Lorentz Invariance and the Global Positioning System

An example is considered (clock riddle) which demonstrates that opposite results are obtained for the length of an object depending on whether FitzGerald-Lorentz contraction (FLC) is assumed or instead the determination is based on the elapsed time required for a light pulse to traverse between its endpoints. This lack of internal consistency in relativity theory is traced to an undeclared assumption Einstein made regarding a normalization factor appearing in his original derivation of the Lorentz transformation (LT). If the empirical relationship between clock rates employed in the methodology of the Global Positioning System (GPS) is used to fix the value of this factor, an alternative Lorentz transformation (ALT) is shown to result that removes the above inconsistency, while still satisfying Einstein’s two postulates of relativity and remaining compatible with Einstein’s relativistic velocity transformation (VT) as well.