Special Relativity(in greek)

35
ΔΙΟΡΘΩΣΕΙΣ ΣΤΗΝ ΕΙΔΙΚΗ ΘΕΩΡΙΑ ΤΗΣ ΣΧΕΤΙΚΟΤΗΤΑΣ To ςύμοαμ είμαι μη μεσπήςιμξ, ξμξιόμξπφξ χωπίρ όπια, αμαγεμμάσαι και ενελλείςεσαι διημεκώρ, ερ αεί και αδιάλειοσα, ςε χώπξ και χπόμξ. Ν.ΜΑΝΤΖΑΚΟΥΡΑΣ e-mail:[email protected]

description

ΔΙΟΡΘΩΣΕΙΣ ΣΤΗΝ ΘΕΩΡΙΑ ΤΗΣ ΣΧΕΤΙΚΟΤΗΤΑΣ

Transcript of Special Relativity(in greek)

To , , , , . . e-mail:[email protected] , . , 7 :1. , . 2. .3. . 4. 5. 2mc E = . 6. 7. . . . . . 2 : 1. 1. .2. 2. . ,Lorenntz. , , .2, . 1. u, - . . ,1 To , - :

cdt2' = A(1) , s d.H t u s A = A(2) 2l - :2 2)2(t ud lA+ = (3). c. l s t A (t ) : ct udclt2 2)2( 22'A+= = A (4) A (4) : 2 2) ( 1'uttA= A(5) -To 2 . - ' ' , - , ' '. . . - . . - , , ' ' , , , .

2 ,2 . .

clt02' = A ( 6) 0l . , 1 1t u l d A + =

(7) 2 2t u l d A = (8) , , 2 1d d +l . . 2 21 1t c t u lt c t u lA = A +A = A (9) 2 1t t t A + A = A (10)

) / 1 (22 2c u clu clu clt=++= A (11) (5) ) / 1 (/ 2) ( 1/ ' 22 22 2c uc luc lt== A (12)?? . .. 221 'cul l =(13) ?? (l) o (l) . " ". , . , . .

o o 2 :1 , u, o d ' t A t , x. O

CDCD Au x B ,3 .3 , =2=2L. 2 2)2(t uD AOA+ = 2 / ' , , 2 / t c D t u AB t c AO A = A = A =

M :

') ( 1'2 2tutt A =A= A (5) . , . =u/c :

| c||1 2 / ' 22 /= =AA= =ut u t ABD L D : t c L t c D A = A = '& L= , D :

221cuDL D L= =

:

| D Dcut u AB = = A = ) 2 / ' ( 2 / , :

1222=ucDAB . 1222=ucDAB 2/u2>1 u 2 . c uuc7071 . 0221 122= > < 3 . c uuc7071 . 0221 122= = = AB/2 D, /2=D. 2 , u . . d , d, x.

| 1 |2|A BCu L 2 x1,x2 :2 21 1t u xt u xA =A =

, : 2 21 1''t c t u Lt c t u LA = A +A = A : ) / 1 (/ ' 2) / 1 (' 2 ' '2 2 2 2 2 1c uc Lc u cLu c Lu c Lt t t==++= A + A = A : ) / 1 (/ ' 22 2c uc Lt= A , cLt' 2' = A

) / 1 ( ') / 1 ('2 22 2c u t tc u tt A = A A= A ) 2 ( '/ 1) / 2 ( '/ 1/ ' 2) / 1 (1) ' 2 ( ) (22 2 2 2 2 2 22 1 2 1| Lc uc u Lc uc L uc u ccL u t t u x x x ==== A + A = + = L ( , 2L (L=)) 22 2 222 1 2 11' 2 ' 2' 'cuLu cc Lt c t c x x L== A + A = + =t L=d+d : ) 2 ( '/ 1'222 2tLc uLL == L 22 22 21) / 1 ( 'ttLc u L L = = 2 , 2 u. 1. c u |DucDABDcuDLtutt====A =A= A12 /1') ( 1'22222 2 2. c u // 22 222 222 2' 2/ 1' 22 2) / 1 ( '') / 1 ('tLc uLLL Lc u Ltc u tt=== =A = A= A t . x,L u/c : 1 .-L x.

c u c uucc u x LiootouotoA =.... 4142 . 0.... 4142 . 02) / 1 ( / '2 2 2 . -x L. c u c uc u cuL xuotoiootoE =.... 4142 . 0.... 4142 . 0) / 1 (1 2' /2 2 t,t, L,L , , .

