Fresnel Dragging Explained

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1 Fresel Draggig Explaied 07/05/008 Decla Traill The Fresel Draggig Coefficie required o explai he resul of he Fizeau experime ca be easily explaied by usig he priciples of Eergy Field Theory se ou i my earlier papers (see refereces a he ed of his paper). The key o udersadig why he effec occurs lies i he udersadig ha as he ligh propagaes hrough moig waer i is beig coiually absorbed ad re-emied by each waer molecule. Whils absorbed by he waer molecules, he ligh is slowed by refracie idex facor ad carried by he waer molecules a heir full elociy; bu whe raellig bewee waer molecules i raels a he ormal, full speed of ligh (hrough he backgroud eergy field ha is cosidered o be saioary wih respec o he waer). The assumpio ha he ligh wae is slowed eely ad raels a a cosa c hrough saioary waer is wrog. The realiy is ha he rasmissio is a sop/sar ype of process, wih he ligh slowig as i ieracs wih each waer molecule, bu raellig a full ligh speed bewee molecules. As a resul of his, he c erms used i he equaios ha describe he rael imes i he Fizeau experime eed o be modified o accou for his differece. Each paricle of waer is iself a sadig wae comprised of eergy waes ha are moig hrough he backgroud eergy field, which acs as a medium. The backgroud eergy field is comprised from he sum of all of he paricles (boh ear ad far) i he causally coeced Uierse. Whe a ligh wae is absorbed by a waer molecule i causes he sadig waes of he molecule o oscillae as hey rael hrough he backgroud eergy field. The, as he oscillaio wae passes hrough he molecule ad emerges o he oher side, he oscillaios cause reemissio of ligh io he backgroud field, whereupo he ligh will he rael uimpeded o he ex waer molecule ad so o.

2 Armed wih his udersadig, we ca ow aalyse he experime successfully: Whe he waer is flowig dow he ubes i he experime, he wae of disurbace due o he ligh wae propagaig i he waer is carried alog wih he waer a he waer s full elociy, as oe would expec i a classical sese, causig he rae of passage of ligh o be icreased or decreased, depedig if he ligh is raellig i he same direcio as he waer flow, or agais i. Howeer, as he waer molecules do o ake up he whole olume of space, here exiss space bewee hem where he ligh raels a he ormal speed of ligh wih respec o he saioary referece frame. The disace ha he ligh raels before i ecouers aoher waer molecule is a fucio of he speed a which ligh raels hrough space (he backgroud eergy field) ad he speed a which he waer is raellig. Thus, due o he waer s moio whils he ligh is raellig hrough he space bewee molecules, he disace he ligh mus rael hrough space uil i ecouers aoher waer molecule will eiher icrease or decrease. By akig io accou hese wo effecs ha are occurrig simulaeously ad i opposie direcios, he oal delay o he rael of he ligh beam ca be calculaed. The differig disace ha he ligh raels bewee waer molecules depedig if i is raellig wih or agais he flow of he waer ca be reaed mahemaically as a differeial i he speed of ligh i he up/dow sream direcios. Thus, effeciely, he ligh raels i he upsream direcio a a speed ha is higher ha c (he ormal speed of ligh hrough he backgroud eergy field), ad a a speed ha is slower ha c i he dowsream direcio. To proe ha his approach works, see he followig mahs. The wo ligh pah rael imes i he Fizeau experime are: 1 L c (1) L c + () I he ew aalysis, we eed o use he followig ew defiiios:

3 c up c + (3) c dow c (4) The reaso for hese defiiios is ha if he ligh raels uimpeded a speed c whe bewee waer molecules, raher ha a c hrough he whole disace, he he disace raelled by he ex waer molecule ha is abou o receie he propagaig sigal will be differe by he amou per ui of ime. If he propagaig force bewee he waer molecules were raellig a c, he i oe ui of ime, he ex waer molecule o receie he sigal would hae raelled a disace of o mee he icomig sigal. Howeer, he propagaig force is raellig bewee he waer molecules a a speed of c (hrough he backgroud eergy field of space, as explaied earlier) so he disace raelled i oe ui of ime by he ex waer molecule will be. So he amou we mus ary he c erm i equaios (1) ad () is. Thus we hae equaios (3) ad (4) as show aboe. If we cosider he Upsream direcio as a case i poi: c Fig 1: If he force bewee he molecules moed a c, he would be he disace he waer had moed durig i s rael bewee molecules before i mees he ligh wae comig from he opposie direcio. c

4 Fig : Bu he force bewee he molecules moes a c, so he waer has moed less durig i s rael bewee molecules before meeig wih he ligh wae. Explaaio for he chage o c i equaios (1) & (): Igore for he mome he sebacks o he ligh s pah by he waer molecules ha carry i backwards, ad udersad ha for he ligh wae o rael hrough he space i he apparaus i mus coer he full legh of i o reach he ed, he realize ha durig he passage hrough his empy space i is raellig a full ligh speed c, o a c. This beig he case i becomes obious ha i will coer his disace imes more quickly. So, as he waer is moig a speed hrough he apparaus, durig he ime ha he ligh akes o rael hrough he empy space regio (a speed c raher ha a speed c ), i will hae raelled imes less disace: so period. less disace raelled by he waer i he same ime So his meas ha durig he ligh s passage hrough he apparaus here is a disace of less i which i will ecouer waer molecules ad be slowed by facor as a resul of he ecouer. Thus whe applyig he facor o he disace per ui of ime ha he ligh akes o rael hrough he apparaus his disace per ui of ime mus be ake io accou (added o or subraced from c ) o gie he correc umber. Therefore we hae calculaed he disace per ui ime ha he disurbace wae has effeciely raelled ( c + upsream or c

5 dowsream) ad he subsiue hese ew alues io equaios (1) ad () where he speed of ligh c appears: Noe: The facor sill eeds o be applied o he effecie speed of ligh calculaed aboe as he absorpio/re-emissio processes & waer molecule spacig/desiy is wha accous for he facor, ad hese effecs sill occur ad impede he rael of he ligh wae hrough he waer colum as before. So equaios (1) ad () become: L L L 1 cup c c (5) L L L cdow + c c (6) Makig he subsiuio: 1 1 (7) The equaios (5) ad (6), become: 1 L c (8) L c + (9) The o ge he oerall resul, we combie he wo imes: L L 1 c c +

6 c c L + 1 c 1 4L c (10) This is he same as equaio (5) i my paper iled The Fizeau Experime (see referece a he ed of his paper). So he oal frige shif is: c δ λ 0 4cL c λ0 (11) Noe: This resul assumes moochromaic ligh is used i he experime, as he effec of dispersio due o spreadig of differe compoe frequecies is o icluded here. A small correcio eeds o be made if o usig moochromaic ligh. Refereces Relaiely Simple? A Iroducio o Eergy Field Theory 001, Decla Traill hp:// Decla Traill The Fizeau Experime hp://

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