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The Imagineer's Chronicles:
A theoretical blog
Gravitational forces are caused by a curvature in a three-dimensional space manifold with respect to a fourth *spatial* dimension 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.
Chapter two defined the quantum properties of mass in terms of a resonant system generated by a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
Chapter ten showed forces can be derived in terms of a displacement in a "surface" of a three-dimensional space manifold.
Therefore, if one can derive gravity in terms of a displacement in a "surface" of a three-dimensional space manifold one may be able to define a physical link between it and the quantum properties of mass. This is because they would share a common element in that the peaks and valleys of matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension that defined a particles energy in Chapter two also cause a displacement in that surface.
One can understand how a curvature in a three-dimensional space manifold causes gravity comparing it to a marble and rod on a 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.
As mentioned earlier Chapter ten derive all forces in terms of a curvature or displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Therefore, objects will experience a force generated by a curvature in a "surface" of three-dimensional space directed towards the apex of that curvature. This force is called gravity.
This force is analogous to the force which caused the marble to roll towards the apex of a curvature in the "surface" of the rubber diaphragm.
However, the force on the marble is a result of its displacement of a two dimensional surface with respect three-dimensional space whereas gravity is the result of a displacement of a three-dimensional volume or manifold with respect to a fourth *spatial* dimension.
Some say that is it impossible to define gravitational forces only in terms of the geometry of four *spatial* dimensions.
However, observations of our environment indicate otherwise.
We observe that 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 independently with respect to each axis of three-dimensional space.
Similarly we observe we can move or rotate three-dimensional objects independently in any direction in three-dimensional space.
This suggests each axis of three-dimensional space may be embedded in a universe consisting of four *spatial* dimensions. 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.
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 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 three-dimensional space 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 a curvature in a "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 suggest that gravity may be a result of a spherical curvature in a "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension.
Additionally it shows is possible to derive gravity in only in terms of the geometry of four *spatial* dimensions.
The difference between gravitational and electromagnetic force is related to the causality of the physical mechanism responsible for their generation.
Electromagnetic forces were defined in Chapter eleven in terms of a slope caused by the "peaks" and "valleys" of a matter 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 with respect to a fourth spatial dimension. 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
because it extends the reality of
one's environment.""
Copyright 1995 Jeffrey O'Callaghan