1. // xx c u B xx . , , .

.4 , =2=2L =D. , /u, / / . t,t . ( )...

' t c D OKt u AKt c AOA = =A =A = c u : ... ' // , xx u c u 12 /1, ') ( 1'22222 2== A =A= AucDABcuDL tutt 2. // xx c u , xx u, c u , . 00 .5 a) ( )...

'212t c D OKt c AOt AKA = =A =A = 2+2=2 : 0 ' 12' 1 1'41222222222 2 2 2 4 2> A .A = A A = A + Atctt t c t c t ... 2222' ' 0 ' 1cDccDtctt s s = A . s A > A . b) B(K )... - , ,0u 0 ') (41' )21(2 222 20 320 4222 2 2 2 2 20= A + A+ A A A = A + A At tcc utcutct c t c t t u 4 t t AK u 20 = 3. u xx 0 090 | = Zc u , , u , xx , , 0' | = Zxx u .

00 6 u xx a) 0( )... OE t1 1t c OEt u At AxA =A = EA = O 2 2 2AO EO AE = + :

2 2 21222t tt u t c t cx A + A = A (1)u

xx 0 090 | = Zc u , | | sin , cos = = u u u uy x , 6. b) B( )... , t ,B t2, : 2t c Bt u Ot BxA = EA = EA = O 6 , 2 2 2B = BE + E O O :

2 2 22222k x kt u t c t c A + A = A (2) D : 2 21 1t c t u Dt c t u DyyA = A A = A + .. yyu cDtu cDt+= A= A21(3) k tt t tolA + A = A {1,2,3} : )1(2)2( ) (2 22 222 22 2 2 2yxyxy yxolu cu cD cu ccDu ccu cDu cDu cct==++= A T ...)sin 11(cos 1/ 2222222||cucuc Dtol= A (4) 2 ,,, 22221/ 22 / )1/ 20 )cu c Dtcuc Dtiolol= A== A=t | ii| (.): 1. . // xx c ux ,c u y 2 x,y , : X uCttC 2 , t t x-y : 2 202 20) ( 1/ 2,) ( 1/ 2uc ltuc lty x= ' A= A 2. u xx 0 090 | = Zc u i) 2 x,y ux , uy - t //c, ux io t' c, ux io down up xt t t' c, u + = :

222022201) /( 2,1) /( 2uu c ltuu c ltyxdownyxup+= A= A :

= A= A= A22202202222201) /( 2' ,) 1 (/ 2,) 1 (11/ 2uu c ltcu c ltcuuc ltyxy xysum ii) A ux , uy t //c, uy io

t' c, uy io o , : ...

= A= A= A22202202222201) /( 2' ,) 1 (/ 2,) 1 (11/ 2uu c ltcu c ltcuuc ltxyx yxsum X- C uY -CuXuYut tY -uCYutX- C uX ut ..u Y=F(x) .7

uXuYuXuYSADO . 7 S, dydydxSD}+ =02) ( 1 .7 - ) () (xkxu cDSctu cDSct+= A= At , )1(2)2( ) (2 222 2x x x xolu c S D cu ccDScu cDu cDSct==++= A 22 2022) / ( 11) cos( , ) tan( ), cos()1() ( 12dx dydxdyu uu cdydydxD ctxx Dol+= = =+= A}| | | 4. // xx c u // , // (A) u . , d= t1 , d=ct2. L=d+d, , . | d1 |d2|A BCu L 2 x1,x2 :1 022 2 0 221 12121tt t xt x u u=+ ==

