Generalization of Galilean Transformation

Transcription

1 enerlizion of lilen Trnsformion Romn Szosek Rzeszów Uniersiy of Tehnology Deprmen of Quniie ehods Rzeszów Polnd Absr: In he rile generlized lilen rnsformion ws deried. Obined rnsformion is he bsis for deelopmen of new physil heory whih ws lled he Speil Theory of Eher. The generlized lilen rnsformion n be epressed by relie speeds 6-7 or by he prmeer 7-8. Bsed on onlusions of he ihelson-orley s nd Kennedy- Thorndike s eperimens he prmeer ws deermined. This llows he rnsformion o ke speil form 8-8 whih is onsisen wih eperimens in whih eloiy of ligh is mesured. On he bsis of obined rnsformion he formuls for summing speed nd relie speed were lso deermined. The enire rile inludes only originl reserh ondued by is uhor. Keywords: kinemis of bodies uniersl frme of referene oordine nd ime rnsformion one-wy speed of ligh summing speed relie speed PACS: 0.90.p 0.0.p. Inroduion The rile eplins resuls of ihelson-orley s [] nd Kennedy-Thorndike s eperimens [] ssuming h here is uniersl frme of referene eher in whih eloiy of ligh hs onsn lue. In moing ineril frme of referene he eloiy of ligh my ry. In he rile rnsformions beween ineril sysems were deried wih nlyil mehod. Deried rnsformion is generlizion of lilen rnsformion beuse she beomes lilen rnsformion in priulr se. Thus i hs been shown h i is no rue h ihelson-orley s nd Kennedy-Thorndike s eperimens proe h here is no uniersl frme of referene nd h eloiy of ligh in uum is onsn. The resoning presened in his rile is bsed on obserion h one-wy speed of ligh hs neer been mesured urely. In ll ure lborory eperimens s in ihelson- orley s nd Kennedy-Thorndike s eperimen he erge eloiy of ligh on losed rjeory h reurns o is sring poin ws only mesured. Therefore ssumpion of onsn eloiy of ligh in uum insnneous eloiy doped in he Speil Theory of Reliiy hs no sri eperimenl jusifiion. In works [6]-[] we he shown h ihelson-orley s nd Kennedy-Thorndike s eperimens n be eplined by he heory wih uniersl frme of referene. In he work [] we he shown h here is infinie number of suh heories. Thus i is no rue h hese eperimens he shown h here is no eher in whih ligh propges.

2 enerlizion of lilen Trnsformion Szosek Romn Deriion presened in his rile is bsed on hese findings i.e. ssumpions h for eh obserer he erge eloiy of ligh moing forh nd bk is onsn nd h here is uniersl frme of referene.. Adoped ssumpions In presened nlysis he following ssumpions were doped: I. There is frme of referene in relion o whih he eloiy of ligh in uum hs he sme lue in eh direion. This uniersl frme of referene is lled eher. II. Aerge eloiy of ligh on he ligh ph forh nd bk is for eery obserer independen from he direion of ligh propgion. This resuls from ihelson-orley s eperimen. III. Aerge eloiy of ligh on he ligh ph forh nd bk does no depend on he obserer s eloiy in relion o uniersl frme of referene. This resuls from Kennedy- Thorndike s eperimen. IV. In perpendiulr direion o he eloiy direion of body in relion o eher is onrion or eension does no our. V. «Ineril sysem ineril sysem» rnsformion is liner. VI. Beween ineril sysems here is symmery of he following form when ineril sysems U nd U moe in relion o uniersl frme of referene long heir es nd whih re prllel o eh oher. d d d 0 d 0 d d d d Assumpion VI indies h in oordine rnsformion he module oeffiien is he sme in primry nd reerse rnsformion oeffiien e in rnsformions 5. Deried rnsformion presened in his rile differs from deriion of Lorenz s rnsformion on whih STR is bsed. In STR in deried Lorenz s rnsformion i is ssumed h reerse rnsformion hs he sme form s he primry rnsformion. This ssumpion is bsed on belief h ll ineril sysems re equilen. In deriion presened in his rile we do no ssume wh form he whole reerse rnsformion kes. We only ssume wh form one reerse rnsformion for hs ssumpion VI. Adoped ssumpions in his rile on he eloiy of ligh re lso weker hn hose doped in STR. The STR ssumes h eloiy of ligh is bsoluely onsn een hough no eperimen hs proed i. In his rile he ssumpion ws mde resuling from eperimens h he erge eloiy of ligh on ph forh nd bk o he mirror is onsn ssumpion II nd III. In presened disserions ligh eloiy is ssumed o be onsn in only one uniersl frme of referene eher ssumpion I. Assumpions IV nd V re idenil o hose on whih STR is bsed. In works [6]-[] n idenil rnsformion ws deried s 8-84 bu in differen wy using he geomeri mehod.. Deried rnsformion beween ineril sysems An im is o deermine oordine nd ime rnsformion beween ineril sysems U nd U Figure. Sysems moe in relion o eh oher prllel o is. The U sysem moes relie o U sysem wih eloiy. The U sysem moes relie o U sysem wih eloiy 0.

