Michelson's Repetition of the Fizeau Experiment:

Transcription

1 Mihelso's Repetitio of the Fizeau Experimet: A Review of the Derivatio ad Cofirmatio of Fresel's Drag Coeffiiet A. A. Faraj a_a_faraj@hotmail.om Abstrat: I this ivestigatio, Mihelso's 1886 repetitio of the Fizeau experimet is briefly reviewed. Ad several derivatios of the Fresel's drag oeffiiet are preseted ad aalyzed i detail. I additio, it's demostrated that although the searh for measurable hages, due to refratio, i the values of stellar aberratio was the primary motivatio for the origial derivatio of the Fresel's drag oeffiiet, o effets of refratio o stellar aberratio, i the related ases, are physially possible. Ad also, it's established that, otrary to the basi assumptio of the derivatio of Fresel's drag oeffiiet by A. Mihelso, a prism of glass movig i a straight lie ad water flowig iside statioary brass tubes are ot kiematially equivalet to eah other; sie the latter always exhibits variatios i mass depedig o the diretio of iidet light; while the former does ot show ay variatios at all. Ad fially, it's poited out, i the urret ivestigatio, that the Larmor-Loretz theory, the speial theory of relativity, ad the ew-soure emissio theory fae theoretial diffiulties i explaiig away the reported result of the Fizeau experimet. Ad that is beause the three physial theories, i questio, must take it for grated that the speed of refrated light, as measured i the

2 referee frame of the flowig water, is equal to the speed of light i vauum divided by the refrative idex of water ; i.e., /. Otherwise, the Fresel drag oeffiiet aot be derived o the basis of those three physial theories. That is o oe had. O the other had, the assumptio of / is learly iosistet with the experimetal result reported by H. Fizeau ad A. Mihelso, whih implies eessarily that the speed of refrated light, as measured i the referee frame of the flowig water, is always equal to (/ ± v/ ). Keywords: Fizeau experimet; Fresel's drag oeffiiet; idex of refratio; aether; Mihelso's 1886 experimet; frige displaemet; movig refrative media; desity ratio; iverse ratio; lassial wave theory; Larmor-Loretz theory; speial relativity; ew-soure emissio theory; elasti-impat emissio theory. Itrodutio: The mai objetive of the origial Fizeau water-tube experimet ad its repetitio by A. Mihelso was to test ad to verify experimetally the preditio of the Fresel drag oeffiiet [Ref. #3]. Historially, the aether drag oeffiiet was iitially derived by Augusti-Jea Fresel i 1818, o the basis of the lassial wave theory of light, i a attempt to explai away, i a satisfatory maer, the egative result of Arago's 1810 experimet [Ref. #10]. The Arago experimet was based upo the suppositio that a prism of glass o the surfae of the movig earth should produe umerial values for light aberratio otieably differet from those measured through the earth's atmosphere. The very same suppositio was, also, the stated ratioale for the water-filled-telesope observatios by G. B. Airy i 1870; although this time aroud, the expeted umerial values for light aberratio, i the wake of L. Fouault's 1850 disovery [Ref. #9] that light travels through water at a osiderably redued speed ad muh less tha that of light travelig through air, were more defiitive. But oe agai, the experimetal result was egative [Ref. #7]. I additio, the basi reasoig, behid arryig out the latter water-filled-telesope experimet, was muh learer ad more solid, from theoretial viewpoit, tha that of the former experimet by F. Arago, who really did't kow exatly what to expet, beause he was't really sure whether light travels faster or slower i glass tha it does i air: The speed of light i water, aordig to L. Fouault, is w :

3 where is the refrative idex; ad is the speed of light i vauum. Ad, by usig a telesope without water, light aberratio Δβ is: w v si D b si b where β is the agle betwee the apparet positio of the light soure ad the orbital veloity vetor of the earth v; ad is the speed of light i free spae. Ad therefore, G. B. Airy expeted that, by usig a telesope filled with water, the value of light aberratio Δβ i free spae should hage to the muh higher value of light aberratio i water Δβ w : where is the refrative idex. v v si D b w si si b b However, a ruial requiremet, for observig the predited result, was't poited out expliitly i the above alulatios; ad hee, the ull result of Arago's experimet as well as the ull result of Airy's experimet were offiially deemed, at that time, usuessful. The missig requiremet was, of ourse, the sequeig order of the two effets of the proess of refratio ad the proess of light aberratio, i the ase uder disussio, o the iidet light. w If the iidet light is shifted by the proess of light aberratio, aordig to the law of light aberratio, firstly; ad the that shifted light is refrated by the proess of refratio, aordig to Sell's law, seodly, the o hages i the values of light aberratio, aused by refratio, a be observed. That is beause the proess of refratio, i this partiular ase, takes the diretio of iidet light, whih is already shifted by the proess of light aberratio, at the etrae poit of the prism or the water-filled telesope, as its mai iput; ad the refrats it i aordae with the Sell's law. As a result, wheever the data redutio proedures, as madated i experimets like these, are applied to the raw observatioal data, ad the agle of refratio is take out, the remaiig diretioal agle is eessarily the apparet positio of the star with respet to the lie of sight, to whih the telesope is poited ad set from the start alog its diretio i the first plae. By otrast, if the iidet light is refrated by the proess of refratio, aordig to the Sell's law,

