The Imagineer's Chronicles: A theoretical blog

Chapter Ten

A boundary between a
Third and Fourth *spatial* Dimensions

We have postulated that the universe is composed of only four *spatial* dimensions and that all of the forces of nature are due to a distortion or curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

We can use an analogy of a two-dimensional creature living on surface of a piece of paper to explain how and why a curvature in a "surface" of at three-dimensional space manifold is responsible for the force of nature.

A two dimensional creature "living" on the surface of a piece of paper would not be aware the paper he was living on existed in a three-dimensional universe because his field of vision would be limited to surface or length and width of the paper.

Therefore, he or she would not be aware of the existence of the dimension of height or the third *spatial* dimension because he or she could not look in the direction of a third *spatial* dimension.

As will be shown latter, the energy three-dimensional beings use to activate their senses does NOT travel through a fourth *spatial* dimension but only on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, similar to the two-dimensional creature, the field of vision of three-dimensional beings would be limited to the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This means three-dimensional beings would not be aware of the existence of a fourth *spatial* dimension because they cannot "look" in the "direction" of a fourth *spatial* dimension.

But before we begin exploring a universe consisting of four *spatial* dimensions we must first have an understanding of how they are orientated.

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.

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.  It will be shown in Chapter fifteen that 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. 

It will be shown in Chapter twelve this spherical curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is responsible for gravitational forces.

In Chapter one it was postulated that space is composed four *spatial* dimension and a continuous non-quantized form of mass.

it will be shown that a curvature or distortion in a "surface" of a three-dimensional manifold caused energy gradients in four *spatial* dimensions is the causality of all forms of energy.

How and why an energy gradient in four *spatial* dimensions can distort a "surface" of a three-dimensional space manifold would be analogous to how and why the "surface" of a liquid in a barometer is distorted by the energy of air molecules in high and low pressure areas in the earth's atmosphere.

Although high and low-pressure areas have properties of three-dimensional space because they extend vertically into the atmosphere, they affect the two-dimensional surface of a liquid in a barometer.

In a high-pressure area, the surface of the liquid in a barometer becomes depressed or distorted because the energy of the air molecules is directed downward towards the surface of the liquid.

While in areas of low atmospheric pressure, the surface of the liquid in a barometer becomes elevated with respect to where it would be in a high-pressure area because the pressure is directed upward away from the surface of the liquid.

This is a result of the transfer of the energy associated with the three-dimensional high or low-pressure areas to the two-dimensional surface of the liquid. 

Similarly, the energy of a continuous non-quantized form of mass will generate four dimensional high and low "energy volumes"  in a three-dimensional space similar to the high and low pressure areas in the earth's atmosphere.

In a four-dimensional “high-energy volume”, the "surface" of a three-dimensional space manifold becomes "depressed" with respect to a fourth *spatial* dimension because the “energy pressure" is directed “downward” towards the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This would be analogous downward force of the three dimensional high-pressure area in the earlier example depressing the two-dimensional surface of the liquid in a barometer.

Conversely in a four dimensional “low energy volume” the "surface" of a three-dimensional space manifold becomes "elevated" with respect to where it would be in a four-dimensional high energy volume because the "energy pressure" is directed “upward” away from the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

These "elevations" or "depressions" in a "surface" of a three-dimension space manifold with respect to a fourth *spatial* dimension are the causality of all of the forces of nature.

How and why this is true can be understood by using the earlier analogy involving the paper.

As mentioned earlier the orientation of the x and y plains of a surface of a piece of paper are not fixed to the dimension of height or the vertical plain of three-dimensional space because the paper can be pick up, rotated, or distorted with respect to three-dimensional space.

This causes its surface to become distorted with respect to the z or third dimension plain.  The force of gravity would then have tangential components relative to its surface because it surface it curved or distorted with respect to the three-dimensional forces associated with gravity.

Similarly as mentioned earlier the x, y, and z planes of three-dimensional space fixed to the axis of four-dimensional space.  Therefore, a "surface" of a three-dimensional space manifold could be "curled" or distorted with respect to the axis of four-dimensional space.

The tangential component of the energy associated with a distortion in "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is responsible for the forces of nature. 

This would be analogous to how gravitational forces would be developed along a distorted surface of a piece of paper in the earlier example. 

 (This "curvature" or distortion in the "surface" of a three-dimensional space manifold with respect to the fourth *spatial* dimension is analogous to the space-time curvature that Einstein postulated was responsible for the force of gravity in his General Theory of Relativity.)