3 enerlizion of lilen Trnsformion Szosek Romn Fig.. Two ineril sysems U nd U moe relie o eh oher wih relie speeds nd. enerlizion of lilen rnsformion is o llow he possibiliy h modules of eloiy lue nd n be differen. In onsidered ineril sysems loks re synhronized. Now we re only esblishing h in momen when beginnings of sysems oerlp oordine 0 from U sysem is ne o oordine 0 from U sysem hen loks found hese oordines re rese. Thnks o suh n esblishmen here re no onsn erms in rnsformions nd. Assumpion V gurnees h he Newon s firs lw is pplible in eery ineril frme of referene i.e. if body moes uniformly in one ineril frme of referene hen is moion obsered from noher ineril frme of referene will lso be uniform. This mens h oordine nd ime rnsformion beween ineril sysems U nd U hs form of e b g Coeffiien > 0 s in no sysem he ime nno flow bkwrds. Now we will wrie he reerse rnsformion. If in U sysem he ime flows quiker hus in U sysem i is slower. Therefore in reerse rnsformion he oeffiien mus be repled by. Similrly if in one sysem lengh onrion ours in he seond is n eension. Hene in he reerse rnsformion i is neessry o reple oeffiien g by g. This mehod o deermine lues of wo oeffiiens in reerse rnsformion on nd g we ll he nurl wy of deermining oeffiiens in he reerse rnsformion. There re no ssumpions for oeffiien b' nd herefore in he reerse rnsformion ny oeffiien b" ws eped. The reerse rnsformion hs form of b e g If he eloiy of U sysem relie o U is posiie he eloiy of U sysem relie o U is negie. Hene oeffiiens e' nd e" re opposie signs. Assumpion VI regrds lues of hese oeffiiens. I is possible o lule differenils ppering in his ssumpion from nd. They he form of i.e d d e d gd e g 4 d d e d d e 5 g d g d U U d d d d

4 Due o ssumpion VI we obin enerlizion of lilen Trnsformion Szosek Romn d d d d d 0 e 6 d d 0 e 7 d e e e 8 Pling from he reerse rnsformion o rnsformion we will obin e b b e b g e b be b g g e eg b e g Sine formul 9 should be rel for ll he equions mus be fulfilled 9 b e 0 b b g e eg b e As from he ssumpion sysems moe in relion o eh oher hus e 0. On his bsis from 0 resuls h b' 0. By nlogy from resuls h b" 0. From resuls Serhed rnsformions n be wrien in form of e g 4 e We will deermine he differenils from hese rnsformions d d d ed d d d d ed d On he bsis of hese differenils i is possible o deermine relie eloiies of U nd U sysems. If we onsider ny poin wih fied oordinion in U sysem hen from he firs rnsformion 6 we obin eloiy of U sysem in relion o U sysem d d 5 6 ed d d e d e 0 7 d d d If we will onsider ny poin wih fied oordinion in U sysem hen he seond rnsformion 6 we obin eloiy of of U sysem in relion o U sysem 4

