Th thoy of lctomagntic fild motion. 6. Elcton L.N. Voytshovich Th aticl shows that in a otating fam of fnc th magntic dipol has an lctic chag with th valu dpnding on th dipol magntic momnt and otational vlocity. A hypothsis was statd that th lctic chag of lmntay paticls, and in paticula th lcton chag, is causd by otation of thi magntic fild. It was shown that th lcton is th systm composd of bound ngativ and positiv chags whos nt chag is qual to th chag of a classical singl point lcton, and that in xtnal unifom lctic filds th lcton bhavs lik a singl point chag. It is noticd that all chagd lptons lctons, muons and tau-lptons a dscibd by simila quations. Diffnc of lptons fom ach oth is causd by distinction in magnituds of thi magntic momnts and th magntic fild angula vlocity, bing invsly popotional to th magntic momnt of a cosponding paticl. Th was statd an assumption that paticls diff fom thi antipaticls only by diction of th magntic fild otation. Th lcton - positon annihilation pocss is xplaind by th fact that all filds bcom fully zo povidd paticls with opposit magntic momnts a supposd. 6.1. Intoduction It was noticd in pcding wok [1] that otation of a od-lik pmannt magnt about longitudinal axis dos not lad to magntic fild otation. So long as w hav not any possibility to foc magntic fild otation, w ty to consid magntic fild poptis of th magnt o th solnoid fom th point of viw of th obsv who is locatd in a otating fam of fnc. To abstact away fom th ffcts latd to th fnc fam otation, th otation is considd to b ath slow. Th sults obtaind can b also asily usd in cas of magntic fild otation in motionlss fam of fnc. 6.. Rotation of a magntic dipol At distancs much long than magnt adius it is possibl to bliv with sufficint accuacy that all lctons a concntatd at a magnt axis, so it is possibl to nglct thi tanslation motion about th magnt axis. It RELATIVISTIC ELECTROMAGNETISM NO., 013 3
would b notd onc again that such an assumption is not valid whn a unipola gnato is considd, howv w consid th filds at lag distancs, whn a pmannt magnt is appad to b th point magntic momnt. In ths conditions, magntic filds of a solnoid and a pmannt magnt a quivalnt to ach oth. Lt's tun to th solnoid. To otat th solnoid is unasonabl, thfo a uniqu possibility to consid th solnoid otating magntic fild is to consid it fom a otating fam of fnc. Th otating fam of fnc is a nonintial fam of fnc. Howv, as it is known, Lontz tansfomations fo lctic and magntic filds in cas of th acclatd fam of fnc main valid fo an instantly concomitant intial fam of fnc at a givn point. Along with th angula vlocity and distanc fom a otation axis a considd to b so Fig. 6.1. Magntic dipol p m in a otating fnc fam. small that th lina vlocity is low than th vlocity of light. As it is known (s, fo xampl, []), th vcto quation fo magntic fild induction B of a point dipol with th magntic momnt pm is as follows: 3npn 4 p 0 m m B 3, (6.1) wh n is a unit vcto in th diction of position vcto, and μ0 is a magntic constant. In a sphical coodinat systm (fig. 6.1) with th pola axis dictd along pm, th quation (6.1) bcoms: B p cos 0 m 3, (6.) 4 RELATIVISTIC ELECTROMAGNETISM NO., 013
B 0 p m sin 3 4, (6.3) Bφ = 0. (6.4) Lt's obsv th magntic fild fom a otating fam of fnc whos axis of otation coincids with th pola axis of ou sphical coodinat systm. Thn magntic flux lins lativ to this fam of fnc otat in a diction shown in fig. 6.1, with angula vlocity ω, and thi lina vlocity V is qual to: Vφ = ω sin, V = 0, V J = 0. (6.5) Sinc an lctic componnt of th lctomagntic fild in a motionlss fam of fnc is absnt, lctic fild E in a otating fam of fnc, accoding to (.5) is qual to[3]: E = [BVm], (6.6) wh Vm is th vlocity of th magntic fild in a otating fam of fnc. Fom (6.) - (6.6) it follows in a sphical coodinat systm E p sin 4 0 m BV, (6.7) E BV p sincos 0 m, (6.8) Eφ = 0. (6.9) Fig. 6. shows th viw of lctic and magntic flux lins of th lctomagntic fild fom a magntic dipol in a otating fam of fnc. Diction of th magntic dipol otation (clockwis, th top RELATIVISTIC ELECTROMAGNETISM NO., 013 5
