Primary Particle, the Relation of Particle Mass to
its Velocity and Wave Length or Frequency, Integration of
Gravitational and Electromagnetic Forces

De Broglie Electron Waves:

An important conceptual progress in quantum theory was made after a
while in 1924. Louis de Broglie, a young French physicist, suggested
in his doctoral dissertation that light waves behave like particles
in certain conditions; particles also can behave like waves.
Particularly, he presented that electrons formerly assumed like hard
charged and impenetrable spheres, in fact can behave similar to
light or water waves like widespread waves resulted of diffraction
or interference.

According to de Broglie's theory, a particle wavelength (λ),
is inversely proportional to its momentum (P). Moreover,
proportionality constant is Planck's quantum constant (h):

It is not necessary to elaborate that the above equation is taken
from equations of photon momentum given below:

Therefore, the greater the momentum of a particle, the shorter its
wave length is. It is worth mentioning that de Broglie's theory is
not only applicable to electron and other elementary particles but
also applicable to all the particles. For example, a billiard ball
rolling on a billiard table has a wavelength but because Planck's
constant is very small, ball momentum is big in the same proportion.
Wavelength of a billiard ball is about 10^{-34}m. This value
is of course several orders of magnitude different from ordinary
dimensions of a billiard ball. Therefore, a ball would never show a
wave-like behavior. Typical momentum of electrons could make
wavelengths of about 10^{-10} meters which are ordinary
magnitudes in atomic distance scale. Hence, one can expect them to
show wave characteristics while interacting with atomic structures.
This was first shown by American physicists, Clinton Davidson and
Lester Germer, in 1927. They proved that electrons could be
diffracted by passing through lattice structure of a crystal in the
same way of diffraction of light passing through a filter.

Where P stands for momentum, m_{0} for a body or particle
static mass, v for a body or particle speed, λ for wavelength
and h for Planck's constant. As you know there is no static status
in natural status of materials and particles in which speed equals
zero. Therefore, wavelength would not be infinity.

c stands for speed of light. Now we can have a better understanding
of the general concept of mass (m) in physics:

Mass of every particle or body is a result of its own vibration and
speed or its constituents'.

The above relation determines mass of every particle or body only by
knowing its wavelength and speed. For example, for a proton
traveling by half of speed of light we have:

And now we can have relativity mass of a particle in motion just by
knowing wavelength and speed and of course without knowing electric
charge, static mass and even type of particle itself:

It is obvious that static mass of a particle is also calculable just
by knowing its wavelength and speed:

The equation below shows the relation between mass of every particle
or body and ratio of its frequency over speed:

A few questions rise here stating that: What is the general
difference among particles in quantum mechanics? And how can motion
and vibration of particles result in occurrence of mass and gravity
force?

Certainly, general difference of particles is their mass and it
seems that all the fundamental (elementary) particles at last have a
unique identity, i.e. they are made of a unique particle while
storing different amount of energy in themselves. As a result, they
would have different masses and consequently, they would have
different wavelengths and momentums in motion. It is predicted that
finally this primary particle will be revealed in researches being
done on particle accelerators. It is interesting that this particle
has no mass, electric charge and consequently has no energy and
momentum. It means a perfectly pure particle and no detector or
method could be considered to identify it for now. But it would
definitely have a very strong interaction with electromagnetic waves
therefore it would be traceable and would create a new and known
particle at once absorbing electromagnetic waves. As you know, the
earthquake waves are divided into two groups in geophysics, P or
longitudinal waves and S or transverse waves. The waves on the water
surface are transverse while sound spreads in water and air
longitudinally. Our final prophecy on this subject is that since
wavelength of particles are due to their permanent vibration, these
vibrations might be able to create and spread longitudinal
electromagnetic waves which are the main factor to appearance of
gravity force since motion of a charged particle and its vibration
generate and spread electromagnetic field and electromagnetic waves
respectively. Of course as you know light is a transverse
electromagnetic wave and it is very probable and logical for its
longitudinal type to exist while it has not been recognized or
generated by human yet. This point is important that Einstein's
general theory of relativity is still a classic theory which does
not take into account gravity in quantum mechanics field. No
successful theory on quantum gravity has been formulated yet and the
agreement between general theory of relativity and quantum mechanics
is still a main issue in theoretical physics left unresolved. It
might be wrong at all to make these two theories agree or merge.
Anyway, in this subject we are trying to merge Newton's gravity
force formulation and the recent relation obtained from combination
of quantum mechanics and relativity equations to understand the
identity of gravity force and to unify it with electromagnetic
force. Assuming that two particles or bodies are stationary relative
to each other and are in motion with the same velocity, we have:

It states that gravitational force completely has an electromagnetic
identity and we might be able to recognize or even generate and
spread these waves in close future. Without considering relativity
mass the above formulations would be: