Academic Open Internet Journal

ISSN 1311-4360

www.acadjournal.com

Volume 22, 2008

 

 

Metrical analysis in cosmology by a unified theory

 

 

Nikos Alexandris 

e-mail : nalxchal@yahoo.com

My articles: http://www.cerglobal.org

And   http://profiles.yahoo.com/nalxhal

 

 

Abstract

By the below analysis arises the substance of fine structure constant and the connection of mole of proton with gravity , also prediction of neutrino energy . using the law of Stefan-Boltzman and our function , we have results in agreement with CMB radiation while Wien’s law cannot. We can propose a model for universe in extra dimension and the connection of proton and positron in a process of particle creation . Using a unified mass meg we can calculate and explain the nuclear energies of particles proton, π0+ , W ,…..The mass meg related with mass of plank , gravity and electricity .We explain the length 7,25fermi of proton’s spectrum .

 

 

INTRODUCTION

We use the functions of paper with title :

Electromagnetic interaction of gravity. Proposal for unified field theory.

Author : Nikos Alexandris

Bourgas “Prof. Assen Zlatarov University” - Bulgaria.

Academic Open Internet Journal, ISSN 1311-4360

 http://www.acadjournal.com , April 2006, http://www.acadjournal.com/2006/V17/part5/p2/

 

 

Symbols

meg = 4,66.10-9.kg = 2.61x1018.GV/C2 of 5.1a), function 108 of paper: m=e/k > 0 
e : electron charge , Ke: Coulomb constant , k =(G/Ke)1/2 = 8,6164×10-11 C/Kg , G: gravity constant , function (106) ,π=3.14..,c:velocity of light ,λplank:length of plank , h: plank constant , le:length of charge or length of H , 5.29x10-11.m , Na:avogadro’s number , kb: Boltzman’s constant . 

Main article

 

The following analysis gives us the character or the nature of the fine structure constant and its connection with a mole of protons and with gravity. From the same analysis also arises a prediction of neutrino energy. The application of the law of Stefan-Boltzman and our Equation, offers results which are in agreement with MCB radiation while Wien’s law cannot. We can propose a model for universe in extra dimension and the connection of proton and positron in a process of particle creation

It is usefull to study some of the basic subjects of our work and try the application of the proposed equations. 

Function 8 : electric potential Ue=Um/k and Ue=c2/k , Um=c2 , k=q/m ,

q : electrical charge , m : equivalent mass of the electric charge , c : speed of light,  k : a constant .

These equations are referred to some kind of equivalence between the electric charge and a mass having some specific properties. The potential cannot be of the form Ue=v2/2k because it is not relativistic; the charge remains constant with velocity and its equivalent mass of the charge too. This mass follows the Principle of charge conservation. 

This mass has been called meg . The meg exists into the laws of the Nature as a simple factor; it has the property of gravity mass but it has not the property of the inertial mass. 

The meg is introduced into Newton’s, Coulomb’s, and Einstein’s laws. The absence

of the relativistic variation of the meg is compensated by the relativistic length variation.

Function (2): The ½ factor in the energy of the self-induction E= (1/2) L.i2 is found in the 8π2 of function (16) or as θο2/2 (θο is the coefficient of the shape); the factor ½ is seen in the functions (38) and (46) as parameter of β (disappearing from the final equations).

The ½ in function (18) does not affects the function (20) i.e. τ=Cgx2/k2 . The relativity

exists into the equations but the results remain the same.

For small velocities  probably  the length lg is double and the reaseant perhaps is relativity :

 γ is relativity parameter 1/sqrt(1-v2/c2) 

for υ<<c  , γ-1=1/2 and the length is duplicated 2lg and the constant of the (102) takes the half of the original value; thus the (102) gives Wien’s law for N=1, n1=10 , n2 =12 , and must lg = lc . Does not exist expotential field at low velocities .