5 d d enerlizion of lilen Trnsformion Szosek Romn d ed d d 0 e e 8 d d d We diide he equion 8 by equion 7 nd we will obin 9 From he relion 9 nd on he bsis of 7 nd 8 i is possible o deermine unknown oeffiiens e 0 e Sine eloiy of nd he differen signs nd herefore i is possible o show h relions nd re equilen below in ± hrer is ppers when < 0 while hrer ppers when > 0 e ± ± ± If we muliply nd we will obin nd hus he sme s from we will obin ± ± e e 4 e 5 e Coeffiien e my he differen sign. From resuls h oeffiien e > 0 when eloiy > 0 while e < 0 when eloiy < 0. On he bsis of 0 nd rnsformions 5 n be epressed from relie speeds nd n be wrien in form of 6 5

6 enerlizion of lilen Trnsformion Szosek Romn 7 We he obined ompleely symmeril rnsformions. In rnsformion 6 we my jus oner indees ino nd ino in order o obin rnsformion 7. This is despie he f h pprenly non-symmery ws inrodued in deried rnsformion formul nd. Assumpion V nd VI ws enough o obin rnsformion 6-7 s well s nurl wy of deermining he lue of oeffiiens in reerse rnsformion. Trnsformion 6-7 is generlized lilen rnsformion epressed from relie speeds. If ours for U nd U sysems hen hese rnsformions me down o lilen rnsformion. From ime rnsformion 6-7 resuls h if in some ineril sysem he lok indies ime 0 hen in eery ineril sysem he lok found by his lok lso indies ime 0. This mens h loks in ineril sysems re synhronized wih he eernl mehod proposed in he rile []. I resuls h his mehod of lok synhronizion is onsequene of ssumpions on he bsis of whih he rnsformion 6-7 ws deried foundions V nd VI nd he nurl mehod of deermining lues of oeffiiens in reerse rnsformion. Synhronizion of loks wih he eernl mehod onsiss in seing ll loks on he bsis of loks indiions of one disinguished ineril sysem le i be U sysem. Cloks in U sysem re rese when beginnings of U nd U sysems oerlp. If he lok of U sysem indies ime 0 hen lok ne o i of U sysem is lso rese i.e. 0. This wy of loks synhronizion enbles o synhronize loks in ll ineril sysems if here is possibiliy o synhronize loks in some firs ineril sysem. A his sge we do no resole how he synhronized loks in U sysem he been synhronized. The problem of loks synhronizion in he firs sysem will be soled in Chper Implemenion of uniersl frme of referene To rnsformion 6 nd 7 we will implemen uniersl frme of referene eher. By were indied eloiies of U nd U sysem relie o uniersl frme of referene bsolue speeds. Sine here is uniersl frme of referene eery moemen in he spe n be desribed by bsolue speeds in relion o h sysem. Therefore relie speeds nd depend epliily on bsolue speeds. We ssume h funion F ombines relie speeds of sysems nd heir bsolue speeds in he following wy of F F From equions 8 fer muliplying hem by sides resuls h funion F hs form Triil soluions of his funionl equion re 8 F 9 F F 0 6

7 enerlizion of lilen Trnsformion Szosek Romn 7 nd F The firs of hese soluions gies lilen rnsformion. The seond leds o onrdiion. Nonriil soluion of his funionl equion is funion F in form of F F We ssume h for our needs funion F is suffiien wih diided ribles hen i is possible o wrie i wih quoien of erin funions nd N N N N F From he equion resuls h N. Now i n be wrien in form of 0 0 F 4 Funion his sge is unknown. Bsed on 4 i is known o be dimensionless. Wihou loss of generliy i n be ssumed h i is posiie funion nd in zero ssumes lue one beuse On he bsis of 8 nd 4 we will obin 6 On his bsis rnsformion 6-7 n be wrien in he form epressed from prmeer 7 8

