(Presented at Days on Diffraction Conference, St. Petersburg, Russia, June 2005)

Transcription

1 Theetial, Numeial, and Expeimental Evidene f Supeluminal Eletmaneti and Gavitatinal Fields Geneated in the Neafield f Diple Sues (Pesented at Days n Diffatin Cnfeene, St. Petesbu, Russia, June 005 Abstat William D. Walke Öeb Univesity, Depatment f Tehnly, Sweden Reseah papes [] william.walke@teh.u.se Theetial and numeial wave ppaatin analysis f an sillatin eleti diple is pesented. The esults shw that upn eatin at the sue, bth the lnitudinal eleti and tansvese maneti fields ppaate supeluminally and edue t the speed f liht as they ppaate abut ne wavelenth fm the sue. In ntast, the tansvese eleti field is shwn t be eated abut / wavelenth utside the sue and launhes supeluminal fields bth twads and away fm the sue whih edue t the speed f liht as the field ppaates abut ne wavelenth fm the sue. An expeiment usin simple diple antennas is shwn t veify the pedited supeluminal tansvese eleti field behavi. In additin, it is shwn that the fields eneated by a avitatinal sue ppaate supeluminally and an be mdeled usin quadaple eletdynami they. The ase speed, up speed, and infmatin speed f these systems ae mpaed and shwn t diffe. Pvided the nise f a sinal is small and the mdulatin methd is knwn, it is shwn that the infmatin speed an be appximately the same as the supeluminal up speed. Adin t elativity they, it is knwn that between mvin efeene fames, supeluminal sinals an ppaate bakwads in time enablin vilatins f ausality. Seveal explanatins ae pesented whih may eslve this dilemma. Intdutin The eletmaneti fields eneated by an sillatin eleti diple have been theetially studied by many eseahes usin Maxwell s equatins and ae knwn t yield the fllwin well-knwn esults (MKS units: System diffeential equatin x p φ z θ E B φ E θ y V System PDE V t Field analysis Slvin the hmeneus equatin (Eq. f a diple sue yields [,,, 5, 6]: i i( ωt pk V N Cs( θ + e whee: N ( ( πε The fields an then be alulated usin the fllwin elatins [6]: E θ Fi. ρ ε ( Vaiable definitins E Radial eleti field E θ Tansvese eleti field B φ Tansvese maneti field V Sala ptential ρ Chae density ε Fee-spae pemittivity Laplaian Speed f liht t Time p Diple (q d ω Anula fequeny k Wave numbe B ω ( V i E ( B ( pcs( θ ω i( ωt yieldin: E [ i( ] e πε psin( θ i( ωt ωpsin( θ i( ωt [{ ( } i( ] e B [ i] e φ ( πε πε

2 Phase analysis The eneal fm f the eletmaneti fields eneated by a diple is: i[ ωt ] Field ( x + iy e If the sue is mdeled as Cs( ω t, the esultant eneated field is: Field Ma Cs + ωt Ma Cs θ ωt [{ } ] ( whee: Ma x + y It shuld be nted that the fmula desibin the ase is dependent n the quadant f the mplex vet. y y θ + Tan x θ Cs θ (5 x x + y x θ Phase speed analysis Phase speed an be defined as the speed at whih a wave mpsed f ne fequeny ppaates. The ase speed ( f an sillatin field f the fm Sin( ωt, in whih k k( ω,, an be detemined by settin the ase pat f the field t ze, diffeentiatin the esultant equatin, and slvin f t. ( 0 t ωt k ω ω k 0 (6 t t t k k + Diffeentiatin θ with espet t yields: θ k k (7 Cmbinin these esults and insetin the fa-field wave numbe (k ω/ yields: Gup speed analysis ω θ k θ (8 The up speed f an sillatin field f the fm: Sin( ωt, in whih k k( ω,, an be alulated by nsidein tw Fuie mpnents f a wave up [7]: Sin( ω t k + Sin( ω t Sin( ωt Sin( ωt (9 in whih: ω ω ω k k, k, ω ω ω + k + k, k The up speed ( an then be detemined by settin the ase pat f the mdulatin mpnent f the field t ze, diffeentiatin the esultant equatin, and slvin f t : ω k ( ωt 0 ω k t t t 0 t k k + (0 Diffeentiatin θ with espet t yields: θ k k ( Cmbinin these esults and usin the fa-field wave numbe (k ω/ yields: ω θ θ ω θ ω lim θ small ω θ k It shuld be nted that the deivatins f the abve ase and up speed elatins ae available in pevius publiatins by the auth [8, 9, 0,,, ] and in the fllwin well-knwn efeene []. (

