# Expansion of Universe and Time dilation

1. Mar 6, 2009

### earamsey

I saw on Science Channel that the expansion of the Universe, distance between galaxies was specified, is occuring faster than speed of light.
1.If this is the case, relative to Milkyway, other galaxies must be moving away faster than speed of light?
- must there be a time dilation between galaxies?
- is perception of an earth hour observed from the Andromeda galaxy, for instance, different from here in Milkyway?
2.Does this rate of expansion affect my perception of the speed of light via the time dilation; I think what I mean is this rate a factor in perception of speed of light?
3.Is it strange that something moving away faster than the speed of light can be viewed at all?

2. Mar 6, 2009

### neopolitan

Hi earamsey,

I think you might have misheard or misunderstood what they said. The only things that could be moving away from us at the speed of light are about 14 billion light years away, which is pretty much everything since the universe is considered to be 14 billion light years old.

What you might have misunderstood is that a galaxy 10 billion light years away from us and another galaxy in the opposite direction, have an apparent separation speed of greater than the speed of light, if we use simple velocity addition.

We can't do that, and if we use the correct form of velocity addition, we find that their separation speed is actually less than the speed of light. Oddly enough, although we might think that those two galaxies are 20 billion light years apart, they won't be more than 14 billion light years apart according to each other. (The single distances between us and them will be 10 billion light years according to all of us but according to each of the galaxies, the distance between us and the other galaxy will be a lot less.)

cheers,

neopolitan

3. Mar 6, 2009

### jefswat

I read somewhere that parts of the universe could be expanding away from us at speeds greater than the speed of light. Whatever I read this from said it fit with SR because it was the actual space that was expanding. Not because the two objects were actually moving >c but because there was more and more space between them. For some reason I think it had something to do with Inflation

4. Mar 6, 2009

### robousy

Imagine an infinite length of elastic that doubles its length in 1 second, and you are located at L=0m.

If you look at the L=1m location after 1 second it will be located at L=2m. This implies v=1m/s.

If you look at the L=2m location after 1 second it will be located at L=4m. This implies v=2m/s.

If you look at the L=3m location after 1 second it will be located at L=6m. This implies v=3m/s.

In fact, the further along the elastic you look, the FASTER it looks like it is moving away from you.

Even though along the full length the elastic is expanding at the same rate, the further away you look the faster it appears to be receeding.

If you were look far enough away, it would appear to be moving at the speed of light.

The analogy holds with the expansion of spacetime.

5. Mar 7, 2009

### Fredrik

Staff Emeritus
Neopolitan and Robousy, you both got it wrong. Unfortunately I don't have time to elaborate, because I have to get some sleep.

6. Mar 7, 2009

### v2kkim

People figured out that space expansion making far away galaxies apart fast does not follow special relativity, because every galaxies are roughly at rest with only space expanding -- this way there is no center of expansion as in balloon analog. The special relativity applies only local motion. The redshift from a far away star calculation formula does not include relativity but includes only space scale factors because as space expands the wave length also increases. The space between very far away galaxies can expand faster than 'c'. The balloon analogy of space expansion is a key on this topic and there are many good discussions in cosmology section so I may not need to repeat here.
For example if you shoot a light to one direction, then the distance the light traveled later can be larger than c*(time elapsed) because of space expansion. My calculation of the light traveled show that it includes only some math no relativity as posted in cosmology section discussion:

Last edited: Mar 7, 2009
7. Mar 7, 2009

### earamsey

But they can still move because galaxies can collide due to gravitational attraction?

So, between these galaxies there is a time dilation, ie, length of earth hour in far away galaxy would be shorter than that observed on earth? Hmm, but from this far away galaxy perspective, I am the one moving away faster than c?

By the way, why do you guys associate 'c' with speed of light? Is this fair to the other particles that travel at speed 'c'? For instance, the gravity tacheon particle also travels at speed 'c'. Why not call it cosmological speed limit instead of "speed of light"?

8. Mar 7, 2009

### neopolitan

I think I know what Fredrik was talking about and what the science show was talking about:

a distant galaxy which see today because the photons started their journey 10 billion years ago is not today 10 billion light years away but in fact a lot further away and the rate of separation between us and that galaxy would now be greater than the speed of light - assuming that the Hubble constant has been sufficiently high throughout the period.

Its just that we are seeing light today which back then was a lot closer than the source is now.

I do wonder how that theory takes into account the universal expansion during the intervening years. Starlight which reaches us after 10 billion years was not originally 10 billion light years away, because the space between us expanded during the journey.

So, how close were we when the starlight started on its journey?

More pertinently, how long would it take starlight to travel from:

a galaxy sufficiently distant today that starlight today took 10 billion years to get here (galaxy A)

to:

another galaxy in the other direction sufficiently distant that starlight today also took 10 billion years to get to us (galaxy B)? - note that I am talking about source to observer times, not about how long it would take a photon emitted 10 billion years ago to get from one distant galaxy to another. I am also making the unwarranted assumption of a very long lived star.

Since simultaneity is involved and Fredrik loves to tangle himself in it, I should point out that if distant galaxies only move because the intervening space expands, then some of his simultaneity issues don't arise. To address the other, let's say: when starlight hits our planet after travelling 10 billion years from a star in a distant galaxy A, and light from our sun hits that same star after travelling 10 billion years, how long has the light from the star in the distant galaxy B been travelling?

cheers,

neopolitan

9. Mar 7, 2009

### robousy

I don't believe I did.

