Journal of Theoretics

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1 Jurnal f Thrtics PLANCK S CONSTANT AND THE MODEL OF THE ELECTRON Ph. M. Kanarv Th Kuban Stat Agrarian Univrsity. Dpartmnt f Thrtical Mchanics. Dctr f Txnical Scincs, Prfssr. kanphil@mail.kuban.ru Abstract: It is shwn th mdling f th lctrn and analyzing its lctrmagntic and physical natur n th bas f th laws f classical physics. Kywrds: lctrn, lctrmagntic fild, lctrn nrgy, lctrn mass, wavlngth, radius. It has bcm clar nw that in th nw millnnium physics will b rturn t its classical surcs. Nt th whl thrtical hritag f physics f th 0th cntury will b substitutd, but th intrprtatin f sm f its thrtical fundatins will b changd [1], [], [3], [4], [5], [7], [6], [1]. Planck s cnstant is knwn t b n f such fundatins, which srvs as a basis f quantum mchanics [6], [7], [8], [13], [14], [18]. Lt us cnsidr hw a rfinmnt f intrprtatin f th physical ssnc f this cnstant allws t mak a thrtical pntratin int th dpth f lctrmagntic structur f th lctrn and t cnnct this structur with th rsults f th xprimnt [8], [9]. Difficultis ncuntrd in xplaining th radiatin f th thrtical «black bdy» wr vrcm in Dcmbr 1900 whn Max Planck suppsd that nrgy,, in EM frm is nt mittd cntinuusly, but discrt amunts Planck namd quanta; that is: Ep = hν, (1) whr ν - frquncy f EM radiatin; h - a univrsal cnstant latr calld Planck s cnstant. As it is assumd, anthr frmula fr th dtrminatin f nrgy f a singl phtn has bn suggstd by Albrt Einstin. Ep = mc, () whr m - th mass f a phtn; C - th vlcity f a phtn. Th frquncy f a phtn s scillatins is ν, its vlcity C, and its wavlngth λ ar rlatd by: C = λ ν (3) Slving (1), () and (3) w find: kg m h = mλ ν... (4) S It is difficult t undrstand why Planck has ascribd physical sns f actin t his cnstant, h, which ds nt ncssarily crrspnd t its dimnsinality. «If Planck had E p

2 а dtrmind his cnstant as a quantum f angular mmntum mdrn physics wuld hav bn quit diffrnt» [10]. Actually Planck s cnstant has dimnsinality f angular mmntum, which has vctr prprtis. But as sm Physicists think, it ds nt man that Planck s cnstant is a vctr valu. W shall nt cntradict thir strtyp mntality, lt us us th suitabl pssibility f hypthtical apprach t this prblm and cnsidr its fruitfulnss. As it is clar, dimnsinality f Planck s cnstant is that f angular mmntum, hw can w crdinat this dimnsinality with th squar f th wavlngth, λ? Th mattr is that in th mathmatical xprssin f Planck s cnstant h = mλν mass m is multiplid by squar valu f wav lngth λ and by frquncy ν. But wav lngth charactrizs wav prcss, and dimnsinality f Planck s cnstant dmnstrats that an lctrmagntic frmatin, which is dscribd by it, rtats rlativ t th wn axis, and w ar facd with th task t crdinat th wav prcss with th rtatin n. Dtaild invstigatins carrid ut by us [1], [], [3], [8], [9] hav shwn that th phtn and th lctrn hav such lctrmagntic structurs during rtatin and mvmnt which radii r ar qual t lngths f thir wavs λ, i.. Nw Planck s cnstant has th fllwing apparanc: λ = r (5) h = mr ν. (6) It bcms clar that mr is mmnt f inrtia f th ring, and mr ν is angular mmntum f th rtating ring. It pints ut t th fact that th phtns and th lctrns hav a frm which is similar t th frm f th rtating ring. It is knwn that if angular mmnt is cnstant, th law f cnsrvatin f angular mmntum, n f th main laws f natur, is accmplishd. As Planck s cnstant is cnstant ( h = cnst ) and has dimnsinality f angular mmntum, it charactrizs th law f cnsrvatin f angular mmntum. Thus, th law f cnsrvatin f angular mmntum, n f th main laws f Natur, gvrns cnstancy f Planck s cnstant [9], [17]. Th fllwing itms f th mdls f th lctrn hav bn cnsidrd: matrial pint and matrial ring as wll as thir rbital mvmnts in th hydrgn atm. It has turnd ut that such mdls f th lctrn d nt crrspnd t th law f frmatin f th spctra f th atms and th ins and d nt charactriz th whl cmplx f pculiaritis f bhavir f th lctrns dtrmind xprimntally [8], [9], [16], [18]. Th lctrn in th frm f a ring rtating in th atm nly rlativly t its axis f symmtry is dscribd by th mathmatical rlatins which agr with many xprimntal rsults. It is knwn that th lctrn has its wn nrgy which is usually dtrmind accrding t th frmula E = mc. But th maning f such an assumptin is dciphrd nt always. And th maning is that if th whl nrgy f th lctrn is transfrmd int nrgy f th phtn, its nrgy bcms qual t E = mc. This fact has a strng xprimntal cnfirmatin. It is knwn th masss f lctrn and psitrn ar qual. Whn thy intract thy frm tw γ - phtns. That s why th nrgy bing qual t th nrgy f th phtn which has th crrspnding mass can b 31 attributd t th lctrn. Elctrn rst mass m = kg is dtrmind with grat accuracy. Lt us call lctrn nrgy E bing qual t phtn nrgy a phtn nrgy f th lctrn. First f all, lt us invstigat th pssibilitis f th ring mdl f fr lctrn. It is knwn that th lctrn has kintic nrgy and ptntial nrgy which ar qual t ach thr.