3 In additin, in de f the up speed t be valid, a sinal shuld nt distt as it ppaates. It is knwn fm eletni sinal they that in de t minimize sinal disttin, the ase vs. fequeny uve must be appximately linea ve the bandwidth f the sinal and the amplitude vs. fequeny uve must be appximately nstant ve the bandwidth f the sinal [5]. It is shwn belw that the amplitude vs. fequeny uve an even be appximately linea ve the bandwidth f the sinal, pvided the ati f the slpe f the uve t the sinal amplitude is small. Assumin that the amplitude vs. fequeny uve is ineasin and appximately linea ve the bandwidth f a mdulated aie sinal, eah sinal manitude (A Fuie mpnent (w m will be ineased by (u and the Fuie mpnent symmeti abut the aie (w will be edued by (u: [( A u Sin( w t w t + ( A + u Sin( w t w t ] m + A Cs( w t Sin( w t + u Sin( w t Cs( w t ( m The tw Fuie mpnents fm an amplitude mdulated sinal whee the manitude f the aie is: A m m Cs ( w t + u Sin ( w t A Cs( w t ( m It shuld be nted that disttins t the manitude ae minimal pvided: u /A << m k A whee (u an be appximated usin the deivative elatin: u, (5 k pvided the amplitude vs. fequeny uve is appximately linea ve the bandwidth f the sinal. In additin, it shuld be nted that ase speed and up speed an als be detemined fm tw diffeent fequeny mpnents (ω, ω usin elatins (Eq. 8, : ω θ yields: θ ω ω ω ω Given ω ω m, + ω ω ω ωm (6 θ + θ θ θ Given tw diffeent fequenies, plts f the ase speed and up speed an then be detemined f eah field mpnent by insetin the espndin ase elatin (Eq. 7, 0,. It shuld be nted that these elatins yield the same esults as (Eq. 8, pvided the ase and manitude vs. fequeny uves ae appximately linea ve the bandwidth f the sinal. m u w W m W m A u Wave ppaatin analysis f nea-field eleti diple EM fields T detemine hw the EM fields ppaate in an eleti diple system, ne an apply the abve ase and up speed elatins (Eq. 8, t the knwn theetial slutin f an eleti diple (Eq..

4 Radial eleti field (E slutin y x Tan θ ( ( << (7 + ( << ( >> (8 ( + ( (9 << >> ( + ( E Phase vs. Fi. E / vs. E / vs. Fi. Fi. Tansvese eleti field (E θ slutin y x ( ( θ Cs (0 ( + ( ( + ( ( ( + ( ( ( + ( 6 8 6( + 7( ( + ( ( E θ / vs. Fi. 6 E θ Phase vs. Fi. 5 E θ / vs. Fi. 7 Tansvese maneti field (B φ slutin y x Cs + ( + ( θ ( ( ( + ( B φ / vs. Fi. 9 + ( ( (5 B φ Phase vs. Fi. 8 B φ / vs. Fi. 0

