Superparticles from the Initial Universe and deduction of the Fine Structure Constant and Uncertainty Principle directly from the Gravitation Theory

Superparticles from the Initial Universe and deduction of
the Fine Structure Constant and Uncertainty Principle
directly from the Gravitation Theory.
Fran De Aquino*
Physics Department, Maranhao State University, S.Luis/MA,Brazil.

*
Permanent Address: R.Silva Jardim, 521-centro, 65020-560 S. Luis/MA, Brazil.( E-mail: deaquino@uema.br ).
ABSTRACT
In a previous work it was shown that the gravitational and inertial masses are correlated by an
adimensional factor, which depends on the incident radiation upon the particle. It was also shown that
there is a direct correlation between the radiation absorbed by the particle and its gravitational mass,
independently of the inertial mass. This finding has fundamental consequences to Unified Field
Theory and Quantum Cosmology. Only in the absence of electromagnetic radiation the mentioned
factor becomes equal to one. On the other hand, in specific electromagnetic conditions, it can be
reduced, nullified or made negative. This means that there is the possibility of the gravitational
masses can be reduced, nullified and made negative by means of electromagnetic radiation. This
unexpected theoretical result was recently confirmed by an experiment (gr-qc/0005107). A
fundamental consequence of the mentioned correlation is that , in specific ultra-high energy
conditions, the gravitational and electromagnetic fields can be described by the same Hamiltonian ,
i.e., in these circumstances, they are unified ! Such conditions can have occurred inclusive in the
Initial Universe , before the first spontaneous breaking of symmetry. Taking as base this discovery,
and starting from the gravitational mass of superparticles from the Initial Universe we show here that
it is possible to deduce the reciprocal fine structure constant and the uncertainty principle directly
from the Gravitation Theory(Unified Theory).
INTRODUCTION
In a recent paper1 we have shown
that the gravitational mass and the
inertial mass are correlated by an
adimensional factor, which depends
on the incident radiation upon the
particle. It was shown that only in the
absence of electromagnetic radiation
this factor becomes equal to 1 and
that, in specific electromagnetic
conditions, it can be reduced, nullified
or made negative.
The general expression of
correlation between gravitational mass
mg and inertial mass mi , is given by
( ) )1(11)/(1
2
12
2
2
2 i
rr
i
ig m
cm
U
mm
ï
þ
ï
ý
ü
-
ï
î
ï
í
ì
ï
þ
ï
ý
ü
ï
î
ï
í
ì
+++-= wes
me
where U is the electromagnetic energy
absorbed by the particle; e =e r e 0 ,
m =m r m 0 and s are the electromagnetic
characteristics of the outside medium
around the particle in which the
incident radiation is propagating.
In the GUTs, the Initial Universe
was simplified for just two types of
fundamental particles: the boson and
the fermion. However, bosons and
fermions are unified in Supergravity:
One can be transformed into another ,
just as quarks can be transformed into
leptons in the GUTs. Thus, in the
period where gravitation and
electromagnetism were unified. (which
would have occurred from time zero
up to a critical time tc @ 10-43s after
Big-Bang ) , the Universe should have
been extremely simple - with just one
particle type ( superparticle or
protoparticle ) .
Starting from the gravitational
mass of these superparticles we will