viw) is opposit to its magntic momnt. Dak blu lins indicat magntic flux lins, and d ons a fd to th lctic fild. It coms und notic that lctic flux lins, unlik magntic ons, a not closd and, as appas fom (6.7) and is sn fom th dawing, th adial componnt of lctic fild E is dictd insid vywh, xcpt fo th otation axis. At th otation axis E = 0. Hnc, th flux of th lctic stngth vcto though a sphical sufac in whos cnt th magntic dipol is locatd is always ngativ. In oth wods, it mans that in a otating fam of fnc at whos axis of otation th magntic dipol is placd, a ngativ lctic chag will b found. Lt`s find th valu of this chag. Fig. 6.. Th lctomagntic fild of a magntic dipol in a otating fam of fnc. Th diction of th otation vcto is opposit to th diction of magntic momnt. - magntic flux lins; - lctic flux lins; and - accodingly th positiv and ngativ bound chags; - a ngativ chag of th lcton co. Flux of lctic stngth vcto Φ though closd sufac S is qual by dfinition: Φ Eds, (6.10) S wh E is th lctic stngth vcto. Fo a sphical coodinat systm lt`s mak us of placmnt ds = sin d dφ. As sufac S w choos sph of adius and with th 6 RELATIVISTIC ELECTROMAGNETISM NO., 013
cnt at th oigin of th coodinats. In this cas it is only possibl to consid a componnt of lctic fild E, and quation (6.10) bcoms: p p Φ E sin d d 0 0 = òò J J j. (6.11) Lt's compa usual chag q with sphical symmty and th quid chag which is locatd insid a sph with th cnt coinciding with dipol position pm. Fo usual singl point chag q with sphical symmty E q =, (6.1) 4p 0 wh ε0 is an lctic constant. By substituting (6.1) in (6.11), w obtain th known lation fo th chag and th flux of lctic stngth vcto Φ though th closd sufac coving chag q: Φ q =. (6.13) 0 Similaly, substituting (6.7) in (6.11), aft simpl tansfomations w obtain: Φ m p w 0 m 3 By quating (6.13) and (6.14), w obtain: =. (6.14) 3qc, (6.15) p m RELATIVISTIC ELECTROMAGNETISM NO., 013 7
wh c is th vlocity of light. In xpssion (6.15) it is takn into account that c 1 =. (6.16) m 0 0 At th angula vlocity of fnc fam ω dfind by xpssion (6.15), total vcto fluxs of th lctic fild stngth (6.14) and (6.15) a qual. In oth wods, th sph of any adius with th cnt at th oigin of th coodinats of ou otating fam of fnc contains lctic chag q. W considd th lctic fild aising in a otating fam of fnc with a motionlss dipol placd at th otation axis. But it mans that if in a motionlss fam of fnc th solnoidal magntic fild is focd by som way to otat about th longitudinal axis, an lctic chag will mg. Ctainly, it is impossibl. W noticd ali that otation of a solnoid o a pmannt magnt dos not lad to th magntic fild otation. Now, w can say that such a otation would lad to infingmnt of th chag consvation law. Th a no focs in macounivs which could foc th magntic fild to otat. On th oth hand, if such a otation, nvthlss, occus, th a no focs which could stop it, it should occu tnally as should also xist an lctic chag latd to th magntic fild otation. 6.3. Elcton In this connction lt`s stat a hypothsis that an lctic chag of lmntay paticls, in paticula, an lcton chag, is causd by otation of thi magntic filds. Such a hypothsis, in cas of its validity, should not contadict any known xpimntal fact, which is xplaind within th concpts of th lctomagntic fild classical thoy, and at th sam tim must xplain at last som of th phnomna conflicting with ths concpts. In this cas, th lctomagntic fild configuation shown in fig. 6. is valid not only fo a magntic dipol in a otating fam of fnc, but 8 RELATIVISTIC ELECTROMAGNETISM NO., 013
