Relativistic Rate of Clocks and Stability of the Gravitational Constant G

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1 International Journal for Reearh in Alied Siene & Engineering Tehnology (IJRASET ISSN: -965; IC Value: 45.98; SJ Iat Fator :6.887 Volue 6 Iue I, January 08- Aailable at Relatiiti Rate of Clok and Stability of the Graitational Contant G Arit Sorli, Santanu Kuar Patro, R.N.Patra Foundation of Phyi Intitute, Reearher Id htt://orid.org/ , Sloenia Deartent of Matheati, Berhaur Unierity, Reearher Id- htt://orid.org/ , Odiha, India Deartent of Matheati, Berhaur Unierity, Reearher Id- htt://orid.org/ berhaur, Odiha, India Abtrat: The Introdution of Plank etri in quantu auu odel how that the Lorentz fator and eloity of relatiiti hyial objet are related with the diinihed energy denity of quantu auu in the entre of the relatiiti objet. Ma of a gien hyial objet ha the origin in ariable energy denity of quantu auu whih allow deribing GR relatiiti rate of lok a the henoenon whih ha it hyial origin in inial ariable energy denity of quantu auu. The ain otto of thi aer i to how that the inial ariation of quantu auu energy denity do not influene the ize of graitational ontant G. Keyword: relatiiti rate of lok, Lorentz fator, energy denity of quantu auu, graitational ontant G I. INTRODUCTION Lorentz fator i at the ore of relatiiti hyi. It obiou to ee that ( We'll derie how thi reletiiti fator i related to the hyial roerty of quantu auu on the entre of a gien relatiiti objet. And alo the alue of energy denity of quantu auu in the entre of ret hyial objet with a and oluev i [,,] ( V. So the a and the energy E of a gien hyial objet i related with the diinihed energy denity of quantu auu in it entre a ( E ( V ( (4 V Relatiiti objet i gaining it relatiiti energy and a by taking the energy fro the quantu auu[4]. We an exre abortion of energy with following forula ( (5 V Relatiiti a aue additional diinihing of quantu auu energy denity objet, and i diretly related to the Lorentz fator. Forula (5 an be deeloed a following in the entre of relatiiti hyial IJRASET (UGC Aroed Journal: All Right are Reered 799

2 International Journal for Reearh in Alied Siene & Engineering Tehnology (IJRASET ISSN: -965; IC Value: 45.98; SJ Iat Fator :6.887 Volue 6 Iue I, January 08- Aailable at (6 V i the alue of energy denity of quantu auu in the entre of relatiiti hyial objet. Now the Lorentz fator an be exreed ubjet to the ariable energy denity of quantu auu a (7 ( V Now, one an write following forula for relatiiti rate of lok in SR (8 t 0 t ( V t i the elaed tie in a oing inertial yte (in ae of GPS atellite and t Where, 0 inertial yte (in ae of GPS urfae of the Earth. i the elaed tie in the tationary II. RELATIVISTIC VELOCITY AND VARIABLE ENERGY DENSITY OF QUANTUM VACUUM Fro equation-(7, we an write the following forula (9 ( ( V or, ( or, 4 ( V or, 4 V 4 ( The equation(9 how that the relatiiti eloity an be exreed in ubjet to the eed of light, a, olue of a gien relatiiti objet and diinihed energy denity of quantu auu in the entre of a gien relatiiti objet. III. RELATIVISTIC RATE OF CLOCKS IN GR The forula for relatiiti rate of lok in GR i a following V V (0 t 0 t GMr IJRASET (UGC Aroed Journal: All Right are Reered 800

