eb1ng\tm\u1ed9t s\u1ef1\t bi\u1ec3u\t th\u1ecb\t ch\u00ednh\t x\u00e1c.\t L\u1ed1i\t bi\u1ec3u\t th\u1ecb\t tr\u01b0\u1edbc\t \u0111\u00e2y:\t \\\"T\u1ea5t\t c\u1ea3\t v\u1eadt\t th\u1ec3\t quy chi\u1ebfu\t K,\t K\u2019,\t v.v.\t l\u00e0\t t\u01b0\u01a1ng\t \u0111\u01b0\u01a1ng\t v\u1edbi\t nhau\t trong\t vi\u1ec7c\t m\u00f4\t t\u1ea3\t c\u00e1c hi\u1ec7n\tt\u01b0\u1ee3ng\tt\u1ef1\tnhi\u00ean\t(s\u1ef1\tbi\u1ec3u\tth\u1ecb\tc\u00e1c\t\u0111\u1ecbnh\tlu\u1eadt\tt\u1ef1\tnhi\u00ean\tph\u1ed5\tqu\u00e1t), b\u1ea5t\tk\u1ec3\ttr\u1ea1ng\tth\u00e1i\tchuy\u1ec3n\t\u0111\u1ed9ng\tc\u1ee7a\tch\u00fang\\\"\tkh\u00f4ng\tth\u1ec3\t\u0111\u1ee9ng\tv\u1eefng \u0111\u01b0\u1ee3c,\tb\u1edfi\tv\u00ec\tvi\u1ec7c\ts\u1eed\td\u1ee5ng\tc\u00e1c\tv\u1eadt\tth\u1ec3\tr\u1eafn\ttrong\tvi\u1ec7c\tm\u00f4\tt\u1ea3\tkh\u00f4ng- th\u1eddi-gian,\t theo\t ngh\u0129a\t c\u1ee7a\t ph\u01b0\u01a1ng\t ph\u00e1p\t \u0111\u00e3\t \u0111\u01b0\u1ee3c\t s\u1eed\t d\u1ee5ng\t trong thuy\u1ebft\tt\u01b0\u01a1ng\t\u0111\u1ed1i\th\u1eb9p,\tn\u00f3i\tchung\tl\u00e0\tkh\u00f4ng\tth\u1ec3\t\u0111\u01b0\u1ee3c.\tH\u1ec7\tth\u1ed1ng\tt\u1ecda \u0111\u1ed9\t Gauss\t \u0111\u00e3\t thay\t th\u1ebf\t v\u1ecb\t tr\u00ed\t c\u1ee7a\t v\u1eadt\t th\u1ec3\t quy\t chi\u1ebfu.\t M\u1ec7nh\t \u0111\u1ec1\t sau \u0111\u00e2y\t l\u00e0\t t\u01b0\u01a1ng\t \u1ee9ng\t v\u1edbi\t \u00fd\t t\u01b0\u1edfng\t n\u1ec1n\t t\u1ea3ng\t c\u1ee7a\t nguy\u00ean\t l\u00fd\t t\u01b0\u01a1ng\t \u0111\u1ed1i r\u1ed9ng:\t \\\"T\u1ea5t\t c\u1ea3\t c\u00e1c\t h\u1ec7\t th\u1ed1ng\t t\u1ecda\t \u0111\u1ed9\t Gauss\t l\u00e0\t thi\u1ebft\t y\u1ebfu\t t\u01b0\u01a1ng\t \u0111\u01b0\u01a1ng nhau\ttrong\tvi\u1ec7c\thi\u1ec3u\tth\u1ecb\tc\u00e1c\t\u0111\u1ecbnh\tlu\u1eadt\tph\u1ed5\tqu\u00e1t\tc\u1ee7a\tt\u1ef1\tnhi\u00ean.\\\" Ch\u00fang\tta\tc\u0169ng\tc\u00f3\tth\u1ec3\tph\u00e1t\tbi\u1ec3u\tnguy\u00ean\tl\u00fd\tt\u01b0\u01a1ng\t\u0111\u1ed1i\tr\u1ed9ng\tn\u00e0y \u1edf\t m\u1ed9t\t d\u1ea1ng\t kh\u00e1c.\t N\u00f3\t c\u00f3\t th\u1ec3\t l\u00e0m\t cho\t ng\u01b0\u1eddi\t ta\t c\u00f2n\t nh\u1eadn\t d\u1ea1ng nguy\u00ean\tl\u00fd\tt\u01b0\u01a1ng\t\u0111\u1ed1i\tr\u1ed9ng\tr\u00f5\th\u01a1n\tv\u1edbi\tt\u00ednh\tch\u1ea5t\tl\u00e0\tm\u1ed9t\ts\u1ef1\tn\u1edbi\tr\u1ed9ng t\u1ef1\t nhi\u00ean\t c\u1ee7a\t nguy\u00ean\t l\u00fd\t t\u01b0\u01a1ng\t \u0111\u1ed1i\t h\u1eb9p.\t Theo\t thuy\u1ebft\t t\u01b0\u01a1ng\t \u0111\u1ed1i h\u1eb9p,\t c\u00e1c\t ph\u01b0\u01a1ng\t tr\u00ecnh\t m\u00f4\t t\u1ea3\t c\u00e1c\t \u0111\u1ecbnh\t lu\u1eadt\t t\u1ef1\t nhi\u00ean\t ph\u1ed5\t qu\u00e1t \u0111\u01b0\u1ee3c\t chuy\u1ec3n\t bi\u1ebfn\t sang\t th\u00e0nh\t c\u00e1c\t ph\u01b0\u01a1ng\t tr\u00ecnh\t c\u00f3\t c\u00f9ng\t d\u1ea1ng, n\u1ebfu\t ch\u00fang\t ta\t thay\t th\u1ebf\t c\u00e1c\t bi\u1ebfn\t s\u1ed1\t kh\u00f4ng-th\u1eddi-gian\t x,\t y,\t z,\t t\t c\u1ee7a m\u1ed9t\t v\u1eadt\t th\u1ec3\t quy\t chi\u1ebfu\t K\t (Galilei),\t th\u00f4ng\t qua\t ph\u00e9p\t bi\u1ebfn\t \u0111\u1ed5i Lorentz,\tb\u1eb1ng\tc\u00e1c\tbi\u1ebfn\ts\u1ed1\tkh\u00f4ng-th\u1eddi-gian\tx\u2019,\ty\u2019,\tz\u2019,\tt\u2019\tc\u1ee7a\tm\u1ed9t\tv\u1eadt th\u1ec3\t quy\t chi\u1ebfu\t m\u1edbi\t K'.\t M\u1eb7t\t kh\u00e1c,\t theo\t thuy\u1ebft\t t\u01b0\u01a1ng\t \u0111\u1ed1i\t r\u1ed9ng, th\u00f4ng\tqua\ts\u1ef1\tthay\tth\u1ebf\tb\u1ea5t\tk\u1ef3\tc\u00e1c\tbi\u1ebfn\ts\u1ed1\tGauss\tx1,\tx2,\tx3,\t x4,\t c\u00e1c ph\u01b0\u01a1ng\ttr\u00ecnh\tph\u1ea3i\t\u0111\u01b0\u1ee3c\tchuy\u1ebfn\tsang\tth\u00e0nh\tc\u00e1c\tph\u01b0\u01a1ng\ttr\u00ecnh\tc\u00f3 c\u00f9ng\t d\u1ea1ng;\t b\u1edfi\t v\u00ec\t m\u1ed7i\t ph\u00e9p\t bi\u1ebfn\t \u0111\u1ed5i\t (kh\u00f4ng\t ch\u1ec9\t ph\u00e9p\t bi\u1ebfn\t \u0111\u1ed5i Lorentz)\t t\u01b0\u01a1ng\t \u1ee9ng\t v\u1edbi\t s\u1ef1\t chuy\u1ec3n\t \u0111\u1ed5i\t t\u1eeb\t m\u1ed9t\t h\u1ec7\t t\u1ecda\t \u0111\u1ed9\t Gauss sang\tm\u1ed9t\th\u1ec7\tkh\u00e1c. N\u1ebfu\t ch\u00fang\t ta\t mu\u1ed1n\t gi\u1eef\t c\u00e1ch\t nh\u00ecn\t ba\t chi\u1ec1u\t quen\t thu\u1ed9c\t th\u00ec ch\u00fang\t ta\t c\u00f3\t th\u1ec3\t \u0111\u1eb7c\t tr\u01b0ng\t s\u1ef1\t ph\u00e1t\t tri\u1ec3n\t \u0111\u00e3\t di\u1ec5n\t ra\t b\u1edfi\t \u00fd\t t\u01b0\u1edfng n\u1ec1n\t t\u1ea3ng\t c\u1ee7a\t thuy\u1ebft\t t\u01b0\u01a1ng\t \u0111\u1ed1i\t r\u1ed9ng\t nh\u01b0\t sau:\t Thuy\u1ebft\t t\u01b0\u01a1ng\t \u0111\u1ed1i h\u1eb9p\t \u00e1p\t d\u1ee5ng\t cho\t c\u00e1c\t mi\u1ec1n\t Galilei,\t ngh\u0129a\t l\u00e0\t c\u00e1c\t mi\u1ec1n\t \u1edf\t \u0111\u00f3\t kh\u00f4ng c\u00f3\t tr\u01b0\u1eddng\t h\u1ea5p\t d\u1eabn.\t V\u1eadt\t th\u1ec3\t quy\t chi\u1ebfu\t \u0111\u01b0\u1ee3c\t s\u1eed\t d\u1ee5ng\t \u1edf\t \u0111\u00f3\t l\u00e0\t m\u1ed9t v\u1eadt\t th\u1ec3\t Galilei,\t ngh\u0129a\t l\u00e0\t m\u1ed9t\t v\u1eadt\t th\u1ec3\t r\u1eafn\t v\u1edbi\t tr\u1ea1ng\t th\u00e1i\t chuy\u1ec3n","\u0111\u1ed9ng\t \u0111\u01b0\u1ee3c\t ch\u1ecdn\t sao\t cho\t \u0111\u1ed1i\t v\u1edbi\t n\u00f3,\t \u0111\u1ecbnh\t l\u00fd\t Galilei\t v\u1ec1\t chuy\u1ec3n \u0111\u1ed9ng\tth\u1eb3ng\t\u0111\u1ec1u\tc\u1ee7a\tc\u00e1c\t\u0111i\u1ec3m\tv\u1eadt\tch\u1ea5t\t\\\"c\u00f4\tl\u1eadp\\\"\tc\u00f3\thi\u1ec7u\tl\u1ef1c. Nh\u1eefng\tsuy\tngh\u0129\tnh\u1ea5t\t\u0111\u1ecbnh\tg\u1ee3i\tra\tr\u1eb1ng\tch\u00fang\tta\tc\u0169ng\tn\u00ean\tquy nh\u1eefng\tmi\u1ec1n\tGalilei\tn\u00e0y\tl\u00ean\tc\u00e1c\tv\u1eadt\tth\u1ec3\tquy\tchi\u1ebfu\tphi-Galilei.\tNh\u01b0 v\u1eady,\t\u0111\u1ed1i\tv\u1edbi\tc\u00e1c\tv\u1eadt\tquy\tchi\u1ebfu\tn\u00e0y\ts\u1ebd\tc\u00f3\tm\u1ed9t\ttr\u01b0\u1eddng\th\u1ea5p\td\u1eabn\td\u1ea1ng \u0111\u1eb7c\tbi\u1ec7t\tt\u1ed3n\tt\u1ea1i\t(\u00a7\t20\tv\u00e0\t\u00a7\t23). Tuy\tnhi\u00ean,\ttrong\tc\u00e1c\ttr\u01b0\u1eddng\th\u1ea5p\td\u1eabn\tkh\u00f4ng\tc\u00f3\tc\u00e1c\tv\u1eadt\tth\u1ec3\tr\u1eafn v\u1edbi\t c\u00e1c\t t\u00ednh\t ch\u1ea5t\t Euclid\t nh\u01b0\t th\u1ebf;\t do\t \u0111\u00f3\t s\u1ef1\t t\u01b0\u1edfng\t t\u01b0\u1ee3ng\t v\u1ec1\t m\u1ed9t v\u1eadt\tth\u1ec3\tr\u1eafn\tch\u1ec9\tl\u00e0\t\u1ea3o\tt\u01b0\u1edfng\ttrong\tthuy\u1ebft\tt\u01b0\u01a1ng\t\u0111\u1ed1i\tr\u1ed9ng.\tChuy\u1ec3n \u0111\u1ed9ng\tc\u1ee7a\t\u0111\u1ed3ng\th\u1ed3\tc\u0169ng\tb\u1ecb\t\u1ea3nh\th\u01b0\u1edfng\tb\u1edfi\ttr\u01b0\u1eddng\th\u1ea5p\td\u1eabn,\t\u0111\u1ebfn\t\u0111\u1ed9 m\u1ed9t\t \u0111\u1ecbnh\t ngh\u0129a\t v\u1eadt\t l\u00fd\t v\u1ec1\t th\u1eddi\t gian,\t tr\u1ef1c\t ti\u1ebfp\t v\u1edbi\t s\u1ef1\t gi\u00fap\t \u0111\u1ee1\t c\u1ee7a \u0111\u1ed3ng\t h\u1ed3,\t ho\u00e0n\t to\u00e0n\t kh\u00f4ng\t c\u00f3\t m\u1ee9c\t \u0111\u1ed9\t h\u1ee3p\t l\u00fd\t nh\u01b0\t trong\t thuy\u1ebft t\u01b0\u01a1ng\t\u0111\u1ed1i\th\u1eb9p. Do\t \u0111\u00f3\t ng\u01b0\u1eddi\t ta\t s\u1eed\t d\u1ee5ng\t c\u00e1c\t v\u1eadt\t quy\t chi\u1ebfu\t kh\u00f4ng-r\u1eafn,\t ch\u00fang kh\u00f4ng\t nh\u1eefng\t chuy\u1ec3n\t \u0111\u1ed9ng\t b\u1ea5t\t k\u1ef3\t nh\u01b0\t m\u1ed9t\t kh\u1ed1i\t to\u00e0n\t th\u1ec3,\t m\u00e0 ngay\ttrong\tl\u00fac\tchuy\u1ec3n\t\u0111\u1ed9ng\tc\u0169ng\tc\u00f2n\tch\u1ecbu\tnh\u1eefng\tbi\u1ebfn\td\u1ea1ng\tb\u1ea5t k\u1ef3.\t \u0110\u1ec3\t \u0111\u1ecbnh\t ngh\u0129a\t th\u1eddi\t gian,\t ng\u01b0\u1eddi\t ta\t s\u1eed\t d\u1ee5ng\t c\u00e1c\t \u0111\u1ed3ng\t h\u1ed3\t v\u1edbi m\u1ed9t\t quy\t lu\u1eadt\t v\u1eadn\t h\u00e0nh\t b\u1ea5t\t k\u1ef3,\t d\u00f9\t kh\u00f4ng\t \u0111\u1ec1u\t th\u1ebf\t n\u00e0o\t \u0111i\t n\u1eefa,\t v\u00e0 t\u01b0\u1edfng\t t\u01b0\u1ee3ng\t g\u1eafn\t m\u1ed7i\t c\u00e1i\t t\u1ea1i\t m\u1ed9t\t \u0111i\u1ec3m\t c\u1ee7a\t v\u1eadt\t th\u1ec3\t quy\t chi\u1ebfu kh\u00f4ng-r\u1eafn.