The Change of the Distances between the Wave Fronts

Transcription

1 Joural of Physical Mahemaics IN: 9-9 Research Aricle Aricle Joural of Physical Mahemaics Geadiy ad iali, J Phys Mah 7, 8: DOI: 47/9-97 OMI Ope Ieraioal Access Opical Fizeau Experime wih Movig Waer is Explaied wihou Fresel's Hypohesis ad oradics pecial Relaiviy Geadiy * ad iali Idepede Researcher, verdlovsk Oblas, Yekaeriburg, 66, Russia Absrac Fizeau experime acually proves o parial, as he special relaiviy assers, bu complee draggig of he ligh by movig medium he decrease of he frige shif i he Fizeau's wo-beam ierferomeer is explaied o wih wrog Fresel's aeher drag hypohesis bu wih he phase deviaios arisig i he ierferig beams because of Doppler shif of he frequecies Fizeau experime does o prove bu, o he corary, refues Eisei's heory of relaiviy Keywords: Fresel; Doppler; Ierferomeer Iroducio years ago, Fresel, ryig o explai resuls of he opical Arago's experimes by he aeher wave hypohesis, suggesed ha a movig a speed medium drags he ligh oly parially ad he speed of he ligh chages by drag coefficie o es his hypohesis, i 85 Fizeau carried ou ierferece experime wih movig waer A he speed of he waer 7,59 m/s, he legh of pipe L974 m, he legh of ligh wave o 56-9 m ad refracio idex 33, He expeced o receive he frige shif 4799 i he case if he ligh was compleely draggig by movig waer However, he shif i he experime was less ad equal o 3, ha is i differed almos by 4346 [,] Alhough ha ime Doppler has already showed ha he ligh chages is frequecy whe eers movig medium, Fizeau did o ried o explai ha resul somehow differely ad decided ha he cofirmed Fresel's aeher drag hypohesis abou parial draggig of he ligh by movig medium I 886 Michelso ad Morley repeaed Fizeau experime ad wih higher accuracy cofirmed he decrease of he frige shif i movig medium akig io accou he dispersio of he medium, Lorez derived a formula for he drag coefficie o cofirm his formula, Zeema i experimes wih movig waer ad Harres i he experime wih he liearly movig quarz cylider deermied drag coefficies for he red ad gree ligh However, as we kow, i he calculaio of he ierferomeer wih movig waer, obody ivesigaed ad obody cosidered he chage of he he frequecies ad he phase deviaios, arisig i ierferig beams whe hey eer io movig waer [3] he erroeous explaaio of Fizeau's experime, a sigifica role of which i he creaio of he special relaiviy was repeaedly emphasized by Eisei, is sill cosidered as oe of he mos impora cofirmaio of he special relaiviy [] As show below, he beams i Fizeau ierferomeer ravel a speeds + ad ha is complee bu o parial draggig akes place he frige shif is less ha 4799 o because of Fresel's hypohesis abou parial draggig bu because of phase deviaios arisig i ierferig beams i movig waer ad herefore Fizeau experime does o cofirm bu, o he corary, disproves special relaiviy he oveioal alculaio of he Fizeau Ierferomeer I Fizeau ierferomeer, he beam ravels i direcio of movig waer ad he beam ravels oward movig waer Isead real scheme of Fizeau ierferomeer i which he beams ravel i he same pipe ad pass he same disace L i opposie direcios, we cosider more simple equivale scheme explaied i Figure, where he beams ad pass ideical disaces i wo pipes i which waer moves a speed i opposie direcios Jus as i he experime Fizeau, phoos exi from movig waer a he same disace from he scree, as i immovable waer A he mome, he phoos of he frequecy ν wih ideical iiial phase equal o zero simulaeously eer i boh pipes If waer is a res, phoos ravel wih ideical frequecy ν ad speed, pass he disaces L for ideical ime L ad ierferece friges are i iiial posiio e-8 Whe waer moves a speed, he speeds of he phoos ad heir frequecies chage v v I he beam, phoos move a speed v v + - relaive o waer ad a Figure : Moveme of phoos a / relaive speed *orrespodig auhor: Geadiy, Idepede Researcher, verdlovsk oblas, Yekaeriburg, 66, Russia, el: ; sokolovg@yahoocom, viali@sokolovrealycom Received July 4, 6; Acceped December 3, 6; Published Jaaury 5, 7 iaio: Geadiy, iali (7) Opical Fizeau Experime wih Movig Waer is Explaied wihou Fresel's Hypohesis ad oradics pecial Relaiviy J Phys Mah 8: 7 doi: 47/9-97 opyrigh: 7 Geadiy e al his is a ope-access aricle disribued uder he erms of he reaive ommos Aribuio Licese, which permis uresriced use, disribuio, ad reproducio i ay medium, provided he origial auhor ad source are credied J Phys Mah, a ope access joural IN: 9-9 olume 8 Issue 7

