On the Physical Significance of the Lorentz Transformations in SRT. Department of Physics- University of Aleppo, Aleppo- Syria ABSTRACT

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1 On he Phsal Sgnfane of he Loen Tansfomaons n SRT Na Hamdan Sohel aa Depamen of Phss- Unes of leppo leppo- Sa STRCT One show all fas ha seem o eqe he naane of Mawell's feld eqaons nde Loen ansfomaons [nsen's ela []] an be deed fom assmpons dffeen fom hose sed b nsen. In geneal we sa wh he phsal law eqaons [345] and appl he ela pnple o hem. Wh hs appoah nsen's ela SRT s efomlaed n a smple manne ha has dnamal applaon [6] who sng he Loen ansfomaons LT and s knemaal onadons. Ke Wods: Speal Rela Theo Loen Tansfomaon.

2 . Inodon end of he seenh en Gallo's epemens showed ha moon ms be elae n onas o he aeped ew. These epemens led hm also o sae wha s now alled he pnple of Gallean ela he laws of mehans ae he same fo a bod a es and a bod mong a onsan elo. Newon also deeloped hs laws of moon and hs onep of ela he laws of mehans ms be he same n all neal fames. De o Galleo and Newon he onep of absole spae beame edndan b absole me was eaned. The deelopmen of he eleomagne heo n he nneeenh en demonsaed a poblem wh Newonan ela. I seemed noneable o phsss ha M waes old popagae who a medm he ehe. as a onseqene of Newonan ela an obsee mong hogh he ehe wh elo wold mease he elo of a lgh beam as. The Mhelson - Mole epemen showed ha no ehe absole efeene fame esed fo eleomagne phenomena. Ths esl opened he wa fo a new appoah. nsen s ela [] poslaed ha he speed of lgh s naan n all neal fames whh mahemaall led o a new elaonshp beween spaes and me.e. he Loen ansfomaon LT. To emoe he onadon onenng he smmeal popees of spae-me beween lassal mehans and eleodnams he aleed lassal mehans o make ompable wh LT. nsen s mehod [] n deng LT onaned he naane of lgh speed whh was no nlded n Gallan ansfomaon. He onsdeed he Caesan pons n he fame S o be he same n he fame S podng ha we manan he onsan of lgh speed fo he moemen of hs pon n boh fames. Then a pale wh es mass m was eplaed wh he engneeng pon and SRT seeded n applng he pnple of mass eneg eqalene o he mong pale alhogh hs pnple was eale esed o he eleomagne feld befoe. The SRT poslaes fo aos knemaal effes lke lengh onaon and me dlaon. Seeal qesons ase when eamnng hese knemaal effes [98] and man onadons es [7]. Moeoe SRT and pale dnams ae nompable sne he dnams of a mong pale ae esed o aommodae LT. The nompabl beween SRT and pale dnams ases bease LT and s knemaal effes hae pma oe he phsal law n deng he elas dnamal qanes and n he nepeaon of elas phenomena. Ths nompabl an be negleed n m appoah whh begns wh he followng poslaes phsal laws and he ela pnple [345]. - le-magne felds Tansfomaons; elo ansfomaons and Loen-Tansfomaons. The Mawell s eld qaons n fame S ma be epessed as ρ a ; J ε b ; d In pape [4] o nenon was o dee he elas ansfomaon of he eleomagne feld as well as he elas ansfomaon of he hage and en dens. In he soe-fee ase:

3 a ; ; b d ollowng he same eason sed n [4] we now ge he elas ansfomaon of he eleomagne feld.e.; 3 In addon we ge Loen ansfomaon elaons: : 4 O ppose s now o dee he 3 eo elo who LT n he same manne n [3]. We sa fom he Loen foe q 5 ssme ha a haged pale q moes wh elo n fame S. The - omponen of q. 5 s: q 6a Now b applng he ela pnple o qs. 6a he wll pesee he fom n fame S mong wh elo paallel o he ommon - as as follows: q 6b fom qs.6 we hae a Usng qs.3 n qs.7 we ge b 7 8a To oban anohe elas ansfomaon of elo we assme ha he elo n fame S n he fom: 9a q.9a n fame S has he fom: 9b

4 Sbsng q.8a n q.9b we hae / O On he ohe hand q.8a old be wen as O Now we sa fom q. and assmng he ald of qs. and fo he elo n fame S hen q. ma be wen as O 4 4 Usng q.9a n he las elaon afe eaangemen we hae O 3 Compang boh qs. and 3 we ge: 8b

5 The same esl an be deed fom he eqaons 9 f we assme ha and.e.: I s obos ha o deaon poess dffes fom ha n SRT sne LT was no sed n hs poess. s fo he 3-eo elas elo ansfomaons he wee deed as a esl of mahemaal onsdeaons onl who akng no aon he defnon of elo as a ae of hange of poson wh me. Ths s seems naal sne he elo of a pale s no a pa of s nns popees b a meased qan ha old be edefned Deaon he eleomagne feld enso ν fom Loen oe I was known ha he 3-eo fo he eleomagne feld he sala and eo poenal as follows: o s epesened b 4 q.4 defnes a seond ank enso.e.; ν f one we n 4-dmensonal eos whh s wen n hs oodnae ssem ν ν 5 ν 4 ; as 6 ν I s well known ha SRT has emoed he bae beween mae and eneg b eaed a new bae whh an no be ansended aodng o hs heo. Ths bae sepaaes wha s known as he non-elas fom elas phss doman. The phsal laws appopae fo non-elas phss an no ansend hs bae and hene he fom lassal phss. The phsal laws appopae fo