\t C\u00e1c\t \u0111\u1ed3ng\t h\u1ed3\t n\u00e0y\t ch\u1ec9\t th\u1ecfa\t m\u00e3n\t m\u1ed9t\t \u0111i\u1ec1u\t ki\u1ec7n,\t r\u1eb1ng c\u00e1c\ts\u1ed1\t\u0111\u1ecdc\t(th\u1eddi\tgian)\t\u0111\u01b0\u1ee3c\tquan\ts\u00e1t\tc\u00f9ng\tm\u1ed9t\tl\u00fac\t\u1edf\tc\u00e1c\t\u0111\u1ed3ng\th\u1ed3 l\u00e2n\tc\u1eadn\tnhau\t(v\u1ec1\tkh\u00f4ng\tgian)\tch\u1ec9\tkh\u00e1c\tnhau\tv\u00f4\tc\u00f9ng\tnh\u1ecf.\tV\u1eadt\tth\u1ec3 quy\tchi\u1ebfu\tkh\u00f4ng-r\u1eafn\tn\u00e0y,\tc\u00e1i\tng\u01b0\u1eddi\tta\tc\u00f3\tth\u1ec3\tg\u1ecdi\tl\u00e0\t\\\"nhuy\u1ec5n\tth\u1ec3\u2019 quy\t chi\u1ebfu\\\"[59]\t kh\u00f4ng\t ph\u1ea3i\t kh\u00f4ng\t ch\u00ednh\t \u0111\u00e1ng,\t v\u1ec1\t c\u01a1\t b\u1ea3n\t t\u01b0\u01a1ng \u0111\u01b0\u01a1ng\tv\u1edbi\tm\u1ed9t\th\u1ec7\tt\u1ecda\t\u0111\u1ed9\tGauss\tb\u1ed1n\tchi\u1ec1u\t\u0111\u01b0\u1ee3c\tch\u1ecdn\tb\u1ea5t\tk\u1ef3.\t\u0110i\u1ec1u \u0111\u00e3\t t\u1ea1o\t cho\t \\\"nhuy\u1ec5n\t th\u1ec3\\\"\t m\u1ed9t\t t\u00ednh\t tr\u1ef1c\t quan\t nh\u1ea5t\t \u0111\u1ecbnh,\t nh\u01b0\t khi so\t s\u00e1nh\t v\u1edbi\t h\u1ec7\t t\u1ecda\t \u0111\u1ed9\t Gauss,\t \u0111\u00f3\t l\u00e0\t s\u1ef1\t gi\u1eef\t \u0111\u01b0\u1ee3c\t v\u1ec1\t m\u1eb7t\t h\u00ecnh\t th\u1ee9c (th\u1ef1c\tra\tkh\u00f4ng\tch\u00ednh\t\u0111\u00e1ng)\ts\u1ef1\tt\u1ed3n\tt\u1ea1i\tri\u00eang\tc\u1ee7a\tc\u00e1c\tt\u1ecda\t\u0111\u1ed9\tkh\u00f4ng gian\t tr\u01b0\u1edbc\t t\u1ecda\t \u0111\u1ed9\t th\u1eddi\t gian.\t M\u1ed7i\t \u0111i\u1ec3m\t c\u1ee7a\t nhuy\u1ec5n\t th\u1ec3\t \u0111\u01b0\u1ee3c\t xem nh\u01b0\t m\u1ed9t\t \u0111i\u1ec3m\t kh\u00f4ng\t gian,\t m\u1ed7i\t \u0111i\u1ec3m\t v\u1eadt\t ch\u1ea5t\t \u0111\u1ee9ng\t y\u00ean\t \u0111\u1ed1i\t v\u1edbi n\u00f3\tl\u00e0\t\u0111\u1ee9ng\ty\u00ean\tn\u00f3i\tchung,\tbao\tl\u00e2u\tnhuy\u1ec5n\tth\u1ec3\t\u0111\u01b0\u1ee3c\txem\tnh\u01b0\tv\u1eadt th\u1ec3\t quy\t chi\u1ebfu.\t Nguy\u00ean\t l\u00fd\t t\u01b0\u01a1ng\t \u0111\u1ed1i\t r\u1ed9ng\t y\u00eau\t c\u1ea7u\t t\u1ea5t\t c\u1ea3\t m\u1ecdi\t v\u1eadt nhuy\u1ec5n\tth\u1ec3\tc\u00f3\tth\u1ec3\t\u0111\u01b0\u1ee3c\ts\u1eed\td\u1ee5ng\tc\u00f9ng\tm\u1ed9t\tc\u00e1ch\tc\u00f4ng\tb\u1eb1ng,\tv\u00e0\tv\u1edbi s\u1ef1\t th\u00e0nh\t c\u00f4ng\t nh\u01b0\t nhau,\t trong\t vi\u1ec7c\t bi\u1ec3u\t th\u1ecb\t c\u00e1c\t \u0111\u1ecbnh\t lu\u1eadt\t ph\u1ed5 qu\u00e1t\tc\u1ee7a\tt\u1ef1\tnhi\u00ean\tv\u1edbi\tt\u01b0\tc\u00e1ch\tl\u00e0\tv\u1eadt\tth\u1ec3\tquy\tchi\u1ebfu;\tc\u00e1c\t\u0111\u1ecbnh\tlu\u1eadt c\u1ea7n\tph\u1ea3i\tho\u00e0n\tto\u00e0n\t\u0111\u1ed9c\tl\u1eadp\tv\u1edbi\ts\u1ef1\tch\u1ecdn\tl\u1ef1a\tnhuy\u1ec5n\tth\u1ec3. 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Ch\u00fang\tta\tb\u1eaft\t\u0111\u1ea7u\tb\u1eb1ng\tvi\u1ec7c\txem\tx\u00e9t\tm\u1ed9t\tmi\u1ec1n\tGalilei,\tngh\u0129a\tl\u00e0 m\u1ed9t\tmi\u1ec1n\tm\u00e0\ttrong\t\u0111\u00f3,\t\u0111\u1ed1i\tv\u1edbi\tv\u1eadt\tth\u1ec3\tquy\tchi\u1ebfu\tGalilei\tK,\tkh\u00f4ng c\u00f3\ttr\u01b0\u1eddng\th\u1ea5p\td\u1eabn\tt\u1ed3n\tt\u1ea1i.\tS\u1ef1\tv\u1eadn\th\u00e0nh\tc\u1ee7a\tc\u00e1c\tthanh\t\u0111o\tv\u00e0\t\u0111\u1ed3ng h\u1ed3\t\u0111\u1ed1i\tv\u1edbi\tK\t \u0111\u00e3\t \u0111\u01b0\u1ee3c\t bi\u1ebft\t t\u1eeb\t thuy\u1ebft\t t\u01b0\u01a1ng\t \u0111\u1ed1i\t h\u1eb9p,\t c\u0169ng\t nh\u01b0\t s\u1ef1 v\u1eadn\t h\u00e0nh\t c\u1ee7a\t c\u00e1c\t \u0111i\u1ec3m\t v\u1eadt\t ch\u1ea5t\t \\\"c\u00f4\t l\u1eadp\\\";\t c\u00e1c\t \u0111i\u1ec3m\t n\u00e0y\t chuy\u1ec3n \u0111\u1ed9ng\t\u0111\u1ec1u\tv\u00e0\ttheo\t\u0111\u01b0\u1eddng\tth\u1eb3ng. 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Ti\u1ebfp\t theo,\t ng\u01b0\u1eddi\t ta\t nghi\u00ean\t c\u1ee9u\t s\u1ef1\t v\u1eadn\t h\u00e0nh\t kh\u00f4ng-th\u1eddi-gian c\u1ee7a\t tr\u01b0\u1eddng\t h\u1ea5p\t d\u1eabn\t G\t \u0111\u01b0\u1ee3c\t suy\t ra\t t\u1eeb\t tr\u01b0\u1eddng\t h\u1ee3p\t \u0111\u1eb7c\t bi\u1ec7t\t Galilei \u0111\u01a1n\tgi\u1ea3n\tth\u00f4ng\tqua\tph\u00e9p\tbi\u1ebfn\t\u0111\u1ed5i\tt\u1ecda\t\u0111\u1ed9.\tS\u1ef1\tv\u1eadn\th\u00e0nh\tn\u00e0y\t\u0111\u01b0\u1ee3c bi\u1ec3u\t th\u1ecb\t b\u1eb1ng\t m\u1ed9t\t \u0111\u1ecbnh\t lu\u1eadt,\t lu\u00f4n\t lu\u00f4n\t c\u00f3\t gi\u00e1\t tr\u1ecb\t cho\t d\u00f9\t v\u1eadt\t th\u1ec3 quy\t chi\u1ebfu\t (nhuy\u1ec5n\t th\u1ec3)\t \u0111\u01b0\u1ee3c\t s\u1eed\t d\u1ee5ng\t cho\t s\u1ef1\t bi\u1ec3u\t th\u1ecb\t \u0111\u01b0\u1ee3c\t l\u1ef1a ch\u1ecdn\tth\u1ebf\tn\u00e0o. \u0110\u1ecbnh\tlu\u1eadt\tn\u00e0y\tch\u01b0a\tph\u1ea3i\tl\u00e0\t\u0111\u1ecbnh\tlu\u1eadt\tph\u1ed5\tqu\u00e1t\tc\u1ee7a\ttr\u01b0\u1eddng\th\u1ea5p d\u1eabn,\tb\u1edfi\tv\u00ec\ttr\u01b0\u1eddng\th\u1ea5p\td\u1eabn\tG\t\u0111\u01b0\u1ee3c\tnghi\u00ean\tc\u1ee9u\tl\u00e0\ttr\u01b0\u1eddng\tc\u00f3\td\u1ea1ng \u0111\u1eb7c\tbi\u1ec7t.\t\u0110\u1ec3\tt\u00ecm\tra\t\u0111\u1ecbnh\tlu\u1eadt\ttr\u01b0\u1eddng\tph\u1ed5\tqu\u00e1t\tc\u1ee7a\th\u1ea5p\td\u1eabn\tng\u01b0\u1eddi ta\tc\u1ea7n\t\u0111\u1ebfn\ts\u1ef1\tkh\u00e1i\tqu\u00e1t\th\u00f3a\tc\u1ee7a\t\u0111\u1ecbnh\tlu\u1eadt\tv\u1eeba\tthu\tho\u1ea1ch\t\u0111\u01b0\u1ee3c.\tS\u1ef1 kh\u00e1i\t qu\u00e1t\t h\u00f3a\t n\u00e0y\t tuy\t nhi\u00ean\t c\u00f3\t th\u1ec3\t \u0111\u01b0\u1ee3c\t t\u00ecm\t th\u1ea5y\t kh\u00f4ng\t ph\u1ea3i","m\u1ed9t\tc\u00e1ch\tt\u00f9y\tti\u1ec7n,\tm\u00e0\td\u01b0\u1edbi\ts\u1ef1\tch\u00fa\t\u00fd\t\u0111\u1ebfn\tc\u00e1c\ty\u00eau\tc\u1ea7u\tsau\t\u0111\u00e2y: a)\tS\u1ef1\tkh\u00e1i\tqu\u00e1t\th\u00f3a\t\u0111\u01b0\u1ee3c\tt\u00ecm\tth\u1ea5y\tc\u0169ng\tph\u1ea3i\tth\u1ecfa\tm\u00e3n\t\u0111\u1ecbnh\t\u0111\u1ec1 t\u01b0\u01a1ng\t\u0111\u1ed1i\tr\u1ed9ng. b)\t N\u1ebfu\t c\u00f3\t v\u1eadt\t ch\u1ea5t\t t\u1ed3n\t t\u1ea1i\t trong\t mi\u1ec1n\t nghi\u00ean\t c\u1ee9u,\t th\u00ec\t ch\u1ec9\t c\u00f3 kh\u1ed1i\tl\u01b0\u1ee3ng\tqu\u00e1n\tt\u00ednh\tc\u1ee7a\tn\u00f3,\tv\u00e0\tdo\t\u0111\u00f3\ttheo\t\u00a7\t15,\tch\u1ec9\tn\u0103ng\tl\u01b0\u1ee3ng c\u1ee7a\tn\u00f3\tl\u00e0\tc\u00f3\tt\u00ednh\tch\u1ea5t\tquy\u1ebft\t\u0111\u1ecbnh\tcho\tt\u00e1c\td\u1ee5ng\tg\u00e2y\tra\ttr\u01b0\u1eddng\tc\u1ee7a n\u00f3. c)\tTr\u01b0\u1eddng\th\u1ea5p\td\u1eabn\tc\u00f9ng\tv\u1edbi\tv\u1eadt\tch\u1ea5t\tph\u1ea3i\tth\u1ecfa\tm\u00e3n\t\u0111\u1ecbnh\tlu\u1eadt v\u1ec1\tb\u1ea3o\tto\u00e0n\tc\u1ee7a\tn\u0103ng\tl\u01b0\u1ee3ng\t(v\u00e0\tc\u1ee7a\txung\tl\u1ef1c). Cu\u1ed1i\t c\u00f9ng,\t nguy\u00ean\t l\u00fd\t t\u01b0\u01a1ng\t \u0111\u1ed1i\t r\u1ed9ng\t cho\t ph\u00e9p\t ch\u00fang\t ta\t x\u00e1c \u0111\u1ecbnh\t\u1ea3nh\th\u01b0\u1edfng\tc\u1ee7a\ttr\u01b0\u1eddng\th\u1ea5p\td\u1eabn\tl\u00ean\tdi\u1ec5n\tbi\u1ebfn\tc\u1ee7a\tt\u1ea5t\tc\u1ea3\tc\u00e1c hi\u1ec7n\t t\u01b0\u1ee3ng\t \u0111\u00e3\t di\u1ec5n\t ra\t theo\t nh\u1eefng\t \u0111\u1ecbnh\t lu\u1eadt\t \u0111\u00e3\t bi\u1ebft\t khi\t tr\u01b0\u1eddng h\u1ea5p\t d\u1eabn\t v\u1eafng\t m\u1eb7t,\t ngh\u0129a\t l\u00e0\t ch\u00fang\t \u0111\u00e3\t kh\u1edbp\t v\u00e0o\t khu\u00f4n\t kh\u1ed5\t c\u1ee7a thuy\u1ebft\t t\u01b0\u01a1ng\t \u0111\u1ed1i\t h\u1eb9p.\t Khi\t l\u00e0m\t vi\u1ec7c\t \u0111\u00f3,\t ng\u01b0\u1eddi\t ta\t v\u1ec1\t nguy\u00ean\t t\u1eafc th\u1ef1c\t hi\u1ec7n\t theo\t \u0111\u00fang\t ph\u01b0\u01a1ng\t ph\u00e1p\t \u0111\u00e3\t \u0111\u01b0\u1ee3c\t tr\u00ecnh\t b\u00e0y\t tr\u01b0\u1edbc\t \u0111\u00e2y cho\t thanh\t \u0111o,\t \u0111\u1ed3ng\t h\u1ed3,\t v\u00e0\t c\u00e1c\t \u0111i\u1ec3m\t kh\u1ed1i\t l\u01b0\u1ee3ng\t chuy\u1ec3n\t \u0111\u1ed9ng\t t\u1ef1 do. Thuy\u1ebft\t tr\u01b0\u1eddng\t h\u1ea5p\t d\u1eabn\t \u0111\u01b0\u1ee3c\t suy\t di\u1ec5n\t nh\u01b0\t th\u1ebf\t t\u1eeb\t nguy\u00ean\t l\u00fd t\u01b0\u01a1ng\t \u0111\u1ed1i\t r\u1ed9ng\t c\u00f3\t \u01b0u\t \u0111i\u1ec3m\t v\u01b0\u1ee3t\t tr\u1ed9i\t kh\u00f4ng\t nh\u1eefng\t \u1edf\t v\u1ebb\t \u0111\u1eb9p\t c\u1ee7a n\u00f3,\t m\u00e0\t n\u00f3\t c\u00f2n\t lo\u1ea1i\t b\u1ecf\t kh\u00f4ng\t nh\u1eefng\t khuy\u1ebft\t \u0111i\u1ec3m\t \u0111\u00e3\t \u0111\u01b0\u1ee3c\t gi\u1ea3i th\u00edch\t \u1edf\t \u00a7\t 21\t v\u1ed1n\t n\u1eb1m\t trong\t b\u1ea3n\t ch\u1ea5t\t c\u1ee7a\t c\u01a1\t h\u1ecdc\t c\u1ed5\t \u0111i\u1ec3n;\t n\u00f3 kh\u00f4ng\tnh\u1eefng\tdi\u1ec5n\tgi\u1ea3i\t\u0111\u01b0\u1ee3c\t\u0111\u1ecbnh\tlu\u1eadt\tc\u1ee7a\tkinh\tnghi\u1ec7m\tv\u1ec1\t\u0111\u1eb3ng th\u1ee9c\t gi\u1eefa\t kh\u1ed1i\t l\u01b0\u1ee3ng\t qu\u00e1n\t t\u00ednh\t v\u00e0\t kh\u1ed1i\t l\u01b0\u1ee3ng\t h\u1ea5p\t d\u1eabn,\t m\u00e0\t c\u00f2n \u0111\u00e3\t gi\u1ea3i\t th\u00edch\t \u0111\u01b0\u1ee3c\t hai\t k\u1ebft\t qu\u1ea3\t quan\t s\u00e1t\t quan\t tr\u1ecdng\t v\u1edbi\t b\u1ea3n\t ch\u1ea5t kh\u00e1c\t nhau\t c\u1ee7a\t thi\u00ean\t v\u0103n\t h\u1ecdc\t m\u00e0\t c\u01a1\t h\u1ecdc\t c\u1ed5\t \u0111i\u1ec3n\t \u0111\u00e3\t b\u1ea5t\t l\u1ef1c.