Expansion redshift VS gravitational redshift?

[anya2]

While objects closer to us tend to shift both in direction red or blue, depending on their movement in relation to us, distant objects such as galaxies tend to only shift to the red.

As I understand this is the base of the idea that the universe is expanding. But how are we sure that is the case, and redshifts are not due to the gravitational pull of all those objects that lie between us and the observed objects?

 

[sylas]

While objects closer to us tend to shift both in direction red or blue, depending on their movement in relation to us, distant objects such as galaxies tend to only shift to the red.

As I understand this is the base of the idea that the universe is expanding. But how are we sure that is the case, and redshifts are not due to the gravitational pull of all those objects that lie between us and the observed objects?

Because gravitation effects of stuff in between the source and the observer cancel out.

It is the difference in gravitational potential between source and observer that matters. Dropping a little bit into and then out of the gravitational well along the way may alter the direction of light, but that's all. This change in direction is measured and used in study of gravitational lensing.

Cheers -- sylas

 

[anya2]

Yep, that makes sense, thanks a lot

The only gravity that would not cancel out is that of the observed object, as it is the starting point it can only pull light back

I am not sure but I think I've read that the CMBR has shifted uniformly, but if space indeed expanded in such a high rate - shouldn't different regions of the CMBR be redshifted by a different amount, depending on their position relative to our point of observation?

 

[Ich]

Because gravitation effects of stuff in between the source and the observer cancel out.

No, it results in a blueshift.
If it'd cancel out, there would be no deceleration of expansion either.

 

[Chalnoth]

No, it results in a blueshift.
If it'd cancel out, there would be no deceleration of expansion either.

Huh? Sylas is correct. On average, the effects completely cancel, because compared to the average density, there are just as many voids as collapsed objects (by some appropriate measure).

 

[Wallace]

I think we probably all agree and are just using the words differently, but in fact gravitational effects play a crucial role in cosmological redshift. The distance vs redshfit relationship is a key cosmological probe and the very reason it tells us about the composition of the Universe is because the gravitational effects at play can be modeled and that tells us how much stuff (and how much of different kinds of stuff) are around. This is true even if we ignore structure (i.e. the simplest homogenous FRW model).

To see how gravity is important, try modelling a matter only Universe using Newtonian physics only. You will see that even for quite large distances, you get pretty close to the correct answer by modelling the redshift as a combination of a Doppler redshift plus a blueshift due to the gravitation matter enclosed in a sphere centred on the observer with a radius equal to the distance to the emmitter (Gauss's law let's us ignore everything outside in a homogenous universe). In the Newtonian case you can work out the gravitational blueshift by thinking about the potential energy difference between the emmitter and observer.

Now, in the full relativistic case, there is an inherent ambiguity in dividing up the redshift into the 'doppler' and 'graviational' parts, and it depends on the co-ordinates you choose as to which label gets what. There have been various bun fights in the literature about this, but the bottom line is that both motion and gravity are at play in determining what redshift is observed.

 

[Ich]

Thanks, Wallace.

On average, the effects completely cancel, because compared to the average density, there are just as many voids as collapsed objects (by some appropriate measure).

If we have, as a toy model, a whole universe filled with static dust, the gravitational effects between any two points do not "cancel out". Instead, they make the whole thing collapse. This concernes photons also, they get blueshifted.

It is the difference in gravitational potential between source and observer that matters.

Exactly.
But "potential" is not a basic feature of GR; for example, it is not defined in
homogeneous coordinates. That does not mean that there are no gravitational effects.
To define a potential, you have to use static coordinates. The potential is then \sqrt{g_{tt}} \simeq g_{tt}/2.
Static coordinates are centered around one (arbitrary, of course) point r=0. The potential is then (in Newtonian limit)
\frac{2 \pi G}{3 c^2} \rho r^2
As long as there are no significant density changes during the light travel time, you can decompose photon redshift unambiguously into gravitational blueshift and doppler redshift.
In case of a static spacetime, like de Sitter, an unambiguous decomposition is always possible.

 

[sylas]

If we have, as a toy model, a whole universe filled with static dust, the gravitational effects between any two points do not "cancel out". Instead, they make the whole thing collapse. This concernes photons also, they get blueshifted.

Not so. The simplest such model, the Milne model, is a flat universe filled with dust at critical density, and it keeps expanding indefinitely, though slowing down indefinitely as well. Photons in this universe are always redshifted.

The only way you get blue shift is with supercritical densities, which can reverse expansion into contraction and a Big Crunch. You can get blue shifts once contraction gets underway, which is perfectly obviously not going on in our universe.

As Wallace points out, you can, depending on how you work with co-ordinates, regard the redshift (or blueshift, in a contracting universe) as a gravitational effect, associated with the difference in density between emission and observation of a photon in different regions of the dust filled universe. Whether you do this with Newtonian approximations or the more correct relativistic methods only makes a difference on sufficiently large scales.

If the dust is inhomogenous on small scales, then you end up with something a bit more like our own universe, with local motions and clusters of galaxies and so on. If a photon passes by clumps of matter between emission and observation, this makes no difference, which is the point I was trying to make. What counts is the state at emission, and at observation. Going into and out of a localized gravitational well along the way has no effect, except perhaps on directions, which is the basis of gravitational lensing.

Cheers -- sylas

 

[Ich]

Not so. The simplest such model, the Milne model, is a flat universe filled with dust at critical density, and it keeps expanding indefinitely, though slowing down indefinitely as well. Photons in this universe are always redshifted.

No, the Milne Model is massless, filled only with "expanding" test particles. Consequently, it has zero density and is negatively curved. Redshift is purely doppler, there are no gravitational effects.
I'm talking ablout homogeneous static dust, like a closed universe at maximum expansion. Just to illustrate that gravitational effects definitely do not cancel out.

The only way you get blue shift is with supercritical densities, which can reverse expansion into contraction and a Big Crunch. You can get blue shifts once contraction gets underway, which is perfectly obviously not going on in our universe.

I'm not talking about a net blueshift. I said that gravitation results in a blueshift, which is outweighed by doppler redshift in an expanding universe.

As Wallace points out, you can, depending on how you work with co-ordinates, regard the redshift (or blueshift, in a contracting universe) as a gravitational effect, associated with the difference in density between emission and observation of a photon in different regions of the dust filled universe.

That's not how I read Wallace's post, and I wouldn't agree either. As i understand it, Wallace and I are claiming that the "potential" approach is valid in an homogeeous universe. (quote:"This is true even if we ignore structure (i.e. the simplest homogenous FRW model).")

