Post on 26-Nov-2015
.
2 0 1 0
iii
1 1.1 ................................................................................................2 1.2 ................................................................................................................5 1.3 ...........................................................................................9 1.4 ......................................................................................10 1.5 Michelson Morley .........................................................................................11 1.6 ................................................................16 2 2.1 . . . .........................................................21 2.2 ...............................................................................................22 2.3 .......................................................23 2.4 ..............................................................................................24 : C.Kittel .. .....................................................26 3 3.1 .........................31 3.1.1 .........................................................................................................36 3.1.2 ........................................................................................................38 3.2 ......................................................................40 3.2.1 ..........................................................40 3.2.2 ...................................................................40 3.2.3 , ..................................................................42 4 4.1 ...................................................................................................................43 4.1.1 CERN .......46 4.2 . Sagnac ...........................................................................48 4.3 Hafele Keating ...............................................................................................50 ...........................................................................................................52 4.4 ...................................................................................................53 4.5 ..............................................................................................................54 4.6 ...................................................................................................................55 4.7 .............................................................................................................57 : C.Kittel .. .....................................................59 5 5.1 . ...................................................................62 5.2 ....................................................................................................................66 5.3 ..................................................................................................................68 5.4 .............................................................................................70 5.5 .....................................................................................................70 5.6 ......................................................................................72 5.7 ................................................................................................75 5.8 ...................................................................................................76
iv
6 6.1 ..................................................................................................................79 6.2 ..............................................................................................82 6.3 .................................................84 6.4 .............................................................................86 6.5 ............................................................................................89 6.6 .......................................................................................................................91 6.7 ......................................................................92 6.7.1 ..................92 6.7.2 .................94 : C.Kittel .. .....................................................96 7 7.1 ......................................................................................................................................103 7.2 .....................................................................................105 7.3 ...............................................105 7.4 ...........................................................................109 7.5 ....................................112 1 1.1 . ...........................................................115 2 2.1 .........................................................................................................118 2.2 ............................................119 2.3 ...................................................122 3 MAXWELL LORENTZ 3.1 ................................................................................................................129 3.2 Lorentz ..................132 3.3 Maxwell ........................................................................................................134 3.4 ..................................................135 3.5 Lorentz ......................................................135 3.6 Lorentz Maxwell .............................................136 3: ...............................................................................139 4: .........................................146 5: ...................................................................................151 6: .............................................162 7: ......................................................................................170
v
- . , . 4 10 13 (C. Kittel .., ) 5 (E.M. Purcell, -) Berkeley ( ...). -. 10 , , - 50 . - . , - , , , - . , -, . , . , - , . , . . 1 2010
vi
. .
Lorentz:
( )tVxx = yy = zz =
= xcVtt 2 c
V 21
1
: 0LL = =0L
: =t =
: , . , , .
:
21 cVVx
xx
=
=
21 cVx
yy
=
21 cVx
zz
: ( )( )
( )2 2 2 2
22
1 / 1 /1
1 /x
c V cc
V c
=
: 21x
P PVc
= Doppler:
: 011
f f = + . :
20 1f f = . :
2
01
1 cosf f
= +
: 0 02 2( ) 1 /MM M
c = = : 0M
: 0 02 21 /MM M
c= = =
p GG G G 0p M c=
: ddt
= pFGG
02 21 /
d Mdt c =
FGG
( + ): 20 0( )E E K M c K = + = +
2 20E Mc M c= = 2
2
2
1c
cME = . : 20 0(0)E E M c= =
: 2
2 200 02 2
( 1)1 /
M cK M c M cc
= = 2McEK =
vii
2 2 2 2 40E p c M c = : 2 2 4 2 20E M c p c= +
: 2Ec
=p G G : 2cME = :
==
n
ii
1
.pG
- : =
=n
iiE
1
. :
x xp p Ec = yy pp = zz pp = ( )xpcEE =
: pcE = c= : hE = pcE =
hp = ( h = Planck s J 1062,6 34= ) :
2 2
2 2
/ /1 / 1 /
y zx x y z
x x
V c V cF F F FV c V c = ,
2 2
21 /
1 /y yx
V cF FV c = ,
2 2
21 /
1 /z zx
V cF FV c =
: x xF F = yy FF = zz FF
= XAZ : H n X( )M Zm A Z m M = + XAZ : [ ]2 2H n X. . ( )B E M c Zm A Z m M c= = +
Maxwell: 0 0 00
, 0, , .t t
= = = = + G GG G G G GB EE B E B J
: 2
22 2
1c t
= GG EE
22
2 21c t
= GG BB
0 0
1 299 792 458 m/sc = = .
:
x xE E = ( )y y zE E VB = ( )z z yE E VB = +
x xB B = ( )2/y y zB B VE c = + ( )2/z z yB B VE c =
=E E& &G G
=B B& &G G
( ) = + E E V BG G G G ( )2/ c = B B V EG G G G
viii
.
A. Einstein, Relativity. Methuen, 1962. , 1916,
.
A. Einstein, ( ).
A. Einstein, H.A. Lorentz, H. Weyl H. Minkowski, The Principle of Relativity. Dover. , .
M. Born. Einstein's Theory of Relativity. Dover Publications, 1964.
V.A. Ugarov, Special Theory of Relativity. Mir Publishers, 1979. , .
A.P. French, Special Relativity. Norton, 1968. ... Introductory Physics Series, C. Kittel .., -
.
E.F. Taylor J.A. Wheeler, Spacetime Physics. Freeman, 1966. , .
C. Mller, The Theory of Relativity. Clarendon Press, Oxford, 1972, 2nd ed. . .. .. , . 1998. .
, . ( ). , 1995.
( 1940, 1960).
J. Bernstein, . , 1995. .
A. Pais. 'Subtle is the Lord...' The Science and the life of Albert Einstein. Oxford, 1982.
. . (.). . . , 2006.
1
, . . , 1,2,3,4,5. .
1632 : - .
1676 (Rmer). 1687 : (Philosophiae Naturalis Principia Mathematica). 1782 (Bradley). . 1842 (Doppler). 1851 (Foucault). 1849 (Fizeau), 1862 (Foucault). -
. 1851 . . 1856-1864 (Maxwell). . 1881 (Michelson-Morley). 1883 (Mach), Die Mechanik in ihrer Entwicklung. 1887 . 1896 (Becquerel). 1894-1896 (J.J. Thomson). 1902 -
, (Kaufmann). 1892-1904 (Lorentz) . 1895-1905 (Poincar) . 1905 (Einstein) , Ann. d. Phys. 17, 891. 1909 (Minkowski) , Phys. Zs. 10, 104.
1 E.T. Whittaker, A History of the Theories of Aether and Electricity. Vol. 1: The classical theories (2nd ed.
1951), Vol. 2: The modern theories 1900-1926, (1953). London, Nelson. 2 M. Born, (1964). Einstein's Theory of Relativity. Dover Publications. 3 A. Pais (1982). 'Subtle is the Lord...' The Science and the life of Albert Einstein. Oxford. 4 O. Darrigol, (2000), Electrodynamics from Ampre to Einstein, Oxford: Clarendon Press 5 . . (.) (2006). . . -
.
2
1.1
, . , . - . , -, . - . . , - (20 000, 4 , ) . John Harrison - , 1735-1772, , . 1616 , , , , , , 6. , , , , . - . , . (Ole Christensen Rmer, 1644-1710), - Uraniborg, , Hven. Jean Picard , , 1671, 140 , . (Giovanni Domenico Cassini, 1625-1712) , -. , , . , 1675, 10 11 ! 2,3
82,5 10 m/s . . , , , - . , 1676, , , - 45 5:25 .. 9 , 10 ! , 10 .
6 . (1611), , , : , , , , , , . , .., , ... , , , - : , -... , - . . .. G. Holton, . ..., 2002. . 65.
3
, - , 10 . . 1.1, . () , FGHLK. - , . C (), . - L , K, LK, 10 . - . -
, , - . - (.. FG ) , (.. LK). - 42,5 , - , , . 40 - 22 - , , -. , - 22 80 ( FG FG). . -, /c c :
80 42,5 60 930022
c
= = . (1.1)
- 6140 10 km , 28,3 km/s , , 260 000 km/sc = . , (Christian Huygens), , 22 - , 220 000 km/s. Op-ticks, , 1704, , 7 8 - 8 - 20 . -, , 670 10 , 235 000 270 000 km/s. , :
1. .
1.1 , (), ().
( , 1676, .)
4
2. , . 3. - .
Harrison, , , 30% ! , , , - . . , , , GPS (Global Positioning System) 5 m (. 1.2). 24 32 . - , . 7,2 s , . - 45,9 s - , . 38,6 s , 0,45 , .