8 enerlizion of lilen Trnsformion Szosek Romn This rnsformion form required one ddiionl ssumpion in relion o ssumpions on whih rnsformions 6 nd 7 re bsed. This is ssumpion on he eisene of uniersl frme of referene. * * * If hen here is full symmery for he obserer reled o eher beween U nd U sysems. If he spe is supposed o be isoropi i.e. ll direions in eher re supposed o be equilen hen mus our. On he bsis of 7 nd 8 we will obin On his bsis we will obin noher fer 5 uniersl propery of funion 4 5. Designion of funion bsed on ihelson-orley s eperimen Funion ws deermined in subseion ssuming h resuls of ihelson-orley s nd Kennedy-Thorndike s eperimens re fulfilled. Eperimens show h mesured erge eloiy of ligh śr on he ph forh nd bk is onsn in eh ineril frme of referene U' nd is he sme in eh direion ssumpion II nd III. We ssume h in U sysem i.e. eher he eloiy of ligh is onsn in eh direion ssumpion I. y' D' U' śr ' śr ' D' ' y D' U - eher b S S D D' L L Fig.. Ligh flow phs in wo sysems moing relie o eh oher: ineril sysem U' he flow prllel o is ' nd y' b ligh flows seen from U sysem eher. 8

9 enerlizion of lilen Trnsformion Szosek Romn From ssumpion II nd III resuls h erge eloiy of ligh śr in ineril frme of referene is he sme s eloiy of ligh in eher. I will be suffiien o noie h ligh signl hs he sme erge eloiy of ligh śr in U' sysem when U' sysem does no moe in relion o U sysem i.e. 0. Sine hen eloiy of ligh śr is ely he sme s eloiy nd herefore for eh eloiy ours śr. Phs of ligh flow re shown in Figure. U sysem lies in eher while U' sysem moes in relion o eher onsn eloiy. Aes nd ' lie on one srigh. Disne D' whih is perpendiulr o eloiy is he sme from poin of iew of boh frmes of referene ssumpion IV. Therefore on Figure is he sme lengh D' in pr nd prs b. In U' sysem he mesured erge eloiy is onsn in eh direion whih n be wrien in form of Similr dependenies n be wrien for U sysem eher D D D śr 4 D L L 4 If for rnsformion 7 he following new deerminions will be doped: U U' nd U U eher hen ording o 0 0 Then ime rnsformion 7 will ke he form of On he bsis of equion 4 nd equion 4 we will obin he relion of D D Afer reduion by nd pplying deermined ime rnsformion 45 we will obin 46 i.e. D D 47 D D

10 enerlizion of lilen Trnsformion Szosek Romn D D 49 D 50 D 5 On he bsis of 4 we will obin 5 D 5 Finlly funion for whih he rnsformion mees ondiions of ihelson-orley s eperimen kes he form of 54 Trnsformions 7 nd 8 wih funion 54 required ddiionl ssumpions I II III nd IV. By inroduing ino he heory of uniersl frme of referene in whih one-wy speed of ligh is onsn i is possible o sole menioned boe problem of loks synhronizion. In uniersl frme of referene he loks n be synhronized by mens of ligh inernl mehod. I will be sysem o whih loks in ll ineril sysems eernl mehod will be synhronized. 6. Summing speed nd relie speed Le us onsider siuion presened in Figure. All onsidered eloiies re prllel o eh oher U U U Fig.. Ineril sysems U U U moing relie o eher wih eloiies. On he bsis of 7 nd 8 rnsformions from U sysem o U sysem nd from U sysem o U sysem will he form of 0

11 enerlizion of lilen Trnsformion Szosek Romn 55 Combining hese wo rnsformions by puing from he seond o he firs one we will obin rnsformion from U sysem o U sysem 56 Afer reduion we will obin 57 Trnsformion from U sysem o U sysem n lso be obined direly from 8 58 Combined rnsformion presened in 57 mus he he sme form s rnsformion 58. Hene we will obin 59 Afer reduion he equion kes he form of 60 On his bsis we obin he formul for summing prllel relie speeds 6 An nlogous equion s 60 n be wrien beween oher sysems by hnging indees in 60. For hree sysems here re si suh equions. For emple fer repling indees nd we will obin 6