Whether you do this with Newtonian approximations or the more correct relativistic methods only makes a difference on sufficiently large scales.

Yep, but the underlying physics is more accessible in the Newtonian formulation. You can see easily that it's exactly the matter between two points which accelerates them, not some other dubious effect.

Going into and out of a localized gravitational well along the way has no effect, except perhaps on directions, which is the basis of gravitational lensing.

Again: perfectly homogeneous dust (or DE, for that matter) does not mean that there is no potential difference. It means that, by choosing an origin for static coordinates, you can define where the global minimum is. Every photon being observed at r=0 comes from a higher potential in that picture.

 

[Wallace]

Edit: Crossed posts with Ich. We seem to be in good agreement though...

Not so. The simplest such model, the Milne model, is a flat universe filled with dust at critical density, and it keeps expanding indefinitely, though slowing down indefinitely as well. Photons in this universe are always redshifted.

Right, but when you add a homogenous matter distribution what do you find? (Edit: missed seeing that you suggest Milne model is at critical density, as Ich points out it is empty, there is no dust in it. In the Milne model nothing ever slows down, all proper velocites remain fixed). You find that the more matter you add, the less redshift you see for objects a fixed distance from you (however you define that). This is because of the effects of gravity "adding a blueshift" in some loosely defined way as the photon travels.

The only way you get blue shift is with supercritical densities, which can reverse expansion into contraction and a Big Crunch. You can get blue shifts once contraction gets underway, which is perfectly obviously not going on in our universe.

I think we are talking at cross purposes. Ich explained how you get a component of the redshift which is gravitational (and in fact this componet reduces the redshift), not how any gravity gives you a net blueshift.

 

[Chalnoth]

If we have, as a toy model, a whole universe filled with static dust, the gravitational effects between any two points do not "cancel out". Instead, they make the whole thing collapse. This concernes photons also, they get blueshifted.

After the collapse has begun, sure. But our universe is expanding.

 

[sylas]

No, the Milne Model is massless, filled only with "expanding" test particles. Consequently, it has zero density and is negatively curved. Redshift is purely doppler, there are no gravitational effects.

Sorry! You are quite right; I mixed up the names of my models. I meant what is sometimes called the "Einstein-de Sitter" model, which is confusing because neither Einstein nor de Sitter proposed it. I meant "dust", with mass, at critical density; not the massless test particles of the Milne model. My mistake.

I'm talking ablout homogeneous static dust, like a closed universe at maximum expansion. Just to illustrate that gravitational effects definitely do not cancel out.

Ah! I had take the "static" to mean no peculiar motions, sometimes the taken as the defining quality of "dust". My apologies again. Yes, this model will contract from that static starting point, and you will have blue shifts. The gravitational effects can be considered as gravitational in the sense Wallace described, and I think we are all on the same page with that.

My original remark about "cancellation" was strictly intended to refer to the effect of a photon passing near a massive object, in a inhomogeneous universe. Fritz Zwicky considered whether something like this could work (it is a form of "tired light" model). But it doesn't work. A localized patch of higher density matter along the photon's path has no net effect. You can think of the photon being blueshifted as it moves into the denser local region, and then redshifted as it moves back out again, with net cancellation as if that intervening clump of matter had not been there at all. Apart from a change in direction, possibly, as in gravitational lensing.

Cheers -- sylas

 

[Chalnoth]

My original remark about "cancellation" was strictly intended to refer to the effect of a photon passing near a massive object, in a inhomogeneous universe. Fritz Zwicky considered whether something like this could work (it is a form of "tired light" model). But it doesn't work. A localized patch of higher density matter along the photon's path has no net effect. You can think of the photon being blueshifted as it moves into the denser local region, and then redshifted as it moves back out again, with net cancellation as if that intervening clump of matter had not been there at all. Apart from a change in direction, possibly, as in gravitational lensing.

Well, actually this is only the case for matter domination. In the case of some form of dark energy, there is some net effect because gravitational potentials decay with time: the photon has less of a well to climb out of on the way out than in.

This is why I added the point that on average, due to the various underdensities and overdensities of the universe, these effects tend to cancel. In a more detailed analysis, they don't cancel exactly, but instead have some extra directional variation as a result (there's still no average effect when taken over the entire sky).

 

[sylas]

Well, actually this is only the case for matter domination. In the case of some form of dark energy, there is some net effect because gravitational potentials decay with time: the photon has less of a well to climb out of on the way out than in.

That's an interesting idea... I had not thought of that. The effect would have to be phenomenally tiny in our universe, but I see how it could work. I wouldn't like to try and calculate it, however!

Cheers -- sylas

 

[Chalnoth]

That's an interesting idea... I had not thought of that. The effect would have to be phenomenally tiny in our universe, but I see how it could work. I wouldn't like to try and calculate it, however!

Cheers -- sylas

Good stuff! It's known as the Integrated Sachs-Wolfe Effect, and basically it slightly increases the fluctuations in the CMB at large scales (at small scales the effect cancels more).

 

[Ich]

After the collapse has begun, sure. But our universe is expanding.

That's why doppler redshift dominates. In fact, there is additional redshift due to a negative dark energy potential.

Now I understand why you meant that the effects cancel on average. What cancels are the inhomogeneities (except our own cluster, of course). I'm talking about the total matter distribution, which adds a blueshift component to incoming light.

 

[Chalnoth]

Now I understand why you meant that the effects cancel on average. What cancels are the inhomogeneities (except our own cluster, of course). I'm talking about the total matter distribution, which adds a blueshift component to incoming light.

That doesn't make any sense to me. If you take, for instance, a closed universe, and take two times equidistant from the turnover point, there will be no net redshift or blueshift between them, whereas by your claim, one would expect a net blueshift.

 

[Ich]

If you take, for instance, a closed universe, and take two times equidistant from the turnover point, there will be no net redshift or blueshift between them, whereas by your claim, one would expect a net blueshift.

Sorry, I'm not sure I understand that phrase.
If you mean a photon emitted dt before maximum expansion and received the same dt after maximum expansion:
The distance r is then 2dt*c.
In this case, you have a gravitational blueshift of
<br /> \frac{2 \pi G}{3 c^2} \rho r^2<br />
The coordinate acceleration of the emitter is
<br /> \frac{4 \pi G}{3} \rho r<br />
Since emitter and observer were at relative rest at turnaround, and the signal was sent dt = r/2c before, the relative velocity at the time of emission was
<br /> dv=\frac{4 \pi G}{3} \rho r*dt = \frac{2 \pi G}{3c} \rho r^2<br />
giving a redshift of
<br /> \frac{2 \pi G}{3c^2} \rho r^2<br />
which exactly cancels the blueshift above.