 

175 function A=2,5041x10-24.J.m , is valid for T.lg = 5,755x10-3.m.K :171 function

and n1=10,5 and n2=12,6 , but for n1=10 and n2=12 , A=2,383x10-24.J.m : 177 function

so we call this factor A177=2,383x10-24.J.m

From 172,174 functions A= n1.N.kb(lg.T) arises in Wien’s law system:

 

Awien= n1.N.kb(lg.T)/2 = 1,1918x10-24.J.m, n1=10 , N=3 (01)

 

We believe that we can use the squares of energies (179,180 functions ) in variable lengths , for atom of hydrogen (H) and proton wile in former paper we used the function 179 for lengths close to Plank lengths . 

The approximation in 176,178 can be zero by the following analysis :

Function (179) Εcge2 = -4.Ec2- Eg2 +9.Ee2 

 Ec =-3.h.c/ lc ,  Eg= -3.G.m2 / lg , Ee=3.(Ke.(k.m)2 /lc , lg=lc.sqrt(2π)

From (158) function : m = mcge = 1,7209×10-7.kg and this mass comes from function 155 : fc2.fG1= fe3 the relation of forces : electromagnetic , gravitational and electrical

force . We rename the Εcge to Εsqrt =sqrt( -4.Ec2- Eg2 +9.Ee2 )  (02)

Εsqrt =6,5963x10-14.J (03)

From 162,172 could be : Εcge = A175/sqrt(2). lc ,  Εsqrt / Εcge = 1,97 or (04)

for A177 sqrt(2). lc  , we have :Εsqrt / Εcge = 2,07 ,  (05) 

thaus Εcge = 2.A/sqrt(2). lc or     (06)

Εcge = A/(sqrt(2)/2). lc =   A/(sqrt(2)/2). lc =   A/cos45o. lc   (07)

so Εcge = A/cos45o. lc   (08)

 

 

Applications :

1. cosmic radiation CMB

2. Fine structure constant analysis with proton and neutrino

 

 

 

1.cosmic radiation CMB

Function 171 of paper

The relation of length and temperature incites us to examine whether the system works at low temperatures T.lg = 5,755x10-3 .m.K . The system seems to work at the Planck temperature as the proton’s temperature in a range between 1032 .K- 1012 .K - why not lower even at temperature than these ?
It is interesting that we can get values near the cosmic irradiation (CMB).

Function 171 of paper
T.lg = 5,755x10-3.m.K , this constant is the double the Wien’s constant ( 1893 )and it is the same for N=6 .
lg=sqrt(2.π).lc ,
n1/n2=10/12 , N=3 if lg=1mm then T=5,75K
if radiation comes from lc=1mm Then T=2K
The Wien’s constant is half and for lg=1mm , T=2,73K in Wien’s law
Function 102 in the paper gives the Wien’s law for
Wien’s constant = (constant102/2).sqrt(2π) (09)

 

T =(n1/n2)-3/2. N-3/2.1,085×1016.Q/ (λ.lc)1/2 ,  λ = lc , a = ap

 
for N=1 , n1/n2=10/12 , Q = e
sqrt(2.π) comes from values of length λ=2πlc=lg.sqrt(2π), hypothesis 5

and 2 comes from 2.lg
the functions 102 and 171 are not the same but they give the same constant for N=1 (102)and N=3 (171)
in function 171

constant171=2.constant of Wien's constant
CMB radiation has energy P/S = 1,9X10-3.w/m2 ,

this value in the law of Stefan-Boltzman ( function 166 ) P/S=σ.T4,

gives 13,52K

Then in modified law of Wien ( in function 171 ) T.lg=5,755×10-3.m.K so

lg = 0,42mm
λ=2πlc , lg=sqrt( 2π ).lc so

λ=sqrt(2π).lg =1,052mm ,  (10)

the cosmic microwave background radiation (CMB).

This length λ is length of meg or the length of remnant force as we extracted in http://www.wbabin.net/science/alexandris9.pdf

So CMB radiation is the radiation of meg = e/k

First proceeding in this solution was in below paper

But we must fix the type errors: http://www.wbabin.net/science/alexandris5.pdf

 

 We get the same results by using 102 function with N=1
The mathematical error of approximation will be in any method sqrt(2π) =N.(n1/n2) =5/2 , with N=3 n1=10,n2=12

 Using the law of Stefan-Boltzman , function 102 or 171 for an appropriate length and N we have results in agreement while Wien’s law cannot .
Wien’s law is a case without gravity but has gravity . Gravity affects to Wien’s law and calculations are in disagreement with the law of Stefan - Boltzman
the function 102 also gives the Tplank for lplank without sqrt(2π). The Wien’s constant is not valid.

