# Need help in how Universe grows

1. Oct 14, 2009

### S.Vasojevic

If we take some super telescope and go to the North pole, point it straight up, observe some distant galaxy, measure its red shift, and find out that it is 10 Bly from us, and then go to the South pole, find galaxy at a similar distance we will say that they are 20 billion light years away from each other. But we are looking at them as they were 10 billion years ago, when they should be much closer to each other.

Why is that so:

1. Space is expanding much faster than speed of light.

2. We are measuring distance, not through space, but through spacetime, and it is not straight but hyperbolic.

3. Something else

2. Oct 15, 2009

### Chalnoth

Well, it just depends upon which distance measure you're using. One measure estimates the distance the galaxy was when the light was emitted from the object. Another measure estimates its current distance. Typically we use the latter when explaining distances because the former first increases as you go to higher redshifts, then decreases.

3. Oct 17, 2009

### S.Vasojevic

Lets say that we are talking about observable universe, so distances are measured when light was emitted.

4. Oct 17, 2009

### Chalnoth

Okay. Then what's your question?

I'm pretty sure that nothing that we can see was as far as 10 billion light years out at the time its light was emitted.

Edit: Just did some calculations, and it looks like the light that was emitted from objects furthest away was emitted by objects that were, at that time, 6 billion light years away, emitted around 10 billion years ago. The universe has expanded since then, which is why it took longer than 6 billion light years for the light to reach us (as it traveled part of the distance, there was more left to travel due to the time elapsed).

Last edited: Oct 17, 2009
5. Oct 17, 2009

### S.Vasojevic

I guess that my question comes to how we define term "now" in cosmological terms. Is it a sum of "pasts" whose influence we can feel or observe, or is it what we contemplate that is happening "right now" for any arbitrary point.
BTW, can the gravitational wave itself be redshifted (not referring to gravitational redshift) due to cosmological expansion?

6. Oct 17, 2009

### Chalnoth

One easy way to define "now" in cosmological terms is the time at which every location sees the same CMB temperature.

Certainly. In fact, it has to be redshifted in the same way that light waves are.

7. Oct 17, 2009

### S.Vasojevic

If we put a giant clock in a far far away galaxy, which has no significant peculiar velocity to ours, but is speeding away due to cosmological expansion, and observe it from Earth, would it run slower then our clocks?

8. Oct 17, 2009

### Chalnoth

It would appear to, yes. You can see this trivially by considering the redshift. Imagine a clock that basically consists of a laser pointed in our direction, with the "ticks" consisting of the peaks of the wave. If the source is sitting at z=1, then the wavelength will be increased by a factor of two, which means that we will see a factor of two increase in time between "ticks", ergo time dilation.

9. Oct 17, 2009

### S.Vasojevic

So If we define "now" as same reading of CMBR temperature, from ours (or any) point of view it would have a "shape" of inverted (future) light cone?

10. Oct 17, 2009

### Chalnoth

Well, "now" is a space-like surface, so you can't actually see it anywhere except where you are. If we imagine, for a moment, all of the surfaces that we would have called "now" at various time in the past, though, each of them would be a plane (well, a 3-dimensional plane, but it's easiest if we visualize it as a 2D-plane). What we see of that plane is just a thin circle (in three dimensions, the part that we see is the surface of a sphere).

11. Oct 19, 2009

### S.Vasojevic

That is exactly how I think about time dilatations, considering redshifted wave as a clock. But then I get in serious trouble with special relativity. Blueshifted objects tick their time faster? "Twin paradox" is not a paradox. If they speed away, they see each others time, respectively, goes slower? Accelerated particles here on Earth decay slower, that same particles at rest. What am I missing?

Last edited: Oct 19, 2009
12. Oct 19, 2009

### Ich

No, Blueshift/Redshift is not the same as time dilatation, there's also the classical doppler effect. Essentially, relative motion leads to time dilatation, regardless of the direction.
Exactly. But bear in mind that time dilatation has to do with the definition of simultaneity. Cosmological coordinates use not the standard SR definition or an approximation of it, global cosmological time is defined differently. Therefore, comparing cosmological times tells you nothing about time dilatation.

13. Oct 19, 2009

### Chalnoth

Well, this isn't special relativity we're talking about, though, and it also isn't a doppler shift (which is the effect that causes blue shifting). The doppler shift isn't all about time dilation (which is part of the effect), but is also about just traveling through space. If the next crest of the wave is emitted closer to the observer than the first crest was, then that is perceived as a blue shift.

Edit: To expand a bit on this, in the case of the cosmological redshift, one can think of the different objects motion relative to one another as being zero (apart from the local motions, like a planet orbiting a star, a star orbiting a galaxy, and a galaxy orbiting a cluster). With no relative motion, the entire redshift can be thought of as a perception of time dilation.

Last edited: Oct 19, 2009
14. Oct 19, 2009

### Ich

No, this is evil.
To declare something stationary doesn't make it stationary. Nearby galaxies are moving away from each other. Either the coordinate system or the galaxies are not stationary, and both reduce to one fact: there is relative motion. Really.
Generally, there is a frequency shift in FRW spacetimes, called "cosmological redshift" in our case. People often want to know the peculiar mechanism that causes this shift, and this normally means to call it either gravitational or doppler - some relatively well-known kinds of redshift.
But both have a meaning, and this meaning (warning: technobabble) depends on weak field approximations. In our case, it's exactly the time dilatation encountered in fermi normal coordinates. This always works for nearby galaxies, for farther galaxies the distinction gets blurry (due to time evolution), and for the overall whole of the universe some kind of "no motion through space speak" :yuck: might be helpful. But extremely harmful to simple statements concerning our neighbourhood.