Really, I'm not claiming new physics. This is simply a local Newtonian approximation to an FRW metric - weak field, small velocity, no pressure.

 

[Chalnoth]

Sorry, I'm not sure I understand that phrase.
If you mean a photon emitted dt before maximum expansion and received the same dt after maximum expansion:
The distance r is then 2dt*c.
In this case, you have a gravitational blueshift of
<br /> \frac{2 \pi G}{3 c^2} \rho r^2<br />
The coordinate acceleration of the emitter is
<br /> \frac{4 \pi G}{3} \rho r<br />
Since emitter and observer were at relative rest at turnaround, and the signal was sent dt = r/2c before, the relative velocity at the time of emission was
<br /> dv=\frac{4 \pi G}{3} \rho r*dt = \frac{2 \pi G}{3c} \rho r^2<br />
giving a redshift of
<br /> \frac{2 \pi G}{3c^2} \rho r^2<br />
which exactly cancels the blueshift above.

Really, I'm not claiming new physics. This is simply a local Newtonian approximation to an FRW metric - weak field, small velocity, no pressure.

How do they have a net relative velocity, though? At emission, the emitter would have been moving away from the observer. But at the same time, since the system is symmetric, the observer would be moving towards the emitter by the same amount when the photon was observed, canceling that redshift.

 

[Chronos]

Gravity works both ways, matter on the far side counters gravitational effects from the near side. A net zero effect. Expansion is the only logical explanation.

 

[Wallace]

How do they have a net relative velocity, though? At emission, the emitter would have been moving away from the observer. But at the same time, since the system is symmetric, the observer would be moving towards the emitter by the same amount when the photon was observed, canceling that redshift.

You are double counting somehow.

Lets look at this in two ways. The simplest way is to place to origin of some co-ordinates at the reciever such that they remain fixed. Imagine a spherical region around them with the emmitter at the edge of that region. When they fire the photon towards the centre they are moving away from the reciever. Since the reciever is always fixed, this means there is a redshift from the original motion so it doesn't matter that later on the emmitter starts moving towards the observer when the Universe begins contracting. The gravitational blueshift, in this case, exactly cancels this original redshift. It looks like this:

Motion at emmission causing a Doppler redshift
Obs . . . . . . Em ->

Photon is falling towards the bottom of the potential well, causing a blueshift
Obs . . . . . . << Photon

We can instead define the co-ordinates to be centred on the emmitter. In this case it remains fixed. If you think about this it means that compared to the rest frame of the emmitter, the observer will be moving towards the emmitter when the photon is observed. Thus you will have a blueshift due to motion. This might be confusing, until you realize that in these co-ordinates, the photon is moving away from the origin, climbing out of the potential well we have define, and therefore in this system the effect of gravity is to cause a redshift, in this case exactly cancelling the Doppler blueshift. It looks like this:

Motion at reception, causing Doppler blueshift
Em . . . . . . <- Obs

Photon is climbing out of potential well, causing gravitational redshift
Em . . . . . >> Photon

We could also place the origin between the emmitter and observer. In this case the relative motion cancels out, so there is no Doppler contribution. But also, we now define the bottom of the potential well to be between the two, so the photon picks up a blueshift falling in, which exactly cancels the redshift of it climbing out. It looks like this

Motion at emmission

<-Obs . . . . . . O . . . . . . Em ->

Motion canceled at reception, no net Doppler effect

Obs -> . . . . . . O . . . . . . <- Em

Photon falls into potential well, gaining energy

. . . . . . O . . . . . . << Photon

But then loses the same amoung climbing out again

<< Photon . . . . . . O . . . . . .

This might sound like a bit of mathemagic, but it is all just co-ordinate tricks with classical physics. As with any problem to do with energy, you have to be very careful about where you are defining the arbitary zero point, and make sure you are referencing everything consistantly with respect to that.

 

[Chalnoth]

In any case, these things are vastly easier to understand if you just take them in co-moving coordinates, where both the emitter and observer are stationary (up to local peculiar velocities). In co-moving coordinates, the only source of redshift is the overall expansion, and so the redshift is simply:

z + 1 = \frac{a_{obs}}{a_{emit}}

 

[Wallace]

But hang on, we know that we can always just use these co-ordinates. The question is what the hell do they mean? The OP asked how motion and or gravity is responsible for causing redshift, which is a very reasonable question. Simply stating the above equation tells you how to calculate it, but it doesn't tell you what that means and doesn't answer the question. Reducing everything to the effect of 'the overall expansion' leaves you at sqaure one; what precisely is that motion, and how does it cause redshift? In fact the 'motion' implied by looking at da/dt is nothing like the intuitive motion we see in day to day life, since it encodes gravitational effects as well. This is very very convenient for cosmologists, since it reduces everything to the single function a(t), but it is horrible for people new to the area trying to work out what that function means in terms that are familiar.

Ich and I explained how you can understand the interplay between motion and gravity by looking at how the more familiar Newtonian physics gives you the same answer, but more obviously demonstrates how both motion and gravity are both at work, even in a homogenous universe.

Writing down a simple relation, and really understanding what that means are two vastly different things.

 

[Chalnoth]

But hang on, we know that we can always just use these co-ordinates. The question is what the hell do they mean?

I guess I just don't see those sorts of questions as very productive. There are so vastly many ways of looking at the situation that one can't say that they mean anyone particular thing in these terms. So I'd rather just go by the simplest explanation, which is that the photons are expanded along with space.

 

[Wallace]

Well then I have to disagree. When you say 'photons are expanded along with space' you are talking about something that is only true for one specific set of co-ordinates and you also imply a false causality; that there is a physical effect called 'expansion of space' which causes photons to stretch.

Simply saying 'there are many ways of looking at this, so none of them mean anything' is not very useful. In fact, as has been explained, the physics is universal, and can be seen readily by looking at the Newtonian picutre, to which all co-ordinate descriptions will converge to for small distances. The co-ordinates are what are malleable, yet you want to fix on just one co-ordinate system and force the physics to conform to that (since you remove gravity and motion and invent a new placeholder fictious effect which acts for both). I'm afraid that is bass-ackwards.

