天体物理学と航空宇宙技術

GPS-Compatible Lorentz Transformation that Satisfies the Relativity Principle

Abstract

Robert Buenker J

In relativity theory there are two versions of time dilation: symmetric and asymmetric. In the first case, it is assumed that a moving clock always runs slower than the observer's local clock, so it is just a matter of perspective which of two clocks runs faster. By contrast, asymmetric time dilation assumes that if two clocks are running at different rates, one of them is unambiguously slower. The Lorentz transformation (LT) of Einstein's special theory of relativity (STR) predicts that only symmetric time dilation occurs in nature. However, experimental studies of the rates of atomic clocks on airplanes, as well as of the second-order Doppler effect using high-speed rotors, find that time dilation is exclusively asymmetric, in clear contradiction to the LT. In the present work, it is shown that there is another space-time transformation that also satisfies Einstein's two postulates of relativity, but one which assumes that clock rates in different rest frames are strictly proportional to one another. It is therefore in complete agreement with the results of the above time-dilation experiments and also with the clock-rate adjustment procedure applied to satellite clocks in the methodology of the Global Positioning System; hence the designation GPS-LT for this alternative space-time transformation. Unlike the original LT, the GPS-LT is consistent with the absolute remote simultaneity of events, and it eliminates the necessity of assuming that space and time are inextricably mixed. It also disagrees with the FitzGerald-Lorenz length-contraction prediction of STR, finding instead that isotropic length expansion always accompanies time dilation in a given rest frame. The results of the Ives-Stilwell study of the transverse Doppler effect and also those of experiments with accelerated muons are shown to be in complete agreenment with the latter conclusion.