12 enerlizion of lilen Trnsformion Szosek Romn If we will ssume h U sysem is eher uniersl frme of referene hen eloiy 0. On his bsis we he nd 0. From equions 60 nd 6 we will obin equions Afer onersion we will obin relions Afer king ino oun 54 formuls 6 for summing prllel speeds ke he form of Afer king ino oun 54 formuls 64 for relie speeds ke he form of * * * In he nlogous wy i is possible o pu rnsformions beween sysems epressed wih relie speeds 6 nd 7. Trnsformions from U sysem o U sysem nd from U sysem o U sysem he form of king hese rnsformions by puing from he seond o he firs one we will obin rnsformion from U sysem o U sysem On his bsis we will obin

13 enerlizion of lilen Trnsformion Szosek Romn Trnsformion from U sysem o U sysem n lso be obined direly from 7 Puing rnsformion presened in 69 mus he he sme form s rnsformion 70. Hene we will obin From he relion 7 nd 7 fer inresing o squre n idenil equion is obined From he relion 7 fer onersion we will obin From he equion 74 i is known h for is equl hene i.e Using 74 we will obin he formul for summing relie speeds 0 78 On he bsis of 6 nd 54 we will obin Now he formul 78 for summing relie speeds hs form of 79

14 enerlizion of lilen Trnsformion Szosek Romn Trnsformion epressed from bsolue speed On he bsis of 54 nd 66 rnsformion 7-8 n be epressed from bsolue speed nd. Then generl form 6-7 nd 7-8 is los bu we will obin is speil form whih is onsisen wih eperimens in whih he eloiy of ligh ws mesured Trnsformion beween eher nd ineril sysem We dop he following deerminions: U U' nd U U eher. Then relions our 44. We lso dop he following deerminions: ' nd '. Wih suh deerminions on he bsis of 8 nd 8 we obin rnsformions from he ineril sysem U' o eher U nd eher U o ineril sysem U' in form of 8 84 This rnsformion is idenil s rnsformion deried in works [6]-[] in whih i ws deried wih oher mehod bsed on geomeril nlysis of ihelson-orley s nd Kennedy- Thorndike s eperimen. In monogrph [6] on he bsis of his rnsformion new heory of kinemis nd dynmis of bodies ws deried lled he Speil Theory of Eher. Trnsformion 8-84 ws lso deried bu wih oher mehod in riles [] nd []. In work [] he uhor obined his rnsformion from Lorenz s rnsformion hnks o loks synhronizion in ineril sysems wih he eernl mehod. The rnsformion obined in work [] is differenly wrien Lorenz s rnsformion fer he hnge of he wy of mesuring ime in he ineril frme of referene nd herefore he uhors he ssigned i he properies of

