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).

tHHa0

c α⋅:= avo 1 12..:=nvod 5.137− 1087×:=ρH 3

Md4 π⋅ a0

3⋅⋅:=

2.

tHH1−( )( )2 8

3π⋅ G⋅ ρH⋅−

a02.− me⋅

2⋅ 13.607 eV=

13.60636

0.378=

tH31−( )( )2 8

3π⋅ G⋅ ρsv4⋅− Rgsv

2Msv

nvod avo2⋅

⋅

⋅

13.6063.4021.512

0.850.5440.3780.2780.2130.1680.1360.1120.094

eV

=

EnHH tHH1−( )( )2 8

3π⋅ G⋅ ρH⋅−

a02.− me⋅

2⋅:=

EnH tH31−( )( )2 8

3π⋅ G⋅ ρsv4⋅− Rgsv

2 Msv⋅( )⋅:=

Koeficijent proporcionalnostiEnHEnHH

5.137− 1087×=

R0 3.061 1018× cm:= a 1 8..:= r1 1.758 1016× cm:=

tH31−( )( )2 8

3π⋅ G⋅ ρsv4⋅− Rgsv

2Msvnvod

⋅

⋅ tH31−( )( )2 8

3π⋅ G⋅ ρsv4⋅− Rgsv

2⋅Msv

avo nvod⋅⋅−

06.8039.071

10.20510.88511.33911.66311.90612.09512.24612.36912.473

eV

=

akvant 1 8..:=a0 4⋅

c α⋅9.676 10 17−× sec=

tvoda

a0 a⋅

c α⋅:=

tvoda2.419·10 -17

4.838·10 -17

7.257·10 -17

9.676·10 -17

1.209·10 -16

1.451·10 -16

1.693·10 -16

1.935·10 -16

sec

= nt 1.276 1034×:=

tH31−( )( )2 8

3π⋅ G⋅ ρsv4⋅−

1−1−⋅ akvant⋅

nt2.419·10 -17

4.837·10 -17

7.256·10 -17

9.675·10 -17

1.209·10 -16

1.451·10 -16

1.693·10 -16

1.935·10 -16

sec

=

9.675 10 17−⋅ sec⋅ 2.419 10 17−⋅ sec⋅−( ) 1−

2

a02 me⋅( )⋅ 3.024eV=

tH31−( )( )2 8

3π⋅ G⋅ ρsv4⋅−

1−1−⋅

nt4⋅

2

1−

a02⋅ me⋅ 2⋅ 3.402eV=

3tH3

2

3− 8 π⋅ G⋅ ρsv4⋅ tH32⋅+( )

1

2

⋅ 3.086 1017× sec=

3tH3

2

3− 8 π⋅ G⋅ ρsv4⋅ tH32⋅+( )

1

2⋅ 3.086 1017× sec=

nmkr 3.004 1092×:=amkr 1 14..:=

tH31−( )( )2 8

3π⋅ G⋅ ρsv4⋅− Rgsv

2−⋅ Msv

nmkr amkr2⋅ kb⋅

⋅

2.70.675

0.30.1690.1080.0750.0550.0420.0330.0270.022

K

=

0.0220.0190.0160.014

tH31−( )( )2 8

3π⋅ G⋅ ρsv4⋅−

Rgsv2− Msv⋅

nmkr kb⋅⋅ 2.7 K=

2.32710 4− eV⋅

kb2.7 K=

nmkr1 8.111 1092×:=

tH31−( )( )2 8

3π⋅ G⋅ ρsv4⋅−

Rgsv2− Msv⋅

nmkr1 kb⋅⋅ 1 K=

8 111 1092

nnaj 8.111 1092×:=

tH31−( )( )2 8

3π⋅ G⋅ ρsv4⋅−

Rgsv2− Msv⋅

nnaj kb⋅⋅ 1 K=

nsunce 6.264 1022×:=

tH31−( )( )2 8

3π⋅ G⋅ ρsv4⋅−

Rgsv2− Msv⋅

nsunce kb⋅⋅ 1.295 1070× K=

nzemlja 2.085 1028×:=

tH31−( )( )2 8

3π⋅ G⋅ ρsv4⋅−

Rgsv2− Msv⋅

nzemlja kb⋅⋅ 3.89 1064× K=

tH31−( )( )2 8

3π⋅ G⋅ ρsv4⋅−

Rgsv2− Msv⋅

nzemlja⋅ 5.371 1048× erg=

Svemirska skala vremena

23

8 π⋅ G⋅⋅

1

ρsv4⋅

3.086 1017× sec=

avodonik 1.276 1034×:=

aV 1 8..:=

a0 4⋅

cα⋅2

2.419 10 17−× sec( )8=

( )

