Quantum Theory of Gravity - "QTG"

                We will now calculate the influence of the change of gravitational potential on the velocity of the electron of a hydrogen atom that is moved within the solar system from the Earth’s orbit (1 AU) to a distance of 50 AU from the sun. In this manner, we can determine the degree to which the sun influences the gravity-time of all the material around it, given that the sun is the dominant mass in the region and thus primarily responsible for the definition of the regional time reference. We can calculate as follows:

                Where:  Φ_1AU  =  Φ_Earth  =  the gravitational potential on Earth [m²/s²],

                            m_Sun = the mass of the sun    = 1.99 x 10³⁰ kg, and

                            L_S-E = the distance from the Earth to the sun    = 1.49 x  10¹¹  m.

                Solving, we find:

                Where: Φ_50AU = is the gravitational potential at 50 AU [m²/s²].

                Solving, we find:

                The change in gravitational potential at this distance is:
               

                Solving, we find:

                 From the General Theory of Relativity, we know that we can calculate the change in temporal frequency for a parallel gravitational field using the following equation:

                Where: ΔT_Time1 is the period of time that passes in location 1 [s], and

                            ΔT_Time2 is the period of time that passes in location 2 [s].

                On this basis, we can derive the formula to determine the change in velocity of the electrons in an atom:

                Where: Δυ_electron1 is the change in velocity of the electron at location 1 [s], and

                            Δυ_electron2 is the change in velocity of the electron at location 2. [s]

                We can use the change in electron velocity obtained from equation 30 at 1 AU:

                Using the change in gravitational potential, the new change in velocity at 50 AU will be:

                Where: Δυ_electron-1AU   is the change in velocity of the electron at 1 AU [s], and

                            Δυ_{electron-50AU}   is the changed in velocity of the electron at 50 AU [s].

 
                Solving, we find:

               

 

                We can use the velocity of the electron in its fundamental state, with no gravitational influence, as determined in equation 3:

                The velocity of the electron at 50 AU is calculated as in equation 30:

               

 

                Solving, we find:

                We can call this “the velocity of the electron at 50 AU from the sun, modulated by the gravitational potential of the time reference location”.
                At a distance of 50 AU, this velocity generates a gravity of:

                Solving, we find:

               

                This can be compared to the gravity at an orbit of 1 AU:

                The difference is:

                We have a further option for determining the mass, which is:

                The two methods yield exactly the same result.

                We should remember that the universal gravitational constant was determined on Earth, taking into account a great quantity and diversity of atoms. On Earth and in this region of the Solar System, Newton’s laws and the Universal Gravitational Constant should therefore work very well.

                The mass increases, but remains limited at the infinite. This shows that the Universal Gravitational Constant conspires in some way against what would be expected of great distances, suggesting that this constant may not be so reliable, or perhaps that it is not so universal.

                Perhaps the problem of dark matter is not that we do not see the missing matter, but that we do not know how to calculate the force of gravity at great distances. Perhaps we do not have dark matter but “dark gravity”.

                We can conclude that, as time passes at different rates in different locations in the universe, so the perception of mass should also vary.

                More details are available at:

                http://arxiv.org/PS_cache/gr-qc/pdf/0506/0506139.pdf

                http://en.wikipedia.org/wiki/Pioneer_anomaly

                http://spaceprojects.arc.nasa.gov/Space_Projects/pioneer/PNStat.html

                http://www.space.com/scienceastronomy/mystery_monday_041018.html