, : 1 0222 2 012121'21'tct t t Lct t L u u== = + L ( , 2L (L=)) 2 1' ct ct d d L + = + = : . . u . 2 . 2 : i) .. 1.Y u , .. 2 2) ( 1/ ' 2uc lt= A . 2. .. ) / 1 (/ 22 2c uc lt= A l0 , : 2 202 22 20) ( 1) / 1 (/ 2) ( 12ul lc uc luc lt = == A3. u xx, x ) 1 (11/ 2222220cuuc ltyxsum= A . , xx ux//c ... ) 1 (11) 1 (/ 2) 1 (11/ 222 222022222220cu ul lcuc lcuuc ltyxx yxsum = == A :) sin( ), cos() 1 (11) 1 (/ 2) 1 (11/ 222 222022222220| | = = = == Au u u ucu ul lcuc lcuuc lty xxyy xy . , . . - 1. . , 1 ) 1 ( 1 ) , (22222< =cuuu fxy| ... 0 0 038 322 218 142 < < . < < | |2 . , ... 1 ) 1 ( 1 ) , (22222> =cuuu fxy| ... 0 0 0 0322 218 38 142 < < . < < | | . ( /) ) 1 (1/ 1/ 1) 1 (/ 2) 1 (11/ 2022220cu c uc ul lcuc lcuuc lty xxx yx+ = == A 1. . o , 1) 1 (1/ 1/ 1) , ( +=cu c uc uu fy xx| ... 0 0225 45 < < | ) sin( ), cos( ........) 1 (11/ 2222220| | = == Au u u ucuuc lty xxy 1. . o , 1 ) 1 ( 122222< cuuxy u/c + =cuuu fxy| ... 0 0 0 0360 270 360 90 < < . < < | | 2. ( ) ... 1 ) 1 ( 1 ) , (222< + =cuuu fxy| ... 0 0270 90 < < |

2mc E = , , . , . . dx F W = } 3 / 222)( 1a m= F } } = = du u m dx (du/dt) m W 21/22223/222c m)( 1c m)( 1du u mK = = =}u012W . , . ... dxLx1cxu .......d c m /L x21c 2mdxLx1Lx1 c x cm 2 du u m 2 WLx1 c ucu1xL222 2 2 20L22220L2 1 1 2 2222= = == = = = =} } - 2c m =sumW u , u L. xx ) 1 (1122 222cu uL xxy = u, u=F(x). mathematica : Reduce[(1-y^2*a^2)^2==x/L*(1-y^2*b^2),y],) sin( ), cos( | | = = b a y=u/c. 0 , 0 = = b a y=u/c y x, ... mathematica M =/2 2c m W = =/6 24 c m W = , , u. - V=dxdydz , x, V, V=dxdydz .. dydz. .) (.) .. 2 20 0 0) ( 1 ' ' ' ' ' ' 'uL L L L L dydzL dydzL ct V mVm = = = = = = = ... 2 20 2 20) ( 1' ) ( 1 'uu= = . , , . nm = ,n= , m . .) u//c 2 20/ 12'c uLL= , 2 20) ( 1'u= , , . 1 : ., 1/2220)u(1mm= , , , c u m . 2: 2 20) ( 1'u= ,c u , . . . .. , , , 2 d dP = , dP . c , d . -, , . . :0 / = + c c u div t Lorentz , .. (1) u . O '(x', ', ') O (x, y, z) xx. , (2) (1,2) .. (3) 1,2,3 ...