4 firstly; ad the that refrated light is shifted by the proess of light aberratio, aordig to the law of light aberratio, seodly, the the expeted hages i the values of light aberratio, as predited by the alulatios above, a be observed. Now, what is the right astroomial settig, i whih the omputed preditio above a be obtaied by usig, for example, the Airy's water-filled telesope? Believe it or ot, the oly astroomial settig, i whih this predited value for light aberratio Δβ w : v v si D b w si si b b w a be measured, by usig Airy's water-filled telesope, is a hypothetial galati system, i whih the etire earth ad the distat stars, i questio, are loated ompletely immersed together iside oe sigle galati oea of fresh water! I suh a highly ulikely settig, it's ertaily possible for starlight to be refrated first by the fresh water of the galati oea; ad the to be shifted seod by the proess of light aberratio due to the orbital motio of the earth aroud the baryeter of the solar system. Beause of the iorret ad somewhat misleadig way, i whih light aberratio was ad is still iterpreted i aordae with the lassial wave theory, however, F. Arago ad G. Airy were etirely justified i expetig to obtai positive results i their experimets. Light aberratio, ad espeially stellar aberratio, o the basis of the lassial wave theory, is assumed to be aused by the small displaemet that the movig earth makes, durig the very short iterval of light travel time from the top to the bottom of the observatioal telesope; i.e., the iidet light is firstly refrated ad the shifted seodly by light aberratio upo traversig the whole legth of the measurig telesope. But, of ourse, light aberratio, i reality, is just the diretio of the relative veloity resultat of the veloity vetor of iidet light ad the orbital veloity vetor of the earth, regardless of the distae betwee the objetive les ad the eyepiee les or the atual legth of the telesope; ad hee o positive results are expeted to be obtaied by Arago's experimet or by Airy's experimet. 1. Mihelso's Repetitio of the Fizeau Experimet: I this repliatio of the Fizeau experimet, by A Mihelso, brass tubes of.8 m (iteral diameter) are mouted o a woode support; ad the refratometer is mouted o brik piers. Distilled water flows ito the brass tubes, through a three ih pipe, from a filled tak plaed about 3 meters above the apparatus.

5 A light beam from a eletri lamp at a is divided to two parts by a half-silvered mirror at b, where oe part traverses the path b d e f b g ad the other parts traverses the path b f e d b g. Figure #1: Refratometer The two parts of the light beam, upo uifiatio, form frige patters, whih are observed through a telesope; where the followig result is obtaied: whih is the result obtaied i this experimet Ad therefore, A. Mihelso has oluded that the result aoued by H. Fizeau is essetially orret [Ref. #1].

6 . Mihelso's Derivatio of the Fresel Drag Coeffiiet: Aordig to A. Mihelso, the Fresel drag oeffiiet: -1 x a be derived, o the basis of the aether wave theory, as follows: Assume that the prism, AC i the Figure #, is i motio relative to the aether i the diretio AB with a uiform veloity v. Figure #: Prism Ad assume that the desity of the exteral aether is 1; ad the desity of the aether, withi the prism, is 1+Δ. I the time t, the prism advaes a distae: vt BB

7 At the begiig of that time, the quatity of aether i the volume BC is: Svt where S is the surfae area of the base of the prism. Ad at the ed of that time, the aether quatity is: ( 1+ D) Ad hee, i this time, the quatity of aether itrodued ito this volume is: Svt SvtD Let the veloity of the aether otaied i the prism be xv; ad hee, the quatity of the aether is: whih is the same as: Sxvt ( 1+ D) ad aordigly, SvtD x D 1 + D But the ratio of the veloity of light i the exteral ether to that withi the prism is the idex of refratio, whih is equal to the iverse ratio of the square root of the desities:

8 1+ D ad therefore, -1 x whih is the Fresel drag oeffiiet. Udoubtedly, the above derivatio of the Fresel oeffiiet by A. Mihelso, o the basis of the aether assumptio, is very oise ad simple. Noetheless, there are, obviously, sigifiat differees betwee the movig prism, upo whih Mihelso's derivatio of the Fresel drag oeffiiet is based, ad the flowig water iside statioary tubes of brass i his experimetal setup, by whih the reported result is obtaied: 1. The refrative medium of flowig water, iside the statioary brass tubes, forms a otiuous loop, i whih a speifi amout of water per uit time eters eah brass tube through oe ed, ad a equal amout of water per uit time exists eah brass tube from the other ed.. The refrative medium of glass iside the prism is movig as a sigle uit whose amout remais, at all times, ostat ad the same. 3. Whe the movig water, iside oe of the statioary brass tubes, approahes light from a statioary light soure, its atual amout, traversed by the iidet light throughout the brass tube, ireases liearly i diret proportio to the speed of its flow iside that brass tube. 4. Whe the movig prism approahes light from a statioary light soure, the atual amout of its glass, traversed by the iidet light throughout the prism, remais ostat ad exatly the same regardless of the speed of that prism. 5. Whe the movig water, iside oe of the statioary brass tubes, reedes from light emitted by a statioary light soure, its atual amout, traversed by the iidet light throughout the brass tube, dereases liearly i iverse proportio to the speed of its flow iside that brass tube. 6. Whe the movig prism reedes from light emitted by a statioary light soure, the atual amout of its glass, traversed by the iidet light throughout the prism, remais ostat ad exatly the same regardless of the speed of that prism. 7. The oly major shared harateristis that the movig prism ad the flowig water, iside the statioary brass tubes, have i ommo, are the derease i the legth of the mea free path, upo approahig the statioary light soure, i iverse proportio to the speed of approah; ad the irease i the legth of the mea free path, upo reedig from the statioary light

