t H 3.08627 10 17 × sec := t H 3.086 10 17 × 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. n 1.591 10 21 × := Hablovo vreme t H3 7987220447284.3450480 gm π G ⋅ ⋅ ( ) 313 ⋅ gm π ⋅ G ⋅ cm ⋅ ( ) 1 2 ⋅ cm ⋅ := 1 M sv a 0 2 ⋅ M sv Md ⋅ a 0 ⋅ Rg sv ⋅ ( ) 1 2 ⋅ t e ⋅ Rg sv ⋅ t H3 1 = t H3 3.086 10 17 × sec = Veliki magicni brojevi su kolicnici energije svemira i energija sa kvantnim brojevima 10^n gde je n=od 10 do 40 u deseticama.
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tH 3.08627 1017× sec:=tH 3.086 1017× sec=
Rgsv tH 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.
n 1.591 1021×:=
Hablovo vreme
tH37987220447284.3450480
gm π G⋅⋅( )313⋅ gm π⋅ G⋅ cm⋅( )
1
2⋅ cm⋅:=
1
Msv a02⋅
Msv Md⋅ a0⋅ Rgsv⋅( )1
2⋅ te⋅ Rgsv⋅
tH31=
tH3 3.086 1017× sec=
Veliki magicni brojevi su kolicnici energije svemira i energija sa kvantnim brojevima 10^n gde je n=od 10 do 40 u deseticama.
n11 2.704 1083×:=
n10 1.352 1083×:=
n9 8.111 1082×:=
n8 1.351 1083×:=
n7 4.054 1082×:=
n6 2.703 1082×:=
n5 1.351 1082×:=
n4 8.109 1081×:=
n3 4.054 1081×:=
n2 2.703 1081×:=
n1 1.351 1081×:=8.109 1092× K
Temperatura svemira.Koeficijenti proporcionalnosti na Vajnbergovoj skali iz knjige "Gravitacija i kosmologija" na ruskom,str.577 Tablica 15.4
tH31−( )2 4
3π⋅ G⋅ ρsv4⋅− 0
1sec2
=
ρsv43
4 tH32 π G⋅⋅⋅( )
:=
tH31−( )2
1.05 10 35−×1
sec2=
n12 8.111 1083×:=
n13 2.704 1084×:=
n14 8.111 1084×:=
n15 8.111 1085×:=
n16 8.111 1086×:=
n17 8.111 1087×:=
n18 8.111 1088×:=
n19 2.028 1089×:=
tH31−( )2 8
3π⋅ G⋅ ρsv4⋅− Rgsv− Rgsv⋅⋅
Msvkb n1⋅
⋅ 6.004 1011× K=
tH31−( )( )2 8
3π⋅ G⋅ ρsv4⋅− Rgsv
2−⋅Msv
kb n2⋅⋅ 3.001 1011× K=
tH31−( )( )2 8
3π⋅ G⋅ ρsv4⋅− Rgsv
2−⋅Msv
kb n3⋅⋅ 2.001 1011× K=
tH31−( )( )2 8
3π⋅ G⋅ ρsv4⋅− Rgsv
2−⋅Msv
kb n4⋅⋅ 1 1011× K=
tH31−( )( )2 8
3π⋅ G⋅ ρsv4⋅− Rgsv
2−⋅Msv