As can be readily evidenced in this forum, blanket use of this phrase without context leads to much wailing and nashing of teeth, such as 'why don't galaxies get expanded by space?' 'does the expansion of space drive electrons further from the nucleus of atoms?'. These are reasonable questions to ask when you've been told to just think of everything in terms of some ill-defined 'expansion of space' but the are easily done away with when you break it down into the simple underlying physics.

Again, I go back to the OP. It was asked whether motion and/or gravity is responsible for the observed redshift of galaxies. How does writing down 1 + z = a/a_0 and saying 'the photons get stretched by expanding space' answer this question? Redshift can be understood in simple well understood terms like motion and gravity, I see no reason to force people to abandon these intuitive notions in favour of a co-ordinate dependant mathematical function which has no universal physical meaning.

It depends on what we are trying to help people with. If you want to learn how to calculate cosmological quantities, then you need to learn the maths behind co-moving co-ordinates, and learn the easiest way to make calculations. If someone wants to a good non-mathematical intuitive understanding in terms of familiar concepts, then this is clearly not the best way to go.

 

[Chalnoth]

Your description is no less coordinate-dependent and has no greater universal physical meaning. I just don't think your description is any more intuitive, though it is certainly more convoluted.

 

[Ich]

At least this time I dropped out of the discussion in time.

 

[Wallace]

:sigh: I should know better than to continue, but "Once more unto the breach"...

The only reason any of this got at all convoluted is because you were incorrectly applying Newtonian physics, and thus I had to explain in gory detail how your re-collapsing dust ball example was perfectly consistant with a Newtonian description. Remember that you introduced the re-collapsing idea, and when doing so failed to correctly apply Newtonian physics.

If we just return to the original question, how to understand how gravity and motion play a role in the redshifts we see in the Universe, we see that there is one single unique way to describe this using Newtonian physics (we don't have general covariance in Newtonian physics, so it all becomes much simpler). Now, even given the gauge freedoms in GR, all co-ordinate systems will converge for small distances to satisfy the equivalence principle. Hence, the Newtonian description tells you clearly how the underlying physical mechanism are at play, in a way free from co-ordinate transformations. You don't even need to define any co-ordinates, you can just use words, but when you do so you are using words that have a direct physical meaning; gravity, motion etc.

On the other hand, when you wrap everything into a(t) and repeat the phrase 'expansion of space' to explain anything without any context you aren't learning, teaching or understanding anything more than the properties of one arbitrary foliation of the FRW space-time.

I'm not against the use of the phrase 'expansion of space' or the analogies that go along with it, I just object to their mis-use in contexts where it is not appropriate. When someone has asked how gravity and motion play a role in redshift, then this is clearly not the time to be invoking this concept.

 

[Chalnoth]

The only reason any of this got at all convoluted is because you were incorrectly applying Newtonian physics,

I was never even touching on Newtonian physics in the discussion.

 

[sylas]

:sigh: I should know better than to continue, but "Once more unto the breach"...

For my part, I think it is worth explaining this point as often as necessary. The trick is to remain relaxed about repeating it every time; because it will probably be a new perspective for at least some readers each time you explain it again.

I'm speaking up here, because it was a previous time you explained this that represents for me one of the latest AHA moments which come at me from time to time as I'm trying to deepen my own understanding. Grasping this point has meant several aspects of cosmology and relativity now click together better for me.

Cheers -- sylas

 

[Wallace]

Posts #17 and #19. You were commenting and making predictions based on the Doppler + gravitational explanation Ich and I gave ("whereas by your claim" etc). In doing so you incorrectly applied basic Newtonian physics, making a false prediction and thus claiming that the physics was in error.

 

[Wallace]

The trick is to remain relaxed about repeating it every time

I try, I really do!

The problem is that there are some very bad misconceptions thouroughly ingrained in the modern pop-sci view of cosmology. It is so very difficult to remove some of these, because there is a constant feedback loop of people telling each other they are so right about an entire false lexicon that has replaced understanding of physics with a canonical verbal description at odds with some fundamental (and very important!) concepts in GR.

Then again I do have a tendency to suffer from http://xkcd.com/386/" syndrome

 

[Chalnoth]

Posts #17 and #19. You were commenting and making predictions based on the Doppler + gravitational explanation Ich and I gave ("whereas by your claim" etc). In doing so you incorrectly applied basic Newtonian physics, making a false prediction and thus claiming that the physics was in error.

Well, no. Post #17 was merely pointing out that this description doesn't make intuitive sense. In post #19, since I am perhaps not used to dealing with a Newtonian approximation (as in this case it's often even easier to just do the full GR calculation), I chose as a reference point the point of symmetry: the turnaround, at which point the photon was equidistant between emission and absorption. I didn't fully explain this, and it's my fault for doing so. But this is why I really don't like these sorts of descriptions: how much of the redshift or blueshift is contributed by velocity vs. gravity is entirely dependent upon what coordinates you use.

So even though these descriptions may provide the impression of understanding, they don't provide any real understanding because none of the extra statements made are non-arbitrary (e.g. gravitational vs. doppler redshift).

 

[marcus]

While objects closer to us tend to shift both in direction red or blue, depending on their movement in relation to us, distant objects such as galaxies tend to only shift to the red.

As I understand this is the base of the idea that the universe is expanding. But how are we sure that is the case, and redshifts are not due to the gravitational pull of all those objects that lie between us and the observed objects?

In any case, these things are vastly easier to understand if you just take them in co-moving coordinates, where both the emitter and observer are stationary (up to local peculiar velocities). In co-moving coordinates, the only source of redshift is the overall expansion, and so the redshift is simply:

z + 1 = \frac{a_{obs}}{a_{emit}}

But hang on, we know that we can always just use these co-ordinates. The question is what the hell do they mean? ...
Writing down a simple relation, and really understanding what that means are two vastly different things.

I guess I just don't see those sorts of questions as very productive. There are so vastly many ways of looking at the situation that one can't say that they mean anyone particular thing in these terms. So I'd rather just go by the simplest explanation, which is that the photons are expanded along with space.

Well then I have to disagree. When you say 'photons are expanded along with space' you are talking about something that is only true for one specific set of co-ordinates and you also imply a false causality; that there is a physical effect called 'expansion of space' which causes photons to stretch.

...
Again, I go back to the OP. It was asked whether motion and/or gravity is responsible for the observed redshift of galaxies. How does writing down 1 + z = a/a_0 and saying 'the photons get stretched by expanding space' answer this question? Redshift can be understood in simple well understood terms like motion and gravity, I see no reason to force people to abandon these intuitive notions in favour of a co-ordinate dependant mathematical function which has no universal physical meaning.