9 soure, i diret proportio to the speed of reessio. At first glae, therefore, it appears highly ulikely for the flowig water ito the brass tubes of Mihelso's experimetal apparatus, ad the movig prism of glass i his theoretial derivatio, to have the same fator for the Fresel drag oeffiiet, whih is equal exatly to: -1 x where stads for the refrative idex of water ad the refrative idex of glass, respetively. Ad the mai reaso for that, evidetly, is the variatio i the amout of the flowig water iside the brass tubes, depedig o the diretio of iidet light. So, ow, is Mihelso's derivatio of the Fresel drag oeffiiet theoretially iorret? The aswer to this questio depeds, etirely, o the physial mehaism behid the proess of refratio i refratig media i geeral, ad i the refratig medium of flowig water ad the refratig medium of glass i partiular. But before ay attempt at aswerig the above questio, we have to make sure first ad to demostrate, quatitatively, that the amout of the flowig water, iside the statioary brass tubes, does vary, ideed, with the diretio of its veloity vetor with respet to iidet light. 3. Water Mass Variatios i Fizeau-Type Experimets: Sie i the above-desribed Mihelso's experimet as well as i the origial Fizeau experimet, water flows through statioary tubes relative to the laboratory, its mass varies eessarily with the diretio of its veloity vetor with respet to iidet light. To demostrate that is ideed the ase, let's assume that the legth of the brass tube is L; ad the area of its ross setio is A. Whe the experimetal water is at rest relative to the laboratory, its total mass M 0, iside the brass tube, is give by the followig equatio: M 0 rla

10 where ρ is the desity of water. But whe the experimetal water is movig relative to the laboratory at a veloity v, a ertai amout of water per uit time otiually exists the brass tube from oe ed; ad at the same time, a equal amout of water per uit time otiually eters the brass tube from the other ed. Ad therefore, if the travel time of iidet light, through the brass tube, is t, the the amout of water that exists the brass tube, durig that time, as well as the equal amout that eters it, a be obtaied by usig this equatio: where ΔM is the variable amout of water. D M r Avt Aordigly, iidet light that takes a iterval of time t to travel through the brass tube i the opposite diretio of the approahig water, must eouter a total amout of water equal to M A, before emergig from the other ed of the brass tube: M M + D M M + r Avt A 0 0 where A is the ier area of the ross setio of the brass tube. By otrast, iidet light that takes a iterval of time t to travel through the brass tube i the same diretio as that of the reedig water, must eouter a total amout of water equal to M R, before exitig from the other ed of the brass tube: M M - D M M - r Avt R 0 0 where ρ stads for the desity of water. The similarity betwee the variatios i the amout of flowig water, as omputed here, ad the variatios i the amout of dragged aether, as alulated by A. Mihelso i his aforemetioed derivatio of the Fresel drag oeffiiet, from theoretial stadpoit, is strikig ad itriguig. Presumably, if the above variatios i the amout of flowig water are used to obtai orrespodig variatios i the amout of free spae iside eah brass tube, ad the total aether quatity is replaed with the total spae quatity, iside ad outside the brass tubes, the a aether-free derivatio of the followig fator of the Fresel drag oeffiiet may, well, be withi reah ad readily obtaiable:

11 -1 x where is the refrative idex. 4. The Physial Mehaisms of Refratio: I the published literature, there are two proposed physial mehaisms for determiig the behavior of eletromageti radiatio travelig through refratig media: I. The Absorptio-Re-emissio Mehaism: Aordig to this physial mehaism, iidet light is absorbed ad re-emitted otiually by the partiles of the refrative medium, i questio. Statistially, the free spae, betwee eah two adjaet partiles of the refrative medium, is the mea optial path, through whih light, from a statioary light soure, always travels at its iidet speed. It follows, therefore, that, through the refrative medium, the speed of light ': is etirely apparet ad due maily to the itegrated time delay of absorptio ad re-emissio of iidet light throughout the refrative medium. Ad subsequetly, o the basis of this physial mehaism, the Fresel drag oeffiiet: -1 x is othig more tha the apparet speedig up ad the apparet slowig dow of iidet light due to the total sum of the small displaemets, eah of whih is made by every refrative partile durig the short iterval of time betwee the proess of absorptio ad the proess of re-emissio of iidet light.

12 Ad the questio, oe agai, is this: Is, i this ase, the above-metioed Mihelso's derivatio of the Fresel drag oeffiiet iorret? Sie the umber of refrative partiles, i the ase of the movig glass prism, is ostat, regardless of the diretio of iidet light; ad sie the umber of refrative partiles, i the ase of the flowig water, is highly variable ad depedet o the diretio of the flowig water with respet to the iidet light, the it should follow that the above Mihelso's derivatio of the Fresel drag oeffiiet is defiitely iorret, o the basis of the absorptio-re-emissio mehaism. By how muh is the Fresel drag oeffiiet for the movig glass prism x g is quatitatively differet from the experimetally obtaied value of the Fresel drag oeffiiet for the flowig water x? The fator of the Fresel drag oeffiiet for the movig glass prism x g has, of ourse, to be obtaied by experimetal meas. However, based o the experimetal result, obtaied by Mihelso ad Fizeau, regardig the fator of the Fresel drag oeffiiet for the flowig water x: -1 x it a be dedued, to a reasoable degree of ertaity, that, puttig the differet umerial values of i these two ases aside, the fator of the Fresel drag oeffiiet for the movig glass prism x g ought to be less tha that for the flowig water, if the absorptio-re-emissio mehaism is physially true; i.e., -1 xg < i the ase of approah ad i the ase of reessio, respetively, eve though the refrative idex of glass g is greater tha the refrative idex of water w. Now, is there ay pratial way, by whih the Mihelso's movig prism of glass a be made equivalet kiematially to Fizeau's flowig water? Certaily, if Mihelso's movig prism of glass is trasformed somehow ito a rotatig irular dis of glass, the the refratig medium of rotatig glass, i this ase, will be kiematially equivalet, i every respet, to the refratig medium of flowig water. Also, if a brass tube filled with statioary water is moved i a straight lie at a veloity v, the the

