Strong
(nuclear) gravitation
In Astronomy the only one available
characteristic empirical physical constant is the gravitational constant. Without
completing the chargemass unification or final unification: one cannot say,
whether it is an ‘input to the unification’ or ‘output of unification’. The
same idea can be applied to the atomic physical constants also. Sitting in a
grand unified roof one cannot make an ‘absolute measurement’ but can make an
‘absolute finding’. Up till now, no atomic model has implemented the
gravitational constant in the atomic or nuclear physics. Then, whatever may be
its magnitude, measuring its value from existing atomic principles is
impossible. Its value has been measured in the lab only within a range of 1 cm
to a few metres, whereas the observed nuclear size is
1.2 fermi. Until one measures the value of the gravitational constant in
microscopic physics, the debate of strong (nuclear) gravitation can be
considered positively. The idea of strong gravitation originally referred
specifically to mathematical approach of Abdus Salam
of unification of gravitation and quantum chromodynamics, but is now often used
for any particle level gravitation approach. Now many persons are working on
this subject. The main advantage of this subject is: it couples black hole
physics and particle physics.
Strong
gravitational constant
The strong gravitational
constant, denoted or , is a grand unified physical constant of
strong gravitation, involved in the calculation of the gravitational attraction
at the level of elementary particles and atoms.
According to Newton's law of
universal gravitation, the force of gravitational attraction between two
massive points with masses and , located at a distance between them, is:
The coefficient of
proportionality in this expression is called gravitational constant. It is assumed,
that in contrast to the usual force of gravity, at the level of elementary
particles acts strong gravitation. In
order to describe it in
the formula for gravitational force must be replaced on :
Contents

The dimensions assigned to the
strong gravitational constant may be found from the equation above — length
cubed, divided by mass and by time squared (in SI units, metres
cubed per kilogram per second squared).
There are several ways to assess
the value of .
J. Dufour, under the assumption that the
strong gravitational constant depends on the type of objects, from the
interaction of two deuterium nuclei determined, ^{[1]}
that .
Based on the analogy between
hadrons and KerrNewman black holes ^{[2]} Sivaram, C. and Sinha, K.P, ^{[3]} ^{[4]} and Raut, Usha and Shina,
KP ^{[5]} accepted value .
This value of the strong
gravitational constant allowed estimating the strong spintorsion interaction
between spinning protons. ^{[6}^{]}
In paper of Mongan
^{[7]} strong gravitational constant is .
According to Robert Oldershaw ^{[8]} value of the strong gravitational constant is .
As in Oldershaw’ paper, strong
gravitational constant could be related ^{[9]} with the
proton radius , the proton mass and
the speed of light :
.
According to Tennakone
who identified the electron and the proton as black holes in the strong
gravitational field, strong gravitational constant is: ^{[10]}
.
Recami et al ^{[11]} ^{[12]} define strong gravitational constant through the
mass of the pion as
follows:
,
where – Planck constant.
From this they derive constant of
strong interaction of two nucleons in the following form:^{ [13]}
, where indicates a strong charge, is
reduced Planck constant.
Stanislav Fisenko
et all found ^{[14]} ^{[15]}
a spectrum of steady states of the electron in proper gravitational field
(0.511 MeV …0.681 MeV) on the base of strong coupling constant
.
U. V. S. Seshavatharam
and S. Lakshminarayana ^{[16]}
in determining repelled from the Fermi constant, which led
them to the value .
In the paper ^{[17]}
strong gravitational constant equal to .
Sergey Fedosin entered the strong
gravitational constant in 1999 on the basis of equality between the Coulomb
electric force and gravitational force in the hydrogen atom on the Bohr radius.
This leads to the following expression for the value of the strong
gravitational constant: ^{[18]}
,
where –
elementary charge, – pi, –
vacuum permittivity, –
the mass of proton, –
the mass of electron.
The small mass and large charge
of matter do not allow the electron to be entirely in some small volume near
the nucleus, and it gets disklike axisymmetric shape,
which is limited by size of atom. In the hydrogen atom electrical forces
between the nucleus and matter of the electron are attractive, but they are
compensated by the repulsion of the intrinsic charge of the electron. There are
the centripetal force of rotation of the electron around the nucleus, and the
gravitational attraction between massive nucleus and matter of the electron.
From here follows that the action of strong gravitation between the masses of
nucleus and electron on the one hand, and the electric force between charges of
the nucleus and the electron, on the other hand, allows to estimate the value
of .