, , , . , , , . dr dt dr0 dt0 , . - . , , . ..(4) dr0 dt0 , . dt0 dr0 . , . . (4) . . , , (4): (dr / dt) (dr0/ dt0) () (c0). , , , . , , . / (..) . . =E(x, y, z, t), : E Ert = ( , )r x y z = + + ( )/ 2 2 2 1 2 :cccccccc222222 2221ExEyEz uEt+ + = ( x r = sin cos ,y r = sin sin ,z r = cos ) : 222 222 2 2221sin1sinsin1 1EEuErEr rErr r cc=cc+|.|

\|cccc+|.|

\|cccc| u uuu u E(r,,,t)=E(r,t). ccE ccE : 222221 1tEu rErr r cc=|.|

\|cccc ' , ( )222 22222 22222 221) (1 1 1 2tEru rrEtEu rrEr tEu rEr rEcccccccccccccc= = = + r t :cccc22 2221( ) ( ) rEr urEt= : rE f r ut g r ut E r tf r utrg r utr= + =+( ) ( ) ( , )( ) ( ) g r utr( ) + . ( /) . . Maxwell. :E r tf r utr( , )( )=. r. r=0 y(r) . r=0. E uV = u : . dtdE udV uAdr = = : dEdtu Adrdtu A = = : . i. (22) 1 2 : dEdtdEdtu A u A u u uA A|\

|.|= |\

|.| = == =1 21 1 1 2 2 2 1 21 2 1 2 = , u Eo2 : Eo o = ' () . ii. : u A u A u r u r ur,A r ,A ru Eo1 1 1 2 2 24 41 122 2221 2 1 122 2224 41 = = = = = Ero 1 Y . .2 .. 1. . 2./, . uAdr uV E = = u :,: ,dr: ... u uAdtdruAdtdEuAdr uV E = = = =

= 2 .. 222 2 121 1 2 2 2 1 1 1 2 14 4 / / u t u t u u r u r u A u A u dt d dt dE = = E =(1) 31322 1 232 2 131 1/34,34rru u u r E u r E = = = t t(2) (1,2)=>2 1 2 1/ / r r = u u(3) : , : 1) ( ) V , 2) So ro , S R. (3) / . Hubble : V R R=Vt. A (3) 2 o..

t f trVcrRc c = = = ) (0000 f .

212121ttttffcc= =

) / 1 (/12 0 11 21211 2t t ct tcttc c = = = t2= X (+) (-).... t0=50.000 ,t2=1,51010 ( ) : ...sec / 000 . 300000033334 . 1 510 . 1 000 . 50 1 / 10102 0km ct t== + = +

sec / 001 . 300 ) / 1 (2 0 0 2km t t c c = + = FRESNEL. - Fresnel ( 2), sec / 5 , 001 . 300 ) / 1 (2 / 32 0 0 2km t t c c = + = , Fresnel. : 1. c , . 2., c , t, . K- H , , , , . To , ( ) ( ) ( ). Bing Bang . Bing Bang , - . , . , , - - , . ... 1. Smarandache, Florentin, Absolute Theory of Relativity & Parameterized Special Theory of Relativity &NoninertialMultirelativity, 92 p., 1982, Somipress, Fs, Morocco. 2. Smarandache, Florentin, New Relativistic Paradoxes and Open Questions, 126 p., 1983, Somipress, Fs, Morocco. 3. Bell, J. S., On the Einstein-Podolsky-Rosen Paradox,Physics 1, pp. 195-200, 1964. 4. Bohm, D., The Paradox of Einstein, Rosen, and Podolsky,Quantum Th., pp. 611-623, 1951. 5. Einstein, A.; Podolsky, B.; and Rosen, N., Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?, Phys. Rev. 47, pp. 777-780, 1935. 6. Smarandache, F., There is No Speed Barrier in the Universe, mss., Liceul Pedagogic Rm. Valcea, Physics Prof. Elena Albu,1972. 7. Rindler, W., Length Contraction Paradox, Am. J. Phys., 29(6), 1961. 8. Einstein, A., ZurEletrodynamikbewegterKrper, Annalen der Physik, Vol. 17, pp. 891-921, 1905. 9. A. Einstein, On the Electrodynamics of Moving Bodies, Annalen der Physik, 17, 891-921, 1905.