It depends on what we are trying to help people with. If you want to learn how to calculate cosmological quantities, then you need to learn the maths behind co-moving co-ordinates, and learn the easiest way to make calculations. If someone wants to a good non-mathematical intuitive understanding in terms of familiar concepts, then this is clearly not the best way to go.

Interesting discussion. I note that Chalnoth did not say 'the photons get stretched by expanding space'

and what Chalnoth did say does not, as far as I can see, imply a false causality; that there is a physical effect called 'expansion of space' which causes photons to stretch.

What it seems to me that Chalnoth did do was give a straightforward response to the OP by confirming what anya already offered as an intuitive explanation. That expansion of wavelength correlates pretty much exactly with expansion of distance (that occurred while light was in transit.)
This is a relation which I believe we do well to stress to newcomers, before delving into more complicated matters. It refers to the standard FRW metric and standard model cosmo.

 

[Old Smuggler]

The OP asked how motion and or gravity is responsible for causing redshift, which is a very reasonable question. Simply stating the above equation tells you how to calculate it, but it doesn't tell you what that means and doesn't answer the question. Reducing everything to the effect of 'the overall expansion' leaves you at square one; what precisely is that motion, and how does it cause redshift?

Right. This boils down to a little exercise in differential geometry. I have already had a discussion how
to do this exercise in another thread last year, and I see no reason to reiterate it here. Rather I give part of
the result, which is that for FRW models with flat or spherical spatial sections, the contribution to spectral shift
from motion in flat space-time is 0%, and the contribution from space-time curvature is 100%.

Another way of arriving at this result can be found in arXiv:0911.1205. Using the fact that the geometry of
the FRW models is preserved under certain holonomy transformations that change the topology,
it is shown that the interpretation of spectral shift as a Doppler shift in flat space-time leads to a
mathematical contradiction if the spatial sections are flat or spherical. This applies to all distances, i.e.,
for arbitrary close comoving observers.

Ich and I explained how you can understand the interplay between motion and gravity by looking at how the more familiar Newtonian physics gives you the same answer, but more obviously demonstrates how both motion and gravity are both at work, even in a homogenous universe.

Unfortunately, your explanation is in general mathematically inconsistent with the geometry of the FRW
models.

Writing down a simple relation, and really understanding what that means are two vastly different things.

Sure. But are you absolutely certain that you have understood this relation yourself?

 

[proteus13]

Wow, this thread gave me a headache. Some say that's an indication I've learned something but who knows.


The first answer to the question of anya was in regard only to the space between the observer and the observed object. My question is "What about the rest?"

What I mean is, if the universe is much bigger compared to the observable universe, and keeping in mind gravitational waves never fully stop, they are endless and just decay over distance, isn't the pull from OUTSIDE to observable universe, that can potentially be HUGE, isn't it's pull going to always EXCEED the gravitational lensing that occurs inside the bubble of observable universe, that could be tiny compared to the whole universe? In other words, it might not be the universe that's expanding, but gravity pulling light back outside the observable universe, creating similar effect to the proposed expansion?

And just to illustrate my point:
http://img503.imageshack.us/img503/4650/univ.png

If the universe is infinite, then it's pull will always exceed the pull of the finite, visible universe. So, in the center, our point of observation gravity from the whole universe is equally pulling light, neutralizing it's effect. But if we observe distant objects like A and B, the center of gravity will shift relative to our POV and the further the observed object, the more it's light will be pulled in direction, opposite of our observation. B will appear more redshifted than A not because space between has expanded, but because it is more affected from the pull in the direction, opposite to our POV. Now if the universe is endless, every point in it can be seen as it's center, so the effect exhibited is only present relative to our position and the position of the observed object. In other words - no expansion redshifts, only gravitational.

 

[Chalnoth]

People have looked into the effect that super-horizon anisotropies would have on our local universe. These were presented a few years ago as a potential explanation for the recently-detected acceleration of the expansion. But it turned out that when you work out the mathematics in detail, their effects simply cancel.

But I think you have this erroneous idea that gravity waves can somehow outrun light waves. This is not true. Both travel at the same speed, and neither can outrun the other. So, for instance, gravity waves from within a black hole can never reach the outside of the black hole.

 

[proteus13]

Yes, that's what I said, the effect will cancel out relative to the observed object, but relative to the point of observation a shift in light distribution may occur. Not to mention we know nothing about the region beyond our observation - the universe might not be that uniform as we think, and there might be a different portion of it that has everything blueshifted, the opposite of what we have. It is only natural, like it's summer in the northern hemisphere but it is winter in the southern.

I don't say gravity waves can "outrun" light waves in speed, they are supposed to be the same speed. However a flashlight cannot pass through the floor of the room, while gravity does pass, if it didn't we had to flow in the air. Also gravity affects light obviously. So gravity can extend further than light, effectively outrunning it.

Noone knows what a black hole really is, if it is a pinch in space, a form of very compressed space, where both light and gravity from our point of view will travel slower, infact they won't, they will just travel more space concentrated into a smaller volume in our perception. You say nothing leaves the black hole, but Steven Hawking says otherwise. I don't generally agree with most of his ideas, but for this one I think he is right.

The difference between a standard model mathematical black hole and an actual black hole might be huge, do we really want to rule out possibilities, just because they are not consistent with a theory?

I have the feeling people sometimes get so caught up with things, the forget it is MERELY A THEORY, and there is a high possibility for the theory to be wrong, historically every theory has been working for a given period of time, after that it gets obsolete and replaced with a better one. Do you really think we got the read deal now? It is just another version, and not a very consistent one. The idea that the world might be suspended on elephants and tortoises does not sound any more crazy than the big bang theory, and all its hypothetical fundamentals like dark matter and energy, which conveniently enough cannot be observed, measured or proved to exist in any way.

I know this words will be taken as bad as Galileo's when he said Earth revolves around the sun, because then the "mainstream" was that the whole universe revolves around us, but like every other concept it worked for a while but got old. I hope you do know history and you can extract some wisdom from it - looking back at a few thousands years of human history I'd say chances that the current model is "the real deal" are equal to 2012 being the end of time. In other words pretty slim. Cosmology is whatever me make out of it, and it is kind of sad to see science got so narrow minded and directed 100% in the current, pretty flawed, 100% hypothetical and theoretical model.

 

[Ich]

I count 85 points, not bad.

