Are galaxies moving faster than the speed of light?

Drakkith

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.

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.

Drakkith

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.

turbo

Much bigger can of worms! Can we assume that we are the center of the observable universe, and that individual galaxies and entire clusters are racing away from us? That's not a tenable position. You could invoke another mechanism (like the discredited "tired light" idea) to explain cosmological redshift, but it is not reasonable to assume that all objects at cosmological distances are rushing away from us. I'm tired and may not be explaining this well, but I'll try again later if you still have questions.

Drakkith

I'm not trying to invoke anything here. I've just never seen an explanation for why we say cosmological redshift isn't due to doppler shift. Like why isn't doppler shift compatible with observations of redshift. If both are indistinguishable from each other by comparing redshift alone, then I'm assuming that the reason lies elsewhere?

marcus

It can be thought of either way but becomes very complicated if thought of as doppler.

The basic underlying thing is the assumption that we live in a solution to the Einstein GR equation. GR has been tested a lot and is considered pretty reliable. Plus the model derived from GR fits the data well.

So there is an expansion history a(t) and the redshift satisfies 1+z = a(now)/a(then).

Now this CAN be treated as the result of a concatenation of an infinite number of infinitesimal doppler effects, occurring in little almost flat Minkowski patches along the way. You can hop from one coordinate patch to the next all along the way the light traveled, and perform a cumulative doppler shift.

Because the cumulative redshift depends NOT ON A SINGLE SPEED or rate of recession, say at the time of emission, but on a whole history of recession rates that prevailed at different times during the light's travel.

But you can analyze the cosmo redshift as the cumulative result of many many small dopplers. And therefore you can say that it IS A DOPPLER. what you say depends on how you treat it mathematically. Poincaré said that mathematics is not right it is *convenient*. It is a sophisticated attitude, he was a smart man. Don't ask what nature IS, ask what is the most convenient way to describe it. Call it a succession of many tiny doppler shifts if you like. Or call it stretching out the lightwave, if you like. They give the same answer.

Drakkith

You're saying that because of the way GR works simply thinking of the redshift as doppler only works if you make little short hops and stay "local" the whole time? Alright, I can understand that. Thanks Marcus.

Khashishi

It seems to me there are two different ways to create redshift. The first is if the light source is moving away from us in a static spacetime. The second is if spacetime is expanding and the source is being carried away with it. In general there would be some combination. How can we observe the difference? Is the difference real or just in the coordinate system used?

cng99

Well, I know it might be too late to point out, but there's this really awesome link for anyone who hasn't understood.
http://www.exploratorium.edu/hubble/tools/center.html

The tiny widget they have created, makes things really clean.

Chalnoth

Cosmological redshift is correlated with distance measures. Doppler redshift isn't.

Chalnoth

If you're using these to describe the expansion of the universe, there is no difference whatsoever between these two descriptions. It's just a coordinate system choice.

Drakkith

Wouldn't there be a difference in recession velocity, since doppler shift doesn't really work well with galaxies receding faster than light? Or would either work fine as long as you are using GR appropriately?

Chalnoth

Recession velocity isn't well-defined anyway. There is no absolute definition of the relative velocities between far-away objects. So it shouldn't be a surprise that you'll get different velocities in different coordinate systems.

Drakkith

I was not aware of this. Got any links that explain?

Chalnoth

I'm not aware of any popular sources for this, sorry. You might be able to find something by searching for "relative velocity general relativity".

But in the mean time, in General Relativity the only time vector subtraction is well-defined is at a single point. When you try to subtract one vector at one point from a vector at another point in space-time, ambiguities arise as to how to do that.

To take a simple example, one method in General Relativity that allows you to subtract two vectors at different locations is through parallel transport. Parallel transport moves one vector across some path towards the other vector, keeping this vector parallel to itself along the entire path.

The problem is that in curved space-times, parallel transport can lead to different answers depending upon which path you choose. And there is no a priori way of saying that one path is better than any other path.

Drakkith

I see. Alright, I'll see if I can find some more information on it. Thanks guys.

emailanmol

I would like to point out that the quality of discussion on this thread has been phenomenal.
They have given a huge boost to my conceptsThanks :-)