t H = sec Rg sv

t H.086 0 7 sec t H :.0867 0 7 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 :.59 0 7987044784.450480 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.086 0 7 sec Veliki magicni brojevi su kolicnici energije svemira i energija sa kvantnim brojevima 0^n gde je nod 0 do 40 u deseticama.

( t H ).05 0 5 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 :.5 0 8 8.09 0 9 K n :.70 0 8 n : 4.054 0 8 n 4 : 8.09 0 8 n 5 :.5 0 8 n 6 :.70 0 8 n 7 : 4.054 0 8 n 8 :.5 0 8 n 9 : 8. 0 8 n 0 :.5 0 8 n :.704 0 8

n : 8. 0 8 n :.704 0 84 n 4 : 8. 0 84 n 5 : 8. 0 85 n 6 : 8. 0 86 n 7 : 8. 0 87 n 8 : 8. 0 88 n 9 :.08 0 89 ( t H ) 8 π G ρ sv4 Rg sv Rg sv k b n 6.004 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.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 5 6.004 0 0 K H )) 8 π G ρ sv4 Rg sv k b n 6.00 0 0 K

H )) 8 π G ρ sv4 Rg sv k b n 7.00 0 0 K H )) 8 π G ρ sv4 Rg sv k b n 8 6.004 0 9 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 5.999 0 9 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

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 4 0 8 K H )) 8 π G ρ sv4 Rg sv k b n 5 0 7 K H )) 8 π G ρ sv4 Rg sv k b n 6 0 6 K H )) 8 π G ρ sv4 Rg sv k b n 7 0 5 K H )) 8 π G ρ sv4 Rg sv k b n 8 0 4 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 : 5.7 0 87.

HH )) 8 π G ρ H a 0. m e.607ev.606 6 0.78 H )) 8 π G ρ sv4 Rg sv.606.40 ev n vod a vo.5 0.85 0.544 0.78 0.78 0. 0.68 0.6 0. 0.094 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 :.06 0 8 cm a :.. 8 r :.758 0 6 cm

H )) 8 M π G ρ sv4 sv Rg sv n vod 0 6.80 9.07 0.05 0.885.9.66.906.095.46.69.47 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 9.676 0 7 sec a kvant :.. 8 H )) 8 π G ρ sv4 n t a kvant t voda.49 0-7 4.88 0-7 7.57 0-7 sec n t :.76 0 4.49 0-7 4.87 0-7 7.56 0-7 9.675 0-7.09 0-6 sec 9.676 0-7.09 0-6.45 0-6.69 0-6.95 0-6.45 0-6.69 0-6.95 0-6

( 9.675 0 7 sec.49 0 7 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 ).086 0 7 sec t H ( + 8 π G ρ sv4 t H ).086 0 7 sec n mkr :.004 0 9 a mkr :.. 4 H )) 8 π G ρ sv4 Rg sv.7 K 0.675 0. 0.69 0.08 0.075 0.055 0.04 0.0 0.07 0.0 n mkr a mkr k b

0.0 0.09 0.06 0.04 H )) 8 π G ρ sv4 Rg sv n mkr k b.7 K.7 0 4 ev k b.7 K n mkr : 8. 0 9 H )) 8 π G ρ sv4 Rg sv n mkr k b K 8 0 9

n naj : 8. 0 9 H )) 8 π G ρ sv4 Rg sv n naj k b K n sunce : 6.64 0 H )) 8 π G ρ sv4 Rg sv n sunce k b.95 0 70 K n zemlja :.085 0 8 H )) 8 π G ρ sv4 Rg sv n zemlja k b.89 0 64 K H )) 8 π G ρ sv4 Rg sv n zemlja 5.7 0 48 erg Svemirska skala vremena a V :.. 8 8 π G ρ sv4 a vodonik :.76 0 4.086 07 sec a 0 4 c α.49 0 7 sec ( ) 8

n V :.804 0 4 ( ).49 0 7 sec (( )) 9.77 0 6 sec Nize je postignuta potpuna analogija sa Vajnbergovom jednacinom a V n V 4 π 0 7.58 0-7.96 0-6.69 0-6 5.807 0-6 8.468 0-6.6 0-5.54 0-5 sec G ρ sv4 n V 4 π G ρ sv4 a 0 a c α V 0 7.57 0-7.95 0-6.68 0-6 5.805 0-6 8.466 0-6.6 0-5.54 0-5 a 0 c α sec ( π G) β ρ sv4 4 4 6 6 ( π G) β ρ sv4 ( π G) c α.76 0 4 a 0 ρ sv4

