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In 1998 the Hubble Space Telescope when observing distant supernovae discovered that the Universe was expanding more slowly in the past than it is today. In other words the Universe has not been slowing due to gravity, as everyone thought, it has been accelerating.  No one expected this, no one knew how to explain it.

Eventually theorists came up with three sorts of explanations for what has come to be called Dark Energy.  Maybe it was a result of a long-discarded version of Einstein’s theory of gravity, one that contained what was called a “cosmological constant.” Maybe there was some strange kind of energy-fluid that filled space. Maybe there is something wrong with Einstein’s theory of gravity and a new theory could include some kind of field that creates this cosmic acceleration. Theorists still don’t know what the correct explanation is, but they have given the solution a name. It is called dark energy.


However it can be shown that the currently accepted version of Einstein’s General Theory of Relative not a discarded one can explain why the universe expansion is accelerating.

However one of the difficulties in integrating the expansive force called Dark Energy into Einstein’s space-time universe is that observations tell us that three-dimensional space is expanding towards a higher spatial dimension not a time or space-time dimension.  

Therefore to explain the observed spatial expansion of the universe one would have to assume the existence of a fourth *spatial* dimension in addition to the three spatial dimensions and one time dimension that Einstein’s theories contain.

This would be true if Einstein had not given us a means of quantitatively 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 universe 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  he provided a method of converting a unit of energy he associated with time in a space-time universe to a unit of space in one consisting of only 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 quantitative means of redefining his space-time universe in terms of geometry of four *spatial* dimensions.

Observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein’s one must assume that energy also must have spatial properties.

As mentioned earlier Einstein equation E=mc^2 tell us there is a dynamic relationship between the geometric properties of our universe and mass/energy in that when one coverts mass to energy in a closed three-dimensional *spatial* environment, the space it is made up of expands while if one coverts energy to mass that environment contracts.  Yet it is difficult to understand how three-dimensional space can both expand and contract in a space-time universe because our experiences tell with time tells us that it only moves in one direction forward.  However it is easy to understand how it could in one consisting of four *spatial* dimension because our experiences it tell us that we can move in two direction in a spatial environment up down forwards of backwards.

The fact that one can use the equation E=mc^2 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 displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimensions.

We know from the study of thermodynamic that energy flows from areas of high density to area of 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 and that the force associated with that expansion will decline as its surface spread out.

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 “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 and that the force associated with that it will decline as it surface increases. 

This shows one can explain what the force called dark energy is and why it is causing the accelerated expansion of the universe in terms of the geometry of four *spatial* dimension.

However it should be remembered this solution was derived directly from Einstein’s current General Theory of Relativity not a discarded one.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

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