t H = sec Rg sv

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1 t H sec t H : sec Rg sv : t H c Ovde sam pokusao da pronadjem tacne cifre magicnih brojeva sa Vajnbergove skale.moja istrazivanja su dovela do zakljucka da su magicni brojevi samo koeficijenti srazmernosti izmedju clanova na skali.kad je rec o koincidenciji velikih brojeva to,cini se, nema neko dublje znacenje. Rec je,naime, samo o blizini clanova na skali.sve su to razliciti brojevi kad vodimo racuna o tacnosti. Hablovo vreme n : t H : gm π G gm π G ( ) ( cm) cm a 0 Md ( a 0 Rg sv ) t e Rg sv t H t H sec Veliki magicni brojevi su kolicnici energije svemira i energija sa kvantnim brojevima 0^n gde je nod 0 do 40 u deseticama.

2 ( t H ) sec ρ sv4 : 4 t H π G ( ) ( t H ) 4 π G ρ sv4 0 sec Temperatura svemira.koeficijenti proporcionalnosti na Vajnbergovoj skali iz knjige "Gravitacija i kosmologija" na ruskom,str.577 Tablica 5.4 n : K n : n : n 4 : n 5 : n 6 : n 7 : n 8 : n 9 : n 0 : n :

3 n : n : n 4 : n 5 : n 6 : n 7 : n 8 : n 9 : ( t H ) 8 π G ρ sv4 Rg sv Rg sv k b n K H )) 8 π G ρ sv4 Rg sv k b n.00 0 K H )) 8 π G ρ sv4 Rg sv k b n.00 0 K H )) 8 π G ρ sv4 Rg sv k b n 4 0 K H )) 8 π G ρ sv4 Rg sv k b n K H )) 8 π G ρ sv4 Rg sv k b n K

4 H )) 8 π G ρ sv4 Rg sv k b n K H )) 8 π G ρ sv4 Rg sv k b n K ( ( t H )) 8 π G ρ sv4 Rg sv k b n 9 00 K a :.. 0 H )) 8 π G ρ sv4 Rg sv n 0 k b K H )) 8 π G ρ sv4 Rg sv k b n 0 9 K H )) 8 π G ρ sv4 Rg sv k b n 0 9 K

5 H )) 8 π G ρ sv4 Rg sv k b n 0 8 K H )) 8 π G ρ sv4 Rg sv k b n K H )) 8 π G ρ sv4 Rg sv k b n K H )) 8 π G ρ sv4 Rg sv k b n K H )) 8 π G ρ sv4 Rg sv k b n K H )) 8 π G ρ sv4 Rg sv k b n K Iz skalarne Fridmanove jednacine kosmosa izracunati energije vodonika, to jest mini-crne rupe sa masom Md (a to je identicno). ρ H : Md 4 π a 0 a 0 t HH : a c α vo :.. n vod :

6 HH )) 8 π G ρ H a 0. m e.607ev H )) 8 π G ρ sv4 Rg sv ev n vod a vo En HH (( t HH )) 8 π G ρ H a 0 : (( )) 8. m e ( ) En H : t H π G ρ sv4 Rg sv En H 5.7 En HH 0 87 Koeficijent proporcionalnosti R 0 : cm a :.. 8 r : cm

7 H )) 8 M π G ρ sv4 sv Rg sv n vod ev (( )) 8 t H π G ρ sv4 Rg sv a vo n vod t voda : a 0 a c α a 0 4 c α sec a kvant :.. 8 H )) 8 π G ρ sv4 n t a kvant t voda sec n t : sec

8 ( sec sec ) a 0 ( ) m e.04ev H )) 8 π G ρ sv4 4 n t a 0 m e.40ev t H 8 ( + π G ρ sv4 t H ) sec t H ( + 8 π G ρ sv4 t H ) sec n mkr : a mkr :.. 4 H )) 8 π G ρ sv4 Rg sv.7 K n mkr a mkr k b

9 H )) 8 π G ρ sv4 Rg sv n mkr k b.7 K ev k b.7 K n mkr : H )) 8 π G ρ sv4 Rg sv n mkr k b K 8 0 9

10 n naj : H )) 8 π G ρ sv4 Rg sv n naj k b K n sunce : H )) 8 π G ρ sv4 Rg sv n sunce k b K n zemlja : H )) 8 π G ρ sv4 Rg sv n zemlja k b K H )) 8 π G ρ sv4 Rg sv n zemlja erg Svemirska skala vremena a V : π G ρ sv4 a vodonik : sec a 0 4 c α sec ( ) 8

