On The Fine-Structure Constant Physical Meaning

Transcription

1 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 1 On Th Fin-Structur Constant Physical Maning Gorg P. Shpnkov Institut of Mathmatics & Physics, UTA, Kaliskigo 7, Bydgoszcz, Poland; shpnkov@janmax.com Abstract Th fin-structur constant α, formd from th four basic physical constants (,, c, and ε ), is rgardd in modrn physics as a convnint masur of th strngth of th lctromagntic intraction. Th unknown arlir maning of α, originatd mainly from th uncovrd tru valus and dimnsionalitis of its two constitunts, th lctric constant ε and lctron charg, is lucidatd in this papr. It is shown that α rflcts th scal corrlation of thrshold stats of conjugat oscillatory-wav procsss inhrnt in wav motion. PACS Numbrs: b, t, 1.9.+b Kywords: fin-structur constant, lctron charg, lctron mass, lctric constant, spd of light, Planck constant, oscillation spd, wav spd, basis, suprstructur

2 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 1. Introduction Th fin-structur constant α is a dimnsionlss quantity formd from th four basic physical constants,, c, and ε : whr α = / 4πε c = (SI) (1.1) 9 = C is th lctron charg, 4 = J s is th Planck constant h dividd by π, 8 c = m s is th spd of light, ε = F m is th so-calld prmittivity of fr spac (or lctric constant ) [1-]. Th fin-structur constant is considrd in modrn physics as a convnint masur of th strngth of th lctromagntic intraction. In othr words, α is th coupling constant or masur of th strngth of th lctromagntic forc that govrns how lctrically chargd lmntary particls (.g., lctron, muon) and light (photons) intract. Th invrs quantity of α is α 1 = (1.) Th constant α was introducd by Arnold Sommrfld (1916) during his studis on th Balmr sris in th framwork of th Bohr Thory [4] (bfor th introduction of wav mchanics), first as th quantity 8 α = υ / c, (1.) whr υ = cm s is th spd of th lctron on th Bohr first orbit in th hydrogn atom. Thn, aftr som simpl transformations, Sommrfld rducd this ratio to / c (in th CGSE systm). Thus Sommrfld introducd th valu xprssd in th SI units as α = υ / c = / c (CGSE) (1.4) 4 α = υ / c = / πε c (SI) (1.4a)

3 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) H calld α th fin-structur constant bcaus th combination of thr fundamntal constants in it (in th right part of th quality (1.4)) ntrs in th formula of spctral trms, dfining th amount of th fin structur splitting. From th xprssion (1.4) it follows that α has a doubl maning. Th first of thm, xprssd by th ratio of spds υ and c, has nvr bn discussd. Th scond on stats only th fact that α is th combination of th spcific univrsal physical constants, which charactriz, rspctivly: th discrt natur of lctric chargs (), quantum thory ( ), and rlativity thory (c). Th fin-structur constant α ntrs in th so-calld rlativistic corrction in th sam formula of spctral trms (drivd arlir by Sommrfld), obtaind whn th hydrogn atom is calculatd by Dirac s rlativistic wav mchanics. Thus, w should rcogniz that th principal qustion about th tru physical maning of both ratios in (1.4a) rmains opn. What do thy xprss? From our point of viw, th rason of such a gap in our knowldg on this mattr is th absnc in contmporary physics of a concpt on th natur of mass and charg of lmntary particls, and in particular, of lctron mass and lctron charg. In this papr, basd on th dynamic modl of lmntary particls (DM), put forward first in th last dcad [5], and on th othr nw data prsntd in [6], w answr to th abov qustion and lucidat th physical maning of th α-constant. Th DM uncovrs th tru dimnsionality of lctric chargs, and hnc, th tru maning of th lctron charg that is th principal ky for rsolution of th fin-structur constant problm postd hr. Th collctiv natur of wav procsss, takn into account in th prsnt work, is th scond such ky. From th qualitis (1.1) and (1.) it follows that th lctron charg can b prsntd in th following form: = 4πε υ. (1.5) Th constant = h / π, ntrd in th abov formulas, is in ssnc th orbital momnt of momntum of th lctron on th Bohr first orbit (of th radius r ); it has th form whr 8 m = P = m υ. (1.6) orb r = g is th lctron mass, 8 r = cm is th Bohr radius.

4 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 4 Th Planck constant h is th quantity th valu of which is qual to th orbital action of th lctron on th Bohr first orbit in th hydrogn atom, namly to its orbital momnt of momntum P orb multiplid by π: h = πp = πm υ r, (1.7) orb Putting (1.6) in (1.5), w arriv at th formula of lctron charg xprssd through lctron mass m and th two charactristic paramtrs, υ and r, of th stady-stat circular motion of th lctron around a proton in th hydrogn atom: Hnc, th dimnsionality of th lctron charg is = 4πεmυ r. (1.8) Or, bcaus 1 1 [ ] = F kg m s. (1.9) 9 1F 9 1 m, (1.1) 1 [ ] = kg m s (1.11) Th sam dimnsionality of lctric chargs (basd on th units of mattr, kg, spac, m, and tim, t) originats also from th Coulomb s law in th SI units. In th CGSE systm, th dimnsionality is g cm s. It is impossibl to rval th natur (a sns) of lctric chargs of such a strang (rathr snslss) dimnsionality formd on th basis of fractional powrs of rfrnc units. Obviously, th dimnsionality problm is hiddn in Coulomb s law F = kq1 q / r. To b xact, it is in th cofficint of proportionality k btwn th rsulting Coulomb forc F and intracting lctric chargs q 1 and q. Th cofficint k was first accptd (in th CGSE systm) to b qual to th dimnsionlss unit, k = 1 (rsultd in [ ] th SI units, it gaind th form k = 1/ 4πε 1 1 = g cm s ). Latr on, in m F, which ld to th dimnsionality [ ] = C, th coulomb. Applying (1.1) to th lattr form, w find that k is in ssnc th dimnsionlss quantity, as th lctric constant ε (th constitunt of k), which is qual actually to 1 / 4π [6, 7]. W will

