Deriving the Useful Expression for Time Dilation in the Presence Of the Gravitation by means of a Light Clock

Transcription

1 IOSR Journal of Applied Physis (IOSR-JAP) e-issn: Volue 7, Issue Ver II (Mar - Apr 5), PP 7- wwwiosrjournalsorg Deriing he Useful xpression for Tie Dilaion in he Presene Of he Graiaion by eans of a Ligh Clok Dr Hasabalrasoul Ges Allah Isail Haza, Mr Wasil Abdalgader Abdalla Alhassan Deparen of Physis & Maheais, fauly of duaion Hasaheisa /Gezira Uniersiy - Wad Madani, Sudan Deparen of Physis,Tahseen Aladaa Training Cener /Salan bin Abdulaziz Uniersiy,Saudi Arabia Absra: Generalized speial relaiiy is one of he os proising odels ha is found o ure any defes of speial relaiiy These defes inlude un apabiliy of explaining graiaional red shif and saisfaion of he Newonian lii Despie hese suesses generalized speial relaiiy suffers fro noieable sebaks Firs of all is way of deriaion ake i resried o weak fields only Alhough reen deriaion ake i appliable o fields oher han he weak and graiaional field, bu his deriaion needs o be srenghed In his sudy a ligh lok is used o derie a useful expression for ie in General speial relaiiy These expressions are ypial o ha deried before by using ured spae Tie, bu hey are no resried graiaional and weak fields The expressions for ie hold for all fields Keywords: aligh lok irror, Generalized, graiaional, ie Dilaion I Inroduion insein heory of speial relaiiy (GR) is one of he bigges ahieeens in physis I hanges radially he lassial onep of spae and ie The GR heory is based on wo posulaes One of he is onerned wih he hoogeneiy of spae and ie he oher is onerned wih he onsany of speed of ligh[] The heory of GR sueeds in explaining a large nuber of experienal obseraions, like eson deay, pair produion and nulear ass defe [] Unforunaely GR suffers fro noieable sebaks Firs of all, i anno explain he hange of neurino ass, i does no saisfy orrespondene priniple, sine is expression of relaiisi energy does no saisfy Newonian lii sine i does no onsis of a er represening he poenial energy I anno explain also he graiaional red shif whih indiaes ha he phoon ass as well as is periodi ie hange wih he graiaional field[3] II Se baks of he Theory of Speial Relaiiy In GR heory he expression of ie, ass,spael and energy () l l () (3) DOI: 979/ wwwiosrjournalsorg 7 Page

2 Deriing he Useful xpression for Tie Dilaion in he Presene Of he Graiaion by eans (4) Where, l, and ass in frae oing wih eloiy wih respe o he res frae The expression of relaiisi ass in he Newonian lii, where he ligh speed is law is by[4,5,6,7] sands for ie, lengh, and ass in arres frae While, l,, and represens ie, lengh ( ) (5) This is no ypial o he Newon expression of energy[8] V T V (6) Sine i does no onsiss of on expression represening he poenial energy The graiaional red shif phenoenon is also relaed o GR I is onerned wih he hange of phoon frequeny fro f o f when i eners a graiaional field of poenial V Aording o he priniple of Newonian energy onseraion V (7) Sine he phoon energy is also gien by (4) i follows ha (8) Thus V V (9) quaion (9) indiaes ha he phoon hanges wih he poenial whih is in dire onfli wih he equaion (3), whih saes ha he ass does no hange wih he poenial V [9] III General xpression for Kinei and Poenial nergy d d V F V x For independen of x and dependen on x only [9] () DOI: 979/ wwwiosrjournalsorg 8 Page

3 Deriing he Useful xpression for Tie Dilaion in he Presene Of he Graiaion by eans When V d dx dx d d dx d d () () (3) This an be also be died fro ay (4) (5) V poenial Fy (6) ay ay (7) IV Deriaion of Tie Dilaion in he presene of Fields Consider an araie field like graiaional field Le a ligh irror of lengh l oe upward wih iniial speed Figure () a lok in free spae When lok oing up is speed be oes a a ie For he lok in free spae he ie o is gien by l l (8) DOI: 979/ wwwiosrjournalsorg 9 Page

4 Deriing he Useful xpression for Tie Dilaion in he Presene Of he Graiaion by eans Figure () For a lok oing under he aion of he field y x l (9) The eloiy and he erial displaeen y an be expressed in ers of he iniial eloiy aeleraion a as follows f Sine he aerage eloiy is gien by f a y a ( a) f a a and Figure (3) ligh oing wih speed for p o p Assuing he ligh oing wih speed for p o p in a rajeory inlined o he erial plane i follows ha l y y DOI: 979/ wwwiosrjournalsorg Page

5 Deriing he Useful xpression for Tie Dilaion in he Presene Of he Graiaion by eans Bu y () y y () Thus he ie in he presene of he field is gien by This expression holds for any field () V Disussion A useful expression for ie dilaion were found in equaions () These expressions were deried by onsidering a ligh irror lok oing in a field The oion of his lok is obeys he ordinary equaions of oion in any arbirary field Forunaely he expressions is found o be ypial o ha obained in GSR VI Conlusion This odel whih uses a ligh lok o derie GSR, shows ha he GSR an hold for any field, graiaional or non-graiaional Referenes [] OD Jefienko,"leroagnei Reardaion, and heory and Relaiiy " nd diion, lere Sienifi, ISBN , 997 [] FL Derek "an Inroduion o Tensor Calulus and Relaiiy "3 rd diion Jon Wily &Sons Ld, New York 98, ISBN (plk) [3] M H M Hilo, e al, "Using of Generalized Speial Relaiiy in siaing he Proon (Nulear) Mass o xplain he Mass Defe,"Naural siene Vo l 3, No, 4-44 () [4] RF ens and J Dunning Daies "The Graiaional Red-Shif "Uniersiy of Hull, ngland, arxi:gr-q/438v4p3 [5] Rohrlih, F An eleenary deriaion of = A J Phys 58: [6] Thoas, G Wha s so speial abou = ur J Phys 6: 5-3, 5 [7] Shara, A The Origin of he Generalized Mass-nergy quaion = and Is Appliaions in General Physis and Cosology Physis ssays 7: 95-4 [8] RC Tolan,"Relaiiy, Therodynai- and Cosology s diion Oxford uniersiy press, oxford 934 LCCN Reissued (987) New York: Doer ISBN p59 [9] H I Haza,Mubarak Dirar Abdalla Speed of Ligh and Moenu wihin he frae work of Generalized Speial Relaiiy, Uniersiy of Afria Journal of Sienes,olue No 3 3 DOI: 979/ wwwiosrjournalsorg Page