Документ взят из кэша поисковой машины. Адрес оригинального документа : http://temporology.bio.msu.ru/RREPORTS/oleinik_izmenenie.pdf Дата изменения: Fri Feb 28 02:00:31 2014 Дата индексирования: Fri Feb 28 02:51:47 2014 Кодировка: Поисковые слова: m 63

..
Department of General and Theoretical Physics, National Technical University of Ukraine "Kiev Polytechnic Institute", Prospect Pobedy 37, Kiev, 03056, Ukraine; e-mail: yuri@arepjev.relc.com , , 2, .20-37, 2001. . , , . , ( ). , . - , . . ,

- .
Oleinik V.P. The change of the course of time in a force field and imponderability. Abstract. It is shown that the force in relativistic mechanics is not only the cause of acceleration of particle relative to an inertial frame of reference, but also the cause of change of the course of time along the particle's trajectory. Therein lies the physical content of the dynamical principle underlying the special theory of relativity (relativistic mechanics). The general formula for the relative course of time between the points lying on the trajectory of motion of particle under the action of a force field in an inertial reference frame is derived. The applications of the theory developed to homogeneous fields - to the field of gravity and electromagnetic field, and to the gravitational field produced by a point mass particle are considered. Physical properties of the state of imponderability of particle in an external force field are investigated. It is noted that the change in the course of time in a force field is in

no way connected with the change in space-time metric and is a direct consequence of the causality principle of relativistic mechanics. 1. , , . , , - , , . , , [1-4]. . , , , , , . . , : ", - ". ,


2 , , , . , , , , , , . : , , ? , , . , . , - 4- -. , "" . , ; . , . , , , , , , , . , , , . , 4- - () , , .. , , [5-8]. , , -. . 4- . ( ), t t + 0 . . , , , , . .. [9]. , , () , , . , [9-13], , ,


3 , , . . [12] . . [13] . . [14]. [6-8], - . : . , : , , . , . K K , . , , , , , x, y, z K x, y, z K , x x K V0 K x . dl A A K dt A , dl K A . dt dt A ­ dt A A [6]: V u (t ) (1) dt = 1 - 0 x2 A dt A , A c V2 = 1 - 02 , u x (t ) - x - u( t ) K c t . dt A A dt A K K . (1), x - ( u x ( t ) const ), dt ( A const ). , dt A , .. ( u( t ) = const ), dt A : = const . , dt A , , , , .
-1 2


4 (1), , dt dt A , A A . , , , , . , , . A B , , , (1): V u (t ) dt B = 1 - 0 x2 B dt B . c (1) , V0 u x (t B ) 1 - dt A c2 dt . A (2) = dt B V0 u x (t A ) dt B 1 - c2 dt dt A A A B dt B dt B K K , . (2), dt A dt = A , .. A B u x ( t A ) = u x ( t B ) , dt B dt B K K . , . (2), dt A dt B dt = dt B , A B . A , dl = dl B , , , dl A dl B , .. , A K , , K . A B , , . : ? , , , ? , . , , , , , , . K , , ~ K , , . , ~ K , .. ( ) [15,16]. , , ,


5

~ ( ). K , A B , ~ K , K K , A B K . , , , . , (1) , , . , , [5-8]. , , . . , () , " -, " ([4], .26). , () . , , , , . , , , 4 . , , , , , . , . . V dx = 1 + 0 dx , (3) u (t ) x x x K K . , (3) , . , (3) dx , K , dx , K , t . , , ( ) . (3) : , , , , ( ). , , , :


6

dx = u x dt = ( u + V0 ) dt , dx = u dt . x x
V dx = 1 + 0 dx . u x (3). : dx = u x (t ) dt , dx = u (t )dt . x , , (3). , , (.. ) . , : , . , . 2 , . , . ­ 3. , - . : , . 4 . . 5 , . , , , . . 2. m ! F = F ( r , r , t) , K , !! (4) mr = F , r = r( t ) - - t , ~ K , K . r0 = r0 ( t ) r = r ( t ) -, K ~ ~ K , - K . r r (5) r = r + r0 ( t ) . ~ , K K . ,


