Κ. ΧΡΙΣΤΟΔΟΥΛΙΔΗΣ - Η ΕΙΔΙΚΗ ΘΕΩΡΙΑ ΤΗΣ ΣΧΕΤΙΚΟΤΗΤΑΣ...

.

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 ..

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 ..

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 ..

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

Κ. ΧΡΙΣΤΟΔΟΥΛΙΔΗΣ - Η ΕΙΔΙΚΗ ΘΕΩΡΙΑ ΤΗΣ ΣΧΕΤΙΚΟΤΗΤΑΣ...

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Transcript of Κ. ΧΡΙΣΤΟΔΟΥΛΙΔΗΣ - Η ΕΙΔΙΚΗ ΘΕΩΡΙΑ ΤΗΣ ΣΧΕΤΙΚΟΤΗΤΑΣ...