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The Imagineer's Chronicles: A theoretical blog
Gravitational forces are caused by a "depression" or curvature in four *spatial* dimensions and not by a curvature in a space-time manifold as postulated by the "General Theory of Relativity".
Chapter one postulated space is composed of four *spatial* dimensions and a continuous non-quantized form of mass.
Chapter eight showed the relative masses of a proton and electron were the result of a curvature in a "surface" of a three-dimensional space manifold caused by energy gradients in a continuous non-quantized form of mass.
How and why energy gradients cause a curvature in a "surface" of three-dimensional space manifold with respect to a fourth *spatial* dimension can be understood by comparing them to the energy gradients called high pressure areas in the earth's atmosphere.
The downward movement of the air molecules in high-pressure area generates a downward force on the "surface" it contacts causing it to become depressed or curved.
A similar affect occurs in four *spatial* dimensions where the energy of a continuous non-quantized form of mass is directed "downward" towards the "surface" of a three-dimensional space manifold.
The energy that is directed "downward" or "perpendicular" to a "surface" of a three-dimensional space manifold will cause its "surface" to become "curved" with respect to a fourth *spatial* dimension.
(The curvature in space is analogous to the space-time curvature "The General Theory of Relativity" uses to define the force of gravity. However, they differ in that "Shadows" defines this curvature in terms of four *spatial* dimensions instead of four-dimensional space-time.)
How a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension effects objects in three-dimensional space can be understood by comparing it to a marble and a rod on surface of a rubber diaphragm.
The marble on the diaphragm will represent a particle or object on a "surface" of a three-dimensional space manifold and the rod will represent the “W” axis of a fourth *spatial* dimension.
(The "W" axis of a fourth *spatial* dimension was defined earlier in Chapter ten.)
If the end of the rod is orientated perpendicular to the "surface" of the diaphragm and is allowed to touch it without putting any pressure on it, the surface of the diaphragm will remain flat. The marble on the flat diaphragm would not move.
However, if pressure is applied to the rod, the "surface" of the diaphragm will become depressed and will no longer be perpendicular to the rod.
Gravitational forces will then have a tangential component along the "surface" of the rubber diaphragm. The tangential component of the gravitational force directed along the "surface" of the diaphragm will cause the marble to move towards the apex of the depression.
In Chapter ten, the magnitude of all forms of energy was derived in terms of a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
As mentioned earlier "downward" pressure of a continuous non-quantized form of mass will generated a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
The energy (defined in Chapter ten) directed along a curvature in a "surface" of a three-dimensional space manifold is responsible for gravitational forces. It causes particles and objects to "roll" towards the apex of that curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
This is analogous to the marble rolling along the "surface" of the apex of the depression in rubber diaphragm.
The accumulation of a particles at the apex of a "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is responsible for the mass of planets, stars and galaxies.
Some say that is it impossible to define gravitational forces in terms of only four *spatial* dimensions.
However, observations of our environment indicate otherwise.
We observe that we can move independently in any direction in three-dimensional space. This indicates that the axes of three-dimensional space are not fixed to each other but are embedded into each other.
This is why we are not limited in how we can move or change the orientation of a two-dimensional plane such as the surface of a piece of paper in three-dimensional space.
This indicates that our three-dimensional space is embedded in a universe consisting of four *spatial* dimensions in a similar manner. In other words the origins of the axes of a four dimensional universe is not rigidly fix to each other but are embedded in it allowing for the independent movement of each individual axis of four *spatial* dimensions with respect to the other axis of four *spatial* dimensions. Therefore, it would be possible to orient each axes of a "surface" of a three-dimensional space manifold independently of its orientation to the axes of four *spatial* dimensions. This would be analogous to how it is possible to orient a two-dimensional surface of piece of a paper in any way we chose in three-dimensional space.
If we accelerate a two-dimensional surface of a piece of paper through three-dimensional space by pushing on its center, its surface will develop a curvature with respect to three-dimensional space because of the drag generated by the space it is moving through. A two dimensional creature living on the "surface" of the paper would not realize that the surface of the paper is curved with respect to three-dimensional space because he or she could not "look" in that direction.
Similarly if a three-dimensional object is accelerated through a fourth *spatial* dimension, its three-dimensional "surface" will develop a curvature due to the "drag" generated by its movement through four *spatial* dimensions. This is similar to how the surface of the paper developed a curvature due to it movement through three-dimensional space. This curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is the causality of kinetic forces.
We as three-dimensional beings would not be aware the "surface" of a three-dimensional space manifold was curved with respect to a fourth *spatial* dimension because we could not look in the direction of a fourth *spatial* dimension.
We also observe that it is possible to curl a two-dimensional surface into a sphere forming a balloon in three-dimensional space because as mentioned earlier the axes of a two-dimensional surface are not fixed to the axis of our three-dimensional space. Additionally we observe that we can increase or decrease the magnitude of the curvature of the "surface" of the balloon by increasing or decreasing its internal pressure.
Similarly, a "surface" of three-dimensional space manifold can be curled to form a three-dimensional "sphere" in four *spatial* dimensions because axes of the "surface" of a three-dimensional space manifold are not fixed to the axes four *spatial* dimensions. This is analogous to how a two-dimensional surface can be curled to forum a three-dimensional sphere in three spatial dimensions. The force developed by this spherical curvature is responsible for gravitational forces.
Similar to the spherical surface of the balloon curvature in the "surface" of three-dimensional sphere will contract or expand if mass is added to or removed from its center. This will result in increasing or decreasing the magnitude of the curvature in the surface of the three dimensional sphere. This spherical curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is responsible for gravitational forces.
This indicates that gravitational energy could be defined in terms of a magnitude of a spherical curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
The difference between gravitational and electromagnetic force is related to the causality of the physical mechanism responsible for the generation.
Electromagnetic forces were defined in Chapter eleven in terms a slope caused by the "peaks" and "valleys" of a matterenergy wave moving at the velocity of light on a "surface" of a three-dimensional space manifold with respect to a fourth "spatial" dimension. This would cause a tangential "movement" with respect to a "surface" of three-dimensional space of objects affected by a by the "peaks" and "valleys" of a matterenergy wave.
However, gravity is caused by a "perpendicular" force on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension by a stationary "depression" in a "surface" of a three-dimensional space manifold. This will cause the movement of an object along a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension towards the apex of the cone generated in a "surface" of a three-dimensional space manifold.
“The
universe's most powerful enabling tool is
not knowledge or understanding
but
imagination"
Jeffrey O'Callaghan