1.1.3 Mechanism of Expansion
Given that the universe is a closed volume of energy, its internal pressure will ensure that energy density takes up the same value at each point. Any deviation from uniform energy distribution will result in an automatic correction. If energy is equally distributed the continuum will seek a symmetrical shape, which in the case of closed volume is a hyper-sphere. This is a natural process and in an ideal case the shape of the continuum would be a perfect hyper-sphere. However, local imperfections in energy distribution manifest themselves as fields or material objects contained in the universe.
In order to help visualization of three dimensional, curved volume, it is proposed to use analogues of one and two dimensions (circle and sphere). Energy is imagined to be contained on the line of a circle or the surface of an ordinary sphere. The space inside this circle/sphere is empty (a void) and has no properties. Likewise, the space outside is also a void. Material objects, including light, cannot enter the void because they are part of the energy continuum.
The nature of energy is that it seeks to expand, and it is significant that the units of energy density are also those of pressure. We can imagine that it is this pressure which causes expansion of the universe, and a later section will present an analysis of energy density and volume which confirms this. Here we accept that the expansion of the universe is caused by the internal pressure of its energy density.
To understand how energy density causes expansion, a one dimensional analogue (circle) is sufficient. We imagine the curved circumference of a circle to consist of a very large number of identical ’arc-segments’, each having the same radius of curvature. If each arc-segment contains energy, then when connected together to form a circle, any segment with excess energy will allow this excess to ’flow’ to adjacent segments which have less energy. This process is self-equalizing so that energy becomes evenly distributed over the entire circumference of the circle. That is, each arc-segments will have the same energy content as well as the same radius of curvature.
The pressure of energy acts to increase the size of each segment so that its length and radius of curvature both increase. This will cause the circle to expand because the radius of curvature is also the radius of the circle, and the total connection of arc-segments is its circumference.
An analogous process occurs in the energy continuum of a hyper-sphere. Essentially, energy pressure acts to equalize energy density and the radius of curvature at each point. This ensures that the continuum takes up a symmetrical shape with increasing radius of curvature. Hence, the universe is able to expand while maintaining the shape of a hyper-sphere.
To aid visualization of expansion, its convenient to imagine that each point on the spherical surface exists as the tip of a radius vector which originates at the nominal center inside the sphere. A radius vector at a given point on the spherical surface is also its radius of curvature. We imagine these vectors to emanate from the center of the sphere and to be of equal length. This construction is valid for circles, spheres and hyper-spheres.
It's important to keep in mind that radius vectors are imaginary, and serve only as aids to visualization. An increase in the length of a small group of vectors will cause an increase in the local surface area, or in a hyper-sphere, an increase in the local volume. Radius vectors are only assumed to be of equal length when analyzing larger structures within the universe.
In analyzing tiny regions of high energy density, the deviations in length of a tiny region of radius vectors provides the intense, local curvature which is the basis of particle structure. The region surrounding an atomic particle is also curved to a lesser degree, and it is this peripheral curvature that is the basis of gravity. Since all matter is made up of atoms, their individual curvature combines in large objects such as planet Earth, where it is perceived as gravity.
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