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.

One possible explanation is that each axis of three-dimensional space is expanding outwards towards another spatial dimension.  This means the universe must be composed of at least six spatial dimensions to allow each of them to individually expand towards another dimension.

This type of expansion is the mathematical basis for the Standard Model of physics which for the past 25 years, has given us a complete mathematical description of the particles and forces that shape our world.  Its predictions have matched experimental data, decimal place for decimal place; with so much precision that many feel it is the ultimate theory of matter and energy.

But if it were true that the uniform expansion of space is a result of each dimension expanding towards another they should be able to explain why we observe it is so uniform.  This is because if each dimension was able to move independently towards another dimension we would expect expansion of space to show some non-uniformity with respect to each dimensional axis.

However, there is another possibility that has largely been ignored by physicists that would answer this question and provide a connection between an expanding universe and gravity.

If the dimensions that comprise our universe are scalar invariant with respect to a single fourth *spatial* dimension the movement of any point in three-dimensional space with respect to a fourth *spatial* dimension would result in the uniform expansion of three-dimensional space around that point. 

One way of understanding how this would explain the uniform expansion of the universe 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 single fourth *spatial* dimension and that it’s individual axes are scalar invariant with respect to it.

In the article "Gravity in terms of four *spatial* dimensions" Feb 1, 2010 it was shown it is possible to explain gravity in terms of a curvature or contraction in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

If three-dimensional space was 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” to be responsible for gravity.

However, this also provides a theoretical connection gravity and the observed properties of an expanding universe because it define both the terms of a common mechanism related to the existence of a fourth *spatial* dimension.

Later Jeff

The *Shadows* of four spatial dimensions

Copyright 2010 Jeffrey O’Callaghan

(In a PDF format)

Write a comment