Fizeau s Experiment with Moving Water. New Explanation. Gennady Sokolov, Vitali Sokolov

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1 Fizeau s Experimet with Movig Water New Explaatio Geady Sokolov, itali Sokolov sokolov@vitalipropertiescom The iterferece experimet with movig water carried out by Fizeau i 85 is oe of the mai cofirmatios of special relativity I this experimet the frige shift is less tha the expected shift ad therefore it is geerally assumed that Fizeau s experimet proves that movig at speed the medium drags the light oly partially ad chages its speed less tha o I Fizeau s iterferometer the coheret beams ad travel i opposite directios the same distace i the pipe with water Whe the water is at rest, both beams go i the water with idetical speed ( - the idex of refractio of the water), pass the distace durig the idetical time iitial positio a (Fig) t ad the iterferece friges are i some water A B 5 a) Friges b) Fig Whe the water moves at speed, the beam passes the distace durig the time t, the beam passes the distace durig the time t ad the iterferece friges shift It is geerally assumed that i Fizeau s iterferometer the frige shift depeds o the differece ( t t) oly ad therefore is determied by the expressio

2 ( t t) () However, i the experimets the frige shift is less tha ad correspods to the expressio () I this article it is show that Fizeau made a mistake whe he supposed that the frige shift i his iterferometer with movig water is determied, as it takes place i usual iterferometers, by expressio () that is, the frige shift depeds o the differece ( t ) t oly It is show i the article that expressio () is wrog because it is derived uder the coditio that the iterferig beams eterig the movig water do ot chage the frequecy ad go i the water with idetical frequecy Our aalysis of the iterferometer with movig water shows that i reality i Fizeau s iterferometer the light is completely dragged by movig water ad beams ad go relative to the iterferometer with speeds ad The photos pass the distace durig the times t ad t but the additioal phase deviatio arises because the photos eterig movig water chage their frequecies ad go with frequecy < i beam ad with the frequecy > i beam Because of the additioal phase deviatio, the frige shift becomes less tha ad is determied exactly by expressio () The additioal phase deviatio is the systematic bias of Fizeau s experimet The iteractio of the light with a medium The beam of light is the stream of photos I the moochromatic beam every photo has a frequecy ad the oscillatios i the photos have a period T I the vacuum the photos move at speed relative to the light source ad durig time T every photo passes the distace which is equal to the wavelegth T Some distace i the vacuum every photo passes durig the time t

3 3 The phase of photo oscillatios chages o π durig the time T Durig the time t while the photo passes i the vacuum the distace its phase chages o t π π π, (3) T T t where - the umber of the oscillatios occurrig durig the time t or T T the umber of the wavelegths cotaied i the distace The passig of the light through the trasparet medium we imagie thus: I ay trasparet medium the speed of light is less tha i a vacuum because the photos move i the medium itermittetly Every photo periodically meets the reradiatig atom which absorbs this photo ad after some delay radiates a ew photo i the same directio Durig the timeτ the photo moves betwee the atoms at speed relative to the reradiatig atom Durig the reradiatig time τ the photo does ot shift, that is its speed relative to the medium equals zero After the time delay τ the atom radiates a ew photo i the same directio ad cycle recurs The resultat speed of the photos is determied by the ratio of τ to τ τ ad is equal to < where τ τ - the idex of refractio of the medium τ The phase of the photo oscillatios chages durig the time τ whe the photo really exists ad moves at speed betwee the atoms That is, the phase of the photos chages durig the time τ ad does ot chage durig the time τ I the medium every photo moves at speed ad passes the distace durig the τ τ timet But becauseτ, the total time t durig which the photo moves o the distace at speed is times less tha t ad is equal to t t That is, the total time t is equal to the time durig which the photo passes the same distace i the vacuum Passig the distace i the medium, the photo really does ot exist durig the timet but oly durig the time t Therefore

4 4 durig the time t while the photo passes the distace i the medium its phase t t does ot chage o π but chages oly o π : T T t π T t π T π T π that is, the chage of phase of the photo oscillatios depeds oly o the distace ad the wavelegth ad is determied by the same expressio (3) as for a vacuum The chage of frequecy of the photos takes place whe they eter the movig medium For example, whe light with frequecy ad wavelegth T eter the glass rod movig at speed i the same directio, the photos eter the glass at speed ( ) I accordace with Doppler-effect, their oscillatio period icreases to T I the glass, the reradiated photos move from atom to atom at speed ad its frequecy is equal to ( ) that is, the observer movig together with T the glass rod sees the frequecy which is less tha If to eglect the dispersio, i the movig glass the light goes with the same resultat speed as i immovable glass G The photos exit the glass at speed relative to the glass ad with the wavelegth But because the glass rod moves at speed the speed of the ( ) photos relative to immovable air is equal to ( ) Eterig the immovable air with the speed ( ) ad with the wavelegth the photos chage their frequecy ad go ( ) i the air with the frequecy ( ) ( ) I the air the photos are re-radiated by the atoms of the air ad go with the resultat speed ad A with the frequecy ( ) that is, the immovable observer sees the frequecy ( ) which is less tha Thus, i cosequece of the iteractio with movig re-radiator the light decreases its frequecy The frequecy decreases i both cases: whe the re-radiator moves i the directio of the light beam ad whe it moves i

