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" % ( $ $$ $ $Ss124 8@ 695 65 5 2 787 ::I 9 :55 47 *2 "4 822 8"573 955 ;955 "3 85 157 @ 8 ;72% 1%.92 8: ;951/   55 5 27 !2 :: 92 92  ) 88 4 44 # ;59; 573 :5 8 8184 "4 "7 84:255 "8 "# 6:2 88 55 9:5% 4% :53 8 4 92 548 %2 95( 4:9 "8 972 6:5 7 4 48% 84 445 *528#7 ; "9( 5 4 :95 7 "35 8 + 4:2 45 :2 84 495 !:2 PB7 ! 8572 6:2 :92 865 845% $ G44 45 5%  *85$cτ = 660v+a0%J%.1KC?#%32:57 97 2 7 : 867 .2 + 81 2+ 2 45% 5 5732 8 69 62 " :2 45 84 8 45 2 8 4 97 44': 5 " + ( 8 425579M %!#7 ; 455:65 8 5 8 7 2 2258789846 5 7 2  897 2 ;7 2 2 9 4:5 89 %7:9  22 6:5 57 15 553 ;7 8 :55 57 ,8%7 *2 87729 27 54822 6:: 4:9 82 4:2 ;:57 5527 842% 8 897 9573 9572 9 8% :7 52;5 52 ;957 8 857 655( 9 2 8% 4452 5 57 6:2 2 17/:55% 2 6( 4% 48:2 44 +7 2 45 :92 6:7 :2 82 8897 6: 6: 52( 8( 27 "4% 97 92 857 2 22 :) ;57 :9 8 :2 2 8285%4551* 2;2 5 84 ;52 652( 8 + 2 84 452 848( 22 84 :5 ;:57 45 4 6 :9 897 .8% 8 5 "9 2 57 48 6 52( 2 4 ;7 53 :2 81 ; 5 57 5 + 877* 442% 2 9 9& 82( 86 ;2 ;5 827 955 6952 2 48; 9 22;:5 57 52 877 42 52( & :5( ;:55 15 4:#5 9 5 ;;2 5$7 5$73 22 +$ 5 ' 8$2 87 9$2 87 ; 8$77 5$ :$2S0∠BACv=V =1v = V = 0, 8 cv1 = v2 = 0, 8 cα = 60◦r1t2r2l12 = |r1 − r2|t1 − t2l12(t2, r2)c2(t1 − t2)2 − (r1 − r2)2.(7.1)s21256: 95(22 2 :2 7 B4557 8845 PB,4822 844ds =dτp928184)224;5:55τds p= 1 − (dr/cdt)2 · dt =dτ =crS0(t + dt, r + dr)c dt > |dr|(c dt)2 − (dr)2 .v21 − 2 · dt.c(7.2)$s212 < 027 48 :252 2245 4:592:92 4515 482 9527; 4( 69) "9 :575 27 4: 6:5 977:47 P4 "44279 4 #2( P4 ;55: 8 82: 45 8:9 :57 17/ 457814  4 "45 9 155";47% 2556892 5 ,%2 :52 973 :55 9576:2 5 :5(3 44522 17% 63:5(3 455 489% :92 8! 527945 6:2 5 6;5 "138 22 4:2 857 "4:5 445 ! 453 & :94!2 % 52 68: 42268: 6:22 1 2%5 '9 8523 ;62 92 877278 :22 87 :5 524$ % $$ 4$ %dτx0 = γx00S0s212 = 0AµxµA0 = γA00V 0V 00+ Ax , Ax = γ Ax + A0 ,cc$ $V00c(t2 − t1) = γ(V ) c(t2 − t1) − (x2 − x1) > 0 .c P : 1GP"PFF 8 #@IBGB : 49 GB P: 4P: 4 84 *5 84  :7" 8182 5:$ 5 48287 68: 9;$2 "19 *24:5 55) 96:52 ;9 2 895 1527 55 ;6557 :57-845 4: 84,4822 97 :92 ;9 5: > 0SS08 5 8: :$ 982 8 279;$2 9$72 849:"5 ;:5 84:3 9 5:95 4 6:52 28182 ,%2 :5(34 49" 83 5% 22 ::7 4!5 :8:9 2) 5t2 > t1645 48 4(42 #5 "92" : 2! 