relativity 2011
TRANSCRIPT
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.
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1
-
1 3
2 T 5
3 9
4 11
5 14
5.1 . . . . . . . . . . . 16
6 Lorentz 18
7 23
7.1 M . . . . . . . . . . . . . . . . . . . . . . . . . 25
8 H 26
8.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
8.2 . . . . . . . . . . . . . . . . . . . . . . . . . 27
9 H - 28
10 32
10.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
10.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
10.3 . . . . . . . . . . . . . . 33
10.4 - . . . . . . 37
10.5 - Compton . . . . . . . . . . . . . . . . . . . . . 38
10.6 . . . . . . . . . . . . . . . . 41
10.7 Doppler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
11 Minkowski 45
11.1 , . . . . . . . . . . . . . . . . . . . . . . . . 45
11.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
11.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
12 - Lorentz 49
50
.1 . . . . . . . . . . 50
.2 Lorentz . . . . . . . . . . . . 51
2
-
1
-
(). Albert Einstein 20o
[1],
Larmor, Fitzgerald, Michelson, Morley, Lorentz, Poincar,
Minkowski, , 19 .
[2].
. -
.
.
,
, ,
. -
. ,
1
,
Albert Einstein
20
2
.
.
.
:
137 N !136 C + e+ + e (1)
, -
( )
23892 U !23490 Th+42 He (2)
, ,
.
M v
p =Mv ; E =12Mv2 (3)
. -
.
. ,
, .
1
.
1016cm, .
1033cm.2
Time 1999.
3
-
(3) , -
.
(3) , ,
.
. ,
. -
,
. ; ,
,
, .
,
3
. ,
. -
, .
, .
,
. (3).
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,
. ,
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-
. , - -
,
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, ,
, ,
.
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,
. , , (
) , ,
.
3
.
4
-
2 T
, ,
, -
, ,
. ,
Einstein 1905 [1].
/,
.
1. Einstein:
.
2. H .
c = 2:998108m/sec 4.
-
:
) T Einstein
, ,
.
.
) ; -
,
, .
, ,
, .
. -
. -
. ,
.
,
.
. , ()
,
, .
, 1.
,
x.
4
1983 , (1m) 1/299792458 sec.
1-3 , .D.
Young, 1994.
5
-
x
y
z
x
y
z
V
1: fx; y; zg 0fx0; y0; z0g, V x.
-
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. -
,
-
. , ,
.
2 ,
.
; . -
. ,
.
. -
.
-
. ,
5
.
5
. , , -
Coriolis.
6
-
V
2: V .
) . , Einstein,
.
, ,
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,
.
-
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.
, -
,
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,
, .
,
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) , Einstein -
.
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.
, -
Einstein. -
.
A
, . -
,
.
7
-
: ;
;
;
.
: ;
;
-
.
)
,
, ,
.
2
v0 . t v0t . , t Vt. , , (v0 +V )t. H , ,
v = v0 + V (4)
o ( ).
. c0 ,
c = c0 + V 6= c0 ! (5) , ,
; ;
;
Michelson Morley,
.
,
, -
t
,
. ,
, .
, -
.
8
-
3
-
. -
, .
,
,
.
2. -
V 3.
, ,
. -
. ,
O, , ,
.
O0, ; E O0 - ,
. A : B : ,
B A.
V
A B
BA
-V
3: . B - , A .
, t = 0 , t0 6= 0. , -
. O t, O0 t0 6= t.
, , ,
,
, , . ,
9
-
-
, .
10
-
4
t t0 - V ; ,
.
,
. -
V , 1.
,. :
() -
, .
() ( ) -
V , .
. -
.
() .
. -
. ,
, .
t t0 , ,
, : ,
,
4.
t
A
B
d
t c2
t c2
t 2
v t
2
v
d
4: .
,
. =
=
() .
2()=2d c, ,
(t) =2dc
(6)
O , V
, 4. ,
c . ,
2d, t0
11
-
A B t. . Vt0
2
2+ d2 =
ct02
2(7)
d .
, ,
.
, 1 2 -
. 1 2 -
.
2 1.
,
, 2 1.
, 2
2 1, 1 -
. , (
) .
,
.
(7) t0 , (6), o
t0 =tq1 V 2
c2
(8)
. , -
() , -
()
.