13 refratig medium iside the movig prism, i this ase, will be kiematially equivalet, i every respet, to the refratig medium iside the movig tube. II. The Deposited-Mometum Mehaism: Aordig to this mehaism, iidet light gives away a ertai amout of its mometum to the refrative medium, upo eterig; ad takes it bak upo existig that refrative medium. Ad therefore, the speed of light, through the refrative medium, ': is the atual speed of iidet light throughout the refrative medium, whih is eessarily redued beause of the redued mometum of iidet light iside the refrative medium. Ad osequetly, o the basis of this physial mehaism, the followig Fresel drag oeffiiet: -1 x is merely the maifestatio of the atual speedig up ad the atual slowig dow of iidet light due to small variatios i its mometum depedig o the diretio of its veloity vetor with respet to the veloity vetor of the refratig medium. So, oe agai, is the above-metioed Mihelso's derivatio of the Fresel drag oeffiiet theoretially iorret? Sie the variatios i the speed of light, through the refrative medium, are olletively aused by variatios i its mometum with respet to the veloity vetor of the refrative medium, ad ompletely idepedet of the atual umber of the refratig partiles, it follows that the abovemetioed Mihelso's derivatio of the Fresel drag oeffiiet is defiitely orret; ad hee the flowig water ad the movig glass prism should have the same fator of the Fresel drag oeffiiet: -1 x

14 i aordae with the deposited-mometum mehaism. 5. Replaig the Aether with Vauum i Mihelso's Derivatio: The aforemetioed variatios, i the amout of water flowig through statioary tubes relative to the laboratory, with the diretio of its veloity vetor with respet to iidet light, lead aturally to a simple modifiatio of Mihelso's derivatio of the Fresel drag oeffiiet. Beause the volume of the brass tubes remais ostat, the variatios i the quatity of flowig water, with the diretio of iidet light, imply, eessarily, that the amout of free spae, overed by the iidet light iside eah brass tube, varies iversely with the variatios i the amout of the flowig water. I other words, whe the amout of flowig water ireases, the amout of free spae dereases. Ad, by otrast, whe the amout of flowig water dereases, the amout of free spae, iside eah brass tube, ireases; i.e., where q w is the quatity of flowig water; ad q v is the quatity of free spae. q v 1 µ q It's, therefore, theoretially permissible, to replae the variatios i the quatity of aether q a, i the origial Mihelso's derivatio of the Fresel drag oeffiiet, with the variatios i the quatity of free spae q v, i order to use the refrative idex of vauum i exatly the same way as A. Mihelso used the refrative idex of aether to derive the Fresel drag oeffiiet. w Let's assume that L deotes the legth of the statioary tube; A deotes the area of the ross setio of the brass tube; v deotes the veloity of the flowig water; ad ρ deotes the desity of water. Whe the flowig water is approahig diretly the statioary light soure, its total amout q w is give by this equatio: q q + Dq w 0 w where q 0 is defied i aordae with this equatio:

15 q0 r AL ad where Δq w is alulated by usig the followig equatio: D q r Avt w ad where t is the travel time of light through the brass tube. Ad sie the quatity of free spae q v varies with the quatity of water q w i aordae with the followig quatitative relatio: q v 1 µ q it follows, aordigly, that, whe the flowig water approahes diretly the statioary light soure, the quatity of free spae q v iside the brass tube, dereases as give by this equatio. w q q - Dq v v0 v where q v0 is the quatity of free spae i a brass tube filled with statioary water. Ad sie the veloity ratio of light, aordig to the aforemetioed Mihelso's rule, is iversely proportioal to the square root of the desity ratio; i.e., x D 1 + D we a use, here, the quatity ratio of free spae: x v Dqv q - Dq v0 v to obtai the speed of light ' through the brass tube:

16 1 æ ö - v ç 1- è ø where v is the speed of the flowig water; ad is the refrative idex. Likewise, whe the flowig water is reedig diretly from the statioary light soure, its total amout q w with respet to the iidet light is give by this equatio: q q - Dq w 0 w where q 0 is: q0 r AL ad where Δq w is: D q r Avt w ad where t is the travel time of light through the brass tube. Ad sie the quatity of free spae q v varies with the quatity of water q w i aordae with this relatio: q v 1 µ q it follows that, whe the flowig water reedes diretly from the statioary light soure, the quatity of free spae q v iside the brass tube, is give by this equatio: w q q + Dq v v0 v

17 where q v0 is the quatity of free spae i a brass tube filled with statioary water. Ad sie, the veloity ratio of light i vauum to that withi the reedig water is equal to the square root of the quatity ratio of free spae: x v q v0 Dqv + Dq v it's possible to obtai the speed of light ' i the reedig refrative medium of flowig water, iside the brass tube: 1 æ ö + vç 1- è ø where v is the speed of the flowig water; ad is the refrative idex. Ulike the previous Mihelso's derivatio, however, this urret derivatio of the Fresel drag oeffiiet is orret, if ad oly if the absorptio-re-emissio mehaism is true. 6. Theoretial Preditios: Although the Fresel drag oeffiiet applies oly to the speial ase of refratio, i whih the light soure is at rest ad the refrative medium is i motio, with respet to the statioary referee frame of the laboratory, a brief survey of other related ases of refratio is eessary for larifyig its kiemati ad physial aspets i geeral, ad for hekig for whether or ot its various iterpretatios, o the basis of several physial theories, are iterally osistet. I. The Preditios of the Classial Wave Theory: The lassial wave theory makes several preditios, with regard to the speed of light i refrative media; but oly these two preditios, with regard to the speed of light i refrative media, have bee experimetally verified: The speed of light emitted by a statioary light through a refratig medium at rest with respet

