Let us begin from the common definition of the inertial rest state m_o , r_o  and  E_o  of an isolated baryonic particle (small sphere s) which is stated by the Einstein's famous equation:

If we defined a closed sphere (big sphere S) formed of number of protons p, distributed homogeneously in much more number of neutrons n, and if we equated the quantity  with the number one we can get

This is a nontrivial solution defines the initial conditions

We can consider r_c unknown that we have to estimate its value in the bound state.

From the above we can do the next intuitive mathematic operation 

That is if (and only if) the in-between brackets equal half.

And then we choose a very small cut of energy ?E equivalent to the extra ?r of equation 2    

Where µ is a new unknown we have to find its value, and   

Or, we can write it in the form

It looks like Coulomb's form: its right side represents the kinetic energy as defined by the forthcoming equation 12, while its left side represents half the electric potential energy of each charged particle of the sphere. The particles of the sphere S possesses motional property (v ~ c) representing the microstates inside the sphere. The above is the first face of the coin, while its second face appears when we insert the approximate relation of equation 5 into the Einstein's equation by adding the positive term (which is equation 3) to appear as the next strict equality

The speed v in equation 5, appears in the above macro state as intrinsic physical property or (silent) speed; v=c

If the free isolated particle was defined by 

Then the bound one inside the big sphere gets new additional definition                            

This gives intrinsic property for the particles:

If equation 3 equals the gravitational potential

Then, we can rewrite equation (1) as follows: 

The quantity between the brackets arises only from the spaces between the particles as defined by equations 3, 7 and 8, but when we add the gravitational energy we get the whole equation (the macrostate). The quantity u_g inside the brackets is the cut energy mentioned in equations 3, 4 and 5 due to the extra size ?r mentioned in equations 2

All the microstates inside the sphere should be defined finally by the initial conditions of equation 1.

The kinetic energy in our alternative relativistic solution is defined by the initial condition (look at equation 1):      m = m_o

Therefor this enables us to put the mass outside the next integral      The free particle loses a bit of its mass to reside in a bound state. Here in our sphere, the particle- like rest energy loses a bit of energy ?E ≡ u_g. After adding the gravitational kinetic energy ?E = u_g we get the general form of equation 1 and 10.

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