10. Mar 7, 2009

### Fredrik

Staff Emeritus
Your analogy suggests that the reason why very distant galaxies (say 5 billion light-years) are moving away faster than closer galaxies (say 1 billion light-years) is the acceleration of the expansion of the universe, but a constant rate of expansion is sufficient. Suppose e.g. that the distance between two galaxies grows linearly with time. Then we can write the distance A(t) from us to some specific galaxy as

$$A(t)=A_0t/t_0$$

where A0. is the distance at time t0. The speed at time t is

$$A'(t)=A_0/t_0$$

and this is clearly twice as big when we pick a galaxy that was twice as far away at time t0. Note also that when A0>ct0, the speed is >c. It doesn't just appear to be >c. It is >c.

11. Mar 7, 2009

### Fredrik

Staff Emeritus
I agree with this part.

I'm not sure what you meant here. I'm pretty sure you didn't mean to say that almost everything is 14 billion light-years away. You probably meant to suggest that everything we see today must be closer than 14 billion light-years. It isn't, but you seem to have figured that out now.

The SR velocity addition law doesn't apply here. The velocity of the first galaxy relative to the second is definitely >c.

The Lorentz contraction formula doesn't apply either. The first galaxy will say that the second is 20 billion light-years away.

12. Mar 7, 2009

### Fredrik

Staff Emeritus
I searched the cosmology forum for posts made by Marcus, because I think he has dealt with these questions many times, but I gave up looking for those posts when I found this link in his signature:

This (Scientific American) article explains most of the things discussed in this thread.

Last edited by a moderator: May 4, 2017
13. Mar 7, 2009

### robousy

Sure - in my analogy the constant rate of expansion is the idea that the elastic band doubles in size per unit time. This is a constant rate of expansion.

Also in my analogy, the rate of expansion increases with distance. This is exactly what is encoded in Hubbles constant.

$$H=77 (km/s)/Mpc$$

The units are velocity PER unit distance. E.g the further away from Earth you look, the faster the galaxies receed.

This is again, the same as with my analogy. The further from the origin of the elastic band you go, the faster the band appears to be receeding.

They are identical concepts and I maintain that the analogy holds.

14. Mar 7, 2009

### Fredrik

Staff Emeritus
No, it isn't. You're describing a rate of expansion that's increasing exponentially. The distance between our galaxy and some distant galaxy would be

$$A(t)=A_0 2^{t/t_0-1$$

A constant rate of expansion means that A'(t) is a constant.

I disagree. The Hubble stuff doesn't imply an exponential increase of the rate of expansion.

As I explained in my previous post, we get that result with the formula $A(t)=A_0 t/t_0$. There's no need to assume that the rate of expansion is increasing exponentially.

15. Mar 7, 2009

### neopolitan

Robousy,

Think balloon or, if you don't like the implication of curved space, think of the elastic skin of a drum, the frame of which is moving away from the centre at the speed of light.

But I am butting in on someone else's conversation.

Fredrik,

I have to admit the answer looks like Lorentz transformations etc, and also that I had them sort of in my mind when I responded to the OP's question.

However, I also had in mind that 1. the universe is about 14 billion years old and 2. the distance at which things are moving away from us at light speed is 14 billion light years.

If the period of hyperinflation after the big bang had things moving away from each other at greater than the speed of light (even at cosmologically short distances), then it won't be an issue - but I am wondering if hyperinflation is not just the period at the beginning where the Hubble constant was huge. Is it a coincidence that 1/age of the universe = Hubble constant? Maybe, maybe not. If it isn't, then the Hubble constant would have indeed been huge at the beginning - meaning the "edges" of the universe would expand away at light speed at short distances and slowing down as the age of the universe increased.

If that is the case (not saying it is, just if) then nothing in the universe would today be further than 14 billion light years away from anything else in the universe.

We do know there was that period of hyperinflation, if it were based on some other principle than very high Hubble constant (which is possible, if we insist that modern day physics did not apply in an immediately post big bang era) then we could have things which are, today, further away from us than 14 billion light years and, therefore, apparently travelling faster than the speed of light relative to us.

cheers,

neopolitan

16. Mar 7, 2009

### harrycohen

If we look in all directions... and see the universe expanding wouldn't that mean that we were the center of the universe?

17. Mar 8, 2009

### LongLiveYorke

The overall point is that the fact that space is curved means that it is impossible and meaningless to compare velocities of things that aren't adjacent (or close enough to adjacent such that the space locally is to a good approximation Minkowski).

18. Mar 8, 2009

### Al68

Hi Fredrik,

I have to disagree with this. It seems to me that the first galaxy would not see the second galaxy at all.

19. Mar 8, 2009

### atyy

20. Mar 8, 2009

### Dmitry67

Imagine that we dont know about the Hubble expansion. So we look at galaxies movement and calculate their speed (based on their redshift) and distance (sending them signal and waiting for the signal back from them).

Obviously, SR holds, there are no speeds >c.

Speeds >c appear when you use a 'brid's' view (look at the baloon from the 'outside') - in that case you use standard velocity addition. Also energy conservation laws do not apply.

Speeds >c can also appear if you are talking about where are the galaxies we observe NOW (hence emmitted light billions years ago) in the current moment

Finally they appear if spacetime is curved enough