18 to the statioary referee frame of the laboratory. Ad the speed of light emitted by a statioary light through a refratig medium i motio with respet to the statioary referee frame of the laboratory. 1. The Light Soure ad the Refrative Medium at Rest: If the light soure, outside or iside a refrative medium at rest, is statioary i the referee frame of the laboratory, the the speed of its light iside that refrative medium, as predited by the lassial wave theory, a be obtaied through the use of this stadard equatio: where is the refrative idex; ad is the speed of light i vauum.. The Light Soure i Motio ad the Refrative Medium at Rest: Whe the light soure is i motio ad the refrative medium is at rest, i the referee frame of the laboratory, the speed of light through the statioary refrative medium, aordig to the lassial wave theory, remais uhaged ad the same as i the statioary ase; i.e., where is the refrative idex; ad is the speed of light i vauum. That is beause light, o the basis of this theory, does ot iherit the veloity of its movig soure. 3. The Light Soure at Rest ad the Refrative Medium i Motio: Whe the light soure is at rest ad the refratig medium is i motio, the lassial wave theory makes two differet preditios, i the referee frame of the refratig medium ad i the referee frame of the laboratory, respetively. However, oly the latter preditio has bee tested

19 experimetally by the Fizeau experimet ad its repetitio by A. Mihelso. I the Referee Frame of the Refrative Medium: I the referee frame, i whih the refrative medium is at rest, the speed of light ', from a statioary light soure, through the movig refrative medium, aordig to the lassial wave theory, a be alulated by usig the followig equatio: v + for the ase, i whih the refrative medium is approahig the light soure; ad by usig this equatio: v - for the ase, i whih the refrative medium is reedig from the light soure. I the Referee Frame of the Laboratory: I the statioary referee frame of the laboratory, whe the light soure is at rest ad the refrative medium is i motio, the speed of its light ' through the refrative medium, aordig to the lassial wave theory, is alulated, i the ase of approah, by usig this equatio: 1 æ ö - v ç 1- è ø where v is the speed of the refrative medium with respet to the statioary light soure i the referee frame of the laboratory. Ad likewise, the speed of light from a statioary light soure ' iside a reedig refrative medium is omputed by usig the followig equatio:

20 1 æ ö + vç 1- è ø where is refrative idex. 4. The Light Soure ad the Refrative Medium Movig with the Same Veloity: Although, i the surveyed literature, there is o metio of ay speifi equatios for the speial ase of a light soure ad a refrative medium movig together with the same speed i the same diretio relative to the laboratory, it's possible, from theoretial stadpoit, to work out the details of omputig the speed of light ' through the refrative medium, o the basis of the lassial wave theory, i these two frames of referee, respetively: I the Referee Frame of the Light Soure ad the Refrative Medium: I the referee frame, i whih the light soure ad the refrative medium are at rest, the speed of light ' through the refrative medium, a be alulated i aordae with the followig equatio: regardless of whether the light soure is outside or iside the refrative medium. Ad that is beause the umerial value of the veloity of the refratig medium with respet to the light soure, i this speial ase, is always equal to zero. However, beause the whole system, o the basis of this theory, is movig relative to the uiversal medium alled 'Aether', the seod-order effets, whih the Mihelso-Morley experimet has bee desiged to look for, should be amplified further, i this partiular ase, by a additioal fator equals to the refrative idex. I the Referee Frame of the Laboratory: I the referee frame of the laboratory, the speed of light ' through the refrative medium, aordig to the lassial wave theory, has to be alulated by usig the stadard equatios of the Fresel drag oeffiiet.

21 Ad that is learly beause the motio of the light soure has o effet at all o the speed of light, withi the framework of this theory. Therefore, i the referee frame of the laboratory, the speed of light ' through the refrative medium, aordig to the lassial wave theory, is alulated by usig this equatio: 1 æ ö - v ç 1- è ø i the ase, i whih the refrative medium is trailig the light soure. Ad i aordae with this equatio: 1 æ ö + vç 1- è ø i the ase, i whih the light soure is trailig the refrative medium. 5. The Light Soure ad the Refrative Medium i Motio: Eve though the published literature does ot otai ay mathematial formulas for the speial ase of a light soure ad a refrative medium i motio relative to eah other as well as with respet to the laboratory, it's relatively easy, from theoretial viewpoit, to work out the details of alulatig the speed of light ' through the refrative medium, i aordae with the lassial wave theory. Let's assume that v s is the veloity of the light soure; ad v m is the veloity of refrative medium, with respet to the statioary referee frame of the laboratory. Sie, withi the framework of the lassial wave theory, the veloity of the light soure has o effet o the veloity of its light, we eglet the veloity of the soure v s ompletely, ad take ito osideratio oly the veloity of the refrative medium v m, i omputatios doe i the referee frame of the refrative medium ad i the referee frame of the laboratory, orrespodigly. I the Referee Frame of the Refrative Medium: I the referee frame, i whih the refrative medium is at rest, the speed of light ', whether the

22 light soure is at rest or i motio, through the refrative medium, aordig to the lassial wave theory, a be alulated by usig the followig equatio: v + for the ase, i whih the refrative medium is approahig the light soure; ad by usig this equatio: m v - for the ase, i whih the refrative medium is reedig from the light soure. m I the Referee Frame of the Laboratory: I the referee frame of the laboratory, whether the light soure is i motio or at rest, whe the refrative medium is i motio, the speed of light ' through the refrative medium, aordig to the lassial wave theory, is alulated, i the ase of approah, by usig the followig equatio: 1 æ ö - vm ç 1- è ø where v m is the speed of the refrative medium with respet to the laboratory. Ad i the same way, the speed of light ' iside a reedig refrative medium is omputed by usig this equatio: 1 æ ö + vm ç 1- è ø where is refrative idex.

