# Are galaxies moving faster than the speed of light?

1. Mar 15, 2012

### Gregory.gags

Its been noted through the Doppler Effect (or red shift maybe? not 100% sure atm) that some of the farthest galaxies seem to be moving away from us faster than the speed of light
(c+). Since there is no axis point to measure the speed of these galaxies from, other than the milky way, could it not be said that our galaxy is/is also moving through space at ≥c? (once i get some feedback on this i'll get to my main point :D)

2. Mar 15, 2012

### alexg

From the point of view of the farthest galaxies, yes.

But remember, it's not motion through space.

3. Mar 15, 2012

### Gregory.gags

its NOT motion through space? Would that mean that were not physically travelling THROUGH spacetime but more like spacetime is being stretched out and were just being pulled along with it? like a marker dot on an inflating balloon

4. Mar 16, 2012

### alexg

Exactly.

5. Mar 16, 2012

### Gregory.gags

OK, on to my second point...
because of space contraction and time dilation it is widely accepted that the faster you go through space the slower you move through time...
so moving at c, time would = 0 and >c time would = <0
therefore going 'backwards in time"

6. Mar 16, 2012

### Chalnoth

On these scales, you have to use general relativity, not special relativity. No, they don't ever appear to go backward in time from our perspective. In fact, you can get the apparent time dilation directly from their redshift. An object at $z=3$, for example, has a recession velocity greater than the speed of light (by the usual definition of recession velocity), but the time dilation factor is $1/(z+1) = 1/4$, so that to us, time on that galaxy appears to be moving at 1/4th the speed it moves here on Earth.

7. Mar 16, 2012

### Mark M

Remember, relativity forbids objects from moving through spacetime faster than light.
Galaxies barely move, for example, the Milky Way moves about 600 KPS. The galaxies appear to be red shifted and moving away from us because the space in between the galaxies is expanding.

You can imagine putting two dots on the surface of a balloon. As you blow up the balloon, they move away from each other, but only because the balloon is expanding.

GR places no limit on how fast space can expand.

EDIT: As Marcus pointed out, the 600 KPS is in respect to the Cosmic Microwave Background, mistake on my part.

Last edited: Mar 16, 2012
8. Mar 16, 2012

### marcus

Mark, this is clear accurate concise. I tend to be more talky and I think this brief style communicates better to most people. I offer one small change:
It's moving about 600 kilometers per second relative to the ancient light, the microwave background, in the general direction of the southern constellations Hydra and Centaurus. All our local group of galaxies is headed that way pretty much. A little fleet of a dozen or so, the main other one being Andromeda. I checked one time and the exact southern constellation is a small little-known one called Crater which is in the general region of Hydra and Centaurus.

It's easy to forget and write KPH instead of KPS. If you see the error and are still able to edit your post I will delete this. I hope I'm not misunderstanding. The most common way to express the small local random motions of galaxies is relative to the CMB. Those KPS speeds (relative microwave background) certainly are small compared with either the speed of light or with the rate at which distances to most galaxies are expanding! Distances to most of the galaxies we can see are indeed expanding faster than the speed of light, but that is just geometry change, not motion thru space (as you say.)

Last edited: Mar 16, 2012
9. Mar 16, 2012

### Mark M

Thanks for the correction! I just did a quick Google search for the velocity of the Milky Way galaxy, I should have been more specific.

10. Mar 16, 2012

### Drakkith

Staff Emeritus
Marcus or Chalnoth, is there a local redshift due to actual motion away from us equivalent to z=3 redshift? IE would an object moving away from us here in local space have the same redshift at a certain velocity?

11. Mar 16, 2012

### marcus

To translate local velocities into doppler one uses the relativistic doppler shift formula
If β is the speed (as a fraction v/c of speed of light) then
1+z = sqrt((1+β)/(1-β))
so if you want the speed that would give a doppler shift (not a cosmological redshift but an actual doppler shift) of 3, then you have to set that sqrt = 1+3 = 4
so what's inside the sqrt must = 16.
And you can solve for β.

Let's see what that would be, in the example of shift=3 that you proposed.

16(1-β) = (1+β)
15 = 17β
β = 15/17 of the speed of light.

That is a purely special rel. thing, the calculation applies in local nonexpanding geometry and the speed you get has essentially nothing to do with expansion that occurs while light is traveling long distances.