\t K\u1ebft qu\u1ea3\tth\u1ee9\thai\tc\u1ee7a\thai\tk\u1ebft\tqu\u1ea3\tn\u00e0y\tch\u00ednh\tl\u00e0\ts\u1ef1\tu\u1ed1n\tcong\tc\u1ee7a\tc\u00e1c\ttia s\u00e1ng\t d\u01b0\u1edbi\t t\u00e1c\t d\u1ee5ng\t tr\u01b0\u1eddng\t h\u1ea5p\t d\u1eabn\t c\u1ee7a\t m\u1eb7t\t tr\u1eddi,\t \u0111i\u1ec1u\t \u0111\u00e3\t \u0111\u01b0\u1ee3c ch\u00fang\t ta\t nh\u1eafc\t t\u1edbi.\t K\u1ebft\t qu\u1ea3\t th\u1ee9\t nh\u1ea5t\t li\u00ean\t quan\t \u0111\u1ebfn\t qu\u1ef9\t \u0111\u1ea1o\t c\u1ee7a h\u00e0nh\ttinh\tSao\tTh\u1ee7y[60]. N\u1ebfu\t ch\u00fang\t ta\t \u1ee9ng\t d\u1ee5ng\t c\u00e1c\t ph\u01b0\u01a1ng\t tr\u00ecnh\t c\u1ee7a\t thuy\u1ebft\t t\u01b0\u01a1ng \u0111\u1ed1i\t r\u1ed9ng\t l\u00ean\t tr\u01b0\u1eddng\t h\u1ee3p\t \u0111\u1eb7c\t bi\u1ec7t\t khi\t c\u00e1c\t tr\u01b0\u1eddng\t h\u1ea5p\t d\u1eabn\t c\u00f3\t th\u1ec3 \u0111\u01b0\u1ee3c\t xem\t l\u00e0\t y\u1ebfu,\t v\u00e0\t khi\t t\u1ea5t\t c\u1ea3\t c\u00e1c\t kh\u1ed1i\t l\u01b0\u1ee3ng\t chuy\u1ec3n\t \u0111\u1ed9ng\t \u0111\u1ed1i v\u1edbi\th\u1ec7\tt\u1ecda\t\u0111\u1ed9\tv\u1edbi\tm\u1ed9t\tv\u1eadn\tt\u1ed1c\tnh\u1ecf\tso\tv\u1edbi\tv\u1eadn\tt\u1ed1c\t\u00e1nh\ts\u00e1ng,\tch\u00fang ta\ts\u1ebd\t\u0111\u01b0\u1ee3c\tthuy\u1ebft\tNewton\tnh\u01b0\tm\u1ed9t\tx\u1ea5p\tx\u1ec9\tb\u1eadc\tnh\u1ea5t.\tDo\t\u0111\u00f3\tthuy\u1ebft sau\t \u0111\u01b0\u1ee3c\t suy\t ra\t \u1edf\t \u0111\u00e2y\t m\u00e0\t kh\u00f4ng\t c\u1ea7n\t m\u1ed9t\t gi\u1ea3\t thi\u1ebft\t \u0111\u1eb7c\t bi\u1ec7t\t n\u00e0o, trong\tkhi\tNewton\t\u0111\u00e3\t\u0111\u01b0a\tra\tgi\u1ea3\tthuy\u1ebft\tr\u1eb1ng\tl\u1ef1c\th\u00fat\tgi\u1eefa\tc\u00e1c\t\u0111i\u1ec3m","kh\u1ed1i\t l\u01b0\u1ee3ng\t t\u00e1c\t d\u1ee5ng\t l\u00ean\t nhau\t t\u1ec9\t l\u1ec7\t ngh\u1ecbch\t v\u1edbi\t b\u00ecnh\t ph\u01b0\u01a1ng kho\u1ea3ng\t c\u00e1ch\t ch\u00fang.\t N\u1ebfu\t ch\u00fang\t ta\t t\u0103ng\t \u0111\u1ed9\t ch\u00ednh\t x\u00e1c\t c\u1ee7a\t ph\u00e9p t\u00ednh,\t nh\u1eefng\t kh\u00e1c\t bi\u1ec7t\t v\u1edbi\t thuy\u1ebft\t Newton\t s\u1ebd\t xu\u1ea5t\t hi\u1ec7n,\t nh\u01b0ng\t v\u00ec qu\u00e1\t nh\u1ecf\t n\u00ean\t h\u1ea7u\t h\u1ebft\t ch\u00fang\t v\u1eabn\t c\u00f2n\t vu\u1ed9t\t kh\u1ecfi\t s\u1ef1\t quan\t s\u00e1t\t c\u1ee7a ch\u00fang\tta. Ch\u00fang\t ta\t \u1edf\t \u0111\u00e2y\t c\u1ea7n\t quan\t t\u00e2m\t \u0111\u1eb7c\t bi\u1ec7t\t \u0111\u1ebfn\t m\u1ed9t\t trong\t nh\u1eefng kh\u00e1c\tbi\u1ec7t\tn\u00e0y.\tTheo\tthuy\u1ebft\tNewton,\tm\u1ed9t\th\u00e0nh\ttinh\tchuy\u1ec3n\t\u0111\u1ed9ng quanh\tm\u1eb7t\ttr\u1eddi\ttr\u00ean\tm\u1ed9t\tqu\u1ef9\t\u0111\u1ea1o\tellip,\tv\u00e0\tellip\tn\u00e0y\ts\u1ebd\tgi\u1eef\tv\u1eefng\tv\u1ecb tr\u00ed\tc\u1ee7a\tn\u00f3\tm\u00e3i\tm\u00e3i\t\u0111\u1ed1i\tv\u1edbi\tc\u00e1c\tv\u00ec\tsao\tc\u1ed1\t\u0111\u1ecbnh,\tn\u1ebfu\tch\u00fang\tta\tb\u1ecf\tqua t\u00e1c\t d\u1ee5ng\t c\u1ee7a\t nh\u1eefng\t h\u00e0nh\t tinh\t kh\u00e1c\t l\u00ean\t h\u00e0nh\t tinh\t \u0111ang\t x\u00e9t,\t v\u00e0 b\u1ecf\t qua\t chuy\u1ec3n\t \u0111\u1ed9ng\t t\u1ef1\t th\u00e2n\t c\u1ee7a\t c\u00e1c\t v\u00ec\t sao\t c\u1ed1\t \u0111\u1ecbnh.\t B\u1ecf\t qua\t hai lo\u1ea1i\t \u1ea3nh\t h\u01b0\u1edfng\t n\u00e0y,\t v\u00e0\t n\u1ebfu\t thuy\u1ebft\t Newton\t l\u00e0\t \u0111\u00fang\t m\u1ed9t\t c\u00e1ch ch\u00ednh\tx\u00e1c,\tth\u00ec\tqu\u1ef9\t\u0111\u1ea1o\tc\u1ee7a\th\u00e0nh\ttinh\tl\u00e0\tm\u1ed9t\tqu\u1ef9\t\u0111\u1ea1o\tc\u1ed1\t\u0111\u1ecbnh\t\u0111\u1ed1i v\u1edbi\tc\u00e1c\tv\u00ec\tsao\tc\u1ed1\t\u0111\u1ecbnh.\tS\u1ef1\tsuy\tdi\u1ec5n\ttr\u00ean,\tv\u1ed1n\tc\u00f3\tth\u1ec3\t\u0111\u01b0\u1ee3c\tki\u1ec3m\ttra ch\u00ednh\tx\u00e1c\tcao,\tc\u00f3\tth\u1ec3\t\u0111\u01b0\u1ee3c\tx\u00e1c\tnh\u1eadn\tcho\tt\u1ea5t\tc\u1ea3\tc\u00e1c\th\u00e0nh\ttinh\tv\u1edbi \u0111\u1ed9\t ch\u00ednh\t x\u00e1c\t \u0111\u1ea1t\t \u0111\u01b0\u1ee3c\t b\u1edfi\t \u0111\u1ed9\t tinh\t vi\t cho\t ph\u00e9p\t h\u00f4m\t nay,\t tr\u1eeb\t Sao Th\u1ee7y\t l\u00e0\t h\u00e0nh\t tinh\t g\u1ea7n\t m\u1eb7t\t tr\u1eddi\t nh\u1ea5t.\t Tuy\t nhi\u00ean\t \u0111\u1ed1i\t v\u1edbi\t h\u00e0nh tinh\tSao\tTh\u1ee7y\tch\u00fang\tta\tbi\u1ebft\tt\u1eeb\tLe\tVerrier,\th\u00ecnh\tellip\tc\u1ee7a\tqu\u1ef9\t\u0111\u1ea1o, sau\tkhi\t\u0111\u00e3\t\u0111\u01b0\u1ee3c\ttu\tch\u1ec9nh\ttheo\tngh\u0129a\ttr\u00ean,\tkh\u00f4ng\th\u1ec1\t\u0111\u1ee9ng\ty\u00ean\t\u0111\u1ed1i v\u1edbi\t c\u00e1c\t v\u00ec\t sao\t c\u1ed1\t \u0111\u1ecbnh,\t m\u00e0\t chuy\u1ec3n\t \u0111\u1ed9ng\t quay,\t m\u1eb7c\t d\u00f9\t v\u00f4\t c\u00f9ng ch\u1eadm\t trong\t m\u1eb7t\t ph\u1eb3ng\t c\u1ee7a\t qu\u1ef9\t \u0111\u1ea1o,\t v\u00e0\t theo\t ngh\u0129a\t c\u1ee7a\t chuy\u1ec3n \u0111\u1ed9ng\tqu\u1ef9\t\u0111\u1ea1o.\tTr\u1ecb\ts\u1ed1\tquan\ts\u00e1t\t\u0111\u01b0\u1ee3c\tc\u1ee7a\tchuy\u1ec3n\t\u0111\u1ed9ng\tquay\tv\u00f2ng n\u00e0y\t c\u1ee7a\t qu\u1ef9\t \u0111\u1ea1o\t ellip\t l\u00e0\t 43\t gi\u00e2y\t cung\t trong\t m\u1ed9t\t tr\u0103m\t n\u0103m,\t m\u1ed9t con\ts\u1ed1\tch\u00ednh\tx\u00e1c\tv\u1edbi\tsai\ts\u1ed1\tv\u00e0i\tgi\u00e2y\tcung\ttr\u1edf\tl\u1ea1i.\tS\u1ef1\tgi\u1ea3i\tth\u00edch\thi\u1ec7n t\u01b0\u1ee3ng\t n\u00e0y\t theo\t c\u01a1\t h\u1ecdc\t c\u1ed5\t \u0111i\u1ec3n\t ch\u1ec9\t th\u00e0nh\t c\u00f4ng\t b\u1eb1ng\t vi\u1ec7c\t ch\u1ea5p nh\u1eadn\tnh\u1eefng\tgi\u1ea3\tthuy\u1ebft\tt\u1ef1\tngh\u0129\tra,\tr\u1ea5t\t\u00edt\tkh\u1ea3\tn\u0103ng\tc\u00f3\tl\u00fd,\tch\u1ec9\td\u00e0nh ri\u00eang\tcho\tm\u1ee5c\t\u0111\u00edch\tn\u00e0y\tm\u00e0\tth\u00f4i. Tr\u00ean\t c\u01a1\t s\u1edf\t c\u1ee7a\t thuy\u1ebft\t t\u01b0\u01a1ng\t \u0111\u1ed1i\t r\u1ed9ng,\t ng\u01b0\u1eddi\t ta\t t\u00ecm\t th\u1ea5y\t qu\u1ef9 \u0111\u1ea1o\t ellip\t c\u1ee7a\t m\u1ed7i\t h\u00e0nh\t tinh\t xung\t quanh\t m\u1eb7t\t tr\u1eddi\t t\u1ea5t\t y\u1ebfu\t ph\u1ea3i quay\t theo\t c\u00e1ch\t tr\u00ecnh\t b\u00e0y\t tr\u00ean;\t m\u1ed7i\t chuy\u1ec3n\t \u0111\u1ed9ng\t quay\t n\u00e0y\t \u0111\u1ed1i v\u1edbi\tt\u1ea5t\tc\u1ea3\tc\u00e1c\th\u00e0nh\ttinh,\ttr\u1eeb\tSao\tTh\u1ee7y,\tl\u00e0\tqu\u00e1\tnh\u1ecf\t\u0111\u1ec3\tc\u00f3\tth\u1ec3\tquan s\u00e1t\t\u0111\u01b0\u1ee3c\tv\u1edbi\t\u0111\u1ed9\tch\u00ednh\tx\u00e1c\tc\u1ee7a\tkh\u1ea3\tn\u0103ng\tquan\ts\u00e1t\tc\u00f3\tth\u1ec3\t\u0111\u1ea1t\t\u0111\u01b0\u1ee3c h\u00f4m\tnay;\tnh\u01b0ng\tchuy\u1ec3n\t\u0111\u1ed9ng\tquay\t\u0111\u00f3\t\u1edf\tSao\tTh\u1ee7y\tph\u1ea3i\tc\u00f3\ttr\u1ecb\ts\u1ed1 43\tgi\u00e2y\tcung,\tch\u00ednh\tx\u00e1c\tnh\u01b0\tk\u1ebft\tqu\u1ea3\tc\u00e1c\tquan\ts\u00e1t\t\u0111\u00e3\tcho\tth\u1ea5y. Ngo\u00e0i\tra,\t\u0111\u1ebfn\tnay\tch\u1ec9\tc\u00f2n\tm\u1ed9t\th\u1ec7\tlu\u1eadn\tc\u00f3\tth\u1ec3\t\u0111\u01b0\u1ee3c\tr\u00fat\tra\tt\u1eeb\tl\u00fd thuy\u1ebft,\t v\u00e0\t c\u00f3\t th\u1ec3\t \u0111\u01b0\u1ee3c\t ki\u1ec3m\t ch\u1ee9ng\t b\u1eb1ng\t quan\t s\u00e1t,\t \u0111\u00f3\t l\u00e0\t s\u1ef1\t d\u1ecbch chuy\u1ec3n\t c\u1ee7a\t c\u00e1c\t v\u1ea1ch\t quang\t ph\u1ed5\t c\u1ee7a\t \u00e1nh\t s\u00e1ng\t t\u1eeb\t nh\u1eefng\t v\u00ec\t sao","l\u1edbn\t \u0111\u1ebfn\t ch\u00fang\t ta,\t so\t s\u00e1nh\t v\u1edbi\t c\u00e1c\t v\u1ea1ch\t t\u01b0\u01a1ng\t \u1ee9ng\t c\u1ee7a\t \u00e1nh\t s\u00e1ng \u0111\u01b0\u1ee3c\t t\u1ea1o\t ra\t m\u1ed9t\t c\u00e1ch\t t\u01b0\u01a1ng\t t\u1ef1\t tr\u00ean\t m\u1eb7t\t \u0111\u1ea5t\t (ngh\u0129a\t l\u00e0\t b\u1edfi\t c\u00f9ng lo\u1ea1i\tph\u00e2n\tt\u1eed).