  Considering two static, electrically charged, elementary particles, we
demonstrate a possible way of proving that all known fundamental forces in the
nature are the manifestations of the single, unique interaction. We re-define
the gauging of integration constants in the Schwarzschild solution of Einstein
field equations. We consider the potential energy in this context regardless it
is gravitational or electric potential energy. With the newly gauged constants,
we sketch how the unique interaction can be described with the help of an
appropriate solution of the well-known Maxwell equations. According the
solution, there are two zones, in the system of two oppositely charged
particles, where the force is oscillating. The first particle can be in a
stable, constant distance from the second particle, between the neighbouring
regions of repulsion and attraction. In an outer oscillation zone, the
corresponding energy levels in the proton-electron systems are identical (on
the level of accuracy of values calculated by the Dirac's equations) to some
experimentally determined levels in the hydrogen atom. For each system of two
particles, there is also the zone with the macroscopic, i.e. monotonous
behavior of the force. As well, the solution can be used to demonstrate that
the net force between two assemblies consisting each (or at least one) of the
same numbers of both positively and negatively charged particles is never zero.
A secondary electric force, having the same orientation as the primary electric
force between the oppositely charged particles, is always present. It can be
identified to the gravity. Finally, the solution of the Maxwell equations can
be used to calculate the inertia force of a particle. The consistent formulas
for both acting and inertia forces enable to construct the dimensionless
(without gravitational constant, permitivity of vacuum, etc.) equation of
motion.