() ()
1.2 GPS: () , () . , , , , !
5
1.2
3 - .. , - (4 ..). , - , 5 . , - , - . - , - . , - , - , , - (. 1.3). 1 , , ( ). , - . ,
arctan ( / )R D = , R D . (2), , , (3), - 2 . , - . , C, 0,786 , - 1/0,786 = 1,27 (pc, parallax second) 4,2 , 260 000 ( , ua). , , . , 1543, . Thomas Digges, 1573, . - : Jean Picard, 1680, 40 . John Flamsteed, 1689, . Robert Hooke, 1674, , , -, 23 , . , , - . , (Friedrich Bessel, 1784-1846), 1838 61 0,294 , 3,4 11,1 . , (James Bradley, 1693-1762) 1725 -
1.3 .
6
, 7. - , -, 39,6 o75 , - (. 1.4). - . , , .
1.4 , -, o75 , 1727-1728,
. - . - - - . Thomson8 - , . - - , -. , , , . - -
7 J. Bradley, Phil. Trans. Roy. Soc., 35, 637 (1729). . : A. Stewart, The Discovery of Stellar Aberra-
tion, Scientific American, 210 (3), 100 (1964). 8 T. Tomson, History of the Royal Society, (London, 1812), . 346.
1.5
7
(. 1.5). ( ) - . - 1, , , - 1. , - , , , .
: t
1 2 c t = , , - 1 2T T t= . 1 2 1 2tan T T / = , tan / c = . (1.2) , - (. 1.6). - / cos ( )c c > . , - , (. 1.7). , o0 75 = , - (. 1.8). , 0 : () , () G . - 0 . - G (. 1.8). , :
0sintanc c = = . (1.3)
,
0sinc
= . (1.4)
1.6 ,
.
1.7 ,
.
8
1.8 0
. (. 1.9), . - A, B, C D . 1.9, abcd . 1.9. . 1.9 . 1.9. B D, / c = , A C - 0( / )sinc = . , , B, D, - C A, . - . :
2 39,6 = 519,8 219,8 rad 9,6 10 rad3600 360
= = = . (1.5)
o0 75 = 430 km/s 3 10 m/s = = 0( / )sinc = , :
4
80 5
(3,0 10 m/s)sin 0,966 3,02 10 m/s9,6 10
c = = = (1.6)
, 299 792 458 m/sc = . . , , - , . , . 100 .
9
1.9 . () - . () . ()
, . , ( ). - . , , - . 1.3
. ,
. C. Kittel .. , . 10, . 328-332
, 1983, (, m) (, s) , ,
299 792 458 m/sc . ( ) .
10
1.4
,
2
22 2
1c t
= EEGG
2
22 2
1c t
= GG BB , (1.7)
0 01 299 792 458 m/sc = = , - . Mitchel9, 1784 . O Arago10, , . (. 1.10), , , - 2 ( ) 6 ( ). , - , . - , / c . 310 . 5 m, - 3 22 / 2 10 5 10 m 1 cmc = = = . , Arago , - .
1.10 Arago , , ( ) ( ).
, - . . , , . - . , , .. . 1.11. . , , . , , - ( 2). , , ( 5 6). , , , . D , , c /h c . c c, - 2( / )t D c c = . 9 J. Mitchel, Phil. Trans. 74, 35 (1784). 10 F. Arago, Compt. Rend., 8, 326 (1839) 36, 38 (1853).
11
. , . , - . , .
1.11 - . -.
, Michelson11 1881 Michelson Morley12 1887. 1.5 Michelson Morley
Michelson Morley, 1887, . , , - , . ,
. . , - , , . , - Michelson (. 1.12, Michelson Morley). -
11 A.A. Michelson, Amer. Jour. of Sci., 22, 20 (1881). 12 A.A. Michelson and E.W. Morley, Amer. Jour. of Sci., 34, 333 (1887).
1.12 Michelson Morley.
12
, - ( 313,6 gr/cm , 32,75 gr/cm ). , - . - -. , , . . 1.13. s . , a, -. a , c, a , df. , b, a, . , . 1.12, -. , - Michelson Morley, . - .
() ()
1.13 Michelson. , . - . - . s , - . , , ( ) . . 1.13, , .
13
() ()
1.14 , x .
() ()
1.15 ( )ac a ( )ab a .
, V x (. 1.13 1.14). , c V x, c V+ x, c - (. 1.14). , - ab ac D. a c
1DT
c V= . (1.8)
c a
1DT
c V= + . (1.9)
( )aca (. 1.15)
1 1 2 22cT T D
c V+ = . (1.10)
14
2
1 1 1 2 2( ) 2cL c T T D
c V= + = . (1.11)
( / )V c ,
2
1 22 1VL Dc
+ . (1.12)
, 2 2T T t = = ab, b 2VT Vt= x, a 22 2VT Vt= (. 1.15). a b 2L . ,
( ) ( )2 222 2/ 2L D VT= + . (1.13) 2 /T D c= , ( ) ( )2 222 / 2 /L D DV c= + (1.14)
2
2 22 1VL Dc
= + . (1.15)
( / )V c ,
2
2 22 1 2VL Dc
+ . (1.16)
1.16 90 (. 1.13). -.
2
1 2 2
VL L L Dc
= = . (1.17) . . . - 90 (. 1.16), .
2
22 2VL Dc
= . (1.18) ,
15
, 2 L ,
2
22V Dnc = . (1.19)
- , . - 410V c , . (1.19) -
82 10 Dn = . (1.20)
Michelson Morley, - 62 10D = 0,04n = . - , -. , 10 72 10D = . - 0,4n = . . . 1.17 Michelson Morley. 1
8 . . -, . - 180 .
1.17 Michelson Morley. - 18 - -. - . -, . - 180 . .
. -. , , -, , , . Michelson Morley 1.1. 13. ,
13 !
16
, . - .
1.1 Michelson-Morley
( : Shankland et al., Rev. Mod. Phys., 27, 167 (1955).)
l (cm) ( )
/
Michelson (1881) Michelson Morley (1887) Morley Miller (1902-4) Miller (1921) Miller (1923-4) Miller ( , 1924) Tomaschek ( , 1924) Miller (1925-6) Kennedy (1926) Illingworth (1927) Piccard Stahel (1927) Michelson .. (1929) Joos (1930)
120 1100 3220 3220 3220 3220
860 3200
200 200 280
2590 2100
0,04 0,40 1,13 1,12 1,12 1,12 0,3 1,12 0,07 0,07 0,13 0,9 0,75
0,02 0,01 0,015 0,08 0,03 0,014 0,02 0,08 0,002 0,0004 0,006 0,01 0,002
2 40 80 15 40 80 15 13 35
175 20 90
375
, l, . , - . - / .
1.6
Becquerel 1896, , , . - . W. Kaufmann14, 1901, - . Kaufmann - . 1.18. N S , yB , - yE . , y (). - , , , , - z, . - x, , y, . - . . 1.18 - Kaufmann.
14 W. Kaufmann, Gttingen Nach. 2, 143 (1901).
17
() ()
1.18 () W. Kaufmann. ()
, z, , z,
2
22 ye zy Em = (1.21)
yE ,
2
2 ye zx Bm = (1.22)
yB . , - x y . x y - . (1.21) (1.22), .
22 22y
y
Emy xe B z
= (1.23)
. Kaufmann , . , - . 1.18, ( 0x = , 0y = ) x (- . 1.18, ). ( 0x = , 0y = ) . Kaufmann . 1.19 ( ), - m0 . , -, , - . Kaufmann . M. Abraham (1903) H.A. Lorentz (1904), Kaufmann . Kaufmann .
18
1.19 y ( ) x ( ), Kaufmann ( ).
m0 ( ) 4m0.
Bucherer15, 1909, , Wien (. 1.20). . , , 4 cmb = , 0,25 mm. , yE , V/m. , - , 100 gaussxB = . - 9 cmb s+ = , -. , - . - ,
sin
y
x
EB
= (1.24) . , - , , , y xz. ,
zx
mre B= , (1.25)
z z . , , z . y -, , r , (1.25), e/m . . 1.20 - 0 180, .
15 A.H. Bucherer, Ann. d. Phys. 28, 513 (1909).
19
() ()
1.20 () Bucherer e/m . ()
.
min /y xE B = . . e/m . , -, . e/m . , Lorentz16, 1904
02 21 /
mmc= , (1.26)
. Lorentz 0/m m Kaufmann 1903, - . . 1.21, Kaufmann Bucherer Lorentz. Bucherer / 0,7c = > , . 0/m m 1915 Guye Lavanchy
17. .
0( ) / ( )m m ( )m 0( )m 0 . 2000 , 0,26c = 0,48c = , Lorentz-Einstein [. (1.26)] - 1 2000 ( 0,05%). Guye La-vanchy . 1.21.
16 H.A. Lorentz, Proc. Acad. Sci. Amsterdam 6, 809 (1904). : A. Einstein, H.A. Lor-entz, H. Weyl H. Minkowski, The Principle of Relativity, Dover (1952). 17 C.E. Guye C. Lavanchy, Compt. Rend. 161, 52 (1915).
20
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,00
1
2
3
4
Kaufmann, 1901 Bucherer, 1909 Guye Lavanchy, 1915
m / m0
= / c
1.21 Kaufmann, Bucherer, Guye Lavanchy, .
20 1 ( / )m m c= .
2
2.1 . . .
, - , . - . -, - . -, . , , , , , . ( , , - ), , . , .
1. , , - , . - :
- .
. . : , . , , , . - , , , . . :
ddt
=p FG G
(2.1)
, , , . , : , . . - 1 , , 1632.
22
, , - . -. , . -, ( Coriolis) . -, , , . , -, . , -, . , . 2.2
S ( , , , )x y z t , , . , S , S V=V xG , 0t t= = - . , -. t t = . x , O OO Vt = . x x Vt = y y = , z z = .
2.1 - ( , , , )x y z t - S , ( , , , )x y z t S ,
V=V xG S .
x x Vt = , y y = , z z = , t t = (2.2) . , -, . (2.1), . , . (2.2) dx dx Vdt = , dy dy = , dz dz = , dt dt = , (2.3) :
xdx dx dt dx dtV Vdt dt dt dt dt
= = = , ydy dy dydt dt dt
= = = , zdz dz dzdt dt dt
= = = (2.4) , , x x V = , y y = , z z = . (2.5) , S S VG 0t t= = , :
23
t = r r VGG G , t t = . (2.6) , :
= VGG G . (2.7) , :
=a aG G . (2.8) . (2.1) m=F aG G (2.9) m =F aG G . (2.10) =F FG G , (2.11) . (2.9) . 2.3
- . ( , , , )x y z t . -. . - - . - -:
() ()
, . . , , - . . . , . . : , . 1t , . , Bt , . - , 2t . , , . ,
2 11 2t tt + , Bt .
2 1( )t t . . - . .
24
2.4
: , . - V. , O . , . O , , - , , (. 2.2). . 2.2 V . - O . , , , , . O , (. 2.3): 2.3 O , , , , .
. . , , , .
, (. 2.4), :
. , . , , . - , -. , .
2.4 , , - , . () , - (). , , .
25
, , - , . - .
26
: C.Kittel ..
27
28
29
30
3
3.1
, S S , . S S V=V xG (. 3.1). - , 0t t= = .
() () 3.1 () , S S , . S S V=V x . 0t t= = , . () -. ( , ) ( , , , )t x y z t=r S , ( , ) ( , , , )t x y z t =r S (. 3.1). , P S , ( , , )x y z , - S ( , , )x y z . , ( , , )x y z P S t, /x dx dt= , /y dy dt= , /z dz dt= , S /x dx dt = , /y dy dt = , /z dz dt = . ( , , , ) ( , , , )x y z t x y z t , : , , ,x x t y y z z t x t = + = = = + , (3.1) , , , . , :
() ( , , , ) ( , , , )x y z t x y z t , () S S , y y = z z = .
:
32
() , - . . , ( , , , ) ( , , , )x y z t x y z t ( , , , ) ( , , , )x y z t x y z t , -, 1S - 2S , 2S
3S , 1S 3S . () y y = z z = S S , . - y z . x x . , , x x , - x S , x S . - , (. 3.2), (0, 0, 0) - yz y z . - S S , a. S S V=V xG . , y z , S , , ( 1)ak k < . , , S (. 3.2). S . , - V = V xG ( 1)ak k < . - - . (. 3.2). - . , - y y = z z = . , , - .
3.2 . () , , . () , , S V . () S , , S V . , , .
33
, , . :
() . () c .
. (3.1), :
, , ,dx dx dt dy dy dz dz dt dx dt = + = = = + . (3.2) , ,
, ,dx dx dt dy dy dz dzdt dx dt dt dx dt dt dx dt
+= = = + + + , (3.3)
, ,yx zx y zx x x
+ = = =+ + + . (3.4)
P ,
2 2 2x y z + += 2 2 2x y z + + = , :
( )
( )2 2 2
22
x y z
x
+ + + = +
( )
( )2 2 2 2
22
1 2x x
x
+ + + = + (3.5)
, P S , 0, 0, 0x y z = = = , S x V= =
Gx V x . . (3.4), -
:
0 VV
+= + V = (3.6)
, P S , 0, 0, 0x y z = = = , - S x V = = x V x . . (3.4), - :
V = . (3.7) . (3.6) (3.7) :
V = = . (3.8)
. (3.5),
( )
( )2 2 2 2 2 2
22
1 2x x
x
V V
+ + = + . (3.9)
P c, c . . (3.9)
34
( )
( )2 2 2 2 2 2
22
1 2x x
x
c V Vc
+ + = + . (3.10)
x . x , :
( ) ( ) ( )2 2 2 2 2 2 2 2 2 21 2 0x xc c V c c V + + + + = . (3.11) x , :
( ) ( ) ( )2 2 2 2 2 2 2 2 21 0, 2 0, 0c c V c c V + = + = = . (3.12)
2 2
11 /
V c
=
. (3.13)
, . (3.12)
2
2 2
/1 /V cV c
=
. (3.14)
. (3.13) (3.14) (3.12).
2 2
11 /
V c
=
, 2
2 2
/1 /V cV c
=
, 2 21 /
VV c
=
, 2 2
11 /V c
=
(3.15)
:
2
2 2 2 2
( / ), , ,1 / 1 /x Vt t V c xx y y z z tV c V c = = = =
. (3.16)
0V x x t t , . ( , , , )x y z t ( , , , )x y z t :
2
2 2 2 2
( / ), , ,1 / 1 /x Vt t V c xx y y z z tV c V c = = = =
. (3.17)
S S V
c (3.18)
2 2
11 /V c
(3.19)
: ( ) ( ), , , ( / )x x ct y y z z t t c x = = = = (3.20) ( , , , ) ( , , , )x y z t x y z t S S . (3.20) , , ,x y z t , V V ( ). -:
35
( ) ( ), , , ( / )x x ct y y z z t t c x = + = = = + (3.21) , S S , S V
G S ,
2 2( 1) ,t t tV c = + =
r V r Vr r VG GG GGG G (3.22)
2 2( 1) ,t t tV c = + + = +
r V r Vr r VG GG GGG G (3.23)
( , , )x y z=rG ( , , )x y z =rG . S
2 2 2 2 2 0x y z c t+ + = , (3.24) S 2 2 2 2 2 0x y z c t + + = , (3.25) . (3.21) . (3.22).
3.1
S ( 1 m, 2 m, 2 m, 1 ns)x y z t= = = = . S , S - V=V xG , 45V c= . 0t t= = .
, 2 2 545 3/ , 1 / 1 / V c V c= = = = . 1 m, 2 m, 2 m, 1 nsx y z t= = = = , . (3.20) :
( ) ( )8 95 4 51 (3 10 )(1 10 ) 1 0,24 1,27 m3 5 3
x x ct = = = = 2 m, 2 my y z z = = = =
( ) 9 985 4 1 5 40( / ) 1 10 1 10 2,78 ns3 5 3 153 10t t c x = = = = .
( 1 m, 2 m, 2 m, 1 ns)x y z t= = = = S , ( 1,27 m, 2 m, 2 m, 2,78 ns)x y z t= = = = S . - S ( 1 m, 2 m, 2 m)x y z= = = - 1 nst = ( 1 ns ), S ( 1,27 m, 2 m, 2 m)x y z= = = 2,78 nst = ( 2,78 ns !).
36
3.1 , , 222222 tczyxs ++= Lorentz ( , - 0== tt ). 3.2 , S x ct= ( ), S x ct = . 3.3 S 600 m - 0,8 s. , S , S , ; 3.4 S :
1: ( )0,0/, 110101 ==== zycxtxx . 2: ( )0,02/,2 220202 ==== zycxtxx .
() S, - . S. S S 0== tt . .: 12 =
() S; .: 01 2 3xt tc
= =
3.1.1
; . , - . S , x, 0L . 0L (. 3.3). , S , S V=V xG . S 1x 2x , 0 2 1L x x= . S , t , -, 1x 2x . S 2 1L x x = . -
( )1 1x x Vt = + ( )2 2x x Vt = + . (3.26)
( )2 1 0 2 1x x L x x L = = = . (3.27) 2 20 0/ 1 /L L L V c= = . (3.28) . 1 / . , 0L , . . , . - ,
37
3.3 . , 0L . , 0 /L L = . . S , 1x 2x t . , S ,
1 12Vt t xc
= + 2 22Vt t xc
= + . (3.29)
2 1 2 12 ( )Vt t x xc = 2 1 02Vt t Lc = . (3.30)
S S - , , 2x - 1x . . , , . , -, -.
3.5 99% ; 3.6 V , c, , S.I., 12243 c = . 3.7 S , 2L, - . , S 35V c= S. . 0t t= = . () S;
38
() 0t = S . S , - S.
