For other waves like water or sound, it is easy to understand Doppler effect, because for those waves, the speed of wave in different inertia reference frames changes.
But for light wave, the speed is a constant regardless which inertia frame the observer is in.
Think about the following experiment. There are two inertia refernece frames:
Y: Moving away from X at a constant speed (zero acceleration)
A laser receiver is fixed to the stationary reference frame X, which can only be triggered by blue laser.
A laser emitter is fixed to the moving reference frame Y, which only emits blue laser.
For an observer in Y, he sees blue laser shining on the receiver, so he sees that the receiver is triggered.
But for another observer in X, he sees red laser (due to Doppler redshift) shining on the receiver, so he see that the receiver is not triggered.
How do you explain this paradox? What is wrong? If there is no redshift, everything reconciles.