“The Flatness Problem†as it has come to be called by many cosmologist relates to the observation that some of the initial conditions of the universe appear to fine-tuned to very “special” values, and that a small deviation from these values would have had massive effects on the physical properties of the universe as it evolved.
In the case of the flatness problem, the parameter, which appears to be fine-tuned, is the density of matter and energy in the universe because they must be close to a specific critical value to explain why the universe appears to be flat. However because the total density departs rapidly from the critical value over cosmic time, their density in the early universe must have even closer to the critical density, departing from it by one part in 1062 or less. This leads cosmologists to question how the initial density came to be so closely fine-tuned to this ‘special’ value.
The problem was first mentioned by Robert Dicke in 1969.
The most commonly accepted solution among cosmologists is cosmic inflation or the idea that the early universe underwent an extremely rapid exponential expansion by a factor of at least 1078 in volume, driven by a negative-pressure vacuum energy density.
This solves the flatness problem because the act of inflation actually flattens the universe. Picture an uninflated balloon, which can have all kinds of wrinkles and other abnormalities. As the balloon expands, though, the surface smoothes out. According to inflation theory, this happens to the fabric of the universe as well.
However, many view the inflationary theory as a contrived or “adhoc” solution because the exact mechanism that would cause it to turn on and then off is not known.
However, if one defines energy/mass density of our universe in terms of four *spatial* dimensions as is done many times in one can explain and predict why our universe appears to be flat by extrapolating the laws of classical physics in a three-dimensional environment to one of four *spatial* dimensions.
Einstein gave use the ability to do this 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. However when he used the constant velocity of light in the equation E=mc^2 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 quantitative and qualitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.
One advantage to this approach is that allows one to derive the kinetic and gravitational potential of the components or the universe in terms of as was done in the in the article “Defining potential and kinetic energy?†Nov. 26, 2007 oppositely directed curvatures in “surface†of a three-dimensional space manifold with respect to a fourth *spatial* dimension. In other words if one can defines gravity in terms of a depression in its “surface†one could derive kinetic energy as an in terms of elevation in it.
This differs from Einstein’s theoretical definition of energy in that he only defines gravitational in terms of in terms of a displacement in a four dimensional space-time manifold.
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.
However, as was shown in the article “Defining potential and kinetic energy?†on can define the potential energy of gravity in terms of a “downward” directed curvature in a “surface” of a three dimensional space with respect to a fourth spatial dimension while define kinetic energy in term an upwardly directed one. 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.
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.
Later Jeff
Copyright Jeffrey O’Callaghan 2009