5 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 5 analyz it blow in dtail. Thus, w hav as bfor k = 1, and 1 [ ] = kg m s. W procd now to considr just this qustion, which is th principal mattr for undrstanding th natur of lctric chargs, th fin-structur constant, tc., and hnc for lctrodynamics (and physics) ntirly.. An xplicit valu and dimnsionality of th lctric constant ε Th aim of th prsnt sction is to prform a dimnsional analysis of th constant ε, ntrd in (1.1), which rvals its tru valu of dimnsionality. Why is this so important? Bginning from th Coulomb s tim, nothing changd in uncovring of th tru natur of lctric chargs. This status quo strngthnd for long aftr an introduction of th SI units (Systèm Intrnational d Unités) givn birth to th lctric constant ε. Th lattr imposd its imprint on all furthr dvlopmnt of physics. A functional dpndnc btwn two intracting, at th distanc r, point chargs q 1 and q, discovrd first by Coulomb, is 1 q / r F = kq, (.1) whr k is th unknown at that tim cofficint of proportionality btwn th rsulting forc F and th obsrvd functional dpndnc. At k = 1 (that was accptd in th CGSE systm), th Coulomb law rducs to th following form (in vacuum) F CGSE = q1 q / r. (.) Hnc, th dimnsionality of th lctric charg in th CGSE systm is 1 [ q ] = g cm s. (.) In ordr to gt rid of th fractional powrs of th abov dimnsionality, th unit of lctric currnt ampèr was introducd in physics as th bas (rfrnc) unit, additionally to th triad of truly bas units of mattr-spactim: th units of mass, lngth, and tim. This was mad contrary to th fact

6 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 6 that actually th ampèr is th drivd unit dfind from Ampèr s law for intracting currnts. Th dimnsionality of th ampr contains th fractional powrs of th two bas units (of lngth and mass), namly c 1 r cr 1A = CGSEI = g cm s. As a rsult, th cofficint of 1 1 proportionality k in Eq. (.1) in th SI units was turnd out to b qual to k = 1/ 4πε. (.4) Th constant ε ntring in k was calld th lctric constant; its valu and dimnsionality ar prsntd as 11 1 F m F m ε = 1. (.5) 4πc r Thus, causd by an introduction of th ampr and basd on th tangld manipulations during th conductd rationalization of dimnsionalitis into th SI units, th nw physical constant ε was introducd as a rsult. Coulomb s law ((.1) in SI units) took th following form: F SI Q Q =. (.6) 4πε r 1 It is asy to show that ε is actually th dimnsionlss magnitud. Indd, th cr 9 unit of capacity th farad F (in th SI units) is 1F = m 9 1 m, whr c r = ( c r = c / c, c = cm s and c = 1 cm s ) is th rlativ spd of light; hnc, from Eq. (.5) it follows that 11 1 cr 1 ε = =, (.7) 11 4πc 1 4π r and w arriv finally at F SI Q1Q = or 4π(1/ 4π) r Q1Q F SI =. (.8) r

7 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 7 i.., at th sam situation that took plac mor than yars ago at th Coulomb tim (s (.)). This mans that actually th cofficint of proportionality in Coulomb s law, in SI units just lik in th CGSE systm, rmains unknown both in valu and dimnsionality, and, as bfor, it is qual to th dimnsionlss unit, k = 1. Thus, th qustion about th tru valu and dimnsionality of k in Coulomb s law (.1) still rmains opn. Th actual dimnsionality of th charg in th SI units is xprssd through th triad of bas units (of lngth, mass, and tim), two of which hav th fractional powrs 1 [ Q ] = kg m s, (.9) as in th CGSE systm (s (.)). Thrfor, it is no wondr that th sam dimnsionality originats also from th xprssion (1.8). Th drivd SI unit of th lctric charg, th coulomb, dos not contain th fractional powrs in th accptd dimnsionality, bcaus in this cas 1C = 1A 1s and [ Q] = A s. Howvr, xprssd with us of th two rfrnc units of mass and lngth (mattr and spac), th coulomb contains th fractional powrs of th units (lik th ampr): c 1 r cr 1C = CGSEq = g cm s (CGSE) (.1) 1 1 c 1 r 1 1C = kg m s (SI) (.11) Th rronous valu of k in Coulomb s law (.6) gav ris to a phnomnological systm of notions with masurs having fractional powrs of bas units that ar rally maninglss. Cognition of th natur of lctric chargs has bcom impossibl. It is obvious that without solving th k-constant problm (in (.1)), physics of lctromagntic phnomna (and rlatd filds) will mak no hadway. Lt us tak a look at th law of univrsal gravitation, which is similar in form to Coulomb s law: F = Gm1 m / r. (.1) Th valu of th cofficint of proportionality G (th gravitational constant) in th law is known, and its dimnsionality has th dfinit non-contradictory

8 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 8 8 physical maning, G = g cm s, xprssd by intgr powrs of rfrnc units. Th similar situation should b clarifid for th cofficint of proportionality k in Coulomb s law (.1). Sinc th rronous systm of masurs of th lctromagntic fild involvs all physical formula, xprimnts basd on ths formula ar unabl to dtct th accumulatd rrors. Thus, vrything is formally corrct and consistnt, although th lctron charg is dfind incorrctly, qualitativly and also quantitativly (w show it blow). This situation has givn ris to numrous additional atomic constants, complicating cognition of th Univrs on th atomic lvl yt mor. Wrong masurs may unfortunatly giv ris to fals thoris, within th framwork of which formally corrct rsults ar possibl only on th basis of nw rrors in full agrmnt with th dialctical law of doubl ngation: No 1 No = Ys, whr No 1 is th initial li, No is a nw li, and Ys is th formal truth. Th rsult of this cours of vnts can only b an impass. Howvr, not all is so hoplss now. Th mattr is that th k-constant problm and th problm of th dimnsionality of lctric chargs hav bn rcntly solvd in th framwork of th DM [5-7]. As it turnd out, th cofficint of proportionality k in th Coulomb law (.1) is qual to k = 1/ 4πρ, (.1) whr ρ = 1 g cm is th absolut unit dnsity of mattr, so that its dimnsionality is 1 [ k] = g cm. (.14) In such a cas th dimnsionality of th lctric charg q is [ q ] = g s. (.15). Th lattr mans that lctric charg is th rat of mass xchang (intraction), or brifly th powr of mass xchang. And th lctron charg is th lmntary quantum of th rat of mass xchang or, simply, th lmntary quantum of xchang. Thus, th lctric charg gains at last th dfinit physical maning. If w now introduc th symbol ε for th absolut unit dnsity, instad of ρ, and pass to Coulomb s law (.1) by putting (.1), w obtain