 

[Chalnoth]

Yes, that's what I said, the effect will cancel out relative to the observed object, but relative to the point of observation a shift in light distribution may occur.

Nope, there is no effect on the redshift.

Not to mention we know nothing about the region beyond our observation - the universe might not be that uniform as we think, and there might be a different portion of it that has everything blueshifted, the opposite of what we have. It is only natural, like it's summer in the northern hemisphere but it is winter in the southern.

There might well be regions of the universe that are collapsing. But it doesn't matter: they don't affect us. At all.

I don't say gravity waves can "outrun" light waves in speed, they are supposed to be the same speed. However a flashlight cannot pass through the floor of the room, while gravity does pass, if it didn't we had to flow in the air.

That's a different issue, though, one of how these waves interact with matter. Light interacts very strongly with matter, and so some sorts of matter are opaque (at least in certain wavelengths). Gravity doesn't have this issue: it interacts only extremely weakly with matter (around 10^40 times weaker than electromagnetism).

So gravity can extend further than light, effectively outrunning it.

No, it can't. To take a simple example, a black hole can also have electric charge, and if it does, will have an electromagnetic field extending out of it in the same way it has a gravitational field extending out of it. The two forces have the exact same properties where their range is concerned. They only differ in a couple of respects (gravity is weaker, always attractive, and couples to stress-energy instead of the electromagnetic charge).

Noone knows what a black hole really is, if it is a pinch in space, a form of very compressed space, where both light and gravity from our point of view will travel slower, infact they won't, they will just travel more space concentrated into a smaller volume in our perception. You say nothing leaves the black hole, but Steven Hawking says otherwise. I don't generally agree with most of his ideas, but for this one I think he is right.

Hawking radiation doesn't affect my statement in the least. For any astrophysical black hole, that is, one that came from the collapse of a star (or any more massive black hole), the Hawking temperature is dramatically smaller than the CMB temperature, and so might as well not be there at all (at least for the time being). So what I was attempting to show still holds: the gravitational field of the black hole extends outside the black hole without gravity waves from the interior reaching the exterior.

If you still think your statement here has any merit, consider this: as the black hole evaporates, the Hawking radiation increases in intensity, while the gravitational field gets weaker. How could one be the source of the other and still hold to this inverse relationship?

I have the feeling people sometimes get so caught up with things, the forget it is MERELY A THEORY, and there is a high possibility for the theory to be wrong, historically every theory has been working for a given period of time, after that it gets obsolete and replaced with a better one.

The thing is, proteus, everybody in science is aware of this. It's a worthless argument to make. You might as well be arguing vociferously that the sky is blue, as if people had forgotten the fact.

If you really want to attempt to claim that theory X might not be entirely accurate, then you only have two options before you:
1. Present an argument for why theory X breaks down at a certain point. Provide experimental support if possible, or some mathematical argument if that isn't available (finding a contradiction in the theory is usually a great way to do this).
2. Present a different theory. Preferably show how it fits experiment better than existing theory. Alternatively present an argument for why this theory is simpler and more elegant than existing theories.

But the thing is, you haven't even bothered to do either one. You haven't even presented a different theory: you've just thrown up a physical model of how the universe might be, and how things outside our horizon might affect stuff inside.

Any and all such models are correctly and properly analyzed by examining their effects based upon current theory. By current theory, stuff outside of our cosmological horizon can have no effect upon us. That means that it can't even have an effect upon anything we observe, by the way, such as redshifts.

Now, if you want to present some new theory where matter beyond our cosmological horizon can have an effect on our observations, by all means work carefully through its implications and present it. But merely attempting to claim that some theory might support your assertions is just being intellectually dishonest.

 

[Ich]

Ok, it seems unlikely right now, but maybe some day I'll discuss these issues again.

In case there is an interested reader somewhere, I'll follow https://www.physicsforums.com/showpost.php?p=2531175&postcount=30" and explain my position once more, for the record, so to speak. I'm still working on the "remain relaxed" trick, however.

1)

But how are we sure that is the case, and redshifts are not due to the gravitational pull of all those objects that lie between us and the observed objects?

Because gravitation effects of stuff in between the source and the observer cancel out.

Gravity works both ways, matter on the far side counters gravitational effects from the near side. A net zero effect.

Pull from the whole universe

One answer to all: If I draw a sphere around observer and emitter, the gravitational effects of everything outside that sphere cancel out.
This leaves the gravitational effect of all matter inside the sphere.
This effect causes deceleration or even collapse, and an additional blueshift to the doppler redshift (in regions where the distinction makes sense).

2)

Another way of arriving at this result can be found in arXiv:0911.1205

OMG. Topology.
Just let me stipulate that the topology is R³ on the scales we (Bunn, Wallace, and I) are talking about, and forget about that paper. If someday they find out that Andromeda is the Milky Way, I'll be the first to send the author my apologies.

 

[marcus]

The original poster used the idea "expansion redshift" in the thread title. Here is the original post:

expansion redshift VS gravitational redshift?

While objects closer to us tend to shift both in direction red or blue, depending on their movement in relation to us, distant objects such as galaxies tend to only shift to the red.

As I understand this is the base of the idea that the universe is expanding. But how are we sure that is the case, and redshifts are not due to the gravitational pull of all those objects that lie between us and the observed objects?

It seems appropriate here to give the basic equation for expansion redshift, what in cosmology discussions is often simply called redshift. And to confirm the correlation between the increase in distances and the increase in wavelength (i.e. how scalefactor ratio relates to wavelength ratio 1+z).

... In co-moving coordinates, the only source of redshift is the overall expansion, and so the redshift is simply:

z + 1 = \frac{a_{obs}}{a_{emit}}

However apparently the discussion became "convoluted"...

:sigh: I should know better than to continue, but "Once more unto the breach"...

The only reason any of this got at all convoluted is because you were incorrectly applying Newtonian physics, and thus I had to explain in gory detail how your re-collapsing dust ball example was perfectly consistant with a Newtonian description. Remember that you introduced the re-collapsing idea, and when doing so failed to correctly apply Newtonian physics.

If we just return to the original question, how to understand how gravity and motion play a role in the redshifts we see in the Universe, we see that there is one single unique way to describe this using Newtonian physics (we don't have general covariance in Newtonian physics, so it all becomes much simpler). Now, even given the gauge freedoms in GR, all co-ordinate systems will converge for small distances to satisfy the equivalence principle. Hence, the Newtonian description tells you clearly how the underlying physical mechanism are at play, in a way free from co-ordinate transformations. You don't even need to define any co-ordinates, you can just use words, but when you do so you are using words that have a direct physical meaning; gravity, motion etc.

