A well-known prediction of the Lorentz transformation (LT) of Einstein’s theory of Special Relativity (SR) is that when two observers exchange light signals, they will both measure a red shift (lowering in frequency). An experiment with gamma rays was reported by Hay et al. in 1960 in which an absorber is mounted at the rim of a high-speed centrifuge while the source is located near the rotor axis. There is general agreement that because of its acceleration, the clock attached to the absorber must be retarded relative to the gamma ray source. Despite the claim that this result is a confirmation of the Symmetry Principle, the fact remains that the slowing down of the absorber clock means that the frequency of the signals it receives from the source will be greater than the standard value, i.e. a blue shift will be observed because more waves are counted per second by virtue of the absorber clock’s reduced rate. This experience therefore stands in direct contradiction of the Symmetry Principle. In addition, it is pointed out that the three space-time predictions of the LT (equal speeds of light, time dilation and FitzGerald length contraction) are incompatible with one another. An alternate theory is presented (Uniform Scaling method) which is in full agreement with the results of the ultra-centrifuge experiment and also avoids any incompatibility with regard to it space-time predictions.