23 The Classial Wave Theory ad the Result of the Fizeau Experimet: I the ase of a statioary light soure ad a approahig refrative medium, the origial Fizeau experimet as well as the Mihelso's repetitio have verified that the speed of light ' through the refrative medium, as measured i the statioary referee frame of the laboratory, is i aordae with this equatio: 1 æ ö - v ç 1- è ø where v is the speed of the refrative medium with respet to the statioary light soure i the referee frame of the laboratory. Aordigly, this experimetal result implies, eessarily ad idepedetly of ay physial theory, that, i the referee frame, i whih the refrative medium is at rest, the speed of light ', from the same statioary light soure, through the approahig refrative medium, is i aordae with this equatio: v + where is the idex of refratio. Ad likewise, i the ase of a statioary light soure ad a reedig refrative medium, the origial Fizeau experimet as well as the Mihelso's repetitio have ofirmed that the speed of light ' through the refrative medium, as measured i the statioary referee frame of the laboratory, is aordig to this equatio: 1 æ ö + vç 1- è ø where v is the speed of the refrative medium with respet to the statioary light soure i the referee frame of the laboratory. Ad so, this experimetal result implies, eessarily ad idepedetly of ay physial theory, that, i

24 the referee frame, i whih the refrative medium is at rest, the speed of light ', from the same statioary light soure, through the reedig refrative medium, is i aordae with this equatio: where is the idex of refratio. v - The lassial wave theory predits that i the referee frame, i whih the refrative medium is at rest, the speed of light ', from the same statioary light soure, through the movig refrative medium, is aordig to this equatio: v + i the ase, i whih the refrative medium is approahig the statioary light soure; ad i aordae with this equatio: v - i the ase, i whih the refrative medium is reedig from the statioary light soure. Ad it follows, therefore, that the lassial wave theory is osistet with the experimetal result obtaied by H. Fizeau ad A. Mihelso. II. The Preditios of the Larmor-Loretz Theory: The Larmor-Loretz theory makes several preditios, with regard to the speed of light i refrative media; but oly these two preditios have bee verified experimetally: The speed of light emitted by a statioary light through a refrative medium at rest with respet to the statioary referee frame of the laboratory. Ad the speed of light emitted by a statioary light through a refrative medium i motio with

25 respet to the statioary referee frame of the laboratory. 1. The Light Soure ad the Refrative Medium at Rest: If a light soure, outside or iside a refrative medium at rest, is statioary i the referee frame of the laboratory, the the speed of its light iside that refrative medium, as predited by the Larmor- Loretz theory, a be obtaied through the use of this stadard equatio: where is the refrative idex; ad is the speed of light i vauum.. The Light Soure i Motio ad the Refrative Medium at Rest: Whe the light soure is i motio ad the refrative medium is at rest, i the referee frame of the laboratory, the speed of light through the refrative medium, o the basis of the Larmor-Loretz theory, remais uhaged ad the same as i the statioary ase; i.e., where is the refrative idex; ad is the speed of light i vauum. That is beause, aordig to the Larmor-Loretz theory, the motio of the light soure has o effet at all o the veloity of its light. 3. The Light Soure at Rest ad the Refrative Medium i Motio: Whe the light soure is at rest ad the refratig medium is i motio, the Larmor-Loretz theory makes two differet preditios, i the referee frame of the refratig medium ad i the referee frame of the laboratory, respetively; but, oly the latter has bee tested experimetally by the Fizeau experimet ad its repetitio by A. Mihelso. I the Referee Frame of the Refrative Medium:

26 I the referee frame, i whih the refrative medium is at rest, the speed of light ' through the refrative medium, aordig to the Larmor-Loretz theory, a be alulated by usig the followig equatio: for the ase, i whih the refrative medium is approahig the light soure; ad by usig this equatio: for the ase, i whih the refrative medium is reedig from the light soure. That is beause, withi the framework of this theory, the speed of light, i the referee frame of the refratig medium, must be assumed first to be ostat ad exatly equal to: i those two ases, i order to derive the Fresel drag oeffiiet for the experimetally verified ase i the statioary referee frame of the laboratory. I the Referee Frame of the Laboratory: I the referee frame of the laboratory, aordig to the Larmor-Loretz theory, whe the light soure is at rest ad the refrative medium is i motio, the speed of light ' through the movig refrative medium, is alulated, i the ase of approah, by usig the followig equatio: æ1- v ö 1 æ ö ç» - v ç 1- è 1+ v ø è ø where v is the veloity of the approahig refrative medium with respet to the statioary light soure i the referee frame of the laboratory; ad is the refrative idex.

27 Ad, i the same way, the speed of light from a statioary light soure ' iside a reedig refrative medium is omputed by usig this equatio: æ1- v ö 1 æ ö ç» + v ç 1- è 1- v ø è ø where v is the veloity of the reedig refrative medium with respet to the statioary light soure i the referee frame of the laboratory; ad is the refrative idex 4. The Light Soure ad the Refrative Medium Movig with the Same Veloity: Although the published literature, oerig the Larmor-Loretz theory, otais o speifi equatios for the speial ase of a light soure ad a refrative medium movig together with the same speed i the same diretio relative to the laboratory, it's possible, theoretially, to work out the alulatios of the speed of light ' through the refrative medium, o the basis of this theory, i these two frames of referee, orrespodigly: I the Referee Frame of the Light Soure ad the Refrative Medium: Aordig to the Larmor-Loretz theory, i the referee frame, i whih the light soure ad the refrative medium are at rest, the speed of light ' through the refrative medium, a be alulated i aordae with the followig equatio: regardless of whether the light soure is iside or outside of the refrative medium. Noetheless, beause the light soure ad the refrative medium, o the basis of the Larmor-Loretz theory, are movig relative to the uiversal medium amed 'Aether', the seod-order effets, whih the Mihelso-Morley experimet has bee desiged to measure, are expeted to be magified further, i this partiular ase, by a additioal fator equals to the refrative idex. Ad as a result, the postulated legth otratio, withi the framework of this theory, may ot be adequate, without further adjustmets, for explaiig away the ull results of the Mihelso-Morley experimet ad similar experimets. I the Referee Frame of the Laboratory: I the referee frame of the laboratory, the speed of light ' through the refrative medium,

