A

ny positional field imposes on all other particles its spherical positional field.
Such curvatures cancel overall but local concentrations of countable units (particles) generate deviations.

The claim of any positional field to impose its reference frame on all others is inversely proportional to the total number of other particles presently in its field and directly proportional to its mass (field density).
This means that although the curvature of a field is less at greater distances from the source it has the same claim to impose that curvature on another particle as one closer to that particle. It simply imposes a lesser curvature. This holds true for all particles of equal mass.

The claim to impose a reference frame is less for a particle of lesser mass even though it may be the same distance away as another more massive particle. Thus, if a particle's field is squeezed down it will have the identical degree of curvature that it possessed previously but the new curvature will 'count' for more when imposed on another particle.

These steps must be true in order to maintain consistency with observation.

The source of the gravitational interaction is the lateral component of the reaction velocity which is curved in the direction of the concentration which caused the curved reference frame.

Because the reaction velocity increases (and therefore the strength of the force also) in proportion to the square root of the baryon number, the net force of gravity decreases as the square root of the baryon number, i.e.

10^39 (see Reaction velocity increase) / 10^78 (Number of other particles imposing reference frames from random directions yielding a flat Euclidean frame) = 10^(-39) .

The bend influencing the lateral component of the reaction velocity is

B = { (r^2 + D^2)^1/2 } - r

Where B is the bend, r is the distance to the concentration and D is the particle confinement (Compton wavelength).

Clearly for large r the field decreases as 1/r but when r is less than D, B increases thereby preventing a singularity. (see LP #15)

The macroscopic (Newtonian) formula for gravity is then

[m(1)/r] x [m(2)/r] = m(1)m(2) / r^2 .

Addendum: 2/10/00 It may seem physically unfounded to separate r 2 in the above familiar equation. Observe the figure below. Two objects attract each other with a force of "one". There is one gravitational coupling f(1). Then, with two bodies the force of attraction is quadrupled because there are now four equal couplings. Hence, to double the mass on each side is to multiply the strength of the force on each side by two and thus the total force by four. Now, halve the distance of the first example ... and ... if the gravitational field strength falls off as 1/r as I propose, each body is now in a position exactly equivalent to the second example wherein the attractive force is quadrupled by doubling the total mass. Hence, halving the distance quadruples the total attractive force between the two bodies. Therefore, the strength of the gravitational force is inversely proportional to the square of the distance between two bodies only if the field emanating from each falls off as 1/r. I have seen figures like the following which indicate a misconception since they show a dependence on area whereas the gravitational force is linearly dependent.

By reaction, the curvature is 'straightened out' by the particle whose lateral component is curved. Such a distortion pulls the source of the curvature by interaction with its own field. 'Self-interaction' is inertia.

A particle accelerating in a gravitational field can increase its rate of acceleration only to the extent allowed by its own field which is left behind owing to the fact that no signal can be propagated at infinite velocity. The field cannot follow its center instantaneously and is therefore distorted in such a way as to prevent further increase in the rate of acceleration by self-interaction. Two different test masses will fall at the same rate in a given gravitational field since it is the rate of acceleration which causes the distortion and not the mass itself.