Investigation on the transverse Doppler effect

The widely accepted viewpoint asserts that the transverse Doppler effect for plane light waves is a red shift, a purely relativistic effect caused by the time dilation or the slowing down of a moving clock. However, rigorous proof for the assertion is absent in available literature. Here, we investigated the transverse Doppler shifts for plane and spherical waves. The results show that for plane light waves, the red shift may not be a purely relativistic effect, and the true transverse Doppler effect might be a blue shift, which might mean that a moving clock can also run faster than an identical clock at rest. For spherical light waves, the transverse Doppler effect is a blue shift when a source is at the center of a rotating disk and the receiver is at its rim; on the contrary, it is a red shift. The results might not only reflect new features of special relativity but also benefit physics teaching.