\tT\u00f4i\tkh\u00f4ng\tnghi\tng\u1edd\tr\u1eb1ng\th\u1ec7\tlu\u1eadn\tn\u00e0y\tc\u1ee7a\tl\u00fd\tthuy\u1ebft c\u0169ng\ts\u1ebd\tnhanh\tch\u00f3ng\tt\u00ecm\t\u0111\u01b0\u1ee3c\ts\u1ef1\tx\u00e1c\tnh\u1eadn.","Ph\u1ea7n\tIII SUY\tNGH\u0128\tV\u1ec0\tV\u0168\tTR\u1ee4\tNH\u01af\tM\u1ed8T\tT\u1ed4NG\tTH\u1ec2 (\u00a7\t30\t-\t\u00a7\t32) \u00a7\t30 Nh\u1eefng\tKh\u00f3\tKh\u0103n\tV\u0169\tTr\u1ee5\tH\u1ecdc\tc\u1ee7a\tThuy\u1ebft\tNewton Ngo\u00e0i\t nh\u1eefng\t kh\u00f3\t kh\u0103n\t \u0111\u00e3\t \u0111\u01b0\u1ee3c\t tr\u00ecnh\t b\u00e0y\t trong\t \u00a7\t 21,\t c\u00f2n\t c\u00f3 m\u1ed9t\tkh\u00f3\tkh\u0103n\tc\u01a1\tb\u1ea3n\tth\u1ee9\thai\tti\u1ec1m\tt\u00e0ng\ttrong\tc\u01a1\th\u1ecdc\tthi\u00ean\tth\u1ec3\tc\u1ed5 \u0111i\u1ec3n,\t\u0111\u01b0\u1ee3c\tth\u1ea3o\tlu\u1eadn\t\u0111\u1ea7u\tti\u00ean\tm\u1ed9t\tc\u00e1ch\tchi\tti\u1ebft,\ttheo\tt\u00f4i\tbi\u1ebft,\tb\u1edfi nh\u00e0\tthi\u00ean\tv\u0103n\th\u1ecdc\tSeeliger.\tN\u1ebfu\tng\u01b0\u1eddi\tta\tsuy\tngh\u0129\tv\u1ec1\tc\u00e2u\th\u1ecfi,\tv\u0169 tr\u1ee5\t \u0111\u01b0\u1ee3c\t hi\u1ec3u\t th\u1ebf\t n\u00e0o\t nh\u01b0\t m\u1ed9t\t t\u1ed1ng\t th\u1ec3,\t th\u00ec\t c\u00e2u\t tr\u1ea3\t l\u1eddi\t \u0111\u1ea7u\t ti\u00ean t\u1ef1\t n\u00f3\t g\u1ee3i\t ra\t cho\t ch\u00fang\t ta\t ph\u1ea3i\t l\u00e0\t nh\u01b0\t sau.\t V\u0169\t tr\u1ee5\t l\u00e0\t v\u00f4\t h\u1ea1n\t v\u1ec1 kh\u00f4ng\tgian\t(v\u00e0\tth\u1eddi\tgian).\t\u1ede\tkh\u1eafp\tn\u01a1i\tc\u00f3\tsao,\tsao\tcho\tm\u1eadt\t\u0111\u1ed9\tc\u1ee7a v\u1eadt\t ch\u1ea5t,\t x\u00e9t\t v\u1ec1\t chi\t ti\u1ebft\t r\u1ea5t\t kh\u00e1c\t nhau,\t nh\u01b0ng\t x\u00e9t\t v\u1ec1\t b\u00ecnh\t qu\u00e2n tr\u00ean\tdi\u1ec7n\tr\u1ed9ng\tth\u00ec\t\u1edf\tkh\u1eafp\tn\u01a1i\t\u0111\u1ec1u\tgi\u1ed1ng\tnhau.\tN\u00f3i\tm\u1ed9t\tc\u00e1ch\tkh\u00e1c: d\u00f9\t\u0111i\txa\tth\u1ebf\tn\u00e0o\tv\u00e0o\tv\u0169\ttr\u1ee5,\tch\u00fang\tta\tv\u1eabn\tt\u00ecm\tth\u1ea5y\tkh\u1eafp\tn\u01a1i\tm\u1ed9t \u0111\u00e1m\t\u0111\u00f4ng\t\u0111\u00fac,\tr\u1eddi\tr\u1ea1c\tc\u00e1c\tv\u00ec\tsao\tc\u1ed1\t\u0111\u1ecbnh\tc\u00f3\tg\u1ea7n\tc\u00f9ng\tt\u00ednh\tch\u1ea5t\tv\u00e0 m\u1eadt\t\u0111\u1ed9. Quan\t ni\u1ec7m\t n\u00e0y\t kh\u00f4ng\t dung\t h\u1ee3p\t \u0111\u01b0\u1ee3c\t v\u1edbi\t thuy\u1ebft\t Newton. Thuy\u1ebft\tn\u00e0y\t\u0111\u00fang\tra\t\u0111\u00f2i\th\u1ecfi\tv\u0169\ttr\u1ee5\tph\u1ea3i\tc\u00f3\tm\u1ed9t\tlo\u1ea1i\ttrung\tt\u00e2m,\t\u1edf \u0111\u00f3\tm\u1eadt\t\u0111\u1ed9\tc\u00e1c\tv\u00ec\tsao\tc\u00f3\ttr\u1ecb\ts\u1ed1\tc\u1ef1c\t\u0111\u1ea1i,\tv\u00e0\tgi\u1ea3m\td\u1ea7n\tkhi\tch\u00fang\tta\t\u0111i ra\t ngo\u00e0i\t kh\u1ecfi\t trung\t t\u00e2m,\t \u0111\u1ec3\t cu\u1ed1i\t c\u00f9ng\t \u1edf\t nh\u1eefng\t v\u00f9ng\t xa\t x\u00f4i\t ch\u1ec9 c\u00f2n\tl\u1ea1i\tm\u1ed9t\tkh\u00f4ng\tgian\tv\u00f4\tc\u00f9ng\tr\u1ed7ng.\tV\u0169\ttr\u1ee5\tc\u1ee7a\tnh\u1eefng\tv\u00ec\tsao\tdo \u0111\u00f3\tph\u1ea3i\tl\u00e0m\tth\u00e0nh\tm\u1ed9t\th\u00f2n\t\u0111\u1ea3o\th\u1eefu\th\u1ea1n\ttrong\tc\u00e1i\t\u0111\u1ea1i\td\u01b0\u01a1ng\tv\u00f4 h\u1ea1n\tc\u1ee7a\tkh\u00f4ng\tgian[61]. Quan\tni\u1ec7m\tn\u00e0y\tt\u1ef1\tn\u00f3\tl\u00e0\t\u00edt\tth\u1ecfa\t\u0111\u00e1ng.\tL\u1ea1i\tc\u00e0ng\t\u00edt\tth\u1ecfa\t\u0111\u00e1ng\th\u01a1n v\u00ec\tn\u00f3\t\u0111\u01b0a\t\u0111\u1ebfn\th\u1ec7\tlu\u1eadn\tr\u1eb1ng,\t\u00e1nh\ts\u00e1ng\tph\u00e1t\tra\tt\u1eeb\tc\u00e1c\tv\u00ec\tsao,\tc\u0169ng nh\u01b0\t c\u00e1c\t v\u00ec\t sao\t ri\u00eang\t l\u1ebb\t c\u1ee7a\t h\u1ec7\t th\u1ed1ng\t tinh\t t\u00fa,\t li\u00ean\t t\u1ee5c\t \u0111i\t v\u1ec1\t mi\u1ec1n v\u00f4\t c\u1ef1c,\t kh\u00f4ng\t bao\t gi\u1edd\t tr\u1edf\t l\u1ea1i\t v\u00e0\t kh\u00f4ng\t m\u1ed9t\t l\u1ea7n\t c\u00f3\t t\u01b0\u01a1ng\t t\u00e1c\t v\u1edbi c\u00e1c\tv\u1eadt\tth\u1ec3\tt\u1ef1\tnhi\u00ean\tkh\u00e1c.\tV\u0169\ttr\u1ee5\tv\u1edbi\tv\u1eadt\tch\u1ea5t\tt\u1eadp\ttrung\tv\u00e0o\tmi\u1ec1n h\u1eefu\th\u1ea1n\tnh\u01b0\tth\u1ebf\tph\u1ea3i\td\u1ea7n\td\u1ea7n\tngh\u00e8o\t\u0111i\tm\u1ed9t\tc\u00e1ch\th\u1ec7\tth\u1ed1ng. \u0110\u1ec3\t tho\u00e1t\t kh\u1ecfi\t t\u00ecnh\t h\u00ecnh\t kh\u00f3\t x\u1ee9\t tr\u00ean,\t Seeliger\t \u0111\u00e3\t c\u1ea3i\t bi\u00ean\t \u0111\u1ecbnh lu\u1eadt\tNewton\ttheo\th\u01b0\u1edbng\t\u0111\u1ec3\tcho\tl\u1ef1c\th\u1ea5p\td\u1eabn\tc\u1ee7a\thai\tkh\u1ed1i\tl\u01b0\u1ee3ng\t\u1edf","c\u00e1c\tkho\u1ea3ng\tc\u00e1ch\tl\u1edbn\tgi\u1ea3m\t\u0111i\tnhanh\th\u01a1n\tl\u00e0\ttheo\t\u0111\u1ecbnh\tlu\u1eadt\t1\t\/r\t2\t(r l\u00e0\t kho\u1ea3ng\t c\u00e1ch).\t B\u1eb1ng\t c\u00e1ch\t \u0111\u00f3\t ng\u01b0\u1eddi\t ta\t c\u00f3\t th\u1ec3\t l\u00e0m\t cho\t m\u1eadt\t \u0111\u1ed9 b\u00ecnh\t qu\u00e2n\t c\u1ee7a\t v\u1eadt\t ch\u1ea5t\t l\u00e0\t m\u1ed9t\t h\u1eb1ng\t s\u1ed1\t \u1edf\t kh\u1eafp\t n\u01a1i,\t ngay\t t\u1eadn\t c\u00e1c mi\u1ec1n\t v\u00f4\t c\u1ef1c,\t m\u00e0\t kh\u00f4ng\t c\u00f3\t c\u00e1c\t tr\u01b0\u1eddng\t h\u1ea5p\t d\u1eabn\t v\u00f4\t c\u00f9ng\t l\u1edbn\t n\u00e0o h\u00ecnh\t th\u00e0nh.\t Nh\u01b0\t th\u1ebf\t ng\u01b0\u1eddi\t ta\t v\u1ee9t\t b\u1ecf\t \u0111\u01b0\u1ee3c\t quan\t ni\u1ec7m\t kh\u00f4ng \u0111\u01b0\u1ee3c\t thi\u1ec7n\t c\u1ea3m\t cho\t r\u1eb1ng\t v\u0169\t tr\u1ee5\t v\u1eadt\t ch\u1ea5t\t ph\u1ea3i\t c\u00f3\t m\u1ed9t\t lo\u1ea1i\t trung t\u00e2m\t\u0111i\u1ec3m.\tD\u0129\tnhi\u00ean\tng\u01b0\u1eddi\tta\tmua\t\u0111\u01b0\u1ee3c\ts\u1ef1\tgi\u1ea3i\tph\u00f3ng\tn\u00e0y\tkh\u1ecfi\ts\u1ef1 b\u1ebf\t t\u1eafc\t c\u00f3\t t\u00ednh\t c\u00e1ch\t nguy\u00ean\t l\u00fd\t \u0111\u00e3\t \u0111\u01b0\u1ee3c\t tr\u00ecnh\t b\u00e0y,\t \u0111\u1ec3\t chu\u1ed1c\t l\u1ea5y m\u1ed9t\t s\u1ef1\t bi\u1ebfn\t c\u1ea3i\t v\u00e0\t ph\u1ee9c\t t\u1ea1p\t h\u00f3a\t \u0111\u1ecbnh\t lu\u1eadt\t Newton,\t nh\u1eefng\t th\u1ee9 kh\u00f4ng\th\u1ec1\tl\u00fd\tgi\u1ea3i\t\u0111\u01b0\u1ee3c\tt\u1eeb\tkinh\tnghi\u1ec7m\thay\tl\u00fd\tthuy\u1ebft.\tCh\u00fang\tta\tc\u00f3 th\u1ec3\th\u00ecnh\tdung\tm\u1ed9t\ts\u1ed1\tnhi\u1ec1u\tb\u1ea5t\tk\u1ef3\tc\u00e1c\t\u0111\u1ecbnh\tlu\u1eadt\tc\u00f9ng\tcho\tra\tm\u1ed9t k\u1ebft\tqu\u1ea3,\tnh\u01b0ng\tch\u00fang\tta\tl\u1ea1i\tkh\u00f4ng\tth\u1ec3\t\u0111\u01b0a\tra\t\u0111\u01b0\u1ee3c\tm\u1ed9t\tl\u00fd\tdo\t\u0111\u1ec3 bi\u1ec7n\tminh\tt\u1ea1i\tsao\tm\u1ed9t\ttrong\tc\u00e1c\t\u0111\u1ecbnh\tlu\u1eadt\t\u0111\u00f3\tl\u1ea1i\t\u0111\u01b0\u1ee3c\t\u01b0u\t\u0111\u00e3i\th\u01a1n nh\u1eefng\t c\u00e1i\t kh\u00e1c;\t b\u1edfi\t v\u00ec,\t c\u0169ng\t gi\u1ed1ng\t nh\u01b0\t \u0111\u1ecbnh\t lu\u1eadt\t Newton,\t m\u1ed7i \u0111\u1ecbnh\tlu\u1eadt\tkia\tc\u0169ng\t\u00edt\t\u0111\u01b0\u1ee3c\tx\u00e2y\td\u1ef1ng\th\u1ee3p\tl\u00fd\ttr\u00ean\tnh\u1eefng\tnguy\u00ean\tl\u00fd l\u00fd\tthuy\u1ebft\tph\u1ed5\tqu\u00e1t\th\u01a1n.","\u00a7\t31 Kh\u1ea3\tN\u0103ng\tc\u1ee7a\tM\u1ed9t\tV\u0169\tTr\u1ee5\t\\\"H\u1eefu\tH\u1ea1n\\\"\tnh\u01b0ng\t\\\"Kh\u00f4ng\tGi\u1edbi\tH\u1ea1n\\\" Tuy\t nhi\u00ean,\t nh\u1eefng\t suy\t \u0111o\u00e1n\t v\u1ec1\t c\u1ea5u\t tr\u00fac\t c\u1ee7a\t v\u0169\t tr\u1ee5\t c\u0169ng\t c\u00f2n di\u1ec5n\t bi\u1ebfn\t theo\t m\u1ed9t\t h\u01b0\u1edbng\t ho\u00e0n\t to\u00e0n\t kh\u00e1c.\t S\u1ef1\t ph\u00e1t\t tri\u1ec3n\t c\u1ee7a h\u00ecnh\th\u1ecdc\tphi-Euclid\tth\u1ef1c\tt\u1ebf\t\u0111\u00e3\t\u0111\u01b0a\t\u0111\u1ebfn\tnh\u1eadn\tth\u1ee9c,\tr\u1eb1ng\tng\u01b0\u1eddi\tta c\u00f3\t th\u1ec3\t nghi\t ng\u1edd\t v\u1ec1\t t\u00ednh\t v\u00f4\t h\u1ea1n\t c\u1ee7a\t kh\u00f4ng\t gian\t ch\u00fang\t ta,\t m\u00e0 kh\u00f4ng\t r\u01a1i\t v\u00e0o\t m\u00e2u\t thu\u1eabn\t v\u1edbi\t c\u00e1c\t \u0111\u1ecbnh\t lu\u1eadt\t c\u1ee7a\t t\u01b0\t duy,\t hay\t v\u1edbi kinh\t nghi\u1ec7m\t (Riemann,\t Helmholtz).