-
t ()-(). , -
,
.
1: H -. ' 2:2 106sec. 6 e, e.
,
V. 0 ( ) ;
(). (8)
0 =q
1 V 2c2
(9)
,
6
, -
.
12
-
l0 = V 0 =V q1 V 2
c2
(10)
2: .
V . ( )
=76 .
0 =q
1 V 2c2
(11)
V , ,
76
, . .
,
, ,
2 .
1:
( ) 2 ;
V
V 1yearq1 V 2
c2
= 2 106years c (12)
V
c 1 1
8 1012 (13)
2:
;
(8)
0 =1 yearq1 V 2
c2
2 106 years (14)
,
.
13
-
5
. V
, -
.
/
. ,
V .
V
5: .
t t .
t =t0q1 V 2
c2
(15)
,
L = Vt (16)
L0 = Vt0 = Vt
s1 V
2
c2(17)
, L = Vt
L0 = L
s1 V
2
c2(18)
A, -
, .
, ( )
.
14
-
1: ,
L=2000000 , ,
L0 = L(1 V 2/c2)1/2. c , -
! c,
!!
: ( )
1 ;
V
6: .
: - . - -
- h=10000 m (
) V=0.999 c.
; -
2:0 106sec; ;
V
7: - .
15
-
5.1
. ,
,
, !!
, -
, .
!
,
. , -
t=t L=L -
1V 2/c2. O - V 1080km/h = 0:3km/sec. s
1 V2
c2=p1 1012 1 1
2 1012 (19)
, ,
T 0 =T
1 12 1012 T (1 + 0:5 1012) (20)
T T 1012: (21) ,
1 sec, T 105. - ,
,
, ,
.
, ,
7
.
1. : () 0:992
. () 0:9999994 .()
p1 0:0012 .
2. N0 = 1020 0:999999c. () t = 102sec; () ;
' 2 106sec.3. V0 ( )
v . () V ; ()
n0 , n ;
7
....
16
-
4. v=0.9999999999c
, L = 2106 . () ; () -
; ()
;
5. 75 km.
150 km/h. ,
75 km/h;
17
-
6 Lorentz
V,
.
xx
x x
V V
t=0 t=0 t t
8: V.
,
-
. ,
(x; y; z; t) (x0; y0; z0; t0). - (xA; yA; zA; tA) (x0A; y
0A; z
0A; t
0A) .
-
, (x0; y0; z0; t0) (x; y; z; t).
, -
Lorentz
.
x x
. ,
, -
,
t=0=t.
E,
x = y = z = 0 = t ; x0 = y0 = z0 = 0 = t0 (22)
.
-
,
(22)
8
x0 = 1x+ 2t ; t0 = 3x+ 4t (23)
1; 2; 3; 4, , V .
:
8
y z .
x t.
18
-
() , ,
, xA = xB , t0A t0B tA tB :
t0A t0B =tA tBq1 V 2
c2
(24)
(23) :
t0A = 3xA + 4tA ; t0B = 3xB + 4tB (25)
A (24)
4 =1q
1 V 2c2
(26)
() , -
, V . 9.
x B xA
x
x
xxB A
t=12:00
9: .
:
x , :
, 12:00,
. xA xB ,
L = xA xB (27)E (23) -
x0A = 1x + 2tA ; x0B = 1x + 2tB (28)
, tA = tB
x0A x0B = 1(xA xB) (29)
xA xB =s1 V
2
c2(x0A x0B) (30)
19
-
1 =1q
1 V 2c2
(31)
() ,
.
. -
x = ct ; x0 = ct0 (32)
, . , x t
x = ct, x t (23) x0 = ct0.
1c+ 23c+ 4
= c (33)
() , (x=0) -
x = V t (34)
, t 0 = 1x+2t = (1V +2)t,
1V + 2 = 0 (35)
(26), (31), (33) (35)
t0 =t V x/c2q
1 V 2c2
; x0 =x V tq1 V 2
c2
; y0 = y ; z0 = z (36)
A Lorentz -
8.
