Generalized The General Relativity Using Generalized Lorentz Transformation

Size: px

Start display at page:

Download "Generalized The General Relativity Using Generalized Lorentz Transformation"

Gavin Lester
5 years ago
Views:

1 P P P P IJISET - Inernaional Journal of Innoaie Siene, Engineering & Tehnology, Vol. 3 Issue 4, April 6. ISSN Generalized The General Relaiiy Using Generalized Lorenz Transformaion PMubarak Dirar Abdallah, P PHashim Mohammed Ali & P PSawsan Ahmed Elhouri Ahmed PInernaional Uniersiy of Afria- College of Siene-Deparmen of Physis & Sudan Uniersiyof Siene & Tehnology-College of Siene-Deparmen of Physis Kharoum- Sudan PSudan Uniersiyof Siene & Tehnology-College of Siene-Deparmen of Physis Kharoum- Sudan 3 PUniersiy of Bahri - College of Applied & Indusrial Sienes-Deparmen of Physis Kharoum Sudan Absra Generalized non linear Lorenz ransformaion is uilized o derie modified speial relaiisi spae ime equaions. The equaions are found for pariles moing in a poenial field. The ransformaion is based on he usual Newonian relaion displaemen in erms of iniial eloiy for onsan aeleraion. The displaemen in all frames are epressed in erms of spaial oordinae ime and poenial per uni mass. The epressions for Lorenz ransformaion parameer, spae and ime redues o ha of ordinary speial relaiiy in he absene of field. The energy relaion redues o speial relaiiy for no field and o Newonian one for law eloiy. 3 Key words : generalized Lorenz ransformaion, generalized speial relaiiy, relaiisi energy, Newon energy. - Inroduion Einsein speial heory of relaiiy SR is one of he mos imporan physial heories, sine i make radial modifiaion o he onep of spae and ime. Aording o Newon laws of moion, he oneps of spae, ime and mass are absolue in he sense ha hese quaniies hae he same alue in all frame of referenes. Unforunaely his onep is iolaed by Mihelson Morley eperimen. In his eperimen i was shown ha he speed of ligh in auum is onsan and is independen of he moion of he obserer or he soure. This moiaes Einsein o propose his relaiiy heory whih is known as speial relaiiy (SR. In (SR heory he spae and ime depends on he relaie moion of he frame of referenes whih moes wih onsan eloiy o eah oher. Einsein (SR sueeded in eplaining he onsany of ligh speed The SR also eplains he ime dilaion for fas moing deaying meson, i also eplains suessfully pair produion and annihilaion phenomena. Howeer SR suffers from noieable sebaks. Firs of all i does no saisfy orrespondene priniple. This is beause in he Newonian limi, is energy 9

2 IJISET - Inernaional Journal of Innoaie Siene, Engineering & Tehnology, Vol. 3 Issue 4, April 6. ISSN epression does no gie a poenial erm. The lak of poenial erm, in SR energy relaion is in dire onfli wih ommon sense and physial heories. For insane, if one hae an eleron moing in free spae wih a erain eloiy and anoher one wih he same eloiy moing in an eleromagnei field, SR energy for boh is he same. This does no agree wih ommon sense and quanum mehanis whih predis differen energy alues. The SR heory anno eplain also ime dilaion by graiaion beside he phoon red shif due o he graiy field. This draw baks moiaes some physiiss o searh for an alernaie heory ha keeps he same framework of SR bu aouns for he effe of poenial. These aemps sueeded in uring SR defes bu some of hem deals wih he weak field, while ohers looks omple. This moiaes us o searh for simple alernaie ha keeps SR framework and holds for all fields. This is done in seion (. seions (3 and (4 are deoed for disussion and onlusion. - New deriaion of general speial relaiiy Aording o Newon's seond law of moion he fore F an be epressed in erms of he mass m and aeleraion a as F ma ( Thus he poenial V is gien by F d mad ma d V m. m a Where is defined as he poenial per uni mass. Thus Hene m ma a ( Le wo referene frames (, and (, moes wih iniial eloiy and onsan aeleraion a wih respe L o eah ohers.thus he 9