9 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 9 F q q =. (.16) 4πε r 1 In this cas Coulomb s law dos not diffr in form from th commonly usd prsntation of th law (.6). Howvr, it ssntially diffrs from th lattr in contnts of its constitunts. Th law (.16) is basd on th tru valu of th constant proportionality k, whr ε = 1 g cm is th absolut unit dnsity of mattr. Whras (.6) is basd on th lctric constant of th maninglss (as was shown abov) valu and dimnsionality, (.5) or (.7), artificially attributd to Natur by crators of th SI units. W show blow th main xprssions (dtails ar in [5-7]), which ld to th uncovring of th tru dimnsionality and maning of th lctric charg. Th lctron charg is indissolubl rlatd with th lctron mass. Thrfor, both aformntiond paramtrs ar considrd in th nxt sction in thir intrrlation.. Th natur of lctron mass and lctron charg In accordanc with th dynamic modl (DM) [5, 8], an lmntary particl prsnts by itslf a dynamic sphrical formation of a complicatd structur bing in a dynamic quilibrium with nvironmnt through th wav procss of th dfinit frquncy ω. Th wav shll of a particls rprsnts by itslf a charactristic sphr of th radius r = a, which rstricts th main part of th particl from its fild part mrging gradually with th ambint fild of mattrspac-tim. Longitudinal oscillations of th wav shll of a particl in th radial dirction provid an xchang (intraction) of th particl with othr objcts and th ambint fild of mattr-spac-tim. Th oscillatory spd of wav xchang at th sparating surfac (charactristic sphr) of th particl is prsntd in th form υ ˆ = υ( kr)xp( iωt), (.1) whr k = π / λ = ω/ c is th wav numbr corrsponding to th fundamntal frquncy ω of th fild of xchang at th subatomic lvl, and c is th wav spd of xchang at this lvl qual to th spd of light.

10 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 1 Th notion xchang (instad of intraction) is widr and mor corrct for th DM dvlopd in [5, 6] bcaus it rflcts bhavior of lmntary particls in thir dynamic quilibrium with th ambint fild, at rst and motion, and intractions with othr objcts (and particls thmslvs). In othr words, th notion xchang is mor appropriat from th point of viw of th physics of th complx bhavior of lmntary particls, as th dynamic formations, blonging to on of th intrrlatd lvls of th Univrs. All masss of dynamic formations (micro-particls) in th Univrs, according to th DM, hav an associatd fild charactr with rspct to th dpr lvl of th fild of mattr-spac-tim; thrfor, thir own (propr, rst) masss do not xist. An quation of th powr of xchang, at th xchang of motion, for a particl with on radial dgr of frdom taks in th DM th form dυˆ m + Rυ ˆ = Fˆ, (.) dt whr R is th cofficint of rsistanc, or th disprsion of rst-motion at xchang, 4πa εε r R = kaω; (.) 1 + k a m is th associatd mass of th particl, or brifly th mass of th particl, εεr 4πa m =. (.4) 1+ k a Hr and furthr ε = 1 g / cm is th absolut unit dnsity, and ε r is th rlativ dnsity. Th symbol ^ xprsss th contradictory (or complx) potntial-kintic charactr of physical spac-filds [9, 1]. Th dtails of th drivation of th abov and blow prsntd xprssions ar in Rf. [5, 6, 8]. Th quation of xchang powrs, at th mass xchang, has th form dmˆ υ ˆ = Fˆ, (.5) dt whr dm / dt is th volumtric rat of mass xchang of th particls with nvironmnt, which w call th xchang charg, or mrly th charg

11 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 11 Q ˆ = dmˆ / dt. (.6) Th charg of xchang Qˆ, obtaind from som ncssary transformations, has th activ-ractiv charactr εεr εεr a a Q ˆ 4π 4π = kaω + i ω = Qa + iqr, (.7) 1+ k a 1+ k a whr 4πa εε r Qa = kaω (.8) 1+ k a is th activ charg, and 4πa εεr Qr = ω (.9) 1+ k a is th ractiv charg. Th activ componnt Q a (qual to R, s (.)) dfins th disprsion during xchang, which in a stady-stat procss of xchang is compnsatd by th inflow of motion and mattr from th dpr lvls of spac. Th ractiv componnt of charg Q r, calld in contmporary physics th lctric charg (furthr for brvity, th charg of xchang Q) is connctd with th associatd mass m (.4) by th rlation Q = mω. (.1) Th dimnsionality of th xchang charg is g s. Thus, th DM rvals th tru physical maning of th lctric charg, which is on of th fundamntal notions of physics. Th xchang ( lctric ) charg is th masur of th rat of xchang of mattr-spac-tim, or brifly th powr of mass xchang. Equation (.1) dtrmins th fundamntal frquncy of th fild of xchang, which is th distinctiv tim frquncy of xchang at th atomic and subatomic lvls. Th drivation carrid out first in [11] (dtails can b found in [8], accssibl in Intrnt) lads to th following formula of corrspondnc btwn xchang charg Q and Coulomb charg q C : Q = q C 4πε (.11)

12 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 1 Hnc, th xchang (ractiv) charg of an lctron at th lvl of th fundamntal frquncy is whr = C 4πε = g s, (.1) C = CGSE is th Coulomb charg of an lctron 1 q of th dimnsionality g cm s. Th xchang charg of th valu (.1) (lctron charg) rprsnts an lmntary quantum of th rat of mass xchang. On th basis of (.1) and (.1), knowing th mass of th lctron m w find th fundamntal frquncy of th wav fild of xchang at th subatomic lvl (th frquncy of lctrostatic fild) 9 18 ω = / m = s. (.1) Th corrsponding spd of xchang at th boundary sphr of an lctron of th radius r is dtrmind by th rlation υ = r ω. (.14) W hav thus prsntd th basic concpts and formalism, according to which th problm posd can b tratd. W will considr th abov data and solutions in thir application for lucidation of th quality (1.4). But bfor to mak this, w will xplain first th binary charactr of wav motion, dirctly rlatd to th problm in qustion. 4. A corrlation of basis and suprstructur in wav procsss A wav procss is a contradictory complx of basis-suprstructur. In a wav fild of xchang of th basis, th composit oscillating movmnt of discrt micro-, macro-, and mgaobjcts occurs. This motion forms togthr with th objcts th suprstructur of th wav fild. Thus, th basis is th continuous sid of th wav procss, whras th suprstructur rprsnts its discrt sid. In turn, th suprstructur is a contradictory discrt-continuous complx whr th discrt sid is rprsntd by an objct with a mass m, and th continuous sid is rprsntd by th oscillatory rst-motion of th objct. Mutatis mutandis, th basis is