7

~ , K K , . (5) : !!! !! !! !! (6) r = r + r0 ( t ) r = r + r0 ( t ) . ~ (5) (6) (4), K : ~ !! (7) mr = F , ~ !! (8) F = F ( r + r0 (t), r + r0 (t), t) - m !!0 (t ) . r !! ! , F in , F in = - m r0 (t ) , r r , ~ K , t . , F in . ~ F , (7), r ! ! ! r , r r r0 ( t ) r0 ( t ) , , : !! (9) F (r + r0 (t), r + r0 (t), t) = F 0 + F1 , ! F 0 = F (r0 (t), r0 (t), t) F 0 (t ),
! ! ! F1 = ( r a + r b )F ( a , b, t) F1 (r , r , t) a = r0 (t), b = r0 (t) . , !! (10) m r0 ( t ) = F 0 ( t ) . (9) (10) (7) : !! m r = F1 .(11) ! F1 , F1 = 0 r = 0, r = 0 . , , ~ K , : ! r = 0, r = 0 F . F , [15,16]. ( ) , F . ~ , K , . , , , (.. : ~ ! F 0 ), K F ( r , r , t) ! r = 0 r = 0 (. (9)-(11)). -, , ~ K , , , ~ K . ~ , K , , , ! : F ( r , r , t) F , , f , ( f = const ) ,


8 . (4), F f + F , ~ K , (. (7) (8)): ~ !! (12) mr = f + F . - ( P ), ~ (13) F << f , ~ F (12) f !! m r = f , ~ K f , . , ~ P K . , P , ~ (14) F = 0, ~ , K , , (13). , , , .. (14), -, . . , . , , , ~ -, F f . , ~ (12), F , ! . , (12) r0 r0 , - . . dp =F, (15) dt u2 2 p = m u, m = m0 1 - 2 , c ! u = r , r = r( t ) , m0 - . (15) d (16) mc2 = uF , dt (15) , [4]:
-1

du u( uF ) u 2 2 1 - . = F - m0 dt c 2 c 2

1

(17)


9 [4], , . - . ~ K , (5) (6) : ! ! ! u = r, u = r , u0 = r0 ( t ) . (6) (17) , 2 uu0 u0 << u0 , << 1 - 2 , (18) u c2 c (17) r u . , ~ K :

du dp u = - 0 - F 0 1 - m0 dt dt c

2 0 2



1

2

+
1 2

2 u ( u0 F ) u( u0 F 0 ) u0 ( uF 0 ) u 0 1 - + F1 - 0 2 1 - - 2 c c2 c2 c

-

(19)

u ( u0 F ) uu - F 0 - 0 2 0 2 c c

0

u 1 - c

2 0 2



-1

2

.
-1

u2 2 (9) : p0 = m0 u0 1 - 0 . c2 ( t ) r0 dp0 = F0 . (20) dt (19) r = 0, u = 0 , , ~ , , K , . r 0, u 0 , . r = 0, u = 0 , , : . K , t , x, y, z , - 2 22 2 2 2 ds = c dt - dx - dy - dz . , t , . ~ K t . d dl ~ K - ds 2 = c 2 dt 2 - dr 2 ~ K , (6), , . :

ds 2 = c 2 dt 2 - (dr + u0 dt
,

)

2

u0 dr 2 - (dr )2 - u0 dr . = c 2 - u 0 dt - 2 c2 - u2 c 2 - u0 0

2

2


10

ds 2 = c 2 (d ) - (dl ) , :
2 2

(dl ) = (dr ) + u20dr 2 . (21) c -u 0 ~ , K , , , , .. . , , , , . A B - , K , t A t B . d A d B - ~ , K , dt A dt B , K A B (, t A t B dt A dt B A B ). (21) , dr = 0 , d A = d B

u 0dr 12 , d = c - u 02 dt - c c c 2 - u 02

2

2

2

2 2 u0 ( t A ) u0 ( t B ) 1- dt A = 1 - dt B . c2 c2 A B K : 2 c 2 - u0 ( t B ) dt A = . (22) 2 dt B c 2 - u0 ( t A ) , r = 0, u = 0 , (6) u0 (t) = u , .. u0 (t) - t K . , dt A dt B (22) , A B . : , , . A B , (22): K c 2 - u02 ( t B ) dt A , (23) = dt A c 2 - u02 ( t ) B

u0 (t ) - t K . (22) (23) (2) , u x ( t ) = u 0 x ( t ) , V 0u 0 x (t B ) 1 - 2 2 c - u (t B ) c2 c - u 0 (t B ) , = c 2 - u (t A ) V 0u 0 x (t A ) c 2 - u 0 2 (t A ) 1 - 2 c
2 2 0 2 0

(24)