-
,
t0 =t Vx/c2q
1 V 2c2
; x0 =x Vtq
1 V 2c2
; y0 = y ; z0 = z (37)
, ,
Lorentz (36) x, -
, 0BB@ct0
x0
y0
z0
1CCA = (V )0BB@ctxyz
1CCA (38) Lorentz (V )
(V ) =
0BBBB@1p
1V 2/c2 V /cp
1V 2/c2 0 0
V /cp1V 2/c2
1p1V 2/c2 0 0
0 0 1 00 0 0 1
1CCCCA 0BB@
(V ) (V )(V ) 0 0(V )(V ) (V ) 0 0
0 0 1 00 0 0 1
1CCA (39)
20
-
(V ) Vc; (V ) 1p
1 (V )2 (40)
-
-
.
1: Lorentz
V /c! 0. , (36)
x0 = x V t ; t0 = t ; y0 = y ; z0 = z : (41)H (
) .
2: E Lorentz (36) -
, Maxwell -
.
3: R ( ) V -
. Rp1 V 2/c2
R .
(: x2 + y2 = R2. - (x0+V t0)2/(1V 2/c2)+y02 = R2. t=0 , : x02/(R2(1 V 2/c2)) + y02/R2 = 1, R
p1 V 2/c2 R . )
; -
. -
-
2
p1 V 2/c2.
, , -
Lorentz.
f(x; y) = 0 , Lorentz f(x(x0; y0); y(x0; y0)) = 0 .
**:
. .
-
,
. -
.
[7].
4: (37)
c2t02 x02 y02 z02 = c2t2 x2 y2 z2 (42)
,
s2 c2t2 x2 y2 z2 (43) -
(t;x;y;z) Lorentz.
21
-
Lorentz. -
x
9
.
*: (37) -
s2 = c2t2 x2 .
5: (36),
, -
(36) x, t x ,t.
t =t0 + V x0/c2q
1 V 2c2
; x =x0 + V t0q1 V 2
c2
; y = y0 ; z = z0 (44)
V 1, V . A V (36) V .
, ,
,
, . -
Lorentz V V ., ,
(V )(V ) = 1 ! (V )1 = (V ) (45)
1 .
.
,
, . ,
, Maxwell
Lorentz
.
,
Lorentz.
Lorentz. ,
,
, -
.
.
9
: s2E x2 +y2+z2 . Lorentz - .
.
22
-
7
() V (). -
,
10.
x
y
z
t
V
u
y
z
x
t
10: .
: (ux; uy; uz) - , (u0x; u0y; u0z) ;
t. (x;y;z;t) , (x0;y0;z0;t0), (36), .
,
u0x =x0
t0=
x Vtt Vx/c2 =
xt V1 V
c2xt
=ux V1 V ux
c2
(46)
u0y =y0
t0=
s1 V
2
c2uy
1 V uxc2
(47)
u0z =z0
t0=
s1 V
2
c2uz
1 V uxc2
(48)
1: -
. V /c juj/c ,
u0x ! ux V ; u0y ! uy ; u0z ! uz (49)
2:
c .
, -
x, ux = c,
u0x =c V1 V /c = c (50)
23
-
, -
Lorentz.
3: 1 2 ,
,
.
: Lorentz
.
V
x
x
11.
:
x
y
z
x
z
y
V
12.
24
-
7.1 M
-
, (a0x; a0y; a0z) , (ax; ay; az) V .
(46) 8 :
a0x dv0xdt0
= ax
1 V 2/c2
3/21 V vx/c2
3 (51)
25
-
8 H
-
. ; -
. -
, p =Mv . ,
.
8.1 .
-
.
, ,
. ,
,
.
ma va
P =Xa
mava : (52)
. -
, 13,
.
m =11m =11
m =11m =11
m =22
m =22
m =22
m =22
2v -v
V V
13: . .
. 13
.
,
V , 13. - u1 u2
26
-
, . :
u1 =2v + V1 + 2vV
c2
; u2 =v + V1 vV
c2
(53)
, u01 u02
u01 =2v + V1 2vV
c2
; u02 =v + V1 + vV
c2
(54)
.
. v = V = c/4. P 0initial = 2c/3, P
0final = 78c/119. , -
.
8.2 .
v
p =Mvq1 v2
c2
(55)
A, Ma va, a=1,2,3,...
P =Xa
pa =Xa
Mavap1 v2a/c2
(56)
(55) -
2, 12 [5].