13 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 1 charactrizd by its own intrnal continuous and discrt sids at th subatomic lvl. In othr words, a wav motion is th mass procss having th binary charactr. It mans that th wav procss of any subspac of th Univrs runs simultanously at th two lvls: th lvl of basis and th lvl of suprstructur. Th basis lvl mbracs an intraction of particls btwn thmslvs in a subspac. This intraction givs ris to its own suprstructur th wav motion th dynamic collctiv intraction of particls with th subspac. Hr, th basis is th caus and suprstructur is th ffct. Thus, any wav procss is a contradictory complx of basis and suprstructur, of caus and ffct. At th sam tim th wav motion is a contradictory procss of rstmotion. Th lattr is charactrizd by strngth vctors of rst E and motion B, at th lvl of th basis, and, rspctivly, by potntial V p and kintic V k spds [9, 1], at th lvl of th suprstructur. Lt us turn to an xampl. An intraction of atoms btwn thmslvs in a string (fixd from both nds) is a procss occurring at th lvl of basis of th string. A disturbanc of th quilibrium intraction (causd by an xtrnal influnc) lads to th xpansion of this disturbanc along a string, which has th wav charactr. With this th oscillatory spd υ of vry atom of th mass m of th string (in th wav of th xpansion) and th wavlngth itslf λ υ rprsnt th collctiv paramtrs of th wav motion rlatd to th lvl of suprstructur. Th nrgy of th wav quantum of suprstructur E = h υ / λ ) (4.1) ( υ gnrats, at th lvl of basis, th qual nrgy of th wav quantum of basis E = h( c / λ), (4.) whr c is th basis spd. For instanc, th wav motion of a string with th frquncy of th fundamntal ton ν 1 and wavlngth λ 1 gnrats in a surrounding air an acoustic wav of th sam frquncy, but with th basis (sound) spd in air c and th wavlngth λ a diffrnt from λ 1: ν / 1 = 1/ T1 = υ / λ1 = c λ a. (4.)

14 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 14 Th similar situation taks plac undr disturbanc of th hydrogn atom, whr υ is th orbital (oscillatory) spd of th lctron suprstructur of th H-atom, and c is th wav spd of radiation of th xcss nrgy at th transition of th xitd H-atom into th quilibrium stat. Th spd c, qual to th spd of light in th last xampl, is th basis spd of xchang of mattr-spac-tim of th longitudinal (radial) wav fild of th proton with th transvrsal (cylindrical) wav fild of th orbiting lctron at th fundamntal frquncy of xchang inhrnt in th subatomic and atomic lvls ω. During th motion in a transint procss, th lctron in th hydrogn atom causs th wav prturbation. Th myriad of particls of th sublctronic lvl is involvd in this procss. Thy hav nothing in common with th mathmatical points-photons of zro rst mass and zro rst nrgy. Thy rprsnt a hug world of particls-satllits of lctrons. For thm, Earth is in th highst dgr th rarfid sphrical spac. Ths particls pirc th Earth just frly as astroids pirc th spac of th solar systm and galaxis. Just thir dirctd motion, fluxs, calld magntic fild, surrounds a conductor with a currnt, a bar magnt, our Earth and fills up intrplantary, intrstllar, and intrgalactic spacs. It is th cylindrical fild-spac of th sublctronic lvl. In a wav procss, th associatd mass m dtrmins th associatd action = mυa, (4.4) υ whr a is an amplitud of displacmnt, which is insparabl from th wav action, c = mca. (4.5) Th simplst rlation α, charactrizing th scal corrlation of th suprstructur and th basis, is th ratio of th transvrs wav of th suprstructur λt = πa to th longitudinal wav of th basis λ = c / ν [1] (Fig. 4.1): λt πa a υ α = = = =, (4.6) λ λ c whr υ = ωa is th oscillatory spd of th wav of suprstructur, and c is th wav spd of basis. Th sam rsult givs th ratio of th actions (4.4) and (4.5).

15 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 15 Thus (4.6) rprsnts th lmntary rlations xistd btwn amplitud of oscillations, wavlngths and spds inhrnt in th wav procss, as a twolvl longitudinal-transvrsal wav systm. Fig A graph of th longitudinal-transvrsal wav fild; c is th wav (bam) spd of basis, iυ is th circular frontal spd of suprstructur. In th dynamic modl of lmntary particls (DM) th spds υ and c hav th analogous maning, namly υ (s (.1)) is th oscillatory spd of boundary wav shlls of particls and c is th bas wav (phas) spd of thir wav xchang at th subatomic and atomic lvls. Th ratio of ths spds rflcts th firm intrrlation (originatd from (.7)), xisting btwn activ and ractiv xchang chargs rlatd with ths spds: Q a / Q = ka = ωa / c = υ / c. (4.7) Th maximal possibl ratio of th oscillatory and wav spds, which th coupld particls can hav, is prsntd by th fin-structur constant, whr υ = υ is th spd of th lctron on th Bohr first orbit: α = υ / c = , (4.8) Thus, th maximal oscillatory spd which a lightr particl of suprstructur can hav, with rspct to th basis spd c of its intraction (binding) with th conjugat havir particl of th basis at quilibrium, is dfind by th ratio: α = υ c = υ / c. (4.9) max /

16 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 16 W can say, running a fw stps forward and gnralizing, that this ratio xprsss th scal corrlation of basis and suprstructur of wav fild-spacs of objcts or conjugat oscillatory-wav procsss in th Univrs at diffrnt its lvls (w show it furthr). Lt us turn now to th wav dynamics at th lvl of th axial wav of basis. W rgard a compact sction of a linar wav of th mass m as a quasiparticl [6]. Such a quasiparticl movs with th wav spd c and simultanously participats in local oscillations with th spd υ. From this standpoint, a running wav can b formally considrd as a flow of quasiparticls (or a wav bam) with two componnts of th complx spd, namly wav c and oscillatory υ. Bcaus th quasiparticl of mass m is localizd simultanously on two sublvls of motion, wav and oscillatory, th following rlation (originatd from (4.4) and (4.5)) is valid υ υ = c c. (4.1) Any oscillating mass (i.., a quasiparticl, according to th abov dfinition) of any microlvl of th Univrs is charactrizd, in wav spac, by an oscillating scalar amplitud momnt of momntum υ of th carrying fundamntal frquncy ω: = mυ m a = Jω, (4.11) υ whr υ m is th amplitud spd of displacmnts, a is th amplitud of displacmnts, J = ma is a scalar amplitud momnt of inrtia of an oscillating lvl. Th amplitud kintic nrgy of th oscillating mass bcoms or, taking into account (4.1), Em = mυm / = Jω / (4.1) E = υ ω/, (4.1a) m whr ω = kc = c /. Thus, w can formally considr th wav spac as a flow of quasiparticls or moving nods (or points of th discrtnss of th wav fild).

