Doppler effect / expanding universetrouble uniting both concepts?

[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 ). I wish I had more time to read physics

 

[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

 

[moe darklight]

A good question

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.

 

[MeJennifer]

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

 

[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.

 

[Garth]

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.

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

 

[Ich]

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.

We agree here.

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.

Distances get dilated, and that is exactly the red shift. I disagreed with your comment:

...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.

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.

 

[George Jones]

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 http://www.astro.ucla.edu/~wright/balloon0.html" of expanding wavelengths.

 

[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:

I disagreed with your comment:

...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.

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.

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

 

[pervect]

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.

 

[Ich]

Hi Garth,

there is no disagreement on cosmological expansion. However, regarding the OP

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 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.

 

[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

 

[Ich]

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

 

[pervect]

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.

 

[marcus]

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

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.

 

[Ich]

You can derive a redshift from the velocity - you just can't use the SR formulas to do it.

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?)

 

[marcus]

(BTW: congratulations to your 10,000th post. Is that the all-time-record here?)

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.

 

[marcus]

v=1.4 c, what is z? ...

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.

 

[cesiumfrog]

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?

Huh? Does such a thing happen?

 

[marcus]

Huh? Does such a thing happen?

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.
Please tell us any news about the GRG conference!

 

[Ich]

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.

The next best thing to know something is knowing where to find it. http://www.astro.ucla.edu/~wright/CosmoCalc.html" includes angular distance as well and gives z=1.65.

 

[marcus]

The next best thing to know something is knowing where to find it. http://www.astro.ucla.edu/~wright/CosmoCalc.html" includes angular distance as well and gives z=1.65.

Good!
I love this strange funhouse optics of the universe.
As you push something farther and farther away, it starts to look bigger.

and the map of the CMB (at redshift z = 1100) is a good example of that "magnification" (those red and blue blotches on the oval map)

about knowing where to find it since I liked Bavaria countryside I looked up Mintraching and discovered that the population is estimated around 2000 and history goes back to 800 Anno Domini. The NAME of the village in early times has a good sound. Maybe you should go back to the old name.
Munirihhinga
http://www.weihenstephan.org/org/orte/mintraching/news.htm

 

[Ich]

since I liked Bavaria countryside

pleased to hear that. Have you ever been there?

I looked up Mintraching and discovered that the population is estimated around 2000 and history goes back to 800 Anno Domini.

Yes, and there is a shop (and traffic lights!). But it's not a bad place to live, you have 8 km to the ESO headquarters, the MPE and the Physik Department of the TUM, where I studied. Equally important, about the same distance down the river there is the world's oldest brewery. And also the "Mons Doctus" where I went to scool and where the pope studied. You see, best premises to tackle the mysteries of the universe from every conceivable vievpoint (science, religion, and beer :tongue2:).
Too bad I chose to work for money, not science, so all that is merely a hobby.

The NAME of the village in early times has a good sound. Maybe you should go back to the old name.
Munirihhinga

Might make no great difference to an english speaker. In our local dialect, it's "Mindring" anyway.

 

[Old Smuggler]

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.

In fact the SR doppler formula can be used to calculate spectral shifts in arbitrary curved space-time if it is used locally. (Hint: use the emitter's 4-velocity, parallelly transported along the null curve connecting the emitter and the receiver, and compare it to the
receiver's 4-velocity locally.)

For the details see (obligatory reading for anybody who wants to have a good understanding of this topic)

J.V. Narlikar, American Journal of Physics, 62, 903 (1994).

 

[Ich]

In fact the SR doppler formula can be used to calculate spectral shifts in arbitrary curved space-time if it is used locally. (Hint: use the emitter's 4-velocity, parallelly transported along the null curve connecting the emitter and the receiver, and compare it to the
receiver's 4-velocity locally.)

Thanks, I stand corrected. So for emitter-absorber-events there is a uniquely defined relative velocity that "happens" to satisfy the doppler shift formula.
I don't have access to the paper you referenced. Is there a layman-compatible explanation why both approaches (expansion of space dimensions - parallel transport of velocity) must lead to the same result?