5 The abve esults (p. wee iinally published by the auth in 999 [0], but the ppaatin f the lnitudinal eleti field and avitatinal field next t a sue was published ealie by the auth in 997 [, ]. It shuld be nted that afte these dates simila esults have been published by the auths [6, 7]. Numeial veifiatin f field mpnent ppaatin T veify the pedited wave ppaatin effets, a numeial simulatin was pefmed. The simulatin nsisted f extatin the tansfe funtin fm the vaius field mpnents f the knwn diple slutin (Eq. and then invese Fuie tansfmin (FT - the Fuie tansfm (FT f a iven sinal multiplied by the diple tansfe funtin [8]: Result Si FT - [ FT [Sinal] x G ], whee "Result Si" is the esultant ppaatin sinal as a funtin f time, and "G" is the tansfe funtin f the wave ppaatin system. A simple amplituded mdulated sinal (00MHz aie, 0MHz mdulatin, eneated by addin tethe tw sinusidal sillatins (80MHz and 0MHz, was applied as an input sinal. The simulatins yielded ppaatin sinal-vesus-time animatins as a funtin f distane ( fm the sue. T mpae the esultin simulatins t theetial expetatins, a ppaatin mdulatin envelpe f the AM sinal was supeimpsed: Md Cs[w m t-(θ -θ /] whee q and q ae the theetially expeted ase shifts f the fequenies used t eate the AM sinal (Eq. 7, 0,. The esults belw shw a vey d math between they and numeial simulatin. Fi. Resultant E vs. time animatin plts as a funtin f distane ( fm sue Theetial mdulatin envelpe (dtted (/5 (/5 (5/5 Fi. Resultant E θ vs. time animatin plts as a funtin f distane ( fm sue (/5 (8/5 (5/ Fi. Resultant H φ vs. time animatin plts as a funtin f distane ( fm sue (/5 (/5 (5/5 5

6 0.00 Fi. Mathematia de f simulatin f E θ wave ppaatin f80*0^6; f0*0^6; f(f+f/; fm(f-f/; w*pi*f; w*pi*f; T/fm; xcs[w*t]+cs[w*t]; (* Input sinal * n0; Cyle.5; tscyle*t/n; fs/ts; fnfs/; vn[table[x,{t,0,cyle*t,cyle*t/n}]]; yfuie[v]*.; k*pi/l; L/f; *0^8; un[table[k,{f,0,fs,fs/n}]]; hy*(-(u**(u*-i*(u*/^*exp[i*u*]; (* FT [Sinal] x G * ltake[h,n/]; <<Gais`Animatin` <<Gais`MultipleListPlt` L/f; L/f; k*pi/l; k*pi/l; km(k-k/; k(k+k/; wm*pi*fm; w*pi*f; k*-acs[(-(-k*^/sqt[(-(k*^+(k*^]]; (* E θ ase elatin f f * k*-acs[(-(-k*^/sqt[(-(k*^+(k*^]]; (* E θ ase elatin f f * tnn[table[t,{t,0,cyle*t,cyle*t*/n}]]; Md*Abs[(-(w/**(w/*-I*(w/*/^]*Cs[wm*tn-(-/]; (* Theetial plt * Animate[MultipleListPlt[Re[InveseFuie[l]],Md,PltJined->Tue, SymblShape\[Rule]Nne],{,0.00,/f,/f/5}] E animatins wee eneated usin the abve de and substitutin the fllwin knwn E elatins hy*(-i*(u*/^*exp[i*u*]; (* FT [Sinal] x G * k*-atan[k*]; (* E ase elatin f f * k*-atan[k*]; (* E ase elatin f f * Md*Abs[(-I*(w/*/^]*Cs[wm*tn-(-/]; (* Theetial plt * Bφ animatins wee eneated usin the abve de and substitutin the fllwin knwn Bφ elatins hy*(-(u*-i*u/^*exp[i*u*]; (* FT [Sinal] x G * k*-acs[-k*/sqt[+(k*^]]; (* B φ ase elatin f f * k*-acs[-k*/sqt[+(k*^]]; (* B φ ase elatin f f * Md*Abs[(-(w/*-I]*w//^*Cs[wm*tn-(-/]; (* Theetial plt * T hek the simulat, the AM sinal was als applied t a liht ppaatin system. The esults yielded a 00 MHz aie, 0 MHz mdulated AM sinal animatin whih linealy ineased its ase shift as expeted. This was veified by substitutin the fllwin knwn elatins: hy*exp[i*u*]; (* FT [Sinal] x G * Md*Cs[wm*tn-( k* - k*/]; (* Theetial plt * It shuld be nted that n sinal disttin was bseved in these simulatins. This an be attibuted t the fat that the ase and amplitude vs. fequeny uves ae appximately linea ve the bandwidth f the sinal ( f/f 0/00 /7.5. The use f lineaity nstaint an be seen t be justified by plttin u /A f eah field mpnent and ntin that it is muh less than ne ve the bandwidth f the sinal (Eq E (u /A vs. E θ (u /A vs. B ϕ (u /A vs. Fi. 5 Fi. 6 Fi E (A vs. 800 E θ (A vs. 700 B ϕ (A vs