11 . , (24) , (. [4], .61) V2 1 - 02 u 02 u 2 c 1 - 2 , 1 - 02 = 2 c V 0u 0 x c 1 - 2 c u 0 u 0 - K K , . (24) . (22) : (t ) U (t 0 ) - U (t A ) 1 + kin A 1+ 2 dt A m 0c m 0c 2 = = , (25) kin (t B ) U (t 0 ) - U (t B ) dt B 1+ 1+ m 0c 2 m 0c 2 kin (t ) U (t ) - t , , kin (t 0 ) = 0 . (22), , u - 0 . c , : dt A 1 ( kin (t A ) - kin (t B ) ) = 1 - 1 2 (U (t A ) - U (t B )) . = 1+ (26) 2 dt B m 0c m 0c 3. () F = const . F 0 = F , F1 = 0 (. (9)) , (10) (11), K F (27) a0 = , m ~ K , F . (11) F1 = 0 , r = a + bt ( a b - ), , , ~ K , . , m F ~ K , (27). . , , . , , .
2


12 , (20), p0 = 0 t = 0 : p0 = F t . u 0 = a 0 t 1 +
2 a 0t , a0 = F . (28) m0 c : 2 c2 1 + a 0 t - 1 , r = r (0) . (29) r0 (t ) = r0 + a 0 2 0 0 a0 c (20) F1 = 0 , (19) : 2 -1

1 du = - 2 [u(u0 F ) + u0 (uF m0 dt c

2 u0 )]1 - 2 c 2 0 2 -1 2

1

2

- (30)

u (u F ) uu u - F - 0 20 2 0 1 - . c c c (30) (11) , . (30) , , u0 (.(28)). (30), - . , ~ , K , - r , u . , ~ , K . , u 0 , . , , : (31) r ( 0 ) = r0 0, u( 0 ) = u0 0 . (28) (29), (5) (6) : (32) r( 0 ) = r0 + r0 , u( 0 ) = u0 . (15), (32), :
- 2 2 u 02 2 p(t ) p(t ) 1 + . (33) p(t ) = F t + m0 u0 1 - 2 , u(t ) = m0 m0 c c (5),(6),(28) (33), : (34) u(t ) = u(t ) - u0 (t ) 0 t . , (15) (. (16)): 1 -1

u 2 (t ) 2 m0 c 1 - 2 - Fr (t ) = const . c (32):
2

-1

(35)


13 u 2 m0 c 1 - 02 c ,
2

2 - F (r0 + r0 ) = C1 = const . (34), (35) (36) :
-1

-1

(36)

u 2 (t ) 2 m0 c 2 1 - 0 2 - F (r (t ) + r0 (t ) ) = C1 t . c r0 ( t ) (20), (. (35)) u 2 (t ) 2 m0 c 2 1 - 0 2 - Fr0 (t ) = C 2 = const . c , F r ( t ) = C 2 - C1 0 t . (37) t = 0 (36), : -1 u02 2 C 2 - C1 = m0 c 2 1 - 1 - 2 + F r0 . c (38) ,
2 -1

(37) (38)

-1 2 2 u0 (t ) - r0 ) = m0 c 1 - 1 - 2 0 t . F (r c , r ( t ) = const , r ( t ) r0 t . , r ( 0 ) 0 , u( 0 ) 0 : r ( t ) = const , u( t ) = 0 t , : , , ( , , r ( ) r ( 0 ) ). , : - , (17) r u . A B , K , (22), (28):

a t 1+ 0 A dt A c. = (39) 2 dt B a 0t B 1+ c : 2 dt A a0 2 2 = 1 + 2 (t A - t B ) . (40) dt B 2c (39), t B > t A , dt B > dt A , .. : .

2


14 F = m0 g , g = const . , g = -ge z , e z - , z , F : " (41) F = -m 0 , = gz + const . (28) (29), a 0 = g , gt . (29) << 1 c K : 1 z = z0 - gt 2 , z0 = const .(42) 2 (39) - (42), . (21) ( dr = 0 ), gt << 1 . (28), (41) (42), : c 1 gt 2 u 2 (t ) (43) d = 1 - 2 dt = 1 - dt = 1 + 2 dt . 2 c c c (41) : = 0 t = 0 . A B , d A = d B , (40), a 0 = g . 4. B = const . e F 0 F1 (.(9)) : e e F0 = [u0 B ], F1 = [uB ] . c c (10) (11) !! (44) r0 = [ u0 ] , !! (45) r = [ u] , eB . (44) (45), = - mc ~ K , , K , . , ~ K (45) (44). (45) , (46) r = r0 + u t r0 = const, uII = const, u II II . , u 2 = const , , u 0 0 (u 0 ) , , .


