# Doppler effect / expanding universe . trouble uniting both concepts?

1. Jun 22, 2007

### moe darklight

doppler effect / expanding universe . trouble uniting both concepts???

Ok, I think I understand both; I just don't understand their relationship.

As I understand the doppler effect, in short, its cause by the difference in velocity (movement through space).

And as I understand the expansion of the universe, it is space itself that is expanding— i.e, things aren't literally "moving away" from each other; it is the actual space between them that is expanding.

Here's my problem: if one of the ways we can detect the universe's expansion is the doppler effect (a star's red-shift)... why is this red-shift happening if the star isn't actually moving away from us— that is, if it is space itself that is expanding, then it is not moving away from us in the same sense that it would be if something was physically pushing it away from us through space, which I understand is a requirement of doppler effect

I'm a bit more comfortable now with equations and mathematical explanations than I used to be, in case they are needed for the explanation (though I'll admit some of the more complicated ones still scare the crap out of me :surprised). I wish I had more time to read physics

Last edited: Jun 22, 2007
2. Jun 22, 2007

### Garth

A good question - the answer is that once atoms are defined as the standard by which the universe is to be measured, their diameter determining the standard length of a steel ruler, their atomic frequencies determining the standard time interval of an atomic clock and their mass determining the standard kilogram, then cosmological red shift is interpreted as a recessional velocity.

That is, if you could lay out N metre rulers end-to-end between here and a distant galaxy then a short time later you would require N+1 metre rulers. Of course this method of measurement is impossible practically and distances have to be defined by other methods of measurement that are found on the Cosmic Distance Ladder.

Garth

Last edited: Jun 22, 2007
3. Jun 22, 2007

### moe darklight

a relief to hear that . I know I'm on the right track when I don't understand the right things

thanks for the answer! what little physics I read every day, this stuff never stops amazing me. I wish I had discovered physics when I was younger; I've been missing out on so much for those first 19 years of my life.

4. Jun 22, 2007

### MeJennifer

One way to think about it is that (relativistic) Doppler effects pertain to the EM field and expansion to the gravitational field.

5. Jun 22, 2007

### Ich

I would disagree with Garth here. As I understood (mostly from the Davis/Lineweaver Paper), there is no sensible definition of cosmological redshift in terms of the doppler effect.
One would rather say that the wavelength of the once emitted light expands just like the whole universe does. Recessional velocity has no direct influence, as both emitter and absorber are "at rest", i.e. without significant peculiar motion.

6. Jun 22, 2007

### Garth

It depends on what you mean by the 'Doppler Effect'.

With cosmological red shift there is no proper motion, proper motions, and the red/blue shift associated with them, are additional to the cosmological red shift.

Physical distances, as measured by 'physical' (metre sticks) rulers, between distant objects and ourselves increase with time, they exhibit red shift, they are moving away from us due to cosmological expansion.

Therefore it is this sense that I am prepared to call that red shift "Doppler" in nature.

Garth

Last edited: Jun 22, 2007
7. Jun 22, 2007

### Ich

We agree here.
Distances get dilated, and that is exactly the red shift. I disagreed with your comment:
Red shift is interpreted rather as the actual dilatation of distances $$a_{now}/a_{then}$$. A recessional velocity would be $$\dot{ a}_{now}/a_{now} \cdot d_{now} = H \cdot d_{now}$$, which does not contain enough information to calculate a red shift.

Last edited: Jun 22, 2007
8. Jun 22, 2007

### George Jones

Staff Emeritus
The colour of light is related to its colour, with blue light having the shortest light and red light the longest. If space expands, then wavelenth expands along with it (as Ich says) redshifting the colour.

We see a change wavelenth, becuase atomic and molecular forces prevent us and our metre sticks from expandin along with space.

Ned Wright's website has a nice illustration of expanding wavelengths.

9. Jun 22, 2007

### Garth

Yes George, and ordinary Doppler red shift can be thought of in a 'hand waving' way as the stretching out of the oscillations of a light wave by the increasing distance between a source and a receding observer, as seen by that observer. The later crests take more time to reach her because the distance has increased. In this way cosmological red shift can be compared with ordinary Doppler red shift.

Ich, we agree, I do not understand why you think we disagree:
The actual dilatation of distances means having to use more metre steel rulers later on in time to span the distance between ourselves and a distant galaxy. The spatial universe is expanding relative to the size of an atom and the length of a steel ruler, made of atoms that we have defined to be the standard of measurement of [M], [L], and [T].

Garth

Last edited: Jun 22, 2007
10. Jun 22, 2007

### pervect

Staff Emeritus
The only thing I'd add is that the usual distance measure places the rulers along a curve of constant cosmological time in order to measure the distance.

If one were to put the rulers along a space-like geodesic, one would get some different distance. As far as I know, though, nobody actually uses this sort of distance.

The standard way to define distance is to first split space-time into space+time. You then measure the distance along a curve of constant time according to this split. Different splits can give different measures of distance. Cosmologists use cosmological time because it's a convenient split - it's the only split that makes the spatial slices homogeneous and isotropic.

11. Jun 25, 2007

### Ich

Hi Garth,

there is no disagreement on cosmological expansion. However, regarding the OP
I think the only answer can be: right, it is not doppler shift due to relative motion, but the expansion of the wavelength while the light is on the way.

Every mention of velocities will confuse rather than clarify, as the relationship between red shift and "velocity" is not straightforward and not causal, but model-dependent and somewhat arbitrary.

12. Jun 25, 2007

### Garth

The distance between a distant source and ourselves, as measured by metre steel rulers, increases with time, and the rate of increase of that distance may be described as a 'velocity'.