On the other hand, when you wrap everything into a(t) and repeat the phrase 'expansion of space' to explain anything without any context you aren't learning, teaching or understanding anything more than the properties of one arbitrary foliation of the FRW space-time.

I'm not against the use of the phrase 'expansion of space' or the analogies that go along with it, I just object to their mis-use in contexts where it is not appropriate. When someone has asked how gravity and motion play a role in redshift, then this is clearly not the time to be invoking this concept.

I was never even touching on Newtonian physics in the discussion.

It seems that the original poster raised the expansion redshift concept up front. We then had what I think was a simple and helpful response, by Sylas and Chalnoth. But somehow, what was said (for example by Chalnoth) was misunderstood, or misinterpreted.
Also, when people (anya, Chalnoth, Sylas in post #8, etc...) referred to expansion they did not AFAICS mention any "analogies that go with it". Nobody spoke of space as a material. Noone talked about space as some kind of rubber which, by stretching, causes wavelengths to stretch. The fact is, such analogies do not immediately "go with" the mention of comoving distance, the type of distance used in stating the Hubble law v = Hd.

So why is this not the time to "invoke the concept" of expansion of distances, or expansion of universe, or whatever? It was already "invoked" by the OP. Shouldn't we be able to use the word "expansion" without this being admonished, sermonized, treated as a bugaboo?

 

[Chalnoth]

One answer to all: If I draw a sphere around observer and emitter, the gravitational effects of everything outside that sphere cancel out.

Well, not quite. This is true if the matter on the outside of that sphere is perfectly isotropic: the same in every direction.

In this situation, that requirement is not needed, as the effects of super-horizon matter that is different in different directions actually cancel out. I'd have to look up the exact physical effect at work here, but it shouldn't really be a surprise: if there was a measurable effect, then we'd be able to obtain information about the structure of the universe beyond our visible universe, which would be an indication of information traveling faster than light, which can't happen.

OMG. Topology.
Just let me stipulate that the topology is R³ on the scales we (Bunn, Wallace, and I) are talking about, and forget about that paper. If someday they find out that Andromeda is the Milky Way, I'll be the first to send the author my apologies.

The paper made no assumptions about the scale of the overall topology. It could well be orders of magnitude greater than our visible universe that it wraps back on itself.

Now, granted, this inconsistency doesn't mean that you can't go to the Newtonian approximation to try to get a feel for the physical interpretation of these variables. But it does mean that the physical description of expanding space is more correct than the Newtonian approximation (because when you insert expanding space into the Newtonian approximation, the contradiction disappears).

 

[Ich]

So the question was

But how are we sure that is the case, and redshifts are not due to the gravitational pull of all those objects that lie between us and the observed objects?

And the answer should be

It seems appropriate here to give the basic equation for expansion redshift, what in cosmology discussions is often simply called redshift. And to confirm the correlation between the increase in distances and the increase in wavelength (i.e. how scalefactor ratio relates to wavelength ratio 1+z).

??
Seems like missing the point.

We then had what I think was a simple and helpful response, by Sylas

Yeah. But it was wrong. (Just to make sure: I enjoy sylas's posts. I'm glad to have him here, this is nothing personal.)

But somehow, what was said (for example by Chalnoth) was misunderstood, or misinterpreted.

...or wrong (#5, 17, 19, 20, 33).

The fact is, such analogies do not immediately "go with" the mention of comoving distance, the type of distance used in stating the Hubble law v = Hd.

They do. Or how do you explain the fact that, when asked to explain Brooklyn's stability, people start handwaving, mentioning everything from quantum mechanics to binding forces stronger than expansion, instead of simply stating that there is no reason whatsoever for Brooklyn to expand.

Shouldn't we be able to use the word "expansion" without this being admonished, sermonized, treated as a bugaboo?

I see. Sorry, I didn't mean to persecute you with my agenda.
I think we will get along just fine as long as you're not telling newbies that galaxies aren't moving. Inform me when I get annoying.

Well, not quite. This is true if the matter on the outside of that sphere is perfectly isotropic: the same in every direction.

Isotropy given, do you agree then?

Now, granted, this inconsistency doesn't mean that you can't go to the Newtonian approximation to try to get a feel for the physical interpretation of these variables.

So the local Newtonian approximation is also declared valid?

But it does mean that the physical description of expanding space is more correct than the Newtonian approximation (because when you insert expanding space into the Newtonian approximation, the contradiction disappears).

Well, the description "maybe there's something going on" is even more correct, as it is consistent with a vast bigger number of cosmologies than the other two.
You see, if you have to describe quasistatic phenomena, static coordinates are most useful. If you have to describe global expansion, you'll choose cosmological coordinates.
Applying the former when topology becomes important can bring you in deep trouble.
Applying the latter to solar system physics is also a catastrophe.
The difference is that I know of no paper spreading misconceptions about the former case, while the latter still is deeply ingrained.

I don't want to discredit the "expansion" idea or cosmological coordinates. I just want to make sure that coordinates are not confused with physics.

 

[Chalnoth]

You see, if you have to describe quasistatic phenomena, static coordinates are most useful. If you have to describe global expansion, you'll choose cosmological coordinates.
Applying the former when topology becomes important can bring you in deep trouble.
Applying the latter to solar system physics is also a catastrophe.
The difference is that I know of no paper spreading misconceptions about the former case, while the latter still is deeply ingrained.

Why on Earth would anyone make use of coordinates that assume a homogeneous and isotropic universe for a system that is obviously very very very far from homogeneous or isotropic? It makes no sense. Who makes this mistake anyway?

 

[marcus]

... Sorry, I didn't mean to persecute you with my agenda.
I think we will get along just fine as long as you're not telling newbies that galaxies aren't moving.

Are you threatening to be obnoxious, then? As far as I know distant galaxies are not moving (except trivially) relative to CMB. You can always choose coordinates so that they move in those coordinates, of course.

But we have no evidence that typical galaxies are moving more than a few hundred km/'s, relative to CMB, and this is an interesting fact. I think it helps newcomers to hear it.

It also helps to explain what the basic equation v = Hd means. This is based on the type of distance which would be measured by timing a lightpulse with expansion frozen. It refers to that distance measured now, and to its rate of increase now.

The idea of now, and comoving distance, is built into the Hubble law and is natural to the standard model. Of course we can define alternative coordinates etc etc. But these are central, and it helps to communicate them up front.