15 enerlizion of lilen Trnsformion Szosek Romn Lorenz s rnsformion. Trnsformion deried in his rile hs differen physil mening hn Lorenz s rnsformion beuse ording o he heory presened here i is possible o deermine he eloiy in relion o uniersl frme of referene by mens of lol mesuremen. This mens h uniersl frme of referene is rel nd is no n rbirrily hosen ineril sysem. 9. One-wy speed of ligh In works [6] [0] nd [] bsed on rnsformion 8-84 formul for one-wy speed of ligh in uum ws deried whih is mesured by he obserer from ineril frme of referene α 85 osα In he work [6] formul for one-wy speed of ligh in he meril medium s ws deried whih is mesured by he obserer from ineril frme of referene s s α 86 osα In hese wo relions ngle α' mesured by he obserer is n ngle beween eor of is eloiy in relion o eher nd eor of he eloiy of ligh. The eloiy s is eloiy of ligh in he moionless meril medium in relion o eher seen by moionless obserer in relion o eher. Alhough he eloiy of ligh epressed by formul 86 depends on ngle α' nd eloiy he erge eloiy of ligh on he ph forh nd bk o he mirror is lwys onsn. I is suffiien o erify h for he eloiy of ligh epressed by formul 86 he erge eloiy on ph L forh nd bk o he mirror is s follows s L L sr 87 α L L s s πα s s osα os π α s s sr s s osα osα From he relion 88 resuls h s is lso n erge eloiy of ligh on he ph forh nd bk o he mirror in he moionless meril medium relie o he obserer. 0. Conlusions Deermined rnsformions 8-8 nd 8-84 re onsisen wih ihelson-orley s nd Kennedy-Thorndike s eperimen. I resuls from boe rnsformions h mesuremen of he eloiy of ligh in uum wih so fr used mehods will lwys gie n erge lue equl o. This is despie he f h for moing obserer he eloiy of ligh hs differen lues in differen direions. The erge eloiy of ligh is lwys onsn nd independen from he eloiy of n ineril frme of referene. Beuse of his propery he eloiy of ligh ihelson- orley s nd Kennedy-Thorndike s eperimens ould no dee eher. The nlysis shows h i is possible o eplin he resuls of ihelson-orley s eperimen on he bsis of eher. A semen is flse h ihelson-orley s eperimen hs s s s s

16 enerlizion of lilen Trnsformion Szosek Romn shown h eloiy of ligh is bsoluely onsn. I is lso flse h ihelson-orley s eperimen hs proed h here is no eher in whih ligh propges nd moes onsn eloiy. Assumpion h eloiy of ligh n depend on he direion of is emission does no disinguish ny direion in spe. I is bou he eloiy of ligh mesured by moing obserer. I is eloiy whih he obserer moes in relion o uniersl frme of referene eher h disinguishes in spe he hrerisi direion bu only for his obserer. For moionless obserer in relion o uniersl frme of referene he eloiy of ligh is lwys onsn nd does no depend on he direion of is emission. If he obserer moes in relion o uniersl frme of referene hen he spe for obserer is no symmeril. In his se i will be like for n obserer siling on wer nd mesuring he eloiy of we on he wer. Despie he f h he we propges onsn eloiy in eh direion for siling obserer he we eloiy will ry in differen direions. Currenly i is belieed h STR is he only heory h eplins he ihelson-orley s nd Kennedy-Thorndike s eperimens. This rile shows h oher heories re possible ording o hese eperimens. In works [6] nd [] bsed on deermined here rnsformion he new physil heory of kinemis nd dynmis of bodies ws deried lled by uhors he Speil Theory of Eher. The work [] shows h here is infinie number of heories wih eher h orrely eplin ihelson-orley s nd Kennedy-Thorndike s eperimens. Een he heory wih eher is possible in whih ime is bsolue. In he work [6] i is shown h wihin eh suh kinemis n infinie number of dynmis n be deried. In order o derie dynmis i is neessry o dop n ddiionl ssumpion whih enbles o inrodue he onep of mss kinei energy nd momenum in he heory. Prediions of he Speil Theory of Eher nd Speil Theory of Reliiy re ery similr. Howeer here re differenes whih my llow for eperimenl flsifiion of hese heories in he fuure. In STR ll ineril sysems re equilen i.e. here is no uniersl frme of referene. For his reson ording o STR i is no possible o mesure bsolue speed using lol mesuremen. This mens h for eh obserer he spe is ompleely isoropi he sme properies in eh direion. Howeer ording o STE he obserer n use lol mesuremens i.e. when is ompleely isoled from he enironmen o deermine he direion of is moemen in relion o eher. This mens h for obserers moing in relion o eher he spe is no isoropi hs differen properies in differen direions. This is he mos imporn differene beween he Speil Theory of Eher nd Speil Theory of Reliiy. Confirmion of his by eperimen is no esy due o he low speed of he Solr Sysem relie o eher. For smll eloiy he effes of non-isoropi spe re ery sligh. On he bsis of presened kinemis i is possible in nurl wy o eplin he nisoropy of osmi mirowe bkground whih in deil is disussed in he rile [5]. This enbles o deermine he eloiy whih he Solr Sysem moes in relion o uniersl frme of referene i.e. 69 kms 000. This ws presens in works [8] [9] nd []. ihelson-orley s nd Kennedy-Thorndike s eperimens were ondued repeedly by differen ems. odified nd improed ersions of his eperimen were lso rried ou suh s eperimen wih spphire rysls in 05 [4]. Eh of hese eperimens only onfirmed h he erge eloiy of ligh is onsn. Therefore ssumpions on whih presened deriions re bsed re jusified eperimenlly. Bibliogrphy [] Kennedy Roy J. Thorndike Edwrd Eperimenl Esblishmen of he Reliiy of Time Physil Reiew

