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

Understanding the origins of the force called of Dark Energy is one of them.

On May 30, 2009, "physicsworld.com" reported in the article Dark Energy, 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."

It also mentioned some researchers suggest Dark Energy is caused by a uniform sea of quantum zero-point energy.  However the problem with this proposal is the zero-point energy density would have to be precisely tuned to a value that is an unbelievable factor of 10¹²⁰ below the theoretical prediction and as of yet no one has been able give a reason why that is consistent with theory.

While others have suggested that it would possible to modify Einstein General Theory of Relativity to incorporate, Dark energy, or a cosmological constant into its theoretical structure.

However, Einstein, because of his preconceived feeling that the universe was static has already tried to integrate a mechanism into it to counter the destabilizing forces of gravity.  He realized a static universe is not sustainable in General Relativity because if the universe were static at one instance in time, then gravity, due to its attractive properties would cause it to collapse.  Therefore, he added a term to it that would counteract it. 

This term, which effectively gives the vacuum a repelling force similar to that of dark energy, came to be called a cosmological constant.

However, he could not develop a theoretical argument to justify incorporating it.  Therefore, to satisfy his preconception that the universe was static he simply added it in an "adhoc" manner.

But if its author could not modify the General Theory of Relativity to incorporate an accelerative force into its theoretical structure it would seem highly unlikely that anyone else would be able to, as was suggested in the "physicsworld.com" article.

However, it may be possible to understand the origins of Dark Energy and theoretically integrate it with gravity if one defines their casualty in terms of the existence of four *spatial* dimensions instead of four dimensional space-time.

We have shown throughout "The Imagineer’s Chronicles" that it is possible to theoretically define a universe in terms of four *spatial* dimensions in such a manner that makes predictions identical to those of Einstein’s theories.  However, unlike his theories it would allow for the seamless integration of the properties of dark energy into its theoretical structure.

Observations of Dark Energy indicate it opposes gravity and that it is causing a *spatial* not a time component of the universe to expand.

The article “Defining energy" Nov. 26, 2007 showed one could theoretically derive all forms of energy including gravitational in terms of a curvature or deformation in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

(This curvature is analogous to a curvature in a four dimensional space-time manifold Einstein predicted was responsible for gravity.)

However, If a gravity is a result of a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension, as we are suggesting then when stars convert mass to energy in nuclear reactions the magnitude of that curvature would decrease.  However, this would result in the expansion of a "surface" three-dimensional space with respect to a fourth *spatial* dimension analogous to how removing the coils or curvature in a rope causes a physical expansion of its two dimensional length when measured with respect to three-dimensional space.  Since this expansion would be in addition to the expansion associated with the Big Bang, it would be perceived as an acceleration.

Additionally the article ”Defining energy" showed one could also derive the temperature or kinetic energy of particles in terms of a curvature in "surface" of a three dimensional space manifold with respect to a fourth *spatial* dimension.  Therefore, as the universe cools the magnitude that curvature would decrease and cause three-dimensional space where that cooling took place to expand for the same reason as a conversion of mass to energy does.  This expansion would be perceived as an acceleration because it would be viewed in addition to the linear expansion associated with the big bang.

This demonstrates one can use a relativistic theory on based on the existence of four *spatial* dimensions to guide them to an understanding of the properties of Dark Energy rather than basing it on expectations as Einstein had to.

The reason Einstein could not integrate it into his theories was that time or a space-time dimension does not have spatial properties required to support the spatial expansion associated with Dark Energy.

However, the "concentration" of Dark Energy relative to gravitational energy would be, according to this mechanism defined by the equation E=mc^2.  This means its strength should be 1/c^2 weaker than gravitational forces.  Therefore, because forces of gravity are much stronger than that of Dark Energy: the space between gravitationally bound objects would not appear to be expanding.

One can also use a theoretical model based on the existence of four *spatial* dimensions to understand why the rate of acceleration appears to be increasing and predicts there should be a crossover where it exceeds the gravitational deceleration caused by the mass density of the universe.  As the universe expands due to the energy of the big bang its mass density decreases, therefore the accelerative properties associated with mass being converted to energy would be larger in proportion to the decelerative gravitational forces. 

This shown that one can seamlessly integrate the observed properties of Dark Energy into a relativistic theory based on the existence of four *spatial* dimensions and why one cannot based four-dimensional space-time.

Later Jeff

The "Shadows" of four spatial dimensions

Copyright Jeffrey O’Callaghan 2009

(In a PDF format)

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