also fo a otating magntic dipol, i.. lcton, in an intial laboatoy fam of fnc. Blow w consid poptis of such an lcton. Lt's wit xpssions (6.) (6.4) by substituting in thm valu of lcton magntic momnt μ and valu μ0 fom (6.16): B cos 3 c, (6.17) 0 B sin 3 4 c, (6.18) 0 Bφ = 0. (6.19) Lt's assum xpssions (6.7) - (6.9) and (6.15) to b valid fo th lcton. Thn by taking into account (6.16) w obtain: E 3sin, (6.0) 8 0 E 3sin cos 4, ( 6.1) 0 Eφ = 0, (6.) wh is th magnitud of an lcton chag (lmntay chag). Th angula vlocity of lcton magntic fild ω, as follows fom (6.15), is dictd to th diction opposit to th diction of lcton magntic momnt μ, and is qual to: 3c. (6.3) Accodingly, th angula momntum of lcton latd to th magntic fild otation is also dictd to th diction opposit to th RELATIVISTIC ELECTROMAGNETISM NO., 013 9
diction of th lcton magntic momnt, which compltly satisfis th concpts of quantum mchanics. If th lcton magntic momnt valu is accptd to b qual to Boh magnton, m = /m, w obtain fom B (6.3) anoth intsting xpssion fo th angula vlocity: B 3 mc, (6.4) wh m is an lcton mass, and is Planck s constant. If th diction of th magntic fild otation is to b changd to th opposit and accodingly signs in th quations (6.0) - (6.) a to b changd to th opposit, th quations will dscib th positon. Thus, it is possibl to daw a conclusion that th antimatt (positon) diffs fom matt (lcton) only by th diction of th magntic fild otation. Lt's nam th chag dscibd by quations (6.0) - (6.) an lmntay lctomagntic fild souc, sinc ths quations ptnd to dscib th lcton chag, and w shall nam a chag of th sam valu but dscibd by quation (6.1) a point chag. Singl point and lmntay soucs of th lctomagntic fild a qual by thi magnituds, but btwn thm th is a pincipal diffnc: lctic flux lins of a singl point chag a of sphical symmty and a dictd fom infinity to th chag cnt (fo a ngativ chag); flux lins of an lmntay lctomagntic fild souc has axial symmty, thy oiginat (o com to th nd fo positon) at th final distanc fom th chag cnt, xcpt fo th quatoial plan (plan xy in fig. 6.1). This diffnc manifsts itslf, in paticula, in that th xpssion fo flux of lctic fild stngth (6.14) is valid only fo th cas if th closd sufac is sphical and th sph cnt coincids with th cnt of an lmntay lctomagntic fild souc. If th sufac diffs fom a sphical on o it is positiond in anoth way, lation (6.14) will b invalid, as a ul. Ths quimnts a not ffctiv fo a singl point chag: xpssion (6.13) is valid in all cass if th chag is locatd insid th closd sufac. Th is th only on xplanation fo th fatus spcifid abov: in th spac suounding th cnt of an lmntay lctomagntic fild souc, lctic chags a dispsd, as is shown in fig. 6.. Nith in th cnt of an lmntay lctomagntic fild souc no in th spac 10 RELATIVISTIC ELECTROMAGNETISM NO., 013
