Dark energy: the cosmological constant

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We have shown throughout this blog and its companion book “The Reality of the Fourth *Spatial* Dimension” observations of our environment suggest the universe is composed of four *spatial* dimensions rather than four-dimensional space-time as is suggested by Einstein’s theories.

The recent discovery of Dark Energy is one of those observations.

As Alexey Vikhlinin of the Smithsonian Astrophysical Observatory in Cambridge, Mass. wrote in the Scientific Frontline article Dark Energy Found Stifling Growth in Universe Dec 16, 2008:

This “study strengthens the evidence that Dark Energy is Einstein’s cosmological constant.  Although a quantum vacuum is the leading candidate to explain Dark Energy, theoretical work suggests it should be about 10 raised to the power of 120 times larger than observed.  Therefore, alternatives to it such as theories involving hidden dimensions are being explored.

However putting all of this data together gives us the strongest evidence yet that Dark Energy is the cosmological constant, or in other words,” said Vikhlinin.  “A lot more testing is needed, but so far Einstein’s theory is looking as good as ever.”

But the fact that Dark Energy or a Cosmological constant was discovered does not alter the fact Einstein introduced it because he was trying to make or “force” the universe to conform to his expectations, rather than using his theory to guide him to an understanding of its properties.

However, it can be shown that the causality of Dark Energy can be seamlessly integrated into his relativistic space time theory if one coverts it to its equivalent one in four *spatial* dimensions because observations of its expansive forces 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 another *spatial* or fourth *spatial* dimension in addition to the three spatial dimensions 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 qualitatively and 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 relationship between mass and energy defined by the equation E=mc^2. However when he used the constant velocity of light to define that balance he provided a method of converting a unit of space he associated with mass to a unit of space-time he associated with energy.  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 the bases for assuming as was done in the article “Defining energy in four spatial dimensions.” Nov 26 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.

As mentioned earlier it is difficult to understand how three-dimensional space can be expanding towards a higher *spatial” dimension in terms of Einstein space-time universe because it does not define a higher spatial dimension.

However it is easy integrate it if one reformulates it, as was done above in terms higher fourth *spatial* dimension.

Yet it also allows one to understand how and why the expansive force called Dark Energy is causing the spatial expansion of our universe in terms of the laws of thermodynamics because it gives one the ability, as mentioned earlier to use his equations to qualitatively and 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 density to one 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 surrounding it while the force associated with that expansion decreases as it expands.

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 surrounding it.

This shows how the causality of Dark Energy can be seamlessly integrated into Einstein relativistic space-time theory if one coverts it to equivalent one in four *spatial* dimensions and why as Vikhlinin pointed.  “so far Einstein’s theory is looking as good as ever” because as of now it is the only one that defines a plausible explanation for its existence.

It should be remember Einstein’s genius allows us to choose to define the universe in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories thereby giving us insight in the causality of its forces.

Later Jeff

Copyright Jeffrey O’Callaghan 2009

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