This is a follow-up question to this answer.
The assumption in this answer is that time dilation always causes a small redshift when an observer looks at an object moving at a significant fraction of the speed of light when not taking into account the shifts caused by the directional Doppler effect.
So, if time going slower always causes a redshift, does that mean that if we see a blueshift it means that time appears to move faster?
In other words, if B, that is far away from A, moves towards A really fast, A will appear to be blueshifted to B due to the relativistic doppler effect and thus B will see A's time moving faster?
The confusion I have is linking the concepts of redshifts and blueshifts with time going slower and faster.
Best Answer
Yes.
The machine that produces the wave-crests that appear to follow each other extra rapidly, appears to work extra rapidly.
For example if wave-crests appear to follow each other at one nano-seconds intervals, then the machine that produces those wave-crests appears to produce one wave-crest each nano-second. I mean, when looked very closely through a big telescope, then the machine can be seen to do that.
Those machines that appear to person X to work extra rapidly work extra slowly according to person X. I mean, person X subtracts the directional blue shift, and notes that there is a redshift.