17 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 17 Th ratio of th amplitud mass m of th compact sction, localizd in such a nod, to th mass of th incompact sction m of th sam volum is qual to th rlativ dformation of th bam sction, m m Ψˆ = l max = υ m dt cdt = υ c m, (4.1) whr Ψˆ is th displacmnt at oscillations, dl / dt = c is th phas (basis) spd of th wav bam. From anothr hand, in th wav procss, th chang of th xtnsion, l, of th wav lmnt of spac (along th wav-bam) taks plac. Th chang of th fild mass, m, rlatd with th lmnt of spac l, occurs as wll. Th following rlation approximatly xprsss this pculiarity: l l m =, (4.14) m whr m is th fild mass rlatd with th quantum of th wav λ. Th l is th local chang, thrfor, l = υ t. But l = c t, hnc w obtain l m υ ωa = = = = ka, (4.15) l m c c whr a is th amplitud of axial displacmnts. Th axial lmnt of th mass of thickning m r (th mass of radiation and scattring of th unit wav quantum, or a quasiparticl) along th wav-bam of th basis is thus dfind by th quality υ m r = m = m = mka. (4.16) c Th local momntum p r (momntum of suprstructur) of a quantum of th mass of radiation m r can b prsntd as p r = m r υ = mυ c h =, (4.17) λ rcalling Louis d Brogli s formula, whr h = πmυa is th orbital action analogous to th Planck action (constant) (1.7).

18 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 18 If th fild mass m is qual to th mass of an lctron m, rgardd as th lctron wav λ, and assuming υ = υ and a = r, th wav thickning m r taks th following valu υ 1 mr = m m. (4.18) c 17 Thus, w s that th ratio υ / c (1.) has univrsal maning in wav procsss whos sourcs ar xitd atoms. As was mntiond abov, th ratio α xhibits itslf at diffrnt lvls, not only lctromagntic. An important xampl rlatd to th lvl of acoustic wavs, prsntd blow, will mak this statmnt clar. 5. Thrshold paramtrs of sound wavs prcivd by man an xampl On of th dynamic paramtrs of man is th thrshold of audibility. Th 4 lattr is qual to th sound prssur P min = 1 dyn cm at th frquncy narly ν = 11 Hz in th air undr normal conditions ( K tmpratur and 1 atm prssur). Th acoustic action h a and acoustic prssur P ar rlatd by th quality h a = mp / ρν, (5.1) whr m is th avrag mass of air molculs, and ρ is th dnsity of air. Hnc, th minimal acoustic action h a,min on th thrshold of audibility of man, corrsponding to th minimal sound prssur P min, is ha, min = mrupmin / ρν = rg s, (5.) whr m r = is th avrag rlativ mass of air molculs, ρ = g cm is th dnsity of air undr normal conditions, 4 u = g is th unifid atomic mass unit. W s that th action h a,min (5.), rlatd to th acoustic procss, practically coincids with Planck s action (th Planck constant) 7

19 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 19 7 h = rg s [1], having th rlation to lctromagntic procsss. It is no wondr, Natur dmonstrats th prfct harmony within any on and btwn diffrnt its lvls. A human body contains 9.5% hydrogn atoms; thrfor, som of th snsitiv paramtrs of man, at th atomic lvl, coincid with on of th basic paramtrs of th hydrogn atom, which is its orbital momnt of momntum h. It should also b notd that at th lvl of th thrshold of audibility th minimal thrshold amplitud of acoustic oscillations a min, at th frquncy Hz, is a = P / πρυ ν = cm, (5.) min min a 1 4 whr υa = cm s is th (basis) spd of sound in air undr normal conditions. Th rsulting valu coincids with th thortical radius of th lctron sphr r, r ( m ) 1 / 4πε = cm = 1, (5.4) obtaind from th formula (.) in th framwork of th dynamic modl of r lmntary particls, whr k << 1 and ε r = 1 [8]. P On th uppr acoustic thrshold of pain, at th sound prssur 4 = dyn cm, th thrshold oscillatory spd is max 1, max = Pmax / ρυa = υosc cm s. (5.5) Th ratio of th obtaind thrshold oscillatory spd wav spd in air, sonic spd, c = υ is qual to a υ osc, max to th bas α = υosc, max / υa = 1/17.8. (5.6) Th rsulting valu (5.6) almost coincids with th accptd valu of th finstructur constant α (1.). Thus, th found rgularity for th ratios of th charactristic spds of basis and suprstructur in two diffrnt wav procsss, lctromagntic (1.) and sound (5.6), confirms th supposition xprssd abov that th constant α has

20 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) th univrsal charactr for wav procsss. In th light of th last xampl, th Bohr spd υ is th thrshold (limiting) oscillatory spd of th lctron on th Bohr first orbit r of th hydrogn atom, whos basis wav spd of xchang with an nvironmnt is qual to th spd of light c. W procd now to considr th physical maning of th α constant, which is hiddn in th right part of th quality (1.4a). Rlying on th concpts and formalism prsntd abov, w will driv α in th form (1.1), containd four basic physical constants,, c, and ε. This tim w will bas on th nrgtic faturs of wav procsss. 6. Th nrgis of xchang and thir intrrlation Lt a st of quasiparticls of a microlvl, rprsnting an lmntary mass-volum, movs (oscillats) rgularly with an avrag spd υ by th xponntial law υ ˆ = υ( kr)xp( iωt). (6.1) If this motion imposs on th wav motion with th spd c, th total nrgy of a quasiparticl is prsntd as Th constitunt of th total nrgy, m( c + υˆ ) mc mυˆ E = = + mcυ ˆ +. (6.) E c = mcυˆ, (6.) υ taks into account th transfr of th additional nrgy causd by th ordrd motion of a quasiparticl. This nrgy can b also obtaind by th following way [6, 11]. For th mass xchang procss, with th bas spd c at th lvl, th following quation is valid: dm F = c. (6.4) dt Hnc, th nrgy of th wav mass xchang is

21 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 1 Ψˆ ˆ = Ψ ˆ d E c υ Fd = cdm = cυˆ dm = mcυˆ, (6.5) dt whr Ψˆ is th displacmnt at th motion with th spd υˆ. Th corrsponding nrgy dnsity of th mass xchang is w ˆ c = ε ε υˆ. (6.6) υ c Th wav flow of motion with th rsulting nrgy dnsity (6.6) is prcivd physiologically as prssur, and thrfor it is calld a prssur. On th lvl of solids this (kinmatic-dynamic) nrgy dnsity is trmd a strss. Th first trm in (6.) is th kinmatic nrgy of th basis lvl dc mc E = m dl =. (6.7) dt Th carrir nrgy of mass xchang at th basis lvl, whr w call it th dynamic nrgy of a particl at th basis lvl, is dl / dt = c, dm E c = = dt F dl = c dl = c dm mc, (6.8) W arriv at th valu, which rcalls in form th wll-known in physics (owing to Einstin) rlativistic nrgy of particls. Th lattr appars in manipulations with th fictitious mathmatical mpty spacs, which wr th subjct of an intrst of som famous scintists, including Einstin. In his formula, th nrgy E = m c (obtaind in 197) is rst nrgy, bcaus m is rst mass. Sinc contmporary physics is basd on th qustiond at prsnt manipulations (rlativity thory) and th Standard Modl of Elmntary Particls (SM) (usd th notion of rst mass), it cannot xplain of principl th natur of th aformntiond rst nrgy. Th first stp on th way of undrstanding of th aformntiond fundamntal xprssion (6.8), from our standpoint, must b uncovring th natur of mass, that has bn undrtakn in works of th prsnt author with L. Kridik (s Sct. and Rfrncs). Th corrsponding dnsity of th dynamic nrgy is w c ε c = ε. (6.9)