 

[Old Smuggler]

Thanks, I stand corrected. So for emitter-absorber-events there is a uniquely defined relative velocity that "happens" to satisfy the doppler shift formula.

Yes. The effect of parallel transport in curved space-time on the 4-velocity of the emitter
is to "rotate" it. When compared to the receiver's 4-velocity locally, this "rotation" yields
a contribution to the velocity which enters into the SR doppler formula. So one might
loosely say that the local doppler velocity is partly due to a "real" velocity (neglecting the effects of curved spacetime) and a "curvature" part due to the curvature of spacetime.

I don't have access to the paper you referenced. Is there a layman-compatible explanation why both approaches (expansion of space dimensions - parallel transport of velocity) must lead to the same result?

The parallel transport procedure is the generally valid approach, whereas the result
for the FRW spacetimes represents special cases only. The equivalence of results
for these special cases is proved in the referenced paper. I'm afraid that you have to
work through the mathematics to see this.

 

[pervect]

Note that in order to find the velocity of a distant object by the parallel transport method, one must specify the path that the velocity is to be transported along.

Some authors, for instance Baez, will go so far as to say that relative velocity is not even defined in GR, see for instance http://math.ucr.edu/home/baez/einstein/node2.html

of which I'll quote a small relevant section

In special relativity, we cannot talk about absolute velocities, but only relative velocities. For example, we cannot sensibly ask if a particle is at rest, only whether it is at rest relative to another. The reason is that in this theory, velocities are described as vectors in 4-dimensional spacetime. Switching to a different inertial coordinate system can change which way these vectors point relative to our coordinate axes, but not whether two of them point the same way.

In general relativity, we cannot even talk about relative velocities, except for two particles at the same point of spacetime -- that is, at the same place at the same instant. The reason is that in general relativity, we take very seriously the notion that a vector is a little arrow sitting at a particular point in spacetime. To compare vectors at different points of spacetime, we must carry one over to the other. The process of carrying a vector along a path without turning or stretching it is called `parallel transport'. When spacetime is curved, the result of parallel transport from one point to another depends on the path taken! In fact, this is the very definition of what it means for spacetime to be curved. Thus it is ambiguous to ask whether two particles have the same velocity vector unless they are at the same point of spacetime.

The point is that you need both two points, and a specific path connecting them (such as the null path that Old Smuggler mentions) to define a velocity.

Just having the points isn't enough to compute the velocity, because if you parallel transport the velocity vector along some different path, you will in general get a different result for the "velocity".

[Query: I think one needs to specify not just any-old null path, but some specific null path. A null geodesic will do, though I suppose it's possible in that one might have multiple geodesic paths, due to gravitatioanl lensing. I don't think there's any practical case where two different images of an object would have different doppler shifts, but I think it's theoretically possible.]

 

[cesiumfrog]

The parallel transport procedure is the generally valid approach, whereas the result
for the FRW spacetimes represents special cases only.

Stands to reason. The photon momentum is just the (parallel transported) tangent vector of its geodesic, the initial and final energies are just the timelike component of this in each observer's frame. I know this from raytracing, but never thought about how it relates to cosmological redshift before. (..and I was so swayed by marcus' argument for the expansion interpretation.)

Note that in order to find the velocity of a distant object by the parallel transport method, one must specify the path that the velocity is to be transported along.

Some authors, for instance Baez, will go so far as to say that relative velocity is not even defined in GR

Baez would have a fair point about relative velocity, but it's not really relevant here since, after all, the path of the photon *does* uniquely specify the connecting path (unlike "expansion of space", which I imagine is equally undefined).

 

[cesiumfrog]

I suppose it's possible in that one might have multiple geodesic paths, due to gravitatioanl lensing. I don't think there's any practical case where two different images of an object would have different doppler shifts, but I think it's theoretically possible.

Lensing by a Kerr black hole?

 

[pervect]

Lensing by a Kerr black hole?

I'm not sure offhand if that would do the trick or not.