15

~ K (19) (45) ~ . K . (20) 2 u0 = const . (22) dt A = dt B , .. K ( ). E B , , B z . e F 0 F1 (.(9)) e e (47) F 0 = eE + [u0 B ], F1 = [uB ] c c ~ K (45). , , , (46) . (10), F 0 (47), : eE e [ E ] , (48) u 0 (t ) = [ r 0 (t )] + II t + u 0 II + m m 2 r 0 (t ) = a (sin(t + 0 ), cos(t + 0 ), 0 ), E = E II + E , eB , mc a , 0 u 0 z - . : 2 2 2 eE z m u 0 (t ) m e kin (t ) = = r 0 (t ) + (49) t + u 0z . E + 2 2 m m (26), kin (t ) (49), . ( E z = 0 ) : dt A e = 1+ E (r 0 (t A ) - r 0 (t B ) ), ( m 0 = m ). dt B mc 2 , E B z . (20), F 0 (47), [17]: p 0 x = p 0 cos (t ), (50) p 0 y = - p 0 sin (t ), ~ p 0 z = eEt + p 0 z , p = const , ~ = const , = (t ) p E II = (0,0, E z ), E , u
0 II

= (0,0, u 0 z ), =

0

oz

d = 0 (t ), 0 (t ) dt

=

eB 2 , m = m0 mc (22),

p + . (51) c (50) (51)

2


16

u 1- c : dt dt

2
2

p2 = 1 + (m c 0 1+

)2

.
0z

-1

p p

2 0

~ + (eEt A + p +

A B

= 1+

2 0

(m0 c )2 (eEt B + (m0 c )2

)2 )2
. (52) =~ p

~ p

0z

(52) , ( E = 0 ) dt A = dt B , p eE (39), a 0 = . m0 5.

0

0z

=0

m , M , K . (4), r (53) F =- 3 , r = GmM , G - . (5), ~ K K , (4) , ~ K : (r + r 0 (t ) ) ~ ! ! - mr!0 (t ) F (r , t ) . (54) mr! = - 3 r + r 0 (t ) ~ , , K , , ~ (55) F ( 0, t ) = 0 , , r0 ( t ) : ! mr!0 (t ) = - r 0 (t ) . r 03 (t ) (56)

t ) r , . : 3 r (t )( r r (t ) ) r - 0 2 0 F1 (r ,t ) . (57) ) r 0 (t ) ~ (57), , K , . r 0 F1 ( r ,t ) , - . , (58) r0 ( t ) = r0 ( t )n ,
0 < r0 ( t ) < , n = const , n = 1 . n , ~ K ,

~ F ( r , r << r0 (t ) , ! mr! = - 3 r 0 (t


17 M . (56) : !0 (59) mr! (t ) = - 2 . r 0 (t ) ~ K . (57) t r0 ( t ) , ( r0 ( t ) = r0 ). ~ K , , e1 , e 2 , e 3 ,

e 3 = n , [e 3 e1 ] = e 2 , [e1e 2 ] = e 3 . (57) : (60) r = e1 A + e 2 A2 + e 3 A3 , 1 An = An ( t ) ( n = 1, 2,3 ) - , : 2 !! !! !! (61) mA1 = - 3 A1 , mA2 = - 3 A2 , mA3 = 3 A3 . r0 r0 r0 (61) :
2 An = An 0 cos(1t + n ), n = 1, 2, 1 = mr 3 , 0
1 1

(62)

2 , 2 = mr 3 , 0 An 0 , n (n = 1, 2), A3 A3 - . (62), , , .. , A3 = 0 , ~ K r = 0 t 0 : e 3 r = 0 , e1 e 2 1 . , F1 ( r ,t ) , ~ K (. (57) (58)) , ~ n , K . ~ , K , K (.. ), . , , , . ~ K , n , (54), r0 ( t ) ~ ~ ~ (59). K , K n ~ K . (x, y, z) r (x, y, z) r r = r + a + bt , a = a n , b = bn , a ,b = const . (54) r r a + bt + r 0 (t ) = r 0(t ) , A3 = A3 e
- 2t

+ A3e

2t

2


18 : (r + r 0(t )n ) ! !0 - m r!(t )n . m r! = - 3 r + r 0 (t )n r0 ( t ) !0 m r!(t ) = -

(63)