3 Where, 0 International Journal for Reearh in Alied Siene & Engineering Tehnology (IJRASET ISSN: -965; IC Value: 45.98; SJ Iat Fator :6.887 Volue 6 Iue I, January 08- Aailable at t i elaed at the ditane r fro the entre of tellar objet (in the ae of GPS Earth, G i graitational ontant and t i elaed tie on the tellar objet urfae (in the ae of GPS i the a of the tellar objet (in the ae of GPS Earth, Earth urfae. Alying equation-(4 in forula-(0 we hae, t t0 GrV ( 4 ( Whih how that the relatiiti rate of lok in GR deend on the ariable energy denity of quantu auu. Now, One an alulate energy denity of quantu auu at the oint of where i laed lok whih eaure elaed tie 0.Going away fro the entre of a gien aterial objet energy denity of quantu auu inreae aording to the following forali: [5] 4 ( r R ( where i the a of the aterial objet, r i radiu of the aterial objet and R i the ditane fro the entre of the aterial objet to a gien oint T ( figure. Haing R 0 one get energy denity of quantu auu in the entre of tellar objet. Haing When R r one get energy denity of quantu auu on the urfae of the tellar objet. Haing R one get energy denity of quantu auu in intergalati ety ae far away fro tellar objet whih i. t Figure : Denity of quantu auu in the entre, on the urfae and ditant fro tellar objet IV. RELATIVISTIC RATE OF CLOCKS IS VALID FOR ALL OBSERVERS Relatiiti rate of lok in SR and GR ha origin in ariable energy denity of quantu auu and i alid for all oberer in all inertial yte. GPS yte roe that without any doubt. If inner and outer oberer in SR would exeriene different tie rate of their lok, GPS ould not work. In SR the relatie rate of lok i alid for all oberer. Stationary lok on the train tation run with the ae rate for the tationary oberer on the latfor and for the oing oberer in the train. The ae i alid for oing lok in the train. If thi would not be o, GPS ould not work. SR effet on rate of lok on the atellite i 7 iroeond lower er day (regarding lok on the Earth urfae and GR effet i 45 iroeond fater er day. Thi 8 iroeond differene i alid for all oberer on the atellite and on the Earth urfae. SR effet i aued by the additional diinihing of quantu auu energy denity on the atellite. GR effet i aued by the inreaing of energy denity of quantu auu whih in generally inreae with the ditane fro the gien hyial objet [5]. IJRASET (UGC Aroed Journal: All Right are Reered 80

4 International Journal for Reearh in Alied Siene & Engineering Tehnology (IJRASET ISSN: -965; IC Value: 45.98; SJ Iat Fator :6.887 Volue 6 Iue I, January 08- Aailable at V. VARIABILITY OF ENERGY DENSITY OF QUANTUM VACUUM IS EXTREMELY MINIMAL AND DOES NOT INFLUENCE THE VALUE OF GRAVITATIONAL CONSTANT G. In intergalati ae, denity of DQV ha a alue of lank denity, a The reiou reearh [6] onfir that the alulation of 000 etre denity of DQV i (7tie / in the entre of blak hole with the a of the un with radiu r of The differene between denity of quantu auu in the intertellar ae and in the entre of blak hole i infiniteial. So the alue of graitational ontant G in the intergalati ae far away fro the tellar objet an be exreed with lank unit a l G ( Where t. l denote lank olue, G. t (4 denote the a and t denote the lank tie. SO whih an be rewritten a? Fro the reiou latet reearh [6], it i onfired that the graitational ontant in the entre of blak hole with a of the un, whih i alo alid for all tellar objet a- (5 G (. 4( r d t Where - a of the tellar objet, r- radiu, and d- ditane fro the entre of the tellar objet A. Cae-I: [when d=0] P l The graitational ontant ee to be in the entre of the tellar objet a P e P / (6 B. Cae-II: [when d=r] G (. 4r t The graitational ontant ee to be in the urfae of the tellar objet a (7 G (. r t IJRASET (UGC Aroed Journal: All Right are Reered 80

5 International Journal for Reearh in Alied Siene & Engineering Tehnology (IJRASET ISSN: -965; IC Value: 45.98; SJ Iat Fator :6.887 Volue 6 Iue I, January 08- Aailable at C. Cae- III : [when d=infinity] The graitational ontant in the intergalati ae a G. t (8 where denote the lank denity The alue of graitational ontant in intertellar ae i G The alulation onfir that the alue of G i not hanging. Howeer the reene of tellar objet diinihe denity & energy denity of quantu auu, till the graitational ontant G reain unhanged. Graitational ontant [at Earth and in it influene] Value [alulated] Gequator Gole Gentre of earth G000k aboe the earth Goon-erihelion Goon-ahilion Gun-erihelion Gun-ahelion (Table-: Credit to Arit Sorli et al, Coology of Eintein NOW, DOI: 0.648/j.aj Table- onfir that there i no differene between the alue of G in Equator, ole and entre of the earth. Alo it how that the otion of Sun and oon ha no influene on G. Reent ubliation of Caligiuri i uggeting that alue of graitational ontant i hanging with hanging of denity of quantu auu and i different in the entre of the Earth than on the Earth urfae [0]. Aording to the alulation in thi aer lanet Earth a whih i uh aller than blak hole a annot influene alue of graitational ontant. Our alulation onfir that reene of aie objet in a gien area of quantu auu do not influene alue of graitational ontant. The latet alulation [6]onfir that een in the entre of the blak hole ite of the Sun with the radiu 000 eter graitational ontant G reain unhanged. See alulation of G in at deade hae oe alulation error [6].Different eaureent of graitational ontant G ine 980 hae gien different reult [7,8,9]. The influene of the oeent of the Earth ore on G i exluded. The differene of different eaureent of G i not exliable and reain an oen quetion to be anwered. We rooe in thi artile that tability of G in tie and in different lae on the Earth urfae ould be erified by the exerient where G would be eaured onequently for onth firt day of eah onth in three different lae on the Earth urfae. VI. CONCLUSIONS Lorentz fator i howing the relation between tationary and relatiiti hyial objet. Lorentz fator ha hyial origin in ariable energy denity of quantu auu in the entre of relatiiti objet. Relatiiti hyial objet i additionally aborbing and o additionally diinihing energy denity of quantu auu. Thi effet aue relatiiti energy, relatiiti a and relatie rate of lok. GR relatiiti rate of lok alo ha origin in ariable energy denity of quantu auu. Variable energy IJRASET (UGC Aroed Journal: All Right are Reered 80