7 Beause f the exellent math between the numeial and theetial methds, the validity f bth methds is nfimed in analyzin the ppaatin f simple sinals in this system. Wheeas the theetial methd enables the ppaatin f simple sinals t be lealy undestd, the numeial slutin is nt nly useful in veifyin the theetial esults, it an als be useful in undestandin the ppaatin f me mplex sinals whih may be diffiult t analyze mathematially. Expeimental veifiatin f E θ slutin A simple expeimental setup usin tw diple antennas, a 7 MHz (68.65 m wavelenth, watt sinusidal tansmitte, and a 500MHz diital sillspe has been develped t veify qualitatively the tansvese eleti field ase vs. distane plt pedited fm standad EM they (Eq. 0, Fi. 5. The ase shift f the eeived antenna sinal (Rx elative t the tansmitted sinal (Tx was measued with an sillspe as the distane between the antennas ( el was haned fm 5 m t 70 m in inements f 5 m. The data was then uve fit with a d de plynmial. The ase speed vs. distane uve was then eneated by diffeentiatin the esultant uve fit equatin with espet t spae and usin (Eq. 8. The up speed vs. distane uve was eneated by usin the diffeential elatin: θ ω θ and insetin it int the elatin (Eq. : whee: Dw Dk θ 60 yieldin: whee: el (6 θ θ el + el el Expeimental setup Fi. 8 el 7 MHz Watt Tansmitte Tx Diple Ant Rx Diple Ant Ch τ Ch T Osillspe Expeimental data E θ ase plt simila t Fi. 5 Fi. 9 Fi. 0 θ (de vs. / E θ uve fit equatin (. + (-6.5 el + (88.9 el + (-5. el (7 7

8 Resultant E θ ase speed and up speed plts - vey simila t the pedited plts (Fi. 6, 7 / vs. / / vs. / Fi. Fi. It shuld be nted that the esults ae nly qualitative due t efletins. Refe t a pevius pape witten by the auth f me details [8]. Othe wave ppaatin systems with simila supeluminal behavi Maneti diple Theetial analysis f a maneti diple eveals that the system is vened by the same patial diffeential equatin as the eleti diple with the E and B fields intehaned [, ]. The esultin fields ae fund t be the same as the fields eneated by an eleti diple (Eq. and theefe the ase speed and up speed f these fields ae the same as (Eq. 8-5, exept that the E and B fields ae intehaned. Eleti and maneti quadaple Usin the same methd f analysis as was dne f the eleti diple, the sala ptential f an eleti quadaple is fund t be []: V N i ( Cs e i( ω θ t (8 ( ( The fields an then be alulated usin the fllwin elatins [6]: B ω i ( V E ( B (9 yieldin: ω B φ 6Nω i ( ( i( ωt [ Cs( θ Sin( θ ] e (0 E 6Nk i + ( ( ( i( ωt [ Cs ( θ ] e ( i( ωt Eθ Nk i + [ Cs θ Sin θ ] e ( ( ( ( ( ( qs k s Diple lenth, q Chae whee: N in all the abve slutins. k Wave numbe, ε πε Pemitivity The fields f a maneti quadaple ae als the same, with the E and B fields intehaned. The ase and up speed f these fields an be detemined usin the elatins (Eq. 8,. These esults ae pesented in the next setin (Eq