kb n5⋅⋅ 6.004 1010× K=
tH31−( )( )2 8
3π⋅ G⋅ ρsv4⋅− Rgsv
2−⋅Msv
kb n6⋅⋅ 3.001 1010× K=
tH31−( )( )2 8
3π⋅ G⋅ ρsv4⋅− Rgsv
2−⋅Msv
kb n7⋅⋅ 2.001 1010× K=
tH31−( )( )2 8
3π⋅ G⋅ ρsv4⋅− Rgsv
2−⋅Msv
kb n8⋅⋅ 6.004 109× K=
tH31−( )( )2 8
3π⋅ G⋅ ρsv4⋅− Rgsv
2−⋅Msv
kb n9⋅⋅
1 1010× K=
a 2 10..:=
tH31−( )( )2 8
3π⋅ G⋅ ρsv4⋅− Rgsv
2−⋅Msv
n10 kb⋅⋅ 5.999 109× K=
tH31−( )( )2 8
3π⋅ G⋅ ρsv4⋅− Rgsv
2−⋅Msv
kb n11⋅⋅ 3 109× K=
tH31−( )( )2 8
3π⋅ G⋅ ρsv4⋅− Rgsv
2−⋅Msv
kb n12⋅⋅ 1 109× K=
tH31−( )( )2 8
3π⋅ G⋅ ρsv4⋅− Rgsv
2−⋅Msv
kb n13⋅⋅ 3 108× K=
tH31−( )( )2 8
3π⋅ G⋅ ρsv4⋅− Rgsv
2−⋅Msv
kb n14⋅⋅ 1 108× K=
tH31−( )( )2 8
3π⋅ G⋅ ρsv4⋅− Rgsv
2−⋅Msv
kb n15⋅⋅ 1 107× K=
tH31−( )( )2 8
3π⋅ G⋅ ρsv4⋅− Rgsv
2−⋅Msv
kb n16⋅⋅ 1 106× K=
tH31−( )( )2 8
3π⋅ G⋅ ρsv4⋅− Rgsv
2−⋅Msv
kb n17⋅⋅ 1 105× K=
tH31−( )( )2 8
3π⋅ G⋅ ρsv4⋅− Rgsv
2−⋅Msv
kb n18⋅⋅ 1 104× K=
Iz skalarne Fridmanove jednacine kosmosa izracunati energije vodonika, to jest mini-crne rupe sa masom Md (a to je identicno).
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 1039:=
Msv c2⋅
tH1−( )( )2 8
3π⋅ G⋅ ρsv4⋅− 1−⋅ Rgsv
2⋅ Msv⋅
n2
10 1077×=
n 1038:=
Msv c2⋅
tH1−( )( )2 8
3π⋅ G⋅ ρsv4⋅− 1−⋅ Rgsv
2⋅ Msv⋅
n2
10 1075×=
n 1:=
Msv c2⋅
tH1−( )( )2 8
3π⋅ G⋅ ρsv4⋅− 1−⋅ Rgsv
2⋅ Msv⋅
n2
1=
n 2:=
Msv c2⋅ a0⋅
tH1−( )( )2 8
3π⋅ G⋅ ρsv4⋅− 1−⋅ Rgsv
2⋅ Msv⋅
n2
2.117 10 8−× cm=
3 Md⋅
4 π⋅ 4 a0⋅( )3⋅9.554 1037×
gm
cm3=
3 Md⋅
Msv c2⋅ a0⋅
tH1−( )( )2 8
3π⋅ G⋅ ρsv4⋅− 1−⋅ Rgsv
2⋅ Msv⋅
n2
3
4⋅ π⋅
9.555 1037×gm
cm3=
tH1−( )( )2 8
3π⋅ G⋅ ρsv4⋅− 1−⋅ Rgsv
2⋅ Msv⋅
kb 8.109 1080×( )⋅1 1012× K=
tH1−
2 8
3π⋅ G⋅ ρsv4⋅− 1−⋅ Rgsv
2⋅ Msv⋅
kb
tH1−
2 8
3π⋅ G⋅ ρsv4⋅− 1−⋅ Rgsv
2⋅ Msv⋅
kb 1012K( )⋅
n5 1011× K=
1012K 1 1012× K=Ovo je temperatura prva po redu na Vajnbergovoj skali istorije svemira.Pre ove temperature Vajnberg analizira najraniji svemir.