. (64) r 0 2 (t ) (63) (64) (54) (59), . , , , . (59), , , ( U (t ) - ): mu 02 (t ) + U (t ) E = const , U (t ) = - . (65) 2 r 0 (t ) r0 ( t ) (59) (65), :
2 du 0 (t ) 1 mu 0 (t ) =- -E . m 2 dt (66) u 0 ( t ) = u 0 = const t = 0 , (66) : 2

(66) (67)

m 2 2E (68) x - m dx = - 4 t . u0 , t = 0 , : u 0 = 0 . (65) (69) r 0 (0) = - r 0 , E < 0 . E 2 mu 0 (t ) << E (68) 2 m2 x . : 2E m3 E2 . u 0 (t ) - u 0 (t ) + # = -t 3E m : 1 u 0 (t ) = g 0t + g 1t 3 + #, r 0 (t ) = r 0 + g 0t 2 + #, 2 . (70) 2 , g1 = - . g0 = - 3m 2 r 05 mr 02 d , ~ K , (21) ( dr = 0 ). kin (t ) + U (t ) = U (0) , :

u 0 (t )

-2


19
2 u 0 (t ) 1 1 . 1- 2 = 1+ - (71) 2 c mc r 0 (0) r 0 (t ) 1 1 (t ) = r (0) - r (t ) , m 0 0 , (43): (t ) (72) d = 1 + 2 dt . c (72) A B : dt A 1 1 1 . = 1 - 2 ((t A ) - (t B ) ) = 1 + - (73) 2 dt B c mc r 0 (t A ) r 0 (t B ) r0 ( t ) (

, (70), u 0 (t ) ), (72) (73) , K . , . , (70) r0 ( t ) - r0 ( 0 ) << r0 ( 0 ) (t ) (t ) = - g 02t 2 2 (73) (40), a 0 g 0 . 6. . , .. . , , · , · , · . [5-8] , , , . , , , . . : , . , , , , , .. , .


20 [17,18] , (). [17] (. .303), . " , -"([17], .313), , , , , 4- . , , -. , (22) (25), . , -. , . , . , : , . , ( ), , (. ), . .. [19]. -, , (, ) [16]. .. .


1. .. (, ., 1970). 2. Prigogine I. From Being to Becoming: Time and Complexity in the Physical Sciences (W. H. Freeman & Co., San Francisco, 1980). 3. Prigogine I. and Stengers I. Order Out of Chaos (Bantam Books, New York, 1983). 4. .. : . .: , 1987. 5. .. : , , , , 4, 3-17 (2000). 6. Oleinik V.P., Borimsky Ju.C., Arepjev Ju.D. New Ideas in Electrodynamics: Physical Properties of Time. Semiconductor Physics, Quantum Electronics & Optoelectronics, 3, 4, 558-565 (2000). E-print: quant-ph/0010027. 7. Oleinik V.P. Superluminal Signals, Physical Properties of Time, and Principle of Self-Organization, Physics of Consciousness and Life, Cosmology and Astrophysics, 1, 68-76, (2001); .., .. , , 6, (2001) ( ). 8. Oleinik V.P. The Problem of Electron and Superluminal Signals. (Contemporary Fundamental Physics) (Nova Science Publishers, Inc., Huntington, New York, 2001).


21
9. Kozyrev N.A., Selected Transactions (Leningrad University Press, Leningrad, 1991) (in Russian). 10. Lavrent'ev M.M., Eganova I.A., Medvedev V.G., Olejnik V.K., and Fominykh S.F. On Scanning of Celestial Sphere by Kozyrev's Sensor, Doklady AN SSSR, 323(4), 649-652 (1992) (in Russian). 11. .., .., .., .., .. .. . - , . -92-5, 1992. - 16 . 12. Eganova I.A. The World of Events Reality: Instantaneous Action as a Connection of Events through Time, Instantaneous Action-at-a-Distance in Modern Physics (Nova Science Publishers, Inc., New York, 1999). 13. Lavrent'ev M.M. and Eganova I.A. Physical Phenomena Predicted and Revealed by N.A.Kozyrev, in the Light of Adequacy of Space-Time to Physical Reality, Phylosophy of Science, 1(3), 34-43 (1997) (in Russian). 14. Jefimenko O.D. Electromagnetic Retardation and Theory of Relativity (Electret Scientific Company, Star City, 1997). 15. .. (, ., 1967). 16. .. . (, ., 1979). 17. .., .. (, ., 1973). 18. . (, ., 1983). 19. .. , .1 2. , 1(7), 79-84 (2000); 1(9), 99-109 (2001).