2show that the reciprocal fine structure
constant and the uncertainty principle
can be deduced directly from the
Gravitation Theory( Unified Theory).
1.CALCULATIONS
According to equation (1) the
gravitational mass of a particle in the
free space (e r=m r =1 and s =0 ) is
given by:
)2(112
2
2 i
i
ig m
cm
U
mm
ï
þ
ï
ý
ü
-
ï
î
ï
í
ì
ï
þ
ï
ý
ü
î
í
ì
+-=
In the case of thermal radiation, it is
usual to relate the energy of
photons to temperature, through the
relation, <h n >~ kT where
k=1.38 · 10-23J/K is the Boltzmann’s
constant. Thus, in this case, the energy
absorbed by the particle will be
U=h <h n >~h kT, h is a particle-
dependent absorption coefficient (in
general, for elementary particles,
h ~ 0.1).
The temperature T of the
Universe in the 10-43s< t < 10-23s period
can be calculated by means of the
well-known expression2
T
~
1022(t/10-23)-1/2
.
(3)
This means that in the period where
gravitation and electromagnetism were
unified (which would have occurred
from time zero up to a critical time
tc @ 10-43s after Big-Bang ) the
temperature was T >>1032K .
According to the Hawking’s3
prediction, collapsed objects cannot
have Schwarzchild’s radius less than
the particle’s wave length. This
correspond to inertial mass mi~10-8kg.
On the other hand, the highest
temperature T >>1032K indicates that
h kT/c2>>10-8kg. Thus, we can assume
that U = h kT>>mspc2. (msp is the
superparticle’s inertial mass.).
For U=h kT>>mspc2 the equation
(2) reduces to:
mg@ - 2U/c2 =- 2 h kT/c2>>10-8kg (3)
which is the gravitational mass of the
superparticles.
It follows that the gravitational
forces between two superparticles is
given by:
( ) )4(ˆ4
ˆ
212
2
5
212
'
2112
mhk
m
r
cT
c
G
r
mm
GFF gg
�
�
��
œ
ß
ø
Œ
º
Ø
÷
ł
ö
ç
Ł
æ
=
=-=
Due to the gravitational and
electromagnetic interactions were
themselves unified in that period, we
can write,
( )
)5(
4
ˆ
4
2
0
2
212
2
52112
r
e
r
cT
c
GFF
p e
mhk
=
œ
ß
ø
Œ
º
Ø
÷
ł
ö
ç
Ł
æ
=-=
�
�
��
From equation above we can write
( ) )6(
4
4
0
2
2
5
p e
hk
e
cT
c
G
=
œ
ß
ø
Œ
º
Ø
÷
ł
ö
ç
Ł
æ
�
�
If now we make in the above equation
( ) )7(4 25 ahk =÷
ł
ö
ç
Ł
æ T
c
G
�
it becomes
)8(
137
1
4 0
2
==
c
e
�
p e
a
which is the well-known reciprocal fine
structure constant .
For T~1032K the equation(7) tell
us that

3( ) )9(
100
14 2
5 @÷
ł
ö
ç
Ł
æ
= T
c
G
hka
�
This value has the same order of
magnitude that the exact value(1/137)
of the reciprocal fine structure
constant.
From equation (4) we can write:
)10(
'
�
�
�
=
÷
÷
ł
ö
ç
ç
Ł
æ
r
rc
mm
G gg
a
The term between parenthesis has the
same dimensions that the linear
momentum p
�
. Thus Eq.(10) gives us
)11(��� =× rp
A component of the momentum of a
particle cannot be precisely specified
without loss of all knowledge of the
corresponding component of its
position at that time ,i.e., a particle
cannot precisely localized in a
particular direction without loss of all
knowledge of its momentum
component in that direction . This
means that in intermediate cases the
product of the uncertainties of the
simultaneously measurable values of
corresponding position and momentum
components is at least of the order of
magnitude of
�
,i.e.,
)12(�
‡D×D rp
This relation, directly obtained here
from the Unified Theory, is the well-
known relation of the Uncertainty
Principle for position and momentum.
Finally, it can be shown by
standard mathematical methods that
)13(1
‡D×D xk
where kD is the approximate spread in
propagation number lp /2=k .
When we combine the
relation(12), with the relation(13), we
obtain the equations kp
�
�
�
= and
hfE = , that are the so-called De
Broglie-Einstein relations. Therefore
the Quantum Mechanics can be
deduced from the New Unified Theory.
2.CONCLUSION
In the present paper we have
shown that it is possible to deduce the
reciprocal fine structure constant and
the uncertainty principle directly from
the Unified Theory .
These are theoretical findings
that validate the discovery of the
correlation between Gravitation and
Electromagnetism and confirm the
Unified Theory, both carried out by the
author.1
3.REFERENCES
1 De Aquino, F.(1999)“ Gravitation and
Electromagnetism: Correlation and
Grand Unification” , Los Alamos
National Laboratory preprint
no.gr-qc/9910036.
2 Carr, B. J. (1976) Astrophys. J.,
206,10.
3 Hawking,S.W.(1971)Mon.Not.R.
Astron.Soc.,152,75.