Hyperspherical Clock Tick Rate
Hyperspherical clock tick rate is founded on the idea of the universe as a hypersphere or 4D sphere. A 3D sphere has a 2D or planar surface. A hypersphere has a 3D or volume surface. In both cases the surfaces are non-Euclidean. This means that they are curved. A 2D plane must be bent to form the surface of a 3D sphere. A 3D volume must be bent to form the surface a hypersphere.
The radius of the hypersphere is the common time axis. Another way of looking at this is that we are considering as simultaneous all events in the universe that occur when they are, more or less, equally displaced in time from the point of the big bang. This view can be seen as a 4D polar plot of the universe, with the big bang at the origin and the common time axis representing the radii of concentric hyperspheres. Each larger hypersphere represents a later moment in time. As time passes the radius of the hypersphere increments correspondingly.
The hyperspherical clock tick rate of a system is the rate at which the system's clock ticks compared to the rate at which the radius of the hypersphere increments.
Now, events within the volume surface of the hypersphere are observed as a result of the movement of energy. This energy has a speed limit of 3 X 108 m/sec. Consequently, during the movement of this energy from point A to point B, time passes. This means that the radius of the hypersphere increments as the energy moves.
In graphic (2-A) two stars A and B have static positions on the surface of the Hypersphere, yet because the radius of the hypersphere increases, they move further apart. The farther apart they get, the longer light takes to travel between them. An observer on a planet orbiting each star sees the other star at moments increasingly in the past, compared to his current hyperspherical moment. As the observations of the distant star slip further and further into the past, the clock of the distant star must appear to be slower than the clock of the observer, since the distant star's clock is constantly losing time as it slips further into the past. This principle applies generally to all divergent world lines.
The reverse applies to converging world lines. Objects moving closer must appear to have a faster clock than the observer's, since these objects are moving from the past to the present and so their clocks gain time.
Since moving objects are always (neglecting the expansion of the universe.) moving away from one place as they move towards another place, these two effects can be observed at the same time from these two locations.
See the graphic presentation: One Shift, Two Shift, Red Shift, Blue Shift
However, this is not the only effect on light signals. The second postulate and distance distortions also affect the light signal. The effects of the second postulate and distance distortion must be combined with those for light propagation delay to get the total observational effect.
The sequence of events occurring relative to incrementing hyperspherical moments in time, is not the same as the experience of observers and objects which must contend with the propagation delay of light. Such observers, and objects cannot perceive even a part of a hyperspherical moment in time. So, the idea of a hyperspherical moment in time may seem somewhat abstract.
However, the concept of a hyperspherical moment in time is useful for comparing clock tick rates for objects which move apart then come back together. If hyperspherical clock tick rate is not affected by such movements, then the clocks for the objects, if synchronized at departure, will still be synchronized when they meet again. If hyperspherical clock tick rate is affected by this motion then their clocks will not be synchronized when they meet again.