suounding a chag, th is ith lctic liquid o solid chagd balls which, accoding to classical psntations, could b an lctic fild souc. Thfo, w com to a conclusion that th lctic chag is only a popty of th lctomagntic fild, but not its souc. Lt's find an lctic chag distibution. Fo this pupos, w us Gauss thom, o on of Maxwll s quations fo th lctic fild stngth divgnc: = dive, (6.5) 0 wh ρ is an lctic chag dnsity. W hav xchangd lft and ight pats of th quation by thi placs in compaison with th standad viw of th quation bcaus a usual viw undlins that th chag is an lctic fild souc, but w us quation (6.5) as a dfinition of th lctic chag. In a sphical coodinat systm, quation (6.5) will bcom [4]: 0 0 E 0 j = ( E ) + ( E sinj J ) + sinj J sinj j. (6.6) Whn xpssions (6.0) - (6.) a substitutd in (6.6), th fist and thid mmbs in (6.6) bcom zo and (6.6) bcoms: æ J Jö 0 3 sin cos = sinj Jç çè 4p 0 ø. (6.7) Aft simpl tansfomations and diffntiation of xpssion (6.7), w finitly obtain: 3 = ( 3c o s J- 1 3 ). (6.8) 4p Lt's summaiz th pliminay sults of lcton poptis study and ast ou attntion to som of ths poptis. RELATIVISTIC ELECTROMAGNETISM NO., 013 11
Th total lcton chag (of an lmntay lctomagntic fild souc), as wll as of a classical singl point lcton, is qual to. Ngativ chags a concntatd in th quatoial aa of th lcton. This follows fom compaison of xpssion (6.0), (6.1) fo th lmntay lctomagntic fild souc with xpssion (6.1) fo a singl point chag bcaus th fild of an lmntay lctomagntic fild souc xcds th fild of a singl point chag in that aa. Th sam conclusion follows dictly fom xpssion (6.8). Fo th sam asons it is possibl to asst that positiv chags a concntatd in pola aas. Th total chag of any sphical lay with th cnt coinciding with th cnt of an lmntay lctomagntic fild souc is qual to zo sinc th full flux though th closd sph dos not dpnd on th sph adius as follows fom (6.14). Th sam sult can b obtaind fom (6.8) by intgating it by th volum of th sphical lay. Chags of th lcton, locatd outsid th cntal zon, lctonа co, about which it is ncssay to spak spaatly, a bound chags, thy cannot b bokn off o spaatd fom th cntal chag. Focs acting on bound chags, a actually applid to th lmntay lctomagntic fild souc as a whol. Th total chag of an lmntay lctomagntic fild souc acts as a f chag and can tak pat in all intactions with oth chags. It follows fom th said abov that in a unifom lctic fild th lmntay lctomagntic fild souc (lcton) will bhav lik a singl point chag: th foc acting on a sphical lay in a unifom fild is qual to zo, and th cntal chag is qual to th singl point chag. This is valid at lag distancs fom oth lmntay soucs of th lctomagntic fild (lctons) o singl point chags sinc, fistly, at lag distancs th lctic fild fom xtnal chags in which lcton is locatd bcoms almost unifom, and, scondly, th dnsity of bound chags, as sn fom (6.8), quickly dcass as invsly popotional to th distanc cubd. And, finally, th fild fom xtnal chags at thi considabl quantity is avagd and bcoms vn mo unifom. That's quit anoth stoy considing small distancs whn th fild, in which th lcton is locatd, is non - unifom. In a non - unifom fild th momnt of foc acts on th lcton and it will bgin pcss, which is unusual in compaison with th classical singl point lcton, but natually nough fom th quantum mchanics point of viw. 1 RELATIVISTIC ELECTROMAGNETISM NO., 013
Whn th diction of th magntic fild otation is changd to opposit, th gnal configuation of th filds will not chang, but th lctic fild diction and also signs of vy chag will xchang to th opposit. Thus, w hav to do with a positon but not with an lcton, as in fig. 6.. W hav vy ason to assum that quations (6.17) - (6.3) also dscib, xcpt fo an lcton and a positon, oth lptons having an lctic chag a muon and a tau lpton as wll as thi antipaticls. As fo an lcton - positon pai, th diction of otation of antipaticls is opposit to th diction of otation of lvant paticls, and th angula vlocity of otation, as it is cla fom (6.3), is invsly popotional to th magntic momnt of a lvant paticl. Th diffnc of lptons fom ach oth by mass is appantly causd by distinction in magnituds of thi magntic momnts and, as consqunc, in th vaious dimnsions of thi cos, th cntal aas of paticls. Lt's not on mo fatu of lptons that hav a chag: paticls hav an anti-paalll magntic momnt and a otation diction (spin), whas fo thi antipaticls thy a paalll, which quit cosponds to th concpts of quantum mchanics. 