We have shown throughout “The Imagineer’s Chronicles” it is possible to define a universe in terms of four *spatial* dimensions in a manner that makes predictions identical with those of Einstein’s General and Special Theories of Relativity.  Additionally we have shown there would be several theoretical advantages to adopting this perspective over that of his theories. 

One it that it allow one to understand why the universe must be flat

A four dimensional universe can be geometrically open, closed, or "flat" and its shape is dependent on the mass and energy within it.

In an opened universe, there is insufficient matter to halt the expansion initiated by the big bang.  This will result in a saddle shape or open universe, which will continue to expand forever.

In a closed universe, the gravitational potential of its mass is large enough to overcome the expansive forces of the big bang.  This will result in the universe having a spherical shape, which would be destined to collapse.

A universe will be flat if the attractive gravitational potential of matter just equals the expansive energy of the big bang.  This will result in the expansion slowing and only stop after an infinite amount of time has passed.

However, recent observations by NASA’s WMAP satellite has shown the universe is flat to within a 2% margin of error.

But why the universe appears to be flat even after 14 billion years of expansion is still a mystery because a flat universe is like the top of a hill.  If you are a little away from it – a bit open or a bit closed – the expansion of the universe soon drives you far away from this value, just as a ball that is a short distance from a hilltop will roll down to the bottom.  Therefore, when the Universe was one second old, it must have deviated from flatness by less than one part in ten-thousand-trillion (10¹⁶).  This is a problem because it is hard to understand how the amount of mass and the energy associated with the expansion could have been adjusted to such precision.

To resolve this issue physicist Alan Guth proposed the universe underwent a very rapid period of expansion increasing it size by more than a trillion in the first few nano-seconds after its birth.  This resolves the flatness problem because its size is magnified by the inflation factor so much that locally it appears flat.

The reason for this can be understood by imagining what a two-dimensional creature who was living on a surface of a balloon would observe regarding the curvature of its surface.  If the size of the balloon were small compared to his field of vision he would notice that it surface was curved.  However, if its size was very large compared to his field of vision it would appear to him to be flat.

Inflation solves the flatness problem because it predicts the size of the universe increased so much in the initial expansion that portion we can observe appears to flat.

However, another reason why the universe appears to be flat is that all of its expansive energy must originate with its mass/energy.  This is because if the universe is a closed system, the first law of thermodynamics tells us the sum of the gravitational potential of its mass/energy and its kinetic or thermal energy is constant.

As mentioned earlier, the curvature of our expanding universe is related to the ratio of total gravitational potential of its mass/energy to the total kinetic energy of its expansion.

However, as was shown in the article "Defining potential and kinetic energy?" Nov 26, 2007 the equivalence between kinetic energy and the gravitational potential of mass/energy can be defined in terms of equation E=mc^2 because it showed that, similar to Relativity mass is equivalent to energy.  Therefore, energy in all its forms must also posses the gravitational potential energy associated with mass.  Additionally the asymmetry of the equation E=mc^2 tells us kinetic energy is oppositely directed from the gravitational potential of mass/energy.

This means a balance must exist between the gravitational potential of the universe’s mass/energy and the oppositely directed kinetic energy associated with its expansion because, as mentioned earlier all of its expansive energy must come from its mass/energy.  However, if one defines "m" as the total gravitational potential of the mass/energy of the universe, the equation E=mc^2 also defines the total energy available for its expansion.  If one then substitutes "c" for "v" in the equation for kinetic energy (KE=1/2mv^2) one arrives at the equation 1/2mc^2.  This equation defines the ratio of the total kinetic energy available to power the universe’s to its mass/energy  This indicates there is a 1 to 1 ratio between the potential energy of the universe’s mass/energy and the total quantity of oppositely directed energy associated with its expansion.

Additionally because the kinetic energy of the universe’s expansion is defined by the non-linear equation  m₀ = sqrt(E²/c⁴ – p²/c²) the ratio of the gravitational potential of its mass/energy will always maintain a 1 to 1 ratio to the its expansive energy if one assumes that its expansion has been as rapid as possible.

This means the universe will be flat now and throughout its history because as mentioned earlier there is a 1 to 1 ratio  between the curvature associated with the gravitational potential of its mass/energy and oppositely directed curvature associated with the kinetic energy of its expansion, which means they will cancel each other.

Therefore, one does not have to assume the universe underwent an inflationary period to explain why it is flat now and has remained that way if one assumes the existence of four *spatial* dimensions, and that it has been expanding as rapidly as possible since the big bang.

This cannot be done in terms of four-dimensional space-time because time or a space-time dimension is observed to move only in one direction forward and therefore could not support the bidirectional movement required to define the symmetry between the potential energy of mass/energy and its kinetic energy.

However, for many this concept of a zero energy universe may sound strange, but it is rather simple to understand.  A ball thrown up in the air has two forms of energy: kinetic and gravitational potential.  If kinetic energy were considered as positive, the potential energy, due to the gravitational pull of the Earth, would be negative.  If the positive portion of the energy beats the negative portion, the ball will escape from Earth.  If the negative energy is greater, it will return.  If the total energy is precisely zero the ball will barely escape – slowing to a stop when it is infinitely far away.

Many would disagree with this concept and point to the observations of Type Ia supernovae (SNe-Ia) which verified the existence of an expansive force or "Dark Energy" that opposes the contractive gravitational energy and is causing the universe to accelerating.  However, physicists have been unable to define a source or mechanism responsible for this energy.

However, as mentioned earlier the equation E=mc^2 defines a dynamic oppositely directed relationship between the gravitational potential of mass/energy and its kinetic energy.  In other words, in a closed system if the mass in a volume decreases the kinetic or thermal energy associated with that volume increase.

Therefore, due to the asymmetry between the quantity of mass and thermal kinetic energy in a closed system we should expect asymmetry between the quantity of forces those systems contain.  In other words, we would expect a force to be generated that is oppositely directed with respect to the gravitational forces associated with mass when we convert mass to energy.  This force would have to added to the linear expansion associated with the force of the big bang therefore, it would be viewed as acceleration.  This force has been give the name Dark Energy and is responsible for the accelerated expansion of the universe.

Therefore, the mechanism responsible for generating the force called Dark Energy would be analogous to one that earlier defined the kinetic energy generated from a mass/energy.  If the universe is a closed system then one must assume the sum of the potential energy of its mass and kinetic or thermal energy must is constant.  This also means that when stars convert mass to energy in nuclear reactions a force must be generated that is oppositely directed with respect to the gravitational forces associated with mass.

However, the "concentration" of this Dark Energy relative to gravitational energy is also defined by the equation E=mc^2c were "c" equals the speed of light.  This means its "concentration" and therefore its strength is 1/c^2 weaker than gravitational forces.

The reason why dark energy is so hard to detect is that, as show above its field strength is so small relative to gravitational.

Later Jeff

The "Shadow’s" of four spatial dimensions

Copyright 2008 Jeffrey O’Callaghan

(In a PDF format)