We get the same results by using 102 function with N=1
The same result we have for volume
V= (3/4).l3 , and S=(3/4).l 2 , with l=1mm (11) 

in the law of Stefan-Boltzman as a mathematical solution of both function 166 and 171
This give an idea about the shape of the system and what is sqrt( 2π ).
1.The shape of particle or
2.microcell structure of space
In conclusion all black bodies in nature seems to have n1=10 and n2=12 numbers
and gravity is not zero
If that happens the extra dimensions exist around us.

Definition of unified field 

 

 In Stefan-Boltzman temperature the length of Wien is 20% of observed (λ) .Also exist light 20% to blue than Wien length (lc). analogies of two radiations λ/lc=2π , Stefan-Boltzman temperature/Plank temperature = 5

Background temperature of universe , Stefan-Boltzman 13,52K = 5xPlank temperature  

So we find first two waves with analogie of lengths λ/lc=2π , next we examine the analogie of temperatures of two laws Stefan-Boltzman and Plank , must have value 5 .

 

We propose two experiments ,  accordance of two laws : modified Wien and Stefan-Boltzman .The explanation of disagreement betwen two laws : Stefan-Boltzman and Plank law or Boltzman-Maxwel .

http://www.wbabin.net/science/alexandris10.pdf

In my papers of unified field theory we do not find the two dimensions of time as we discribe in my phylosophy book :

http://nalxchal.blogspot.com/2008/01/philosophy-book.html

But the two forms of wien law give us the hope to indroduce relativity and numbers of freedom in wave function of plank or Maxwel-Boltzman  . Also Stefan-Boltzman law will be transformed as we can see in first paper .Stefan-Boltzman law is arised in paper first in a few funnctions from hypotheses .The space of unified field is logarithmic and it could be explained by two dimension of time

 

2a.Fine structure constant

 

All the method of the above paper includes a mathematical extraction of Stefan-Boltzman ( T4 )law of irradiation of a black body .

We start with these empirical types of angular momentum of meg

 2π.(5meg).c.λplank/h=1.071   (1)
2π.(6meg).c.(le/Na)/h=6.986    (2)
2π.(5meg).c.λplank/h = 2π.(6meg).c.(le/Na)/7.h so   (3a)

5.(7/6) = le/(Na.λplank) (3b)

le : length of atom of H or length of electrical charge , Na : Avogadro number , λplank : length of Plank

We find the 5.(7/6) parameter in nuclear particle index in proton mass 

 

We use 6/7 to analyse the fine structure 
137,3134.(6/7).meg = Na.me , me = mass of electron also , (4)

 

for proton

Mp:mass of proton , Lp: length of proton

From function 195 of previous  paper we have :

(Na.mp.meg/( 2π ) ½)1/2.c.λplank=10,0067.h

Na.mp = 100.h2.( 2π ) 1/2/meg.c2.λplank2 

Na.mp =A.meg and   (5)

A=100.h2.( 2π ) 1/2/meg2.c2.λplank2 (6a)

From function 5 : A5= 216110,057  (6b)

And from function 6 : A6= 215826,3357 , A5/ A6=1.0013     (7)

Also for electron :

Na.me = B.meg (8)

And B=137,3134.(6/7)=(6/7).( E1/E2) 2  (9)

E1/E2 = (137,3134) ½=1371/2 = 11,7 (10)

11,7.(6/7)=10,04 (11)

so B=10.(E1/E2)=(6/7).(1/a) (12) 

Na.me = 10.(E1/E2).meg (13)

For proton Eplank/ Emeg = 4,670113 = (1/ap) ½  (14a)

Structure constant of proton : ap = 0,04585 

Eplank2/ Emeg2=21,80995 (14b)