9 Gavitatinal quadaple F weak and slwly vayin avitatinal fields, Einstein s equatin bemes lineaized and edues t [9, 0]: V V πgρ t ( Whee: ρ Mass density V Gavitatinal ptential G Gavitatinal nstant Laplaian Speed f liht t Time Exept f the sue tem, the patial diffeential equatin f the ptential is the same as that f an sillatin hae (Eq.. Beause f this similaity ne an then use the sillatin hae slutins by simply substitutin: ε /(πg. In additin, beause mmentum is nseved, a mvin mass must push ff anthe mass. The avitatinal field eneated by the senday mass adds t the avitatinal fields eneated by the mvin mass, esultin in a linea quadaple sue. The avitatinal fields eneated by an sillatin mass ae theefe f the same fm as the fields eneated by an eleti quadaple (Eq ( Cs e i( ω V N i θ t ( ( ( It is knwn that f weak and slwly vayin avitatinal fields, Geneal Relativity they edues t a fm f Maxwell s equatins [9]. The fields an then be alulated usin the fllwin elatins: B ω i ( V E ( B (5 ω whee (E is the avitatinal fe vet and (B is the slenidal avitatinal fe vet. The nstant (N an be detemined by substitutin the elatins: ε /(πg and q m int the value f (N used in the eleti quadaple. In additin, this esult an be heked by lkin at the stati quadaple slutin and mpain it t the abve slutins in the limit ( 0. The esults yield: B φ 6Nω i( ωt i [ Cs θ Sin θ ] e ( ( (6 ( ( E i( ωt 6Nk i + [ Cs ( θ ] e ( (7 ( ( E θ whee: i [ Cs Sin ] e ( ( ( i( ω Nk θ θ t ( ( (8 N G m s k, G Gav nst., m mass, s Diple lenth, k Wave numbe The ase and up speed elatins f these fields an then be detemined by usin the ase and up speed equatins deived ealie in the pape (Eq. 8,. It shuld be nted that all f the plts lk vey simila t thse f an eleti diple (see pae. 9

10 B φ ase, ase speed, up speed analysis ATan + << ( ( ( [ ( + ( + 9] [ 5 + 9( + ( ] π ( O( (9 (0 ( (ad vs. Fi. / / vs. Fi. / / vs. Fi. 5 E ase, ase speed, up speed analysis + ATan + << ( ( [( + ( + 9] [( + 9( + 5] 5 7 ( O( ( ( ( ( (ad vs. Fi. 6 / / vs. Fi. 7 / / vs. Fi. 8 E θ ase, ase speed, up speed analysis 6 + ( 6 ( ( 6 6 ( + ( 6 ( 6( 5 + ATan ( + << 6 [ 6 ( + ( ] 0 O( 7 (5 (6 ( ( ( + 8( + 5( 080( (ad vs. Fi. 9 / / vs. / vs. Fi. 0 Fi. / 0

11 Field ntu plts (linea quadaple in ente and vetial Cntu plts f the fields (Eq. 6-8 usin Mathematia sftwae yields [9]: B φ ntu plt E ntu plt E θ ntu plt Fi. Fi. Fi Ttal E field plts (linea quadaple in ente and vetial unless speified Usin vet field plt ais in Mathematia sftwae [9], the E and E θ an be mbined and pltted as vets (Fi. 5. A me detailed plt f the ttal E field an be btained by usin the fat that a line element ssed with the eleti field 0. A ntu plt f the esultin elatin yields the ttal E field plts belw (Fi Nea-field Nea-field Fa-field Vet plt Cntu plt Cntu plt Fi. 5 Fi. 6 Fi. 7 p p Expeimental evidene f supeluminal avitatinal fields Evidene f infinite avitatinal ase speed at ze fequeny has been bseved by a few eseahes by ntin the hih stability f the eath s bit abut the sun [, ]. Liht fm the sun is nt bseved t be llinea with the sun s avitatinal fe. Astnmial studies indiate that the eath s aeleatin is twads the avitatinal ente f the sun even thuh it is mvin aund the sun, wheeas liht fm the sun is bseved t be abeated. If the avitatinal fe between the sun and the eath wee abeated then avitatinal fes tanential t the eath s bit wuld esult, ausin the eath t spial away fm the sun, due t nsevatin f anula mmentum. Cuent astnmial bsevatins estimate the ase speed f avity t be eate than x0 0. Auments aainst the supeluminal intepetatin have appeaed in the liteatue [, ]