7 4 9 GB68:2 812 9P:46:2 "84 ::5(3 6: 827945 :523 68:8# ( :9:5 +7 .4824!2 ; 8#*;;2 6:5238; :5(5$ 9$%2% 92 85( :5% 6:5987 895 ,65 "53 4:72 8 5 48 97 9 (45 + *62 6:5 4428( 5%3 :952 8#57 5% 4 5 12: :5 ' 897 92 5% 5 8 ;287 47 84 2 45 4522 9 :2 5 :95 42! 5 2 8 5) 52 2 65 4 42 7 445 ;5%18 72 857% :92 895 83& 877 7 4 : 5 2 22 957 527 27 "24:2 5 3"53 8 942 17/ 27 82 ;9957 6:$ 6:5$ 5 55$c(t2 − t1) > |r1 − r2|s2120(t, r) 455 42 65 9 :53"3 8#7 ; 7 48# ;92 8 *452 7 ;5 27 5( 485 5 8 P: 4 9 8597 8 82 9 4!2 F 27 68:57 455 4!8:2 8PF 8145 27 :5(3: 8 # 9 +95.28% 8: 57 57 8 9 85 :22 4 8B4 95 5F: 27:92 4 "83 "83 :I"573 89 445 87 8:: 573 894862 5% 8 4 85F4 8 455 45 72 8:I"8 8: 57355 6 1;5 5 "9( 8 6:5 6:% 42 5 @  I"84"3 8:) 89 ;55 + @ :7 :57 ;5 17/  ;5 @6 :984% 5 93":# B7 497 47 8%7 ) ":5 55 422:92 ;452 8;( , :4 4452 4492 72 ;9 8#57 # ,452 865 145 8# 1:2 ::I 655 55% " :55 "3 +48 "45352 8 "43 1; 9 5% 8% 4 ; 4 9 @ 5 2 ;5 485 4% "9( : 5592 +7 27 45 ;8 :55 6:5 27 + 5 485: $ 8 8 %$ $(s212 = −(r01 − r02)2 < 0S0t01 = t02dtv = 0dτx0 = cttV 0V 00+ x , x = γ x + x0 , y = y 0 , z = z 0 .cc(7.3)xµ = (x0, x, y, z) = (x0, r),s12x2µ ≡ x20 − r2Aµ = (A0, Ax, Ay , Az ) = (A0, A)SSm :92 278347 1789 8! 7 :773 65 27 ,5% 97;:57 55757 488+ 655) ; (27 187 ;57849 9 :57:8 :2 ;545 89 27876:2 ;7 65:53 85 452945 488 ;2 5:5 9 6:24!2 : 228: $7 488942 ;:55 8$87 679$  $ !"  *% (( % % 7 912 257<;5 ;92645 :5542 2" 81882 4+89 4("927  & '$uµ =uµ = (u0, u) , u0 = ru2µ = u20 − u2 =τ = 2 · 10−6dxµdτuµuµcv21− 2cG9:P:6xµ9 8 548: 8% *2- 9849 22 :5 9) "3:8 6: 4!2 812 4(4 82 84 496:2 : 75:3 ; *; ;59( ;; 92 "4:48% 8 2 6::5 847 895(4!2 9 8:9 422 +855 7 45 $245 ;9$2 6: ;92,4822 :5 :523 :9558 5$(45 892 9818 274 84:89456:2:5(39458%:54!24815$:$ 987 :9;$2 :5 84"9;$2:5:857748145;95:(7.4)A2µ ≡ A20 − A2(7.5)AµBµ = A0B0 − AB(7.6)BµAµdxµdτ(7.7a), u=rvv21− 2cc2v2−= c2 .v2v21− 21− 2cc;(7.7b)(7.8)!+ + / !"  ( ! & * " "'  + "* /  ) # "! + .% ) !* ./  ") "$ $ $54 ; 5 42 7 42 2 6 :7 17:952 84:2 492 8 :7 1152 1452 45 8!442 8 :22 195 7 ;:55 1;5 45 ;:5 572 82 6:5854 4 48 ;27 4 7 85 4:2 42 ;852 1;8 2252 877 9 ;55 1 89 7 8 : 8 6952 ; 574 2 15 8: 5 42 :2 43 ; 6 4:# 257 ;27 4 892 8 ;5 7 857 ; 71 ;55 8 48 1 2 95 97 7 ;52 :53:8 6: 65 :2 2 :2 :92 95(9; 4 ;5 857 ; 6:5 482 ;55 "5 4855 8 42 5 4: 2 3 : 495 45 :5 89 5 2 42 :2 6: 59 7 52 957 6 42 5 27887 7 42 52 8 57 2 :9 485 22 :53 8 8 4 :5 ;7 4 42 ( 78 9 :92 :55 5 ; 1$ 5) 6Ay = A0y , Az = A0z .l = 36V = c/4v = 0, 1 ct1t2r1S0r2?S!!" ( %" #"( "  * #% "" #F/ :" %  * ( ( %  "!