. -
,
(52).
dp
dt= 0 (57)
-
,
dp
dt= F (58)
-
. , (57) . -
. ,
-
Coriolis .
dp
dt= F
coriolis
+ :::: (59)
27
-
9 H -
y , x1 x . F(x)
, x,
x
10
. x2 v. W (x1; x2),
x1 x2, v, .
,
, .
W (x1; x2) = Efinal Einitial = K(v) (60) F (x) ,
W (x1; x2) =Z x2x1
F (x)dx =Z x2x1
dp(x(t))dt
dx =Z x2x1
dp
dv
dv
dx
dx
dtdx
=Z v0
dp
dvvdv =
Z v0
m
(1 v2/c2)3/2 vdv
=mc2q1 v2
c2
mc2
K(v), , (60) m v
K(v) =mc2q1 v2
c2
mc2 (61)
m v
E =mc2q1 v2
c2
(62)
: (1) -
, m
E0 = mc2 (63)
.
(2) (62) (55)
p =E v
c2(64)
(3) (62) (55) -
m, ,
E2 c2p2 = m2c4 (65)10
y x.
. .
28
-
(4) .
, , (e), ; (75)
E = jpjc (66)
(64)
v = c : (67)
,
c. E (62)
(55) ,
0/0.
. (66)
. ,
,
11
.
E = h. T
jpj = Ec=h
c: (68)
(5)
K(v). , v/c 1
K(v) = mc2 1q
1 v2c2
1
' mc21 +
12v2
c2 3
8v4
c4+ :::: 1
' 1
2mv2 3
8mv4
c2+ :::
, ,
-
v/c 1.
- .
()/c
2.
me ' 0:511MeV /c2 ; mp ' 938:3MeV /c2 ; mn ' 939:6MeV /c2 (69)
, , .
, ()/c.
1eV = 1:6 1012erg = 1:6 1019Joule. 1MeV = 106eV , 1GeV =109eV ...
11
, ,
.
. , ,
0 1 . , (75), E = p2/2m m! 0. , ,
. (66)
.
29
-
1: v = 0:85c. ;
:
E =mc2p
1 v2/c2 =0:511p1 0:852MeV = 0:97MeV ; K = E mc
2 = 0:459MeV (70)
2: E = 3mpc2. () H mpc2 =938:3MeV . () H
mpc2p
1 v2/c2 = 3mpc2 ! 1 v
2
c2=
19! v =
p8c/3 (71)
() K = E mpc2 = 2mpc2 = 1876:6MeV . ()
p =mpvp
1 v2/c2 =mpc
2p1 v2/c2
v
c
1c= 3mpc2
p83
1c= 2654MeV /c (72)
,
:
1: . -
m v.
(62) (55) .
, ,
1. -
(46), (47) (48). ,
(p0x; p0y; p0z) E , (px; py; pz) . 0BB@
E0
cp0xcp0ycp0z
1CCA = (V )0BB@
Ecpxcpycpz
1CCA (73) (V ) (39) . , - (E; cpx; cpy; cpz) , - (ct; x; y; z) .
: H (73) P -
. P
.
0BB@E0
cP 0xcP 0ycP 0z
1CCA = (V )0BB@
EcPxcPycPz
1CCA (74)
2: (36) (74) ,
(42)
E02 c2P 02x c2P 02y c2P 02z = E2 c2P 2x c2P 2y c2P 2z (75)
30
-
-
. m -
E2 c2P 2x c2P 2y c2P 2z = m2c4 : (76),
.
1. Large Hadron Collider (LHC) CERN ,
=3.5 TeV. () , ()
() .
2. =10 GeV. ()
, () , () . ()
;
3. =10 eV.
() , () ()
V .
4. . supernova L
.
. m , L, E, T
c. : L = 2 106lyrs, E=1MeV, T=1min.5. 0.01 mole X,
X ! Y +A, , = 104kg. mX = 230:422GeV /c2, mY = 226:410GeV /c2
mA = 4:010GeV /c2, , C = 4:19kJ/kgr oC . ()
()
.
31
-
10
,
.
10.1
.
.
K0 ! + + (77)
.
M mK0 = 498MeV /c2 m m = 138MeV /c2. K0.
-
,
.
pi -
pi+ 0
14:
0 .
