r r E x w, y w, z w, (1) Where c is the speed of light in vacuum.

Transcription

1 ISSN: ISO 900:008 Cetified Intentionl Jonl of Engineeing nd Innovtive Tehnology (IJEIT) olme, Isse 0, Apil 04 The Replement of the Potentils s Conseene of the Limittions Set by the Lw of the Self vitions on the Physil Lws Emmnil Mnosos Astophysis Lbotoy, Flty of Physis, Ntionl nd Kpodistin Univesity of Athens, Pnepistimiopolis, GR 578 Zogphos, Athens, Geee Abstt the lw of self vitions detemines ntittively slight inese of the est msses nd eleti hges of the mteil ptiles s the ommon se of ntm nd osmologil phenomen. The Liend- Weihet eletomgneti potentils e omptible with Speil Reltivity, bt e not omptible with the lw of self vitions. In this tile we pesent the eletomgneti potentils tht e omptible with the lw of self vitions. We note tht etions omptible with the lw of self vitions e lso omptible with the Loentz-Einstein tnsfomtions. The eletomgneti potentils of the self vitions e deomposed into two independent pis of sl-vetoil potentils. One pi gives the eletomgneti field tht ompnies the eleti hge in its motion. The othe pi gives the eletomgneti dition. υ () Whee is the speed of light in vm. Index Tems Liend-Weihet potentils, self vitions, speil eltivity. I. INTRODUCTION O ent Physil knowledge, in ombintion with o mthemtil lltions [], llows s to popose the lw of the self vitions s the ommon se of ntm nd osmologil obsevtions. The knowledge we possess in the e of Eletomgnetism plyed il ole in the ntittive detemintion of the self vitions, i.e. in the fomltion of the lw of self vitions. All the mthemtil etions tht e omptible with the lw of the self vitions e lso omptible with the Loentz-Einstein tnsfomtions. Howeve, the opposite does not hold. The Liend- Weihet eletomgneti potentils e omptible with the Loentz-Einstein tnsfomtions, bt e not omptible with the lw of self vitions. In this tile we pesent the potentils tht e omptible with the lw of self vitions nd spplnt the Liend-Weihet potentils. II. THE ELECTROMAGNETIC POTENTIALS IN THE MACROCOSM We onside n eleti point hge moving bitily in n inetil efeene fme Oxyzt, s depited in Fig.. We denote EA, nd Fig : An bitily moving eleti point hge t time t. The soe of the eletomgneti field t point A x, y, z, t is the eleti hge positioned t E x w, y w, z w, w t the deeleting time w t. Fig. efes to the point in time t when the eleti hge is t position P x t, y t, z t, t. The soe of the eletomgneti field t point A x, y, z, t is the eleti hge fom position E x w, y w, z w, w t the deeleted time wt () The eleti field ε nd the mgneti field B t point A x, y, z, t e given by the pi, A of the sl potentil nd the veto potentil A espetively, thogh etions 8

2 ISSN: ISO 900:008 Cetified Intentionl Jonl of Engineeing nd Innovtive Tehnology (IJEIT) olme, Isse 0, Apil 04 A ε () t As it is ledy known []-[4], we lso ive t etions (7) nd (8) fom the Liend-Wiehet eletomgneti potentils: B A (4) x whee και A l A. y z Using the symbols of Fig., the eleti potentil nd the veto potentil A e given by etions [] (5) υ A (6) whee w is the veloity of the eleti hge t point E x w, y w, z w, w. The intensity of the eleti field ε nd the intensity of the mgneti field B eslting fom the bove potentils thogh etions () nd (4) t point A x, y, z, t, e []: A υ 4 0 whee 4 0 w υ (9) (0) is the veloity of the eleti hge t E x w, y w, z w, w. point If we do not tke into ont the self vition of the eleti hge, the pi of potentils given in (5)-(6), s well s the pi of potentils given in (9)-(0), give the sme etions (7)-(8) fo the eletomgneti field. If, howeve, we do onside the lw of the self vitions [], while the potentils (5)-(6) still give etions (7)-(8), the potentils (9)-(0) give fom etions ()-(4) A υ t 0 4 t ε A B υ 4 0 () () (7) (8) 8 with vetos ε nd B s given by etions (7) nd (8). The lw of self vitions gives tht t point A x, y, z, t it is t 0 () theefoe, etion () does not oetly expess the eleti field ε t point A x, y, z, t. Moe genelly it holds tht 0 (4) nd, theefoe, etion () does not oetly give the mgneti field B t point,,, A x y z t, eithe. Conseently, the Liend-Wiehet eletomgneti

