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.. C.E. Dolby and S.F.Gull. On radar time and the twin "paradox". Am. J. Phys. 69 (12), December, 2001. Carl E. Dolbya) and Stephen F. Gullb) Astrophysics Group, Cavendish Laboratory, Madingley Road, Cambridge 0CB3 HE, United Kingdom ( k) . , "" , "" " ". , ( ) . © 2001 . [DOI: 10.1119/1.1407254] , , . , , "" . , " " , - ( ) , " ". 1-4. , " " (, ), , 5, 6. , " " , . 1,2,3,6 . 1. 1 3 , G H , 1 , " E , , N, , !" 3,2, , , , - ( ), " (sweep round)" EG FH, . 2. G H, ( 7,8), . , , , ,


! , , , , !

. 1. " " - .

. 2. " ", " (sweep round)" EG FH .

9 ,9 "k-". " " ( Pauri et al. 10 " -"). . , 1 '2 "k-", " " ( ) . -. " " (, , " ") , , -. -, "" , "" , " ". ( "" " " Pauri et al. 10) , , , . , , , , . 1 2. , , , " " " , ".


, : xµ = x (. 3). : +(x) ( ) , (, ), x, ; ( ) , ( ), x; Ѕ [+(x) + Ѕ [+(x) ­
­ ­ µ ( )

( ) c



­

(x)

(x) (x)
0

(x) ] ­ " "; (x) ] ­ " ";



{x: (x) = 0} = " " 0

. 3. " " (). k-11,1,2 , t -- t ­ = t+ -- t 9 ( , tB -- tA = t'A -- t B). , , , () . , , . " " -. , , " ". (. 7 12, .. 144 145, ); , , " " (


), , . , " " -. , . , " ", .. . - "" ,



.s = tanh() ­ ( c = 1), ­ " ," (u,v) u x + t v = x -- t. . 4.

. 4. - "" .

. 5. - "" .

(u0, v0) u0 v0.


(Region) I: u0 > 0 v0 > 0. , +(u0, v0) u0 = u(+) = e + [ u(+) = e + . 4 , +> 0]. ­ (u0, v0) v0 = v( ­) = - e ­ [ ­ < 0]. , :

(Region) F: u0 > 0 v0 < 0. , (u0, v0) , . 4. (u0,v0) , , , , ­ > 0, u( ­) = - e ­ ( ). , :

(u0, v0) ( , , (2) (Regions) I P

F), + ­ F. , :

" 0", t (t, x) = 0 , :

0

(x),

0 . 5. , F, s, , ; P, -s, , . I II, , ( ­) (+). ( ). , , , " '' (. 1 2).


, , . a c= la.

s = tanh(c). :

, u = exp(±c) v = exp(±c). :




. 6. . 7. - . "" . . 6. , "" "" ( c). I II , F P c, , . , 7,2 .2. c , .




:

, U ,

(Rindler coordinates) U. , - P II, F II . 4 , " ". , , . , " ", " ", (, ) . 8. ds2 = e2(d2 -- d2). , a. g, . (, , , .) , , .. . , , . t, , . 8. (, ) U . 7, t, F P, . 8. "" . . 9 (, ).


, x= ± t , "" . . . . , , " - - " ( ), " - - " ( ), .

. 8. . 9. , , (, ) " (, ) "" ". . , " " , - " ". - , . , ( "" " "), . , . , , , , , . , ­ .


. 10. 10 (: , . 10) , . 5. , , , , ­ , , 1 - s 2 .

. 10. - , . . k-, , . a) Electronic mail: c.dolby@mrao.cam.ac.uk b) Electronic mail: steve@mrao.cam.ac.uk
1 2

D. Bohm, The Special Theory of Relativity (W. A. Benjamin, New York,1965). R. D'Inverno, Introducing Einstein's Relativity (Oxford U.P., Oxford, 1992). 3 L. Sartori, Understanding Relativity: A Simplified Approach to Einstein s Theories (University of California Press, Berkeley, 1996). 4 W. Pauli, Theory of Relativity (Pergamon, New York, 1958). 5 W. G. Unruh. "Parallax distance, time, and the twin 'paradox,' " Am. J.Phys. 49 (6), 5S9-592, (1981). 6 T.A. Debs and M. L. G. Redhead, "The twin 'paradox' and the conventionality of simultaneity," Am. J. Phys. 64 (4), 384-392 (1995). 7 L. Marder, Time and the Space-Traveller (George Allen & Unwin Ltd., London, 1971). 8 C.W. Misner, K. S. Thome, and J. A. Wheeler, Gravitation (Freeman, SanFrancisco, 1973). 9 A. Einstein. "On the Electrodynamics of Moving Bodies," Ann. Phys. (Leipzig) 17, 891-921, (1905). 10 M. Pauri and M. Vallisncri, "Marzke-Wheeler Coordinates for Accelerated Observers in Special Relativity," Found. Phys. Lett. 13 (5), 401-425,(2000). 11 H. Bondi, Assumption and Myth in Phvsical Theory (Cambridge U.P., Cambridge, 1967). 12 P. C. W. Davics, About Time (Orion, London, 1995).