On the asymmetry in relativistic doppler shifts caused by time dilation: proposed two-way experiment

There are two factors responsible for the relativistic Doppler effect. One of these contributions is of first-order in the velocity of the light source relative to the observer and is non-relativistic in nature, but there is also a second-order (transverse Doppler) effect caused by the difference in rates of clocks at the source and in the laboratory (time dilation). It is pointed out that the traditional derivation for the relativistic Doppler effect based on the assumed Lorentz invariance of the phase of light waves is too restrictive. According to the latter argument, when two observers in relative motion send out signals to one another employing an identical light source, their respective measured Doppler shifts should always be the same (totally symmetric). However, an alternative derivation can also be given which indicates that the second-order contribution should in fact be anti-symmetric, although this analysis agrees with the conclusion that the corresponding first-order Doppler effect is symmetric. This is because there is a reciprocal relation between the ratios of the rates of the moving and rest clocks for the two observers. Quantitative calculations of the amount of the predicted anti-symmetry in transverse Doppler shifts are made for several examples on the basis of experimental data reported for the rates of atomic clocks carried onboard airplanes and rockets. Because of the Earth's rotation about its polar axis, the Doppler shifts can be measured in principle by using exclusively land-based atomic clocks located at widely different latitudes. Verification that the transverse Doppler frequency shifts are indeed antisymmetric would be a definitive confirmation that the oftcited symmetry principle of Einstein's special theory of relativity (STR) is incorrect, namely the claim that two observers in relative motion should each find that his/her clocks run faster than the other's. Finally, changes in the formulation of relativity theory that bring it into agreement with modern-day observations of variations in the rates of clocks with state of motion are discussed with reference to the methodology of the Global Positioning System (GPS). Keywords: transverse Doppler effect, time dilation, Global Positioning System, objectivity of measurement, remote simultaneity, Alternative Lorentz Transformation (ALT).
I. Introduction The relativistic Doppler effect differs from its classical counterpart in that there is not only a first-order effect depending on the speed of the source, but also one [...]