22 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) Th third trm in (6.) is th oscillation nrgy E = mυˆ /. (6.1) Th mass xchang nrgy at th oscillation lvl, whr υ ˆ = d Ψˆ / dt, is dm F = υˆ and dt = ˆ dm ˆ E Ψ = υˆ Ψ = υˆ υ F d d dm = mυ. (6.11) dt Th dnsity of th dynamic nrgy at th oscillation (suprstructur) lvl is ευˆ w ˆ = ε. (6.1) υ On th lvl of solids, th nrgy dnsity (6.1) is trmd a modulus of lasticity. Th dnsitis of mass xchang nrgy at th basis-suprstructur lvl ŵ cυ and th basis lvl ŵ c ar rlatd by th quality υˆ wˆ cυ = wˆ c. (6.1) c Th ratio of th dnsity ŵ υ to ŵ cυ lads to th sam rsult. Th xprimntal data shows that th maximal valu of th ratio ˆυ / c at which solids dstroy, calld th ultimat strss, is approximatly qual to α, namly υˆ / c 1/17. (6.14) Not that at th lvl of solids, th basis spd c is qual to th sound spd in thm. Lt us turn now to th cas, whn th oscillatory spd of a quasiparticl υ is qual to th oscillatory spd υ of th lctron on th Bohr first orbit r ; and its mass m is qual to th associatd mass of th lctron m, dfind by th formula (.), m = πε r (6.15) 4 whr k r << 1 and ε r = 1 [6], r is th radius of th lctron sphr (5.4) [8].

23 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) If w apply Equations (6.15) and (.1) to (6.11), and tak into account th condition of th circular motion (cylindrical fild) [6], i.., Kplr s third law, υ r = const, (6.16) w arriv at th nrgy of mass xchang at th oscillatory lvl in th following form: ω υ r ω υ ω m υ m Eυ = mυ = = = =. (6.17) m 4πε 4πε r 4πε r Th oscillatory-wav nrgy of mass xchang (6.5) undr abov conditions is Eυ c = mυc. (6.18) Th ratio of th rsulting nrgis of mass xchang, oscillatory (6.17) and oscillatory-wav (6.18), dfins th fin-structur constant in th form (1.1) which, according to th dfinition, contains th fundamntal constants,, c, and ε : α = E E υ υc υ = c = = 4πε m υ r c 4πε. (6.19) c It is obvious that in th cas of th ratio of oscillatory-wav nrgy (6.18) and wav (dynamic) nrgy (6.8), qual undr th abov conditions to E m c, w arriv at th sam formula (1.4a), so that finally w hav c = α = E E υ υc = E υc E c = υ c = 4πε. (6.19a) c Thus, this tim considring th nrgis of particls, participating in th wav motion, w com again to th sam fundamntal ratio of two charactristic spds inhrnt in wav procsss. To complt th pictur, lt us turn again to th quation (6.8) and xprss our mor xpandd insight into th spd of light c and th lctron radius r.

24 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 4 7. Th fundamntal quanta of wav xchang Th spd of light c ntrs as wll in th rlativistic xprssion for nrgy of particls, which was introducd in physics arlir than th finstructur constant a. In this connction, lt us rcall th rol (or a physical maning if thr is any), which was attributd to c in th aformntiond xprssion. This is ncssary for dpr undrstanding of th prsnt status quo with this fundamntal constant. It is a long tim sinc th famous formula E = m c (7.1) was obtaind by Einstin as a rsult of transformations of mathmatical (fictitious, mpty) spacs. Howvr, hithrto physics has no answr to th principal qustion, what is th natur of th rlationship, which xists btwn rst mass of a particl m and th spd of light c in th formula whr motion is out of th qustion? Or, in othr words, why dos th spd of light c play th fundamntal rol for th intrnal nrgy of a particl? Contmporary physics, stating only th fact of an xistnc of th dirct rlation btwn th nrgy and rst mass, considrs c mrly as th cofficint of proportionality without any objctiv contnt. Th Standard Modl of Elmntary Particls (SM) cannot shd light on this mattr of principl. By this rason, and not only, it is widly rcognizd that th SM "will not b th final thory" and "any fforts should b undrtakn to finds hints for nw physics" [14]. Exprimntalists and thorists all ovr th world ar activly trying to find ways to mov byond th currnt particl physics paradigm. Th SM was dsignd within th framwork of Quantum Fild Thory (QFT), consistnt both with Quantum Mchanics and th Spcial Thory of Rlativity. But QFT is not applid to Gnral Rlativity and, thrfor, th SM cannot unify fundamntal intractions with gravity. Thr ar many promising idas to rplac th SM. In th SM, particls ar considrd to b points. In String Thory, a "string" is a singl fundamntal building block for all particls. Thr ar fiv diffrnt thoris of strings (thr suprstrings and two htrotic strings). Thr is also an undrlying thory calld M-thory of which all string thoris ar only. M-thory considrs that all th mattr in th Univrs consists of combinations of tiny mmbrans, tc. Howvr, many problms of th SM ar still opn.

25 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 5 On of th promising "hints for nw physics" [14] is th Dynamic Modl of Elmntary Particls (DM) [5]. Th lattr rvals th mystry of th formula (7.1) (s (6.8)) and logically and non-contradictory lucidats, as w s from all abov considrd, th natur of th fin-structur constant α. In th DM, particls ar pulsing microobjcts, i.., thy ar dynamic formations but not static. For thm, th spd of light c is thir bas wav spd on which thy raliz an intraction, i.., caslss wav xchang of mattr-spac and motion-rst (mattr-spac-tim for brvity) with nvironmnt. In th framwork of th DM, th nrgy (7.1) obtains its natural physical maning. It is th propr dynamic nrgy of a particl (as a micropulsar) at th subatomic lvl, or in othr words, its (carrir) nrgy of th mass xchang at this lvl. Taking into account that th spd of light is th bas (bam) spd of th wav procss, lt us considr th physics of mutual transformations of basis and suprstructur, for xampl, in a wav procss at th galactic fild lvl [1]. W assum that th propagation of wavs (including th light rang) with th basis spd c runs lik propagation of any matrial wavs, for xampl, sound wavs in an idal gas. And th absolut spd of vry objct is a multidimnsional (multilvl) spd, which is irrspctiv of any frams of rfrnc, bcaus this spd is dtrmind by th motion at all (micro-, macro-, mga-) lvls in th Univrs. During th dfinit tim intrval th bam spd of som wav-basis can ris. Th lattr dos not influnc on th total nrgy of th wav systm, which rmains qual to zro [6]. In th cours of raising th fild of motion, th fild of rst also riss by th sam valu. Actually, th additional growth of kintic nrgy is compnsatd in Natur by th incras of potntial nrgy, at th sam valu but opposit in sign. Whn th bam spd rachs th spd of light c and xcds it, th formation of th suprstructur bgins. Th lattr is xprssd in an apparanc of two mutually prpndicular longitudinal-transvrs wavs of th oscillatory kind. Th rsulting spd of such a systm, as th vctor sum of th initial bam spd c and th additional spd of th suprstructur υ, forms th scrw cylindrical wav (Fig. 4.1) with th right or lft spiral trajctory. Thus, during th suprstructur s birth, th bam spd of th wav is transformd into th scrw spd. Hnc, th absolut spd of an objct-satllit, moving along th scrw trajctory, will b qual to Ĉ = c + iυ, (7.) and th modulus of th spd is

