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 :
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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]}
.
Zane Andrea
Quintili finds a strong gravitational constant based on the similarity between
the Planck mass and radius, and accordingly the mass and radius of the proton: ^{[11]}
.
Recami et al ^{[1}^{2}^{]} ^{[1}^{3}^{]} 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:^{ [1}^{4}^{]}
, where indicates a strong charge, is
reduced Planck constant.
Stanislav Fisenko et all found ^{[1}^{5}^{]} ^{[1}^{6}^{]} 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 ^{[1}^{7}^{]} in determining repelled from the Fermi constant, which led
them to the value .
In the paper ^{[1}^{8}^{]} 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: ^{[1}^{9}^{]}
,
where –
elementary charge, – pi, – electric
constant, – the mass of proton, – the mass of electron.
It is assumed that strong
gravitation, as a universal force, acts on the matter of nucleons, hadrons,
electrons and elementary particles, regardless of the type of these particles.
In contrast, the standard approach considers that strong interaction does not
affect electrons and other leptons.
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. All these forces are equal in
magnitude. 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 . If is the Bohr radius, then the equality of
forces gives:
So that
Bohr radius
becomes equal
where is the orbital speed of the
electron cloud at the first energy level.
Hence , and the kinetic energy of the electron,
taking into account determination of strong gravitational constant, is equal
to:
where is the potential energy of electron in the electric field of the nucleus
of a hydrogen atom.
It turns out the virial theorem in the form . The total electron energy is
also found at the first energy level:
eV.
With the help of the constant the
rest energy of proton in
the form of a ball is equal
to half of its potential
energy of strong gravitational field in accordance with virial theorem, ^{[}^{20}^{]} if we assume
that the binding energy for the proton up to a sign is
equal to the total energy of proton, and becomes very close to
relativistic energy in the form of rest energy:
where m is the
proton radius, (in
the hypothetical case of a uniform mass density of the proton there 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. ^{[2}^{1}^{]}
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}^{2}^{]} 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.
Fine structure
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 ^{[23]}
^{[24]} ^{[25]} . 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.^{[19]} 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}^{6}^{] [2}^{7}^{]}
In particular, for the strong gravitational constant and the ordinary
gravitational constant it is possible to write similar relations, in which
these constants are expressed in terms of the corresponding energy densities of
gravitons’
fluxes in electrogravitational
vacuum and
the parameters of the densest object of the corresponding level of matter: ^{[}^{28]}
where J/m³ is the energy density of the graviton
fluxes for cubic distribution; m² is the crosssection of
interaction of the charged particles of the electrogravitational vacuum (praons) with nucleons, which is very close in magnitude to the
geometrical crosssection of the nucleon and is used to calculate the electric
constant; is the mass of the nucleon; J/m³ is
the energy density of the graviton fluxes at the stellar level for cubic distribution;
m² is the crosssection of interaction between
the gravitons and a neutron star; kg is the mass of the neutron star.
At the
matter level of praons, its own strong
gravitational constant must act. Considering that the
coefficient of similarity in speed between the nucleon and praon levels of
matter is , we can write:
m^{3}•s^{–2}•kg^{–1},
where C is the charge of the praon, kg is the mass of the praon, is the proton to electron mass ratio.
The main
object of unification is to understand the origin of elementary particles mass,
(Dirac) magnetic moments and their forces. Right now
and till today ‘string theory’ with 4 + 6 extra dimensions not in a position to
explain the unification of gravitational and nongravitational forces. More
clearly speaking it is not in a position to bring down the planck scale to the
nuclear size. 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}^{9}^{]} 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. ^{[30]} 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.