() , AT BT , S, ( AT BT ) S;
3.1.2
. x S S . 1t 2t , . -, S , 2 1t t = . (3.31) S , .
3.4 , - . - x S .
1t , (). 2t , (). S , , 2 1t t = . , S , S V=V xG , .
, S ,
V=V xG S , - , ,
1 1 2Vt t xc
= 2 2 2Vt t xc
= . (3.32)
, , T, S , 2 1 2 1( )t t t t = T = . (3.33)
39
. , , , - . : .
3.2
0L , V=V x x S . S . S , 0t = , -. . S .
S , 2 0 / 2x L = ( ) 1 0 / 2x L = ( ). 0 0x = . - 0t = . S 0t = , 0 0x = ,
2 0 / 2x L = , 1 0 / 2x L = . 0 /L L = . S . S , S . x S 0t = - S x t . 0t = -,
, ( / )x x t c x = = . , S , , 2 0 / 2x L = , 2 0 / 2x L= 2 0( / ) / 2t c L = , , 0 0x = , 0 0x = 0 0t = , , 1 0 / 2x L = , 1 0 / 2x L= 1 0( / ) / 2t c L = . S , , x , -,
( / )x x cVt c x
= = = .
c, - , . S , - , - , -
40
1 2 0L x x L = = , 0L . , , S . S
20 0 0 0
22
// 11 / 1
L L L L c LTV c c c
= = = = =
.
3.8 , , 7000 kmr = . ;
- , . 3.9 160 000 , - 60 ; 3.10 100 000 . 50 ; ,
29,81 m/sg = , ;
3.2
3.2.1
P , ( , , ) ( , , )x y z x y z , - . (3.4) . (3.15)
( ) ( )2 2 2, ,1 / 1 / 1 /yx zx y zx x x V
V c V c V c = = = . (3.34)
3.2.2
. (3.34):
21
xx
x
VVc
=
2
2
2
11
yy
x
VV cc
=
2
2
2
11
zz
x
VV cc
=
2 2 2 2x y z = + + , 2 2 2 2x y z = + + . (3.35)
41
:
2 22 2 2 2 2 2 2
2 2 2
2
2 22 2 2 2
2 2 2
2
2 2 22 2
2 2 2
2
1 ( ) 1 11
1 2 1 11
1 2 11
x y z x y zx
x x xx
xx
x
V VVc cV
c
V VV Vc cV
c
V VV Vc cV
c
= + + = + + = = + + =
= + + 2 2 2 2 2 2
2 4 2 2 2 2
2
2 1 1 11
x x
x
c V V V Vc c c c cV
c
=
= + + + =
22 2 2
22 2 2 2
2
1 1 11
x
x
c V Vc c cV
c
= =
2 2
2 22 2
2
2
1 11
1 x
Vc c
cVc
=
2 2
2 2
2
2
1 11
1 x
Vc c
cVc
=
(3.36)
( ) ( )2 22 22
2
1
1
x x
x
V V c
Vc
+ =
. (3.37)
, V c< c < , c < . , c = c = . V c= , x c = , 0y = 0z = , - c = . S c . , c > , V c< c > .
, . (3.36)
( )( )( )
2 2
2
1 11
1P
PPx
= , (3.38)
, , ,xP Px PV = c c c c
= = = . (3.39)
42
3.2.3 ,
S . 2 2 21 1 / 1 1P P c = = . S , - , 2 2 21 1 / 1 1P P c = = . V
2 2 2
1 11 / 1V c
= = , P P ; . (3.38) :
2 22 2
2
1 1
1P xPVc
=
(3.40)
, , 21x
P PVc
= . (3.41)
- .
3.11 , , , . , - , c7,0 . - , , - c4,1 . ; .: 0,94x c = 3.12 0,8c - 0,6c . - ; 3.13 , , , . 4D = . (1 = = m1045,9y..1 15=A ). - S S, S - V, . () , V, -
4t = ; .: 2 / 2, 2 = = () , t , ; .: 5,7t = () -
B / 2x c = . ; .: ( )B 2 2 / 3x c =
() B0 48 ml = , , BA , ; .: B 16 ml =
3.14 S xV S. S, cosx c = siny c = . - S S c . x S;
4
4.1
, , ( 1810 eV ). - . -, GeV. , - 0 , + , , . , , Yukawa 1935. 273 em 264 em , em . - , -, , , . ,
/0( )tN t N e = , (4.1)
0N 0t = , ( )N t - t , , , .
8 0 16 8(2,6 10 s), 2 (0,83 10 s), (2,6 10 s) + + + + , . , . 6 10 . - , , , -.
, - . - !
, ,
6( 2,2 10 s)e ee e + + + + + = , () s. - , , , 660 m . 6 10 . , . -. C. Anderson 1938, ( - !) C.F. Powel G.P.S. Occhialini 1947 Yukawa. - , , Yukawa .
44
4.1 . -. . . Rossi 1,43 1624 m. 100 - -. . . .
B. Rossi1 , 40, - , , Denver Echo Evans (. 4.1), 3240 1616 = 1624 m. 520 MeV , 1,43 . , , - . h . 0t = 0N - , , ( )N t , t , z; - , , -:
() , . (4.1),
/0( )tN t N e = .
, , : z h t= . , ( )/0( )
h zN t N e = . (4.2) l = , e 2,718= . , c, , , 62,2 10 s = , 8 63 10 2,2 10 660 ml = = = . Rossi , 0,98 = 5 = , 0,98 660 647 ml = = . , 0z = , / /0 0( )
h h lN t N e N e = = . (4.3) 1 B. Rossi et al., Phys. Rev. 57, 461 (1940), 59, 223 (1941) 61, 675 (1942).
45
10 kmh = , 0,98 = , / 10000/647 15,5 7 60 0 0 0 0( ) e e e 1,94 10 / 5,2 10
h lN t N N N N N = = = = = . (4.4) , 5,2 .
() , ( ) . - . - . - . : (i) - (ii) .
(i)
/0( )tN t N e = .
0t , 0/
0( ) /tN t N e =
. ( 0,98 = 5 = ). , - /h . , -, 0 / /t h h c = = . ,
/0( ) /
h cN t N e = . /
0( ) /h cN t N e = .
, : 0,98 = , 5 = , 62,2 10 s = 10 kmh = . , : / 10 / 5 2 kmh = = : ( )4 8 60 / 10 3 10 0,98 5 6,8 10 st h c = = = ( ) ( )6 60 / 6,8 10 s 2,2 10 s 3,1t h c = = = . :
/ 3,10( ) / 0,0454 1/ 22h cN t N e e = = = =
22 .
(ii)
/0( )tN t N e = .
t , /0( ) /tN t N e = -
. ( 0,98 = 5 = ). , , / /t h h c = = . , ( ). , / /0( ) /
t h cN t N e e = = . , : 0,98 = , 5 = , 62,2 10 s = 10 kmh = .
46
, : ( )4 8 6/ 10 3 10 0,98 34 10 st h c = = = ( ) ( )6 6/ 34 10 s 2,2 10 s 15,5t h c = = = . :
/ 15,5 /5 3,10( ) / 0,0454 1 / 22tN t N e e e = = = = =
22 . , , 520 MeV,
65,2 10 / 22 236 000 = . . 4.1.1 CERN
. CERN 70 Balley2 . CERN 14 m, 0,9994 =
29,3 = . -. . + - E 64,419 0,058 s + = E 64,368 0,029 s = , . - , E / , . - , . - , + 4E / (2 9) 10
+ +
+ = ,
. 29,3 = , .
16 210 m/s , .
4.1 2m c54= , s 10/1 8== ( ), , , e; ; ;
2 J. Bailey, K. Borer, F. Combley, H. Drumm, F. Krienen, F. Lange, E. Picasso, W. von Ruden, F.J.M. Farley,
J.H. Field, W. Flegel P.M. Hattersley, Measurements of relativistic time dilatation for positive and nega-tive muons in a circular orbit. Nature 268, 301-5 (1977).
47
4.2 cV 54= . - 300 m , e ( ...71828,2=e ). /1= ;
4.3 + 8
0 2,8 10 s = . 410 + - 59,4 m 0,99c = . () ; () , ; 4.4 . . ( ) - . ( + ) 25 ns = . , , ( ee + + ) 2 s = . 10 km 0,99 = , - . () - () . 4.5 -. 0,99 c = - . ( ee + + ) 2 s = -. () , 1%
. .: 19 km () , ; .: 2,7 km 4.6 , S,
0 10 mL = . 45 c=V xG
S. , 0x x= = , 0y y= = , 0z z= = , 0t t= = 0N .
1/2 2 s = . S 0 / 2N ;
48
4.2 , 0,
, , - .