\t Nh\u1eefng\t \u0111i\u1ec1u\t n\u00e0y\t \u0111\u00e3\t \u0111\u01b0\u1ee3c tr\u00ecnh\t b\u00e0y\t chi\t ti\u1ebft\t b\u1edfi\t Helmholtz\t v\u00e0\t Poincar\u00e9\t v\u1edbi\t m\u1ed9t\t s\u1ef1\t s\u00e1ng\t s\u1ee7a kh\u00f4ng\t th\u1ec3\t h\u01a1n\t \u0111\u01b0\u1ee3c\t n\u1eefa;\t \u1edf\t \u0111\u00e2y\t t\u00f4i\t ch\u1ec9\t c\u00f3\t th\u1ec3\t \u0111\u1ec1\t c\u1eadp\t m\u1ed9t\t c\u00e1ch ng\u1eafn\tg\u1ecdn. Tr\u01b0\u1edbc\t ti\u00ean\t ch\u00fang\t ta\t t\u01b0\u1edfng\t t\u01b0\u1ee3ng\t m\u1ed9t\t s\u1ef1\t t\u1ed3n\t t\u1ea1i\t (\u0111\u1eddi\t s\u1ed1ng) di\u1ec5n\t ra\t trong\t kh\u00f4ng\t gian\t hai\t chi\u1ec1u.\t C\u00e1c\t sinh\t v\u1eadt\t ph\u1eb3ng\t \u0111i\t l\u1ea1i\t t\u1ef1 do\t trong\t m\u1ed9t\t m\u1eb7t\t ph\u1eb3ng\t c\u00f9ng\t v\u1edbi\t c\u00e1c\t d\u1ee5ng\t c\u1ee5\t lao\t \u0111\u1ed9ng\t ph\u1eb3ng, \u0111\u1eb7c\t bi\u1ec7t\t v\u1edbi\t nh\u1eefng\t thanh\t \u0111o\t r\u1eafn,\t ph\u1eb3ng.\t Ngo\u00e0i\t m\u1eb7t\t ph\u1eb3ng\t n\u00e0y ra,\tkh\u00f4ng\tc\u00f3\t g\u00ec\tt\u1ed3n\t t\u1ea1i\t\u0111\u1ed1i\tv\u1edbi\t h\u1ecd\tc\u1ea3,\t nh\u1eefng\tg\u00ec\th\u1ecd\t quan\ts\u00e1t\t th\u1ea5y x\u1ea3y\t \u0111\u1ebfn\t cho\t h\u1ecd\t v\u00e0\t cho\t nh\u1eefng\t v\u1eadt\t ph\u1eb3ng\t c\u1ee7a\t h\u1ecd\t l\u00e0m\t th\u00e0nh\t m\u1ed9t th\u1ebf\t gi\u1edbi\t ho\u00e0n\t to\u00e0n\t kh\u00e9p\t k\u00edn.\t \u0110\u1eb7c\t bi\u1ec7t\t vi\u1ec7c\t x\u00e2y\t d\u1ef1ng\t h\u00ecnh\t h\u1ecdc Euclid\tph\u1eb3ng\tv\u1edbi\tc\u00e1c\tque\tcon\tl\u00e0\tkh\u1ea3\tthi,\tth\u00ed\td\u1ee5\tnh\u01b0\tvi\u1ec7c\tx\u00e2y\td\u1ef1ng m\u1ea1ng\ttr\u00ean\tm\u1eb7t\tb\u00e0n\t(b\u1eb1ng\tnh\u1eefng\t\u00f4\tvu\u00f4ng)\t\u0111\u00e3\t\u0111\u01b0\u1ee3c\txem\tx\u00e9t\ttrong \u00a7\t 24.\t V\u0169\t tr\u1ee5\t c\u1ee7a\t nh\u1eefng\t sinh\t v\u1eadt\t n\u00e0y,\t kh\u00e1c\t v\u1edbi\t v\u0169\t tr\u1ee5\t c\u1ee7a\t ch\u00fang ta,\tl\u00e0\thai\tchi\u1ec1u\tv\u1ec1\tkh\u00f4ng\tgian,\tnh\u01b0ng\tc\u0169ng\tnh\u01b0\tv\u0169\ttr\u1ee5\tch\u00fang\tta, \u0111\u01b0\u1ee3c\tn\u1edbi\tr\u1ed9ng\tra\tv\u00f4\th\u1ea1n.\tN\u00f3\tc\u00f3\tch\u1ed7\tcho\tv\u00f4\ts\u1ed1\th\u00ecnh\tvu\u00f4ng\tc\u1ee7a\tc\u00e1c que\t con,\t ngh\u0129a\t l\u00e0\t th\u1ec3\t t\u00edch\t (\u0111i\u1ec7n\t t\u00edch)\t c\u1ee7a\t n\u00f3\t l\u00e0\t v\u00f4\t c\u1ef1c.\t N\u1ebfu\t c\u00e1c sinh\tv\u1eadt\tn\u00e0y\tb\u1ea3o,\tv\u0169\ttr\u1ee5\tc\u1ee7a\th\u1ecd\tl\u00e0\t\\\"ph\u1eb3ng\\\",\tth\u00ec\t\u0111i\u1ec1u\t\u0111\u00f3\tc\u00f3\t\u00fd\tngh\u0129a, b\u1edfi\t h\u1ecd\t mu\u1ed1n\t n\u00f3i\t h\u1ecd\t c\u00f3\t th\u1ec3\t th\u1ef1c\t hi\u1ec7n\t \u0111\u01b0\u1ee3c\t ph\u00e9p\t x\u00e2y\t d\u1ef1ng\t h\u00ecnh h\u1ecdc\tEuclid\tc\u1ee7a\tm\u1eb7t\tph\u1eb3ng\tb\u1eb1ng\tc\u00e1c\tque\tcon\tc\u1ee7a\th\u1ecd,\t\u1edf\t\u0111\u00f3\tc\u00e1c\tque con\t lu\u00f4n\t lu\u00f4n\t t\u01b0\u1ee3ng\t tr\u01b0ng\t c\u00f9ng\t kho\u1ea3ng\t c\u00e1ch,\t v\u00e0\t \u0111\u1ed9c\t l\u1eadp\t v\u1edbi\t v\u1ecb tr\u00ed\tc\u1ee7a\tch\u00fang. B\u00e2y\tgi\u1edd\tch\u00fang\tta\tl\u1ea1i\tt\u01b0\u1edfng\tt\u01b0\u1ee3ng\t\u0111\u1ebfn\tm\u1ed9t\ts\u1ef1\tt\u1ed3n\tt\u1ea1i\thai\tchi\u1ec1u th\u1ee9\t hai,\t nh\u01b0ng\t l\u1ea7n\t n\u00e0y\t tr\u00ean\t m\u1ed9t\t b\u1ec1\t m\u1eb7t\t c\u1ee7a\t h\u00ecnh\t c\u1ea7u\t thay\t v\u00ec tr\u00ean\t m\u1eb7t\t ph\u1eb3ng.\t C\u00e1c\t sinh\t v\u1eadt\t d\u1eb9t\t (d\u1eb9p),\t v\u1edbi\t c\u00e1c\t th\u01b0\u1edbc\t \u0111o\t v\u00e0 nh\u1eefng\t d\u1ee5ng\t c\u1ee5\t kh\u00e1c\t c\u1ee7a\t h\u1ecd,\t n\u1eb1m\t ch\u00ednh\t x\u00e1c\t tr\u00ean\t b\u1ec1\t m\u1eb7t\t n\u00e0y\t v\u00e0 kh\u00f4ng\tth\u1ec3\tr\u1eddi\tkh\u1ecfi\tn\u00f3;\tn\u00f3i\t\u0111\u00fang\th\u01a1n\tc\u1ea3\tv\u0169\ttr\u1ee5\ttri\tgi\u00e1c\tc\u1ee7a\th\u1ecd\ttr\u1ea3i d\u00e0i\tra\tch\u1ec9\ttr\u00ean\tb\u1ec1\tm\u1eb7t\th\u00ecnh\tc\u1ea7u.\tC\u00e1c\tsinh\tv\u1eadt\tn\u00e0y\tc\u00f3\tth\u1ec3\txem\th\u00ecnh h\u1ecdc\t c\u1ee7a\t v\u0169\t tr\u1ee5\t h\u1ecd\t l\u00e0\t h\u00ecnh\t h\u1ecdc\t Euclid\t hai\t chi\u1ec1u,\t v\u00e0\t \u0111\u1ed3ng\t th\u1eddi\t c\u00e1c","que\t con\t c\u1ee7a\t h\u1ecd\t nh\u01b0\t s\u1ef1\t th\u1ec3\t hi\u1ec7n\t c\u1ee7a\t \\\"kho\u1ea3ng\t c\u00e1ch\\\"\t \u0111\u01b0\u1ee3c\t kh\u00f4ng? H\u1ecd\tkh\u00f4ng\tth\u1ec3\tl\u00e0m\t\u0111i\u1ec1u\t\u0111\u00f3.\tB\u1edfi\tv\u00ec\tn\u1ebfu\th\u1ecd\tt\u00ecm\tc\u00e1ch\tth\u1ef1c\thi\u1ec7n\tm\u1ed9t \u0111\u01b0\u1eddng\tth\u1eb3ng,\th\u1ecd\ts\u1ebd\tnh\u1eadn\t\u0111\u01b0\u1ee3c\tm\u1ed9t\t\u0111\u01b0\u1eddng\tcong,\tc\u00e1i\tm\u00e0\tch\u00fang\tta \\\"nh\u1eefng\tsinh\tv\u1eadt\tba\tchi\u1ec1u\\\"\tg\u1ecdi\tl\u00e0\tm\u1ed9t\th\u00ecnh\ttr\u00f2n\tl\u1edbn,\tngh\u0129a\tl\u00e0\tm\u1ed9t \u0111\u01b0\u1eddng\t kh\u00e9p\t k\u00edn\t trong\t n\u00f3\t v\u1edbi\t m\u1ed9t\t \u0111\u1ed9\t d\u00e0i\t h\u1eefu\t h\u1ea1n\t nh\u1ea5t\t \u0111\u1ecbnh,\t v\u00e0 c\u00f3\tth\u1ec3\t\u0111o\t\u0111\u01b0\u1ee3c\tv\u1edbi\tm\u1ed9t\tque\tcon.\tT\u01b0\u01a1ng\tt\u1ef1,\tv\u0169\ttr\u1ee5\tn\u00e0y\tc\u00f3\tm\u1ed9t\tdi\u1ec7n t\u00edch\t h\u1eefu\t h\u1ea1n,\t c\u00f3\t th\u1ec3\t \u0111\u01b0\u1ee3c\t so\t s\u00e1nh\t v\u1edbi\t di\u1ec7n\t t\u00edch\t c\u1ee7a\t m\u1ed9t\t h\u00ecnh vu\u00f4ng\t\u0111\u01b0\u1ee3c\tx\u00e2y\td\u1ef1ng\tb\u1edfi\tc\u00e1c\tque\tcon.\t\u0110i\u1ec1u\tth\u00fa\tv\u1ecb\tl\u1edbn\tt\u1eeb\tsuy\tngh\u0129 n\u00e0y\t n\u1eb1m\t \u1edf\t nh\u1eadn\t th\u1ee9c:\t V\u0169\t tr\u1ee5\t c\u1ee7a\t nh\u1eefng\t sinh\t v\u1eadt\t n\u00e0y\t l\u00e0\t h\u1eefu\t h\u1ea1n nh\u01b0ng\tl\u1ea1i\tkh\u00f4ng\tc\u00f3\tranh\tgi\u1edbi\t[62]. Nh\u01b0ng\t c\u00e1c\t sinh\t v\u1eadt\t tr\u00ean\t b\u1ec1\t m\u1eb7t\t h\u00ecnh\t c\u1ea7u\t n\u00e0y\t kh\u00f4ng\t c\u1ea7n\t l\u00e0m m\u1ed9t\t cu\u1ed9c\t du\t l\u1ecbch\t th\u1ebf\t gi\u1edbi\t m\u1edbi\t c\u00f3\t th\u1ec3\t nh\u1eadn\t th\u1ee9c\t \u0111\u01b0\u1ee3c\t r\u1eb1ng\t h\u1ecd s\u1ed1ng\t trong\t m\u1ed9t\t v\u0169\t tr\u1ee5\t kh\u00f4ng\t ph\u1ea3i\t Euclid.\t H\u1ecd\t c\u00f3\t th\u1ec3\t t\u1ef1\t thuy\u1ebft ph\u1ee5c\t v\u1ec1\t \u0111i\u1ec1u\t \u0111\u00f3\t tr\u00ean\t m\u1ed7i\t ph\u1ea7n\t c\u1ee7a\t v\u0169\t tr\u1ee5\t h\u1ecd,\t mi\u1ec5n\t l\u00e0\t ph\u1ea7n\t n\u00e0y kh\u00f4ng\t qu\u00e1\t nh\u1ecf.\t Xu\u1ea5t\t ph\u00e1t\t t\u1eeb\t m\u1ed9t\t \u0111i\u1ec3m,\t h\u1ecd\t k\u00e9o\t nh\u1eefng\t \\\"\u0111\u01b0\u1eddng th\u1eb3ng\\\"\t (t\u1ee9c\t c\u00e1c\t cung\t tr\u00f2n,\t x\u00e9t\t t\u1eeb\t kh\u00f4ng\t gian\t ba\t chi\u1ec1u)\t c\u00f3\t chi\u1ec1u d\u00e0i\t b\u1eb1ng\t nhau\t t\u1ecfa\t \u0111i\t m\u1ecdi\t h\u01b0\u1edbng.\t H\u1ecd\t g\u1ecdi\t \u0111\u01b0\u1eddng\t n\u1ed1i\t c\u00e1c\t \u0111\u1ea7u\t cu\u1ed1i c\u1ee7a\t c\u00e1c\t \u0111o\u1ea1n\t n\u00e0y\t l\u00e0\t \\\"h\u00ecnh\t tr\u00f2n\\\"\t (c\u00f3\t b\u00e1n\t k\u00ednh\t l\u00e0\t r).\t \u0110\u1ed1i\t v\u1edbi\t m\u1eb7t ph\u1eb3ng,\tt\u1ec9\tl\u1ec7\tgi\u1eefa\tchu\tvi\tv\u00e0\t\u0111\u01b0\u1eddng\tk\u00ednh\tc\u1ee7a\tm\u1ed9t\tv\u00f2ng\ttr\u00f2n,\tc\u1ea3\thai \u0111\u1ec1u\t \u0111\u01b0\u1ee3c\t \u0111o\t b\u1eb1ng\t c\u00f9ng\t m\u1ed9t\t que\t con,\t l\u00e0\t b\u1eb1ng\t \u03c0,\t theo\t h\u00ecnh\t h\u1ecdc Euclid\t c\u1ee7a\t m\u1ed9t\t m\u1eb7t\t ph\u1eb3ng,\t m\u1ed9t\t con\t s\u1ed1\t \u0111\u1ed9c\t l\u1eadp\t v\u1edbi\t \u0111\u01b0\u1eddng\t k\u00ednh c\u1ee7a\th\u00ecnh\ttr\u00f2n.