3 ISSN: ISO 900:008 Cetified Intentionl Jonl of Engineeing nd Innovtive Tehnology (IJEIT) potentils e not omptible with the self vitions. This is why they e epled by the potentils given in (5)-(6). If we denote by L the set of etions tht e omptible with the Loentz-Einstein tnsfomtions, nd by S the set of etions omptible with the self vitions, then it holds tht: S L (5) One sh exmple e the Liend-Wiehet potentils. They belong to set L, bt they do not belong to set S. The lw of self vitions imposes moe sevee estitions on the etions desibing physil lws, thn those imposed by Speil Reltivity. The eletomgneti potentils of the self vitions (5)-(6) hve two fndmentl hteistis. The fist is tht they e deomposed into two individl pis of potentils 4 0 olme, Isse 0, Apil 04 (6) A (7) nd 4 0 (8) A (9) The, A pi gives, thogh etions ()-(4), the eletomgneti field ε, B tht ompnies the eleti hge in its motion: A t 4 0 ε (0) 8 A 4 0 B () The, A pi gives, gin thogh etions ()-(4), the eletomgneti dition: () 4 0 ε A A t () 4 0 B The seond hteisti of the eletomgneti potentils of the self vitions onens the, A pi. Aoding to etions (8) nd (9), the eletomgneti potentils tht give the eletomgneti dition e independent of the distne of point A x, y, z, t fom the eleti hge. In the mioosm, the lw of self vitions [] is elted to the ntm phenomen. This is why we hteized the eletomgneti potentils (5)-(6) s mosopi. These potentils eple the Liend-Wiehet potentils fo the esons we ledy mentioned. I. DISCUSSION The Speil Theoy of Reltivity sets limittions on the mthemtil expessions of the physil lws, whih hve to be invint with espet to the Loentz-Einstein tnsfomtions. The Lw of the Self vitions, s well s the totlity of the etions of the Theoy of Self vitions, e invint nde the Loentz-Einstein tnsfomtions. This is diet onseene, sine the fomltion of the mthemtil expession of the Lw of the Self vitions hs been ondted nde the ssmption of the oetness of the Speil Theoy of Reltivity. The Speil Theoy of Reltivity estits in

4 ISSN: ISO 900:008 Cetified Intentionl Jonl of Engineeing nd Innovtive Tehnology (IJEIT) sh deisive wy ny vition of the est mss o the eleti hge of mteil ptile tht this vition n be done in only one wy whih is the Lw of the Self vitions. The eltion between the Lw of the Self vitions nd the Speil Theoy of Reltivity is even deepe. The genelized photon whih is the most immedite onseene of the Lw of the Self vitions hs itself s onseene ontinos exhnge of signls between mteil ptiles with the veloity of light. Ths the exhnge of signls with veloity between two obseves is not meely hypothesis whih my be stted fo the deivtion of the Loentz-Einstein tnsfomtions, bt ontinos physil elity. This physil elity is expessed by lge set of theoems nd oollies of the Theoy of Self vitions. By lky oinidene Einstein ws sked fo the hoie of the exhnge of signls with veloity between two obseves, in ode to deive the Loentz-Einstein tnsfomtions. Nmely bot the ft tht two obseves exhnge soni o othe kinds of signls with veloity the eslting tnsfomtions e wong. So, we know the nswe he povided: The oetness of the Loentz-Einstein tnsfomtions e jstified by the otome. These tnsfomtions led to oet eslts, in ontst to othe ndidte tnsfomtions, whih led to wong onlsions. The development of the Theoy of Self vitions shows tht the exhnge of signls with veloity vi genelized photons is ontinos physil elity. To this physil elity the Loentz- Einstein tnsfomtions owe thei oetness. Mteil ptiles onstntly exhnge genelized photons, i.e. they onstntly exhnge infomtion with veloity. The Theoy of Self vitions imposes dditionl onstints on the mthemtil fomltion of the physil lws, beyond the ones imposed by the Speil Theoy of Reltivity. The physil lws hve moeove to be omptible with the self vitions. The pesent tile is lssil exmple bot the onseenes of the dditionl onstints imposed by the Theoy of Self vitions on the mthemtil fomltion of physil lws. The Liénd-Wiehet potentils e omptible with the Speil Theoy of Reltivity nd they e lso invint nde the Loentz-Einstein tnsfomtions. On the othe hnd, they e not omptible with the self vitions. Fo this eson they e epled by the potentils of the self vitions, s they e pesented in the pesent tile. The self vitions potentils do not simply eple the Liénd-Wiehet potentils. The eplement indes fndmentl onseenes fo the Theoy of Eletomgnetism. Insted of the one ople of sl- veto potentils s in the Liénd-Wiehet potentils, we hve deived two independent oples. The fist ople gives the eletomgneti field whih ompnies the eleti hge ding its motion. This ople is invesely popotionl to the distne fom the olme, Isse 0, Apil eleti hge. The othe ople of sl- veto potentils desibe the eletomgneti dition. This ople is independent fom the distne fom the soe. As the enegy of the eletomgneti dition is expessed by the intodtion of the ntm of the photon, in simil mnne the potentil giving the eletomgneti dition n be expessed by ntm of potentil whih is independent of the distne fom the soe. The pesent tile is hteisti exmple bot the onseenes of the self vitions on the mthemtil fomltion of the physil lws.. CONCLUSION The one ople of sl- veto potentils 4 0 A, gives the eletomgneti field whih ompnies the bitily moving eleti point hge ding its motion. The othe ople of sl-veto potentil 4 0 A, gives the eletomgneti dition emitted by the bitily moving eleti point hge. The potentils of the self vitions e invint nde the Loentz- Einstein tnsfomtions, while they e lso omptible with the self vitions. The potentil giving the eletomgneti dition does not depend on the distne fom the soe-point hge of dition. REFERENCES [] Mnosos, E., Mss nd hge self vition: A Common Undelying Cse fo Qntm Phenomen nd Cosmologil Dt, Pogess in Physis, ol. 9 (), pp.7-4, Jly 0. [] Giffiths, D, Intodtion to Eletodynmis, Pentie Hll, 999. [] Wngsness, R. K., Eletomgneti Fields, John Wiley, 986.

5 ISSN: ISO 900:008 Cetified Intentionl Jonl of Engineeing nd Innovtive Tehnology (IJEIT) [4] Loin, P., Coson, D., Eletomgneti Fields nd Wves, W.H. Feemn & Compny, 970. olme, Isse 0, Apil 04 85