15. Oct 19, 2009

### Chalnoth

In terms of the redshift, the only relative motion is due to the velocity of each object with respect to the background. There is no relative motion component of the redshift due to the expansion. That redshift is entirely due to the expansion of space from the time the photon was emitted to the time it is absorbed.

So yes, it is perfectly valid to think of all objects in the universe as being stationary (ignoring their peculiar velocities).

16. Oct 20, 2009

### Ich

I'd agree, if this notion did not cause so much confusion among experts.
For example:
Obviously, if there is redshift between two stationary observers, it must be attributed solely to time dilatation. That's ok in SR coordinates, because being statinoary implies constant light travel times. But the conclusion is wrong for cosmological coordinates, because there being stationary has no implications for the status of relative motion. Especially, light travel times are not constant. Further, the proper time between two events is the same for every comoving observer, if those events are simultaneous respectively (same cosmological time for each observer). Using the standard cosmological synchronization scheme, there is no time dilatation, so it could hardly be identified as the reason for redshift in this model.

The "reason" of redshift is completely model-dependent. In cosmological coordinates, you might attribute it to some "stretching of space", and that's it. The downside is, that this sounds like new physics, like a third "mechanism" of redshift in addition to doppler and gravitational time dilatation.
But if you use standard coordinates - which is quite accurately possible in regions <<1/H - this very same redshift now consists of two components, doppler and gravitational. And those galaxies are moving away from each other. The downside: not globally applicable, no easy explanation for 1+z~a. But the invaluable benefit: you have intuition in these coordinates, they match our everyday and SR world. That means that it's much easier to "understand" what's going on, i.e. to trace the local universe back to well known physics. (Not necessarily well known sources of gravity!)

17. Oct 20, 2009

### Chalnoth

Except from the perspective of observers within the cosmology, there is time dilation.

Usually when we talk about time in cosmology, we're talking about the time of comoving clocks. This is the time which I believe I talked about in this thread, where the same time everywhere can be defined as being the time at which observers separated by some distance see the same CMB temperature. The time dilation doesn't arise when we're just talking about laying down our coordinates, though: it arises when we talk about what one observer sees with respect to another.

Consider this situation. Two observers are far enough away from each other at the start that the light travel time is one billion years. We wait for 3 billion years, and now that the universe has expanded, the light travel time between the observers is 2 billion years.

So, when the first observer sees the other, that light will be a billion years old. Three billion years after that light is emitted, according to the other, some new light is emitted, but it takes 2 billion years to reach our observer.

This means that, according to our observer, it has taken 4 billion years for the other to age by 3 billion years. Ergo, time dilation. Simply due to the expansion which caused increases in light travel times.

Well, yes, this works at very low redshifts. But it diverges at high redshifts. Anyway, the redshift due to the expansion of space can be better thought of as just being another form of gravitational redshift due to the space-time curvature over the distance the light travels.

18. Oct 20, 2009

### Ich

??
What you describe here is the simple classical Doppler effect.
signal1 sent at t1=0, received at t2=1, light travel time ltt1=1
signal2 sent at t3=3, received at t4=5, light travel time ltt2=2
Of course t4-t2>t3-t1, but that's redshift, not time dilatation.
You correct for ltt, (t4-ltt2)-(t2-ltt1) = t3-t1, ergo no time dilatation. That's how it is defined, with pairs of simultaneous events.
You see redshift, and you observe time dilatation after interpreting what you see according to your reference frame. People dealing much with SR use this meaning of "see" and "observe" to make clear what they're talking about.
Interestingly, if you interpret redshift according to standard SR coordinates, there is time dilatation. But not as much as redshift.
No, that's exact this confusion Davis & Lineweaver sowed. The coordinates look very different, but both systems work fine up to quite large distances. Of course, if you plug the cosmological "recession velocity" in your SR doppler formula, you get nonsense. You always get nonsense if you confuse different coordinate systems. That does not mean that one of both is "wrong", as D&L assume.
You know how close an empty universe fits the observed SN data. And you know that standard SR coordinates cover all of an empy universe. That's not exaclty "diverging", especially as standard SR coordinates are still not Riemann normal coordinates, where you include gravity as well.

Except that spacetime curvature is not necessary for cosmological redshift. Which makes me think that it is better not being tought of as another form of gravitational redshift. That's exactly this inventing of a third mechanism I referred to. No need for it.
Locally, and by that I mean billions of lightyears, redshift can be explained quite mundanely.

19. Oct 20, 2009

### Chalnoth

Er, that's simply incorrect. Without space-time curvature, you'd have Minkowski space, where there is no cosmological redshift because there is no expansion. When you have expansion, there is definitive space-time curvature.

20. Oct 21, 2009

### Ich

You know that there is an empty expanding universe in the FRW models. Empty==flat, and expansion is just a coordinate transformation away from Minkowski space. This transformation is responsible for nearly all of the weird behaviour of FRW universes. Spacetime curvature becaomes important only at the largest scales.