26 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 6 ˆ C = c + υ, (7.) whr iυ is th frontal kintic spd of th suprstructur, ngating th spd of th basis c. In turn, whn th frontal spd iυ, as th bam spd υ, xcds th light spd c, th wav of suprstructur bcoms th bas wav; as a rsult, on mor suprstructur riss, tc. Thus, th absolut spd of a n-wav lvl bcoms Ĉ = nc + iυ. (7.4) Th abov considrd allows us to suppos that th spd of light c is th fundamntal priod-quantum of th wav spd of xchang of mattr-spactim. Th modulus of th spd of an arbitrary lvl of basis-suprstructur is dfind, to within th priod c, by th formula (7.). In fact, at considrabl absolut spds, th mutual spd of th narst galaxis rachs th spds compard with th priod-quantum of spd c that is obsrvd in astronomy. Th fundamntal priod-quantum of th wav spd of xchang c dfins as wll an avrag discrtnss of spac at th subatomic lvl of xchang (intraction). Actually, th fundamntal wav radius is qual to = c / ω = cm, (7.5) and its doubl valu, D = =. nm, corrlats with th avrag valu of lattic paramtrs in crystals. Taking into account th lmntary rlations (4.6) xistd in wav procsss btwn two particular spds, oscillatory and wav, and also btwn amplitud of oscillations, a, and th wavlngth, λ, w arriv at th following ratios: υ r ω a aω = = =. (7.6) c c c From th lattr it follows that r = a. It mans that th radius of th lctron sphr r can b considrd as th fundamntal quantum-amplitud of oscillations of th fild of mattr-spac-tim. Th valu of th thortical radius of th lctron sphr, originatd in th DM from th formula of lctron mass (6.15), is 8

27 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 7 r = ( m / 4πε ) = cm, (7.7) 1 8 m whr = g, ε = 1 g cm. This radius rstricts th main part of an lctron from its fild part mrging gradually with th ambint fild of mattr-spac-tim. Th oscillatory spd of xchang at th lctron sphr (7.7) is 8 υ = r ω = cm s. (7.8) An quatorial lctron circumfrnc πr, rgardd as an lmntary lctron wav of basis, is locatd two tims at th Bohr radius, bcaus r (πr ), (7.9) as if it wr th radial wav. In this sns, th wav sphr of H-atom is th binary lctron wav. W rturn to th condition (6.16), obtaind from th solutions of th wav quation in cylindrical coordinats [6]. Lt us apply it to th spds of transvrsal oscillatory motion and th radii of two wav surfacs with th radii r and r. Thn, th spd of oscillatory motion υ on th surfac of a sphr of th Bohr radius r, calculatd on th basis of th aformntiond condition, is turnd out to b qual to υ 1 8 = ( r / r ) υ = cm s. (7.1) Th spd obtaind almost coincids in valu with th Bohr spd. This fact indicats that th proton and lctron ar formations of th sam hirarchical lvl of th fild of basis-suprstructur. Th concpt touchd in this sction, on an xistnc in th Univrs th fundamntal priod-quantum of spd c and th fundamntal quantumamplitud of oscillations r, was put forward for th first tim in 1998 [1]. W assum that this concpt will b tstd furthr, just lik it taks plac now with th fin-structur constant introducd first long ago in Bfor to bring a conclusion, lt us rcall that th fin-structur constant α srvs in modrn physics as a convnint masur of th strngth of th lctromagntic intraction. All abov considrd and th nw data, obtaind in th framwork of th DM, nabl xprssing th abov masur of th strngth togthr, for comparison, with th strngths of strong and gravitational

28 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 8 intractions. This possibility is ralizd owing to th concpt of xchang chargs (.1) and nrgtic rlations, originatd from th univrsal law of cntral xchang (8.). W procd now to considr this subjct. 8. Th strngths of strong, lctromagntic, and gravitational intractions W brought abov th quit strong argumnts, which prov that th finstructur constant α dfins th scal corrlation of basis and suprstructur of wav procsss. Mor corrctly, th constant α rprsnt th ratio of two charactristic spds, namly th thrshold oscillatory spd and th basis wav spd. Th fin-structur constant, as th combination of basic physical constants, contains th quilibrium dynamic paramtrs of th lctron in th hydrogn atom (, m, υ, r ) (s Sct. 1). Th lattr rprsnts th simplst proton-lctron systm, which radiats lctromagntic wavs undr th dfinit conditions. Thrfor it is no wondr that α ntrs in th formula of spctral trms of th hydrogn (and hydrogn-lik) atom and is usd for th stimation of th strngth of th lctromagntic intraction. Basing on th unifid approach, originatd from th DM [8], and th corrsponding formula, thr is th possibility to compar th strngths of th thr at onc fundamntal intractions distinguishd in modrn physics, which is impossibl to prform by α. For this aim, w hav to tak into account th fact that vry particular kind of th fundamntal intractions (xchang) is dfind by th corrsponding particular xchang charg. According to th DM [8], th univrsal law of cntral xchang has th form Q1Q F =, (8.1) 4πε r whr Q 1 and Q ar xchang chargs having th dimnsionality g s, ε = 1 g cm is th absolut unit dnsity, 4π xprsss th sphrical charactr of th fild of th cntral xchang [8]. Th xchang chargs Q 1 and Q ar dfind, in full agrmnt with th formula (.1), by associatd masss of intracting particls and fundamntal frquncis on which thy (as dynamic formations) xchang (intract) with nvironmnt at th basis lvl.