-
. , Mc2
K0, m v.
Mc2 = 2mc2p
1 v2/c2 (78)
1 v2
c2=
4m2
M2! v ' 0:832c (79)
10.2
-
. -
.
.
22688 Ra!22286 Rn+42 He (80)
mRa = 226:0254u, mRn = 222:0175u mHe = 4:0026u 12.12
H 1u 1/12 126 C = 1:66 1027kg = 931:5MeV /c2.
32
-
E 1: .
:
Einitial = mRac2 (81)
Efinal = ERn + EHe = mRnc2 +KRn +mHec2 +KHe (82)
K .
K = KRn +KHe = (mRa mRn mHe)c2 (83)H -
, ,
.
K = 0:0053u 931:5MeV /c2uc2 = 4:94MeV (84)
!.
2:
;
: -
4.94MeV. , mole Kmole = NA 4:94MeV =6:0234:941023MeV = 29:751023MeV = 29:751:61010Joules = 4:761011Joules =4:76/4:184 1011cal = 1:14 1011cal.
3: 1
mole Ra . -
200C 900C;: -
Q = MC, C . C =1cal/grgrad 13 Kmole. -
M =Kmole
C= 1:6 106kg (85)
! 70
! ! -
.
.
10.3
. t=0 -
f x. .
, (, ,
) .
13
.
33
-
15. Stanford Linear Accelerator Center (SLAC) .
To
x. x. y z
.
d
dt
Mvq1 v2
c2
= f (86)
v x- .
() v(t). 0 t
Mv(t)p1 v2/c2 = ft (87)
v(t) =ftMq
1 + f2t2
M2c2
(88)
, ft/Mc 1 - ,
v(t) fM
t+ ::: (89)
, ft/Mc 1,
v(t)! c (90)() x(t) . (88)
dx(t)dt
=ft/Mp
1 + f2t2/M2c2(91)
14
x(t) =Mc2
f
s1 +
f2t2
M2c2 1
(92)
14
(f/M)tdt = (Mc2/2f)d(1 + f2t2/M2c2).
34
-
X Taylor
p1 + w 1+w/2+ ::: jwj 1 -
ft/Mc 1
x(t) 12f
Mt2 + :::: (93)
E, (92)
x(t) ct (94)
.
() a(t) (88)
. To :
a(t) =dv(t)dt
=fM
1 + f2t2
M2c2
3/2 (95) f/M t=0 t3 -
. .
.
16: x(t), v(t) a(t) - . x = 0.
() .
;
.
a0 = f/M ., :
. ,
. t
(88). E,
(t; t+dt) v(t) dt .
.
35
-
x
x
V
V
(t)
(t)
17:
. To . -
v(t) .
H (51),
V = vx(t), . To
a0x = ax1 vx(t)
2
c2
3/2(96)
(88) vx(t) a0x = f/M .() : t
t ;
-
(t,t+dt) . dt dt
,
dt =dt0p
1 v(t)2/c2 (97)
A v(t) (88) (0; t) (0; t0) Z t0
0dt0 =
Z t0
dtp1 + f2t2/M2c2
(98)
t0 =Mc
fsh1(ft/Mc) (99)
() a0 = 1g '10m/sec2 ( ) , 2000000 . ;
Z t
, x=2000000 ,
.
x(t0), - ( ), t .
36
-
x(t) , (92). (99)
a0t
c= sh(a0t0/c) (100)
(92)
x(t0) =c2
a0
ch(a0t0/c) 1
(101)
E: a0 = 10m/sec2 x = 2000000 t0 = (c/a0)ch1(1 + a0x/c2) ' ln(1:8 106)years ' 15:2years. , , -
, 2000000 , 15 !!
1000 ! .
10.4 -
x=x(t) ( ) x
. -
t1 t2 ; dt v(t) = dx(t)/dt,
, -
v(t). ,
dt =dp
1 v2(t)/c2 ; (102)
d =q1 v2(t)/c2dt : (103)
,
=Z t2t1
dt
s1 v
2(t)c2
=Z 21
qdt2 dx2/c2 =
Z 21ds/c ; (104)
ds2 = c2dt2 dx2 dy2 dz2 (105) .
