In the model of Complete and Incomplete Coordinate Systems, there is no upper limit on the velocity of a moving coordinate system. In order to explain why this is the case, we have to first understand the reasons behind the belief that Einstein’s equation limit velocity. Einstein presents his final equations as:
Specifically focus on the Beta equation. When v approaches V, that part of the equation approaches 1. When this happens the denominator becomes 0, which yields an undefined result during division. Thus, many have concluded that this means that v cannot be greater than V.
Reinterpreting the denominator
In order to see the problem, we have to look at the meaning of the equation. Revisit the example of the bird flying from the rear to the front of the cage traveling on the back of the trailer. (In our terminology, this is an example of an Incomplete Coordinate System). The equation that defines how long it will take the bird to travel the distance of the cage, x’, when it is flying at a constant velocity w, with the truck (pulling the trailer) traveling at velocity v, is given by x’/(w-v).
Considering only the denominator, one could conclude that the truck can never match that of the bird. When w and v are equal, the denominator is 0, yielding an undefined result in the equation. Clearly, the truck can meet and exceed that of the bird. When the speed of the truck and bird match, the bird will appear to hover in the cage. But since it is making no practical progress toward the front of the cage, it will never reach the front. Hence, this is the context in which the equation applies. The fact that the equation yields an undefined result makes sense as the bird is making no progress toward being able to turn around. This mathematical conclusion in no way limits the velocity of the truck.
What does it mean?
In the model of Complete and Incomplete Coordinate Systems, a coordinate system can go faster than the phenomena under observation.
Remember, in the model of Complete and Incomplete Coordinate System, the fixed-point and wave-front equations do not have a denominator that would limit velocity. There is no mathematical speed limit.
However, in the specific case of an Incomplete Coordinate System, when the velocity of the coordinate system exceeds the speed of the wave, oscillations will not occur (e.g., the bird will never reach the front of the cage and be able to turn around).
