History has shown the advantages to reformulating or expanding an existing theory or law to a wider environment.
For example Kepler’s Laws are wonderful as a description of the motions of the planets. However, they provide no explanation of why the planets move in that way. Moreover, Kepler’s Third Law only works for planets orbiting the Sun and does not apply to moon’s orbiting around the planets.
However 1686, Isaac Newton presented his three laws of motion in the “Principia Mathematica Philosophiae Naturalis” which provided a more general explanation Kepler’s laws and allowed them to be applied not only to of the motions of the planets but also to those of their moons.
This is primarily because Kepler developed his laws directly from the quantitative observational records given to him by Tycho Brahe and did not attempt to generalize them. Additionally he was unable or did not try to understand why those numbers appeared in nature but only to find a way of making the fit them into the consistent mathematical structure we now call Kepler’s laws.
However Newton was able to reformulate them by defining a gravitational mechanism that not only provide a theoretical understanding of their validity but also expanded, as mentioned earlier their domain to a much broader environment.
There are many aspects of modern physics that might gain the same benefits from the reformulation of existing ideas.
One in particular would be Einstein theories because it may allow one to derive a theoretical understanding of the casualty of Dark Energy and what Dark matter is.
Dark Energy or the mysterious force that is causing the accelerated, spatial expansion of the universe does not appear to be integrable into any of the currently accepted theoretical models of our universe.
This is true even though Einstein foresaw its existence when he used his intuition to arbitrarily insert a term, called a cosmology constant into his General Theory of Relativity that would create an expanding force very similar to that of Dark Energy. Similar to Kepler he based this addition only on the observational records of his time that suggested space was static and unchanging and not on any theoretical principal. Additionally like Kepler he either could not or did not try to integrate it or explain why it exists in terms of a theoretical model.
However there are some who feel that we may be able to use his intuitive genius and the concept laid down in his space-time theories to understand the causality of spatial expansion associated with Dark Energy even though Einstein called the insertion of his cosmological constant “His big blunder” when it was discovered that the universe was not static.
As mentioned earlier Einstein either could not or did not try to conceptually integrate his cosmological constant or an expansive force now called Dark Energy into the theoretical structure of Relativity possibly because, as mentioned earlier they are both related to how three-dimensional space expanded or was prevented from contracting with respect to a higher spatial dimension not a time or space-time dimension.
Therefore to understand Dark Energy in terms of Einstein space-time theory one would have to add a new *spatial* dimension to the three that it already contain to define its spatial properties thereby significantly increasing the complexity of its theoretical structure.
This would be true if Einstein had not given us the ability reformulate his space time theories in terms of four *spatial* dimensions when he 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.
As was just mentioned 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 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.
As mentioned earlier it is difficult to integrate and define the causality of why three-dimensional space is expanding towards a higher *spatial” dimension into Einstein space-time universe because it does not define a higher spatial dimension.
However one can easily integrate it into one consisting of four *spatial* dimensions because of the fact that it would allow three-dimensional space to expand toward a higher fourth *spatial* dimension.
In other words if one reformulates Einstein’s equations and quantitatively defines 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 one can understand how the observed spatial expansion of three-dimensional space associated with Dark Energy can occur.
We know from the study of thermodynamics 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.
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.
This shows how reformulating Einstein space-time concept in terms of four *spatial* dimension can provide a theoretical understanding of the accelerative force called Dark Energy which can be generalize to broader environment than a space-time universe.
For example observations tell us that five to seven billion years ago, the expansion of the universe stopped slowing due to gravity and started to accelerate due to Dark Energy.
However this is exactly what one would expect if the theoretical model outlined above was correct because in the early universe the distance between it mass components was small relative to the its energy components. Therefore gravitational forces would predominate. However because gravitation force decease with the square of the distance there would come a time when the expansive forces associated with Dark Energy would be predominate because they would, according the above model decease linearly with respect to gravities.
This shows why reformulating Einstein’s space-time universe into one of four *spatial* dimension allows it to be applied to a more broader more generalized environment and provide a theoretical understand of why we presently observed the expansive forces of Dark Energy overtaking the slowing force of gravity.
It should be remember Einstein’s genius allows us to chose weather to solve problems, such those associated with Dark matter or Dark Energy in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of energy/mass and the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the spatial as well as the time properties of our universe similar to how Newton laws of gravity broaden domain of Kepler’s laws of planetary motion to their moons.
Later Jeff
Copyright Jeffrey O’Callaghan 2013