← Back to Contents

2.2.6 Universal Coordinate System

The concept of an ideal universe as a perfect hyper-sphere automatically provides a coordinate system which allows each point in the energy continuum to be specified uniquely. It has already been shown that a 'straight' line passing through the curved volume of a hyper-sphere will curve back to join up with its origin. Such a line can be viewed as a 'universal great circle' in analogy with the great circles on planet Earth.

If, at a point in a hyper-sphere, three mutually orthogonal, 'straight' lines are projected as universal circles, they will eventually cross at an anti-nodal point, before returning to their origin. Three such lines can be conveniently called, x, y and z curved axes, so that any point in the ideal continuum can be specified in these terms. Since each point in a perfect hyper-sphere is at a radius, \(R_o\), this together with curved xyz coordinates provide specific coordinates. It must be emphasized that these xyz coordinates do not form a Euclidean system since each is a universal circle. However, near the origin of such a system, the axes are effectively orthogonal, even over large volumes the size of a galaxy. This is the case of the astronomical coordinate system which assumes that the universe has the shape of a ball, so that a Euclidean system of coordinates suffices.

The great advantage of a curved, xyz, coordinate system lies in its ability to provide coordinates for the real universe, which, as already proposed, may be regarded as a distorted version of its ideal form. For this purpose, each radius vector in the real universe retains the same xyz coordinates, and deviations from the ideal are represented as increases or decreases in the value of its radius vector, \(R\). It will be shown in a later section that the state of the real energy continuum at each point depends only on the space and time derivatives of \(R\).

Using an xyz system of coordinates assumes that the value of length is fixed, however, since the universe is expanding, xyz values must be increased accordingly. To avoid this it is convenient to express increments of length as arc segments, which allows the xyz coordinates to be replaced by angles, \(\theta_x, \theta_y, \theta_z\) radians. In a universal circle an angle of \(\pi\) radians, corresponds to a distance, \(\pi R_o\), hence, \(\theta_x = x/R_o\). Similarly, \(\theta_y = y/R_o\) and \(\theta_z = z/R_o\), where \(R_o\) is the radius of the continuum at some point in time given as \(t=0\).

← Previous Next →