THE LACK OF INTERNAL CONSISTENCY OF THE LORENTZ TRANSFORMATION AND ITS CONSEQUENCES FOR THE CONCEPT OF SPACE-TIME MIXING

Abstract

The Lorentz transformation (LT) of Einstein's Special Theory of Relativity (STR) is analyzed with respect to its internal consistency.  The LT 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.  On this basis, it is shown that the LT is not internally consistent since it can be used in different ways to obtain opposite answers for the same question, such as whether remote events occur simultaneously for two observers in relative motion.  This characteristic eliminates the LT as a viable space-time transformation.  Experimental results obtained with atomic clocks and other timing devices are shown to be in complete agreement with this conclusion.  They invariably find that the rates of moving clocks are strictly proportional to one another (Universal Time-Dilation Law, UTDL), in disagreement with the space-time mixing expected on the basis of the LT.  Finally, it is shown that a different transformation, referred to as the GPS-LT by virtue of its consistency with the clock-rate adjustment procedure used on Global Positioning System satellites, also satisfies both of Einstein's postulates of relativity while nonetheless remaining consistent with the UTDL.