5 5 opposite directio This decrease of frequecy evidetly cotradicts special relativity ad owadays this effect ca be easy proved by a simple laser experimet with the movemet of the glass re-radiator at a speed of -5 mph or more I Fizeau s iterferometer, whe the beams with frequecy eter the movig water, the frequecy of the photos of beam decreases ad becomes equal to ( ) ad the frequecy of the photos of beam icreases ad becomes equal to ( ) The photos pass the distace i the water with differet frequecies, ad At the momet whe the beams exit the movig water the frequecy of the photos of beam chages ( ) times ad becomes equal to ( ) ad the frequecy of the photos of beam chages ( ) times ad becomes equal to ( ) too Both beams exit the water with idetical frequecy ( ) < ad therefore the iterferece patter o the scree is immovable I the received calculatio of the Fizeau s iterferometer it is assumed that the iterferig beams do ot chage their frequecies at all ad therefore the iterferece patter is immovable because the beams come to the scree with a idetical frequecy The chage of phase of the photos i the movig medium is determied by the expressio π, where - the distace which the photos pass relative to the medium, - the real wavelegth with which the photos go i the movig medium The frige shift i Fizeau s iterferometer et us suppose that i Fizeau s iterferometer the photos of beam ad the photos of beam eter the water with idetical phase ad let us suppose that this phase is equal to zero Whe the water is at rest, the photos pass the distace i the water durig a idetical time t Durig this time their phases chage idetically ad therefore the t photos of both beams have the idetical phase π π The photos go out T from water without relative phase deviatio ad the iterferece friges are i some iitial positio

6 6 Whe the water moves with the speed, the photos pass the distace durig the differet times t ad t Durig these times t ad t the photos pass relative to the water the differet distaces t < ad t > I the received calculatio it is assumed that the photos do ot chage frequecy ad pass the distaces ad i the water with the frequecy While the photos of beam pass durig time t the distace, their phase chages o t π π π T T ad with such phase they exit the water at the momet t While the photos of beam pass durig the time t the distace, their phase chages o t π π π T T ad with such phase they exit the water at the momet t By the time t whe the photos of beam exit the water, the phase of the photos of t beam becomes equal to π too but by this time the photos of beam have T ( t t passed i the air a distace equal to ) t That is, the photos of beam are shifted o t relative to the photos of the beam which have the same phase ad, accordig to expressio (), the iterferece friges shift o

7 7 t I reality the photos go i the movig water ot with idetical frequecy but with differet frequecies ( ), ( ) ad they have the differet oscillatio periods T T, T T Therefore, while the photos of beam pass durig the time t the distace, their phase chages ot o but o ( ) t π π < T T that is the additioal phase delay ) arises i beam : ( ( ) π π π T T Ad while the photos of beam pass durig the time t the distace, their phase chages ot o but o ( ) t π π > T T that is, the additioal phase advace ) arises i beam : ( ( ) π π π T T The photos of beams ad the photos of beam go with additioal phase deviatio ) ( ) : (

8 8 π π π ad because of this additioal phase deviatio the frige shift decreases o π ad resultat frige shift becomes equal to : (4) The expressio (4) determies the frige shift i Fizeau s iterferometer with movig water uder the coditio that the iterferig beams chage the frequecies This expressio is derived strictly ad without ay approximatios ad exactly coicides with expressio () which correspods to the experimetal frige shifts I special relativity ad i all alterative aalyses kow to us, this expressio is derived oly approximately oclusio The received explaatio of Fizeau s experimet with movig water is wrog i priciple The fact that the frige shift i the experimets always is less tha the shift determied by the expressio () does ot prove that the speed of light chages i the iterferometer less tha o The expressio () gives the wrog value of the frige shift because this expressio was derived without regard to the ifluece of the frequecy chage of the iterferig beams o the frige shift Expressio (4) proves that i reality i Fizeau s iterferometer, light is completely dragged by movig water ad goes relative to the iterferometer with the speeds и The multiplier ) / ( is ot the coefficiet of draggig This multiplier determies oly the systematic bias of Fizeau s experimet Fizeau s experimet is ufit for the measurig of the speed of light i movig media ad caot be cosidered a cofirmatio of the mai postulate of special relativity O the cotrary, this experimet proves the falsity of that postulate 675

The Fizeau Experiment with Moving Water. Sokolov Gennadiy, Sokolov Vitali

The Fizeau Experiment with Moving Water. Sokolov Gennadiy, Sokolov Vitali The Fizeau Experimet with Movig Water. Sokolov Geadiy, Sokolov itali geadiy@vtmedicalstaffig.com I all papers o the Fizeau experimet with movig water, a aalysis cotais the statemet: "The beams travel relative