As I'm sure you know but other readers might not, if you go here
http://www.einsteins-theory-of-relativity-4engineers.com/cosmocalc.htm
and plop 3 into the redshift box and press calculate then it tells you that the recession rate was 1.6 c when
the light was emitted and 1.5 c when the light was received here on earth.
The cosmological redshift is the result of all the expansion that was happening all while the light was in transit from there to here. It does not depend just on one instantaneous relative velocity, like doppler does.

That's obviously different from the doppler 15/17 c.

Last edited: Mar 16, 2012
12. Mar 16, 2012

### Drakkith

Staff Emeritus
Awesome, thanks Marcus!

13. Mar 16, 2012

### Drakkith

Staff Emeritus
Hmmm. Just thought of another one.
How can we tell the difference between doppler and cosmological redshift?

14. Mar 16, 2012

### turbo

In our local neighborhood, peculiar motions can be dominant, but as we look farther and farther out, peculiar motions become negligible in the total redshift of an object.

15. Mar 16, 2012

### Drakkith

Staff Emeritus
I'm sorry turbo, I have no idea what you are saying here. What are "Peculiar Motions"?

16. Mar 16, 2012

### turbo

Peculiar motions are motions of objects relative to us. For instance, M31 is quite close to us, so any redshift/blueshift that we observe can be mostly attributed to the motions of our galaxy and M31 relative to each other. If we want to observe a galaxy at the limits of our observational instruments, it can safely be assumed that those galaxies are not flying away from ours (peculiar motion) and their redshifts can be attributed to cosmological effects.

This is OK, though not comprehensive, IMO.
http://en.wikipedia.org/wiki/Peculiar_velocity

17. Mar 16, 2012

### marcus

Turbo is right in everything he says here but I'll try explaining from a different angle:

both have the same effect of shifting the wavelength, so we CAN'T tell the difference just by looking at the bright and dark lines of the spectrum but we can use commonsense or plausible reasoning. If the galaxy is in what looks like a cluster then probably it is roughly the same distance as the other ones in the cluster. If the distance is the same then the cosmo redshift should be the same. So if the shift is very different from the others then probably that is the add-on contribution of a doppler. It is probably moving towards or away with its own individual motion.

And if it is NOT different from the others in the cluster then the natural tendency is to attribute it to cosmo redshift. Unless you have some other handle, like an independent distance determination say by means of some supernova or variable star that can serve as a standard candle. If you can tell the distance you may be able to infer that the whole cluster is moving towards or away and has a doppler contribution adding on to the usual cosmo redshift that happend while the light was in transit.

Things have their own individual motions (called their "peculiar" motions) and it takes some detective work to sort it out.

Stars on the righthand edge of a galaxy might be less red and those on the left edge more red---so you can figure that the thing is rotating! That effect is doppler and is superimposed on the generally more dominant cosmo redshift effect.

18. Mar 16, 2012

### Drakkith

Staff Emeritus
Thanks Turbo and Marcus. All that makes sense. However, what I am asking is how to tell, fundamentally, whether redshift is caused by the doppler effect or cosmological effects. Since we can't tell just by looking at the spectrum, what causes us to say that redshift is due to the expansion of space and not simple motion away from us? AKA we can look at a galaxy cluster and say that redshift due to expansion is z=.3, but why do we say its because space is expanding and not doppler shift?

I've taken it for granted that we can tell, but I've never known what our reasons are.

19. Mar 16, 2012

### turbo

Actually, we can't tell by measuring redshifts, but we can make educated guesses about which mechanisms are responsible for the redshift of individual galaxies, as Marcus explained. If a galaxy appears to be physically associated with others in a string or a cluster, it's probably safe to assume that its redshift is due to a common (cosmological) mechanism. If its redshift is anomalous WRT to its apparent neighbors, we have to consider that it might be a foreground or background galaxy projected by chance on its apparent neighbors. Absent other distance-indicators, we have to rely on best-estimates.

20. Mar 16, 2012

### Drakkith

Staff Emeritus
Perhaps I am wording my question incorrectly.

Since we can't tell by looking at redshift, why do we say "space is expanding" instead of "galaxies are moving away from us THROUGH space". I'm guessing that this is a much bigger can of worms than I thought it was.