6.4. Elcton and th lativity thoy Abov, w obtaind lations fo th lctic and magntic fild of th lcton, and also th lctic chag distibution. Th obtaind lations concn th lcton xtnal aa. W would lik to not th fact which attacts attntion fist of all: at som distanc fom th otation axis th lina otation vlocity of th magntic fild achs th vlocity of light, and thn xcds it. To complt considation of lcton xtnal aa, w consid, whth it conflict with conclusions of th spcial thoy of lativity. With that nd in viw w consid otating magntic fild of an lcton fom th sval vaious points of viw. 1. Lt's consid th lcton fild lativ to a motionlss laboatoy fam of fnc. In sphical coodinat systm,, lina vlocity of a magntic fild V is dfind by xpssions (6.5) and th lcton angula vlocity is dfind by xpssion (6.3). RELATIVISTIC ELECTROMAGNETISM NO., 013 13
Lt's intoduc th dsignation R sin. (6.9) H R is a distanc of any point fom th lcton otation axis. Lt's find R fom (6.5), taking into account dsignation (6.9), by substituting (6.3) in (6.5) and omitting sign in (6.3), sinc w a intstd in th angula vlocity magnitud: R 3c. (6.30) By substituting in (6.30) valu V c, w find distanc R c at which magntic fild vlocity is qual to vlocity of light: V R c 3c. (6.31) Equation (6.31) psnts th quation of th cylind with th adius qual to R. c Thus, at valu R R dfind by (6.31), th magntic fild vlocity is c qual to th vlocity of light, and if R incass, th vlocity of light will b xcdd. By itslf it is not in contast with th conclusions of th spcial thoy of lativity bcaus th vlocity of light cannot b xcdd only by th pocsss which a usd to tansf infomation. It is obvious that th otating fild cannot tansf infomation, hnc, th a no stictions imposd on th magntic fild lina vlocity. Lt's also notic that th fomulas of Lontz tansfomations calculating th intinsic magntic fild moving with th suplight vlocity contain valu R R 1 V c. Thus, if th vlocity of light is xcdd, whn valu c, w obtain an imaginay valu of th intinsic otating magntic fild. In tun, th otation of this imaginay fild with suplight 14 RELATIVISTIC ELECTROMAGNETISM NO., 013
vlocity at R Rc lads to occunc of th al valu of lcton magntic fild obsvabl in a laboatoy fnc fam.. Lt`s consid th lcton fild lativ to a fam of fnc otating togth with th magntic fild. Fo this pupos, w find th intinsic fild of a otating lcton. Fo this pupos, w us th known fomula fo th fist invaiant I1 of th lctomagntic fild (quation (.6) [3]): I1 = c B E. (6.3) Lt's mind that th intinsic fild of a souc is magntic if th lctomagntic fild invaiant in backts of xpssion (6.3) is positiv. Othwis, th intinsic fild of a souc is lctic. Th quality of invaiant to zo (i.. if c B = E ) mans that th intinsic vlocity of both th magntic and lctic filds (s xpssions (.8) and (.9) [3]) is qual to th vlocity of light. To dfin th sign of otating lcton invaiant I1, lt find pliminay th valus of c B and E nting into it. Magntic induction B fo th lcton as it has bn shown ali is dscibd by lations (6.17) - (6.19). Thn, taking into account ths lations, cb c B B. (6.33) By substituting in (6.33) valus B and B fom (6.17) and (6.18), aft lmntay tansfomations w obtain: cb 1 3cos. (6.34) 3 4 0c Similaly, th valu of E is found. Th lctic fild stngth fo th lcton is dscibd by lations (6.0) - (6.). Pocding fom thm, it is possibl to wit down: RELATIVISTIC ELECTROMAGNETISM NO., 013 15
