Expansion of Universe and Time dilation

[earamsey]

I saw on Science Channel that the expansion of the Universe, distance between galaxies was specified, is occurring 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?

 

[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

 

[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

 

[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.

 

[Fredrik]

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

You guys might want to check out some old threads in the cosmology forum. There are lots of threads about this.

 

[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:

Regarding the distance advanced by light in expanding universe , I did some calculation to get the result:

$$D(T)\ = {c \over r} (\left( 1 + {r*dt} \right)^{T \over dt} -1)$$

Taking the limit dt going to 0,
$$D(T)\ = {c \over r} (e^{rT} -1)$$
where
D(T): distance advanced by light during period T.
c: speed of light
T: time from emission to present.
r : space expansion rate 1/140 % per million.
dt: the arbitrary small time intervals in T.
** In case r goes to 0, D(T) goes to c*T as expected.

I got this formula by adding each light path segment advanced for each dt, that is after the last dt, the D1 (distance advanced of the last dt) is D1=c*dt*(1+r*dt), and the 2nd last one D2=c*(1+r*dt)^2, and so on .. Dn=c*(1+r*dt)^n. From summing D1 D2 ..Dn, I got above formula.
I do not want to use the word speed to avoid confusion, but it is just the distance of light advanced after a period T.

 

[earamsey]

because every galaxies are roughly at rest with only space expanding

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

...The space between very far away galaxies can expand faster than 'c'.

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"?

 

[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 traveling 10 billion years from a star in a distant galaxy A, and light from our sun hits that same star after traveling 10 billion years, how long has the light from the star in the distant galaxy B been travelling?

cheers,

neopolitan

 

[robousy]

Neopolitan and Robousy, you both got it wrong...

I don't believe I did.

 

[Fredrik]

I don't believe I did.

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.

 

[Fredrik]

The only things that could be moving away from us at the speed of light are about 14 billion light years away,

I agree with this part.

which is pretty much everything since the universe is considered to be 14 billion light years old.

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.

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.

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

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

 

[Fredrik]

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:

http://www.astro.princeton.edu/~aes/AST105/Readings/misconceptionsBigBang.pdf

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

 

[robousy]

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.

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.

 

[Fredrik]

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.

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.

This is exactly what is encoded in Hubbles constant.

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

E.g the further away from Earth you look, the faster the galaxies receed.

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.

 

[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 traveling faster than the speed of light relative to us.

cheers,

neopolitan

 

[harrycohen]

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

 

[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).

 

[Al68]

The first galaxy will say that the second is 20 billion light-years away.

Hi Fredrik,

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

 

[atyy]

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

"At the end of the brief clip, we see that the distances to the blue and green galaxies have doubled, and so have all distances between all of the galaxies shown!"
http://www.einstein-online.info/en/elementary/cosmology/expansion/index.html

 

[Dmitry67]

Imagine that we don't 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

 

[neopolitan]

Fredrik,

I read the article, it didn't seem to answer all the questions which I would have come up with (or some that I wouldn't necessarily have come up with).

1. Was the big bang orginally a singularity or not?

2. If the big bang was not originally a singularity, then conceivably it could have been an infinite space which was much denser and hotter than today and conceivably had been like that forever. Are there any theories as to what could have triggered two very important events: a. the commencement of a hyperinflationary era and b. the cessation of a hyperinflationary era ?

3. If the big bang was originally a singularity, then the big bang itself could have triggered the initial hyperinflationary era, but are there any theories about what caused its cessation?

4. Is the fact that the Hubble constant is a very good approximation of the age of the universe a coincidence? If not, what does it mean?

5. What is the error in thinking that the Hubble constant is the inverse of the age of the universe, which means (if the big bang was originally a singularity) that the fastest anything else in universe could be receding from us would be the speed of light and that, therefore, there is nothing outside the 14 billion light year radius (nothing as in no stars/galaxies and nothing as in no space for stars/galaxies to be in)?

