Embedded Dimensions

[jeffocal]

We would like to thank everyone who precipitated in the earlier discussion “A four dimensional space manifold?” http://tetraspace.alkaline.org/forum/vi ... &highlight for helping us understand of some of the technical and presentational problems of our paper at http://www.theimagineershome.com/shadows.html . We feel that we have been able to resolve many of them.

One thing that those discussions showed us is that while it is obvious to us why the existence of only four *spatial* dimensions can explain and predict the both the quantum properties of mass and energy and the relativistic properties of space and time, it may not be to others.

Therefore along with our theoretical paper mentioned above we have developed a theoretical blog http://theimagineershome.com/blog/ to explain how the existence of only four *spatial* dimensions can explain and predict different observations of our environment more logically and consistently than the existence four-dimensional space-time.

We hope that we will continue to work together through discussions and comments to promote the acceptance of a “tetraspace” universe to the scientific community.

Thank you

Jeff

Embedded dimensions

In this blog and the paper "The Shadows of four 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.

There are some who say that is it impossible to define gravitational forces in terms of only four spatial dimensions.

However observation 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.

We believe 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 will cause a force to be developed along the "surface" of that three-dimensional space manifold. We as three-dimensional being would not be aware that the causality of this force was a curvature in a "surface" of a three dimensional space manifold with respect to a fourth *spatial* dimension because we could not look in the direction of a fourth *spatial* dimension. However three-dimensional being would be aware of the force because it is directed along the "surface" of 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 our three-dimensional space. Additionally we observe that we can increase or decrease 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 "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.

Observations we make in three-dimensional space indicate that when the internal "pressure" of the "surface" of a three-spatial dimensional "sphere" in four-dimensional space is increased the mass of the object associated with it increases and when we decrease the internal "pressure" the mass of the object decreases. This indicates that gravitational forces may be related to the expansion and contraction of the "surface" of a three spatial dimensional sphere in four-dimensional space.

This is analogous to how increasing or decreasing the pressure in a balloon causes it surface to expand or contract.

Many physicists and mathematicians assume that at least six spatial dimensions are required to explain and predict gravitational forces. This is primarily due to the fact that abstract mathematical equations define the coordinate axes of a gravitational field as being rigidly fixed and perpendicular to each other.

However physical observations of our three-dimensional environment indicate that the origins of axes of dimensional space are not always fixed or perpendicular to each other but are capable of independent movement as is demonstrated by our unlimited ability to move and bend a two-dimensional surface of a piece of paper in three-dimensional space.

Should we allow abstract mathematical equation to define our observations or should we define our abstract mathematical equations based on our observations.
Later Jeff

[wendy]

Downloaded the PDF, see if it's worth the read?

Curvature exists in any manifold, you don't need an extra dimension to house it. All space, of whatever curvature, can exist in a hyperbolic space of higher dimension as a proper curve.

Conversely, deforming a manifold by folding in a higher dimension does not distort its curvature. This happens only by stretching and contracting the surface itself.

Ja guru dev ah, om. Noþing's going to change our world.

[jeffocal]

[quote="wendy"]Downloaded the PDF, see if it's worth the read?

Please keep us posted.

Jeff

[jeffocal]

Downloaded the PDF, see if it's worth the read?

Conversely, deforming a manifold by folding in a higher dimension does not distort its curvature. This happens only by stretching and contracting the surface itself.

Wendy

My apologize for the delay in responding but I wanted to give you a chance to read over the paper so you can put it in context.

This is exactly what we are trying to say. All forces associated with the physical laws of nature are a result of a “stretching” of a three-dimensional space manifold with respect to a fourth *spatial* dimension

I hope that we were able to convey that in our paper.
‘
Please we would appreciate more of your insights.

Jeff