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On the Cosmological Variation of the Fine Structure Constant
Fran De Aquino
Maranhao State University, Physics Department, S.Luis/MA, Brazil.
Copyright © 2011 by Fran De Aquino. All Rights Reserved
Recently, evidence indicating cosmological variations of the fine structure constant, α, has been
reported. This result led to the conclusion that possibly the physical constants and the laws of
physics vary throughout the universe. However, it will be shown here that variations in the value of
the elementary electric charge, e, can occur under specific conditions, consequently producing
variations in the value of α.
Key words: Fine Structure Constant, Elementary Electric Charge, Cosmology, Physics of Black-Holes.
PACS: 06.20. Jr, 98.80.-k, 98.80.Jk, 04.70.-s.
The well-known Fine Structure
Constant determines the strength of the
electromagnetic field and is expressed by the
following equation (in SI units) [1]:
( )1
58(52)137.035999
1
4 0
2
==
c
e
hπεα
However, recently, Webb, J.K et al., [2]
using data of the Very Large Telescope
(VLT) and of the ESO Science archive,
noticed small variation in the value ofα in
several distant galaxies. This led to the
conclusion that α is not a constant [2- 4].
It will be shown here, that variations in
the value of the elementary electric charge, e,
can occur under specific conditions,
consequently producing variations in the
value of α. This effect may be explained
starting from the expression recently
obtained for the electric charge [5], i.e.,
( ) ( )24 0 imGq imgπε=
where are the imaginary gravitational
mass of the elementary particle;
is the permittivity of the
free space and is
the universal constant of gravitation.
( )imgm
mF /10854.8 120
−×=ε
1211 ..1067.6 −−×= kgmNG
For example, in the case of the
electron, it was shown [5] that
( ) ( )( ) ( )
( ) ( )3
1121
0
0
2
2
0
imeie
imei
imei
ime
imge
m
m
cm
U
m
χ=
=
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛+−=
where ( ) ( ) imm realeiimei 0320 −= , ( ) kgm realei
31
0 1011.9
−×=
and ( ) ikTU eeime η= . In this expression
1.0≅eη is the absorption factor for the
electron and is its internal
temperature (temperature of the Universe
when the electron was created);
is the Boltzmann constant.
KTe
31102.6 ×≅
KJk /º1038.1 23−×=
Thus, according to Eq. (3), the value of
eχ is given by . Then,
according to Eq. (2), the electric charge of
the electron is
21108.1 ×−=eχ
( )
( )( )
( )( )
( )( ) CmG
imG
imG
imGq
realeie
realeie
imeie
imgee
19
03
2
0
2
03
2
0
00
0
106.14
4
4
4
−×−==
=−=
==
==
χπε
χπε
χπε
πε
As we know, the absolute value of this
charge is called the elementary electric
charge, . e
Since the internal temperature of the
particle can vary, we then conclude that χ is
not a constant, and consequently the value of
also cannot be a constant in the Universe.
Its value will depend on the local conditions
that can vary the internal temperature of the
particle. The gravitational compression, for
example, can reduce the volume V of the
particles, diminishing their internal
temperature
e
T to a temperature
T ′ according to the well-known equation: ( )TVVT ′=′ [6]. This decreases the value of
, decreasing consequently the value of ( )imU
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χ . Equation (2) shows that e is proportional
to χ , i.e.,
( )
( )( )
( )( )
( ) )real
=
=
( reali i
imi
img
mG
imG
imG
imGe
03
2
0
2
03
2
0
00
0
4
4
4
4
χπε
χπε
χπε
πε
=
=−=
=
=
Therefore, when the volume of the particle
decreases, the value of e will be less
than . Similarly, if the volume
is increased, the temperature
C19106.1 −×
V T will be
increased at the same ratio, increasing the
value of χ , and also the value of . The
gravitational traction, for example, can
increase the volume V of the particles,
increasing their internal temperature
e
T , and
consequently increasing their electric charges
(See Fig.1).
Conclusions – Our theoretical results
show that variations in the value of the
elementary electric charge, e, can occur
under specific conditions, consequently
producing variations of the fine structure
constant, α, as shown in Fig.1. This excludes
totally the erroneous hypothesis that the laws
of physics vary throughout the universe.
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Fig. 1 – A spatial dipole that can explain the dipole variation of α reported by Webb. J.K. et
al.
Extremely large
Black-hole
(QUASAR)
α
Extremely large
White-hole
The strong traction upon
the particles increases
their volumes, increasing
the value of α .
The strong gravitational
compression in this region
decreases the volumes of
the particles, decreasing
the values of α .
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References
[1] P. J. Mohr, and B. N. Taylor, (2000) Rev. Mod. Phys.,
72, 351
[2] Webb, J.K. et al., (2011) Phys. Rev. Lett., 107, 191101.
[3] King, J.A. et al., “Spatial variation in the fine structure
constant- new results from VLT/UVES” to be published.
[4] Koch, F. E. et al., “Spatial variation in the fine structure
constant- a search for systematic effects” to be published.
[5] De Aquino, F. (2010) Mathematical Foundations
of the Relativistic Theory of Quantum Gravity,
Pacific Journal of Science and Technology,
11(1), pp. 173-232.
[6] M.J. Moran and H.N. Shapiro (2000), Fundamentals of
Engineering Thermodynamics, Wiley, 4th Ed.
