There are many axioms that we must accept as a part of modern science including: the dual nature of light, the Heisenberg Uncertainty Principle, the inverse squared relationship of gravity with respect to distance, and, as mentioned in the previous chapter, the Equivalence Principle.
As we discussed back in Chapter 18 on Relativity, the Equivalence Principle roughly states that gravitational mass and inertial mass are the same. While this is fundamental to our understanding of space and time, it has never been proven, and even our dear old Dr. Einstein had to just assume its validity, since he was unable to provide any proof for that assumption.
Of course, this equivalence seems rather obvious to those who don’t study physics. Mass is mass, and just because it sticks to the ground and/or is hard to get started moving, these are just characteristics of mass as it always appears to us, and to the common person, this does not require any additional justification.
But to the physicist, it does; otherwise, Dr. Einstein would not have made such a big deal out of offering it as an assumption.
And, although the author is not offering any reasons for the causes of gravity from mass, the examples from the previous chapter do tend to show that the need for making an assumption that gravitational mass (that is; the mass that is affected by gravity) and inertial mass are the same is superfluous, because, if one assumes that the force of gravity is created by the influence of an acceleration field, then the mass itself need be no different from that mass that is affected by any ordinary force, since, as Newton stated so long ago, it is inertial mass that is affected by acceleration.
Inertial mass is mass. All mass has inertia, and no differentiation between classes is required.
From this perspective, the effects of acceleration and gravity on mass not only appear to be the same, they have the same mathematical basis. The force is created by a change in the velocity of the surrounding field with respect to the subject (inertial) mass.
This means, that when it comes to the expressed force, there is no requirement to differentiate between inertial and gravitational mass, because all of the force effects are due to the interaction between an acceleration vector and an inertial mass.
The effects of gravity and acceleration appear to be the same because they are the same. By eliminating force from the fundamental equation we do not need to consider whether it is potential or expressed, or whether or not there is a gravity field, without other reference objects. Without the presence of a secondary mass, the velocity and acceleration vectors just exist, they can create no force. They are not dependent on the secondary mass for their definition.
Furthermore, this new formulation for gravity explains why unequal masses are affected with unequal force but equal acceleration. Things fall at the same rate regardless of their weight because they must, because the acceleration vector affecting them has the same value. The force is a product of any specific mass times that vector. The acceleration is determined by the change in the velocity of the field.
This also explains why a body becomes weightless in free fall. For, if a mass is traveling and accelerating with the vector potential of the field, it will feel no other acceleration and will experience zero gravity. The field velocity is immaterial to this relationship, since velocity does not interact directly with mass; only acceleration does (except at relativistic speeds and then, only to the outside observer).
The premise for these expressions is that the acceleration, a vector, is established by and dependent on the gradient of the more fundamental quantity, the velocity vector. This supposition is what allows the derivation of the inverse square relationship to the distance and the elimination of the need for the Equivalence Principle.
Therefore, by assuming that the gravitational field may be expressed as an expanding surface velocity integral, the concepts of acceleration and gravity can be shown to all have the same basic mathematical formulation. By placing the emphasis of the source measurement on velocity, one can unify those two seemingly disparate forces: linear accelerational force (F=ma), and gravity (F=mg), into one comprehensive concept that does not require the imposition of extraneous rules such as the ‘inverse squares’ law or the Equivalence Principle.