We now come to the most elusive phenonemon of all. The force of gravity. Although the force of gravity and electroststic forces are both a force at a distance phenonemon that follow the inverse square law, there seems to be no clear connection between them. The force of gravity is much weaker than the electrostatic forces. The electrostatic force between an electron and proton is about 2×10^40 times that of the gravitational force. However, gravitational effects are generally much more noticeable due to the large amount of neutrally charged matter involved.
Using the S-S concept, it is quite possible that the gravitational field around a body could be due to a slightly greater overall sink than source. This would indicate that the proton would sink slightly more versus time than an electron would source. All neutrally charged bodies would then be trying to sink the same space and hence be attracted to each other. The only problem with this approach is that normal electrostatic force equations between neutrally charged bodies, involving larger sinks than sources (or larger sources than sinks), always comes out with a positive force which is one of repulsion.
An alternate approach is to consider that the small added source and sink are imaginary quantities. This can happen if we assume that electrostatic field strength is a complex quantity when it interacts with a charge. Assume that:
Then the force between q1 and q2 would be:
For q+ = qo, q- = -qo,
the force between two protons, a proton and an electron and two electrons becomes:
Digressing for the moment, consider a neutron to be equivelant to a proton and an electron in close proximity. Then, for neutrally charged bodies, and ignoring minor packing fraction variations:
For bodies separated by great distances, all the charges in each bodie can be approximated to be at a single point (principal of superposition). It is not known whether this is true for neutrally charged pairs or not but will be assumed to be true for this development. The total electrostatic force between bodies a and b is the sum of the forces between the positive charges in both bodies, the force between each positive charge in body a and each negative charge in body b, the force between each positive charge in body b and each negative charge in body a and the force between the negative charges in both bodies. This is equivelant to:
Inserting the values for f++. f+- and f-- produces
From Eulers theorum
For small angles
and substituting for n and m:
A minus sign in the electrostatic equation signifies an attraction while a positive sign in the gravitational equation signifies an attraction, consequently:
The quantities qp and qe represent the complex portion of the charges q+ and q-. We have assumed that the original complex reaction between the field and charge is attributable to the charge for convenience. This may or may not be true. In accordance with the S-S concept, the dimensions of q are L^3/T so that charge represents the rate of change of a volume of space. Consequently, the quantity (qp - qe) represents the difference in the rate at which space is sinked and sourced by an electron-proton pair.
We have shown that the gravitational equation can be derived from the electrostatic equations if we assume that the interaction of an electrostatic field and a charge can be considered a complex quantity. We have also shown that the mechanism of gravity can be attributed to the difference in the source and sink rates of the neutrally charged electron-proton pair of which all neutrally charged matter can be considered to consist of.