One might ask how the geometry of four-dimensional space can be altered from three-dimensional space to account for the forces of nature.

This question can be answered by using the earlier analogy involving a barometer.

If the liquid in the barometer used in the earlier analogy were allowed to boil, the pressure on the two-dimensional surface of the liquid would increase because the boiling liquid, in the form of vapor, would expand towards the three-dimensional volume above the surface of the water.  This would increase the pressure on the surface of the water and cause it to move downward or become "distorted" with respect to three-dimensional space.

Similarly Chapter twelve will show that when mass is converted to energy, the energy "expands" towards a fourth *spatial* dimension.  This results in increasing the "pressure" on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension causing it to become distorted with respect to a "vertical" or "W" axis of the fourth *spatial* dimension.

If the "expansion" of mass to energy is directed only along one of the three axes of three-dimensional space, the "pressure" and the force this "pressure" causes will result in acceleration along that axis.

Another way of describing how objects in a third *spatial* dimension can have an affect on a fourth *spatial* dimension is by comparing the mechanism responsible for their interactions with a fourth *spatial* dimension to that of a steam engine.

In a steam engine, water expands in the form of steam from the two-dimensional surface of the water.  This expanding steam generates a force that distorts the two-dimensional geometry of the surface of a piston by causing it to move with respect to vertical axis of four *spatial* dimensions.

As mentioned earlier when mass is converted to energy, it “expands", in the form of energy, from the three-dimensional "surface" of the mass in the "direction" of a fourth *spatial* dimension.  This expanding mass, in the form of energy generates a force on a "surface" of a three-dimensional causing it to "move" with respect to the "vertical" or "W" axis of the fourth *spatial* dimensional.

This is analogous to how the steam in a steam engine generates the force on the surface of the piston that results in the two-dimensional surface of a piston to move or become distorted with respect three-dimensional space.

Again, we can use the analogy of a two-dimensional creature to understand how and why the energy "contained" a three-dimensional mass can alter the geometry of three-dimensional space with respect to the fourth *spatial* dimension.

However instead of "living" on the surface of a piece of paper as in the earlier example, the two-dimensional creature will be “living” on the surface of water which will also be considered the surface of a piston in a steam engine.

If the water were heated to the boiling point the steam would expand towards the volume above the surface of the water putting pressure on the surface of the water or piston causing it to move with respect to vertical axis of three-dimensional space. 

However, the two-dimensional creature living on the surface of the water or piston could not directly tell where the steam had originated that was causing the geometry of the surface of the piston to move with respect to three-dimensional space because, as mentioned earlier he or she could not "look" down in the direction that it was coming from.

But, if the two-dimensional creature had placed marks on the wall of the piston he or she could indirectly tell the geometry of the surface of the water or piston had changed by looking along the surface at those marks as the piston moved passed them.

He or she could determine the distance the surface of the piston had moved because he or she could "see" and count the marks on the wall of the piston as the surface of the piston passed them.  Since the magnitude of the force on the surface of the piston determines the distance it would move the two-dimensional creature would then have a way of determine the total force on the surface of the piston by counting these marks.

Just as a two dimensional creature cannot look down to see the volume of water below its surface where the steam originates from, we as three-dimensional beings cannot look “down” to see the "volume" of mass below a "surface" of a three dimensional space manifold where energy originates from.

When mass "expands" to energy it generates a force on a "surface" of a three-dimensional space manifold, which results in its "surface" "moving" with respect to a fourth *spatial* dimension.

The "separation" in the "surfaces" of two three-dimensional space manifolds with respect to a fourth *spatial* dimension caused by this movement defines the relative energy volume or "energy position" between two different volumes of three-dimensional space.

In addition, three-dimensional beings could not directly tell the "surface" of a three-dimensional space manifold had "moved" or become distorted with respect to a fourth *spatial* dimension because three-dimensional beings cannot look in the direction of a fourth *spatial* dimension.

It has been and will be demonstrated throughout this paper that all forces are associated with a "curvature" , distortion or a "spatial separation" in a "surface" of a three-dimensional space manifold with respect to a  fourth *spatial* dimension.  The depth or magnitude of this "curvature" determines the relative magnitude of the forces between two points in space.

“The universe's most powerful enabling tool is
not knowledge or understanding
but imagination"
Jeffrey O'Callaghan

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