2 iaio: Geadiy, iali (7) Opical Fizeau Experime wih Movig Waer is Explaied wihou Fresel's Hypohesis ad oradics pecial Relaiviy J Phys Mah 8: 7 doi: 47/9-97 Page of 5 + relaive o pipe hey pass he disace L for he ime L less ha +, e-8 For he ime, every phoo passes relaive o waer he disace L L less ha L + L I he beam, phoos move a speed relaive o waer ad a relaive o pipe hey pass he disace L for he ime L more ha e-8 For he ime every phoo passes relaive o waer he disace L L more ha L L Phoos of he beam come o he scree earlier ha phoos of he beam ad he friges shif i ierferomeer I usual wo-beam ierferomeers, he ierferig beams pass he disaces wih ideical frequecy ν ad he frige shif is deermied simply by he differece of he imes : - ( ) L L L () + + If L974 m, m/s, 7,59 m/s, 56-9 m ad 33, he expressio () gives a value of he frige shif uch frige shif, accordig o he Fizeau, should be i his ierferomeer Bu i experime he frige shif was less ha 47 ad equal o 3 he hage of he Frequecies i Movig Waer I Fizeau ierferomeer, he ligh is compleely dragged by movig waer Bu because he beams eer he movig waer from immovable ligh source, i accordace wih Doppler effec, heir frequecies chage ad a observer movig ogeher wih waer will see differe frequecy Addiioal phase deviaios arise i ierferig beams Because of hese deviaios, he resulig frige shif i he ierferomeer wih movig waer cao be deermied by he expressio () ad is less ha 47Phoos of he beam eerig movig waer wih a speed chage he frequecy from ν o ν ν ad wih speed ad frequecy ν <ν pass relaive o waer he disace L A he mome hey exi from movig waer chagig he frequecy from ν o ν ν + ν + ν Phoos ravel i air o he scree wih he speed ad frequecy ν ν ad ierfere wih phoos of he beam Phoos of he beam eerig movig waer chage he frequecy from ν o ν ν + ad wih speed relaive o waer ad frequecy ν >ν pass he disace L A he mome hey exi from movig waer chagig heir frequecy from ν o ν ν ν + ν I he air phoos ravel o he scree wih he speed ad frequecy ν ν ad ierfere wih phoos of he beam he hage of he Disaces bewee he Wave Fros Besides he fac ha phoos chage heir frequecy i movig waer, he disaces bewee he wave fros chage oo, which leads o a addiioal chage of resula frige shif Whe phoos eer he pipe wih immovable waer Figure a, hey do o chage frequecy ad ravel wih frequecy ν ad wavelegh Phoos also do o chage frequecy if o suppose ha he source moves i ierferomeer ogeher wih waer (Figure b) Movig wih waer, he observer will see he same frequecy ν ad wavelegh I he case whe he source is a res relaive o pipe Figure c frequecies of he phoos chage bu he same ime he disaces bewee he wave fros chage oo Movig wih waer, he observer will see ha he beam chages i waer o oly is frequecy bu, depedig o he direcio of waer moveme, i "sreches" or "coracs" I all siuaios, phoos ravel relaive waer a speed ad for he ime each wave fro passes he disace i waer I ν a) b) c) Figure : Illusraig he Moveme of Phoos a a ravel speed + J Phys Mah, a ope access joural IN: 9-9 olume 8 Issue 7

3 iaio: Geadiy, iali (7) Opical Fizeau Experime wih Movig Waer is Explaied wihou Fresel's Hypohesis ad oradics pecial Relaiviy J Phys Mah 8: 7 doi: 47/9-97 Page 3 of 5 boh pipes wih movig waer as show i Figure b ad c, phoos are dragged compleely ad ravel a speed + For each period, hey are ahead a ideical disaces relaive o phoos i pipe wih immovable waer I he pipe Figure b where he source moves ogeher wih waer, phoos ravel wih frequecy ν ad he disaces bewee he wave fros are equal o wavelegh I he pipe Figure c phoos chage frequecy ad ravel i waer wih frequecy ν less ha ν For he ime, each wavefro passes relaive o waer he disace Because waer moves a speed, a he mome, whe ex wave fro eers waer, previous wavefro is a he same disace + as he wave fro i Figure b hough phoos ravel wih frequecy ν, he disace bewee he wave fros is + bu o + he disaces are he same as i Figure b where phoos ravel wih frequecy ν As show below, because of he srechig or coracio addiioal phase shif arises ad resulig frige shif i ierferomeer