28 aordig to the Larmor-Loretz theory, should be alulated through the use of the Fresel drag oeffiiet. That is beause the motio of the light soure has o effet at all o the speed of light, withi the framework of this theory. Ad subsequetly, i the referee frame of the laboratory, the speed of its light ' through the refrative medium, aordig to the Larmor-Loretz theory, is alulated by usig this equatio: æ1- v ö 1 æ ö ç» - v ç 1- è 1+ v ø è ø i the ase, i whih the refratig medium is trailig the light soure. Ad i aordae with equatio: æ1- v ö 1 æ ö ç» + v ç 1- è 1- v ø è ø i the ase, i whih the light soure is trailig the refratig medium. 5. The Light Soure ad the Refrative Medium i Motio: I spite of the fat that, i the published literature, there is o metio of ay speifi equatios for the speial ase of a light soure ad a refratig medium i motio relative to eah other as well as relative to the laboratory, it's quite easy, from theoretial stadpoit, to work out the details of omputig the speed of light ' through the refrative medium, o the basis of the Larmor-Loretz theory. With respet to the statioary referee frame of the laboratory, let v s deote the veloity of the light soure; ad v m deote the veloity of refrative medium. Sie, withi the framework of the Larmor-Loretz theory, the veloity of the light soure has o effet o the veloity of light, we eglet the veloity of the soure v s altogether, ad take ito aout oly the veloity of the refrative medium v m, i alulatios arried out i the referee frame of the refrative medium ad the referee frame of the laboratory, respetively. I the Referee Frame of the Refrative Medium: I the referee frame, i whih the refrative medium is at rest, the speed of light ', through the refrative medium, aordig to the Larmor-Loretz theory, a be alulated by usig the followig

29 equatio: for the ase, i whih the refrative medium is approahig the light soure; ad by usig this equatio: for the ase, i whih the refrative medium is reedig from the light soure. I the Referee Frame of the Laboratory: I the referee frame of the laboratory, whether the light soure is i motio or at rest, whe the refrative medium is i motio, the speed of light ' through the refrative medium, aordig to the Larmor-Loretz theory, is alulated, i the ase of approah, by usig the followig equatio: æ ö» - - è v ø 1- vm æ 1 ö ç vm ç 1 1+ m è ø where v m is the speed of the refrative medium with respet to the laboratory. Ad similarly, the speed of light ' iside a reedig refrative medium is omputed by usig this equatio: æ1- v ö 1 æ ö ç» + v ç 1- è 1- v ø è ø where is refrative idex. The Larmor-Loretz Theory ad the Result of the Fizeau Experimet:

30 I the ase of a statioary light soure ad a approahig refrative medium, the origial Fizeau experimet as well as the Mihelso's repetitio have verified that the speed of light ' through the refrative medium, as measured i the statioary referee frame of the laboratory, is always i aordae with this equatio: 1 æ ö - v ç 1- è ø where v is the speed of the approahig refrative medium with respet to the statioary light soure i the referee frame of the laboratory. Aordigly, this experimetal result implies, eessarily ad idepedetly of ay physial theory, that, i the referee frame, i whih the refrative medium is at rest, the speed of light ', from the same statioary light soure, through the refrative medium, is i aordae with this equatio: v + where is the idex of refratio. Ad i a like maer, i the ase of a statioary light soure ad a reedig refrative medium, the origial Fizeau experimet as well as the Mihelso's repetitio have verified that the speed of light ' through the refrative medium, as measured i the statioary referee frame of the laboratory, is i aordae with this equatio: 1 æ ö + vç 1- è ø where v is the veloity of the reedig refrative medium with respet to the statioary light soure i the referee frame of the laboratory. Ad subsequetly, this experimetal result implies, eessarily ad idepedetly of ay physial theory, that, i the referee frame, i whih the approahig refrative medium is at rest, the speed of light ', from the same statioary light soure, through the refrative medium, is i aordae with the followig equatio: v -

31 where is the idex of refratio. The Larmor-Loretz theory predits that i the referee frame, i whih the refrative medium is at rest, the speed of light ', from the same statioary light soure, through the refrative medium, is aordig to this equatio: i the ase, i whih the refrative medium is approahig the statioary light soure; ad i aordae with this equatio: i the ase, i whih the refrative medium is reedig from the statioary light soure. Ad it follows, therefore, that the Larmor-Loretz theory is iosistet with the experimetal result obtaied by Fizeau ad Mihelso. III. The Preditios of Eistei's Speial Theory: The speial theory of relativity makes a umber of preditios, with regard to the speed of light i refrative media; but oly two preditios, of whih, have bee tested experimetally: The speed of light emitted by a statioary light through a refrative medium at rest with respet to the statioary referee frame of the laboratory. Ad the speed of light emitted by a statioary light through a refrative medium i motio with respet to the statioary referee frame of the laboratory. 1. The Light Soure ad the Refrative Medium at Rest: If the light soure, outside or iside a refrative medium at rest, is statioary i the referee frame of the laboratory, the the speed of its light through that refrative medium, as predited by Eistei's speial theory, a be obtaied by usig the followig stadard equatio:

32 where is the refrative idex; ad is the speed of light i vauum.. The Light Soure i Motio ad the Refrative Medium at Rest: Whe the light soure is i motio ad the refrative medium is at rest, i the referee frame of the laboratory, the speed of light through the refrative medium, aordig to Eistei's theory of relativity, remais uhaged ad the same as i the statioary ase; i.e., where is the refrative idex; ad is the speed of light i vauum. Ad that is beause, withi the framework of the speial theory of relativity, the motio of the light soure has o effet whatsoever o the veloity of its light. 3. The Light Soure at Rest ad the Refrative Medium i Motio: Whe the light soure is at rest ad the refratig medium is i motio, the speial theory of relativity makes two differet preditios, i the referee frame of the refratig medium ad i the referee frame of the laboratory, respetively; but oly the latter preditio has bee ofirmed experimetally by the Fizeau experimet ad its repliatio by A. Mihelso. I the Referee Frame of the Refrative Medium: I the referee frame, i whih the refrative medium is at rest, the speed of light ', from a statioary light soure, through the refrative medium, aordig to the speial theory of relativity, a be alulated by usig the followig equatio: i the ase, i whih the refrative medium is approahig the light soure;

