Special relativity

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  1. 1. To , , , , . . e-mail:nikmatza@gmail.com
  2. 2. , . , 7 : 1. , . 2. . 3. . 4. 5. 2 mcE . 6. 7. . . . . . 2 : 1. 1. . 2. 2. . , Lorenntz. , , . 2 , . 1. u, - . . ,1
  3. 3. To , - : c d t 2 ' (1) , s d.H tus (2) 2l - : 22 ) 2 ( tu dl (3). c. l s t (t ) : c tu d c l t 22 ) 2 (2 2 ' (4) A (4) : 22 )(1 ' u t t (5) To 2 . ' ' , - , ' '. . . - . . - , , ' ' , , , .
  4. 4. 2 ,2 . . c l t 0 2 ' ( 6) 0 l . , 11 tuld (7) 22 tuld (8) , , 21 dd l . . 22 11 tctul tctul (9) 21 ttt (10)
  5. 5. )/1( 2 22 cuc l uc l uc l t (11) (5) )/1( /2 )(1 /'2 22 22 cu cl u cl t (12)?? . .. 2 2 1' c u ll (13) ?? (l) o (l) . " ". , . , . .
  6. 6. o o 2 : 1 , u, o d 't t , x. O C D C D A u x B ,3 .3 , =2=2L. 22 ) 2 ( tu DAO 2/',,2/ tcDtuABtcAO M : ' )(1 ' 22 t u t t (5) . , . =u/c : 12/'2 2/ u tu t AB D L D :
  7. 7. tcLtcD '& L= , D : 2 2 1 c u D LDL : DD c u tuAB )2/'(2/ , : 1 2 2 2 u c D AB . 1 2 2 2 u c D AB 2 /u2 >1 u
  8. 8. 2 , u . . d , d, x. | 1 |2| A B C u L 2 x1,x2 : 22 11 tux tux , : 22 11 ' ' tctuL tctuL : )/1( /'2 )/1( '2'' 222221 cu cL cuc L uc L uc L ttt : )/1( /'2 22 cu cL t , c L t '2 ' )/1(' )/1( ' 22 22 cutt cu t t
  9. 9. )2(' /1 )/2(' /1 /'2 )/1( 1 )'2()( 2 22222222121 L cu cuL cu cLu cuc cLuttuxxx L ( , 2L (L=)) 2 222 2 2121 1 '2'2 '' c u L uc cL tctcxxL L=d+d : )2(' /1 ' 2 2 22 L cu L L L 2 22 22 1 )/1(' L cuLL 2 , 2 u . 1. cu D u c D AB D c u D L t u t t 1 2/ 1 ' )(1 ' 2 2 2 2 22 2. cu // 2 22 2 22 2 22 '2 /1 '2 22 )/1(' ' )/1( ' L cu L L LL cuL t cu t t
  10. 10. t . x,L u/c : 1 .- L x. cu cu u c cuxL ....4142.0 ....4142.0 2 )/1(/' 22 2 . - x L. cu cu cuc u Lx ....4142.0 ....4142.0 )/1( 12 '/ 22 t,t, L,L , , . 1. // xx cu B xx . , , . .4
  11. 11. , =2=2L =D. , / u, / / . t,t . ( )... 'tcDOK tuAK tcAO cu : ... '//, xxucu 1 2/ 1 ,' )(1 ' 2 2 2 2 22 u c D AB c u D Lt u t t 2. // xx cu , xx u, cu , . 00 .5
  12. 12. a) ( )... ' 2 1 2 tcDOK tcAO tAK 2 +2 =2 : 0'1 2 '11 ' 4 1 2 2 2 2 2 2 2 2 222242 t c t ttctct ... 2 2 2 2 ''0'1 c D c c D t c t t . b) B(K )... - , , 0 u 0' )( 4 1 ') 2 1 ( 22 2 22 03 2 04 2 2 222222 0 tt c cu t c u t c tctcttu 4 t t AKu 20
  13. 13. 3. u xx 00 90 cu , , u , xx , , 0 ' xxu . 00 6 u xx a) 0( )... OE t1 1 tcOE tuA tA x