12 Infmatin speed If an amplitude-mdulated sinal ppaates a distane (d in time (t, then the infmatin ntained in the mdulatin ppaates at a speed: inf d/(t+t (8 whee (T is the amunt f time the mdulated sinal must pass by the detet in de f the infmatin t be detemined. The infmatin in the wave is detemined by measuin the amplitude, fequeny, and ase f the wave mdulatin envelpe. If a wave is ppaated ass distanes in the fafield f the sue, then the wave infmatin speed is appximately the same as the wave up speed. This is beause the wave ppaatin time (t is muh eate than the wave infmatin sannin time (T, nsequently: inf d/t. In the neafield f the sue, if nthin is knwn abut the type f mdulatin, then the sannin time (T an be muh lae than the wave ppaatin time (t, theeby makin the wave infmatin speed muh less than the wave up speed. This an be undestd by ntin that seveal mdulatin yles ae equied f a Fuie analyze t be able t detemine the wave mdulatin amplitude, fequeny, and ase. But if the type f mdulatin is knwn, then nly a few pints f the mdulated sinal need t be sampled by a detet in de t uve fit the sinal and theefe detemine the mdulatin infmatin. If the nise in the sinal is vey small then the sinal sannin time (T an be made muh smalle than the sinal ppaatin time (t, nsequently: inf ~ d/t. Relativisti nsequenes Adin t the elativisti Lentz time tansfm (Eq. 9, if an infmatin sinal an ppaate at a speed (w faste than the speed f liht (, then the sinal an be efleted by a mvin fame (v lated a distane (L away and the sinal will aive befe the sinal was tansmitted ( t < 0. Sine the infmatin in the sinal an be used t pevent the sinal fm bein tansmitted, this esults in a lial ntaditin (vilatin f ausality. Hw an the sinal be deteted if it was neve tansmitted? Cnsequently, Einstein in 907 stated that supeluminal sinal velities ae inmpatible with Relativity they [5]. Fi. 8 Statinay fame Sinal w L Mvin fame v x' x whee: v t' γ t L t x L w γ v x Ne (9 w > v Beause Relativity they pedits that a mvin eflet (whih has mass an neve mve faste than liht (v <, then in de f ( t > 0 the sinal ppaatin speed must be less than the speed f liht (w<.

13 Aument aainst the supeluminal intepetatin Sme ysiists have ppsed that a diple sue eneates psitin, velity, and aeleatin-dependent ppaatin fields, eah f whih ppaate at the speed f liht [5, 6]. It is aued that the intefeene f these field mpnents ives the illusin that they ppaate supeluminally. Althuh this is a plausible explanatin it is nt lea that this is tue. It an be shwn usin Maxwell s equatins that the fields eneated by a diple sue an be mdeled by tw upled patial diffeential equatins in tems f the sala ptential (V and the vet ptential (A: ρ V ( A t ε and A j A + ( A + V + (50 t t ε whee (j is the sue uent density, (ρ is the sue hae density, and ( is the speed f liht [5(Ch 8-6, (Ch 6.]. In de t simplify the equatins, an equatin is intdued with n ysial basis in EM they (aue nditin. The mst V mmn is the Lentz aue: A whih yields the fllwin simple t deupled nd de patial diffeential equatins: yieldin slutins: A j A and t V ε πε Vl ρ dvl V V t and A µ π Vl ρ ε j dvl whee the haes and uents in the slutins ae evaluated at a pevius time (etaded: t - /. It is aued hee that the Lentz aue is nt the nly aue that an be used t simplify the tw PDEs. Many the aues ae pssible inludin the Culmb aue ( A 0, whih in patiula is knwn t yield an instantaneus sala ptential [(Ch 6.5]. This shws that althuh the diple slutin is thuht t be aue independent, the fm f the slutin may diffe when diffeent aue nditins ae used, ivin ise t diffeent intepetatins f the speed f the esultin ppaatin fields. Only the PDE s (Eq. 50 ae ysial in EM they, and an pbably nly be slved numeially withut usin a aue elatin, yieldin fields that ppaate as shwn in this pape (see paes -6. Cnlusin The analysis pesented in this pape has shwn that the fields eneated by an eleti maneti diple quadaple, and als the avitatinal fields eneated by a quadaple mass sue, ppaate supeluminally in the neafield f the sue and edue t the speed f liht as they ppaate int the fafield. The up speed f the waves pdued by these systems has als been shwn t be supeluminal in the neafield. Althuh infmatin speed an be less than up speed in the neafield, it has been shwn that if the methd f mdulatin is knwn and pvided the nise f the sinal is small enuh, the infmatin an be extated in a time peid muh smalle than the wave ppaatin time. This wuld theefe esult in infmatin speeds nly slihtly less than the up speed whih has been shwn t be supeluminal in the neafield f the sue. It has als been shwn that Relativity they pedits that if an infmatin sinal an be ppaated supeluminally, then it (5 (5

