A New Large Number Numerical Coincidences

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Morris Ellis
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1 A Nw Lag Numb Numical Coincidncs A.Kitov Abstact. In this aticl th autho givs a bunch of nw hyothsis and snts nw xact and siml lations btwn hysical constant and numbs. Th autho bifly analyzs th discovd coincidncs in tms of thi accuacy and confidnc but h lavs asid any hysical xlanation of th sntd fomulas. Howv all shown lations xinc common natu of ow of two. As xact natu of this is unknown yt so it quis futh invstigation. Psntd matial may also b viwd as logical continuation and dvlomnt of Diac's-Eddington Lag Numbs hyothsis (LNH). Howv oosit to Diac's LNH two of sntd atios a not aoximat but thy hav xact quality. This allows thotical diction of th Univs adius as wll as calculation of xact valu of th gavitational constant G which all fall within th ang of cunt masumnts data and xisting cision. Autho fomulats ths Lag Numb Numical (LNN) coincidncs alizing that futh discovy of thi maning may lad to significant chang in ou undstanding of th Natu. Notations: In this wok, SI units a usd. Th attmts of binging togth hysics and numology had bn don bfo many tims but vy imotant st was don in 198 by Athu Eddington. Accoding to Athu Eddington oosal th numb of oton in nti Univs should qual xactly to: N Edd = 16* 56 ~10 80 [1,]. So, thfo squa oot 56 of N Edd should b clos to Diac's Big numb N~ 16 * = 16 *. Lat on, Eddington changd 16 to 17 and insistd that th fin stuctu constant has to b cisly 1/17, and thn his thoy smd to fail at this conston. Howv, Eddington statmnt also had th numb ( ) which was lft without o attntion. Actually fw yas ali, in 199, it was Gman hysicist R. Füth who oosd to us 16 (which is also ) in od to connct gavitation to atomic constants [10]. Howv, all ths coincidncs hav bn lft unxlaind until snt tim. As it was said by G. Gamov [16]: Sinc th woks of Si Athu Eddington, it has bcom customay to discuss fom tim to tim th numical lations btwn vaious fundamntal constants of natu. Fo xaml, anoth intsting attmt to us "a log-bas- lation" btwn lctomagntic and gavitational couling constant was mad by Saul-Paul Siag, th sach fom San Fancisco in 1979 [1]. Paticulaly ow of, accoding to th autho s ida, should hav significant ol in numical lations fo th hysics constants. Suggstd fou Lag Numb Numical (LNN) lations o coincidncs a sntd blow. Ths coincidncs a not dndnt and latd to ach oth, so ov o disov of on of thm dos not man th sam fo th oths. Thy all hav common numb of. Fist two lations tnd to b xact quations, and scond two a valid with dfind unctainty. Bcaus of that scond two lations a also calld wak. 1. Cosmological coincidnc. Th lation is analog of famous Diac's atio R U / ~10 40 which conncts adius of th Univs and classical lcton adius. Howv Diac's atio is actually valid only aoximatly (with cision of th sam od of magnitud ), in oosit, th suggstd lacmnt is xact quation as following: R U λ = Wh R U is valu fo th adius of th obsvabl Univs and λ =ħ/(m c)=.86..*10-1 (m) is lcton s ducd Comton wavlngth (D Bogli wav). Th lation (1) ovids us with cis siz and ag of th obsvabl Univs. So it lads to xact valu fo th Univs adius of R U =1.1401*10 6 mts cosonding to th Univs ag of billion yas. Rcntly F.M.Sanchz, V.Kotov, C.Bizouad discovd that th us of th ducd lcton Comton wavlngth is dcisiv fo th comatibility of th Hubbl-Lmait lngth with [1-15]. Thy us this (1)

