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To establish a physical link between gravitational and kinetic energy requires an understanding of their causality.
Chapter one postulated the universe is made up of four *spatial* dimension instead of four-dimensional space-time.
Chapter fifteen defined the causality of kinetic energy in terms of a "slope' of a curvature of an "elevation" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
Chapter twelve derived the causality gravitational forces in terms of a "slope" of a curvature of a “depression” in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
(This "curvature" or "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension responsible for gravitational forces is analogous to a curvature in a space-time manifold that Relativity postulates is responsible for gravitational forces.)
The link between gravitational and kinetic forces can be understood by comparing the effects a “slope” in a "surface" of a three-dimensional space manifold have on an object in three-dimensional space to the effects the slope an inclined plane have on a marble.
The direction of the downward force or acceleration experienced by a marble on an incline is proportional to the slope of the incline which in tern is proportional the magnitude of the elevation in the incline.
Chapter fifteen showed the magnitude of a "slope" of the "elevation" in a "surface" of a three-dimensional space manifold would be directly related to velocity or kinetic energy of an object.
This means the forces or accelerations caused by the interaction of the kinetic energy of two moving objects would be directed away from those objects because the direction of the force would be away from the apex of the "elevation" in a "surface" of a three-dimensional space manifold. Additionally, the magnitude of those forces would be directly related to the kinetic energy of the interacting objects because the magnitude of the "slope" in a "surface" of a three-dimensional space manifold is directly related to the magnitude of the kinetic energy of an object.
This is analogous to how the magnitude and direction of the downward acceleration of the marble on the incline in the earlier example was proportional to the slope of the incline.
Chapter twelve derived gravitational force in terms of a "slope" generated by “depression” in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. It was shown the magnitude of a "slope" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension generated by that "depression" is proportional to mass of an object.
Therefore, the magnitude of force or acceleration experienced by an object in three-dimensional space due to an interaction with the "slope" of a gravitational "depression" in a "surface" of a three-dimensional space manifold would be proportional to the mass of that object.
However, the direction of the forces or accelerations associated with the "slope" of a gravitational "depression” in a "surface" of a three-dimensional space manifold will be oppositely directed with respect to the accelerations or forces generated by a Kinetic energy "elevation" in a "surface" of a three-dimensional space manifold.
This is because an object interacting with a gravitational "depression" would attain acceleration towards, not away, from the object it is interacting with.
This defines causality of gravitational and kinetic forces in terms of common “incline” or "slope" in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
The mechanism responsible for gravitational forces is derived in terms of an "incline" caused by a “depression” in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. This results in a force being directed towards the apex of the "depression" in a three-dimensional space manifold associated with the mass of an object.
While the mechanism responsible for forces associated with kinetic energy is derived in terms of a similar "incline" caused by a "elevation" in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. This results in a force being directed away from the apex of the "elevation" in a three-dimensional space manifold associated with the velocity of an object.
Principle of Equivalence or the inability to distinguish gravitational and kinetic or non-gravitational forces is due to the relative characteristics of the "inclines" generated by a kinetic energy "elevation" and a gravitational "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension .
In Chapter fifteen, the forces associated with kinetic energy or non-gravitational forces such as those generated by a rocket engine were defined in terms of the absolute magnitude of a *slope* in a three-dimensional space manifold caused by an "elevation" in a "surface" of a three-dimensional space with respect to a fourth *spatial* dimension.
In Chapter twelve, the forces associated with gravitational forces were defined in terms of the absolute magnitude of a "slope" in a three-dimensional space manifold generated by a "depression" in a "surface" of a three-dimensional space with respect to a fourth *spatial* dimension.
Since the absolute magnitude of a "negative slope" generated by a "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would be indistinguishable form the absolute magnitude of a "positive slope" generated by an "elevation" in the "surface" of a three-dimensional space manifold gravitational and non-gravitational or kinetic forces are indistinguishable.
This defines a physical link between gravitational and kinetic energies in terms of their casualty and in terms of the absolute magnitude of a slope in a common curvature in four *spatial* dimensions.
“The
universe's most powerful enabling tool is
not knowledge or understanding
but
imagination"
Jeffrey O'Callaghan