14 an be efleted by a mvin fame and aive at the sue befe the infmatin was tansmitted, theeby enablin ausality t be vilated. Given these esults, it is at pesent unlea hw t eslve this dilemma. Relativity they uld be inet, pehaps it is et and infmatin an be sent bakwads in time. Pehaps as suested by the Hawkin hnly ptetin njetue [7], natue will intevene in any attempt t use the infmatin t hane the past. Theefe infmatin an be ppaated bakwads in time but it annt be used t hane the past, theeby pesevin ausality. Anthe pssibility is that adin t the many-wlds intepetatin f quantum mehanis [8], multiple univeses ae eated any time an event with seveal pssible utmes takes plae. If this intepetatin is et, then infmatin an be tansmitted int the past f altenative univeses, theeby pesevin the past f the univese fm whih the sinal was tansmitted. In additin t the theetial impliatins f the eseah disussed abve, it may als have patial appliatins, suh as ineasin the speed f eletni systems that will sn be limited by liht-speed-time delays. It shuld als be pssible t edue the time delays inheent in uent astnmial bsevatins by mnitin lwe fequeny EM and eventually avitatinal adiatin fm these sues. Lastly, usin lw fequeny EM tansmissins, it shuld be pssible t edue the ln mmuniatin time delays t spaeaft. Refeenes All eseah by the auth n this tpi fund at: xxx.lanl.v, -q, auth: William D. Walke, seah all ahives, all yeas. W. Panfsky, M. Philips, Classial eletiity and manetism, Addisn-Wesley Pub. C., (96. J. D. Jaksn, Classial eletdynamis, Jhn Wiley & Sns Pub., (975. P. Lain, D. Csn, Eletmaneti fields and waves, W. H. Feeman and Cmpany Pub., ( R. Feynman, R. Leihtn, M. Sands, Feynman letues n ysis, Vl., Ch., Addisn-Wesley Pub., (96. 6 J. Westad, Eletdynamis, Spine-Vela Pub., Ch. 6, ( F. Cawfd, Waves: Bekeley ysis use, MGaw-Hill Pub., Vl., pp. 69-7, ( W. D. Walke, Nea-field analysis f supeluminally ppaatin eletmaneti and avitatinal Fields, Viie IV Sympsium, Pais, Fane, Sept. (00, T be published in sympsium peedins, ef. elet ahive: 9 W. D. Walke, Expeimental evidene f nea-field supeluminally ppaatin eletmaneti fields, Viie III Sympsium Gavitatin and Csmly, Bekeley, Califnia, USA, -5, Kluwe Pub., Auust (000. ef. elet ahive: 0 W. D. Walke, Supeluminal nea-field diple eletmaneti fields, Intenatinal Wkshp Lentz Gup CPT and Neutins, Zaateas, Mexi, June -6, Wld Sientifi Pub. (999. ef. elet ahive: W. D. Walke, Supeluminal ppaatin speed f lnitudinally sillatin eletial fields, Cnfeene n ausality and lality in mden ysis, Tnt Canada, Kluwe Aad Pub., (998. ef. elet ahive: W. D. Walke, J. Dual, Phase speed f lnitudinally sillatin avitatinal fields, Edad Amaldi nfeene n avitatinal waves, Wld Sientifi Pub., (997. ef. elet ahive: W. D. Walke, Gavitatinal inteatin studies, ETH Diss N. 89, Züih, Switzeland, (997. M. Bn and E. Wlf, Piniples f ptis, 6th ed., Peamn Pess, pp. 5-, ( P. Denbih, System analysis and sinal pessin, Addisn-Wesley Pub. C., Ch., ( H. Shantz, Eletmaneti eney aund Hetzian diples, IEEE antennas and ppaatin maazine, Vl., N., Apil (00. ef. elet ahive: 7 Z. Wan, New Investiatins n Supeluminal Ppaatin f Eletmaneti Waves in Nndispesive Media, Nv. (00. ef. elet ahive:

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