33 ad by usig this equatio: i the ase, i whih the refrative medium is reedig from the light soure. Ad that is beause, withi the framework of this theory, the speed of light, i the referee frame of the refrative medium, must be assumed first to be ostat ad exatly equal to: i those two seodary ases, i order to derive the Fresel drag oeffiiet for the primary ase i the statioary referee frame of the laboratory. I the Referee Frame of the Laboratory: I the referee frame of the laboratory, i aordae with Eistei's speial theory, whe the light soure is at rest ad the refrative medium is i motio, the speed of its light ' through the refrative medium, is alulated, i the ase of approah, by usig the followig equatio: æ1- v ö 1 æ ö ç» - v ç 1- è1- v ø è ø where v is the veloity of the approahig refrative medium with respet to the statioary light soure i the referee frame of the laboratory; ad is the refrative idex. Similarly, the speed of light from a statioary light soure ' iside a reedig refrative medium is omputed by usig this equatio: æ1+ v ö 1 æ ö ç» + v ç 1- è1+ v ø è ø where v is the veloity of the reedig refrative medium with respet to the statioary light soure i the referee frame of the laboratory; ad is the refrative idex.

34 4. The Light Soure ad the Refrative Medium Movig with the Same Veloity: Eve though, i the published literature, there are o speifi mathematial formulas for the speial ase of light soures ad refrative media movig together with the same speed i the same diretio relative to the laboratory, it's possible, from theoretial stadpoit, to work out the omputatios of the speed of light ' through ay refrative medium, o the basis of the theory of speial relativity, i these two frames of referee, respetively: I the Referee Frame of the Light Soure ad the Refrative Medium: Aordig to the speial theory of relativity, i the referee frame, i whih the light soure ad the refrative medium are at rest, the speed of light ' through the refrative medium, a be alulated i aordae with the followig equatio: regardless of whether the light soure is iside or outside the refrative medium. Nevertheless, the seod-order effets, whih the Mihelso-Morley experimet has bee desiged to detet, should be ireased further, i this partiular ase, by a additioal fator equals to the refrative idex. Ad as a result, it's highly likely that the Loretz trasformatio, withi the framework of this theory, may ot, without further adjustmets, be able to aout for the ull results of the Mihelso-Morley experimet ad similar experimets. I the Referee Frame of the Laboratory: I the referee frame of the laboratory, the speed of light ' through the refrative medium, aordig to the theory of speial relativity, should be alulated through the use of the Fresel drag oeffiiet. Ad that is beause the motio of the light soure has o effet at all o the speed of light, withi the framework of this theory. Ad hee, i the referee frame of the laboratory, the speed of its light ' through the refrative medium, aordig to the theory of speial relativity, is omputed by usig this equatio: æ1- v ö 1 æ ö ç» - v ç 1- è1- v ø è ø i the ase, i whih the refrative medium is trailig the light soure. Ad i aordae with the followig equatio:

35 æ1+ v ö 1 æ ö ç» + v ç 1- è1+ v ø è ø i the ase, i whih the light soure is trailig the refrative medium. 5. The Light Soure ad the Refrative Medium i Motio: Although, i the published literature, o this theory, there is o metio of ay speifi equatios for the speial ase of a light soure ad a refrative medium i motio relative to the laboratory, it is ot diffiult, from theoretial stadpoit, to work out the details of omputig the speed of light ' through the refrative medium, o the basis of Eistei's speial theory of relativity. Let v s stad for the veloity of the light soure; ad v m stad for the veloity of refrative medium, with respet to the statioary referee frame of the laboratory. Sie, withi the framework of the speial theory of relativity, the veloity of the light soure has o effet o the veloity of light, we igore, here, the veloity of the soure v s etirely, ad take ito osideratio oly the veloity of the refrative medium v m, i all alulatios doe i the referee frame of the refratig medium ad the referee frame of the laboratory, orrespodigly. I the Referee Frame of the Refrative Medium: I the referee frame, i whih the refrative medium is at rest, the speed of light ', through the refrative medium, aordig to speial relativity, a be alulated by usig the followig equatio: for the ase, i whih the refrative medium is approahig the light soure; ad by usig this equatio: for the ase, i whih the refrative medium is reedig from the light soure.

36 I the Referee Frame of the Laboratory: I the referee frame of the laboratory, whether the light soure is i motio or at rest, whe the refrative medium is i motio, the speed of light ' through the refrative medium, aordig to the the speial theory of relativity, is alulated, i the ase of approah, by usig the followig equatio: æ1- vm ö 1 æ ö ç» - vm ç 1- è1- vm ø è ø where v m is the veloity of the refrative medium with respet to the laboratory. Ad likewise, the speed of light ' iside a reedig refrative medium is omputed by usig this equatio: æ1+ vm ö 1 æ ö ç» + vm ç 1- è1+ vm ø è ø where is refrative idex. The Speial Theory of Relativity ad the Result of the Fizeau Experimet: I the ase of a statioary light soure ad a approahig refrative medium, the origial Fizeau experimet as well as the Mihelso's repetitio have verified that the speed of light ' through the refrative medium, as measured i the statioary referee frame of the laboratory, is i aordae with the followig equatio: 1 æ ö - v ç 1- è ø where v is the veloity of the refrative medium with respet to the statioary light soure i the referee frame of the laboratory. Ad therefore, this experimetal result implies, eessarily ad idepedetly of ay physial theory, that, i the referee frame, i whih the refrative medium is at rest, the speed of light ', from the same statioary light soure, through the approahig refrative medium, is i aordae with the