Contradiction between FitzGerald-Lorentz Length Contraction and Time Dilation: A GPS-Compatible Lorentz Transformation

Recent work has shown that the underlying assumptions of the Global Positioning System (GPS) are incompatible with a number of conclusions of conventional relativity theory, including Fitzgerald-Lorentz length contraction (FLC) and the supposed ambiguity in the relative rates of clocks in motion.The challenge is therefore to amend relativity theory so as to bring it into full consistency with the experience of the GPS methodology.This goal must be accomplished while at the same time avoiding conflict with other predictions of relativity theory that have received ample experimental confirmation over the years.It is shown that this can be achieved by eliminating an undeclared assumption in Einstein's derivation of the Lorentz transformation (LT) and replacing it with the GPS axiom of the strict proportionality of clock rates in different rest frames.The standard relativistic velocity transformation still retains its validity thereby.However, the relationships between respective measured values of observers in relative motion for the same quantity are determined in the revised theory with the aid of a simple scaling procedure in each case.