\tTr\u00ean\tb\u1ec1\tm\u1eb7t\tc\u1ee7a\th\u00ecnh\tc\u1ea7u,\tc\u00e1c\tsinh\tv\u1eadt\tc\u1ee7a\tch\u00fang ta\ts\u1ebd\tt\u00ecm\tth\u1ea5y\tt\u1ec9\tl\u1ec7\tn\u00e0y\tb\u1eb1ng\ttr\u1ecb\ts\u1ed1 ngh\u0129a\tl\u00e0\tnh\u1ecf\th\u01a1n\t\u03c0,\tv\u00e0\ts\u1ef1\tkh\u00e1c\tbi\u1ec7t\tn\u00e0y\tc\u00e0ng\tl\u1edbn,\tkhi\tb\u00e1n\tk\u00ednh r\tc\u1ee7a\th\u00ecnh\ttr\u00f2n\tc\u00e0ng\tl\u1edbn\tso\tv\u1edbi\tb\u00e1n\tk\u00ednh\tR\tc\u1ee7a\t\\\"v\u0169\ttr\u1ee5\th\u00ecnh\tc\u1ea7u\\\". B\u1eb1ng\th\u1ec7\tth\u1ee9c\tn\u00e0y,\tc\u00e1c\tsinh\tv\u1eadt\ttr\u00ean\tm\u1eb7t\tc\u1ea7u\tc\u00f3\tth\u1ec3\tx\u00e1c\t\u0111\u1ecbnh\tb\u00e1n k\u00ednh\t R\t c\u1ee7a\t v\u0169\t tr\u1ee5\t h\u1ecd,\t cho\t d\u00f9\t h\u1ecd\t ch\u1ec9\t c\u00f3\t m\u1ed9t\t ph\u1ea7n\t t\u01b0\u01a1ng\t \u0111\u1ed1i\t nh\u1ecf c\u1ee7a\tv\u0169\ttr\u1ee5\tc\u1ea7u\td\u00e0nh\tcho\tvi\u1ec7c\t\u0111o\t\u0111\u1ea1c\tc\u1ee7a\th\u1ecd.\tNh\u01b0ng\tn\u1ebfu\tph\u1ea7n\tn\u00e0y l\u00e0\t qu\u00e1\t nh\u1ecf,\t th\u00ec\t h\u1ecd\t s\u1ebd\t kh\u00f4ng\t th\u1ec3\t nh\u1eadn\t ra\t h\u1ecd\t \u0111ang\t \u1edf\t tr\u00ean\t m\u1ed9t\t v\u0169 tr\u1ee5\t c\u1ea7u,\t v\u00e0\t kh\u00f4ng\t ph\u1ea3i\t \u1edf\t tr\u00ean\t m\u1ed9t\t m\u1eb7t\t ph\u1eb3ng\t Euclid;\t b\u1edfi\t v\u00ec\t m\u1ed9t m\u1ea9u\t nh\u1ecf\t c\u1ee7a\t b\u1ec1\t m\u1eb7t\t c\u1ea7u\t ch\u1ec9\t kh\u00e1c\t bi\u1ec7t\t nh\u1ecf\t so\t v\u1edbi\t m\u1ed9t\t m\u1ea9u\t c\u1ee7a m\u1ed9t\tm\u1eb7t\tph\u1eb3ng\tc\u00f3\tc\u00f9ng\tk\u00edch\tth\u01b0\u1edbc. Do\t \u0111\u00f3,\t n\u1ebfu\t c\u00e1c\t sinh\t v\u1eadt\t s\u1ed1ng\t tr\u00ean\t m\u1ed9t\t h\u00e0nh\t tinh\t m\u00e0\t h\u1ec7\t m\u1eb7t tr\u1eddi\t c\u1ee7a\t n\u00f3\t ch\u1ec9\t chi\u1ebfm\t m\u1ed9t\t ph\u1ea7n\t nh\u1ecf\t kh\u00f4ng\t \u0111\u00e1ng\t k\u1ec3\t c\u1ee7a\t v\u0169\t tr\u1ee5","c\u1ea7u,\th\u1ecd\tkh\u00f4ng\tc\u00f3\tkh\u1ea3\tn\u0103ng\t\u0111\u1ec3\tquy\u1ebft\t\u0111o\u00e1n\txem\th\u1ecd\ts\u1ed1ng\ttrong\tm\u1ed9t v\u0169\t tr\u1ee5\t h\u1eefu\t h\u1ea1n\t hay\t m\u1ed9t\t v\u0169\t tr\u1ee5\t v\u00f4\t h\u1ea1n,\t b\u1edfi\t v\u00ec\t m\u1ea3nh\t v\u0169\t tr\u1ee5\t m\u00e0 trong\t\u0111\u00f3\th\u1ecd\ttr\u1ea3i\tnghi\u1ec7m\t\u0111\u01b0\u1ee3c,\ttrong\tc\u1ea3\thai\ttr\u01b0\u1eddng\th\u1ee3p,\tl\u00e0\tth\u1ef1c\tt\u1ebf nh\u01b0\t ph\u1eb3ng\t hay\t Euclid.\t Nh\u1eefng\t suy\t ngh\u0129\t n\u00e0y\t cho\t th\u1ea5y\t tr\u1ef1c\t ti\u1ebfp r\u1eb1ng\t \u0111\u1ed1i\t v\u1edbi\t c\u00e1c\t sinh\t v\u1eadt\t c\u1ea7u\t c\u1ee7a\t ch\u00fang\t ta,\t chu\t vi\t c\u1ee7a\t m\u1ed9t\t h\u00ecnh tr\u00f2n\ttr\u01b0\u1edbc\tti\u00ean\tt\u0103ng\tc\u00f9ng\tv\u1edbi\tb\u00e1n\tk\u00ednh\tcho\t\u0111\u1ebfn\tkhi\t\u0111\u1ea1t\t\u0111\u01b0\u1ee3c\t\\\"chu vi\t v\u0169\t tr\u1ee5\\\",\t \u0111\u1ec3\t sau\t \u0111\u00f3,\t v\u1edbi\t b\u00e1n\t k\u00ednh\t ti\u1ebfp\t t\u1ee5c\t t\u0103ng,\t l\u1ea1i\t gi\u1ea3m\t d\u1ea7n\t v\u1ec1 s\u1ed1\tkh\u00f4ng.\tTrong\tqu\u00e1\ttr\u00ecnh\t\u0111\u00f3,\tdi\u1ec7n\tt\u00edch\th\u00ecnh\ttr\u00f2n\tlu\u00f4n\tlu\u00f4n\tt\u0103ng, cho\t\u0111\u1ebfn\tsau\tc\u00f9ng\tn\u00f3\tb\u1eb1ng\tt\u1ed5ng\tdi\u1ec7n\tt\u00edch\tc\u1ee7a\tc\u1ea3\tv\u0169\ttr\u1ee5\tc\u1ea7u. B\u1ea1n\t \u0111\u1ecdc\t c\u00f3\t l\u1ebd\t ng\u1ea1c\t nhi\u00ean,\t t\u1ea1i\t sao\t ch\u00fang\t ta\t l\u1ea1i\t \u0111\u1eb7t\t c\u00e1c\t sinh\t v\u1eadt c\u1ee7a\t ch\u00fang\t ta\t l\u00ean\t m\u1ed9t\t h\u00ecnh\t c\u1ea7u\t m\u00e0\t kh\u00f4ng\t l\u00ean\t m\u1ed9t\t b\u1ec1\t m\u1eb7t\t kh\u00e9p k\u00edn\tkh\u00e1c.\tNh\u01b0ng\t s\u1ef1\tl\u1ef1a\t ch\u1ecdn\tn\u00e0y\tc\u00f3\t l\u00fd\tdo\t c\u1ee7a\tn\u00f3,\tb\u1edfi\t v\u00ec\tb\u1ec1\t m\u1eb7t c\u1ea7u,\tso\tv\u1edbi\tt\u1ea5t\tc\u1ea3\tc\u00e1c\tb\u1ec1\tm\u1eb7t\tkh\u00e9p\tk\u00edn\tkh\u00e1c,\tc\u00f3\t\u0111\u1eb7c\t\u0111i\u1ec3m\tduy\tnh\u1ea5t, l\u00e0\t t\u1ea5t\t c\u1ea3\t c\u00e1c\t \u0111i\u1ec3m\t c\u1ee7a\t n\u00f3\t t\u01b0\u01a1ng\t \u0111\u01b0\u01a1ng\t nhau.\t T\u00ed\t l\u1ec7\t gi\u1eefa\t chu\t vi\t c c\u1ee7a\t m\u1ed9t\t h\u00ecnh\t tr\u00f2n\t v\u1edbi\t b\u00e1n\t k\u00ednh\t r\t c\u1ee7a\t n\u00f3,\t tuy\t t\u00f9y\t thu\u1ed9c\t v\u00e0o\t r, nh\u01b0ng\tv\u1edbi\tm\u1ed9t\ttr\u1ecb\ts\u1ed1\tr\tcho\ttr\u01b0\u1edbc\tl\u00e0\tb\u1eb1ng\tnhau\tcho\tt\u1ea5t\tc\u1ea3\tc\u00e1c\t\u0111i\u1ec3m c\u1ee7a\t \\\"v\u0169\t tr\u1ee5\t c\u1ea7u\\\";\t n\u00f3i\t m\u1ed9t\t c\u00e1ch\t kh\u00e1c,\t \\\"v\u0169\t tr\u1ee5\t c\u1ea7u\\\"\t l\u00e0\t m\u1ed9t\t \\\"b\u1ec1\t m\u1eb7t c\u00f3\t\u0111\u1ed9\tcong\th\u1eb1ng\ts\u1ed1\\\". V\u0169\t tr\u1ee5\t c\u1ea7u\t hai\t chi\u1ec1u\t n\u00e0y\t c\u00f3\t m\u1ed9t\t c\u00e1i\t t\u01b0\u01a1ng\t t\u1ef1\t ba\t chi\u1ec1u,\t \u0111\u00f3\t l\u00e0 kh\u00f4ng\t gian\t c\u1ea7u\t ba\t chi\u1ec1u\t \u0111\u01b0\u1ee3c\t Riemann\t kh\u00e1m\t ph\u00e1.\t T\u1ea5t\t c\u1ea3\t c\u00e1c \u0111i\u1ec3m\t c\u1ee7a\t n\u00f3\t c\u0169ng\t t\u01b0\u01a1ng\t \u0111\u01b0\u01a1ng\t nhau.\t N\u00f3\t c\u00f3\t m\u1ed9t\t th\u1ec3\t t\u00edch\t h\u1eefu h\u1ea1n,\t \u0111\u01b0\u1ee3c\t x\u00e1c\t \u0111\u1ecbnh\t b\u1edfi\t \\\"b\u00e1n\t k\u00ednh\\\"\t R\t (2\u03c02R3).\t Ng\u01b0\u1eddi\t ta\t c\u00f3\t th\u1ec3 t\u01b0\u1edfng\tt\u01b0\u1ee3ng\t\u0111\u01b0\u1ee3c\tm\u1ed9t\tkh\u00f4ng\tgian\tc\u1ea7u\tkh\u00f4ng?\tT\u01b0\u1edfng\tt\u01b0\u1ee3ng\tm\u1ed9t kh\u00f4ng\t gian\t l\u00e0\t kh\u00f4ng\t g\u00ec\t kh\u00e1c\t h\u01a1n\t t\u01b0\u1edfng\t t\u01b0\u1ee3ng\t m\u1ed9t\t h\u00ecnh\t t\u01b0\u1ee3ng c\u1ee7a\t c\u00e1c\t kinh\t nghi\u1ec7m\t \\\"kh\u00f4ng\t gian\\\",\t ngh\u0129a\t l\u00e0\t c\u1ee7a\t nh\u1eefng\t kinh nghi\u1ec7m\tm\u00e0\tng\u01b0\u1eddi\tta\tc\u00f3\tth\u1ec3\tc\u00f3\t\u0111\u01b0\u1ee3c\tqua\ts\u1ef1\tdi\tchuy\u1ec3n\tc\u1ee7a\tc\u00e1c\tv\u1eadt th\u1ec3\t\\\"r\u1eafn\\\".\tTheo\tngh\u0129a\tn\u00e0y,\tch\u00fang\tta\tc\u00f3\tth\u1ec3\tt\u01b0\u1edfng\tt\u01b0\u1ee3ng\t\u0111\u01b0\u1ee3c\tm\u1ed9t kh\u00f4ng\tgian\tc\u1ea7u. Gi\u1ea3\t thi\u1ebft\t t\u1eeb\t m\u1ed9t\t \u0111i\u1ec3m\t ch\u00fang\t ta\t k\u00e9o\t m\u1ed9t\t \u0111\u01b0\u1eddng\t th\u1eb3ng\t (nh\u01b0 c\u0103ng\t m\u1ed9t\t s\u1ee3i\t d\u00e2y)\t theo\t t\u1ea5t\t c\u1ea3\t m\u1ecdi\t h\u01b0\u1edbng\t v\u00e0\t \u0111\u00e1nh\t d\u1ea5u\t tr\u00ean\t m\u1ed7i \u0111\u01b0\u1eddng\t \u0111\u00f3\t m\u1ed9t\t \u0111o\u1ea1n\t r\t b\u1eb1ng\t m\u1ed9t\t c\u00e2y\t th\u01b0\u1edbc.\t T\u1ea5t\t c\u1ea3\t nh\u1eefng\t \u0111i\u1ec3m cu\u1ed1i\t c\u1ee7a\t c\u00e1c\t \u0111o\u1ea1n\t n\u00e0y\t n\u1eb1m\t tr\u00ean\t m\u1ed9t\t b\u1ec1\t m\u1eb7t\t h\u00ecnh\t c\u1ea7u.\t \u0110\u1eb7c\t bi\u1ec7t ch\u00fang\t ta\t c\u00f3\t th\u1ec3\t \u0111o\t di\u1ec7n\t t\u00edch\t (F)\t c\u1ee7a\t b\u1ec1\t m\u1eb7t\t n\u00e0y\t v\u1edbi\t m\u1ed9t\t h\u00ecnh vu\u00f4ng\tl\u00e0m\tb\u1eb1ng\tc\u00e1c\tque\t\u0111o.\tN\u1ebfu\tv\u0169\ttr\u1ee5\tl\u00e0\tEuclid,\tch\u00fang\tta\tc\u00f3\tF\t= 4\u03c0r\t2\t;\tn\u1ebfu\tv\u0169\ttr\u1ee5\tl\u00e0\th\u00ecnh\tc\u1ea7u,\tth\u00ec\tF\tlu\u00f4n\tlu\u00f4n\tnh\u1ecf\th\u01a1n\t4\u03c0r\t2\t.\tV\u1edbi nh\u1eefng\t tr\u1ecb\t s\u1ed1\t c\u1ee7a\t r\t t\u0103ng,\t F\t t\u0103ng\t t\u1eeb\t kh\u00f4ng\t \u0111\u1ebfn\t m\u1ed9t\t tr\u1ecb\t s\u1ed1\t c\u1ef1c\t \u0111\u1ea1i, \u0111\u01b0\u1ee3c\t x\u00e1c\t \u0111\u1ecbnh\t b\u1edfi\t \\\"b\u00e1n\t k\u00ednh\t v\u0169\t tr\u1ee5\\\",\t nh\u01b0ng\t n\u1ebfu\t r\t v\u1eabn\t ti\u1ebfp\t t\u1ee5c","t\u0103ng,\t th\u00ec\t di\u1ec7n\t t\u00edch\t s\u1ebd\t gi\u1ea3m\t d\u1ea7n\t v\u1ec1\t kh\u00f4ng.\t \u0110\u1ea7u\t ti\u00ean\t c\u00e1c\t \u0111\u01b0\u1eddng th\u1eb3ng\txu\u1ea5t\tph\u00e1t\tt\u1eeb\tt\u00e2m\t\u0111i\u1ec3m\tti\u1ebfp\tt\u1ee5c\txa\tr\u1eddi\tnhau,\tsau\t\u0111\u00f3\tti\u1ebfn\tl\u1ea1i g\u1ea7n\tnhau,\t\u0111\u1ec3\tcu\u1ed1i\tc\u00f9ng\tch\u1ea1y\tv\u1ec1\t\\\"\u0111i\u1ec3m\t\u0111\u1ed1i\\\"\tc\u1ee7a\t\u0111i\u1ec3m\tban\t\u0111\u1ea7u;\tl\u00fac \u0111\u00f3\tch\u00fang\tchi\u1ebfm\tc\u1ea3\tkh\u00f4ng\tgian\tc\u1ea7u.