With the help of the constant the
rest energy of proton is equal to half of energy of strong gravitation in
accordance with virial theorem: ^{[19]}
where m is the proton radius, (in the hypothetical case of a uniform mass
density of the proton in the form of a ball must be ). This implies that the mass of nucleons is
determined by the energy of the strong gravitation according to the principle
of mass–energy equivalence.
If we assume that the magnetic
moment of the proton is created by the maximum rotation of its positive charge
distributed over the volume of the proton in the form of a ball, when the
centripetal acceleration at the equator becomes equal to acceleration of strong
gravitation, the formula for the magnetic moment is as follows:
where J / T is the magnetic moment of the
proton, (in the case of uniform density and charge should
be ).
From the formulas for the energy and the magnetic moment the radius of
the proton is determined in the selfconsistent model. ^{[20]}
The strong gravitational constant
is also included in the formula describing the nuclear force through strong
gravitation and gravitational torsion field
of rotating particles. ^{[2}^{1}^{]} A feature of the gravitational
induction is that if two bodies rotate along one axis and come close by the
force of gravitation, then these bodies will increase the angular velocity of
its rotation. In this regard, it is assumed that the nucleons in atomic nuclei
rotate at maximum speed. This may explain the equilibrium of the nucleons in
atomic nuclei as a balance between the attractive force of strong gravitation
and the strong force of the torsion field (of gravitomagnetic forces in gravitoelectromagnetism). In
particular, the coupling constant is
,
where is
equal to 0.26 for the interaction of two nucleons, and tending to 1 for bodies
with a lower mass density.
The constant is
close to coupling constant of strong interaction of two nucleons in Standard
Model
, where is the constant of the pseudoscalar nucleonpionic
interaction.
Finestructure constant is coupling
constant of electromagnetic interaction and may be written so:
Role of squared Avogadro number
Considering Avogadro number as a scaling factor, U. V. S. Seshavatharam and S. Lakshminarayana
finally arrived at a value of ^{[22]} ^{[23]} ^{[24]} . It is noticed that in Hydrogen
atom, ratio of total energy of electron and nuclear potential is equal to the
electromagnetic and gravitational force ratio of electron where the operating
gravitational constant is nothing but the atomic gravitational having a value N^{2}G.
This is a direct confirmation of the existence of the atomic or nuclear
gravitational constant in nuclear physics. Therefore, this subject can now be
considered as part of the mainstream research in quantum gravity.
The central idea is: for mole number of particles,
strength of gravity is and force required to bind particles is Force required to bind one particle
is By considering this force
magnitude as the characteristic weak force magnitude, it is observed that, where
is the rest mass of proton
and is the rest mass of electron.
Obtained value of Here the most important point to be
emphasized is can be considered as the
classical or upper limit of gravitational or electromagnetic force. It can be
considered as the grand unified force. It is the origin of Planck scale and of
the black hole astrophysics.
Connection with usual
gravitational constant
With the help of similarity of matter levels and SPФ symmetry in Theory of Infinite Hierarchical Nesting of Matter
the value of can
also be defined in terms of coefficients of similarity and gravitational
constant:
where , , are the coefficients of similarity in mass,
size and speed, respectively, for the degenerate quantum objects at the atomic
and stellar levels of matter.^{[18]} The powers of similarity
coefficients in this equation correspond to the dimension of gravitational
constant according to dimensional analysis.
From the standpoint of Infinite
Hierarchical Nesting of Matter and Le Sage's theory of gravitation, the
presence of two gravitational constant and shows the difference between the properties
of gravitons and properties of matter at different levels of matter. ^{[2}^{5}^{] [2}^{6}^{]}
Note that in the atomic or
nuclear physics, till today no one measured the gravitational force of
attraction between the proton and electron and experimentally no one measured the
value of the gravitational constant. Physicists say – if strength of strong
interaction is unity, with reference to the strong interaction, strength of
gravitation is 10^{−39}. The fundamental question to be answered is: is
mass an inherent property of any elementary particle?
One can say: for any elementary
particle mass is an induced property. This idea makes grand unification easy.
Note that general relativity does not throw any light on the ‘mass generation’
of charged particles. It only suggests that spacetime is curved near the
massive celestial objects. More over it couples the cosmic (dust) matter with
geometry. But how matter is created? Why and how elementary particle possesses
both charge and mass? Such types of questions are not discussed in the frame
work of general relativity.
The first step in unification is
to understand the origin of the rest mass of a charged elementary particle.