#" ) $ % $ $+7 9 72 *:22 ! 482215 5554! ! 15 5,4822 ! ! ! $ ;8% 8( :( ;5 8:4 97 5 *2 45% 5 83 *42 22' 127 8FJ 8:2 17 77 877 +72 8 - 92 BF 8! 657 22 4:7 9 53 445 4 8# 42 5 5 *825: :55% 6:2 655 @5 2 9 445% 17/ :7492-53 557 :22 :"E4 27 ;:57 :4 7 5 8%28 M7 ;5% 9" 8= 2 8 46 95 6 53 B: 53+2 7 27:3 55 5) 7 J4I 45 87 7;4 655 8 B" 45% 227 *899 @4 953 482" 53 4%445 "% 86 955( @PHI"867 2 45 2283  :92 *4 "9 87 1 952 41 "% "# 54 2 7 8428! !: &7 8 9  9 65F(8 4 ) 573 5 5I29F55$ 5 3 8G $% 8$ $597 82 8;92 681:2 68:95 482 : 8 45 :5 92 87 4899 85 87 ;:5 17 9 5 8 4 5( 2 ;7 ; 45 2% 41 5 :52 8 97 Z4822 452 48 892 8:2 42( 482 8 +48 12 8( ^987 84 +2 :7 87 "14 # ) 4( ! 65.25 8# *2 " 4% 95245 ;952 46: 8;7 2 818:2 :95 92 4:52 15) 48284 482 88 87 46:8 9"18 5 "$RSTSF0 .nnF0.544 1 7 482 8# 872 27% 445 ;( 622 5 8: ;8 9 5% 9 42; 95 2 2( 53 2 "87 .22 95(955 45 6:52 :5( 2 ;8 84 2%76:52 57 82 957 1 43 6# 7 6:9 8922 8 6 53 :95 *: 84 482 ;482 :2 :53 7 "6 9572 845 2 92 65%87 6: "42 2%7 8:2 5( ;5 955 5(2%*:" 5 19: 89( 87 892 97%*"4# ;5 45 897 84;58 2 4% 5) 8 6 9 8 5  ;# 4  8# : 5( 5 65 5(6:2 +87 4455 95 *845 2%7 *2 18 9295  85 6% 45 ;8 892 4 9 )57 1:2 2 : 4 9 5 6: ;2 5657 2( " *8 6 "83 92 92 :5 4553 ) 65 4;8 :9 : 12 48 ) $ $ $ 8 $  "+ *(* ( '$&' (,'$(&/&# #+#(*$)($'* & (.&.*/*0 (.' )&$ Fi + " " ! * ( , %* *v 6= const8 ;457 47 8 424 4 5 65 8897787 5 4 5 482 4 92 9 5753 5 27 8571 5 : 4848 ;2 58: 8 7 4:5 ;727 :522;5 4492 4856: :92 15 44 8822 5 15 ;57248 814 412 87 :578 8 482 817 4:2 5 ;45 87 $ $`nv = const.46 45 2 8:2 45%7 8 622: 8 :7 496: " 489 5(* ;84; 12 92 927%7 57/ 8 9:7 2 7 :(22 8 ; 654 5 4 14)+" 9 #+ 4 45 5(2 426:52 87 9%7 22 "5 842 445244 *45 ;5 555 *45+ 9 :" 3 % 5 :84 ) 6:2F0F0FiF ∝ a.|F||a|aiai|Fi| / |ai|i(8.1)SSFikiFik(8.3)ikk72k6=iX:94428+mir̈i = Fi =Fik (ri − rk ); i, k = 1, 2, ..., N.mir̈0i =k6=iXFik (r0i − r0k ) ,$ $k42 5 2%7-45 8!7 17 892 8;95 4:97;5 45 8: 482448:2 686: "4 958: :#22 455 927 52 872 :5485 :9 45 +6: 6 822 4!+ :* 8 53 8:( 6 42:17 !8 95 58! 