Time Co-ordinate

This model is the theoretical representation of the practical drawing system.  The figure shows a four-dimensional rectangular co-ordinate frame.  The four co-ordinates, X, Y, Z and T are all perpendicular to one another.  If the X, Y and Z co-ordinates are represented by a Cartesian frame with its origin the centre of a sphere of reference, then the T or time co-ordinate may be represented by the rotation of the sphere about any axis.  A tangent point on the great circle perpendicular to the axis of rotation represents a point in time: the proper time of that particular reference frame.

An ellipse is shown in a bold line representing a great circle perpendicular to the axis of rotation of the sphere of reference.  This great circle (a great circle is the circle represented by the circumference of the sphere) is the T co-ordinate, against which a value is read in angular rotation.  The rotary movement depicted by the great circle - or arc thereof - may be expressed in terms of rotations about the X, Y and Z co-ordinates.  Since rotary motion can be split into two component vectors, one tangential and the other radial (centripetal acceleration), it will be seen that there is a component tangential vector of the rotation perpendicular to each of the space co-ordinates.  And since the radial vector of the component rotations about each of the three-space co-ordinates is likewise perpendicular to, not one but two of the co-ordinate axes, then the sum total of component vectors of the rotary motion as expressed by motion about the three co-ordinate axes can be said to be perpendicular to each of the three Cartesian space co-ordinates not in turn, but simultaneously, with respect to that system of reference.  The model contains four co-ordinates, three space and one time, all perpendicular to one another.