E E E. (6.35) By substituting xpssions (6.0) and (6.1) in (6.35), aft tansfomations w obtain: E 3sin 1 3cos. (6.36) 8 0 Aft substitution in (6.3) valus cb and E fom (6.34) and (6.36) w find invaiant I1: I 1 3cos 4 1 4 640 c 9 sin. (6.37) Invaiant I1 is qual to zo whn th xpssion insid th backts of quation (6.37) is qual to zo: 4 c 9 sin 0. (6.38) Using substitution (6.9) lt's wit quality (6.38) in a mo convnint fom: 4 9 0. (6.39) cr Solving (6.39) fo R, w obtain valu R coinciding with quation (6.31). In oth wods, at adius valu R R th vlocity of th intinsic lcton c fild, as appas fom (6.31), achs th vlocity of light, and invaiant I1 bcoms qual to zo. Lt's consid th bhavio of th intinsic fild and th intinsic vlocity of th lcton whn R incass fom zo indfinitly. 16 RELATIVISTIC ELECTROMAGNETISM NO., 013
Cas 0 R Rc. Th lft pat of quation (6.39) cosponding to th xpssion in th backts of quation (6.37) is mo than zo. Hnc, invaiant I1 (6.37) is also mo than zo and th lcton intinsic fild in this cas is magntic. Its vlocity magnitud Vm, as appas fom quations (6.5), (6.9) and (6.30) is qual to: 3c Vm R R. (6.40) Cas R Rc has alady bn considd abov: in this cas V c. Cas Rc R. Similaly, as w did it fo th fist cas, w will com to a conclusion that invaiant I1 (6.37) is lss than zo, and th intinsic lcton fild in this cas is lctic. In oth wods, th obsv in a otating intinsic fam of fnc of th lcton will com to a conclusion that at Rc R th intinsic lcton fild is lctic, and it is this fild that movs lativ to th cnt of lcton. Lt`s find lina vlocity V of this movmnt pocding fom xpssion (.8 [3]. Du to th fact that all th vctos nting into this xpssion a othogonal, xpssion (.8) may b simplifid: V cb c E =. (6.41) Valus cb and E fo lcton a dfind accodingly by xpssions (6.34) and (6.36). Thn aft tansfomations, xpssion (6.41) bcoms: V c. (6.4) R It is cla fom h that in cas RELATIVISTIC ELECTROMAGNETISM NO., 013 17 R c R th lcton intinsic fild is th lctic fild. Fom xpssion (. [3] it is sn that at point
V = c th dnominato of xpssion (.) gos to zo, and hnc, numato (.) must also aspi to zo bcaus B at this point has a quit ctain final valu. Sinc V 0 (V = c), intinsic lctic fild E0 at this point gos to zo. It would b notd that it is possibl to show in simila way using xpssion (.4) that th lcton intinsic magntic fild at th sam point is also qual to zo. Thus, gnalizing all th th cass of R valu, w s that as R incass fom zo to R th intinsic magntic fild ducs to zo, and c th intinsic vlocity of a magntic fild incass to th vlocity of light. In futh indfinit incas of R, th intinsic fild bcoms lctic and th intinsic vlocity of th lctic fild lows fom th vlocity of light to zo dpnding on R by invsly popotional law. 3. It is also impotant to notic that th is a ciculation of lctomagntic ngy aound th lcton. Lt`s consid th lcton lctomagntic fild fom this point of viw. Indd, Poynting vcto S is qual to: S 0 c EB. (6.43) In sphical coodinat systm,, vcto S has only on componnt coinciding with th diction of - componnt of th vlocity. A magnitud of Poynting vcto can b found, by substitution of valus cb and E fom (6.34) and (6.36) in (6.43): S 3 sin 1 3cos 1. (6.44) 3c 5 0 It is vidnt fom (6.44) that th ngy flux dnsity ciculating about th cnt of th lcton quickly dcass with distanc fom th cnt of th lcton as invsly popotional to th fifth dg of th distanc. At R R c Poynting vcto has no spcific fatus and is dscibd by th gnal quation (6.44). 18 RELATIVISTIC ELECTROMAGNETISM NO., 013