6. What is the error in thinking (if the big bang was not originally a singularity) that nothing outside our "grapefruit" was ever going to influence us, and the fastest anything else in universe (specifically anything that ever could have influenced us) could be receding from us would be the speed of light and that, therefore, there is nothing that could ever influence us outside the 14 billion light year radius? (I do accept that this has problems in that nearby galaxies could be influenced by galaxies outside our primordial "grapefruit" and that that could in turn influence us, but: a. I could think that the time delay involved in such a "chain of influence" would approach infinity, and b. I lean towards a singularity based big bang anyway.)

7. Is there any significant difference between the universe starting as a singularity and starting as a finite yet extremely highly dense energy concentration - ie one highly dense grapefruit of energy rather than one singularity?

8. I know there are certain things that fit into the theory, such as light sources which today should be much further than 14 billion light years away (as far as 46 billion light years), but that just makes me wonder about the Hubble constant. For us to be able to see light from something which is today 46 billion light years, this implies a period of hyperinflation (very high Hubble constant) putting the source a sufficiently far distance away from us that the light did not reach us during the following period of slow expansion (lower Hubble constant than today, thereby putting the source sufficiently close to us that it never got beyond the varying Hubble distances pertaining to the "modern era" Hubble constant values which are apparently increasing. This means the Hubble constant was initially very high, then went low, then increased (possibly with a jump, but not necessarily). This would imply that the indication that the Hubble constant is very closely corelated with the inverse of the age of the universe is purely a coincidence - which given how the Hubble constant has apparently been all over the place, is a pretty amazing coincidence. Comments?

9. Would a theory which didn't have the Hubble constant going all over the place be an improvement to standard theory? If not, why not?

Perhaps I should post this on cosmology?

cheers,

neopolitan

 

[Fredrik]

I read the article, it didn't seem to answer all the questions which I would have come up with (or some that I wouldn't necessarily have come up with).

Yes, it explains many of the issues that have been brought up in this thread, but it certainly doesn't answer all of your questions. For now, I'll only answer those questions that I can answer immediately, without looking stuff up.

1. It is in some models, and not in others. It certainly is in the FLRW solutions of Einstein's equation, which are the basis of the "standard" cosmology.

5. I don't follow your logic here. (I can't say what the error is since you didn't explain your argument in detail, but you'll probably figure it out on your own if you try to explain the details to yourself). The universe can certainly be much bigger than the part we can see. It's even possible that it was infinite at all times (t>0). Also, I think that the SciAm article I linked to explains that the most distant things we can see are now farther away than 14 billion light-years, because the space between us and them has expanded since the light they emitted started moving towards us.

6. What parts of the universe can influence us depends on the rate of expansion of the universe. The expansion is accelerating now, but if it slows down in the future, and stays slow (let's say that distances grow as t^(2/3) to be specific), then you could in principle travel with a constant velocity of say 6 km/h (walking speed) and still catch up with a galaxy that's already receding from us with a speed that's greater than the speed of light. (I'm not sure what any of this has to do with the big bang being a singularity or not though).

7. I think there is, at least according to models based on GR without inflation, as there are theorems that say that all the relevant solutions have singularities. In models with inflation, I think the region that started expanding could be just a tiny dot in a universe that might be infinitely large and infinitely old.

8. I don't think inflation is necessary for us to see something that's 46 billion light-years away today. An expansion of the sort that's still going on today is sufficient. I don't know how much the Hubble constant has varied, and I don't know anything about that coincidence.

 

[neopolitan]

I'm just going to address two responses, where I probably wasn't being sufficiently clear in what you were responding to. They are related:

5. I don't follow your logic here. (I can't say what the error is since you didn't explain your argument in detail, but you'll probably figure it out on your own if you try to explain the details to yourself). The universe can certainly be much bigger than the part we can see. It's even possible that it was infinite at all times (t>0). Also, I think that the SciAm article I linked to explains that the most distant things we can see are now farther away than 14 billion light-years, because the space between us and them has expanded since the light they emitted started moving towards us.