chages Addiioal Frige hifs Imagie ha i he Fizeau ierferomeer, as well as i Figure, here is a addiioal pipe wih immovable waer, ad cosider propagaio of phoos i he pipes ad he iroducio of addiioal pipe simplifies aalysis of he ierferomeer, as i allows o cosider he moio of phoos i each pipe separaely, comparig he posiios of he phoos i he pipe wih movig waer wih posiios of he phoos i he pipe wih immovable waer I usual wo-beam ierferomeer, sychroous phoos pass differe disaces wih he same speed or he same disace wih differe speeds ad herefore he frige shif arises ice sychroous phoos ravel wih he same frequecy ad come o he scree wih he same phase, he frige shif ca be deermied by he differece ad is I ierferomeer wih movig waer, because wave leghs ad disaces bewee wavefros chage, he frige shif chage ad is less ha he decrease of he frige shif because of he waveleghs chage I Fizeau ierferomeer, he beam ad ravel wih frequecies ν ν ad ν ν + ad wih differe waveleghs Durig he ime while he beams ravel i waer, a phase deviaio arises ad because of i he frige shif decreases I Figure 3, for example beam, i is show he phase shif i he case whe phoos ravel wih differe frequecies ν ad ν ad differe waveleghs ad i pipes wih immovable waer codiioally pipes are show i dashed lies) For oe period phoos ν ν of he same phase as phoos ν are behid a disace i waer Phoos ravel i v v Figure 3: phase shif of phoos ravelig wih he differe frequecies boh pipes wih ideical speed o he mome whe hey pass relaive waer he same disace L ad a he same ime exi from waer, bewee phoos of ideical phase he shif N accumulaes, L ( ) where N is he umber of oscillaios i phoos + ν for he ime ha is, a he mome whe sychroous phoos exi from waer, phoo ν equivale o phoo ν is behid i waer a disace N I Fizeau ierferomeer, phoos ν also eer i imagiary pipe wih immovable waer Whe waer i he pipe is a res, phoos exi from boh pipes wih ideical frequecy ν ad creae ierferece friges Whe he waer moves a speed ad phoos ravel wih frequecy ν i pipe, he frige shif is measured relaive o hese friges Ierferomeer works wih frequecy ν I does o kow ha frequecy chages i movig waer ad reacs wih equivale phoo ν which is behid i waer a N Durig he ime N while equivale phoo passes i waer he disace N, sychroous phoos exi from addiioal pipe ad pass i air he disace N Durig he ime, шierferece friges shif by: N () he friges shif i ierferomeer as if phoos pass he disace L a a speed less ha he icrease of he frige shif because of he periods oscillaios chage I Figure 4, also for example beam, a moveme of he phoos ν i pipe is compared wih he moveme of he phoos ν i pipe wih immovable waer A he same ime as he frige shif decreases by N, i icreases by because he disaces bewee wave fros ν chage ad become less ha wavelegh Phoos eer boh pipes wih ideical phase which we assume o be zero I pipe wih immovable waer, durig he ime phoos pass he disace equal o wavelegh ad heir phase chages by π ha is, wave fros, whose phases differ by π ravel a a disace from oe aoher which is equal o wavelegh I pipe phoos ravel a speed +, frequecy ν ν ad period of oscillaios > Durig he ime hey pass he disace J Phys Mah, a ope access joural IN: 9-9 olume 8 Issue 7

4 iaio: Geadiy, iali (7) Opical Fizeau Experime wih Movig Waer is Explaied wihou Fresel's Hypohesis ad oradics pecial Relaiviy J Phys Mah 8: 7 doi: 47/9-97 Page 4 of 5 + bu disace bewee wave fros is less ha heir wavelegh o he mome whe firs wavefro has o ye passed relaive o waer he disace ad is a disace + from he erace i he pipe, ex wavefro already eers he waer he frequecy wih which wave fros, wih phases π,4π ad so o, ravel i waer, is deermied by he clock frequecy ν ad herefore he disaces bewee wave fros are less ha heir wavelegh Each wave fro eers i movig waer o a he mome bu by ( ) earlier ha is i isaly shifs relaive o waer forward a disace + ( ) Relaive o waer, each wave fro passes durig he ime he disace which is by + ( ) less ha Durig he ime, N oscillaios occur i he phoos of he beam Each wave fro passes relaive o waer he disace which is by N + ( ) less ha he disace L which is passed by phoos i addiioal pipe wih immovable waer show i Figure 5 hus, for he ime while phoos i addiioal pipe pass he disace, phoos exiig from