Derivations of Time Dilation Using Two Different Lorentz-type Transformations
The Lorentz transformation (LT) of Einstein's Special Theory of Relativity (STR) leads to the prediction of time dilation and length contraction in moving rest frames. In addition, the relativistic velocity transformation (RVT) is derived from the LT by simply taking the ratios of its space and time coordinates, and this in turn guarantees satisfaction of Einstein's light-speed constancy postulate. The Global Positioning Transformation (GPS-LT) is similar to the LT but differs from it in a significant way, namely it does not lead to the space-time mixing characteristic of the LT. The way in which time dilation is derived from both transformations is compared and it is shown that only the GPS-LT is self-consistent with respect to this key prediction of relativity theory.