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We have shown throughout this blog and its companion book “The Reality of the Fourth *Spatial* Dimension” there are many observations suggesting space is composed of four *spatial* dimensions instead of four-dimensional space-time.

The expansion of the universe is one of them.
The Standard Model of Cosmology and Particle Physics defines the structure of the universe and the creation of subatomic particles based on the existence of an expanding universe.

This is based on a discovery made by Edwin Hubble that distant galaxies are moving away from us.  They also believe the universe began with a “Big Bang” because if one traces the motion of these galaxies back in time they merge at point in the past.

Alexander Friedmann developed the theoretical foundations for this expansion when he realized a solution to Einstein’s field equations describes an expanding universe, which starts from a point (called a singularity) whose radius expands with time to become the universe, as we know it today.

As mentioned earlier the observation, that the universe is expanding and Friedmann’s solutions provide the foundation for the Big Bang Theory and the Standard Model of Cosmology and Particle Physics, which for the past 25 years has given us a complete mathematical description of the particles and forces that shape our world.  It predicts with such accuracy the observable microscopic properties of particles and the macroscopic cosmologic properties stars and galaxies that many physicists believe it is the ultimate theory of mass and energy.

One can understand how an expanding universe could explain the observations made by Hubble by using an analogy of an ant living on a surface of a balloon.  First, one must imagine that it can only move on the surface of a huge balloon, which to his understanding is the total extent of universe.  At an early stage of the balloon-universe, the ant measures distances between separate points on the balloon, which serves as his standard.  As the balloon is inflated, the distance between the same points is measured and determined to be larger by a proportional factor.  The surface of the balloon still appears flat, and yet all the points have appeared to recede from the ant, indeed every point on the surface of the balloon is proportionally farther from the ant than it was earlier.

Similarly, galaxies in our universe would appear to be receding from us if the universe was a expanding for the same reason that the points on the balloon receded from the ant as his or her universe expands.

As mentioned earlier the Standard Model successfully answers many of the questions regarding the cosmological structure of the universe and the creation of subatomic particles based on the existence of an expanding universe.

However, for all of it successes it has one very obvious shortfall in that it does not answer the question or define “What is the universe expanding into?”

But there are some who say that it would not make any sense to ask that question for the same reason that it would not make any sense for the ant in the earlier example to ask what his “universe” is expanding towards because similar to the ant who will never be able understand or observe the universe his world is expanding towards; we as three-dimensional beings could not understand or observe the universe our world is expanding through.

This would be true if physicists and cosmologists had not used the concept of the dimensional interactions, which they associate with a physically expanding universe to develop the abstract mathematical basis for Standard Model of Cosmology and Particle Physics.  However, because it is based on the assumption that the universe is expanding, what it is physical expanding towards must have an effect on the mechanics of their model.  Therefore, it should be able to define what is expanding towards.

As mentioned earlier, many believe that we cannot understand the properties of universe that is outside of the one we are confined to.

However, even though we are confined to our three-dimensional universe we can get an understanding of what it is expanding towards by observing the effects of this expansion on our universe.

For example, we know that three-dimensional space is expanding towards a higher spatial dimension not a time or space-time dimension because the observations made by Hubble indicate the universe is expanding spatial.

Unfortunately the General Theory of Relativity contains only three spatial and one time dimension.

Therefore, to explain the observed spatial expansion of three-dimensional space one would have to assume the existence of a another *spatial* or fourth *spatial* dimension in addition to the three spatial and one time dimension that Einstein’s theories contain to account for that observation.

This would be true if Einstein had not given us a means of converting the geometric properties of his space-time universe to one consisting of only four *spatial* dimensions.

Einstein defined the geometric properties of a space-time in terms of a dynamic balance between mass and energy defined by the equation E=mc^2. However when he used the constant velocity of light in that equation to define that balance he provided a method of converting a unit of time in a space-time environment with unit of space in four *spatial* dimensions. Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

Doing so not only allows one to understand in terms of Einstein’s General Theory Relativity how three-dimensional space can be expanding towards a higher or fourth *spatial* dimension but also allows one to define the mechanism responsible for that expansion.

For example the one to one to quantitatively and qualitative correspond between the time properties of energy in a space-time universe and its spatial properties in one of four *spatial* dimensions is the bases of assuming as was done in the article “Defining energy” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

In other words one can use Einstein’s equations to quantitatively define energy in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimensions instead of one in a space-time environment.

However we know from the study of thermodynamics that energy flows from areas of high to ones with low density very similar to how water flows form an elevated or “high density” point to a lower one.

For example if the walls of an above ground pool filled with water collapse the elevated two-dimensional surface of the water will flow or expand and accelerate outward towards the three-dimensional environment sounding it.

Yet we know from observations of the cosmic background radiation that presently our three-dimensional universe has an average energy component equal to about 3.7 degrees Kelvin.

However this means that according to concepts developed in the article mentioned earlier “Defining energy”  the three-dimensional “surface” of our universe which has an average energy component of 3.7 degree Kelvin would be elevated with respect to a fourth *spatial* dimension.

Yet this means similar to the two dimensional surface of the water in the pool three-dimensional space will flow or expand outward in the four dimensional or space time environment that Einstein showed us surrounded it.

This shows that one can developed a complete understanding of what three-dimensional space is expanding towards in terms of Einstein’s General Theory of Relativity if one redefines it in terms of it spatial properties.

However this is not possible in a universe consisting of only four dimensional space-time because time or a space-time dimension it does not possess the spatial properties required to define the observed properties of its spatial expansion.

Later Jeff

Copyright Jeffrey O’Callaghan 2008

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