Universe Expansion: Does Speed of Motion Matter?

[DuckAmuck]

TL;DR Summary

How does universe expansion relate to time dilation?

So the universe is expanding, and galaxies are getting farther apart from one another on average. Does this motion count the same as ordinary motion, in that if a galaxy is being expanded away from us at 0.5c, that clocks in that galaxy would appear to tick slower at 0.866 the rate of clocks here?

 

[BvU]

No, they keep perfect time for the inhabitants.

 

[PeterDonis]

Does this motion count the same as ordinary motion, in that if a galaxy is being expanded away from us at 0.5c, that clocks in that galaxy would appear to tick slower at 0.866 the rate of clocks here?

This question cannot be answered as you ask it because time dilation is frame dependent. There are choices of frame for which the distant galaxy's clocks tick slower relative to ours, and there are choices of frame in which the distant galaxy's clocks tick at the same rate as ours. There is no unique answer.

 

[DuckAmuck]

This question cannot be answered as you ask it because time dilation is frame dependent. There are choices of frame for which the distant galaxy's clocks tick slower relative to ours, and there are choices of frame in which the distant galaxy's clocks tick at the same rate as ours. There is no unique answer.

So it is not yet known/understood?

 

[PeterDonis]

So it is not yet known/understood?

No, that's not what I said. Read my post again.

 

[phyzguy]

@PeterDonis, I think we can make the OP's question explicit by asking what we would see if we pointed a telescope at a galaxy receding from us at 0.5c and we could make out one of their clocks. I think we would in fact see the clock ticking at a slower rate, for the same reason that we see light redshifted. Do you agree?

 

[PeterDonis]

I think we can make the OP's question explicit by asking what we would see if we pointed a telescope at a galaxy receding from us at 0.5c and we could make out one of their clocks. I think we would in fact see the clock ticking at a slower rate, for the same reason that we see light redshifted. Do you agree?

Sure, but the redshift factor is not the same as the time dilation factor. The observed redshift is an invariant; it's not frame dependent. The time dilation factor is frame dependent. The OP was asking about the time dilation factor.

 

[BvU]

Yes. But for those who are close enough to see the clock, it will appear to tick at exacty the same rate as our clocks appear to tick to us...

I considered answering with two letters only to nudge ducky to ask further...

[edit] ah, I see there is an anamnesis here...
and actually ducky is expected to be able to phrase the question better ...
$\ \$

 

[PeterDonis]

for those who are close enough to see the clock, it will appear to tick at exacty the same rate as our clocks appear to tick to us...

Not if it's receding at 0.5 c. The redshift factor for that is $1 / \sqrt{3}$, which is easily detectable.

 

[BvU]

Ah, I will have to learn about GR -- wrongly restricted my thinking to SR

 

[Dale]

So it is not yet known/understood?

No unique answer doesn’t mean that the answer is not known/understood. It means that the question was not formulated in a way that provides a unique answer.

As a simple analogy, I can ask you to solve the equation $x^2=4$. The equation and its solution is completely understood, but the answer is not unique. Both $x=2$ and $x=-2$ are valid solutions.

Here you have asked a question with an infinite number of possible solutions.