n 1 8..:=
8.109 1092× K8.109 1080×=
1012K8.109 10×
8.109 1092× K
1 1052× K8.109 1040×=
1.688 1023K1 103× K
1.688 1020×=
1.688 1022K1 102× K
1.688 1020×=
me c2⋅
kb5.93 109× K=
1.688 1010K1 10 10−× K
1.688 1020×=
1.688 109K1 10 11−× K
1.688 1020×=
Msv c2⋅
kb
1.368 1083K( )5.929 109×=
1.671 108× cm
9.899 10 13−× cm1.688 1020×=
1.671 108× cm
re5.93 1020×=
Ja cu sada da nadjem neke clanove u nizu temperaturne istorije svemira od temperature 5..725*10^12 do 2.7K na Vajnbergovoj skali, to jest od trenutka anihilacije parova µ+µ- do trenutka iskljucenja interakcije izmedu materije i zracenja
Msv 1.246 1056× gm= n 1 8..:=
Rgsv 9.252 1027× cm=
ρsv4 3.756 10 29−×gm
cm3= Msv c2⋅
kb8.111 1092× K=
tH31−( )2 8
3π⋅ G⋅ ρsv4⋅−
Rgsv2 Msv⋅
kb⋅ 8.111− 1092× K=
tH31−( )2 8
3π⋅ G⋅ ρsv4⋅− Rgsv
2⋅ Msv⋅
kb n⋅
-8.111·10 92
-4.056·10 92
-2.704·10 92
-2.028·10 92
-1.622·10 92
-1.352·10 92
-1.159·10 92
-1.014·10 92
K
=
M
1.−
tH2
83
π⋅ G⋅ ρsv4⋅+ Rgsv
2⋅Msvkb( )⋅
0.836 n70⋅9.702·10 92
8.218·10 71
3.876·10 59
6.961·10 50
1.145·10 44
3.283·10 38
6.761·10 33
5.896·10 29
K
=
A sada energija :
tH1−( )( )2 8
3π⋅ G⋅ ρsv4⋅− 1−⋅ Rgsv
2⋅ Msv⋅ 1.12 1077× erg=
tH1−( )( )2 8
3π⋅ G⋅ ρsv4⋅− 1−⋅ Rgsv
2⋅ Msv⋅
n89 c2⋅1.246·10 56
2.013·10 29
gm
=
4.283·10 13
325.2267.712·10 -7
6.919·10 -14
7.617·10 -20
5.254·10 -25
A sada vreme :
tH1−( )( )2 8
3π⋅ G⋅ ρsv4⋅− 1−⋅
n89 0.359 1−⋅
1−
5.151·10 17
1.281·10 31
8.786·10 38
3.188·10 44
6.547·10 48
2.186·10 52
2.083·10 55
7.932·10 57
sec
=
5.253 10 25−⋅ gm⋅ c2⋅h
1−
4.447 10 31−× yr=
mµ c2⋅
h
1−
1.24 10 30−× yr=
Masa muona
mµ( ) 1.884 10 25−× gm=
h 6.626 10 27−×gmcm2
sec=
1.241 1015⋅ K103
1.241 1012× K=
2
h1 6.626 10 27−× gmcm2
sec≡
c2 re⋅ 2.533 108×cm3
sec2=
hh1
2 π⋅≡
h c5⋅G
1.221 1028× eV=
h 1.055 10 27−×gmcm2
sec=
Ekr 1.221 1028× eV⋅:=
G mp2⋅
h1 c⋅9.398 10 40−×=
αgG mp
2⋅
h1 c⋅:=
RgsvLPl
2.284 1060×=
1.4 1032⋅ K 8.738 1043×sec2K
gmcm2eV=
v0 4.092 1011×cm2
sec2:=
R0 2.7 K⋅ kb( )⋅ 1− el2⋅
23
⋅:=
reR0
6.83 10 10−×=
el2
R0
R0
v02
1.366 10 27−× gm=
Mikrotalasno zracenje me c2( )⋅
n2 kb⋅
me v02⋅
n2 kb⋅
2.196·10 9
2.196·10 9
2.196·10 9
2.196·10 9
2.196·10 9
2.196·10 9
2.196·10 9
2.196·10 9
=me c2 α2⋅( )⋅
n2 kb⋅
3.158·10 5
7.894·10 4
3.509·10 4
1.974·10 4
1.263·10 4
8.771·10 3
6.444·10 3
4.934·10 3
K
=me v02⋅
n2 kb⋅
2.70.675
0.30.1690.1080.0750.0550.042
K
=
nah 6.166 1044×:=
α0v0
2
c2:=
tH31−( )2 8
3π⋅ G⋅ ρsv4⋅−
1−c2⋅ 1−⋅
nah re⋅
5.325 10 5−×=
h c2tH3
2
3− 8 π⋅ G⋅ ρsv4⋅ tH32⋅+( )
⋅
1
2⋅
3
re2 me c α⋅⋅⋅( )
⋅ 6.166 1044×=
h 1.055 10 27−×gmcm2
sec=
3 c2tH3
2
3− 8 π⋅ G⋅ ρsv4⋅ tH32⋅+( )
⋅
1
2⋅
a0
re2
⋅ 6.166 1044×=