This number comes from angular momentum of electron or positron without 2π

Eplank2/ Emeg2=Je/h=21,80995 ,  (15a)

so positron ,electron and proton are linked

We need to refer the 194 function of previous paper :

meg.le2 .NA-2 = MPlanck.lg2 , charge and length of charge are connected by meg and length of plank 

A.ap = 9895,71     

and ap/a=2π or ap=2π.a , a=1/137,035  (15b)

 

2b.Neutrino

  

An other way to analyse the fine structure constant of electron is :

(6/7).160,1989.(6/7).meg= Na.me (16)

p.(6/7)2.5.25.meg = Na.me , with p=1,0012 and 160= 5.25 (17) 

that’s mean the fine structure constant is :
1/137.14 = (7/6)/5. 25 , (18a)

6/7 belongs to temperature : (7/12)/5. 24 , 12/7 page 9 case 6 of paper .

137,14-137,035 = 0.1 (18b)

We propose for angular momentum of electron in meg system :

Jemeg=137,035.h/2π + h/10.2π or Jemeg=137.h/2π + 0,14h/2π    (19a)

(18) function gives the fine structure 1/137.14 , that’s mean

energy : E = 0.14.h.c/2π.le = 8.36x10-17.J = 522.eV/c2 so   (19b)

for one level the energy is : E/137 = 3.81eV (19c)

also h/10.2π gives energy  :

 E = 0.10.h.c/2π.le = 372,8.eV, E/137 = 2,72.eV   (19d)

I remind you that meg and proton are linked , and these empirical types will give us the potential of spectrum verification .

Proton

Mp:mass of proton , Lp: length of proton

From function 195 of previous paper and function 1 we have :

(Na.mp.meg/( 2π ) ½)1/2.c.λplank=10,0067.h

2π.(5meg).c.λplank=1.071.h , we have

(Na.mp.meg/( 2π ) ½) ½.c.λplank/10=2π.(5meg).c.λplank  (20)

arises :

p.Na.mp = 104.π2.( 2π ) ½.meg , p = 1,1447   (21)

 

Function (1) : 2π.(5meg).c.λplank/h=1.071  (22)

With the angular momentum of proton :

mp.c.Lp = np.h and 2π.(5meg).c.λplank=h  (23)

mp.c.Lp/np = 2π.(5meg).c.λplank (24a)

 

arises : Lp/np = 10.π.meg.λplank/mp = 1.4147 fermi  (24b) 

for np=1 without 2π   (25)

with 2π Lp/np =0.225 fermi  (26)

The length in 25 function could arise from a dynamic of meg c2/2

so Lp/np=1fermi   (27)

if we use the approximation 1,1447 of 21 function

1.4147 fermi/1,1447 =1,2358 fermi

The same result we have h/(mp.c)=1,321fermi and 1,321/1,1447=1,2358 fermi 

These values of proton’s length λ=lc : 0,2f , 1f , 1,2f , 1,4f must use in 102 function of temperature to examine if n1/n2 is 10/12 .

T =(n1/n2)-3/2. N-3/2.1,085×1016.Q/ (λ.lc)1/2 , N = 1,2,3 , Q = e , λ = lc 

 

Nuclear particles

parameter: 6/7 from functions (2),(4),(18)

2π.(6meg).c.(le/Na)/h=6.986 

137,3134.(6/7).meg = Na.me , me = mass of electron

Structure of proton

1/ap=21,8 from functions (14),(15)

Eplank/ Emeg = 4,670113 = (1/ap) ½ 

ap/a=2π or ap=2π.a , a=1/137,035 

  

energy to be 1/ap=21 : E0 =0.8hc/(2π.1fermi)=159,82 MeV/C2 (28)

 

3μ=2 E0

 

Κ+=3 E0

 

 

(6/7).η=3 E0

(6/7).p=5E0

(6/7).n=5.E0

Λ=7 E0

 

 

 

(6/7).Ξ0=7 E0

(6/7).Ξ-=7 E0

(6/7).Ω=9 E0

π+=(6/7)E0

π0=(6/7)E0

 

 