4 48% 4857 84 +7  428$2( 8$72 82 857d3rd2rF = m 2 + c1 3 ,dtdt + /;1 8:(2 !842 1:22( 842% 889 "9757 482 ( 45 7 6255 89 5 :5 65 ;45 7 87 *2 49 "6 ;,4822 "8 57 92 :52 ;8 PF47 5 57 45 ( @84&' 8 9",2 &' 895 482 @@P6 48 68( *42 2 848: 5) 455 7 8 5577 227 53 5 : 8;2 5) 2 4( 48 6575: 8! 495 189 6;52 4573 8 ) 5 5 2 "3 4 :5 2 ;5 8 87:9 2 ;5) 47 86: 242 848 8$ 4 5$ 6:5$!5 7 ia;5 :5 : 87 42/ 7 872 Z6:7 :5 8( 92  ;89 + 17 ":9 877 8!;5 442 2 :5 8 1 "2 8*9 8!7 89( 482 4( 52 "9 9%7+$ J+F 9 8 :"  rFik = −Fki.(8.2)'c1$:827 8: 4 842 58; 527 "% 495 573 8 455 ; :55% 528*9 ,482  6:5 7482 2 815 895( 9546 * ;527 45% 1578:2 857 15% 695 8:2 8% ;8 :22 ;5;84 :(2 48 (2 48 5 7812 5 27 66:5;87 83 ;)7 !:5" 6 88# 3 :2 45:; " 842 4$ 8 $ F = ma = mr̈.442 :2 28 442 499 "#& 9558*482 8' 8%772 22&'+97 5 57:" 145 1/6:#2 ;5% :922 *2 44244 89 8" 9# ;8;8 *4827 9:2 495":9 "6#2$ $6:& 184 29 +42(3 88 4;26#72 4827 :55' 2;89( : 4527 814 74 4" + %7: #2 ;455 48;+5( "6 8652" :92 7 812:( ;7899 +6: 887 1142 897 .+8 :5" 2  2 7 ' 5 2 58#) 17 *45 42 48 4 ;8% 9" 8 8# 8 17 657 :(3+7 *2;95 ( 8;9 152 1 1 (*;45 52 "4 8!742( 52 85 88897 4 87 8757 "2 8# 89(8 6& 9( 527% 15 8 2%98 85$ 5$2% 9$7148; 8 ;85 3 np8: #9 7 6:2 "9 68: #522 927 482 9: +42 57 2 :2 85  889 89 *73 77 87 2 ; ;7 " Z++ # 53 ; (2  7 87 7( 68: 1;27 ;45#58 + 8957 #2 4iF = kma65)58(& 27 3 :4 52 .523 _:22 55 87 482 )889 6:7 7 ;67 77 92 ;5 ! 8:2 Z;5 8 :55 ! 2 42 9 41  48; ! ;2 7 "4#2 ! 8 78 2 "44# 97 98897 ! 12 27!785 8 !;5   % % # * !) % (  ! mkri − rkN(8.4)r̈i = r̈0i, ri − rk = (r0i + Vt) − (r0k + Vt) = r0i − r0k ,(8.5)S S4422 6 4 4892 : 1;827 4:2 82 :2 t82 8:7 : :9 4 5 3 57 2 22 172 457 4:9 : 6:2 6 9 6: 9 8 482 2 5 8 : 84 8 45 4 2 4 :2 5 4 7 6:5 ;972 5 ;2 187 14 82 45 ;:55 ;2 4 83 4:5 7 87 657 89 67 ;55 2 92 4 5 2 5 82 55 73 7 7= 9 44 95 489 9 8 :2 1 18 48 2 187 ; 95 45 87 9 97 8 ;2 ; 42 5 2 :5 5 272 6:2 2 4 87 15 4 45 44 45 7 9 ;4:5 497 ;5 2 42 9 187 495 68: 4 8 ;5 17 48 8; 187 442 8 582 9 198 5 :9 /5 4 42 55 ) 4;; 5 82N&*45' 365 :7 82* 545 5 7187 6244 68: :5:52 :22 65%, 8 53 7:9 4553 4;955442 7 9%82 8 ": 57 *2+54 4495 48&9 "2 >'84822 4452 + 4452 95 % 2%47- : :9 :94492 4482 523 4482282 92 2 62N&65':::95582 5 7 55" 6 65:514 ; 12 ;:552 5 8 54 457 681 45788 82 452 82127 4 : 4;52 65 492 65:$2 :$22 482 :$22,   ,) )(  $ " #" O !""# M"/(,# ( Q ! & ! 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