MsvMd
3.283 1040×=
1−3
3− 8 π⋅ G⋅ ρsv4⋅ tH32⋅+( )⋅
Rgsv2
c2 tH32⋅( )
⋅ 1−=
BASIC SCIENCE REFERENCES
Fundamental Physical Constants
Universal Constants
c 299792458msec
⋅≡
Velocity of light in vacuum
tere 2⋅ π⋅
c≡
re
µ0 4 π⋅ 10 7−⋅newton
amp2⋅≡
Permeability of vacuum
ε0 8.854187817 10 12−⋅farad
m⋅≡
Permittivity of vacuum
G 6.67259 10 11−⋅m3
kg sec2⋅⋅≡
Nuclear magneton
5.0507866 10 27−⋅joule
stattesla⋅
MBor 9.274 10 24−×joule
stattesla=
Bohr magneton
MBor 9.2740154 10 24−⋅joule
stattesla⋅≡
Magnetic flux quantum
Φ0 2.068 10 15−×=
Φ0 2.06783461 10 15−⋅≡
Elementary chargeel 1.60217733 10 19−⋅ coul⋅≡
Electromagnetic Constants
Planck's constant (h)
RgsG Ms⋅
c2≡
h 6.6260755 10 34−⋅ joule⋅ sec⋅≡
Ms 1.989 1033× gm≡
Newtonian constant of gravitation
G 6.6726 10 8−×cm3
gmsec2=
eV 1.60217733 10 19−⋅ joule⋅≡
2.42631058 10 12−⋅ m⋅
Electron Compton wavelength
1.75881962− 1011⋅coulkg
⋅
Electron specific charge (electron charge to mass ratio)
Electron mass
me 9.1093897 10 31−⋅ kg⋅≡
Electron
3.63694807 10 4−⋅m2
sec⋅
Quantum of circulation
Hartree energy
Eh 4.3597482 10 18−⋅ joule⋅≡
Bohr radius
a0 0.529177249 10 10−⋅ m⋅≡
Rydberg constant
Ryd 10973731.534 m 1−⋅≡
Fine structure constantα 7.29735308 10 3−⋅≡
Atomic Constants
ECw 2.42631058 10 12−⋅ m⋅≡
ECw 2.426 10 10−× cm=
re 2.81794092 10 15−⋅ m⋅≡
Classical electron radius
928.47701 10 26−⋅jouletesla
⋅
Electron magnetic moment
Muon
mµ 1.8835327 10 28−⋅ kg⋅≡
Muon mass
N 6 0221367 1023 l 1−
Physico-Chemical Constants
1.31959110 10 15−⋅ m⋅
Neutron Compton wavelength
Neutron mass
mn 1.6749286 10 27−⋅ kg⋅≡
Neutron
26751.5255 104⋅rad
sec tesla⋅⋅
Proton gyromagnetic ratio
Proton magnetic moment
1.41060761 10 26−⋅jouletesla
⋅
1.32141002 10 15−⋅ m⋅
Proton Compton wavelength
1836.152701
Ratio of proton mass to electron mass
Proton mass
mp 1.6726231 10 27−⋅ kg⋅≡
Proton
NA 6.0221367 1023⋅ mole 1⋅≡
Avogadro constant
Atomic mass constant
AMU 1.6605402 10 27−⋅ kg⋅≡
96485.309coulmole
⋅
Faraday constant
8.314510joule
mole K⋅⋅
Molar gas constant
rs 6.9598 105⋅ km⋅≡
Md 3.796 1015× gm=
el me c α⋅( )2⋅ a0⋅≡
LPl 4.051 10 33−× cm=
re 2.818 10 13−× cm=
LPl Gh
c3⋅≡
mPl 5.456 10 5−× gm=
mPl hcG
⋅≡
Mz 5.977 1027⋅ gm⋅≡
Ms 1.989 1033⋅ gm⋅≡
Second radiation constant0.01438769 m⋅ K⋅
First radiation constant3.7417749 10 16−⋅ watt⋅ m2⋅
Stefan-Boltzmann constant
σ 5.67051 10 8−⋅watt
m2 K4⋅⋅≡
22.41410litermole
⋅
Molar volume of ideal gas at STP
Boltzmann's constant
kb 1.380658 10 23−⋅joule
K⋅≡
Data from CRC Handbook of Chemistry and Physics, 73nd editionedited by David R. Lide, CRC Press (1992).