17 enerlizion of lilen Trnsformion Szosek Romn [] nsouri Rez Sel Romn U. A Tes Theory of Speil Reliiy: I. Simulneiy nd Clok Synhronizion enerl Reliiy nd riion Vol. 8 No [] ihelson Alber A. orley Edwrd W. On he relie moion of he erh nd he luminiferous eher Am. J. Si [4] Ngel oriz Prker Sephen R. Kolhuk Egeny V. Snwi Pul L. Hrne John. Ino Eugene N. Peers Ahim Tobr ihel E. Dire erresril es of Lorenz symmery in elerodynmis o 0-8 Nure Communiions 6 Arile number: [5] Smoo eorge F. Nobel Leure: Cosmi mirowe bkground rdiion nisoropies: Their disoery nd uilizion in English. Reiews of odern Physis Volume Смут Джордж Ф. Анизотропия реликтового излучения: открытие и научное значение in Russin Успехи Физических Наук Том Smoo eorge F. Anizoropie kosmiznego mikroflowego promieniowni ł: ih odkryie i wykorzysnie in Polish. Posępy Fizyki Tom 59 Zeszy [6] Szosek Krol Szosek Romn Szzególn Teori Eeru in Polish Wydwniwo Ameli Rzeszów 05 ISBN Szosek Krol Szosek Romn Speil Theory of Eher in English Publishing house AELIA Rzeszow 05 ISBN [7] Szosek Krol Szosek Romn The eomeri Deriion of he Trnsformion of Time nd Posiion Coordines in STE IOSR Journl of Applied Physis IOSR-JAP Volume 8 Issue 4 Version III ISSN [8] Szosek Krol Szosek Romn Выделенная в космологии система отсчета и возможная модификация преобразований Лоренца in Russin: The preferenil referene sysem in osmology nd he possible modifiion of Lorenz rnsformion. Ученые Записки Физического Факультета МГУ emoirs of he Fuly of Physis Lomonoso osow Se Uniersiy ISSN [9] Szosek Krol Szosek Romn The Eplnion of he ihelson-orley Eperimen Resuls by ens Uniersl Frme of Referene Journl of odern Physis Vol. 8 No ISSN [0] Szosek Krol Szosek Romn Deriion of Trnsformion nd One-Wy Speed of Ligh in Kinemis of Speil Theory of Eher Amerin Journl of odern Physis Volume 6 Issue ISSN: [] Szosek Krol Szosek Romn Kinemis in Speil Theory of Eher in English osow Uniersiy Physis Bullein in prin fer posiie reiews. Szosek Krol Szosek Romn Кинематика в Cпециальной Tеории Эфира in Russin Вестник Московского Университета. Серия. Физика и Астрономия in prin fer posiie reiews. [] Szosek Krol Szosek Romn The deriion of he generl form of kinemis wih he uniersl referene sysem Resuls in Physis Volume ISSN: [] Tngherlini Frnk R. The Veloiy of Ligh in Uniformly oing Frme The Abrhm Zelmno Journl Vol. 009 ISSN reprin: A Disserion Snford Uniersiy