# Expansion redshift VS gravitational redshift?

by anya2
Tags: expansion, gravitational, redshift
P: 4,802
 Quote by Ich 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 $$\frac{2 \pi G}{3 c^2} \rho r^2$$ The coordinate acceleration of the emitter is $$\frac{4 \pi G}{3} \rho r$$ 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 $$dv=\frac{4 \pi G}{3} \rho r*dt = \frac{2 \pi G}{3c} \rho r^2$$ giving a redshift of $$\frac{2 \pi G}{3c^2} \rho r^2$$ 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.
 Sci Advisor PF Gold P: 9,445 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.
P: 1,253
 Quote by Chalnoth 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 realise 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 gravitional 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 cancelled 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.
 Sci Advisor P: 4,802 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: $$z + 1 = \frac{a_{obs}}{a_{emit}}$$
 Sci Advisor P: 1,253 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.
P: 4,802
 Quote by Wallace 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 any one 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.
 Sci Advisor P: 1,253 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.
 Sci Advisor P: 4,802 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.
 Sci Advisor P: 1,910 At least this time I dropped out of the discussion in time.
 Sci Advisor P: 1,253 :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.
P: 4,802
 Quote by Wallace 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.
P: 1,750
 Quote by Wallace :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
 Sci Advisor P: 1,253 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.
P: 1,253
 Quote by sylas 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 tendancy to suffer from this syndrome
P: 4,802
 Quote by 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.
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).
Astronomy
PF Gold
P: 23,228
 Quote by 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?
 Quote by 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: $$z + 1 = \frac{a_{obs}}{a_{emit}}$$
 Quote by Wallace 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.
 Quote by Chalnoth 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 any one 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.
 Quote by 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. ... 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.
P: 87
 Quote by Wallace 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.
 Quote by Wallace 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.
 Quote by Wallace 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?
 P: 16 Wow, this thread gave me a headache. Some say thats 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 thats expanding, but gravity pulling light back outside the observable universe, creating similar effect to the proposed expansion? And just to illustrate my point: 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.

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