Expssion (6.44) is impotant in undstanding th lcton lctomagntic fild pocsss. It shows that, ispctiv of distanc R, th is a singl pocss of th lctomagntic ngy ciculation about th cnt of th lcton. Lt`s summaiz th obtaind sults. Th dsciption of th intinsic lcton fild shows that it is ssntially impossibl to masu this fild and, hnc, it is impossibl to chck up xpimntally th conclusions concning th intinsic lcton fild. Th fist appoach to th intinsic fild stimation is basd on th fact that th lcton is psntd as a magntic dipol otating as a igid body. This appoach sults in th fact that th intinsic magntic fild bcoms imaginay at lag distancs, and th otation lina vlocity xcds th vlocity of light. It is had to say what physical maning may b nclosd in th concpt of an imaginay magntic fild; it is mo likly a mathmatical abstaction only. At th sam tim, it cannot b xcludd that in th futu it will, nvthlss, b xplaind. Manwhil, such a psntation dos not lad to contadictions within th scop of th spcial thoy of lativity. In th scond appoach th intinsic fild bcoms lctic at lag distancs, and its vlocity ducs to zo with th distanc fom th cnt of th lcton. This appoach is wll basd within th scop of th dvlopd lctomagntic fild thoy and dos not contadict th gnal physical concpts and th basic postulats of th spcial thoy of lativity. Nvthlss, though it is also ssntially impossibl to masu this ciculating lctic fild and it is only a sult of thotical asoning, its physical maning as wll as in th fist cas may b claifid in th futu. Th thid appoach fully ignos th intinsic lctomagntic fild in a otating fam of fnc, but consids th lctomagntic ngy ciculation only and dos not find out any citical points. In vy of th appoachs th magntic and lctic filds in a motionlss laboatoy fam of fnc a dscibd by quations (6.17) - (6.19) and (6.0) - (6.) spctivly. 6.5. On lctomagntic fild ality Th whol collction of th facts, both of mathmatical and physical chaact, indicats that th lcton is a whil of th lctomagntic fild RELATIVISTIC ELECTROMAGNETISM NO., 013 19
vlocity. Any matial cai is not ncssay fo chags, xcpt fo th lctomagntic fild itslf; chags as it was mntiond abov a a popty of th lctomagntic fild, but not its souc. Th lctomagntic fild substantiality is undstood as th statmnt that all substancs a fomd by th lctomagntic fild and ntily consist of it. On convincing agumnt o vn sval agumnts a not nough to pov th substantiality. Th whol complx of studis and agumnts a ncssay. Two physical ssncs a known in scinc: th substanc and th fild. Th fild cannot b tund into th substanc, but th substanc can b tund into th lctomagntic fild, as shown in th psnt wok. Th following agumnts indicat in favo of th substantiality of th lctomagntic fild: - Th lmntay and fundamntal paticl of th substanc, lcton, psnts an lctomagntic whil; - Th lctic chag has no spcial matial cai; th chag is a popty of th lctomagntic fild; - Th quations obtaind fo th lcton also povid th possibility to dscib oth chagd lptons, muons and tau lptons; - Th fact of xistnc of antimatt, antipaticls of th lcton and of th lptons spcifid abov finds its natual xplanation; - Th physical and mathmatical dsciption of th lcton and th positon claify th mchanism of matt and antimatt annihilation. Th annihilation pocss is in gnal tanspant nough. Whn th lcton and th positon appoachd on anoth, pcssion givs is to a singl photon mission and th stat with oppositly dictd magntic momnts is achd. Thn, th lcton and th positon appoach on anoth up to thi absolut coincidnc. Thus, all th filds a compltly bcam zo and th fild ngy is lasd in th fom of lctomagntic adiation. Ths sults and agumnts a ctainly not nough to pov th idntity of th matt and th lctomagntic fild. To obtain such poof a considabl wok is ncssay to b don on additional substantiation of agumnts. It is obvious that in gnal this poblm is difficult to solv within th scop of on o sval aticls, howv, th solution to spcific poblms can significantly nhanc th agumntation. Among such poblms w outlin th following ons which a plannd to b solvd in th nast subsqunt woks: 0 RELATIVISTIC ELECTROMAGNETISM NO., 013