29 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 9 Accordingly, taking into account (.1), th univrsal law of cntral xchang (8.1) taks th following xplicit (xpandd) form F m m = ω. (8.) 4πε r 1 Hr ω is th fundamntal frquncy of th givn basis lvl; m 1 and m ar th associatd masss of intracting particls. At th atomic and subatomic lvls, th fundamntal frquncy (accurat to 18 thr significant digits aftr comma) is ω = s (s (.1)). Th fundamntal frquncy of th gravitational lvl ω g is dfind from th xprssion G ω / 4πε, (8.) = g obtaind at th comparison of th univrsal law of cntral xchang (8.) with th particular cas of this law, th Nwton law of univrsal gravitation, 8 m1m F = G, (8.4) r whr G = cm g s is th gravitational constant [15]. On this basis w hav 4 ωg = 4πεG = s, (8.5) As th masur of intrconnction of two particls of th mass m, at a distanc r, on can srv th quantity prsntd in th form of th potntial nrgy of mass xchang (takn from [6])) m Q E = ω =, (8.6) 8πε r 8πε r dfind by th xchang chargs Q = mω. Th frquncy ω rprsnts in this xprssion on of th two fundamntal frquncis: ω (.1), in th cas of strong and lctromagntic intractions, or ω g (8.5), for th gravitational intractions. Th mass m is qual to th associatd mass of a nuclon m n, for

30 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) th strong and gravitational intractions; and it is qual to th associatd lctron mass m, in th cas of lctromagntic intractions. 9 Th lctron xchang charg = g s (.1) rsponss for th strngth of lctromagntic intractions, in particular, for intratomic bonds in molculs and crystals [6]. Actually, th nrgy of lctron binding (its absolut valu) is qual to E = V, (8.7) πε 8 8 whr = c / ω = cm is th charactristic distanc in wav atomic spacs [8], i.., th fundamntal wav radius (7.5), dfind by th fundamntal frquncy of th subatomic lvl ω ; ε = 1 g cm. Th nrgy (8.7) practically coincids with th dissociation nrgy of th molculs: H ( 4.48 V ), HD (4.51 V), HT (4.5 V) and clos to th dissociation nrgy of th molculs O (5.1 V) and OH (4.4 V) [16] (p. 45), tc. Th nrgy of lctron binding (8.7) corrlats also with th brak nrgy of bindings in molculs and radicals. For instanc, ractions H O H + OH and N O NO + N rquir nrgy 5. V, NaOH Na + OH rquirs 4.8 V. Th binding nrgy (of th lctron lvl) pr mol of substanc dfins th so-calld charactristic dissociation nrgy of chmical bonds E = E N = 4.11 kj / mol kcal mol. (8.8) d, mol A = / This valu is consistnt with th xprimntal data for th brak nrgy of chmical bonds in CH 4 (11 kcal/mol), C H 4 (14 kcal/mol) [17], tc. Th lctron-binding nrgy at th distanc of th Bohr radius r is 1 E = =.18 1 rg = 1. 6 V. (8.9) 8πε r This valu coincids with th ionization nrgy of th lctron in th hydrogn atom. Strong (nuclar) intractions ar dfind by th rat of xchang (xchang chargs) of nuclons. For xampl, th xchang charg of a nutron is

31 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) 1 4 m n 6 qn = ωmn =.17 1 g s, (8.1) whr = g is th nutron mass. In this cas, according to th shll-nodal atomic modl (multicntr or molcul-lik) [18] and th DM [6, 8], th nrgy of intrnodal bindings, for xampl, of th lngth 8 r = 1. 1 cm, has th valu qn E = =.9 MV, (8.11) πε r 8 which is charactristic for strong (nuclar) intractions. Th rsulting valu corrlats with th xprimntal data for th binding nrgy of a nutron in a carbon nuclus and with th thrshold nrgy of (γ, n) ractions qual to 18.7 MV; and it is clos to th thrshold nrgy. MV of (n, n) ractions [16] (p. 887), tc. Exchang gravitational chargs of H-atoms, to which w rfrrr protons, nutrons and hydrogn atoms, dfins th strngth of gravitational intractions, which ar ralizd on th fundamntal frquncy ω g of th gravitational fild (8.5). For stimats, w tak th avrag associatd mass of H-atoms qual to th unifid atomic mass unit 1 4 m u = m( C) /1 = g. (8.1) W considr th H-atom of th mass m u as th fundamntal quantum of mass and, simultanously, as th fundamntal graviton with gravitational charg of xchang q G qual to 4 qg = muωg = g s. (8.1) Th nrgy of fundamntal intractions (intrchang) on vry lvl (s, for xampl, (8.7) and (8.11)), originatd from th univrsal law of xchang (8.1), is dfind by th squar of th xchang chargs. In this connction, lt th pur numbr masuring th nrgy (strngth) of th lctromagntic intraction is about 1. Thn, on this scal, th strong intraction has th ordr of 6 q n / =.4 1, (8.14) 4 7

32 HADRONIC JOURNAL, Vol. 8, No., 7-7, (5) and th gravitation intraction has th ordr of 6 q G / =.8 1. (8.15) Hnc, th strngths of thr fundamntal intractions: strong, lctromagntic, and gravitational, rlat approximatly as 1 6 :1:1 6, (8.16) ovrlapping th rang of 4 dcimal ordrs in magnitud. W would lik to strss finally that th proposd hr unifid stimation of th strngth of th thr fundamntal intractions is basd on th singl thortical concpt of xchang intraction formulatd in th univrsal law of cntral xchang (8.). 9. Conclusion All abov prsntd shows that th "fin-structur constant" α of th microworld xprsss th scal corrlation of thrshold stats of conjugat oscillatory-wav procsss at diffrnt lvls of th Univrs, including lctromagntic. In particular, th constant α rflcts th scal corrlation of basis and suprstructur of wav fild-spacs of such objcts in th Univrs, having th contradictory sphrical-cylindrical charactr, as, for xampl, th hydrogn atom. Th lattr rprsnts a dynamic paird cntrally symmtrical systm. A cntral sphrical componnt (proton) has th sphrical wav fild. By this radial fild, proton rlats (xchangs) with th surrounding fild-spac and with th orbiting lctron. Th orbital motion, in turn, is associatd with th cylindrical wav fild. Both dynamic componnts of th proton-lctron systm ar dscribd, accordingly, by sphrical and cylindrical wav functions [6]. At th lctromagntic fild lvl, th "thrshold" spd of oscillations (of suprstructur) is qual to th Bohr first spd υ, and th wav spd (of basis) is qual to th spd of light c. In th abov sns, th Bohr spd υ is th thrshold (limit) spd of th lctron on th stationary (first) orbit in th hydrogn atom. Th physical quantitis and fundamntal constants, constitutd th formula (1.1) of th fin-structur constant, hav th dfinit maning in th approach