Time Dilation and Astronomy

Is relativistic time dilation in effect for light we receive/see that traveled from light years away? For example, is it the case that when light travels to us from a source that is 40,000 light years away, in the 40,000 years the light has traveled, much more time has passed at the source due to time dilation? Also, is time dilation in effect for us at the Earth in that case as well? Thank you!
- Travis (age 26)
WA, USA

Time dilation doesn't come from things just being at a distance. If the star isn't moving relative to us, there's no special relativistic dilation effect. At 40,000 light years away, that star is quite close by cosmological standards, so there's no significant effect from the relative velocity associated with cosmic expansion.  At that small distance we can also neglect general relativistic effects from the accelerating expansion of the universe. 

There could be some effects due to random local velocities. These would look like any special relativistic time effects. Say that we say the star  happens to be approaching us and emits some light when it's 40,000 ly away. Then we say it takes the light 40,000 years to reach us. The star says that we're approaching it, so it says that the light takes less than 40,000 years to reach us. It all works equally well the other way. If the star sees some light leave the Sun and take 40,000 years to reach it, we think the star is moving toward us so we say the light takes less than 40,000 years to get there.

You want to know whether when the light reaches us 40,000 years have passed on the star since the light was emitted. According to our view, no. Time is running slow on the star, so less than 40,000 years have passed. That also works in reverse. From the star's point of view, time is running slow here.

Mike W.

(published on 10/11/2014)