3 а 3 E = mc = mr ω = h ω, (7) whr: r - is th radii f th lctrn, h = mr ω - is Planck s cnstant. Th calculatin accrding t this frmula givs th fllwing valu f phtn nrgy f th lctrn: ( ) 5 E = mc = = V (8) If fr lctrn rtats nly rlativly t its axis, angular frquncy ω f rtatin f ring mdl f fr lctrn dtrmind accrding t th frmula (7) is qual t ω 5 19 E h = s., (9) and radius f th ring is qual t r = E m = ω ( ) 1 = m. (10) Vlcity f V pints f th rtating ring is qual t vlcity f light: V = ω r = = m/ s. (11) Lt us try t find such mathmatical mdls which dscrib bhaviur f th ring mdl f th lctrn, which cntain its charg, magntic mmnt M and lctrn lctrmagntic fild strngth B (magntic inductin f lctrn). If w assum that th lctrn charg is distributd unifrmly alng th lngth f its ring mdl, ach lmnt f th ring l will hav mass m and charg (Fig. 1). In this cas th rtating ring mdl f th lctrn will rsmbl ring currnt, and tw frcs which hav qual valus and ppsit dirctins: inrtial frc Fi = m V / r and Lrntz frc F = B (Fig. 1). V Fig. 1. Diagram f ring mdl f th lctrn B V = mv r. (1)