Second step is to understand the combined effects of its electromagnetic (or
charged) and gravitational interactions. Third step is to understand its
behavior with surroundings when it is created. Fourth step is to understand its
behavior with cosmic spacetime or other particles. Right from its birth to
death, in all these steps the underlying fact is that whether it is a strongly
interacting particle or weakly interacting particle, it is having some rest
mass. To understand the first two steps somehow one can implement the
gravitational constant in sub atomic physics.
To bring down the Planck mass
scale to the observed elementary particles mass scale a large scale factor is
required. Just like relative permeability and relative permittivity by any
suitable reason in atomic space if one is able to increase the value of
classical gravitational constant, it helps in four ways. Observed elementary
particles mass can be generated and grand unification can be achieved. Third
important application is characteristic building block of the cosmological dark
matter can be quantified in terms of fundamental physical constants. Fourth
important application is – no extra dimensions are required. Finally nuclear
physics and quantum mechanics can be studied in the view of strong nuclear
gravity where nuclear charge and atomic gravitational constant play a crucial
role in the nuclear spacetime curvature, quantum chromodynamics and quark
confinement. Not only that cosmology and particle physics can be studied in a
unified way. In this connection it is suggested that square root of ratio of
atomic gravitational constant and classical gravitational constant is equal to
the Avogadro number. ^{[2}^{7}^{]} The Avogadro constant expresses the number of elementary entities per mole
of substance and it has the value mol^{–1}. Avogadro's constant is a
scaling factor between macroscopic and microscopic (atomic scale) observations
of nature. It is an observed fact. The very unfortunate thing is that even
though it is a large number it is neither implemented in cosmology nor
implemented in grand unification.
Here the very important question
to be answered is – which is more fundamental either G or G_{s} ? It is proposed that both can
be considered as the 'head' and 'tail' of matter coin. It can also be suggested
that classical G is a consequence of the existence of atomic G_{s}. It is known that there is a difference
in between 'absolute findings' and 'absolute measurements'. Absolute findings
can be understood where as 'absolute measurements' can not be made by nuclear experiments which are being
conducted under the sky of universal gravity with unknown origin of elementary
particles mass.
Till today there is no
explanation for this fantastic and large difference between G or G_{s}
or between gravitation and strong interaction, about 10^{−39}. It can
be supposed that elementary particles construction is much more fundamental
than the black hole's construction. If one wishes to unify electroweak, strong
and gravitational interactions it is a must to implement the classical
gravitational constant G in the sub atomic
physics. ^{[2}^{8}^{]} By any reason if one implements the Planck scale in elementary particle
physics and nuclear physics automatically G
comes into subatomic physics. Then a large arbitrary number has to be
considered as a proportionality constant. After that its physical significance
has to be analyzed. Alternatively its equivalent 'strong atomic gravitational
constant' can also be assumed. Some attempts have been done in physics history.
Whether it may be real or an
equivalent if it is existing as a 'single constant' its physical significance
can be understood. Nuclear size can be fitted with 'nuclear Schwarzschild
radius'. Nucleus can be considered as 'strong nuclear black hole'. This idea
requires a basic nuclear fermion! Nuclear binding energy constants can be
generated directly. Protonneutron stability can be studied. Origin of strong
coupling constant and Fermi's weak coupling constant can be understood. Charged
lepton masses can be fitted. Such applications can be considered favorable for
the proposed assumptions and further analysis can be carried out positively for
understanding and developing this proposed 'Avogadro's strong nuclear gravity'.
Unification means: finding the
similarities, finding the limiting physical constants, finding the key numbers,
coupling the key physical constants, coupling the key physical concepts,
coupling the key physical properties, minimizing the number of dimensions,
minimizing the number of inputs and implementing the key physical constant or
key number in different branches of physics. This is a very lengthy process. In
all these cases observations, interpretations, experiments and imagination play
a key role. The main difficulty is with interpretations and observations. As
the interpretation changes physical concept changes, physical equation changes
and finally the destiny changes.
Note that human beings are part
of this universal gravity. There are some natural restrictions to experiments.
Seeing a black hole is highly speculative. But indirectly its significances can
be well understood. In the similar way in nuclear and particle physics: any
experimental setup which is being run under the influence of the proposed
strong nuclear gravity, without knowing the probing particle’s massive origin,
without knowing the massive origin of the nucleus: based on ‘grand unified
scheme’ one may not be able to unearth the absolute findings. Note that
observer, experimental setup and the probing particle all are under the same
influence of universal gravity. When searching for an experimental proof in
grand/final unification scheme or dark matter projects this fact may be
considered positively for further analysis.
To conclude it can be suggested
that – existence of strong gravitational constant as Atomic gravitational
constant is true and its consequences can be understood easily and can be implemented
easily in grand unification program and dark matter projects.