4.2 . Sagnac
( -) ; . , , , , ns, . P , , (. 4.2). , 0P , , . , 0P V . P , , +V . , At , 0P
22
0 1 cVtt A = (4.5)
P
22)(1
cVtt A
+= . (4.6)
2
2
2
2
0 1
)(1
cVc
V
tt
+=
. (4.7)
0T 0P , T P ,
2/1
2
22/1
2
2
01)(1
+=
cV
cV
TT . (4.8)
, cV
49
0 02 1 2VT T T T
Vc + (4.11)
V
50
2V = . R . 6378 kmR = , 1670 km/h 464 m/sV = = . - , 340 m/s = , . (4.15) 1 1,37
2V + = 0 283 nsT T T
1 0,6342V + = , 0 131 nsT T T .
, 80 , , - - o180 , , , ! - , :
20 207 1 cos ns2T T T
V + (4.16)
- , - . , - . 4.3 Hafele Keating
, . Hafele Keating, 1971. 4 , 41 , 49 , , -3. - . , , . , h ( ) g,
02( )ghT Tc
= (4.17)
0T . -, ,
202( ) 1 cos2VT T
Vc = + (4.18)
3 J.C. Hafele R.E. Keating, Science, 177, 166 (1972).
51
, 0T , 4
2 02 2 1 cos2gh VT T
Vc c = + (4.19)
. , h . - , , :
00
22 2
0 01 cos
2
TT g VT h dt dtVc c
= + (4.20)
4.1. , , . . , .
4.1 Hafele Keating (1971)
(ns)
(49 h)
(41 h)
( . .) 96 10 184 18 : ( . .) 179 18 144 14
275 21 40 23 273 7 59 10
| -| 2 22 19 25
4 J.C. Hafele, Relativistic Time for Terrestrial Circumnavigations. Am. J. Phys., 40, 81-85, (1971).
52
, , . - , - 5, Pound Rebka6. , 57Fe 15/ 2,46 10f f = 22,5 m. 1% ( / 1,00 0,01)f f = . Hafele Keating, 1975, - 15 240 10 km. - 8 , Sagnac . . 6 - . , 52,8 ns 5,7 ns -. 47,1 ns, 47 ns 1,5 ns. 1976, NASA, Gravity Probe, maser 10 000 km 7. 2 - , , , . , - 4 1010. , 70 (0,007%). , 1977, , 2818 . - . , 8. . .
5 . .. C. Kittel, W.D. Knight, M.A. Ruderman, A.C. Helmholz B.J. Moyer, . ..., 1998. . 431.
6 R.V. Pound G.A. Rebka Jr. "Gravitational Red-Shift in Nuclear Resonance". Phys. Rev. Lett. 3, 439-441, (1959). R.V. Pound G.A. Rebka Jr. "Apparent Weight of Photons". Phys. Rev. Lett. 4, 337-341, (1960).
7 R.F.C. Vessot, M.W. Levine, E.M. Mattison, E.L. Blomberg, T.E. Hoffman, G.U. Nystrom, B.F. Farrel, R. Decher, P.B. Eby, C.R. Baugher, J.W. Watts, D.L. Teuber F.D. Wills. "Test of Relativistic Gravitation with a Space-Borne Hydrogen Maser". Phys. Rev. Lett. 45, 2081-2084, (1980).
8 T. Jones, Splitting the Second. The Story of Atomic Time. Institute of Physics Publishing, Bristol and Philadel-phia, (2000).
53
4.4
, - . -, 6.
4.4 . 0T , O S , V=V xG - O S . , - 2x S . 0T . O S , V=V xG S . O S . O O (. 4.4) .
S , 1 0x = 1 0t = . S , 1 0x = 1 0t = .
S 0T , 2x - .
S , 2 0x = 2 0t = . , O , 2 0t T= . , 2 2 0x Vt VT= = .
2 /t x c = O . - , O ,
02 0 0 01(1 )1
VTT t t T T Tc
= + = + = + = + (4.21)
O ,
011
f f += . (4.22)
. - , , - .
54
4.7 4,4 ( ) 13,68 y . , 396,8 nm ,
0,029 nm . ( ) -.
4.5
- , .
() Bradley, cG V
G ,
- cG VG - , - 2 2c V+ -
arctan arctanVc
= = (4.23) - .
() -. y S . , S
0, , 0x y zc = = = . (4.24) S , : , / , 0x y zV c = = = . (4.25) , , S c. S y
4.5 .
4.6 .
55
arctan arctanxy
= = (4.26)
.
2tan
1 = = , sin =
arcsin = . (4.27) (4.23) Ktan = ,
3 5
K arctan ...3 5 = = + (4.28)
(4.27) sin = ,
3 5
1 3arcsin ...
2 3 2 4 5 = = + + + (4.29)
31 K 2 = . (4.30) , 30 km/sV = , 410 = 3 13 71 K 2 5 10 rad (10 ) = = = . (4.31)
2 9 K 12
5 10 = = . (4.32)
. 4.6
2.4 : - O V. , O . , . O O , , , , (. 4.7). . O O S S , O O , , .
0t t= = . S O , (. 4.8): 4.7 V . O . , , , , - .
56
4.8 O , - , - , , . 0L 0 / 2L O , 0 / 2L c O . 0x = 0t = , - :
: 0A 2Lx = , 0A 2
Ltc
= . (4.33)
: 0B 2Lx = , 0B 2
Ltc
= . (4.34) S O , , - S S .
: ( ) 0 0 0A A A 12 2 2 1L L Lx x ct
= + = = + , (4.35)
( ) 0 0 0A A A 1( / ) 2 2 2 1L L Lt t c xc c c
= + = + = + . (4.36)
: ( ) 0 0 0B B B 12 2 2 1L L Lx x ct
+ = + = = , (4.37)
( ) 0 0 0B B B 1( / ) 2 2 2 1L L Lt t c xc c c
+ = + = = . (4.38)
A Ax t c= B Bx t c= , . . 4.9 . , , O 0 /L L = . (. 4.9), O
0A A
12 1Ld x
= = + , 0 / 2L . 4.9 , , - , . () , - (). , , .
57
(. 4.9), O 0B1
2 1BLL d x
+ = = , 0 / 2L . , -
O 0 0 02
1 2 1 12 1 2 1 2 11
BL L Ld L
+ + = = = + .
A Bd d= .
0 0 0 0B A 21 1 /
2 1 2 1 1L L L c Lt t tc c c
+ = = + = = +
,
O . 4.7
. , - (. 4.10). O , - S , O , S , V (. 4.10). O , , O . O , , O . O . - O , S , O , S , - V . O , , O . O , , O . . ; - . O O - , O O S . O O S .
4.10 . () O , S , O , S , V . O , , - O . O , , O . () O , S , O , S , V . O , , O - . O , , O .
58
. ; O O O V , O . O O , ; , - ! ; . O , O , V V , . . . . O O . , , . O ; . O , V . . , , . ; -9. 2( / )V c -. O V O , 0t t= = . O - / 2t V O / 2l V t= . , O a T .
2V O , 2 /T V a= . T t , O , t , O , t t = , . O . O . a , l , T -, , , 2/alT c . / 2l V t= 2 /T V a= , 2 2( / )V c t t = . O , , 212(1 )t t t = + . O , 212(1 )t t t = + .
2 2 21 12 2(1 ) (1 )t t t t + = . , ,
2 2 11 12 2(1 ) (1 ) + , O O 212(1 )t t = + . . . - . - , Langevin10.
9 C. Moller, The Theory of Relativity, Clarendon Press, Oxford, 2nd ed. 1972. 8.17, . 293. 10 P. Langevin, "Lvolution de lespace et du temps". Scientia 10 31-54 (1911).
59
: C.Kittel ..
60
61
5
, Lorentz , . , , - , . , . - . . Tolman1 . , , . , , . 5.1 .
, Tolman, , ( )m m = , -:
,
, m=p G G )(m : S V x S. S, xu u= G , , , , (. 5.1).
5.1 , , .
1 R.C. Tolman, Relativity, Thermodynamics and Cosmology. Oxford, 1934. 23.
63
S, : 1m , xu 11 u=G , 2m xu 22 u=G , m V x . - : )( 111 umm = , )( 222 umm = , )(Vmm = . :
: mmm =+ 21 (5.1) : mVumum =+ 2211 (5.2) S S:
21 /1 cVuVuu +
+= 22 /1 cVuVuu
+= . (5.3)
. (5.1) (5.2) 1
2
2
1
uVVu
mm
= , (5.4)
, . (5.3)
22
2
1
/1/1cVucVu
mm
+= (5.5)
. (5.3) (5.4) , ,
22222
221 /1
/1/1/1cVu
cVcucu += 2
222222
2 /1/1/1/1
cVucVcucu
= (5.6)
[ Lorentz , 1 2 , S S . (3.41):
( )21 1 1 /u V c = + ( )22 2 1 /u V c = . (5.7)] . (5.7), (5.6) :
221
222
2
1
/1
/1
cu
cumm
= (5.8)
2 2 2 21 1 2 21 / 1 /m u c m u c = . (5.9) 2 2( ) 1 /m c . , 0m . ,
22
0
/1)(
c
mm
= , (5.10)
. )(lim00
mm = , - 0m . ,
0)( mm = . (5.11) :
22 /1
1
c
=
.