4 а 4 Lt us pay attntin t th fact that thr ar tw ntins fr th magntic fild charactristic which ar similar as far as physical sns is cncrnd: magntic fild inductin B and magntic fild strngth H which ar cnnctd by th dpndnc: H B =, µ0 whr µ 0 is magntic cnstant. Th analysis xprinc shws that it crats a crtain cnfusin during th frmatin f th idas cncrning magntic fild, that s why sm authrs rfus t us a clumsy trm «magntic inductin» and prsrv nly n, mr flicitus trm «magntic fild strngth» using symbl B fr it. Cl. E. Surtz, th authr f th bk «Unusual physics f usual phnmna» [11], actd in this way, and w fllw his xampl. Magntic fild will b charactrizd by vctr B, it will b calld magntic fild strngth masurd in SI systm in T (tsla). If w writ δ m fr mass dnsity f th ring and δ fr charg dnsity, w shall hav: m= δ l = δ r ϕ, (13) m m As: = δ l = δ r ϕ. (14) m δm = πr, (15) δ = πr (16) and V = C, th quatin (1) assums th frm: B mc dϕ = πr πr r dϕ (17) r whr ω r = C. B m C m ω r = m r r ω, (18) Thus, w hav gt th mathmatical rlatin which includs: mass m f fr lctrn, its charg, magntic fild strngth B insid th lctrn ring which is gnratd by rtating ring charg, angular frquncy ω and radius r f th lctrn ring. Magntic mmnt f lctrn r, as it is calld, Bhr magntn is missing in this rlatin which mathmatical prsntatin is as fllws [13], [15]: h M = 4π m = J / T. (19) Lt us pay attntin t th fact that in th abv-mntind rlatin h is vctr valu; it givs vctr prprtis t Bhr magntn M as wll. It fllws frm th frmula (19) that th dirctins f vctrs h and M cincid. Lt us cnvrt th rlatin (18) in th fllwing way: Th rsult frm it is as fllws: mω 4π mh ω hω E B 4π h 4π M 4π M. (0)

5 а 5 4π B M = E. Nw frm th rlatins (0) w can dtrmin magntic fild strngth md f th lctrn, angular vlcity ω, rtatins f th ring and its radius : 5 19 E B 4π M = T r B insid th ring.. (1) Lt us pay attntin t rathr larg magntic fild strngth in th cntr f symmtry f th lctrn and lt us rmind that it diminishs alng th lctrn rtatin axis dirctly prprtinal t th cub f a distanc frm this cntr [11]. W find frm th rlatins (0): ω = 4π M h B = = = s. () As priphral vlcity f th ring pints is qual t vlcity f light, w hav: r 8 = C = ω = m.. (3) Th main paramtrs f th ring mdl f fr lctrn: ring radius r (10), (3) and angular frquncy f its rtatin (9), () dtrmind frm th diffrnt rlatins (8) and (1) hav turnd ut t b qual. A drawback f th ring mdl is in th fact that it ds nt pn a caus f psitrn birth, that s why th intuitin prmpts that th ring shuld hav sm intrnal structur. Our nxt task is t find ut this structur. Bfr w bgin t slv this task, lt us pay attntin t th diagram f th ring mdl f th lctrn which rsults frm ur calculatins (Fig. 1). A cincidnc f th dirctins f vctrs h, M is th main pculiarity. Th mdl f lctrn prvs vctr prprtis f Planck s cnstant h and Bhr magntn M. W d lik t draw th attntin f th radr t th fact that in all cass f ur lctrn bhaviur analysis Planck s cnstant in th intgr frm plays th rl f its spin. In mdrn physics it is accptd t think that th phtn spin is qual t h, and th lctrn spin is qual t 0.5 h. But th lctrn spin valu (0.5 h ) is usd nly fr th analysis f qualitativ charactristics f lctrn bhaviur. Valu h is usd fr quantitativ calculatins. In ur invstigatins th intgr f angular mmntum h is th spin f th phtn and th lctrn. It is usd fr quantitativ calculatins and qualitativ charactristics f bhaviur f bth phtn and lctrn. Trus is th narst «rlativ» f th ring. Fr th bginning lt us assum that trus is hllw. Lt us writ ρ fr trus sctin circl radius (Fig. ). Th ara f its surfac is dtrmind accrding t th frmula: S = πρ πr = 4π ρ r. (4)

