Does time dilation occur between comoving galaxies?

[eugene pletcher]

As an astronomer observes a galaxy, which is receding, Does time dilation occur between the two comoving galaxies? If so, which (rf) is (t) longer in, as observed here on Earth (Our local Milkyway galaxy or the remote galaxy)? Thank you.

 

[Chalnoth]

As an astronomer observes a galaxy, which is receding, Does time dilation occur between the two comoving galaxies? If so, which (rf) is (t) longer in, as observed here on Earth (Our local Milkyway galaxy or the remote galaxy)? Thank you.

It is certainly true that if we were to look at a clock in a far-away galaxy that has a high redshift, the image that we see of that clock would move more slowly than a clock here on Earth (by an amount exactly proportional to the amount the wavelength has been increased by the redshift.

But how much of that is due to time dilation and how much is due to perspective effects is up to interpretation.

 

[eugene pletcher]

Thanks Chalnoth,
What about velocity, due exclusively to cosmic expansion?

 

[Orodruin]

In order to talk about time dilation at all you need to define a set of simultaneous surfaces in space time. In special relativity there is a canonical choice and so it is the one we use. In GR this often is no longer the case, although in standard cosmology we would often use comoving time. With that choice the answer is no, there will not be any time dilation between comoving galaxies with respect to comoving time simply because the comoving time is defined as the time for a comoving observer.

If you select a different set of simultaneous surfaces, the answer may be different. This is also apparent in SR as selecting the simultaneities of a different observer will lead to the original observer being time dilated instead. As Chalnoth said, what you call "time dilation" is largely a matter of interpretation and thinking about it more I have started thinking it is unfortunate that it is presented the way it is even in SR. Both length contraction and time dilation have been the source of a mountain of misunderstanding, students tend to try to apply it to everything and do not realize that there are requirements in order to use the simple formula with the gamma factor conversion.

 

[Chalnoth]

Thanks Chalnoth,
What about velocity, due exclusively to cosmic expansion?

Again, that's not an easy question to answer. The problem is that the velocity of a far-away object is not a well-defined quantity in General Relativity. You can subtract velocities at a single point, so that the question, "What is the velocity of object X that just passed me, relative to me?" is well-defined. But a far-away galaxy isn't so easy.

In the end, usually people working with General Relativity tend to limit the questions they ask to directly-observable questions. For example, the redshift is a directly-observable quantity. But "time dilation" is not: time dilation is an abstract concept that is well-defined in special relativity, but isn't a directly-observable quantity, and doesn't generalize well to curved space-time.

 

[timmdeeg]

In the end, usually people working with General Relativity tend to limit the questions they ask to directly-observable questions. For example, the redshift is a directly-observable quantity. But "time dilation" is not: time dilation is an abstract concept that is well-defined in special relativity, but isn't a directly-observable quantity, and doesn't generalize well to curved space-time.

Hmm, why not? It seems I'm missing something . Isn't the cosmological time dilation well defined due to its cause, the increase of the scale-factor? To my understanding we observe any phenomenon happening in a far away galaxy, e.g. the duration of a supernova, slower compared to the same phenomenon nearby, which correlates to the increase of the scale-factor during the time of emission and absorption.

 

[Orodruin]

I think you are misinterpreting what "time dilation" is. It is not the fact that we see other clocks ticking slower, it is a question of the proper time of different observers between two different simultaneities. What you are talking about is more related to redshift, which is not the same thing as time dilation (a light source moving towards you will be blue-shifted, even if it is moving and therefore time-dilated).

 

[timmdeeg]

I think you are misinterpreting what "time dilation" is. It is not the fact that we see other clocks ticking slower, it is a question of the proper time of different observers between two different simultaneities. What you are talking about is more related to redshift, which is not the same thing as time dilation (a light source moving towards you will be blue-shifted, even if it is moving and therefore time-dilated).

Ah, got it, I was wrong. Thanks for your good explanation!

 

[timmdeeg]

http://arxiv.org/abs/astro-ph/9602124

There seems to be some ambiguity regarding the meaning of "cosmological time dilation" however.