\tNg\u01b0\u1eddi\tta\tc\u00f3\tth\u1ec3\tth\u1ea5y\td\u1ec5\td\u00e0ng kh\u00f4ng\t gian\t c\u1ea7u\t ba\t chi\u1ec1u\t l\u00e0\t ho\u00e0n\t to\u00e0n\t t\u01b0\u01a1ng\t t\u1ef1\t v\u1edbi\t kh\u00f4ng\t gian hai\t chi\u1ec1u\t (b\u1ec1\t m\u1eb7t\t c\u1ea7u).\t N\u00f3\t h\u1eefu\t h\u1ea1n\t (ngh\u0129a\t l\u00e0\t c\u00f3\t th\u1ec3\t t\u00edch\t h\u1eefu h\u1ea1n),\tnh\u01b0ng\tkh\u00f4ng\tc\u00f3\tranh\tgi\u1edbi. 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Nh\u01b0\th\u1ec7\tqu\u1ea3\tc\u1ee7a\tnh\u1eefng\t\u0111i\u1ec1u\tv\u1eeba\tn\u00f3i,\tm\u1ed9t\tc\u00e2u\th\u1ecfi\tv\u00f4\tc\u00f9ng\tl\u00fd\tth\u00fa \u0111\u00e3\t\u0111\u01b0\u1ee3c\t\u0111\u1eb7t\tra\tcho\tc\u00e1c\tnh\u00e0\tthi\u00ean\tv\u0103n\th\u1ecdc\tv\u00e0\tv\u1eadt\tl\u00fd\th\u1ecdc,\tl\u00e0\tv\u0169\ttr\u1ee5 ch\u00fang\tta\t\u0111ang\ts\u1ed1ng\tl\u00e0\tv\u00f4\tc\u1ef1c,\thay\th\u1eefu\th\u1ea1n\ttheo\tc\u00e1ch\tth\u1ee9c\tc\u1ee7a\tv\u0169 tr\u1ee5\th\u00ecnh\tc\u1ea7u.\tKinh\tnghi\u1ec7m\tc\u1ee7a\tch\u00fang\tta\tc\u00f2n\tl\u00e2u\tm\u1edbi\t\u0111\u1ee7\t\u0111\u1ec3\t\u0111\u01b0a\tra gi\u1ea3i\t \u0111\u00e1p\t cho\t c\u00e2u\t h\u1ecfi\t n\u00e0y.\t Tuy\t nhi\u00ean\t thuy\u1ebft\t t\u01b0\u01a1ng\t \u0111\u1ed1i\t r\u1ed9ng\t cho ph\u00e9p\t ch\u00fang\t ta\t tr\u1ea3\t l\u1eddi\t n\u00f3\t v\u1edbi\t m\u1ed9t\t \u0111\u1ed9\t tin\t c\u1eady\t kh\u00e1\t l\u1edbn;\t \u0111\u1ed3ng\t th\u1eddi qua\t\u0111\u00f3\tc\u00e1i\tkh\u00f3\tkh\u0103n\t\u0111\u01b0\u1ee3c\ttr\u00ecnh\tb\u00e0y\ttrong\t\u00a7\t30\tc\u0169ng\t\u0111\u01b0\u1ee3c\tgi\u1ea3i\tt\u1ecfa lu\u00f4n.","\u00a7\t32 C\u1ea5u\tTr\u00fac\tc\u1ee7a\tKh\u00f4ng\tGian\tTheo\tThuy\u1ebft\tT\u01b0\u01a1ng\t\u0110\u1ed1i\tR\u1ed9ng Theo\tthuy\u1ebft\tt\u01b0\u01a1ng\t\u0111\u1ed1i\tr\u1ed9ng,\tc\u00e1c\tt\u00ednh\tch\u1ea5t\th\u00ecnh\th\u1ecdc\tc\u1ee7a\tkh\u00f4ng gian\t l\u00e0\t kh\u00f4ng\t \u0111\u1ed9c\t l\u1eadp,\t m\u00e0\t \u0111\u01b0\u1ee3c\t quy\t \u0111\u1ecbnh\t b\u1edfi\t v\u1eadt\t ch\u1ea5t.\t Do\t \u0111\u00f3, ng\u01b0\u1eddi\t ta\t ch\u1ec9\t c\u00f3\t th\u1ec3\t c\u00f3\t k\u1ebft\t lu\u1eadn\t v\u1ec1\t c\u1ea5u\t tr\u00fac\t h\u00ecnh\t h\u1ecdc\t c\u1ee7a\t v\u0169\t tr\u1ee5 khi\t ng\u01b0\u1eddi\t ta\t \u0111\u1eb7t\t vi\u1ec7c\t nghi\u00ean\t c\u1ee9u\t tr\u00ean\t n\u1ec1n\t t\u1ea3ng\t c\u1ee7a\t m\u1ed9t\t tr\u1ea1ng th\u00e1i\t c\u1ee7a\t v\u1eadt\t ch\u1ea5t\t \u0111\u01b0\u1ee3c\t cho\t bi\u1ebft\t tr\u01b0\u1edbc.\t Ch\u00fang\t ta\t bi\u1ebft\t t\u1eeb\t kinh nghi\u1ec7m,\tb\u1eb1ng\tc\u00e1ch\tch\u1ecdn\tm\u1ed9t\th\u1ec7\tth\u1ed1ng\tt\u1ecda\t\u0111\u1ed9\tth\u00edch\th\u1ee3p,\tv\u1eadn\tt\u1ed1c c\u1ee7a\tc\u00e1c\tv\u00ec\tsao\tl\u00e0\tr\u1ea5t\tnh\u1ecf\t\u0111\u1ed1i\tv\u1edbi\tv\u1eadn\tt\u1ed1c\ttruy\u1ec1n\tc\u1ee7a\t\u00e1nh\ts\u00e1ng.\tCho n\u00ean,\t m\u1ed9t\t c\u00e1ch\t x\u1ea5p\t x\u1ec9\t th\u00f4\t thi\u1ec3n,\t ch\u00fang\t ta\t c\u00f3\t th\u1ec3\t bi\u1ebft\t \u0111\u01b0\u1ee3c\t \\\"th\u1ec3 ch\u1ea5t\\\"\t c\u1ee7a\t v\u0169\t tr\u1ee5\t m\u1ed9t\t c\u00e1ch\t \u0111\u1ea1i\t th\u1ec3,\t n\u1ebfu\t ch\u00fang\t ta\t xem\t v\u1eadt\t ch\u1ea5t\t l\u00e0 \u0111\u1ee9ng\ty\u00ean. 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M\u1ed9t\tt\u00edn\thi\u1ec7u\t\u00e1nh\ts\u00e1ng\ttruy\u1ec1n\t\u0111i\td\u1ecdc\ttheo\tph\u1ea7n\ttr\u1ee5c\tx\td\u01b0\u01a1ng\ts\u1ebd c\u00f3\tph\u01b0\u01a1ng\ttr\u00ecnh\ttruy\u1ec1n\tl\u00e0 x\t=\tct hay x\t-\tct\t=\t0\t(1) V\u00ec\tc\u00f9ng\tm\u1ed9t\t\u00e1nh\ts\u00e1ng\tc\u0169ng\ttruy\u1ec1n\t\u0111i\tv\u1edbi\tv\u1eadn\tt\u1ed1c\tc\t \u0111\u1ed1i\t trong h\u1ec7\t t\u1ecda\t \u0111\u1ed9\t K\u2019\t n\u00ean\t s\u1ef1\t truy\u1ec1n\t \u0111i\t \u0111\u1ed1i\t v\u1edbi\t K\u2019\t c\u0169ng\t \u0111\u01b0\u1ee3c\t di\u1ec5n\t t\u1ea3\t b\u1edfi c\u00f4ng\tth\u1ee9c\tt\u01b0\u01a1ng\tt\u1ef1 x'\t-\tct'\t=\t0\t(2) nh\u1eefng\t\u0111i\u1ec3m\tkh\u00f4ng-th\u1eddi-gian\t(s\u1ef1\tki\u1ec7n)\tn\u00e0o\tth\u1ecfa\tm\u00e3n\t(1)\tc\u0169ng ph\u1ea3i\tth\u1ecfa\tm\u00e3n\t(2).\tR\u00f5\tr\u00e0ng\t\u0111\u00f3\ts\u1ebd\tl\u00e0\ttr\u01b0\u1eddng\th\u1ee3p\tkhi\th\u1ec7\tth\u1ee9c (x'\t-\tct\t')\t=\t\u03bb(x\t-\tct)\t(3) \u0111\u01b0\u1ee3c\tth\u1ecfa\tm\u00e3n\tm\u1ed9t\tc\u00e1ch\tt\u1ed5ng\tqu\u00e1t,\ttrong\t\u0111\u00f3\t\u03bb\tl\u00e0\tm\u1ed9t\th\u1eb1ng\ts\u1ed1; b\u1edfi\tv\u00ec,\ttheo\t(3),\ts\u1ef1\ttri\u1ec7t\tti\u00eau\tc\u1ee7a\tx\t-\tct\ts\u1ebd\tk\u00e9o\ttheo\ts\u1ef1\ttri\u1ec7t\tti\u00eau\tc\u1ee7a x\u2019\t\u2013\tct\u2019. \u00c1p\td\u1ee5ng\ts\u1ef1\tsuy\tngh\u0129\tt\u01b0\u01a1ng\tt\u1ef1\tcho\t\u00e1nh\ts\u00e1ng\ttruy\u1ec1n\ttheo\ttr\u1ee5c\tx \u00e2m\ts\u1ebd\tcho\tch\u00fang\tta\t\u0111i\u1ec1u\tki\u1ec7n","(x'+ct')\t=\t\u03bc(x\t+\tct)\t(4) B\u1eb1ng\t c\u00e1ch\t l\u1ea7n\t l\u01b0\u1ee3t\t c\u1ed9ng\t l\u1ea1i\t v\u00e0\t tr\u1eeb\t \u0111i\t c\u00e1c\t ph\u01b0\u01a1ng\t tr\u00ecnh\t (3)\t v\u00e0 (4)\tv\u1edbi\tnhau,\tc\u0169ng\tnh\u01b0\t\u0111\u01b0a\tv\u00e0o\tc\u00e1c\th\u1eb1ng\ts\u1ed1\ta\tv\u00e0\tb\tcho\tti\u1ec7n\tl\u1ee3i,\tv\u1edbi ch\u00fang\tta\ts\u1ebd\t\u0111\u01b0\u1ee3c\tc\u00e1c\tph\u01b0\u01a1ng\ttr\u00ecnh B\u00e0i\tto\u00e1n\tc\u1ee7a\tch\u00fang\tta\tdo\t\u0111\u00f3\ts\u1ebd\t\u0111\u01b0\u1ee3c\tgi\u1ea3i,\tn\u1ebfu\tc\u00e1c\th\u1eb1ng\ts\u1ed1\ta\tv\u00e0 b\t\u0111\u01b0\u1ee3c\tx\u00e1c\t\u0111\u1ecbnh.\tV\u00e0\t\u0111i\u1ec1u\tn\u00e0y\tl\u00e0\tk\u1ebft\tqu\u1ea3\tc\u1ee7a\tnh\u1eefng\tsuy\tngh\u0129\tsau. \u0110\u1ed1i\t v\u1edbi\t \u0111i\u1ec3m\t g\u1ed1c\t c\u1ee7a\t K\u2019\t lu\u00f4n\t lu\u00f4n\t ta\t c\u00f3\t x\u2019\t =\t 0,\t do\t \u0111\u00f3\t theo ph\u01b0\u01a1ng\ttr\u00ecnh\t\u0111\u1ea7u\tc\u1ee7a\t(5) n\u1ebfu\tg\u1ecdi\tv\tl\u00e0\tt\u1ed1c\t\u0111\u1ed9\tc\u1ee7a\t\u0111i\u1ec3m\tg\u1ed1c\tc\u1ee7a\tK\u2019\ttrong\tchuy\u1ec3n\t\u0111\u1ed9ng\t\u0111\u1ed1i v\u1edbi\tK,\tth\u00ec\tch\u00fang\tta\tc\u00f3\t(6) Ng\u01b0\u1eddi\tta\tc\u0169ng\t\u0111\u01b0\u1ee3c\tc\u00f9ng\tm\u1ed9t\ttr\u1ecb\ts\u1ed1\tv\tkhi\tt\u00ednh\tv\u1eadn\tt\u1ed1c\tc\u1ee7a\tm\u1ed9t \u0111i\u1ec3m\tkh\u00e1c\tc\u1ee7a\tK'\t\u0111\u1ed1i\tv\u1edbi\tK,\t hay\t v\u1eadn\t t\u1ed1c\t (h\u01b0\u1edbng\t theo\t tr\u1ee5c\t x\t \u00e2m) c\u1ee7a\tm\u1ed9t\t\u0111i\u1ec3m\tc\u1ee7a\tK\t\u0111\u1ed1i\tv\u1edbi\tK'.\tCho\tn\u00ean\tng\u01b0\u1eddi\tta\tc\u00f3\tth\u1ec3\tg\u1ecdi\tng\u1eafn\tv l\u00e0\tv\u1eadn\tt\u1ed1c\tt\u01b0\u01a1ng\t\u0111\u1ed1i\tc\u1ee7a\thai\th\u1ec7\tt\u1ecda\t\u0111\u1ed9. 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Gi\u1ea3\tthi\u1ebft\tv\u00e0o\tth\u1eddi\t\u0111i\u1ec3m\tt\t=\t0\tm\u1ed9t\tt\u00edn\thi\u1ec7u\t\u00e1nh\ts\u00e1ng\t\u0111\u01b0\u1ee3c\tph\u00e1t ra\tt\u1ea1i\t\u0111i\u1ec3m\tg\u1ed1c\tc\u1ee7a\tK.\tN\u00f3\ttruy\u1ec1n\t\u0111i\ttheo\tph\u01b0\u01a1ng\ttr\u00ecnh hay\tl\u00e0,\tb\u1eb1ng\tc\u00e1ch\tb\u00ecnh\tph\u01b0\u01a1ng\tl\u00ean\thai\tv\u1ebf\tc\u1ee7a\tph\u01b0\u01a1ng\ttr\u00ecnh, x\t2\t+\ty\t2\t+\tz\t2\t-c\t2\tt\t2\t=\t0\t(10) \u0110\u1ecbnh\tlu\u1eadt\ttruy\u1ec1n\tc\u1ee7a\t\u00e1nh\ts\u00e1ng\tc\u00f9ng\tv\u1edbi\t\u0111\u1ecbnh\t\u0111\u1ec1\tt\u01b0\u01a1ng\t\u0111\u1ed1i\t\u0111\u00f2i h\u1ecfi\tr\u1eb1ng\ts\u1ef1\ttruy\u1ec1n\tc\u1ee7a\tt\u00edn\thi\u1ec7u\t\u00e1nh\ts\u00e1ng\t\u0111\u01b0\u1ee3c\txem\tx\u00e9t\tph\u1ea3i\tdi\u1ec5n ra\t-\tnh\u00ecn\tt\u1eeb\tK\u2019\t-\ttheo\tc\u00f4ng\tth\u1ee9c\tt\u01b0\u01a1ng\t\u1ee9ng r'\t=\tct' hay x'\t2\t+y'\t2\t+z\u2019\t2\t-c\t2\tt'\t2\t=\t0\t(10a) \u0110\u1ec3\tph\u01b0\u01a1ng\ttr\u00ecnh\t(10a)\tl\u00e0\th\u1ec7\tqu\u1ea3\tc\u1ee7a\tph\u01b0\u01a1ng\ttr\u00ecnh\t(10),\tch\u00fang ta\tph\u1ea3i\tc\u00f3 x'\t2\t+\ty'\t2\t+\tz'\t2\t-\tc\t2\tt'\t2\t=\t\u03c3(x\t2\t+\ty\t2\t+\tz\t2\t-\tc\t2\tt)\t(11) V\u00ec\tph\u01b0\u01a1ng\ttr\u00ecnh\t(8a)\tc\u0169ng\tph\u1ea3i\t\u0111\u00fang\tcho\tc\u00e1c\t\u0111i\u1ec3m\ttr\u00ean\ttr\u1ee5c\tx n\u00ean\t ch\u00fang\t ta\t ph\u1ea3i\t c\u00f3\t \u03c3\t =\t 1.