4 6 ( π G) c α.76 0 4 a 0 ρ sv4 a :.. 8 n ρ : 0.. 0 ρ vod : 4 π G ( t vod ) a 0 t vod : c α ( ) ρ sv4.756 0 9 n.59 0 gm cm 4 π Md ( ) a 0 a 6.5 0 9 9.554 0 7 8.88 0 6.49 0 6.94 0 5. 0 5 5.98 0 4. 0 4 gm cm ρ vod 6.4 0 9 n :.77 0 a :.. 8 gm cm a 0 c α a n 8 π -5.84 0-7 0 G sec ρ sv4 n 8 π G ρ sv4 a 0 a t voda : c α t voda 7.49 0-7 sec

5.84 0-7.68 0-6.75 0-6.6 0-6.9 0-6.504 0-6.49 0 4.88 0-7 7.57 0-7 9.676 0-7.09 0-6.45 0-6.69 0-6.95 0-6.49 0 7 4.88 0 7 0.5 7.57 0 7.49 0 7 4.88 0 7 a.49 0 7.77 0 sec 8 π G ρ sv4 ρ sv4 7.474 0. 0 4.495 0 4.868 0 4.4 0 4.66 0 4.989 0 4 4 6 ( π G) ( ) c α.77 0 a 0 ρ sv4 a 0 4 c α.95 0 6 8 π sec G n 9 ρ sv4.40 0 99 yr a 0 c α a 0 ( c α).49 0 7 sec

( ) ( ) ρ vod.7 0 7 sec 8 π G a :.. 8 ρ 4 π vod 7.085 0-8 sec.09 0-7.4 0-7 G ( ) ρ vod 8 π G a ( ) ρ vod.7 0 7 sec 8 π G.564 0-7.654 0-7.7 0-7.77 0-7.84 0-7 a 0 c α 7.085 0-8.09 0-7.4 0-7.564 0-7.654 0-7.7 0-7.77 0-7.84 0-7 a 0 c α sec a 0 c α a.7 0 7 sec ( a) 4 6 8 0 4 6 ( ) ρ vod.49 0 7 sec 4 π G

ρ vod 6.4 0 9 gm cm ρ vod 6.4 0 9 gm cm 8 π G ρ sv4 8 π G ρ sv4 0 sec Ovo je za me*c^ n e :.67 0 8 n e : 5.6 0 87 Negde oko mikrotalasne temperature ( ( t H )) 8 π G ρ sv4 Rg sv n e m h.9 0 cm sec

n e : 0 80 c α a 0 m.067 0 cm ( t H ) 8 π G ρ sv4 Rg sv 8. 0 8 K cm n e m k b ( t H ) 8 π G ρ sv4 Rg sv 0 80 k b ( 8.09 0 K) K 5. 0 5 k b ( 5.9 0 9 ) ev m e c 5.9 0 9 k b K n dejstvo :.76 0 H )) 8 π G ρ sv Rg sv n α c Rg sv.8 0 40 r e H )) 8 π G ρ sv4 Rg sv 8.988 0 0 cm sec

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 :.8 0 40 ( ρ sv ) Rg sv n Md c.795 05 gm Rg sv.8 0 40 r e Md.796 0 5 gm. 0 77 erg 8 π G ( ρ sv ) n Md c Rg sv 7.59 0 5 gm el Rg sv n Md 8.86 0 7 erg n novo :.07 0 88 n novo.8 0 47 n Md Md c 6.8 0 6 erg 8 π G ( ρ sv ) Rg sv.8 0 n novo erg ω : c α a 0 n novo : 5.7 0 87 4 π G ( ρ sv4 ) n novo Rg sv.606ev 8 G M Rg sv 5 7 0 87