Boson W(kg) =(6/7).100.mp

Mp=mass of proton

 

 MeV/C2

 

 MeV/C2

  diverse  

MeV/C2

 

 

 

 diverse MeV/c2

 

μ

105.7

0.85

106.5466667

 

 

0.004138212

0.85

106.5466667

τ

1784

 

 

 

 

9.568453521

 

 

Κ+

493.7

-14.24

479.46

 

 

2.647951515

-14.24

479.46

Κ0s

497.7

 

 

 

 

2.669405447

 

 

 

 

 

 

 

 

0

 

 

η

548.8

10.57

559.37

 

 

2.943479424

10.57

559.37

p

938.3

-6.02

932.2833333

 

 

5.032556019

-6.02

932.2833333

n

939.6

-7.32

932.2833333

 

 

5.039528547

-7.32

932.2833333

Λ

1115.6

3.14

1118.74

 

 

5.98350154

3.14

1118.74

Σ+

1189.4

 

 

 

 

6.37932658

 

 

Σ0

1192.5

 

 

 

 

6.395953377

 

 

Σ-

1197.3

 

 

 

 

6.421698095

 

 

Ξ0

1315

-9.80

1305.196667

 

 

7.052980034

-9.80

1305.196667

Ξ-

1321

-15.80

1305.196667

 

 

7.085160931

-15.80

1305.196667

Ω

1672

6.11

1678.11

 

 

8.967743434

6.11

1678.11

π+

139.6

-2.61

136.9885714

 

 

 

-2.61

136.9885714

π0

135

1.99

136.9885714

 

 

 

1.99

136.9885714

 

 

Boson W(kg)

1.43326E-25

0.00

1.43368E-25

 

 

 

0.00

1.43368E-25

 

 

 

 

The last work was about nuclear particles . The limit of this method of work is the approximation of 1,14-1,16 that I named 7/6 . This approximation comes from Euclidian equations of angular momentum . If we use mole of particles and expodential equations we will have approximation x/1000 and then we could Know if 1,14 is 7/6 .
We found 1,35fermi in approximation 1,14  ,

so 1,35/1,14=1,18 ≈ 1,16=7/6 and   (29a)

1,16fermi ≈ 5x0,225fermi=1,125f (29b)


From this approach it seems that we talk about unified theory were the particles π+ and boson have very good approximation , also we can see the numbers of particles η ,(p,n) ,Ξ , Ω : 3, 5, 7, 9 in order in an approximation of 0,8-1,5 %. The unified approach was obvious from proton equations in the former paper of applications .
In this paper we can see the lengths of proton 0,225fermi,1f, 1.23f, 1.35f and 1.41f that equalised to a dynamic c2/2.
In particle index the energies come from structure of proton(coefficient 0,8),6/7 and length 1fermi . The same results we can have in 1,072fermi with 0,8 and without 6/7 , also in 0,9fermi without 0,8 and 6/7 .
0,9fermi =4x0,225fermi and 1,2fermi=6x0,225fermi closed to dynamic of Paris. So we can have a list of lengths of proton :
0.225f, 0.4f, 0.6f, 0.9f, 1.1f, 1.2f, 1.5f...
We can experementantly to examine these lengths and particle approach .
proton structure 1/ap=21,8
21,8/3=7,26 this is equal to coefficient of nuclear spectrum function(like Rydberg function)
7,25/6,28 =1,15 ≈ 7/6 or 2π/7,25 ≈ 6/7  (30)

this must be the natural mater of 6/7
7,25fermi/0,225fermi=32,2 (31)
32,2=25+0.2 so in the same way of neutrino prediction we have angular momentum :
J=m.c.r=21,8.h ≈ 3x7,25=21,75 ≈ 3x2π.(7/6).h=21,98.h (32)
J=mc.r = 3x32,2x0,225.h=21,73.h ≈ 3x25x0,225.h=21,6.h ,  (33)

r= nr0 , r0=0,225f ,n=r/0,225f (34)
proton structure is : 3x25x0,225 with diverse 0,2
It remands angular momentum 0,2h and energy in length 7,25fermi 0,20hc/l : 44,4MeV/c2 and for one level energy : 44,4/21,8=2,1MeV/c2 , using the method of neutrino prediction .