11 n V : ( ) sec (( )) sec Nize je postignuta potpuna analogija sa Vajnbergovom jednacinom a V n V 4 π sec G ρ sv4 n V 4 π G ρ sv4 a 0 a c α V a 0 c α sec ( π G) β ρ sv ( π G) β ρ sv4 ( π G) c α a 0 ρ sv4

12 4 6 ( π G) c α a 0 ρ sv4 a :.. 8 n ρ : ρ vod : 4 π G ( t vod ) a 0 t vod : c α ( ) ρ sv n.59 0 gm cm 4 π Md ( ) a 0 a gm cm ρ vod n :.77 0 a :.. 8 gm cm a 0 c α a n 8 π G sec ρ sv4 n 8 π G ρ sv4 a 0 a t voda : c α t voda sec

13 a sec 8 π G ρ sv4 ρ sv ( π G) ( ) c α.77 0 a 0 ρ sv4 a 0 4 c α π sec G n 9 ρ sv yr a 0 c α a 0 ( c α) sec

14 ( ) ( ) ρ vod sec 8 π G a :.. 8 ρ 4 π vod sec G ( ) ρ vod 8 π G a ( ) ρ vod sec 8 π G a 0 c α a 0 c α sec a 0 c α a sec ( a) ( ) ρ vod sec 4 π G

15 ρ vod gm cm ρ vod gm cm 8 π G ρ sv4 8 π G ρ sv4 0 sec Ovo je za me*c^ n e : n e : Negde oko mikrotalasne temperature ( ( t H )) 8 π G ρ sv4 Rg sv n e m h.9 0 cm sec

16 n e : 0 80 c α a 0 m cm ( t H ) 8 π G ρ sv4 Rg sv K cm n e m k b ( t H ) 8 π G ρ sv4 Rg sv 0 80 k b ( K) K k b ( ) ev m e c k b K n dejstvo :.76 0 H )) 8 π G ρ sv Rg sv n α c Rg sv r e H )) 8 π G ρ sv4 Rg sv cm sec

17 H )) 4 π G ρ ( sv4 ) 0 sec sec ρ sv : 4 π G t H ( ) H )) 4 π G ρ ( sv4 ) Rg sv 0 erg Veliki magicni brojevi povezuju gravitaciju, elektromagnetizam,kvantnu mehaniku i kvantnu elektrodinamiku ω : c α r e 4 π G n Md : ( ρ sv ) Rg sv n Md c gm Rg sv r e Md gm erg 8 π G ( ρ sv ) n Md c Rg sv gm el Rg sv n Md erg n novo : n novo n Md Md c erg 8 π G ( ρ sv ) Rg sv.8 0 n novo erg ω : c α a 0 n novo : π G ( ρ sv4 ) n novo Rg sv.606ev 8 G M Rg sv

18 π G ρ sv ( ω h) 8 π G ρ sv4 Rg sv ( ω h) erg erg ( ) ( m e c ). 0 6 sec gmcm c H )) 8 Gρ sv4 Rg sv π n n : 0 0 c H )) 8 Gρ sv4 Rg sv π n n : 0 0 c

19 H )) 8 π G ρ sv4 sv Rg sv r e n : 0 40 H )) 8 π G ρ sv4 Rg sv k r e b Rg sv K Md c erg ( + 8 π G t H ) ρ sv4 r e K ( ) t H k b Ovo su bili samo zaokrugljeni stepeni.u stvari postoji onoliko velikih magicnih brojeva koliko je veliki niz. Oni se sve vise smanjuju i prelaze u male brojeve da bi porasle do velikih negativnih. n : 0 9 c H )) 8 Gρ sv4 Rg sv π n n : 0 8 c H )) 8 Gρ sv4 Rg sv π n n : c H )) 8 Gρ sv4 Rg sv π n n :