3 IJISET - Inernaional Journal of Innoaie Siene, Engineering & Tehnology, Vol. 3 Issue 4, April 6. ISSN disane beween heir origin a any ime is gien by i-e L a a L (3 Using equaion (3 one an rewrie equaion (4 as L (4 This represen he lengh as measured by he obserer O.assuming and o be he same for all obserers, he lengh for obserer O is gien by L a a a L (5 The spae ime oordinae in wo frames an be desribed by Lorenz ransformaion. Aording o Lorenz ransformaion ( L ( ( L ( (7 (6 Consider now a soure of ligh ha emis ligh pulse when he wo frames origin oinide, i.e The ligh pulse whih are emied raels disanes and respeiely, where (8 Subsiuing (8 in (6 yields ( 9

4 IJISET - Inernaional Journal of Innoaie Siene, Engineering & Tehnology, Vol. 3 Issue 4, April 6. ISSN (9 ( Insering also (8 in (7 gies ( From (9 and ( Therefore ( ( ( I is ery ineresing o noe ha when no field eiss ( The faor in equaion ( redues o (3 ( ( Whih is ordinary SR relaion. A dire inserion of equaion ( in (6 and (7 yields (4 ( ( ( 93

5 IJISET - Inernaional Journal of Innoaie Siene, Engineering & Tehnology, Vol. 3 Issue 4, April 6. ( ( ( In he absene of fields again (4 and (5 redues o ha of SR. The epression for energy is gien by (5 ISSN E m m (6 Insering ( in (6 yields E m ( ( (7 When no field eiss he energy relaion redues o m E ( (8 Le now (9 Assuming ( Equaion (7 beomes E m ( ( Bu for law speed Thus ( E m (3 94

6 IJISET - Inernaional Journal of Innoaie Siene, Engineering & Tehnology, Vol. 3 Issue 4, April 6. ISSN Bu aording o Newon's laws (4 Thus E m m m m m T V (5 Where V m T m (6 Whih is he usual Newon energy relaion beside res mass erm. 3- Disussion Non linear Generalized Lorenz ransformaion in equaions (6 and (7 are used o find new generalized SR. This new ransformaion is non linear in. This ransformaions deals wih pariles moing wih onsan iniial eloiy and onsan aeleraion under he aion of a poenial field. The spaial displaemen is found in erms of iniial eloiy and poenial per uni mass. By assuming he speed of ligh is onsan in all frames moing in a poenial field, he ransformaion oeffiien is found o depend on as well as as shown by equaion (. The new spae and ime ransformaions are shown in equaions (6 and (7. I is ery ineresing o noe he epressions for, and redues o ha of SR when no field eiss as shown by equaions (3, (6, (7 and (8 respeiely. Unlike SR, whih reognize res mass and kinei energy only, he generalized energy epression (7 reognize poenial and redues o Newon energy relaion, as equaion (5 indiaes, wih kinei and poenial erm, beside res mass erm. 4- Conlusion The generalized Lorenz ransformaion and generalized SR an desribe suessfully he moion of pariles in a field. I redues o SR when no field eis. I also saisfy Newonian limi by onsising of kinei and poenial erm. 95

7 6P P Ediion IJISET - Inernaional Journal of Innoaie Siene, Engineering & Tehnology, Vol. 3 Issue 4, April 6. Referenes [ ] A. Beiser, onep of modern physis [ ] ISSN Ray mond A. Serway, physis for sieniss and Engineers wih modern physis. h, U.S.A, 4. [ 3 ] W. Pauli, Theory of Relaiiy (Doer Publ., New York, 98; Gosekhizda, Moska; Leningrad, 947, p. 6 of he Russian ediion. [ 4 ] R.Adler, M.Basin and Shiffer, Inroduion o General Relaiiy (MC Graw Hill Book Company, Tokyo, 975, hp.,9. [ 5 ] M.H.M. Hilo, J.of Mod.phy,,37-373,( [ 6 ] M.Dirar eal, Naural siene, V.S,N.6, (3 [ 7] M.H.M. Hilo, Naural siene, V.4, N.5, ( [ 8] M.H.M.Hilo,J. of Mod. physis,, ( [ 9] M. H. M. Hilo, Naural siene, V. 3, N. 4 ( M. Dirar eal, Sudan. J of basi sienes (M, 3 (7 [ ] 96

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

Deriving the Useful Expression for Time Dilation in the Presence Of the Gravitation by means of a Light Clock IOSR Journal of Applied Physis (IOSR-JAP) e-issn: 78-486Volue 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