Chaos and Correlation January 8, 2012

Transcription

1 Chaos and Corrlaon January 8, Chaos and Corrlaon Inrnaonal Journal, January 8, Квантовая электродинамика Лоренца Lornz quanu lrodynas landr P. Trunv (Torono, Canada) landr P. Trunv Обсуждается вопрос о расширении электродинамики Лоренца до квантовой теории. Сформулирована система уравнений квантовой электродинамики Лоренца. Ключевые слова: релятивистская теория, квантовая электродинамика, квантовая механика, электрон, электромагнитное поле. Th quson of ndng h Lornz lrodynas o quanu hory s dsussd. Th sys of quaons of h Lornz quanu lrodynas was sablshd. Kywords: Rlavs Thory, Quanu lrodynas, Quanu Mhans, lron, lroagn Fld. Lornz lrodynas (brf ovrvw) In lassal lrodynas, an lron, jus lk any ohr harg, has h lr and agn fld. To dsrb slf-flds of h lron Lornz [] usng salar and vor ponals sasfyng h quaons: u () hp//haosandorrlaon.org/chaos/cr.pdf

2 Chaos and Corrlaon January 8, Hr -,, u h spd of lgh, h harg dnsy and h vloy of h lron, rspvly. In h spal as of oon wh onsan vloy vor ponal s prssd hrough h salar ponal n h for [] u () Hn, h probl of drnng h flds of h lron s rdud o h probl of ongson hargs ponal wh a gvn dnsy and vloy of nr of ass. s knows, o solv hs probl, Lornz [] usd ransforaon of varabls (Lornz ransforaon), whh allows rdung h probl o h Posson quaon: u Hr β = u /., y z (3) (4) Thus, h probl of fndng h ponal of ovng hargs rdud o h probl of fndng h lrosa ponal of fd hargs wh a gvn dnsy. Indd, h unknown lr and agn flds ar drnd by ponal gradns, whh s h soluon of quaon (4), w hav hp//haosandorrlaon.org/chaos/cr.pdf

3 Chaos and Corrlaon January 8, hp//haosandorrlaon.org/chaos/cr.pdf z z y y z y / /, ) (, ) (, ) ( Hn w fnd h lr and agn flds by forulas y z z y, ) ( H Th ranson fro h sys () o (4) aually s a Lornz ransforaon. Ths ransforaon nluds h Gallo ransforaon, u as wll as h slary ransforaon (3), falar fro rlavs hors. Howvr, h harg dnsy rans an unknown quany, whh n braha hory [] s rplad by h surfa harg dsrbuon on a rgd sphr,.. boundary ondon. Ths approah allows us o solv oplly h probl of h lr and agn fld of an lron ovng wh onsan vloy [- ]. Indd, h nal rgd sphr undr h ransforaons (3) s ransford no an llpsod for whh h soluon of lrosa probl s wll known. Usng

4 Chaos and Corrlaon January 8, hs soluon, braha [] alulad h nrgy and onu of h lroagn fld of an lron n h for of ln 8R G p Hr R - radus of h sphr. ( ) ln 8R Th lng valu of h oal nrgy of h lron s a (5) () 8R Cobnng h frs and sond quaon (5) w fnd h dsprson rlaon, whh w wr n h for f (u / ) = G / s Fgur. hp//haosandorrlaon.org/chaos/cr.pdf

5 Chaos and Corrlaon January 8, Usng h onu prsson (6), w an drn h longudnal and ransvrs ass, aordng o h forulas l dg 3 d 6R ln G ( )ln 3 6R Th longudnal ass hararzs h nra of h body whn h vloy hangs n agnud, and h ransvrs ass hararzs h nra only whn h vloy dron hangs, for apl, an lron ovng n a unfor agn fld. L valus for longudnal and ransvrs ass (6) ond a, n hs as w hav l 6R ssung ha h ass l (7) s qual o h rs ass, w an dfn h lassal lron radus R 6 Kaufan [3] prford a nubr of prns n whh h asurd dflon of ba-lrons n h lr and agn fld. H showd ha h prnal dpndn of h ransvrs ass on h vloy orrsponds wll o h braha hory s Fgur. Kaufan blvd ha h lron ass s nrly of lroagn nrgy, as follows fro prssons (5) - (6). Lornz hory of lrons [], as wll as braha hory [], basd on h da of h sn of a lunfrous hr - a onnuous du n whh (6) (7) (8) hp//haosandorrlaon.org/chaos/cr.pdf