H . x = x(t) t1 t2
=Z t2t1
dtq1 v2/c2 =
Z 21ds/c : (106)
ds = cd , d , - . ().
37
-
10.5 - Compton
O Arthur Compton Washington Saint Louis
. , ,
,
.
: Compton
18.
18: T Compton.
, , . -
, , - 0. Compton 19 .
19: H 0 - . H .
38
-
() 0 = , ()
0 > . ;
:
. -
,
. ; , -
. me, ,
, .
. . -
.
, m . ,
, .
E1 = h p1 = h/c x. E2 = mc2 p2 = 0,.
E01, p01 E02, p02 , :
E01 = h0 ; p01x =
h 0
ccos ; p01y =
h 0
csin
p02x = jp02j cos ; p02y = jp02j sin
M
p = 0
E = M c
2
22
hc
E = h
p = 1
1
cp = 1h
E = h 1
M
2p , E2
20: Compton.
h +mc2 = h0 + E02 (107)
39
-
h
c+ 0 =
h 0
ccos + jp02j cos (108)
0 =h 0
csin jp02j sin (109)
(108) (109)
cjp02j cos = h h 0 cos ; cjp02j sin = h 0 sin (110)
c2p022 = h2(2 + 02 2 0 cos )
= E022 m2c4=
h( 0) +mc2
2 m2c4= h2( 0)2 + 2mc2h( 0)
c2p022 = E022 m2c4, (107).
E
0 0
=h
mc2(1 cos ) (111)
0 = hmc
(1 cos ) (112)
. -
. .
,
.
C h/mc Compton m. C(e) = 2:426 1012cm = 2:426pm. 1850 .
A: 10:0pm = 0:1 -. () 450; :0 = + C(e)(1
p2/2) = 10:0pm+ 0:293 2:426pm = 10:7pm. (b) -
; :
, = 1800. 0 = + 2C(e) ' 14:9pm.
: -
19. () -
, -
. ,
Compton , -
, 0 ' , . ()
19 ,
Compton. ()
, ,
,
.
40
-
10.6
() EA (). EA
A+B ! C1 + C2 + :::+ Cn (113) Ci mi, i = 1; 2; :::n. T ,
mA + mB < m1 + m2 + ::: + mn. .
,
.
15
.
ECMmin = ECMtotal = (m1 +m2 + :::+mn)c
2.
21.
BA
C
C
CC
C
1
2
34
M
21: ,
.
H :
Elabinitial = EA +mBc2 ; P labinitial =
1c
qE2A m2Ac4 (114)
-
ECMfinal = (m1 +m2 + :::+mn)c2 ; PCMfinal = 0 (115)
(Elabinitial)2 c2(P labinitial)2 = (Elabfinal)2 c2(P labfinal)2 (116)
,
2 c2P 2 ,
(Elabfinal)2 c2(P labfinal)2 = (ECMfinal)2 c2(PCMfinal)2 (117)
15
H ,
.
41
-
A
(Elabinitial)2 c2(P labinitial)2 = (ECMfinal)2 c2(PCMfinal)2 (118)
(EA +mBc2)2 (E2A m2Ac4) = (m1 +m2 + :::+mn)2c4 (119) EA
EA =(m1 +m2 + :::+mn)2 m2A m2B
2mBc2 (120)
.
10.7 Doppler
Doppler. -
.
. -
. V .
0 =
s1 + V /c1 V /c (121)
.
, V , ,
0 =
s1 V /c1 + V /c
(122)
(121). -
.
42
-
VV
AB
B A
+ v t
c
22: .
.
t0A t0B
, T 0
T 0 1 0
= t0 = t0B t0A (123)
T : -
. , , t = tB tA ,
t =t0p
1 V 2/c2 (124)
22() 22() .
, ,
l = + Vt. A,
t =lc
=+ Vt
c=
1+V
ct (125)
t
t =1
1 Vc
(126)
(123) (126) (124)
1 V
c
= 0
s1 V 2c2
! = 0s1 + V /c1 V /c (127)
0 =
s1 + V /c1 V /c (128)
43
-
.
1: I, (121) (122) 0 -
V .T -
.
(red shift). , -
, (blue shift).
T Doppler .
, ,
. (
),
.
2: . , -
, Doppler . -
;
4: Doppler.
