30 H. ARSLAN

the virial theorem has the same validity in the relativistic

applications as the applications of it in the classical

physics. Therefore, the virial theorem have to be used to

convert the Lagrangian of the weak interactions to the

form of energy.

In [15,16], the virial theorem states that the potential

energy is two times of the kinetic energy in minus sign.

Since the Lagrangian in classical mechanics is written by

LTV. (16)

The total energy is E = T + V and by the virial theorem

V = 2T. Therefore, the total energy is (3T) and the La-

grangian is (-T). By using these in the Equation (14), the

total energy of the weak interactions, in terms of the La-

grangian, can be written as

() ()

32 2WW

EGJJ

(17)

As a result, the unified equation of interactions is

02

2/() ()

2322

q

rr WW

ee

ic IAmc

tcc

QeGJJ

r

αpA

(18)

The last term in this equation describes the weak in-

teractions. The Equation (18) includes the weak, elec-

tromagnetic, gravitational and the strong interactions

where the strong and the gravitational interactions are

thought to be combined for the considered space.

4. Results and Discussions

The wave function of the gravitational and the strong

interactions is derived in Equation (7) by putting the

Yukawa potential in the Dirac equation, the weak inter-

actions’ energy is written by Equation (17) according to

the virial theorem, and the unified equation of interactions

is derived as Equation (18) to describe the true universe.

5. Conclusions

At GUT scale, the high energy structure of the universe

needs the validity of the four fundamental forces with the

same importance. Since the kinematical and charge ef-

fects on the motion could not be eliminated for highly

energetic and charged particles at too large or too small

distances, the electromagnetic and weak interactions

have the same validity at these distances like the gravita-

tional and the strong interactions. In the same way, in the

highly energetic space, for large distances the space be-

haves like a nucleus. Therefore, the strong interactions

must be used to define the motion of the particles. For

small distances, the highly concentrated mass needs the

gravitational forces to explain the attractive forces. Such

a true space may be considered as the space the Bing

Bang began in. In the world we live in, there is no need

to use this equation, as one knows, in special conditions

some of these interactions are effective and others are

negligible. The application of this equation must be be-

yond the Standard Model.

As a result, the Dirac equation is a strong candidate for

unification of the four fundamental forces, as one is done

in this study.

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