6 а 6 Fig.. Diagram f tridal mdl f th lctrn Lt us writ δ m fr surfac dnsity f lctrmagntic substanc f th lctrn. Thn m m δm S 4. (5) π ρr Lt us dtrmin mmnt f inrtia f hllw trus. W shall hav th fllwing quatin frm Fig. : IZ = m r. (6) m= πρ l δ = πρ δ r ϕ. (7) 1 m m I Z π mr = dϕ = m r π 0. (8) As th lctrn dmnstrats th lctrical prprtis and th magntic ns at th sam tim and has angular mmntum, w hav vry rasn t supps that it has tw rtatins. Lt us call th usual rtatin rlativ t th axis f symmtry with angular frquncy ω kintic rtatin which frms its angular mmntum and kintic nrgy. And scndly, lt us call vrtical rtatin rlativ t th ring axis with angular frquncy ω ρ (Fig. ) ptntial rtatin which frms its ptntial nrgy and ptntial prprtis. It is natural t assum that th sum f kintic nrgy E k and ptntial nrgy E f fr lctrn is qual t its phtn nrgy E. Lt us cnsidr th pssibility f ralizatin f ur suppsitins. Kintic nrgy f hllw trus rtatin is dtrmind accrding t th frmula (Fig. ): E E K IZ ω = m r ω = hω. (9) Frquncy ω f kintic rtatin f trus is qual t ω E h = s.. (30) W shall dtrmin radius r f trus frm th frmula

7 а 7 r = E m ω = ( ) 1 = m. (31) As it is clar, r and ω (30, 31) cincid with th valus f r and ω in frmulas (9), (10), () and (3) in this cas as wll. It is intrsting t find ut if thr is an xprimntal cnfirmatin f valu r btaind by us. It turns ut that thr is such cnfirmatin. In 19 A. Cmptn, th Amrican physicist - xprimntr, fund that dissipatd X-rays had largr wavlngth that incidntal ns. H calculatd th shift f wav λ accrding t th frmula [14], [16]: λ = λ ( 1 cs β). (3) Th xprimntal valu f magnitud λ turnd ut t b qual t m [13], [15]. Latr n a thrtical valu f this magnitud was btaind by mans f cmplx mathmatical cnvrsins basd n th idas f rlativity 1 λ = h / m C = m [15]. Whn w hav studid Cmptn ffct and hav carrid ut its thrtical analysis, w hav shwn that th frmula (3) fr th calculatin f thrtical valu f Cmptn wav-lngth λ is btaind quit simpl if w attach sns f th lctrn radius t th lctrn wav-lngth and cnsidr th diagram f intractin f th ring mdl f lctrn with th ring mdl f rntgn phtn [8], [9], [16]. Th diagram f intractin f th ring mdl f rntgn phtn with th ring mdl f th atmic lctrn is shwn in Fig. 3. Th puls hω 0 / C f th phtn falling n th lctrn and th puls ( hω ) / C f th phtn rflctd frm th lctrn ar cnnctd by simpl dpndnc: hω hω = cs β. (33) C C Fig. 3. Diagram f intractin f th phtn with th lctrn in Cmptn ffct Aftr th intractin f th phtn with th lctrn its puls will b changd by th valu: hω hω hω hω = cs β (34) C C C C r ω ω = ω ( 1 csβ). (35) As s ω = C / λ и ω = C / λ,

8 а 8 r C C C = ( 1 csβ) (36) λ λ λ λ λ = λ ( 1 cs β). (37) Th rlatin can b cnvrtd in th fllwing way: As m λω = h and λω = C, th quatin is as fllws: h λ λ = λ = ( 1 cs β) = λ ( 1 csβ). (38) mc This is Cmptn frmula f th calculatin f th chang f wav-lngth λ f rflctd rntgn phtn. Valu λ bing a cnstant is calld Cmptn wav-lngth. In th frmula (38) it is a cfficint dtrmind xprimntally and having th valu [13]: λ (xpr) = m, (39) which cincids cmpltly with th valu f radius r f th lctrn which has bn calculatd by us thrtically accrding t th frmula (10), (3) and (31): r ( thr) = m. (40) It shuld b ntd that w hav btaind th frmula (38) withut any rlativity ida using nly th classical ntins cncrning th intractin f th ring mdls f th phtn and th lctrn. As th analysis f th rsults f xprimntal spctrscpy has shwn that lctrn wavlngth is qual t radius f its ring mdl and as th rsults f varius mthds f th calculatin f radius f lctrn cincid cmpltly with Cmptn xprimntal rsult, th tridal mdl f th lctrn is nw th fact that is nugh fr th rslut advancmnt in ur sarch. It is dsirabl t knw th valu f radius ρ f trus crss sctin circumfrnc. Lt us try t find this valu frm th analysis f ptntial rtatin f lctrn with frquncy ω ρ (Fig. ). W shuld pay attntin t th fact that th puls f bth th phtn and th lctrn is dtrmind accrding t n and th sam rlatin: h h P. (41) λ r It mans that bth th phtn and th lctrn display thir puls in th intrval f n wav-lngth. This fact has bn rflctd in th mdls f th phtn as an quality btwn wavlngth λ f th phtn and its radius r. As th phtn is absrbd and radiatd by th lctrn, th lctrn shuld hav th sam cnnctin btwn th wav-lngth and radius. Bsids, th mdls f th phtn has six lctrmagntic filds; th sam quantity shuld b in th mdl f th lctrn whn it radiats r absrbs th phtn [8], [9]. Th dscribd cnditins prv t b fulfilld if n assums that angular frquncy ω f kintic rtatin is n-sixth f angular frquncy ω ρ f ptntial rtatin f fr lctrn, i..: ωρ = 6ω. (4) If w assum that vlcity f th pints f th axis ring f trus in kintic rtatin is qual t vlcity f th pints f th surfac f trus in ptntial rtatin, w shall hav: C = ω r = ωρ ρ =. (43) C

9 а 9 Frm ths rlatins w shall find ut: ω ρ = = s (44) and C ρ ω ρ = m. (45) If w substitut th data bing btaind int th frmula (9), w shall find ut th valu f ptntial nrgy f th lctrn E E 1 = m ( ) ( ) ρ ω ρ = = V. (46) If w dubl this rsult, w shall btain cmplt phtn nrgy f fr lctrn (8). Cmplt cincidnc f phtn nrgy f th lctrn btaind in diffrnt ways givs us th rasn t supps that th lctrn is a clsd ring vrtx which frms a tridal structur which rtats rlativly its axis f symmtry gnrating ptntial and kintic nrgy. It rsults frm sixfld diffrnc btwn angular vlcitis ω and ω ρ that radius r is ρ. W pstulat this fact suppsing that, as w hav shwn, th gratr by sixfld than radius mst cnmical mdl f th phtn mvmnt is pssibl nly at six lctrmagntic filds [1], [], [3], [9]. This principl is ralizd whn th vrtx mvs in a clsd hlix f th trus. It rsults frm th diffrnc f radii and angular vlcity that th vrtx which mvs alng th surfac f trus maks six rtatins rlativ t th ring axis in a hlix during n rtatin f trus rlativly its axis f rtatin. A lad f a hlix is qual t radius r f th axis ring and wavlngth λ f th lctrn (Fig. 4) [8], [9], [16]. Fig. 4. Elctrn mdl diagram Bsids rtary mtin, in this cas th lctrn has ptntial (vrtical) rtatin. W hav ntd that a sharp chang f th rlatins btwn kintic and ptntial rtatins f th lctrn lads ithr t absrptin r radiatin f th phtn dpnding n th dirctin f th chang f this rlatin. If this chang slws dwn kintic rtatin, th phtn radiatin prcss taks plac; if this chang acclrats it, th absrptin prcss taks plac. Whn w hav substantiatd th mdl f th lctrn, w hav usd th xisting Culmb s law and Nwtn s law, spctrum frmatin law frmulatd by us, Lrntz lctrmagntic frc and th fllwing cnstants: vlcity f light C, Planck s cnstant h, lctrn rst mass m, its charg, lctrn rst nrgy, Bhr magntn M, lctrical cnstant ε, Cmptn wav-lngth f th lctrn which shuld b calld Cmptn radius f th lctrn.

