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1kWe have shown throughout this blog and its companion book “The Reality of the Fourth *Spatial* Dimension” 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 while defining the theoretical advantages to doing so.
One is it that it allows one to understand why the universe must be flat in terms of our everyday experiences.
Einstein gave us this ability when he used the velocity of light to define the geometric properties of space-time because it allows one to convert a unit of time associated with energy in his four dimensional space-time universe to a unit of a space identical to those of our three-dimensional space. Additionally because the velocity of light is constant it is possible to defined a universe made up of four *spatial* dimensions that makes predictions identical to those he had attributed to four dimensional space-time
For example a four dimensional space-time universe or one made up of only four *spatial* dimension can be geometrically open, closed, or “flat” and its shape is dependent on the quantity 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, a recent observation 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 its 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 the portion we can observe appears to flat.
However, another reason why the universe appears to be flat is because if the universe is a closed system, the first law of thermodynamics tells us the sum of the gravitational potential of its energy/mass and its kinetic or thermal energy is constant.
As was mentioned earlier Einstein’s genius allow us to defined a universe made up of four *spatial* dimensions that makes predictions identical to those he had attributed to one made up four dimensional space-time.
Therefore instead of deriving kinetic and gravitational energy in terms of unidirectional curvature or depression in a “surface” of a space-time manifold one can as was done in the in the article “Defining potential and kinetic energy?” Nov. 26, 2007 one can derive both in terms of oppositely directed curvatures in “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. In other words if one defines gravity in terms of a depression in its “surface” one can derive kinetic energy as an in terms of elevation in it.
This differs from Einstein’s theoretical definition of energy in that he defines both gravitational and kinetic in terms of in terms of a unidirectional displacement in a four dimensional space-time manifold.
However, unlike Einstein’s definition: defining gravity and kinetic energy in terms of oppositely directed curvatures in space is not based entirely on theory because observations tell us that kinetic energy is oppositely directed from gravitational energy. For example, the kinetic energy of an orbiting satellite is oppositely directed from its gravitational energy.
This difference is significant to our understanding of the shape or flatness of our universe because as mentioned earlier its curvature is related to the ratio of total gravitational potential of its energy/mass to the total kinetic energy of its expansion.
This is because the universe is a closed system with respect to its energy/mass the first law of thermodynamics tells us there must exist a 1 to 1 correspondence between the gravitational potential of the universe’s energy/mass and the oppositely directed kinetic energy associated with its expansion because all of its expansive energy must originate from within its energy/mass. This 1 to 1 ratio between gravitational potential and kinetic energy will be maintained throughout the entire history of the universe because kinetic energy also posse gravitational potential that is equivalent to its energy content.Â
However, as was shown in the article “Defining potential and kinetic energy?” this means there must be a 1 to 1 correspondence between the downward directed curvature associated with its gravitational potential and the upward directed one associated with its Kinetic energy. Therefore, on a large scale the universe will appear to be flat because these oppositely directed curvatures will cancel each other.
This means 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 as is done here that the gravitational energy of energy/mass and its kinetic energy are related to oppositely directed curvatures in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
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 bi-directional movement required to define the asymmetry between gravitational potential and kinetic energy.
This concept of a zero energy universe may sound strange to many, 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.
Another way of understanding this concept compare it to the effect crumpling a piece of paper has on its overall flatness.Â
Our experiences with a piece of paper shows us that if one crumples one that was original flat and views its entire surface the overall magnitude of the displacement caused by that crumpling would be zero because the height of it above its surface would be offset by an oppositely directed one below its surface. Therefore, if one views its overall surface only with respect to its height its curvature would appear to be flat.
Similarly, if the gravitational potential of the universe’s energy/mass is oppositely directed form that of its kinetic energy the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension would appear to be flat because, similar to a crumpled piece of paper the “depth” of the displacement below its “surface” caused by it would offset by the “height” of the displacement caused by its kinetic energy.
Therefore, due to the asymmetry between the gravitational potential of energy/mass and its kinetic energy in a closed system we call the universe one can understand why it will appear to be “flat” throughout its entire history based on the first law of thermodynamics and our experiences.
Later Jeff
Copyright 2008 Jeffrey O’Callaghan
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