nV 1.804 1034×:=

2.419 10 17−× sec( )( ) 9⋅ 2.177 10 16−× sec=

Nize je postignuta potpuna analogija sa Vajnbergovom jednacinom

2 aV2⋅

nV

3

4 π⋅ G⋅⋅

1

ρsv4⋅

2 1⋅nV

3

4 π⋅ G⋅⋅

1

ρsv4⋅−

07.258·10 -17

1.936·10 -16

3.629·10 -16

5.807·10 -16

8.468·10 -16

1.161·10 -15

1.524·10 -15

sec

=a0

c α⋅aV

2⋅a0

c α⋅−

07.257·10 -17

1.935·10 -16

3.628·10 -16

5.805·10 -16

8.466·10 -16

1.161·10 -15

1.524·10 -15

sec

=

12

2⋅ 3⋅

1

π G⋅( ) 1

2

β ρsv4

1

2⋅ ⋅ =

β

14

2⋅ 6⋅

1

π G⋅( ) 1

2

β ρsv4

1

2⋅ ⋅ =

β

14

2⋅ 6⋅1

π G⋅( ) 1

2⋅ c⋅

α

a0 ρsv4

1

2⋅ ⋅ 1.276 1034×=

1

14

2⋅ 6⋅1

π G⋅( ) 1

2⋅ c⋅

α

a0 ρsv4

1

2⋅ ⋅ 1.276 1034×=

tvoda0

c α⋅( ):=a 1 8..:= nρ 20 30..:=

n 1.591 1021×=ρvod3

4 π⋅ G⋅ tvod( )2⋅:=

ρsv4 3.756 10 29−×gm

cm3=

3 Md⋅

4 π⋅ a0 a2⋅( )3⋅

6.115·10 39

9.554·10 37

8.388·10 36

1.493·10 36

3.914·10 35

1.311·10 35

5.198·10 34

2.333·10 34

gm

cm3

= ρvod 6.114 1039×gm

cm3=

a 1 8..:=n 3.737 1033×:=

a0c α⋅

an

3

8 π⋅ G⋅1

ρsv4 ⋅

2

n3

8 π⋅ G⋅1

ρsv4 ⋅

−

-5.84·10 -17

017

sec

= tvoda

a0 a⋅

c α⋅:=

tvoda2.419·10 -17 sec

=

5.84·10 -17

1.168·10 -16

1.752·10 -16

2.336·10 -16

2.92·10 -16

3.504·10 -16

2.419 10 4.838·10 -17

7.257·10 -17

9.676·10 -17

1.209·10 -16

1.451·10 -16

1.693·10 -16

1.935·10 -16

2

7.257 10 17−⋅ 2.419 10 17−⋅− 4.838 10 17−×=2.419 10 17−⋅4.838 10 17−⋅

0.5=

a2.419 10 17−⋅ sec⋅

3

8 π⋅ G⋅2

ρsv4

1

ρsv4−

⋅ 3.737·10 33

7.474·10 33

1.121·10 34

1.495·10 34

1.868·10 34

2.242·10 34

2.616·10 34

2.989·10 34

=

14

6⋅1

π G⋅( ) 1

2⋅ 2 1−( )⋅ c⋅

α

a0 ρsv4

1

2⋅ ⋅ 3.737 1033×=

3

8 π⋅ G⋅

n19

ρsv4

⋅ 1.402 1099× yr=

a0 4⋅

c α⋅ 1.935 10 16−× sec=

a0c α⋅

a0 2⋅

c α⋅( )− 2.419− 10 17−× sec=

2 ( )