64
S:
0m u
2 2
11 /u c
= .
:
0 0 0m u m u = (5.12) :
02M m = (5.13) , , , 02m ,
0 02 2 ( 1)m M m m = = (5.14) . : u , 0 ( 1)m .
S, Lorentz . S ( )21 1 /u V c = + ( )22 1 /u V c = .
21 /1 cVuVuu +
+=
22 /1 cVuVuu
+= .
:
1 2 0 1 0 2 0 0 02 22 1 1 0u V u Vm m m m M m m m m mc c
= = = + = (5.15) :
0 1 1 0 2 2
0 0 02 2
2 2
2 1 11 1
xp M V m u m uu V u V u V u Vm V m mu V u Vc c
c c
= + + = + +
( )0 2 0xp m V u V u V = + = . (5.16) . , , , m=p G G , 0( )m m m = = . -, .
...............................
65
, ( )M 0M . 5.2. , c, c = .
5.2 , -
() 0.
5.3 , p. - 0. p .
0 02 2( ) 1 /MM M
c = = , (5.17)
0M ,
0 02 21 /MM M
c= = =
p GG G G . (5.18)
, . 0p M c= . (5.19) - . . , , 0M . - .
66
5.2
ddt
= pFGG
(5.20)
. - . - , . (5.18),
02 21 /
d Mdt c =
FGG
. (5.21)
t, G , pG FG . dW F
G
drG dW d F rG G . (5.22) F
G x
0M . dW . ,
02 21 /
d MW F dx dxdt c
= = . (5.23)
( ) ( )d d ddx dxdt d dt
=
d dxdx d ddt dt = = , ( ) ( )d ddx d
dt d = .
( ) ( )
( )
2 2
0 0 1/2 3/22 2 2 2 2 2
20
0 3/2 2 22 2
1 /1 / 1 / 1 /
1 /1 /
d cW M d M dd c c c
M cM d acc
= = + = = +
(5.24)
a . - , 0W = 0 = . , 200 M c a= + 20a M c= . (5.25)
, 2
2 200 02 2
( 1)1 /
M cW M c M cc
= = . (5.26)
W . - :
2
2 200 02 2
( 1)1 /
M cK M c M cc
= = . (5.27)
2
2 2002 21 /
M cE Mc K M cc = = + (5.28)
67
5.4 , - , - - 0. = 12 0
2.
:
1. 20M c , 0 = : 20 0(0)E E M c = , 2. .
. 0 = , 20 0(0)E E M c= = , .
20 0( )E E K M c K = + = + . (5.29) , , ( )+( ), - ( )+( ) .
2 20E Mc M c= = . (5.30) . 5.4 . - 21 02K M = .
2
11
= , 2 2 2 1 = . 2 40M c ,
2 2 4 2 2 2 4 2 40 0 0M c M c M c = . (5.31) 20E M c= 0p M c= , 2 2 2 2 40E p c M c = . (5.32) 2 40M c , . , 2 2 2E p c .
68
5.5 2 2 4 2 20E M c p c= + .
2 2 4 2 20E M c p c= + (5.33) , . , 2 20 0E M c= , xp c , yp c zp c . . 5.5 (EMp!) (5.33).
2 4 2 20E M c p c= + . (5.34) , 2E Mc= M=p G G ,
2Ec
=p G G . (5.35) 5.3
c 0 1 . -
2
22 2
1 1121 / cc = + . (5.36)
, , ,
2 2
2 2 2 200 0 0 022 2
1 1( 1)2 21 /
M cK M c M c M c Mcc = = = (5.37)
.
2
2 2 2 2 20 0 0 02
1 112 2
E Mc M c M c M c Mc = = + = + . (5.38)
!
2 , 20M c E , xp c , yp c
zp c , 2 4 2 2 2 2 2 2 2 2 2 20 x y zM c E p c p c p c E p c= = .
69
5.1
,
2 200K d Mc M c= = F sG G .
:
20 0 00 0
( ) ( ) ( ) ( )d M dxK F dx dx d M M d dM M d dMdt dt
= = = = + = + 0
2 21 /MM
c=
2 2 2 2 2 20M c M M c = . , 2 2 22 2 2 0Mc dM M d M dM = 2 2M d dM c dM + = , 2 2 2 00 ( )K c dM c M c M
= = .
5.1 - 2010 eV (16 J!) [. J. Linsey, Phys. Rev. Lett. 10, 146 (1963)]. , 1 GeV , . , , , 510 ; - ; 5.2 2 MeV; ; 5.3 . () , , 2400 ml =
s 10=t , , t . m/s 103 8=c . .: s6 =t
() , -16 s 10= , - ( ) ; (: 203 e ). .: 400/1
() 0m , GeV 32
0 =cm , -. .: 2=K GeV
() pc , p , p c/GeV . .: cp /GeV 4= 5.4 , , 2GeV/ 1 cM = , , , x , -
70
. , cx 6,0A = cx 6,0B = .
() ; () ;
5.4
. , . , , - . , -, . 0 0M = , , . (5.34)
E pc= . (5.39) , :
/p E c= . (5.40)
, [. (5.35)], 2Epc= , . (5.39),
c = . 0 0M 2
02 21 /
M cEc= -
c . . ,
hcE hf = = , (5.41) h Planck ( 346,62 10 J sh = ). ,
hf hpc = = . (5.42)
5.5 m E 500 nm;
5.5
. 2E mc= , -
1
. n
ii
m=
= (5.43) :
71
1
. n
ii
E=
= (5.44) ,
1
. n
ii=
=pG , (5.45) -. n , -
=
n
iixx pP
1 , ,
=
n
iiyy pP
1 , ,
=
n
iizz pP
1 , ,
=
n
iiEE
1 (5.46)
S, S. , S, n - , , :
( ) ( ) , , xx PP = ( ) ( ) , , yy PP = ( ) ( ) , , zz PP = ( ) ( ) EE = (5.47)
, , . (, .).
5.6 . : 1m cV 531 = , 2m cV 542 = . () 1m 2m . () 1K 2K , ; 5.7 , , + .
22 2 2
( )2cE m m mm
= + , m , m m . ; - 0m = ; 5.8 1m ( )GeV 121 =cm c8,01 = - 2m ( )GeV 1022 =cm . , M . : () , GeV. .: 11,67 GeV () , cGeV/ . .: 4/3 cGeV/
() M , 2GeV/c . .: 11,59 2GeV/c
5.9 K+ , KM ( 2K 494 MeVM c = ), - . . M (
2 140 MeVM c = ). -
K+ ;
72
.: K 872 MeVE = , 732 MeVE = 5.10 m -
. . .: 2 2
2
2M mE c
M= ,
2 22
2M mE c
M+=
5.11 cV 53= .
: 1m - 2m c54= . 1m 2m . 5.12 . X 0m . , -
; .: 2 2
20 0
02m mE c
m
+= , 2 2
20 0
02m mE c
m
=
5.13 . E . .
; .: 2 1
22
Mc EE E
Mc E+ = +
5.14 : () , . () -. ( -
.) () ,
.
5.6
S 0M =p G G 2
0E M c= , 2 21
1 / c = Lorentz
( V !). ,
0 0 0 02, , , .x y zdx dy dz Ep M p M p M Mdt dt dt c
= = = = (5.48) , , /d dt = . , , : 0 0 0 02, , , .x y z
dx dy dz E dtp M p M p M Md d d c d = = = = (5.49)
S , 0 0 0 02, , , .x y z
dx dy dz E dtp M p M p M Md d d c d = = = = (5.50)
d , , ,x y zp p p
2/E c - x, y, z t, . , Lorentz x, y, z t S S ( ) ( ), , , ( / )dx dx cdt dy dy dz dz dt dt c dx = = = = (5.51)
73
2 2
11 /V c
=
Lorentz
( V ). 01M
d , S S ,
0 0 0 0 0 0 0
0 0 0
, , ,
( / )
dx dx dt dy dy dz dzM M cM M M M Md d d d d d ddt dt dxM M c Md d d
= = = =
(5.52)
. (5.49) (5.50),
( ), , ,x x y y z z xp p E p p p p E E c pc = = = = (5.53)
, , , ,x y zp p p 2/E c
x, y, z t, . -: ,
=cEpp xx
, xp E ( S), xp S . , . , .
5.2 Doppler
V x S. , , S - 0E ( 0 0 /f E h= ,
cEp /00 = , ). xy A, S. - , x, E ( /f E h= , cEp /= ) , S. () , S, E . () ,
:
2
0
11 cos
f Vf c
= = + .