20 c a 0 H )) 8 Gρ sv4 Rg sv π n cm 4 π Md ( ) 4 a gm cm H )) 8 Md c a 0 πg ρ sv4 n Rg sv 4 π gm cm H )) 8 π G ρ sv4 Rg sv k b ( ) 8 πg ρ sv4 t H t H k b 8 πg ρ sv4 ( ) k b 0 K n Rg sv Rg sv 5 0 K 0 K 0 K 0 K Ovo je temperatura prva po redu na Vajnbergovoj skali istorije svemira.pre ove temperature Vajnberg analizira najraniji svemir. n : K

21 0 K K 0 5 K K 0 K K 0 K m e c k b K K 0 0 K K 0 K c k b ( K) cm cm

22 cm r e Ja cu sada da nadjem neke clanove u nizu temperaturne istorije svemira od temperature 5..75*0^ do.7k na Vajnbergovoj skali, to jest od trenutka anihilacije parova µ+µ- do trenutka iskljucenja interakcije izmedu materije i zracenja gm n :.. 8 Rg sv cm ρ sv gm cm ( t H ) 8 π G ρ sv4 Rg sv k b K c k b K ( t H ) 8 π G ρ sv4 k b n Rg sv K M

23 . + t H K π G ρ sv4 Rg sv 0.86 n 70 ( k b ) A sada energija : H )) 8 π G ρ sv4 Rg sv erg (( t H )) 8 π G ρ sv4 Rg sv n 89 c gm.0 0 9

24 A sada vreme : H )) 8 π G ρ sv4 n sec gm c h yr m µ c h Masa muona yr ( m µ ) gm h gmcm sec K.4 0 K 0

25 h gm cm sec c r e cm sec h h π h c 5 G. 0 8 ev h gmcm sec E kr :. 0 8 ev G m p h c G m p α g : h c Rg sv L Pl K sec K gmcm ev v 0 : cm sec R 0 :.7 K ( k b ) el r e R 0 el R 0

26 R 0 v gm m e v 0 n k b.7 K Mikrotalasno zracenje m e ( c ) m e ( c α ) n k b n k b K m e v 0 n k b nah : ( t H ) 8 π G ρ sv4 nah r e c c v 0 α 0 : ( ) t H h c + 8 π G ρ sv4 t H ( ) t H c + 8 π G ρ sv4 t H ( r e m e c α) a 0 r e h gmcm sec

27 Md ( + 8 π G t H ) ρ sv4 Rg sv c ( t H ) BASIC SCIENCE REFERENCES Fundamental Physical Constants Universal Constants c m sec Velocity of light in vacuum r e π t e c µ 0 4 π 0 7 newton amp Permeability of vacuum ε Permittivity of vacuum farad m G m kg sec

28 ev G cm gmsec Newtonian constant of gravitation M s gm joule h Rg s G M s c Planck's constant (h) joule sec Electromagnetic Constants el Elementary charge coul Φ Φ Magnetic flux quantum M Bor joule stattesla Bohr magneton M Bor joule 4 stattesla joule 7 stattesla Nuclear magneton

29 Atomic Constants α Fine structure constant Ryd m Rydberg constant a m Bohr radius E h joule Hartree energy Quantum of circulation m sec Electron m e kg Electron mass Electron specific charge (electron charge to mass ratio) coul kg Electron Compton wavelength m

30 ECw m ECw cm r e m Classical electron radius joule 6 tesla Electron magnetic moment Muon m µ kg Muon mass

31 Proton m p kg Proton mass Ratio of proton mass to electron mass Proton Compton wavelength m joule tesla Proton magnetic moment Proton gyromagnetic ratio rad sec tesla Neutron m n kg Neutron mass Neutron Compton wavelength m Physico-Chemical Constants N l

32 N A mole Avogadro constant Atomic mass constant AMU kg coul mole Faraday constant joule mole K Molar gas constant

33 k b Boltzmann's constant joule K Molar volume of ideal gas at STP.440 liter mole σ watt m K 4 Stefan-Boltzmann constant watt m First radiation constant m K Second radiation constant M s gm M z gm m Pl h c G m Pl gm L Pl G h c cm r e.88 0 cm L Pl ( ) el m e c α a 0 Md gm r s km

34 Rg sv cm r z km Md el m e G G cm gmsec r e α a 0 t H sec c Rg sv G Rg sv cm t H gm Rg sv cm sec Rg sv t H c t H yr gm Md : c r e G a 0 t e c α gm Data from CRC Handbook of Chemistry and Physics, 7nd edition edited by David R. Lide, CRC Press (99).

35 8

36 m sec

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