10 а 10 Thus, th lctrn has th frm f th rtating hllw trus (Fig. 5). Its structur prvs t b stabl du t availability f tw rtatins. Th first rtatin taks plac abut an axis which gs thrugh th gmtrical cntr f trus prpndicular t th plan f rtatin. Th scnd rtatin is a vrtical abut th ring axis which gs thrugh th trus crss sctin circumfrnc cntr. Fig. 5. Diagram f lctrmagntic mdl f th lctrn (nly a part f lctric and magntic lins f frc is givn in th figur) Only a part f magntic lins f frc and th lins which charactriz lctric fild f th lctrn is shwn in Fig. 5. If th whl st f ths lins is shwn, th mdl f th lctrn will assum th frm which rsmbls f th frm f an appl. As th lins f frc f th lctric fild ar prpndicular t th lins f frc f th magntic fild, th lctric fild in this mdl will bcm almst sphrical, and th frm f th magntic fild will rsmbl th magntic fild f a bar magnt. Svral mthds f trus radius calculatin which includ its varius nrgy and lctrmagntic prprtis giv th sam rsult which cmpltly cincids with th xprimntal 1 valu f Cmptn wav-lngth f th lctrn, i.. λ r = m [9]. = CONCLUSION Max Planck livd in th tim whn many physics dnid th pssibility f th implmntatin f th classical laws fr its furthr dvlpmnt. Th ppl wh trid t d it wr calld mchanists. Prbably, h fard ths accusatins and usd an uncrtain ntin «quantum f th last activity» r «quanta», r «actin» fr th dtrminatin f his cnstant. W rturn a tru physical sns t his cnstant. Th Natur has put th law f cnsrvatin f angular mmntum int it. Th rcgnitin f this fact pns wid prspcts fr physics and chmistry f th 1st cntury. Th way fr th xpsur f th lctrmagntic structurs f th lmntary particls, atms, ins and mlculs is pnd. Th bginning fr this way has alrady bn markd [1], [], [3], [8], [9].

11 а 11 REFERENCES 1. Ph.M. Kanarv. Nw Analysis f Fundamntal Prblms f Quantum Mchanics. Krasndar p..ph. M. Kanarv. Th Rl f Spac and Tim in Scintific Prcptin f th Wrld. Galilan Elctrdynamics. Vl. 3, N. 6, pp (Nv./Dc., 199) 3. Ph.M. Kanarv. On th Way t th Physics f th 1 st Cntury. Krasndar pags (English). 4. Richrd H. Wachsman. Th Quirks and Quarks f Physics and Physicists. «Infinit Enrgy». Vlum 4, Issu. Pags -5, Spanil G. And Suttn J.F. Classical Elctrn Mass and Filds. Jurnal f Physics Essays. Vl. 6, N. 1, pp , David L. Brgman, Ph. D. And J. Paul Wsly, Ph.D. Spining Chargd Ring Mdl f Elctrn Yilding Anmalus Magntic Mmnt. Galilan Elctrdynamics. Vl. 1, N. 5, pp (Spt./Oct., 1990) 7.G.K. Grbnshchikv. Hlicity and Spin f th Elctrn. Hydrgn Atm Mdl. Enrgatmisdat. St.-Ptrsburg pags. 8. Ph.M. Kanarv. Crisis f Thrtical Physics. Th third ditin. Krasndar, pags. 9. Ph.M. Kanarv. Watr as a Nw Enrgy Surc. Th third ditin. Krasndar pags (English). 10. Danil H. Dutsch, Ph.D. Rintrprting Plank s Cnstant. Galilan Elctrdynamics. Vl. 1, N. 6, pp (Nv/Dc., 1990). 11. Cl. E. Surts. Unusual Physics f Usual Phnmna. Vlum. M.: «Nauka», Ph.M. Kanarv. Analysis f Fundamntal Prblms f Mdrn Physics. Krasndar pags. 13. Quantum mtrlgy and fundamntal cnstants. Cllctin f articls. M.: Mir E.V. Shplsky. Atmic Physics. Vlum 1. M.: pags. 15. Physical ncyclpadic dictinary. M., «Svtskaya ntsiklpdia» pags. 16. Ph. M. Kanarv. A Nw Analysis f Cmptn Effct. Krasndar, pags. (English). 17. Ph. M. Kanarv, I.I. Artmv, S.A. Zlnsky, Abstract f Lcturs n Thrtical Mchanics, Krasndar, 001, 65 pags. 18. Ph.M. Kanarv. Mdl f th Elctrn. Apirn Vl. 7, n 3-4. pag Jurnal Hm Pag