We have shown throughout this blog and its companion book “The Reality of the Fourth *Spatial* Dimension” there are many theoretical advantages to defining the universe in terms of four *spatial* dimensions instead of four-dimensional space-time.
One is that it would allow one to derive a mechanism responsible for Dark Energy by extrapolating the laws of classical physics in a three-dimensional environment to a fourth *spatial* dimension.
On May 30, 2004, physicsworld.com reported, in the article Dark Energy that “New evidence has confirmed that the expansion of the universe is accelerating under the influence of a gravitationally repulsive form of energy that makes up two-thirds of the cosmos.
But since its discovery, no one has been able to define a mechanism that can account for its existence in terms of four-dimensional space-time.
However, we may be able to understand why by observing how it interacts with our three dimensional environment.
For example we know form observations that it is not causing three-dimensional space to expand towards a time but a spatial dimension.
Unfortunately Einstein theories only contain three spatial dimension and one time dimension.
Therefore, to explain the observed spatial expansion of the universe 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.
In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.
The fact that the equation E=mc^2 allows us to quantitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is one 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.
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.Â
However this means that according to concepts developed in the article “Defining energy” (mentioned earlier) 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 accelerate and flow or expand outward in the four dimensional environment surround it.
This shows that how one can derive the mechanism responsible for the observed properties of Dark Energy in terms Einstein’s General theory of Relativity by converting or transposing his space-time universe to its equivalent in four *spatial* dimensions.
It should be remember that Einstein’s genius allows us to choose whether to describe the properties of our universe in either a space-time environment or one consisting of four *spatial* dimension when he defined its geometry in terms of the constant velocity of light.
Later Jeff
Copyright 2009 Jeffrey O’Callaghan