...

8. I don't think inflation is necessary for us to see something that's 46 billion light-years away today. An expansion of the sort that's still going on today is sufficient. I don't know how much the Hubble constant has varied, and I don't know anything about that coincidence.

5. I wrote:

What is the error in thinking that the Hubble constant is the inverse of the age of the universe, which means (if the big bang was originally a singularity) that the fastest anything else in universe could be receding from us would be the speed of light and that, therefore, there is nothing outside the 14 billion light year radius (nothing as in no stars/galaxies and nothing as in no space for stars/galaxies to be in)?

Start with a singularity, which means everything is in one spot (to the extent possible, noting that there is a limit to how much energy you can squeeze into a small space, but also noting that prior to the big bang it could be said that there was no space which could be too small to take all the energy which was around just after the big bang). If the Hubble constant is the inverse of the age of the universe, you have at t=0 you sort of have everything in one spot and a meaningless Hubble constant (which is ok, because the big bang has not happened yet so nothing really exists).

Then, after the first Planck time you have your "grapefruit" (I can't address what happens in the period in between) and an extremely high Hubble constant. Let's say that at the edges of the "grapefruit", space "wants" to expand at some speed greater than lightspeed (because at t=1.t_pl, if the Hubble constant is 1/age of the universe, things would only have to be one Planck length apart to expand at the speed of light but the "grapefruit" would have been substantially bigger than that). At the same time, you have an extremely high density of energy, which like a galaxy would not be "wanting" to expand. This would lead to a period (an era, if you like) in which you'd have conflicting forces, expansion and gravitational clumping, the end result of which would be a big bang.

Now, there are two options here, depending on what happens in galaxies today. Does space expand less swiftly in galaxies or does space continue to expand at the same rate but the galaxies sort of stick together with the expanding space sliding past the constituent stars. In other words, at the galaxies embedded in space (like two imperfections on an expanding balloon) or just "sitting on" space (imagine an elastic drum skin being stretched with two tethered weights sitting on it, the skin would slide under the weights)?

I think the former, so I will go with that.

If galaxies are embedded in space, then they are locally resisting the expansion. The same phenomenon would have occurred during the big bang with universe's energy resisting a fair proportion of the hyperinflationary expansion, and I suspect that this hyperinflationary era would have lasted until the universe reached a balance point, namely where the edges of what was a "grapefruit" would expand at c, rather than >c.

So, you have an era of hyperinflation and you have then a "modern" era, all guided by a consistent Hubble constant = 1/age of the universe.

I think that at the time of the interface between the two eras, if you were able to exist there and take measurements, you would see that the universe's radius = Hubble distance, or in other words the distance that anything traveling at the speed of light would have traveled since t=0. Since then, the universe's radius would have consistently been the Hubble distance. If that is the case, then the universe would have a radius of 14 billion light years and nothing would lie outside of that radius - no stars, no galaxies, no space for them to be embedded in.

However, it could be that things were not so evenly balanced, so that by the time that things settled down, the universe's radius was greater than the Hubble distance. By how much, I just don't know - possibly enough that the universe's radius today is 46 billion light years. I don't like it, I prefer a 14 billion light year radius universe, but I see that it is possible and the universe is under no obligation to satisfy my preferences.

8. If you have got the gist of what I wrote before, perhaps you can understand why a hyperinflationary era is necessary to see something today which is more than 46 billion light years away, if Hubble constant = 1/age of the universe. The hyperinflationary period is not inconsistent with this Hubble constant. It is just that the early universe's balance between expansion and energy density's resistance to expansion would have been tipped in favour of expansion, rather than in favour of resistance (no big bang) or neutral (modern day universe which has a radius no bigger than 14 billion light years).

cheers,

neopolitan

 

[Phrak]

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

It could. It could also mean there is no center if every other location sees the same thing.