Measurements of the transverse Doppler effect have provided important confirmatory evidence for the validity of Einstein's theory of special relativity (SR) as it pertains to time dilation. However, these investigations fall into two distinct categories depending on whether the light source or the detector is accelerated relative to the rest frame of the observer. In their original work employing a moving light source in the laboratory, Ives and Stillwell state explicitly that they observe a wavelength shift to the red, and therefore a slowing down of the initially accelerated clock, in complete agreement with Einstein's predictions. By contrast, although both Hay et al. and Kündig also report complete agreement with SR on the basis of their ultracentrifuge experiments in which the absorber/detector is under constant high acceleration, their theoretical discussion actually contradicts this assertion. For example, Kündig states that his work demonstrates "that the clock which experiences acceleration is retarded compared to the clock at rest," thereby giving unequivocal support to the conclusion that it is not just a matter of perspective which of two clocks runs slower at any given time, but rather that the measurement process is perfectly objective. This experience has generally been dismissed by SR proponents, arguing that the latter theory is only to be applied for objects in uniform motion, in which case measurement is definitely subjective. It is pointed out that this conclusion overlooks the fact that a version of the Lorentz transformation exists which is consistent with both sets of measurements while still satisfying Einstein's two postulates of SR. [ABSTRACT FROM AUTHOR]