, (121) (122)
0 ' 1 V
c
(129)
.
.
44
-
11 Minkowski
, -
.
. ,
, , -
.
. -
. -
.
11.1 ,
() (ct; x) .
. ct t
.
(b) x=0 .
(b) ct , x=0 x.
(c) v
.
x=-(V/c)(ct)x=0
t=0ct=-(V/c)x
x=ctx=ct
ct=(V/c)x
t=0
ct
x
ct
x
A
23: , , , .
(d) t=0
x=0. c
x.
x = ct - .
(e) x1 t1.(e) T .
45
-
(f) M .
,
. , -
. (f)
.
inkowski.
11.2
, .
. -
.
.
() {x,ct} ,
.
ct
x
x
ct
L
L
0
x=0x+Vt=0
x=-Vt
ct=(V/c)x
t=0
x=L0
AB
24: .
A {x, ct} (), V
, t=0=t. O
x=0
16
. ,
x=0 .
x = V t (130)
(ct) . x
x ct.
16
, , y x-y
x=0.
46
-
H . .
t=0,
. ,
25.
ctct AA
ct
x
ct
x=(V/c)t
xA
A
25.
tA xA. , x0A = 0 t
0A, o
.
tA t0A.
X (42)
c2t2A x2A = c2t02A (131)
A , (130),
xA = V tA (132)
O
tA =t0Ap
1 V 2/c2 (133)
.
, , .
:
Minkowski. -
, (131), ,
.
47
-
11.3
-
.
24.
x = 0 . x = L0. , L0. ct , () 24.
A ,
V. x ct
24. .
t00 , x0 x0 . L = x0 x0A.
.
t=0. T x0A = 0. T - t=0,
x0.
0 x02 = c2t2 L20 ! L2 = L20 c2t2 (134)
t=0. (36)
t = V x/c2.
t = V x/c2 = V L0/c2 (135)
L = L0
s1 V
2
c2(136)
.
48
-
12 - Lorentz
49
-
.1
m
dp
dt= m
dv
dt= m
d2x
dt2= 0 : (137)
V.
v ! v0 = v + V ; x ! x0 = x + Vt+ a (138)
,
dp0
dt= m
dv0
dt= m
d2x0
dt2= 0 : (139)
:
1: ,
V, (138).
2: (3)
.
(138) ,
.
, (137)
( )
,
V.
,
ad2x
dt2+ b
dx
dt+ c = 0 (140)
a, b c
.
.
1: (138) V
ad2x0
dt2+ b
dx0
dt+ c = a
d2x
dt2+ b
dx
dt+ c + bV = bV = 0 (141)
V, b=0.
ad2x
dt2+ c = 0 : (142)
2: c
,
50
-
.
c , c=0,
ad2x
dt2= 0 : (143)
a ,
.
.
,
x0i = Rijxj : (144)
ad2x0idt2
+ ci = aRij d2xjdt2
+ ci = 0 ; (145)
ci = 0, (143). -
(138). ,
V
v ! v0 = v + V : (146)
.2 Lorentz
Maxwell
17
-
, Lorentz.
-
Lorentz.
.
, -
Lorentz.
, Lorentz.
, ,
Lorentz.
. -
Einstein Maxwell
.
17
-
. , Ai = 0. Oij OijAj = 0. . , Ai = 0, OijAj = 0. .
,
d2xidt2
= 0 (147)
. , Rij
d2x0idt2
= Rij d2xjdt2
; (148)
(147) d2x0i/dt2 = 0 .
51
-
[1] A. Einstein: On the electrodynamics of moving bodies, The principle
of Relativity: a collection of original papers on the Special and General Theory of Relativity,
Dover, 1953.
[2] Subtle is the Lord..., A. Pais.
[3] Relativity. The special and the general theory, A. Einstein. University paperbacks, 1970. -
. 58
.
[4] The meaning of Relativity, A. Einstein
[5] C. Kittel, W. Knight M. Ruderman, Mechanics, Berkeley Physics Course Vol. 1. -
.
[6] E. Purcel, Electricity and Magnetism, Berkeley Physics Course Vol. 2.
.
[7] J.S. Bell, Speakable and unspeakable in quantum mechanics, Chapter 9, Cambridge University
Press, 1993.
52