() o o0, 90 , 180 = . () 0f f= ; ;
() /p E c= . , S, - :
74
cos sin 0x y zE Ep p pc c
= = = . () S x
cosxEpc
= . , , S, :
0 ( ) [ ( / ) cos ]xE E E p c E E c c = = = +
0 (1 cos )E E = + . ,
2
0 0
11 cos
E fE f
= = + ,
Vc
= .
Doppler. ()
0, cos 1 = = , 0
11
ff
= +
( Doppler ).
o90 , cos 0 = = , 20
1ff
=
( Doppler).
o180 , cos 1 = = , 0
11
ff
+=
( Doppler ).
() 0f f= 201 cos 1 + =
( )2 o o0 01cos 1 1 , (90 180 ) = < < . 1 , 2 2121 1 10 2cos .
. :
1. ( Doppler),
2. .
0 = .
0 o90 o180 1 :
75
: 0 0,1 0,5 0,9 0,99 0,999 1 0 : o90 o92,9 o105,5 o128,8 o150,2 o163 o180
5.15 2 4 2 2 2 2 2 2 2 2 2 20 x y zM c E p c p c p c E p c= = S S . 5.16 S, M , -. S / 2M . : () . () ,
(i) , E , (ii) , E .
5.7
2E Mc= - . . , . , , , . , . , , - - , - . () -. , , 511 keV , : e e 2 ++ . , . , - 2e2 1,022 MeVm c = , - . () (-). ,
2e2 1,022 MeVm c = , -.
, , . 2e2 1,022 MeVm c = - . , . - .
76
, . , . . , m E , -,
2cmE = . (5.54)
5.17 1 kg 8 kg 810 J -. 1 710 ;
5.8
ddt
= pFGG
(5.55)
, M=p G G . , . ,
02 21 /
d Mdt c =
FGG
. (5.56)
t, G , pG FG . -, , , . -: - - . dW F
G -
drG dW d= F rG G (5.57) ()
dW ddt dt
= = rF F GG G G . (5.58)
0M , G pG -
S , G pG S , S V x . x S
xxdpFdt = . (5.59)
-,
x xp p Ec = (5.60)
77
Vc
= 2
11
= .
x xdF p Edt c
= . (5.61)
, 2Vt t xc
= ,
2 21xdt d V Vt x
dt dt c c = = (5.62)
, d dt ddt dt dt
= ,
22
1
11x x x x
xx
d d dEF p E p E FVVdt c dt c c dtcc
= = =
. (5.63)
x x y y z zdE dW F F Fdt dt
= = = + +F G G , (5.64)
( ) ( )2 2 2 21 / 1 /y zx x y zx xV VF F F F
c V c c V c = . (5.65)
y ,
y yp p = (5.66)
y y yy ydp dp dpdt dtF Fdt dt dt dt dt = = = = (5.67)
. (5.62)
( )2 2
22
1 /1 /1 /
yy y
xx
F V cF FV cV c = = (5.68)
, z zp p = ,
( )2 2
22
1 /1 /1 /
zz z
xx
F V cF FV cV c = = . (5.69)
:
2 2
2 2
/ /1 / 1 /
y zx x y z
x x
V c V cF F F FV c V c =
(5.70)
( )2 2
22
1 /1 /1 /
yy y
xx
F V cF FV cV c = = ( )
2 2
22
1 /1 /1 /
zz z
xx
F V cF FV cV c = = .
( V V , G G F FG G ) :
2 2
2 2
/ /1 / 1 /
y zx x y z
x x
V c V cF F F FV c V c = + + + +
78
(5.71)
( )2 2
22
1 /1 /1 /
yy y
xx
F V cF FV cV c
= = ++ ( )2 2
22
1 /1 /1 /
zz z
xx
F V cF FV cV c
= = ++ .
, Lorentz , -:
( ) 2 222 111 /1 / V ccc = + + + +
F V V F FFV V
G G G G GGG GG GG (5.72)
- . ( 0 =G ),
x xF F = yyF
F = zz FF
= . (5.73)
6
6.1
, , (A.H. Compton) - 1. , , , , - -. . 6.1.
6.1 .
, - , . . . - , Bragg (CRYSTAL ). Bragg - ( ) . , . , , . , . 6.2. . 6.2 o45 = , o90 o135 . , - . ( )
1 A.H. Compton, Bulletin Nat. Res. Council, No.20, 16 (1922) Physical Review, 21, 715 22, 409 (1922).
80
6.2 . o6 30 . . . - 0 o0 =
o180 = . - -
. - . . - . . 6.3. , f, /E hf hc = = , h . , , / / /p E c hf c h = = = . E hf = /p hf c = . - , E hf = /p hf c = . -, , 2eE mc= , m . -, - . c , ep mc = 2eE mc = .
6.3 () . . () .
81
: : 2 2mc hf mc hf + = + (6.1) : cos coshf hf mc
c c = + (6.2)
: 0 sin sinhf mcc
= (6.3) , = , . - . E hf = E hf = , . n n (. 6.2),
Ec
=p nG Ec
=p nG .
, pG . - :
: 2mc E E E + = + (6.4)
: E Ec c = +n n p (6.5)
( ) 2E E mc E + = (6.6) E E c =n n p (6.7) , , :
( ) ( ) ( )22 2 2 22E E E E mc mc E + + = (6.8) 2 2 2 22 cosE E E E c p + = , (6.9) cos =n n . ( )22 2 2 2E mc c p= + . (6.8), : ( ) ( )2 2 2 22E E E E mc c p + = (6.10) 2 2 2 22 cosE E E E c p + = . (6.11) , ( ) ( ) 22 1 cos 2 0E E E E mc = . (6.12) 22E E mc ,
( )21 1 1 1 cosE E mc = . (6.13) /E hc = /E hc = ,
( )1 coshmc
= = . (6.13)
82
. , 122,4 10 mh
mc= . (6.14)
133,86 10 mmc
= = (6.15) / 2h= , Compton .
6.1 E , 0m . , . : () E , () .
6.2
, - , -. , - . , - . . 6.4, :
A , (), - , .
C (), , C .
D -. , .
B , - .
,
C11
= + , (6.16)
/ c = . , ,
C2(1 cos)h h
mc mc = = . (6.17)
400 700 nm,
122 4,8 10 m 0,005 nmhmc
= = . (6.18)
83
6.4 . , .
, C2hmc
< 11
+
50,005 / 500 10= 91 10 20000 . - 2 4(2 10 )(0,5 MeV) 10 GeVE mc= = = . - 10 GeV,
C2hmc
, 2h
mc . (6.19)
,
11 2
1 2h
mc
= + , (6.20)
1 .
2 2
2 2 2 11
mc mcE mc = = = . (6.21)
. (6.20) 1 ,
2 2
2 12 2
h mc h mc hcmc mc E EE
= = . (6.22)
hf E . (6.23) () .
84
6.3
, XAZ , . , ( ) . ( ) , - XAZ . pm ,
nm Xm XAZ ,
p n X( )m Zm A Z m m = + . (6.24) , - , H n X( )M Zm A Z m M = + (6.25) Hm XM X
AZ .
2c . (B.E., binding energy) XAZ :
[ ]2 2H n X. . ( )B E M c Zm A Z m M c= = + . (6.26) , . , . - . - . , . , (6.26), H n( )Zm A Z m+ XAZ , . - . , , - , -. ,
2. .B E M c
A A= . (6.27)
. 6.5 , . , 5626 Fe . , . :
85
6.5 ( MeV/), .
() -4, 42 He , , . - 2, 3, 4 , - 84 Be ,
126C
168O .
() = 56 , (- ) ( ).
, u. - 126C 12 u. mol 126C 12 g - 23 1A 6,022 142 10 molN
= , 271 u 1,660 539 10 kg= . (6.28) 2E mc= u, 101 u 1,492 418 10 J 931,494 0 MeV = . (6.29) , . .
86
6.1 ,
(u)
(kg)
(MeV)
(MeV/)
1 u 1 271,660 539 10 931,494
e 0,000 548 6 319,109 382 10 0,511 p 1,007 276 271,672 622 10 938,272 n 1,008 665 271,674 927 10 939,565 4,001 506 276,644 656 10 3727,379 7,074
11H 1,007 825 271,673533 10 938,783
21H (D) 2,014 102 1876,124 1,112 31H (T) 3,016 049 2809,432 2,827
42 He 4,002 603 3728,401 7,074 12
6C 12,000 000 11 177,93 7,680 16
8O 15,994 915 14 899,17 7,976 5626 Fe 55,934 939 52 103,06 8,790 5828 Ni 57,935 347 53 966,43 8,732
20882 Pb 207,976 64 193 729,0 7,867 23592 U 235,043 925 218 942,0 7,591
23892 U 238,050 786 27395,292 61 10 221 742,9 7,570
6.4
A(a,b)B A a B b Q+ + + . a, b.
2Q M c= (. ).