Well, the description "maybe there's something going on" is even more correct, as it is consistent with a vast bigger number of cosmologies than the other two.
You see, if you have to describe quasistatic phenomena, static coordinates are most useful. If you have to describe global expansion, you'll choose cosmological coordinates.
Applying the former when topology becomes important can bring you in deep trouble.
Applying the latter to solar system physics is also a catastrophe.
The difference is that I know of no paper spreading misconceptions about the former case, while the latter still is deeply ingrained.

OK you have given us a little lecture or sermon about something or other. I'm not sure it's relevant to the basic problem of answering a newcomer's question. Or says anything new.

I don't want to discredit the "expansion" idea or cosmological coordinates. I just want to make sure that coordinates are not confused with physics.

Fine, I was not confusing them. How about keeping a police whistle in your mouth ready to blow whenever you see someone talking about coordinates and talking about physics and explicitly equating them. That could be useful, as long as you don't impute thoughts to other people that they didn't express.

 

[Pierre007080]

Hi Guys,
I have read and am impressed with the complexity of yoyr quoted models and opinions ... enough to scare novices like me off entirely. May I humbly ask two questions regarding red shift and get an answer that behoves the level at which it was asked?

Question 1. If galaxies are moving due to space itself expanding, how is it possible that a "Doppler" redshift can occur? Surely a "Doppler" effect requires the galaxy to be moving through space and not with it.

Question 2. If a light ray passes a large body (e.g. galaxy) tangentially, will the time dilation not cause a redshift? (I would like to separate this effect from the classical gravitational redshift and the difference in gravitational potential between source and observer. Also accept the maintenance of frequency of the wave dipping in and out of various densities or gravitational potentials.)

 

[Pierre007080]

"But we have no evidence that typical galaxies are moving more than a few hundred km/'s, relative to CMB, and this is an interesting fact. I think it helps newcomers to hear it."

Hi Marcus,
If this CBM means Cosmic Background Microwave, then this is knowledge new to me(no surprise) Where can I read more on this topic of galaxies relative movement to the CMB? This relates to my previous question about the Doppler effect only "being visible" if the galaxies are moving through space.

 

[Chalnoth]

Question 1. If galaxies are moving due to space itself expanding, how is it possible that a "Doppler" redshift can occur? Surely a "Doppler" effect requires the galaxy to be moving through space and not with it.

Well, this boils down to sort of the essence of what we've been talking about: there is no well-defined way to talk about something moving with respect to space. Basically, without looking outside, there is no possible way to tell whether or not you are moving. There is no experiment you could possibly perform to determine this (this fact is the very essence of relativity).

What this means is that if you want to know how much of the redshift comes from the Doppler effect, and how much comes from the expansion of space, well, the answer to that depends entirely upon what numbers you use to describe space. So in cosmology, we usually just avoid such questions altogether, and instead simply focus on things that are directly observable.

Question 2. If a light ray passes a large body (e.g. galaxy) tangentially, will the time dilation not cause a redshift? (I would like to separate this effect from the classical gravitational redshift and the difference in gravitational potential between source and observer. Also accept the maintenance of frequency of the wave dipping in and out of various densities or gravitational potentials.)

Well, as the light ray falls into the galaxy's potential well, it gains a blue shift due to the added energy. When it climbs back out, it loses that energy. As long as the galaxy's gravitational potential stays the same during the light ray's passage, then the two effects perfectly cancel and there is no change in the light ray's energy (i.e. no redshift or blueshift).

Time dilation really doesn't impact this picture at all. There also isn't anything related to the "maintenance" you're talking about here. It's just a matter of it entering and leaving the potential well. Or bumping into matter, but that's another story entirely.

 

[marcus]

Pierre,
I agree with Chalnoth's response, and also want to add a comment or two on your question #1

...
Question 1. If galaxies are moving due to space itself expanding, how is it possible that a "Doppler" redshift can occur? Surely a "Doppler" effect requires the galaxy to be moving through space and not with it.

BTW since I hadn't met you before, I looked at a few of your past posts in other threads. I appreciate that they give an impression of depth. I would also guess that you have some mathematical sophistication (terms like differential manifold, diffeomorphism, etc. might not be unfamiliar to you) but I can't point to any concrete reason why i have that impression.

Personally I never talk about "space itself" expanding. I don't like to perpetuate the idea of space as a material. Indeed it may eventually turn out to be some kind of aetherial substance! Fundamentally we humans are not sure we know what space is or what time is. Let's admit it. We don't know. The researchers pursuing various approaches to quantum gravity may provide some insight, but that is work in progress.

But cosmology is done in the context of General Rel, so that makes our life very simple. We talk about space as per GR. I remain skeptical. GR may be wrong or superficial, indeed there probably is something more, and deeper, to say. But let's just accept the situation as per GR.

Then space and spacetime have no objective physical reality---Einstein said this clearly in 1916. "The principle of general covariance [= diffeomorphism invariance] deprives space and time of the last remnant of objective reality."
In GR you make temporary use of a manifold to describe the distribution of matter and the metric, and then you pass to the equivalence class, under diffeos, of all manifolds and metrics which are equivalent to the given one under smooth mapping. So one throws away the manifold, in the end.

All that GR allows to exist is a web of geometric relations among events.

Pierre, please warn me if this sounds useless or strange to you, from your posts I get the impression that you have some philosophy/math sophistication which enables you to be comfortable with this. You seem not to be a newcomer to this kind of thinking. But I could be wrong. If so please let me know.

=========================
There is a lot more to say. Let me mention a couple of papers first, in case you want to read a little background.
Valerio Faroni is reputable (he has co-authored with worldclass people like Stefano Liberati and Thomas Sotiriou). He has a recent paper reviewing the issue of how best to interpret redshift. Because it is recent and (in my judgment) balanced, it has references to different advocacy-papers, and it weighs different sides. It may help with perspective, and pointers to earlier work.

Then there is a paper by Emory Bunn and David Hogg, which I like although I do not agree with their conclusion. They show that it is mathematically possible to set up an infinite chain of observers along the path of a photon and correctly analyze the redshift as the cumulative effect of an infinite series of infinitesimal dopplershifts (as one passes from one observer to the next.) Well this is certainly possible!

However they advocate this interpretation as the "natural" way of looking at the redshift, and in that respect I thing they go too far. Faraoni cites them, but tries to present a more balanced view.

I'll get the links later.
==================
I have to do something else for the moment. Hope to get back soon to this reply.