6 elas phss an oe he doman non-elas phss hogh appomaon; and LT beomes a Gallean ansfomaon. The moe sable mehod s o sa wh he laws of lassal phss and make hem onde o all pale eloes.e. o epand he appopaeness of hese laws o deal wh elas doman. s demonsaed n [3] ha elas epessons wee deed begnnng wh he lassal law.e. q and ela pnple. Cona o wha s ofen lamed n SRT we had all he elas epessons n addon he well known phsal law.e.; d ε d q 7 who sng LT and s knemaal effes. whee q.7 epesens he foh omponen of: dp q ν 8 dτ n he 4-eo fomlaon. nd whee τ s he pope elas me P he 4- eo momenm he 4-eo elo and ν he eleomagne feld enso. In hs wa we old fomlae he SRT sang fom a mehanal base [4].e.; dε 9 d d nsead of esng he fomaon of SRT o eleomagne base alone. In pape [6] we onne hs mehod fo he ase of haged pale q mong wh elo n he fame S sbje o an ele feld and a magne fl dens. and hen qs. 9 has he fom d ε q q d d In he pesen pape we onne hs mehod o ge qs.4 and 6 begnnng wh q.. The Caesan omponens of qs. n fame S ae q d a q d b q d dε q d d Mlplng qs.abb and q.d b hen sbang we hae:

7 q d d d d d ε The Loen foe eqaons q. desbes he moon of a haged pale q nde he aon of an eleomagne feld epesened b he enso ν whee 34 s he oodnae ssem and s he 4-d elo eo and P P s he 4-d momenm eo. hs 4-d noaon q. has he fom: ν τ q d dp 3 Whee enso ν has he same fom as n q.6.e.; ν 4 s one know ha he oaon eo n he 4-eo fomlaon has he fom: ν ν ν 5 whee 4 ;. nd f he fnon has he fom ; hen he omponen 4 old be wen n ems of qs.4 and5 as 6a followng he same appoah we fnd 4 and 34 as: 6b 6

8 s well as he omponen 3 3 and has he fom: 7a 7b 7 s one sees now ha he qs. 6 and 7 has he same eo fom as q.4.e.; o 8 4- Deaon he Tansfomaon Relaons of and he Loen Tansfomaons We an now fnd he elas ansfomaon of fo-eo as fo he Loen ansfomaon elaons he wll be deed as a esl of mahemaal onsdeaons onl. Theefoe b wng qs.6b and 7 n fame S aodng o he ela pnple.e.; On he hand we hae also fom q.3 : and hene: 9a 9b Mlplng boh q.9b b and q.9a hen addng he boh eqaons we ge

9 ompang he las elaon wh q.6b we hen hae 3 a nd now f we mlpl boh q.9a b and q.9b b hen addng boh eqaons we ge ompang he las elaon wh q.7 we hen hae 3b In a smla wa f we ewe he elaons 6 and 7b n fame S aodng o he ela pnple and akng no aon elaons 3 we ge 3a 3b Mlplng he boh q.3b b and q.3a hen addng he boh eqaons we ge ompang he las elaon wh q.6 we hen hae 3 geneal eqemen n SRT ha an phsal heo shold be wen n 4-d fom.e."elasall naan" and hen eded o 3-d fom. In m papes we sa del fom he phsal laws wen ognall n 3-d fom o ge he same esls who sng he mos mpoan hng n 4-d fom.e. he me enso. Conlson Can we now see how gea he msonepon s? f we ake he oneps [lengh onaon me dlaon a elo omponen fo a geomeal pon] whh ae sed solel o sole he poblem of he oodnaon of eens we ma se hem o ped he dnamal popees of a pale. Caefl eamnaons of nsen's agmen n hs pape [] leae no dob ha LT s ndeed ansfomaons ha desbe he oodnaes of a phoon. The eo was n assmng ha hese ansfomaons desbe he oodnaes of a maeal pale. The LT ae aall ansfomaon of he oodnaes of a geomeal pon and he

10 do no hae he powe o make pedons abo phsal qanes mass eneg momenm.. LT b o alenae mehod s smpl a neal ansfomaon onanng no phsal sgnfane [345 and 6]. Refeenes - nsen. 95. On he leodnams of Mong odes. nn. Phs GOLDN S.. Non-Knema of he dlaon of me elaon of nsen fo me-neals. Z. Na fosh 55a a Hamdan N. 3. bandonng he Ideas of Lengh Conaon and me dlaon. Gallean leodnams b Hamdan N. 4. bandonng The Idea of Relas Lengh Conaon n Relas leodnams. Gallean leodnams Hamdan N. On he Inaane of Mawell s eld qaons nde Loen Tansfomaons. o appea n Gallean leodnams. 5- Hamdan N. 5. Newon s Seond Low s a Relas law who nsen s Rela. Gallean leodnams Jl./g.. 6- Hamdan N. 5. Deaon of he Relas Dopple ffe fom he Loen oe. peon Vol No. Jan.. 7- HJR S. and GHOSH. 5. Collapse of SRTI: Deaon of eleodnams eqaons fom he Mawell feld eqaons. Gallean eleodnams Vol. 6 p: JIMNKO O. D On he pemenal poofs of elas lengh onaon and me dlaon. Z. Na fosh 53a SHOZHIX Mahemaal and phsal nsffenes of he Loen ansfomaon. Hadon J. opgh. - WILHLM Phsal poblemas of nsen's ela heoes. Hadon J mals: nhamdan@los.om nhamdan59@homal.om