6 Chaos and Corrlaon January 8, lroagn wavs propaga. Th ngav rsul of Mhlson-Morly prn o d h nflun of h arh's oon hrough h hr on h spd of lgh, ford o ronsdr h bass of Lornz hory of lrons [[. s a rsul, Lornz forulad a gnral for of h lrodynas quaons ransforaon, whh, oghr wh h ransforaons (3) nlud h onvrson by h forula / Lornz suggsd ha all aral bods ar prnng rduon n h sz along h dron of ovn by h forula (3), whh n hs as an b wrn as l l (9) () Th nw odl s h lron ondung sphr n h oordna sys, whr rss, and n h ovng fra h lron s an llpsod of roaon, oprssd no h dron of oon aordng o h quaon (). Lornz found ha, n hs as, h longudnal and ransvrs lron ass s onvrd as follows 3 / / ( ), ( ) l () Lornz has shown ha hs quaons ar applabl no only o lrons and aos, bu also o any aral bods. nsn [4-5] dvlopd Lornz das, basng h on h prnpl of rlavy and h onsany of h spd of lgh. On publshd h frs papr on rlavy hory [4], Kaufann rpad hs prns o opar h hory by braha [], Buhrr [6] and Lornz-nsn [, 4]. Lornz [] and nsn [5] prasd hs prns, nvr doubng hr auhny. lhough h rsuls hp//haosandorrlaon.org/chaos/cr.pdf

7 Chaos and Corrlaon January 8, of Kaufan [3] or onssn wh h braha hory []. In subsqun yars, was pu a lo of prns [7-9] ha onfrd h hory of Lornz-nsn. Howvr, h braha hory was rjd as a bankrup afr h publaon of daa [9], oband n h lrosa analyzr, whh onand only hr pons - s Fgur. Fgur : Dpndn of h ransvrs lron ass on vloy aordng o h braha hory [] and Lornz-nsn hory [, 4], and aordng o prnal daa [3, 7-9]. h, suggsd, rahr, a loss of nrs n h probl, rahr han h dsr o ronl h Lornz-nsn hory wh prn. Indd, a h of publaon [9] n 94 alrady sd Dra rlavs quanu hory of h lron [], and h spru of h hydrogn ao was pland on h bass of h nonrlavs Shrödngr quaon []. Th spal hory of hp//haosandorrlaon.org/chaos/cr.pdf

8 Chaos and Corrlaon January 8, rlavy (STR) was apd by ladng horal physss whou furhr dsusson, as h bass for h onsruon of lnary parl physs. Th bass of Dra's rlavs quanu hory [] s STR, drvd by nsn [4], basd on h analyss of Mawll-Hrz quaons and Lornz lrodynas [], n whh h lron s dsrbd by quaons (). Bu h daa n Fgur, pansakngly olld by a whol gnraon of prnalss o onfr Lornz-nsn hory, oband by analyzng h rajors of lrons, rahr han spnors n h Dra hory []. If, howvr, prfor daa analyss [3, 7-9] on h bass of h Dra hory, w oban h unpd rsul ha h sar of h daa n Fg. ay b assoad wh h aon frquny of naural osllaons of lrons n a agn fld [] - Fgur 3. In hs sns, daa [3, 7-9] and ohrs an b rgardd as f o a known rsul, by adjusng h sng on h playbak of ha parular frquny of quanu osllaons. Consqunly, h Dra hory s a odds wh h orgnal hypohss of Lornz, so dos no allow sng hs hypohss prnally. For apl, s possbl o dsngush h braha hory [] fro h Lornz hory [], whh s qually onssn wh h hory of Dra, whh, n urn, dsrbs wll h nr s of known prnal daa - s Fg. 3. nohr apparn parado s ha, apar quanu hans and lrodynas ar h lnar hory, whh holds h prnpl of suprposon, whras h quanu lrodynas (QD), whh uns h Dra hory and h lrodynas, s a nonlnar hory / 3 /. hp//haosandorrlaon.org/chaos/cr.pdf

9 Chaos and Corrlaon January 8, Fgur 3: Dpndn of h lron onu on h vloy n a hoognous agn fld for wo quanu nubrs [] and aordng o prnal daa [3, 7]. Thus, hsorally Lornz lrodynas provdd h bass for h whdrawal of h Lornz ransforaon, basd on whh, n urn, hr was h Dra rlavs quanu hory []. Consqunly, hs hors us b lnkd, as dsrb on parl - an lron. Mlls hory and s gnralzaon For parados dsrbd abov was found an unpd soluon n h Mlls hory [4]. Mlls an hypohss [4] s ha h lr harg dnsy n h rgh-hand sd of quaons () s dsrbd by h wav quaon of h for v () Hr v spd harg-dnsy wavs. hp//haosandorrlaon.org/chaos/cr.pdf