In above we have seen :
1)the structure of proton constant : 0,225x3x25
2)From fine structure of electron , the electron is divided in 5 parts and from the proton structure constant , the proton is divided in 3 parts

 

An interest calculation is that

21x44,4.MeV/c2 =932MeV/c2 ,  (35)

 21 is the number of structure constant of proton (21,8) This mass epears in particle index .

Fine structure constant of space


What is 0,225fermi?
from the last discussion  that :
Lp/np=2π.0,225fermi=1,41f =
10π.meg.λplank/mp , np=1 with 2π (36)
also 25x0,225fermi =7,2fermi ≈ 7,25fermi (37)

so mp.7,25f=5x25.meg.λplank  (38)
and a.mp.(7,25/2π)fermi=(1/2π).(7/6).meg.λplank ,  (39)

a=1/137,035 and we gave the hypothesis that 1/a=(6/7)x5x25 (40)


The approximation of this equation is 1 if Fermi is 0,993fermi
Also 1,072fermi gives the particles in order η ,(p,n) ,Ξ , Ω : 3,5,7,9 in index particles So the diverse or fermi is :  -0.007f +1fermi + 0,07f

The 0,993fermi gives E0= 0,8hc/(2π.l) = 160,94MeV/c2 , as in particle index arises energy of  proton (7/6)x5x160,94.MeV/c2 = 938.MeV/c2 (41)

it seems that 7,25/2π=7/6 so 1/2π=1/6,28  (42)

must be a fundamental structure constant of space as fine structure and proton constant structure .
The geometry meets the material
The form of this constant must be :
2π=25/5-0,12 (42)
0,12 gives an emition energy  or  particle
0,12.hc/lg , with lg length of gravity wave . (43)

We do not know this length . 
This must be the graviton (neutrino) in order to exist Material in a point of space with Euclidian geometry .
A philosophy conclusion is that the Euclidian geometry is a limit convience and stable for material.
The extension of universe gives the free space in Material to exist in a Euclidian space as in our life .

 

UNIVERSE

 

In conclusion of discussion we try to propose an idea of the universe as a result of imagination and not as a mathematical product

We will do a proposition for the universe compatible with the increased dimensions and its extension. One more dimension can be the carrier of the gravitational force in a two-dimensional horizon of the universe and to distribute homogeneously the gravitational forces in the flat expanding universe. Similarly is distributed the CMB radiation. In the Fig bellow is presented a model of the universe resembling the “two dipole model”. In an other presentation the universe can be similiarized as two-bubbles 

PARTICLE CREATION

In the (15) is seen the relation of the electron - positron and of proton by means of the angular momentum. We can assume that the positron forms a proton as in Fig. bellow:

 

Radiation γ → 3e- →

 3e+

charge=0 charge=0

spin=0 spin=+3/2-3/2=0 

 

(p+,e-):energy(1e-,1e+) + anti-atom:energy(1e-,1e+) 

 

charge=0 charge=0 

spin=3/2 ± ½ spin=-1 or -2 

baryon number B=1 B=-1

 

 

 

END 

 

 

Date copyrights : http://www.wbabin.net , list of authors

 

BIBLIOGRAPHY

 

1. An Introduction to Nuclear Physics, 1992 W. N. COTTINGHAM & D. A. GREENWOOD.

2. General Physics, Electricity, 1974, 5th edition, K. A. ALEXOPOULOS, Greece

3. Modern Physics, 1989 by Saunders College Publishing

Raymond A. Serway, Clement J. Moses, & Curt A. Moyer

4. Particle and Cosmological Physics, 2003 K. E. VAGIONAKIS, University of Ioannina, Greece.

5. Themes of Physics I, 1983, N. A. OIKONOMOU M.Sc., Ph.D., University of Thessaloniki, Greece.

6.Particle and cosmology physics ,2003 K E. VAGIONAKIS , University of Ioannnina

 

Thessaloniki ,Oreokastro , Greece 

Alexandris Nikos

 

 

 

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