- To obtain gnal xpssions and following fom thm spcific xpssions fo chags in lctomagntism; - To study th mchanism of intaction of lctons btwn thmslvs and oth lmntay paticls; - To consid th lation btwn lctomagntic fild poptis and laws of mchanics, othwis it is difficult to spak about th fild substantiality. Th latt poblm focs to tun again to th lctomagntic and intial lcton mass poblm. This poblm was widly discussd at th tun of XX cntuy, in paticula, th gat attntion to this qustion was givn by Lontz, but it has maind unsolvd till now. Th poblm is in th fact that th intial and lctomagntic lcton masss calculatd with th us of xpimntal data w found to b diffnt. It contadicts not only to th hypothsis of th lctomagntic fild substantiality, but also to th conclusions of th spcial thoy of lativity. Conclusions 1. Th magntic dipol is considd in a otating fam of fnc. It was shown that th magntic dipol possss an lctic chag in a otating fam of fnc, th valu of which dpnds on th dipol magntic momnt and th otation vlocity.. Th hypothsis is statd that th lctic chag of lmntay paticls, th lcton in paticula, is causd by otation of thi magntic filds, with th angula vlocity and a configuation of th lcton lctic fild w calculatd. 3. It was shown that lctic chags a not th lctomagntic fild souc. Th chag is a popty of th lctomagntic fild and th lcton psnts a systm of bound ngativ and positiv chags totally qual to th classical singl point lcton chag. Distibution of bound lctic chags in th xtnal lcton shll was calculatd. It was noticd that in xtnal unifom lctic filds th lcton bhavs lik a singl point chag. 4. It was suggstd that all chagd lptons lctons, muons and tau lptons a dscibd by th sam quations (6.17) - (6.3). Lptons a diffd fom ach oth by mass du to distinction in thi magntic momnts and, thof, in sizs of thi cos. Th magntic fild angula RELATIVISTIC ELECTROMAGNETISM NO., 013 1
vlocity is invsly popotional to th magntic momnt of a cosponding paticl. 5. It was suggstd on xampl of th lcton that paticls only diff fom antipaticls by th magntic fild otation diction. Th lcton - positon annihilation pocss is xplaind by th fact that th filds fully com to zo povidd th is a supimposition of paticls with opposit magntic momnts. As a sult of this supimposition, th ngy of paticls is lasd as lctomagntic adiation. 6. Th magntic momnt and th otation diction (spin) of th lcton and oth chagd lptons a antipaalll, whas thos of thi antipaticls a paalll, which compltly cosponds to th concpts of quantum mchanics. 7. Th hypothsis was statd that th lctomagntic fild stuctud in th fom of stationay votx pocsss undlis all kinds of matt. Rfncs 1. L.N. Voytshovich, Th thoy of lctomagntic fild motion. 5. Unipola gnato with a otating magnt, 1, (013), p. 54. www.scinc.by/lctomagntism/m5ng.pdf.. I.E. Tamm, Fundamntals of th thoy of lcticity (И.Е. Тамм, Основы теории электричества), Moscow, Scinc, (1966), p. 59. 3. L.N. Voytshovich, Th thoy of lctomagntic fild motion.. Pincipl of lctomagntic fild componnt motion.1, (013), p. 1. www.scinc.by/lctomagntism/mng.pdf. 4. G. Kon, T. Kon. Mathmatical handbook fo scintists and ngins (Г. Корн, Т. Корн, Справочник по математике для научных работников и инженеров). Moscow, Nauka, (1974), p. 188. Th aticl is publishd on th sit of th REM jounal http://scinc.by/lctomagntism/list0ng.htm on May, 1st, 013 RELATIVISTIC ELECTROMAGNETISM NO., 013