10 Chaos and Corrlaon January 8, Th hypohss () oghr wh h assupon of h harg dsrbuon n h ao on h surfa of h sphr of fd radus, drnd fro Bohr hory, allows on o alula h nrgy lvls of ullron aos and o drn h anoalous agn on of h lron [4]. In hs sns, h Mlls hory s an alrnav o quanu lrodynas (QD), as allows h alulaon of all rlavs quanu ffs wh h sa auray as QD, bu s a lnar hory. Th bas quaon () of Mlls hory, whh h usd o solv h probls of ao physs, hsry, and physs of lnary parls, a frs, no drly rlad o quanu hans. Morovr, Mlls assrs ha quanu hans s a profoundly rronous hory ha onans nrnal logal onradons. In raly, howvr, s asy o show usng h rsuls of our papr [] ha h quaon () an b oband fro h rlavs quanu Dra quaon s [5]. Indd, as shown n [], h harg dnsy and ponal of an lron subj o boh of h Dra quaon and h Lornz quaons () ar rlad by: ( p), p s h nrgy and onu of lron,, I s ndad (3) - h salar and vor ponal of h rnal lroagn fld. Hn w fnd ha n h absn of rnal flds, h harg dnsy dpnds lnarly on h ponal of h lron: (4) Subsung hs prsson no h frs quaon (), w fnally oban hp//haosandorrlaon.org/chaos/cr.pdf

11 Chaos and Corrlaon January 8, hp//haosandorrlaon.org/chaos/cr.pdf (5) Mlls usd hs bas quaon () only o fnd h sngular soluons n whh h dnsy dsrbuon along h radal oordna s dsrbd by h Dra dla funon. On suh soluons q. (5) aks h Mlls for () (6) W gv a spl drvaon of quaon (3), basd on a spal rordng of h Dra quaon n h for of sond-ordr quaon / 3 / ˆ ˆ α H (7) Hr H, s h lr and agn fld of an rnal sour, and h orrspondng rs n quaon (7) dsrb h nraon of h lron spn wh an rnal lroagn fld. Typally, h nrgy of hs nraon s rlavly sall, so an b ngld. s a rsul, quaon (7) rdus o h Kln-Gordon (8) Th rsulng quaon onans only h dny ar, so rdus o a sys of four ndpndn quaons. Bu h sys () also onsss of four ndpndn quaons, so bwn h soluons of () and (8) us b a rlaonshp, as hy dsrb h sa of h sa physal obj - an lron. ssung ha hs rlaonshp s lnar, and ha Lornz albraon s prford, w arrv a quaon (3). No ha n quanu lrodynas, urrn and

12 Chaos and Corrlaon January 8, hp//haosandorrlaon.org/chaos/cr.pdf wav funon ar nronnd nonlnar way. I s no known, howvr, whhr hs onnon s always o b nonlnar. Mlls hory [4], basd on h lnar quaon (), allows us o prd h anoalous agn on of h lron and h uon, and h Lab shf wh h sa auray as QD, bu whou ahaal arfs pular o hs hory. Lornz quanu lrodynas W forula a opl sys of quaons of h Lornz lnar quanu lrodynas, u (9) ) ( p ordng o h rul of h opraors of onu and nrgy w pu n h rgh-hand sd of quaon (9) p, () Undfnd valu s h lron vloy on h rgh sd n h sond quaon (9). W us h fa ha h Lornz ransforaon lads o prsson p u Mulply boh sds of h sond quaon (9) o on h lf, as a rsul w oban

13 Chaos and Corrlaon January 8, u p Rplang n hs quaon, h nrgy and onu o h opraors of dffrnaon aordng o (), w fnd W us h prsson of h lr fld hrough lroagn ponals, w hav W prss hr h drvav of h vor ponal wh rsp o and subsu no quaon (). s a rsul, onsdrng h frs quaon (9), w fnally fnd ha h lr fld of h lron s dsrbd by h wav quaon () () quaon () us b supplnd by a sandard quaon for h dvrgn fld, whh, akng no aoun h prsson of harg dnsy has h for ( p) No ha h ranson fro h sond quaon (9) o () fll fro h dsrpon of h agn fld of h lron. To rsor h syry nhrn hp//haosandorrlaon.org/chaos/cr.pdf