π G ρ sv 5.7 0 87 ( ω h) 8 π G ρ sv4 Rg sv ( ω h).65 0 87. 0 77 erg. 0 6.68 0 8 erg ( ) ( m e c ). 0 6 sec gmcm c H )) 8 Gρ sv4 Rg sv π n.96 0 67 n : 0 0 c H )) 8 Gρ sv4 Rg sv π n 0 0 9 n : 0 0 c

H )) 8 π G ρ sv4 sv Rg sv.8 0 40 r e n : 0 40 H )) 8 π G ρ sv4 Rg sv k r e b Rg sv 7.54 0 K Md c.4 0 6 erg ( + 8 π G t H ) ρ sv4 r e 7.54 0 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 0 0 77 n : 0 8 c H )) 8 Gρ sv4 Rg sv π n 0 0 75 n : c H )) 8 Gρ sv4 Rg sv π n n :

c a 0 H )) 8 Gρ sv4 Rg sv π n.7 0 8 cm 4 π Md ( ) 4 a 0 9.554 0 7 gm cm H )) 8 Md c a 0 πg ρ sv4 n Rg sv 4 π 9.555 0 7 gm cm H )) 8 π G ρ sv4 Rg sv k b ( 8.09 0 80 ) 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 :.. 8 8.09 0 9 K 8.09 0 80

0 K 8.09 0 8.09 0 9 K 0 5 K 8.09 0 40.6880 K 0 K.688 0 0.6880 K 0 K.688 0 0 m e c 5.9 0 9 k b K.6880 0 K 0 0 K.688 0 0.6880 9 K 0 K.688 0 0 c k b (.680 8 K) 5.99 0 9.67 0 8 cm 9.899 0 cm.688 0 0

.67 0 8 cm 5.9 0 0 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.46 0 56 gm n :.. 8 Rg sv 9.5 0 7 cm ρ sv4.756 0 9 gm cm ( t H ) 8 π G ρ sv4 Rg sv k b 8. 0 9 K c 8. 0 9 k b K ( t H ) 8 π G ρ sv4 k b n Rg sv -8. 0 9-4.056 0 9 -.704 0 9 -.08 0 9 -.6 0 9 -.5 0 9 -.59 0 9 -.04 0 9 K M

. + t H 8 9.70 0 9 K 8.8 0 7.876 0 59 6.96 0 50.45 0 44.8 0 8 6.76 0 5.896 0 9 π G ρ sv4 Rg sv 0.86 n 70 ( k b ) A sada energija : H )) 8 π G ρ sv4 Rg sv. 0 77 erg (( t H )) 8 π G ρ sv4 Rg sv n 89 c.46 0 56 gm.0 0 9

4.8 0 5.6 7.7 0-7 6.99 0-4 7.67 0-0 5.54 0-5 A sada vreme : H )) 8 π G ρ sv4 n 89 0.59 5.5 0 7.8 0 8.786 0 8.88 0 44 6.547 0 48.86 0 5.08 0 55 7.9 0 57 sec 5.5 0 5 gm c h 4.447 0 yr m µ c h Masa muona.4 0 0 yr ( m µ ).884 0 5 gm h 6.66 0 7 gmcm sec.4 0 5 K.4 0 K 0

h 6.66 0 7 gm cm sec c r e.5 0 8 cm sec h h π h c 5 G. 0 8 ev h.055 0 7 gmcm sec E kr :. 0 8 ev G m p h c 9.98 0 40 G m p α g : h c Rg sv L Pl.4 0.84 060 K 8.78 0 4 sec K gmcm ev v 0 : 4.09 0 cm sec R 0 :.7 K ( k b ) el r e 6.8 0 0 R 0 el R 0