\t Ph\u00e9p\t bi\u1ebfn\t \u0111\u1ed5i\t Lorentz\t th\u1ecfa\t m\u00e3n ph\u01b0\u01a1ng\t tr\u00ecnh\t (11)\t v\u1edbi\t \u03c3\t =\t 1,\t \u0111i\u1ec1u\t \u0111\u00f3\t ch\u00fang\t ta\t th\u1ea5y\t d\u1ec5\t d\u00e0ng;\t v\u00ec (11)\tch\u00ednh\tl\u00e0\tm\u1ed9t\th\u1ec7\tlu\u1eadn\tc\u1ee7a\t(8a)\tv\u00e0\t(9),\tcho\tn\u00ean\tc\u0169ng\tl\u00e0\th\u1ec7\tlu\u1eadn c\u1ee7a\t(8)\tv\u00e0\t(9).\tDo\t\u0111\u00f3\tph\u00e9p\tbi\u1ebfn\t\u0111\u1ed5i\tLorentz\t\u0111\u00e3\t\u0111\u01b0\u1ee3c\tch\u1ee9ng\tminh. Ph\u00e9p\t bi\u1ebfn\t \u0111\u1ed5i\t Lorentz\t \u0111\u01b0\u1ee3c\t di\u1ec5n\t t\u1ea3\t b\u1edfi\t (8)\t v\u00e0\t (9)\t c\u00f2n\t c\u1ea7n\t m\u1ed9t","s\u1ef1\t kh\u00e1i\t qu\u00e1t\t h\u00f3a.\t R\u00f5\t r\u00e0ng\t kh\u00f4ng\t ph\u1ea3i\t l\u00e0\t \u0111i\u1ec1u\t quan\t tr\u1ecdng\t khi ng\u01b0\u1eddi\t ta\t ch\u1ecdn\t c\u00e1c\t tr\u1ee5c\t c\u1ee7a\t K\u2019\t v\u1ec1\t kh\u00f4ng\t gian\t song\t song\t v\u1edbi\t c\u00e1c tr\u1ee5c\t c\u1ee7a\t K.\t C\u0169ng\t kh\u00f4ng\t ph\u1ea3i\t l\u00e0\t \u0111i\u1ec1u\t quan\t tr\u1ecdng\t khi\t ch\u00fang\t ta ch\u1ecdn\tv\u1eadn\tt\u1ed1c\tc\u1ee7a\tph\u00e9p\tt\u1ecbnh\tti\u1ebfn\tc\u1ee7a\tK\u2019\tc\u00f3\th\u01b0\u1edbng\tc\u1ee7a\ttr\u1ee5c\tx.\tM\u1ed9t suy\t ngh\u0129\t \u0111\u01a1n\t gi\u1ea3n\t cho\t th\u1ea5y\t ch\u00fang\t ta\t c\u00f3\t th\u1ec3\t t\u1ea1o\t ph\u00e9p\t bi\u1ebfn\t \u0111\u1ed5i Lorentz\t t\u1ed5ng\t qu\u00e1t\t b\u1eb1ng\t hai\t ph\u00e9p\t bi\u1ebfn\t \u0111\u1ed5i,\t \u0111\u00f3\t l\u00e0\t ph\u00e9p\t bi\u1ebfn\t \u0111\u1ed5i Lorentz\t trong\t tr\u01b0\u1eddng\t h\u1ee3p\t \u0111\u1eb7c\t bi\u1ec7t\t (nh\u01b0\t tr\u00ean)\t v\u00e0\t c\u00e1c\t ph\u00e9p\t bi\u1ebfn \u0111\u1ed5i\tthu\u1ea7n\tt\u00fay\tv\u1ec1\tkh\u00f4ng\tgian.\tPh\u00e9p\tbi\u1ebfn\t\u0111\u1ed5i\tsau\tnh\u1eb1m\tthay\tth\u1ebf\th\u1ec7 t\u1ecda\t\u0111\u1ed9\tvu\u00f4ng\tg\u00f3c\tb\u1eb1ng\tm\u1ed9t\th\u1ec7\tm\u1edbi\tv\u1edbi\tc\u00e1c\ttr\u1ee5c\t\u0111\u1ecbnh\th\u01b0\u1edbng\tkh\u00e1c. B\u1eb1ng\t to\u00e1n\t h\u1ecdc,\t ch\u00fang\t ta\t c\u00f3\t th\u1ec3\t \u0111\u1eb7c\t tr\u01b0ng\t ph\u00e9p\t bi\u1ebfn\t \u0111\u1ed5i Lorentz\t\u0111\u01b0\u1ee3c\tkh\u00e1i\tqu\u00e1t\th\u00f3a\tnh\u01b0\tsau:\tN\u00f3\tdi\u1ec5n\tt\u1ea3\tx\u2019,\ty\u2019,\tz\u2019,\tt\u2019\tb\u1eb1ng nh\u1eefng\th\u00e0m\ts\u1ed1\ttuy\u1ebfn\tt\u00ednh\tv\u00e0\tthu\u1ea7n\tnh\u1ea5t\tc\u1ee7a\tx,\ty,\tz,\tt\tsao\tcho\th\u1ec7 th\u1ee9c x'\t2\t+\ty'\t2\t+z'\t2\t-\tc\t2\tt'\t2\t=\tx\t2\t+y\t2\t+z\t2\t-\tc\t2\tt\t2\t(11a) \u0111\u01b0\u1ee3c\tth\u1ecfa\tm\u00e3n\tm\u1ed9t\tc\u00e1ch\t\u0111\u1ed3ng\tnh\u1ea5t.\t\u0110i\u1ec1u\tn\u00e0y\tmu\u1ed1n\tn\u00f3i:\tN\u1ebfu trong\tv\u1ebf\ttr\u00e1i\tta\tthay\tth\u1ebf\tx\u2019,\ty\u2019,\tv.v.\tb\u1eb1ng\tc\u00e1c\tbi\u1ec3u\tth\u1ee9c\tc\u1ee7a\tch\u00fang theo\tx,\ty,\tz,\tt,\tth\u00ec\tv\u1ebf\ttr\u00e1i\tc\u1ee7a\t(11a)\ttr\u00f9ng\tv\u1edbi\tv\u1ebf\tph\u1ea3i.","Ph\u1ee5\tL\u1ee5c\tII Kh\u00f4ng\tGian\tMinkowski\tB\u1ed1n\tChi\u1ec1u\t(\\\"Th\u1ebf\tGi\u1edbi\\\") (B\u1ed5\tsung\tv\u00e0o\t\u00a7\t17) Ph\u00e9p\tbi\u1ebfn\t\u0111\u1ed5i\tLorentz\t\u0111\u01b0\u1ee3c\tt\u1ed5ng\tqu\u00e1t\th\u00f3a\tc\u00f3\tth\u1ec3\tc\u00f2n\t\u0111\u01b0\u1ee3c\t\u0111\u1eb7c tr\u01b0ng\tm\u1ed9t\tc\u00e1ch\t\u0111\u01a1n\tgi\u1ea3n\th\u01a1n\tn\u1ebfu\tch\u00fang\tta\tl\u1ea5y\ts\u1ed1\t\u1ea3o\t \tthay v\u00ec\tt,\tl\u00e0m\tbi\u1ebfn\ts\u1ed1\t.\tTheo\t\u0111\u00f3,\tn\u1ebfu\tch\u00fang\tta\t\u0111\u1eb7t x1\t=\tx x2\t=\ty x3\t=\tz v\u00e0\t l\u00e0m\t m\u1ed9t\t c\u00e1ch\t t\u01b0\u01a1ng\t t\u1ef1\t v\u1edbi\t h\u1ec7\t t\u1ecda\t \u0111\u1ed9\t K',\t th\u00ec\t \u0111i\u1ec1u\t ki\u1ec7n\t m\u00e0 ph\u00e9p\t bi\u1ebfn\t \u0111\u1ed5i\t (Lorentz)\t th\u1ecfa\t m\u00e3n\t m\u1ed9t\t c\u00e1ch\t \u0111\u1ed3ng\t nh\u1ea5t\t c\u00f3\t th\u1ec3 \u0111\u01b0\u1ee3c\tdi\u1ec5n\tt\u1ea3\t\u1edf\td\u1ea1ng x\u20191\t2\t+\tx\u20192\t2\t+\tx\u20193\t2\t+\tx\u20194\t2\t=\tx1\t2\t+\tx2\t2\t+\tx3\t2\t+\tx4\t2\t(12) Ph\u01b0\u01a1ng\t tr\u00ecnh\t n\u00e0y\t ch\u00ednh\t l\u00e0\t d\u1ea1ng\t m\u1edbi\t c\u1ee7a\t ph\u01b0\u01a1ng\t tr\u00ecnh\t (11a) v\u1edbi\tc\u00e1c\tt\u1ecda\t\u0111\u1ed9\tv\u1eeba\t\u0111\u01b0\u1ee3c\tch\u1ecdn. 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V\u1eadt\tl\u00fd,\tt\u1eeb\tm\u1ed9t\t\\\"s\u1ef1\tki\u1ec7n\\\"\t(Geschehen)\ttrong\tkh\u00f4ng\tgian\tba\tchi\u1ec1u,\t\u1edf m\u1ee9c\t \u0111\u1ed9\t n\u00e0o\t \u0111\u00f3,\t \u0111\u00e3\t tr\u1edf\t th\u00e0nh\t m\u1ed9t\t t\u1ed3n\t t\u1ea1i\t (Sein)\t trong\t \\\"th\u1ebf\t gi\u1edbi\\\" b\u1ed1n\tchi\u1ec1u. \\\"Th\u1ebf\tgi\u1edbi\\\"\tb\u1ed1n\tchi\u1ec1u\tn\u00e0y\tmang\tm\u1ed9t\ts\u1ef1\tt\u01b0\u01a1ng\t\u0111\u1ed3ng\ts\u00e2u\ts\u1eafc\tv\u1edbi \\\"kh\u00f4ng\tgian\\\"\tba\tchi\u1ec1u\tc\u1ee7a\th\u00ecnh\th\u1ecdc\tgi\u1ea3i\tt\u00edch\t(Euclid),\t\u1edf\th\u00ecnh\th\u1ecdc n\u00e0y,\tn\u1ebfu\tch\u00fang\tta\t\u0111\u01b0a\tv\u00e0o\tm\u1ed9t\th\u1ec7\tt\u1ecda\t\u0111\u1ed9\tDescartes\tm\u1edbi\tx\u20191,\tx\u20192, x\u20193\t c\u00f9ng\t c\u00f3\t m\u1ed9t\t \u0111i\u1ec3m\t g\u1ed1c\t v\u1edbi\t h\u1ec7\t t\u1ecda\t \u0111\u1ed9\t c\u0169,\t th\u00ec\t x\u20191,\t x\u20192,\t x\u20193\t l\u00e0 nh\u1eefng\th\u00e0m\ts\u1ed1\ttuy\u1ebfn\tt\u00ednh\tthu\u1ea7n\tnh\u1ea5t\tc\u1ee7a\tc\u00e1c\tt\u1ecda\t\u0111\u1ed9\tx1,\tx2,\tx3\tv\u00e0 th\u1ecfa\tm\u00e3n\tph\u01b0\u01a1ng\ttr\u00ecnh\tm\u1ed9t\tc\u00e1ch\t\u0111\u1ed3ng\tnh\u1ea5t","x\u20191\t2\t+x'2\t2\t+\tx'3\t2\t=\tx1\t2\t+\tx2\t2\t+\tx3\t2\t(12a) S\u1ef1\t t\u01b0\u01a1ng\t t\u1ef1\t v\u1edbi\t (12)\t l\u00e0\t ho\u00e0n\t h\u1ea3o.\t Ch\u00fang\t ta\t c\u00f3\t th\u1ec3\t g\u1ecdi\t th\u1ebf\t gi\u1edbi Minkowski\tv\u1ec1\th\u00ecnh\tth\u1ee9c\tl\u00e0\tm\u1ed9t\tkh\u00f4ng\tgian\tEuclid\tb\u1ed1n\tchi\u1ec1u\t(v\u1edbi t\u1ecda\t \u0111\u1ed9\t th\u1eddi\t gian\t \u1ea3o).\t Ph\u00e9p\t bi\u1ebfn\t \u0111\u1ed5i\t Lorentz\t t\u01b0\u01a1ng\t \u1ee9ng\t v\u1edbi\t m\u1ed9t \\\"ph\u00e9p\tquay\\\"\tc\u1ee7a\th\u1ec7\tt\u1ecda\t\u0111\u1ed9\ttrong\t\\\"th\u1ebf\tgi\u1edbi\\\"\tb\u1ed1n\tchi\u1ec1u[68].","Ph\u1ee5\tL\u1ee5c\tIII V\u1ec1\tS\u1ef1\tX\u00e1c\tNh\u1eadn\tTh\u1ef1c\tNghi\u1ec7m\tc\u1ee7a\tThuy\u1ebft\tT\u01b0\u01a1ng\t\u0110\u1ed1i\tR\u1ed9ng T\u1eeb\tquan\t\u0111i\u1ec3m\tnh\u1eadn\tth\u1ee9c\tlu\u1eadn\tm\u1ed9t\tc\u00e1ch\th\u1ec7\tth\u1ed1ng,\tng\u01b0\u1eddi\tta\tc\u00f3 th\u1ec3\t ngh\u0129\t qu\u00e1\t tr\u00ecnh\t ti\u1ebfn\t h\u00f3a\t c\u1ee7a\t m\u1ed9t\t ng\u00e0nh\t khoa\t h\u1ecdc\t th\u1ef1c nghi\u1ec7m\t l\u00e0\t m\u1ed9t\t qu\u00e1\t tr\u00ecnh\t quy\t n\u1ea1p\t li\u00ean\t t\u1ee5c.\t C\u00e1c\t l\u00fd\t thuy\u1ebft\t xu\u1ea5t hi\u1ec7n\tnh\u01b0\tnh\u1eefng\ts\u1ef1\tt\u1ed5ng\tk\u1ebft\tc\u1ee7a\tm\u1ed9t\tkh\u1ed1i\tl\u01b0\u1ee3ng\tl\u1edbn\tnh\u1eefng\tquan s\u00e1t\t ri\u00eang\t l\u1ebb\t th\u00e0nh\t nh\u1eefng\t \u0111\u1ecbnh\t lu\u1eadt\t th\u1ef1c\t nghi\u1ec7m,\t m\u00e0\t t\u1eeb\t \u0111\u00f3\t c\u00e1c \u0111\u1ecbnh\tlu\u1eadt\tph\u1ed5\tqu\u00e1t\t\u0111\u01b0\u1ee3c\tph\u00e1t\thi\u1ec7n\tb\u1eb1ng\tph\u01b0\u01a1ng\tph\u00e1p\tso\ts\u00e1nh.\tS\u1ef1 ph\u00e1t\ttri\u1ec3n\tc\u1ee7a\tkhoa\th\u1ecdc,\ttheo\tc\u00e1ch\tsuy\tngh\u0129\tn\u00e0y,\tmang\tt\u00ednh\tch\u1ea5t gi\u1ed1ng\t nh\u01b0\t c\u00f4ng\t vi\u1ec7c\t x\u1ebfp\t lo\u1ea1i\t danh\t m\u1ee5c,\t nh\u01b0\t m\u1ed9t\t t\u00e1c\t ph\u1ea9m\t ch\u1ec9 thu\u1ea7n\tth\u1ef1c\tnghi\u1ec7m. 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