6 International Journal for Reearh in Alied Siene & Engineering Tehnology (IJRASET ISSN: -965; IC Value: 45.98; SJ Iat Fator :6.887 Volue 6 Iue I, January 08- Aailable at denity of quantu auu i not influening the alue of graitational ontantg. Reult of lat 0 year of eaureent of graitational ontant how that there i oe eaureent error or either oe trange influene i affeting ot of GN eaureent: The ituation i diturbing learly either oe trange influene i affeting ot G eaureent or, robably ore likely, eaureent of G ine 980 hae unreognized large yteati error. The need for new eaureent i lear []. Oerall aying, we hae rooed in thi artile that the graitational ontant ha a table alue, for whih we hae lanned for the erifiation of thi reult in three different lae on the earth urfae. REFERENCES [] Sorli A, Fialetti D and Magehwaran M. Adaned Relatiity, Unifiation of atter, ae and onioune. NeuroQuantology 06; 4(4: [] Fialetti D and Sorli A. About a three-dienional quantu auu a the ultiate origin of graity, eletroagneti field, dark energy... and quantu behaiour. Ukrainian Journal of Phyi 06; 6(5: 4-4. [] Fialetti, D. Found Phy (06 46: 07. htt://doi.org/0.007/ z [4] Arit Sorli, Magi Magehwaran, Daide Fialetti, Energy - Ma - Graity Theory, Aerian Journal of Modern Phyi. Seial Iue:Inuffiieny of Big Bang Coology. Vol. 5, No. 4-, 06, doi: 0.648/j.aj [5] Fialetti, D. Sorli A. Dynai Quantu Vauu and Relatiity, Annale Phyia, Vol 7 (06. [6] Arit Sorli, Vlad Koroli, Andrei Nitreanu, Daide Fialetti. Coology of Eintein NOW. Aerian Journal of Modern Phyi. Seial Iue: Inuffiieny of Big Bang Coology. Vol. 5, No. 4-, 06,. -5. doi: 0.648/j.aj [7] Gundlah, J. H. Adelberger, E. G., Hekel, B. R. and Swanon, H. E.: New tehnique for eauring Newton ontant G, Phyial Reiew D 54, 56R (996. [8] S. Shlainger, J.H. Gundlah, R.D. Newan, Reent eaureent of the graitational ontant a a funtion of tie, Phy. Re. D 9, 0 (05, arxi: [9] J. D. Anderon, G. Shubert, V. Trible and M. R. Feldan."Meaureent of Newton' graitational ontant and the length of day." EPL 0 (05 000, doi: 0.09/ /0/000. [0] Luigi Maxilian Caligiuri, Graitational Contant G a a Funtion of Quantu Vauu Energy Denity and it Deendene on the Ditane fro Ma, International Journal of Atrohyi and Sae Siene. Seial Iue: Quantu Vauu, Fundaental Arena of the Uniere: Model, Aliation and Peretie. Vol., No. 6-, 04, doi: 0.648/j.ija [] S. Shlainger, J.H. Gundlah, R.D. Newan, Reent eaureent of the graitational ontant a a funtion of tie, Phy. Re. D 9, 0 (05, arxi: IJRASET (UGC Aroed Journal: All Right are Reered 804