R 0 v 0.66 0 7 gm m e v 0 n k b.7 K 0.675 0. 0.69 0.08 0.075 0.055 0.04 Mikrotalasno zracenje m e ( c ) m e ( c α ) n k b n k b.58 0 5 7.894 0 4.509 0 4.974 0 4.6 0 4 8.77 0 6.444 0 4.94 0 K m e v 0 n k b.96 0 9.96 0 9.96 0 9.96 0 9.96 0 9.96 0 9.96 0 9.96 0 9 nah : 6.66 0 44 ( t H ) 8 π G ρ sv4 nah r e c 5.5 0 5 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 6.66 0 44 ( r e m e c α) a 0 r e 6.66 0 44 h.055 0 7 gmcm sec

Md.8 0 40 ( + 8 π G t H ) ρ sv4 Rg sv c ( t H ) BASIC SCIENCE REFERENCES Fundamental Physical Constants Universal Constants c 9979458 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 0 8.8548787 0 Permittivity of vacuum farad m G 6.6759 0 m kg sec

ev.6077 0 9 G 6.676 0 8 cm gmsec Newtonian constant of gravitation M s.989 0 gm joule h 6.660755 0 4 Rg s G M s c Planck's constant (h) joule sec Electromagnetic Constants el.6077 0 9 Elementary charge coul Φ 0.067846 0 5 Φ 0.068 0 5 Magnetic flux quantum M Bor 9.74054 0 4 joule stattesla Bohr magneton M Bor 9.74 0 joule 4 stattesla 5.0507866 0 joule 7 stattesla Nuclear magneton

Atomic Constants α 7.97508 0 Fine structure constant Ryd 0977.54 m Rydberg constant a 0 0.597749 0 0 m Bohr radius E h 4.59748 0 8 joule Hartree energy Quantum of circulation.6694807 0 4 m sec Electron m e 9.09897 0 kg Electron mass Electron specific charge (electron charge to mass ratio).758896 0 coul kg Electron Compton wavelength.46058 0 m

ECw.46058 0 m ECw.46 0 0 cm r e.879409 0 5 m Classical electron radius 98.4770 0 joule 6 tesla Electron magnetic moment Muon m µ.8857 0 8 kg Muon mass

Proton m p.676 0 7 kg Proton mass Ratio of proton mass to electron mass 86.570 Proton Compton wavelength.400 0 5 m.406076 0 6 joule tesla Proton magnetic moment Proton gyromagnetic ratio 675.555 0 4 rad sec tesla Neutron m n.674986 0 7 kg Neutron mass Neutron Compton wavelength.9590 0 5 m Physico-Chemical Constants N 6 067 0 l

N A 6.067 0 mole Avogadro constant Atomic mass constant AMU.660540 0 7 kg 96485.09 coul mole Faraday constant joule 8.450 mole K Molar gas constant

k b.80658 0 Boltzmann's constant joule K Molar volume of ideal gas at STP.440 liter mole σ 5.6705 0 8 watt m K 4 Stefan-Boltzmann constant.747749 0 6 watt m First radiation constant 0.048769 m K Second radiation constant M s.989 0 gm M z 5.977 0 7 gm m Pl h c G m Pl 5.456 0 5 gm L Pl G h c cm r e.88 0 cm L Pl 4.05 0 ( ) el m e c α a 0 Md.796 0 5 gm r s 6.9598 0 5 km

Rg sv 9.5 0 7 cm r z 6.787 0 km Md el m e G G 6.67 0 8 cm gmsec r e α a 0 t H.086 0 7 sec c Rg sv G Rg sv 9.5 0 7 cm t H 9.78 0 9.46 0 56 gm 65.564 4 60 60 Rg sv 9.5 0 7 cm sec Rg sv t H c t H 9.78 0 9 yr.46 0 56 gm Md : c r e G a 0 t e c α.46 0 56 gm Data from CRC Handbook of Chemistry and Physics, 7nd edition edited by David R. Lide, CRC Press (99).

8

m sec

n,