However, as we agree, this velocity is due to the expansion of space itself, not to any proper motion within that space.

So long that is clear all is well.

Garth

13. Jun 25, 2007

### Ich

Of course you can derive a velocity from expansion (and distance). But you can't derive red shift from that velocity.

14. Jun 25, 2007

### pervect

Staff Emeritus
You can derive a redshift from the velocity - you just can't use the SR formulas to do it. I can probably find the page in MTW that does the full GR derivation with some effort, but I'm not sure how helpful that would actually be.

It's fairly well known, though, that the correct answer in GR for the redshift is proportional to the scale factor of the universe at the time of reception divided by the scale factor of the universe at the time of emission, where all times here are "cosmological times". This assumes that the transmitter and receiver have low "peculiar" velocities, i.e. that they are both stationary with respect to the CMB.

15. Jun 25, 2007

### marcus

that is the important point, I think.

the cosmological redshift of some light that is now reaching us is the cumulative result of the whole history of expansion during the time the light was traveling on its way.

But people normally think of velocity as an instantaneous property: a velocity is defined at a particular moment in time.

And "averaging" offers no satisfactory way out either, because in the real universe of nature, there is NO OFFICIAL CLOCK. Even for observers who are all at rest with respect to CMB or Hubble flow, even then they are all in gravity wells of different depth and time goes at different rates for them----one can usefully approximate a "global time" but not rely on it as an absolute.

so there is no very useful meaning to averaging expansion rates (where? they vary by location) over the whole time of travel,
or pointing to some single moment when the expansion rate was somehow typical of the period the light was on its way.

What it always comes down to is that the wavelength is stretched by exactly the ratio that the distance traveled has stretched
so if the distance doubled while the light was covering it, the wavelength will have doubled.

For this reason I think that Ich has been maintaining the pedagogically clearest position.

I also think that it is misleading people, and confusing them, when one distorts the meaning of the words "Doppler shift" and applies them to the cosmological redshift. The clearest writers are like Lineweaver and Davis who make a sharp distinction between the cosmological redshift and the Doppler effect.

When you say Doppler, people immediately try to picture some definite instantaneous velocity to which the shift corresponds---and in the cosmological case there IS NO DEFINITE VELOCITY there is a whole history of expansion at rates which may have varied a great deal over many billions of years.

Anyway that's my tuppence of opinion and advice.

Last edited: Jun 25, 2007
16. Jun 26, 2007

### Ich

When I say "derive" I mean something like: v=1.4 c, what ist z? You can't give an answer unless you have a model of the expansion that is valid for the whole time since the light has been emitted. Because both things are causally independent, just two different numbers that can be derived from the model.
But a=.25, what is z? can be answered most easily, because a and z are only different formulations of the same quantity.

Needless to say that I fully agree with marcus. (BTW: congratulations to your 10,000th post. Is that the all-time-record here?)

Last edited: Jun 26, 2007
17. Jun 26, 2007

### marcus

Thanks! I suppose 10K is not any sort of record, but I have no idea what the real maximum is.
I post mostly in Beyond and Cosmology forums. We have a lot of very active members in the other forums.

18. Jun 26, 2007

### marcus

you are challenging us

let's say that 1.4 c was the recession speed AT THE INSTANT THE GALAXY EMITTED THE LIGHT that we are now receiving. Then I think if we agree on parameters like (0.27 current matter fraction, 0.73 dark energy fraction, current Hubble 71) so we know the whole expansion history----then I can give approximately what is the redshift z

(it is an awkward problem, and not beautiful, but one can fumble around and get the answer by trial and error)

I think that if the initial recession speed (when the light was emitted) was 1.4 c
then it must be z = 2.5

Actually that was my second guess using Morgan's cosmology calculator
http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html
To use it, you have to plug in 0.27 for matter, and 0.73 for lambda or dark energy, and 71 for the current value of the Hubble parameter.
===============

BTW knowing or not you chose a very interesting redshift!

If z = 2.4, then the speed of the object now is just slightly LARGER than the speed when the light begin its journey.
But if z = 2.6 then the speed of the object now is slighly LESS than it was when it emitted the light.
Only for z = 2.5 are the two speeds equal----because then the previous slowing down of expansion is balanced by the recent acceleration.
===============

BTW Ich, this is a problem for you. Do you happen to know the redshift z at which the ANGULAR SIZE of a standard size object stops decreasing and begins to get larger and larger the farther away it is? If you don't then I think you would like to know this--it is a fun-to-know number.

Last edited: Jun 26, 2007
19. Jun 26, 2007

### cesiumfrog

Huh? Does such a thing happen?

20. Jun 26, 2007

### marcus

Yes! Isn't that wonderful?
It is like a funhouse mirror---weird. Things look bigger the farther away

=========ICH WATCH OUT===SPOILER===I TELL FROG THE ANSWER===

Frog, if I remember correctly the z where the angular size distance reaches its maximum is around z = 1.6

it is because when you look back in time you see a smaller universe so samesize objects loom larger in it, and this effect eventually dominates the familiar effect that farther makes things smaller

You can see the same thing when you see the TEAR-DROP SHAPE OF LIGHTCONES. the same thing that makes the lightcones have a teardrop shape also makes there be an angularsizedistance maximum----which means same as angular size minimum for equalsize objects----at I think 1.6

Frog, your esteemed thesis advisor is organizing the GRG. How is it coming? It is next month!
I apologize for earlier flippancy. I think she has done a great job especially to have invited plenary talks by Loll and Freidel.