pipe pass i he air he disace ad are ahead a(-) ha is, because of decrease of he disace passed i waer by wave fros of he beam, ierferece friges addiioally shif ahead by N ( ) ( ) + ( ) (3) Resulig frige shif i Fizeau ierferomeer he frige shif i Fizeau ierferomeer wih movig waer is deermied by hree compoes: ( ) - he frige shif because of ime differece, N - he frige shif because of chage of he waveleghs, v v v v " L ( ) Figure 5: Illusraio of phoos i he addiioal pipe wih fixed waer - he frige shif because of chage of he periods he same as above, we cosider separaely he movemes of he phoos i pipes ad comparig hem wih he moveme of he phoos i pipe wih immovable waer ad deermie he frige shifs + arisig i he ierferig beams ad Propagaio of he Phoos of he Beam ad he Frige hif a) Phoos of he beam are compleely dragged by movig waer, ravel a speed + ad come o he exi from waer a L L L he mome by earlier ha i + addiioal pipe e-8 s Because of ime differece he frige shif has o arise: Ñ L b) Phoos of he beam ravel i movig waer wih frequecy ν ν ad wih wavelegh + + by ( ) more ha wavelegh i immovable waer Durig each period equivale phoos ν are behid from phoos ν by o he ( ) L ( ) mome he delay N N accumulaes where - + he umber of he oscillaios i phoos ν durig he ime L (4) v v + s e-9 m e-9 m e-9 m N ( ) + Figure 4: ompariso of Differe moveme of he phoos s N e-9 m While equivale phoos pass he disace N i waer, phoos ν from addiioal pipe pass i he air he disace N N ad he frige shif arises Because of, resulig frige J Phys Mah, a ope access joural IN: 9-9 olume 8 Issue 7

5 iaio: Geadiy, iali (7) Opical Fizeau Experime wih Movig Waer is Explaied wihou Fresel's Hypohesis ad oradics pecial Relaiviy J Phys Mah 8: 7 doi: 47/9-97 Page 5 of 5 shif decreases as if phoos of he beam ravel relaive o waer wih he speed less ha c) Durig each period, wave fro ν isaly shifs relaive o movig waer a disace + ( ) Durig he ime he shif N + ( ) accumulaes ad, because of his shif, wave fros ν are ahead by ( ) relaive o he wave fros ravelig i pipe wih immovable waer Addiioal frige shif arises: ( ) (5) e-6 m hus, phoos of he beam are compleely dragged by movig waer ad ierferece friges shif by Propagaio of he Phoos of he Beam ad he Frige hif a) Phoos of he beam are compleely dragged by movig waer, ravel a speed ad come o he exi from waer a he L L L mome by earlier ha i addiioal pipe e-8 s Because of ime differece ierferece friges have o shif by Ñ L b) Phoos of he beam ravel i movig waer wih frequecy ν ν + ad wih wavelegh by less ha + ( + ) wavelegh i immovable waer Durig each period equivale phoos ν are ahead before phoos ν by o he ( + ) L ( + ) mome he advace N accumulaes where N While equivale phoos pass he disace i waer, phoos ν from addiioal pipe pass i he air he disace N ad he N frige shif arises Because of, resulig frige shif decreases as if phoos of he beam ravel relaive o waer wih he speed more ha c) Durig each period, wave fro ν isaly shifs relaive o movig waer a disace ( ) Durig he ime he shif N ( ) accumulaes ad, because of his shif, wave fros ν are behid i he air by ( ) relaive o he wave fros ravelig i pipe wih immovable waer Addiioal frige shif arises: ( ) (6) e-6 м hus, phoos of he beam are compleely dragged by movig waer ad ierferece friges shif by Resulig Frige hif Resulig frige shif is equal o sum of he frige shifs ad ad is pracically equal o he frige shif which Fizeau received i his experime i 85 oclusio he frige shif i he ierferomeer wih movig waer is less ha frige shif i usual wo-beam ierferomeers because of he chage of he frequecies ad addiioal phase deviaios arisig i ierferig beams Fresel's explaaio of he frige shif decrease by hypohesis ha he ligh is dragged parially by oexise aeher is wrog ad cao be cosidered as cofirmaio of Eisei's special relaiviy Refereces Frakfur UI (968) pecial ad Geeral Relaiviy Nauka, Moscow 968 Fizeau AH (86) O he Effec of he Moio of a Body upo he elociy wih which i is raversed by Ligh Philosophical Magazie ad Joural of ciece 9: okolov G, okolov (7) he Fizeau Experime wih Movig Waer: A New Explaaio Galilea Elecrodyamics - he umber of he oscillaios i phoos ν durig he ime e-9 m e-9 m N N e-9 m J Phys Mah, a ope access joural IN: 9-9 olume 8 Issue 7