Experiments can't prove something which is logically flawed. Einstein's invalid procedure in deriving his transformation equations besides (see http://www.physicsmyths.org.uk/lightspeed.htm), motion is always only relative, so each of two obervers moving relatively to each other can claim that he is resting and the other moving, which makes it ambiguous which of the two clocks is going slower. In transverse Doppler effect experiments with source and receiver moving uniformly relatively to each other, an observer moving with the source would have to claim that the receiver has a lower than the rest frequency due to the motion, so he would have to lower the frequency of the emitter for the signal to match the receiver frequency. On the other hand, an observer moving with the receiver would claim that the emitter has a lower frequency due to the motion, so he would have to lower the receiver frequency in order to be able to receive the signal. This is obviously a logical contradiction because if both the emitter and receiver frequency are lowered by the same amount, it might as well remain unchanged. Yet in corresponding experiments the frequencies are not the same but detuned by a corresponding amount. This shows that the notion of moving clocks running slower is wrong. The observed 'transverse Doppler effect' either has to be a physical effect due to forces acting on emitter or receiver, or is in fact the normal Doppler effect associated with small distance changes between source and receiver which have not been taken into account for the experiment.