We have shown throughout “The Imagineer’s Chronicles” there are many theoretical advantages to defining the universe in terms of the existence of four *spatial* dimensions instead of four-dimensional space-time.

One is that it would allow for the development of a more logical and consistent solution to the flatness problem than the presently accepted inflationary one.

Wikipedia defines the cosmological fine-tuning within the Big Bang model of the universe as “The Flatness Problem”.   It involves 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 nature of the universe at the current time.

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.  This value affects the curvature of space-time, with a very specific critical value being required for a flat universe.  The current density of the universe is observed to be very close to this critical value.  Since the total density departs rapidly from the critical value over cosmic time, the early universe must have had a density 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 universe went through a brief period of extremely rapid expansion in the first fraction of a second after the Big Bang.  The flatness problem is one of the three primary motivations for inflationary theory.

However, if one defines mass and energy in terms of only four *spatial* dimensions as we have done in “The Imagineer’s Chronicles” one can derive a classical mechanism that can predict and explain why our universe appears to be flat without having to resort to exotic or "adhoc" hypotheses such as Cosmic Inflation.

In the article ”Defining energy“ Nov 26, 2007 it was shown the "quantity" or density of matter in the universe could be derived in terms of a curvature or displacement in "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension while the density of its energy can be derived in terms of an oppositely directed displacement in that same surface.  

This curvature is analogous to the space-time curvature Relativity defines as being responsible for mass and energy.

However, it differs in that one derives mass and energy in terms of unidirectional displacement in the geometry of space-time while the other in terms of a bi-directional one in a "surface" of a three dimensional space manifold with respect to a fourth *spatial* dimension.

If it were true the density of mass and energy are the result of oppositely directed curvatures in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension the "flatness" of our universe would be an intrinsic property of its existence and would not require the fine-tuning of any of its components to explain it.

If one crumples a piece of paper 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.

However, if density of mass and energy are a result of opposite directed displacements in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension their overall density would appear to be flat because, similar to a crumpled piece of paper the "depth" of the displacement below its "surface" caused by mass would offset by the "height" of the displacement caused by energy.

Many proponents of the Big Bang Model assume it began from the expansion of mass and energy around a one-dimensional point.  However, if we are correct in assuming that mass and energy are a result of oppositely directed curvatures in a "surface" of a three-dimensional space manifold, the universe must have been flat with respect to their density at the time of the Big Bang.  This is because a one-dimensional point would have no "vertical" component with respect to a fourth *spatial* dimension and therefore the "surface" of three-dimensional space originating from it would be "flat".

However, if the universe was flat with respect to the density of mass and energy in the beginning it would remain flat throughout its entire expansive history because its expansion would result in a proportional reduction in the displacements above and below its three-dimensional surface as it expanded.

This would be analogous to why the overall flatness of a crumpled piece of paper does not change if one smoothes or stretches it because that would result in a proportional decrease in the height of the wrinkles above and below its original surface.

This is not possible if one defines universe in terms of four-dimensional space-time because time moves only in one direction forward and therefore cannot support the bi-directional movement required define the apparent flatness our universe in terms of its geometry.

Therefore, if one theoretically defines mass and energy in terms of four *spatial* dimensions as we have done here one does not have to assume that their densities were fine turn to ‘special’ values when the universe began to expand but only that it was flat when the expansion began as is hypothesized by the Big Bang theory.

Jeff

The Shadows of four spatial dimensions

Copyright Jeffrey O’Callaghan 2009

(In a PDF format)

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