Q (MeV)
Q (MeV)
2 3H(n,) H 6,26+ 7 7Li(p,n) Be 1,65 6 4Li(d,) e 22,17+ 9 8Be(,n) Be 1,67 9 6Be(p,) Li 2,25+ 14 17N(,p) 1,15 10 11B(d,n) C 6,38+ 18 18O(p,n) F 2,45 14 15N(n,) N 10,83+
28 31Si(,p) P 2,25
87
6.1
(d) (D), (H), - . .
p n d E+ + E Q = . p n d 0,002 388 uM m m m = + = , 4,4 -. - : 2 2 2p n dm c m c m c E+ = + : 2p 1,007 276 u 938,272 MeV /m c= = 2n 1,008 665 u 939,565 MeV /m c= = , 2p n 1877,837 MeV /m m c+ = , 2d 2,013 553 u 1875,613 MeV /m c= = 2 2,224 MeVE M c = = 1,112 MeV/.
, , .
5% , ( p n ,
, / 2xx p = , ). , - . 2% , (pp) . 1H 2 H -. -! (. C.P.W. Davies, The Accidental Universe, C.U.P. : , , 1995.)
6.2
23592 U , , 14156 Ba ,
9236 Kr
3 . .
235 1 141 92 192 0 56 36 0U n Ba Kr 3 n Q+ + + + .
88
23592 U 7,6 MeV/, 14156 Ba
9236 Kr 8,5 MeV/. ,
Q = ( , ) ( ) Q = 235 (8,5 7,6) = 220 MeV .
6.3 .
: (1) 1 1 21 1 1 ep p d e 0,420 MeV++ + + + (2) 2 1 3 21 1 2d p He 5,493 MeV+ + + (3) 3 2 3 2 4 2 12 2 2 1He He He 2 p 12,860 MeV
+ + + , 2 (1), 2 (2) (3) ;
:
2 (1) 1 1 21 1 12 p 2 p 2 d+ e2e 2 0,840 MeV++ + + 2 (2) 212 d 112 p+ 3 222 He 2 10,986 MeV+ + 1 (3) 3 222 He 4 2 12 1He 2 p + 12,860 MeV+
: 1 4 21 2 e4 p He 2e 2 2 24,686 MeV + + + + +
, 2 , 2 2 , 24,7 MeV . - , , . ( ) ( )1 4 21 2 e4 p He 4 0,0265 um m m m = + = 2 25 MeVm c =
6.2 . , - . . 6.3 . 898 s 15 = ( 1/2 622 s 10 = ) en p e E + + + . .
: C. Kittel .., , . 391 393.
89
6.4 -235. 6 MeVE = 235 90 142 192 36 56 0U Kr Ba 3 n+ + + . ; u: ( )23592 U 235,043915M = , ( )9036 Kr 89,91972M = ,
( )14256 Ba 141,91635M = , 1,008665nm = . 6.5
() . - . . . , - , , .
.
( )1 2, ,..., ,...,i Np p p pG G G G S , , S , VG , ( )1 2( ), ( ),..., ( ),..., ( )i N p V p V p V p VG G G GG G G G - : ( ) 0i
N
=p VGG . VG . , - , , , .., . - .
6.4
E , - . () . () V
, 2p
EVc E M c
= + , pM -.
() ;
(Kittel .., , 12, 9).
90
() E
pc
= () ( ), V c= , V ,
21 cVVx
xx
= 0x = , pp 21
M cp
=
.
11
E E
= + Doppler, E
pc
= .
, . pp p = .
, pE
pc = p
2
11 1
E M cc
=+
p(1 )E
M cc =
pE E
M cc c = + 2p
EE M c
= +
.
() 2
p2
p
11 2
M cE E E E
E M c
= =
91
6.7 , e+ , m , , e , m . - , - -, 1 2 , ( -), - (. 1). k
G, 1PG
2PG
-, , 1 2 1P
G 2P
G
kG
(. 2). () 1 2=P P
G G 1 2 = .
() 1 2 = + 1PG
2PG
m.
6.6
- . -, . , -, . . Coulomb . , - , . . ,
( )12 1 13 13C N* Np + + 13 N 12C . Coulomb 12C . , - 12C 13 N ( 13 N* ). - . Coulomb, - . ,
0p p + + - 0 , - 0 , 135 MeV. , . -
92
144,7 MeV 0 - p 0 . - 0 . . , - . . , . - , , . . .
6.8 . , ( m), (
mM 3= ), + = + . - ; : . .: 27mcEK = 6.9 p n ++ + - . .: 21
2 p
mE m cm
= +
6.7
6.7.1
q , xE , . -
02 21 /
Mc= pGG , (6.30)
0M G , , -
0 2 21 /dM qdt c
= E . (6.31)
x, , , (0) 0 = (0) 0x = . ,
0 2 21 /M q t
c = E, (6.32)
: C. Kittel .., , . 415-418.
93
( )( )2
02 22
0
/
1 /
q t M cc
q t M c = +
EE
(6.33)
( )0
20
/
1 /
q t M
q t M c =
+EE
. (6.34)
, c . . 6.6. c . - . (6.34)
( )201 /c
M c q t =
+ E (6.35)
: 012M c cq t
E . (6.36) 6.6 , q 0M ,
- E . - -
.
. (6.35) 2
2 20
1 11 /
q tM cc
= = +
E . (6.37)
, ,
( ) ( )2 22 20 0E M c M c q ct= = + E . (6.38) 2 2 2 20E M c p c= + p q t= E, (6.39) qE t. . (6.35)
22
20
0
1M c q tx t kq M c
= + + E
E (6.40)
94
k . 0t = 0x = ,
2
0M ckq
=E
22
20
0
1 1M c q tx tq M c
= + E
E. (6.41)
6.7.2
q 0M x 0p , , L, -, yE (. 6.7).
6.7 q 0M x 0p , , L, , yE .
:
0, yxdpdp q
dt dt= = E , (6.42)
0 ,x yp p p q t= = E, (6.43) (. . 6.8). :
() ()
6.8 . () .
() x y.
95
( ) ( )2 22 2 4 2 2 2 4 2 2 20 0 0 0E M c p c M c p c q ct E q ct= + = + + = +E E , (6.44) 0E . 2
Ec
=p G G ,
( ) ( )2 2
02 22 2
0 0
,x yp c q c t
E q ct E q ct = =
+ +E
E E. (6.45)
y , , x (. . 6.8). x y - :
( )2
10 022 00 0
sinht
p c dt p c q ctxq EE q ct
= =+
EEE
(6.46)
( ) ( ) ( )22 2
22 200222 0 00 0
1 1t
tq c tdt q c E q cy E q ct tq Eq cE q ct
= = + = + +
E E EEEEE
. (6.47)
Lt L x . (6.46) x L= , 0
0
sinhLE q Ltq c p c
= EE
. (6.48)
x . (6.45),
0
tan ( ) yx
qt tp
= =E . (6.49)
L x,
00 0
tan sinhLE q Lp c p c
= E . (6.50)
96
: C.Kittel ..
97
98
99
100
101
102
7
7.1
- . , - , - . - Maxwell, 19 , 1862. Maxwell, :
0 0 00
, 0, , .t t
= = = = + G GG G G G GB EE B E B J (7.1)
Coulomb Gauss . ( E
G) ,
.
, - , - .
Faraday, - .
, - , .
, , 0 = , , 0=JG :
0 00 0 t t = = = =
B EE B E BG GG G G G
(7.2)
EG
2 2 2 2
2 2 2 2 21
x y z c t + + = G G G GE E E E
22
2 21c t
= GG EE , (7.3)
BG
2 2 2 2
2 2 2 2 21
x y z c t + + = G G G GB B B B
22
2 21c t
= GG BB . (7.4)
0 0
1 299 792 458 m/sc = = . (7.5)
EG
BG
, . , .
104
, , , , . , , , , , . , , :
, , ,x x Vt y y z z t t = = = = . (7.6) Maxwell . , , - ,
2 2 2
2 22 2 2 2
1 1 2V Vx tc t c x
= + E E EEG G GG
. (7.7)
, , - ! Michelson Morley, 1887, - . Michelson Morley . . . Lorentz , - S : ( , , , )x y z t - S : ( , , , )x y z t , V=V xG S, - Maxwell . Lorentz :
1. ( 2 ).
2. , . 3. -
. 4. Maxwell -
. (1) (2) . - . Narliker1 - - . Lorentz , , :
( )tVxx = yy = zz =
= xcVtt 2 . (7.8)
3 Maxwell, . , , . - . , , . Lorentz q q= + F E BG G GG - ,
1 V.V. Narliker, Proc. Camb. Phil. Soc., 28, 460 (1932).
105
. - E
G B
G Maxwell.
7.2
, 2. . - . , - /137c . , . , , . 1960, J.G. King3 - 2010 . , King - . q E
G
BG
, Lorentz, q q= + F E BG G GG . B
G.
0M q EG
BG
, ,
02 21 /
d M q qdt c = +
E BG G GG . (7.9)
. -, Maxwell -, . 7.3