14 Chaos and Corrlaon January 8, n Mawll quaons, apply h opraon of h roor o h hrd quaon (9), as a rsul w oban I s ndad H H. H u (3) N, w us h rlaon bwn h onu, vloy and nrgy n h Lornz-nsn hory. Mulplyng h lf and rgh sd of quaon (3) on o h lf, as a rsul, w hav H H u p Fnally, rplang h opraors of onu and nrgy du o quaons (), and nong ha h url of h gradn of any funon s zro, w fnally fnd H H (4) Gvn h fa ha n quanu hans an lron anno b rprsnd as a sa sour, s possbl o rdu h ordr of (4), so along wh quaon (4) holds and h sandard quaon dsrbng h agn fld of lroagn wavs H H (5) Fnally, usd h dfnon of h vor agn fld, w fnd h las quaon n h Lornz quanu lrodynas, hp//haosandorrlaon.org/chaos/cr.pdf

15 Chaos and Corrlaon January 8, hp//haosandorrlaon.org/chaos/cr.pdf H (6) N, w no ha h frs quaon (9) wh rgard o h prsson of h harg dnsy gvn by h hrd quaon (9) rdus o h Kln-Gordon quaon (8). Thrfor, h opl sys of quaons of h Lornz quanu lrodynas has h for (7) H H ) ( p H Hr h frs quaon dsrbs h lron nraon wh h rnal fld, h sond and hrd quaons dsrb h lroagn radaon, and h fourh quaon dsrbs h dsrbuon of h lron harg, du o quanu ffs. s follows fro quaons (7) o dsrb h lron n Lornz quanu lrodynas, dos no rqur a wav funon, as h sys of quaons (3) s losd, and h parars of h hory hav a lar physal anng. Nurous applaons of h Lornz quanu lrodynas o h dsrpon of varous physal phnona an b found n h onograph [4]. I ay b nod ha h agrn bwn Mlls hory and prn s suffnly aura, as n sandard QD, bu du o h lnary of h hory s

16 Chaos and Corrlaon January 8, ahvd by h raordnary sply of h dsrpon of h bas quanu rlavs ffs. Rfrns. Lornz, Hndrk noon, Th hory of lrons and s applaons o h phnona of lgh and radan ha; a ours of lurs dlvrd n Coluba unvrsy, Nw York, n Marh and prl 96, Nw York, [NY.]: Coluba Unvrsy Prss. Ma braha. Prnzpn dr Dynak ds lkrons// nnaln dr Physk, 35 (), 93, Kaufann, W. Übr d Konsuon ds lkrons// nnaln dr Physk, 9, 96, lbr nsn. Zur lkrodynak bwgr Körpr// nnaln dr Physk, 3 (), 95, Альберт Эйнштейн. Собрание научных трудов в четырех томах. Т.. М., Наука, Buhrr. H. Übr dn nfluß dr rdbwgung auf d Innsä ds Lhs// nnaln dr Physk, 36 (6), 93, Nuann, Günhr. D räg Mass shnll bwgr lkronn//nnaln dr Physk 35 (): 94, hp://galla.bnf.fr/ark:/48/bp6k53486.ag.f54.pagnaon 8. Ch.. Guy Lavanhy, Vrfaon prnal d la forraul d Lогηz-ηsη par ls rayons ahodqus d grand vss. rh, dss Phys Na. XLII, pp. 87, 353, 44; Rogrs, M. M. al. Drnaon of h Masss and Vlos of Thr Radu B Ba-Parls, Physal Rvw, 57, 94, Paul.M. Dra. Thory of lrons and Posrons/Nobl Lur, Dbr, 933, hp://noblprz.org/nobl_przs/physs/lauras/933/dra-lur.pdfrwn. Shrödngr. Th Fundanal Ida of Wav Mhans/Nobl Lur, Dbr, 933, hp://noblprz.org/nobl_przs/physs/lauras/933/shrodngr-lur.pdf.. P. Trunv. Sruur of lron n h lass and quanu lrodynas//chaos and Corrlaon, 7,, hp://haosandorrlaon.org/chaos/cr7.pdf 3. Ландау Л.Д., Лифшиц Е.М. Теоретическая физика: Учебное пособие. В т. Т. IV/В.Б. Берестецкий, Е.М. Лифшиц, Л.П. Питаевский. Квантовая электродинамика. 3-е изд., испр. М.: Наука, Гл. Ред. Физ.-мат. Лит., 989, - 78 с. 4. Mlls, Randll L. Th Grand Unfd Thory of Classal Physs. Blaklgh Powr, 8. hp:// 5.. P. Trunv. lron sruur, hydrno and old fuson//chaos and Corrlaon,, D. 5,, hp://haosandorrlaon.org/chaos/cr_.pdf hp//haosandorrlaon.org/chaos/cr.pdf