1

ρvod( )3

8 π⋅ G⋅⋅ 1.71 10 17−× sec=

a1 1 8..:=

1

ρvod

3

4 π⋅ G⋅⋅

1

ρvod( )3

8 π⋅ G⋅⋅

1

a1⋅−

7.085·10 -18

1.209·10 -17

1.431·10 -17

1.564·10 -17

1.654·10 -17

1.721·10 -17

1.772·10 -17

1.814·10 -17

sec

=

1

ρvod( )3

8 π⋅ G⋅⋅ 1.71 10 17−× sec=

a0c α⋅

a0

c α⋅ 2⋅ a1⋅−

7.085·10 -18

1.209·10 -17

1.431·10 -17

1.564·10 -17

1.654·10 -17

1.721·10 -17

1.772·10 -17

1.814·10 -17

sec

=

2 a1⋅( )2

2468

10121416

=

a0c α⋅ 2⋅

1.71 10 17−× sec=

1

ρvod( )3

4 π⋅ G⋅⋅ 2.419 10 17−× sec=

ρvod 6.114 1039×gm

cm3= ρvod 6.114 1039×

gm

cm3=

23

8 π⋅ G⋅⋅

1

ρsv4⋅

23

8 π⋅ G⋅1

ρsv4⋅− 0 sec=

Ovo je za me*c^2

ne 1.367 1083×:=

ne2 5.136 1087×:=

Negde oko mikrotalasne temperature

tH31−( )( )2 8

3π⋅ G⋅ ρsv4⋅− Rgsv

2−⋅Msv

ne2 m2⋅ h⋅⋅

3.291 1011×1

cm2sec=

ne3 1080:= c α⋅

a0 2⋅ m2⋅2.067 1012×

cm=

tH31−( )2 8

3π⋅ G⋅ ρsv4⋅− Rgsv

2−⋅Msv

ne3 m2⋅ kb⋅⋅ 8.111 108×

K

cm2=

tH31−( )2 8

3π⋅ G⋅ ρsv4⋅− Rgsv

2−⋅Msv

kb 8.109 1012× K( )⋅⋅ 1 1080×=

me c2⋅

kb5.93 109× K=kb 5.93 109× K( )⋅ 5.11 105× eV=

ndejstvo 3.276 10121×:=

tH1−( )( )2 8

3π⋅ G⋅ ρsv1⋅−

Rgsv2−

nα⋅ c2= Rgsv

re3.283 1040×=

tH31−( )( )2 8

3π⋅ G⋅ ρsv4⋅− Rgsv

2−⋅ 8.988 1020×cm2

sec2=

8 2 G MRgsv

2

5 137 1087

43

π⋅ G⋅ ρsv4( )⋅ Msv⋅ Rgsv2⋅

nnovo313.606 eV=

nnovo3 5.137 1087×:=

83

π⋅ G⋅ ρsv1( )⋅ Msv⋅ Rgsv2⋅

nnovo22.181 10 11−× erg=

ω cα

a0 2⋅⋅:=

nnovo2nMd

3.128 1047×=

Md c2⋅ 2⋅ 6.823 1036× erg=nnovo2 1.027 1088×:=

83

π⋅ G⋅ ρsv1( )⋅ Msv⋅ Rgsv2⋅

nMd c2⋅

7.591 1015× gm=

el2

RgsvnMd

8.186 10 7−× erg=1.12 1077× erg

Md 3.796 1015× gm=43

π⋅ G⋅ ρsv1( )⋅Msv Rgsv

2⋅

nMd c2⋅⋅

3.795 1015× gm=

ωc α⋅re

:=

Rgsvre

3.283 1040×=nMd 3.283 1040×:=

Veliki magicni brojevi povezuju gravitaciju , elektromagnetizam ,kvantnu mehaniku i kvantnu elektrodinamiku

tH31−( )( )2 4

3π⋅ G⋅ ρsv4( )⋅− Rgsv

2⋅ Msv⋅ 0 erg=

tH31−( )( )2 4

3π⋅ G⋅ ρsv4( )⋅− 0

1sec2

=ρsv1

3

4 π G tH2⋅⋅⋅( )

:=

sec

3π2⋅ G⋅ ρsv1⋅ Msv⋅

ω h⋅( )⋅ 5.137 1087×=

83

π⋅ G⋅ ρsv4⋅ Msv⋅Rgsv

2

ω h⋅( )⋅ 1.635 1087×=

1.12 1077⋅ erg⋅ 1.221 106⋅( )⋅ 1.368 1083× erg= me c2⋅( ) 1−1.221 106×

sec2

gmcm2=

Msv c2⋅

tH1−( )( )2 8

3π⋅ G⋅ ρsv4⋅− 1−⋅ Rgsv

2⋅ Msv⋅

n2

1.396 1067×=

n 1020:=

Msv c2⋅

tH1−( )( )2 8

3π⋅ G⋅ ρsv4⋅− 1−⋅ Rgsv

2⋅ Msv⋅

n2

10 1039×=

n 1030:=

Msv c2⋅

1=

tH1−( )( )2 8

3π⋅ G⋅ ρsv4⋅− 1−⋅ Rgsv

2⋅ Msv⋅ 1

Rgsvre

3.283 1040×=

n 1040:=

Md c2⋅ 3.411 1036× erg=tH1−( )( )2 8

3π⋅ G⋅ ρsv4⋅− 1−⋅ Rgsv

2⋅ Msv⋅ Rgsv

re

2

kb⋅

7.524 1011× K=

13

3− 8 π⋅ G⋅ ρsv4⋅ tH2⋅+( )⋅ Msv⋅

re2

tH2 kb⋅( )

⋅ 7.524 1011× K=

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).

Mdc2 re⋅

G:=

Msv 1.246 1056× gm=tea0

c α⋅≡

Msv 1.246 1056× gm≡

tH 9.78 109⋅ yr⋅≡

Rgsv tH c⋅≡

Rgsv 9.252 1027× cm=

tH 9.78 109⋅ 365.2564⋅ 24⋅ 60⋅ 60⋅ sec⋅≡

Rgsv 9.252 1027× cm=

c2 Rgsv⋅

G1.246 1056× gm=

tH 3.086 1017× sec=

re α2 a0⋅≡

G 6.673 10 8−×cm3

gmsec2≡

Mdel2

me G⋅≡

rz 6.37817 103⋅ km⋅≡

Rgsv 9.252 1027× cm=

8

1m2sec

n,