2 lngth unit bcaus of oosd hologahic lation involving it. H th autho indndntly dvlod this ida suggsting that (1) is xact lation. Th masud ag of th Univs, accoding to th Wilkinson Micowav Anisotoy Pob (WMAP) 7-ya sults, is 1.75 ± 0.1 billion yas [9]. Latst NASA obsvation by Hubbl givs th ag of th Univs as 1.7 billion yas []. It is vy clos to th obtaind valu and lis in th xisting o ang. So, th coincidnc (1) tnds to dfin th xact Univs lasd lif tim as: T U = λ /c* (1.1) Imotant to not, that having (1.1), initial Diac s lation may b xssd in th following fom: RU 1 N 1 = = α (1.) 1 wh α = is invtd fin stuctu constant and = k /m c classical lcton adius with liminatd numical facto (i.. qual to unity) and N 1 is xact valu fo th lag numb intoducd by Diac (4.66*10 40 ). As w know fo su that Univs is xanding R U (t), so th quation (1) suggst that on o fw of th fundamntal constants (ħ, c, m ) should also vay in tim. Howv, cunt unctainty in R U masumnt still lavs a oom fo anoth altnativ idas and ossibl coincidncs. Fo xaml, noting that m /m ~ 40 1 / α, lation (1) can hav anoth fom: m 1 k R = 4 10 U (1.) m mc which would cosond to Gy. As this valu is cuntly out of th snt WMAP data fam, thfo it is not suotd by th autho h.. Elcton-oton Radius Coincidnc. Anoth intsting ida conncts th classical oton adius and gavitational adius of th lcton by xact quation as following: g = wh = ( 1 / )( / 5 ) k / (m c ) - classical oton adius an =Gm /c gavitational lcton adius (i.. th Schwazschild adius fo th lcton mass). Of cous som commnts a quid gading cofficints ( 1 / ) and ( / 5 ). Usually numical factos a ignod and assumd to b unity whn dfining classical (lcton) adius. Howv suggstd nw dfinition has xact numical facto ( / 10 )= ( / 5 )*( 1 / ), so it is obvious to hav following xlanations fo that on by on: * Ratio / 5 in classical oton adius dfinition. Th only imotant diffnc with modn sntation of classical adius is th cofficint / 5. It is wll known fom th lctostatics that th ngy quid to assmbl a sh of constant chag dnsity of th adius and chag is E= ( / 5 ) k /. Usually factos of / 5 and 1 / a ignod whil dfining classical lcton adius. Suisingly th coincidnc advics th us of / 5 which mans that chag is qually sad within th sh of th lcton o oton adius. * Ratio 1 / in classical oton adius dfinition. Usual dfinition of th classical adius dos not qui having ½ bcaus initially on lats total lctostatic ngy (E ) of th lcton (o oton) to st mass ngy as following: E = mc. Facto ½ aas if w ostulat that lctomagntic ngy (E m of th lcton o oton) is just a half of aticl s st mass ngy: E m = ½ mc. Th a two ossibl altnativ xlanations fo th ½ facto: 1) Th Viial Thom that tlls us that th otntial ngy insid a givn volum is balancd by th kintic ngy of matt and quals to half of it. So if on consids lctomagntic ngy as kintic and st mass as otntial ngy w would hav: E m = ½ mc ) Simly assuming that half of total ngy may b a magntic ngy o of anoth natu. On may also oos that th could b no ½ in classical oton adius dfinition, but th is 19 instad of is in fomula (). Fom th autho s oint of viw this dos not cosond to ality and - - ()

3 aticulaly th numb should hav stong and unchangabl ow in all numical xssions of th Natu. It is asy can b sn that = (m /m ), so anoth way to wit () is: m = (.1) m And this lads to anoth ossibl sntation of th initial fomula as: = (.) g g wh - is classical lcton adius, g is gavitational adius of th oton. Th xssion (.) is vy simila to (). So, w may actually combin thm into anoth intsting quation: = (.a) g g Th cision of th Elcton-oton coincidnc givn by () is 0.0%. Fom th autho s oint of viw this dviation oiginats fom cunt unctainty in gavitational constant (G) masumnt. If w consid that th lativ G unctainty nowadays is aound and not lss than 0.0% than w must acct this amazing and unxlaind coincidnc that allows us to dict xact valu fo th gavitational constant (G). So, this founding suggsts that at last following ossibl consquncs a valid: 1) Bcaus of / 5 atio oton o lcton still may b considd as classical aticl with unifom chag dnsity insid its adius. ) Dictly fom () on can xss th valu of Nwtonian constant of gavitation (G) which xactly follows as: k G = 0 m (.) m It lads to xact valu fo G = * This valu is within th fam of 010 CODATAcommndd valu with standad unctainty givn by: ± * [6] (S also figu). On may coma this xssion with th simila on obtaind in 199 by R. Füth [10]: hc = 16 π ( m + m ) G that is ad in SI units fo G as: hc 16 G = ( m + m ) It is intsting to coma it to (.) to not obvious similaity. Howv, on may s that th xssion is not satisfactoy bcaus it would lad to gat dviation (0.59%) fom th cuntly stablishd valu fo G and would b out of 010 CODATA ang (6.6466* ). - -

4 ) It is asy to not that Diac s Lag Numb N cisly quals to: 0 N = Gm = k m (.4) This mans that vaiation of Diac s Lag Numb (N) in tim is hadly ossibl, bcaus snts simly th constant numb. So th atio of th lctomagntic foc to th gavitational on mains always constant duing th cunt och.. Wak cosmological coincidnc. G m c () t Wh c- is sd of light, G is th gavitational constant, t =ħ/(m c ) iod of ducd Comton wav of th oton. This quation may b inttd as lation of at of mass gowth o th xansion at of th Univs [4, 5] to hamonic otis of th oton as wav. Howv th lativ cision of () is 0.48% (o vn 0.49% if w acct dfinition of G as in.) which is unsatisfactoy fo modn masumnts and it maks th xssion valid only aoximatly. In od to bcom mo cis th xssion should hav a following sntation: c m + 9m (.1) G t O altnativly to bcom xactly cis: c m 0 = α 1 G t (.) But futh discussion of this toic will b xlod mo dtaild in futh autho s woks. 4. Wak Elcton-oton mass atio. Th attmts to xlain lag numbs by lacing invtd fin stuctu constant in xonntial function w don many tims bfo [11,1]. Anoth intsting hyothsis could lat oton to lcton atio with fin stuctu constant and th numb in th following mann: m (4) m - 4 -