  14. 14. 222 AOEOAE : 222 1 222 tutctc x (1) u xx 00 90 cu , sin,cos uuuu yx , 6. b) B( )... , t ,B t2, : 2 tcB tuO tB x 6 , 222 OO : 222 2 222 kxk tutctc (2) D : 22 11 tctuD tctuD y y .. y y uc D t uc D t 2 1 (3) tttol {1,2,3} : ) 1 ( 2 ) 2 ()( 2222 2 222222 yxyxyyx ol ucuc Dc uc cD uc c uc D uc D uc c t
  15. 15. T ... ) sin1 1 ( cos1 /2 2 2 2 2 2 2 c u c u cD tol (4) 2 ,,, 2 2 2 2 1 /2 2/) 1 /2 0) c u cD t c u cD t i ol ol (.): 1. . // xx cu x , cu y 2 x,y , : Xu C t t C 2 , t t x-y : 22 0 22 0 )(1 /2 , )(1 /2 u cl t u cl t yx
  16. 16. 2. u xx 00 90 cu i) 2 x,y ux , uy - t//c,u x t'c,u x d o wnupx ttt'c,u : 2 2 2 0 2 2 2 0 1 )/(2 , 1 )/(2 u ucl t u ucl t y x down y x up : 2 2 2 0 2 2 0 2 2 2 2 2 0 1 )/(2 ', )1( /2 , )1( 1 1 /2 u ucl t c u cl t c u u cl t y x yxy sum ii) A ux , uy t//c,u y t'c,u y o , : ... 2 2 2 0 2 2 0 2 2 2 2 2 0 1 )/(2 ', )1( /2 , )1( 1 1 /2 u ucl t c u cl t c u u cl t x y xyx sum X-C u Y-Cu Xu Yu t t Y-uC Yu t X -C u Xu t
  17. 17. ..u Y=F(x) .7 uX uY uX uY S A D O . 7 S, dy dy dx S D 0 2 )(1 .7 - )( )( x k x uc D S c t uc D S c t , ) 1 ( 2 ) 2 ()( 22 2 22 xxxx ol ucS Dc uc cD S c uc D uc D S c t 2 22 0 2 2 )/(1 1 )cos(,)tan(),cos( ) 1 ( )(1 2 dxdydx dy uu uc dy dy dx Dc t x xD ol 4. // xx cu // , // (A) u
  18. 18. . , d= t1 , d=ct2. L=d+d, , . | d1 |d2| A B C u L 2 x1,x2 : 10 2 2202 2 11 2 1 2 1 t ttx tx , : 10 2 2 220 1 2 1 2 1 ' 2 1 ' t ctttL cttL L ( , 2L (L=)) 21 ' ctctddL : .
  19. 19. . u . 2 . 2 : i) .. 1.Y u , .. 22 )(1 /'2 u cl t . 2. .. )/1( /2 22 cu cl t l0 , : 22 022 22 0 )(1 )/1( /2 )(1 2 u ll cu cl u cl t 3. u xx, x )1( 1 1 /2 2 2 2 2 2 0 c u u cl t yx sum . , xx ux//c ... )1( 1 1 )1( /2 )1( 1 1 /2 2 22 2 2 0 2 2 2 2 2 2 2 0 c u u ll c u cl c u u cl t y x xyx sum
  20. 20. : )sin(),cos( )1( 1 1 )1( /2 )1( 1 1 /2 2 22 2 2 0 2 2 2 2 2 2 2 0 uuuu c u u ll c u cl c u u cl t yx x y yxy . , . . - 1. . , 1)1(1),( 2 2 2 2 2 c u u uf xy ... 000 38322218142 2 . , ... 1)1(1),( 2 2 2 2 2 c u u uf xy ... 0000 32221838142
  21. 21. . ( /) )1( 1 /1 /1 )1( /2 )1( 1 1 /2 0 22 2 2 0 c ucu cu ll c u cl c u u cl t yx x xyx 1. . o , 1 )1( 1 /1 /1 ),( c ucu cu uf yx x ... 0000 450360225 2. . o , 1 )1( 1 /1 /1 ),( c ucu cu uf yx x ... 00 22545 )sin(),cos(........ )1( 1 1 /2 2 2 2 2 2 0 uuuu c u u cl t yx xy 1. . o , 1)1(1 2 2 2 2 2 c u u xy
  22. 22. u/c