We have shown throughout The Imagineer’s Chronicles there would be many theoretical advantages to defining the universe in terms of four *spatial* dimensions instead of four-dimensional space-time.

One of them is it would allow for a common theoretical explanation of gravity and how space is expanding.

In 1915, Albert Einstein wrote the General Theory of Relativity, which defined how gravity works.  He showed that gravity could be explained in terms of a curvature in a "surface" of a four-dimensional space-time manifold. 

However, when he applied his theory to the whole universe, he found that it predicted space should not be stable.

Later, in 1929 Edwin Hubble determined the redshifts of a number of distant galaxies and their relative distances and found it increased as a linear function of their distance.  The only explanation for this observation is that the universe was expanding.

These observations made by Hubble confirmed Einstein theoretical predictions that his four-dimensional space-time geometry was unstable and that it was expanding.  However, neither he nor Einstein could define how or in what direction this expansion was occurring.

This is because Hubble’s observation showed three-dimensional space was not expanding through a time dimension but in a spatial one.  Therefore, one must add dimensions to Einstein’s gravitational theory to explain how three-dimensional space can be undergoing a uniform spatial expansion.

However, if one could, as done in the article "Defining gravity" Dec 15, 2007 define it and the relativistic properties of motion, as was done in the article "The relativity of four *spatial* dimensions" Dec. 01, 2007 in terms of a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of one in a four-dimensional space time manifold one could replace the time dimension with a spatial one.

But if true one should also be able to explain how and why the expansion of the universe is so uniform in terms of four *spatial* dimensions. 

As was shown in the article “Embedded Dimensions" Oct. 24, 2007 each axis of three-dimensional space is scalar invariant with respect to a fourth *spatial* dimension.  Therefore, the movement of any point in three-dimensional space with respect to a fourth *spatial* dimension would result in the expansion of three-dimensional space around that point. 

One way of understanding how this would be to compare it to the expansion of a balloon’s surface. 

As a balloon is inflated, the length and width of its surface expands around a point on it.  However, the magnitude of this expansion is not defined by its movement through three-dimensional space but by the bending or curvature caused by its movement in it.  This is illustrated by the fact that the surface of a balloon only stretches when its curvature is increased by inflation and not when one moves it in its entirety to a different point in space.

This shows that the expansion of each axis of the surface of a balloon is scalar invariant with respect to its movement in a third dimension.

A similar effect would occur if three-dimensional space were scalar invariant with respect to a fourth *spatial* dimension.  Its movement "outward" with respect to a fourth *spatial* dimension would result in a uniform stretching of the three-dimension around a point in three-dimensional space.

Therefore, one could understand how space is expanding and eliminate the problem of having to explain why, as mentioned earlier it is so uniform if one assumes three-dimensional space is expanding towards a fourth *spatial* dimension and that it’s individual axes are scalar invariant with respect to it.

However, this also provides a theoretical connection gravity and the observed properties of an expanding universe because it defines both in terms of a common mechanism related to the existence of a fourth *spatial* dimension.  This is  because if three-dimensional space is scalar invariant with respect to a four *spatial* dimension, the movement of a point in three-dimensional space "inward" with respect to it would result in its "contracting" spherical along all three-dimensional axis.  This contraction would result in a force being directed towards its center, which can be shown, as was done in the article “Gravity in terms of four *spatial* dimensions” Jun 01, 2009 to be responsible for gravity.

This cannot be done as mentioned earlier if one assumes as Einstein did that gravity is caused by a curvature in a space-time manifold because one cannot define the spatial expansion of the universe in terms of only three spatial and one time dimension.

Later Jeff

The *Shadows* of four spatial dimensions

Copyright 2010 Jeffrey O’Callaghan

(In a PDF format)