5 Howv th lativ cision is still comaably high (0.06%) and is out of th o fam within th cunt ximntal data. Howv, using this lation as aoximation, on can find simila connctions of divd fomulas to th simila ons in wok [1]. Conclusion. Th basic maning of all ths lations may b viwd in th fom of xact quality fo lag Diac s numb N (s.4). Howv all ths oosals disov on of Diac s hyothsis of th quality of th big numbs [s, ag 100]. So, th autho has shown that N N 1 N. It mans that th numb N, as th atio of th lctomagntic foc to its gavitational foc givn by (.4), is actually not qual to numb N 1 which is th atio of Univs adius to classical lcton adius (1.), howv thy diff by numical facto of 0.55=α -1 */0. So, th main collusions of this study a following: Cunt Univs ag and adius can b calculatd xactly ( Gy); Th valu of Nwtonian constant of gavitation (G) can b divd xactly (6.6746*10-11 ); Th numb should hav th al significanc. Gnally th conct of «ow of two» could b gadd as having two otis in th scinc. Fistly it is digital (logical) math wh ow of two has common us. So this may suot an ida of hologahic conct of th Univs o som of th factal thois. Scondly, it is usd in wav mchanics, and it could b viwd in accodanc with wav otis of th lmntay aticls in quantum hysics. In tms of wav conct, th numb of cosonds to th ton of -th octav o to som high hamonic ( ovton ) of th main ton. Intstingly to mntion, that a vy clos ida has bn bought fw as ago. Th ida lats aticls mass lvls within two squncs that dscnd in gomtic ogssion fom th Planck Mass. Sublvls a aangd in subsquncs of common atio which uss a ow of [7,8]. Th autho is also vy suotiv to th oint of viw givn in [1-15], howv it is imotant to stss that th hysics should b f fom aoximat lations and should hav only cis qualitis and fomulas. Som of th xact fomulas which may hl to suot such gnal idas hav bn sntd in this wok. If nw suggstd lations fo Lag Numbs a coct thn it should obably lad to nw sach fo its hiddn maning. As always, w must acct th fact that in oftn cass nw founding lads to nw qustions instad of th answs and that might bcom a nw challng fo nw invstigations and thois. Assuming that at last on of th discovd lations is coct in th futu w may bcom a bit clos to th tu viw on th hysical ality. Alxand Kitov (Novmb 01) Rfncs: 1. A. Eddington, lctu "Th Philosohy of Physical Scinc." (199). John D. Baow, Th Constants of Natu Fom Alha to Omga - Th Numbs that Encod th Dst Scts of th Univs. (00) Panthon Books. ISBN NASA wbsit, "NASA's Hubbl Finds Most Distant Galaxy Candidat Ev Sn in Univs" (011) 4. Ludwik Kosto, "PHYSICAL INTERPRETATION OF THE COEFFICIENTS c/g, c /G, c /G, c 4 /G, c 5 /G THAT APPEAR IN THE EQUATIONS OF GENERAL RELATIVITY" 5. Chistoh Schill, "Gnal lativity and cosmology divd fom incil of maximum ow o foc" (008) 6. Pt J. Moh, Bay N. Taylo, and David B. Nwll "CODATA commndd valus of th fundamntal hysical constants: 006" (008), "CODATA Rcommndd Valus of th Fundamntal Physical Constants: 010" (Datd: Mach 15, 01) 7. Bnad F. Rily, "Paticl mass lvls " (009) 8. Bnad F. Rily, "A unifid modl of aticl mass" (00) 9. htt://lambda.gsfc.nasa.gov/oduct/ma/cunt/bst_aams.cfm Edd - 5 -

6 10. R. Füth, "Vsuch in quantnthotischn Bchnung d Massn von Poton und Elkton, Physikalisch Zitschift" (199), fom Hlg Kagh, "Magic Numb: A Patial Histoy of th Fin- Stuctu Constant" (00) 11. J. Bandmüll and E. Rüchadt, Di Sommfldsch Finstuktukonstant und das Poblm d sktoskoischn Einhitn, Di Natuwissnschaftn 7 (1950), R. Baggiolini, On a makabl lation btwn atomic and univsal constants, Amican Jounal of Physics 5 (1957) 1. Saul-Paul Siag, "Physical constants as cosmological constaints" (1979) 1. F.M.Sanchz, V.Kotov, C.Bizouad, ''Evidnc fo a stady-stat, hologahic, tachyonic and susymmtic cosmology'' Galilan Elctodynamics 0, Scial Issus, N,. 4-5, (009) 14. F.M.Sanchz, V.Kotov, C.Bizouad, ''Towads a synthsis of two cosmologis'', Jounal of Cosmology, vol 17, (011) 15. F.M.Sanchz, V.Kotov, C.Bizouad, 'Towads Cohnt Cosmology'', Galilan Elctodynamics (in ss 01) 16. G. Gamov, "NUMEROLOGY OF THE CONSTANTS OF NATURE", (1967) - 6 -

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