<p>Firstly, I think it's important to note that in general relativity there is only <em>one</em> redshift, and that a cosmological redshift can be interpreted as the result of infinitely many infinitesimal redshifts between infinitesimally small inertial frames receding from one another. But I still think it makes sense to distinguish between &quot;regular&quot; Doppler shifts and redshifts due to expanding space, for the reason you quote me for.</p>
<p>If we make that distinction, then it seems to me that your scenario is mixing two things: If space is expanding when a photon leaves a distant galaxy, then that photon experiences a cosmological redshift from the beginning. But the galaxy is not moving <em>through</em> space away from us, so it does not experience a Doppler shift.</p>
<p>In reality, the Universe <em>is</em> in fact expanding from the beginning (although it doesn't expand as fast close to the galaxy, because the mass density is above average).</p>
<h4>Peculiar velocities</h4>
<p>Also in reality, the galaxy does in factmove through space, so there <em>is</em> actually a Doppler shift, albeit not because of the effect you mention. This motion is called the <em>peculiar velocity</em> of the galaxy, and in principle there is no way to distinguish, although various methods exist to estimate it. For instance, you can deduce the peculiar motion by measuring the redshifts of the galaxies in a group or a cluster, all assumed to be at the same cosmological distance and hence have the same cosmological redshift.</p>

CC BY-SA 4.0
2022-02-15T16:38:32.153Z
I understand what you've written.  Isn't it true that as long as the distance between us and a distant galaxy is increasing, we will observe a Doppler shift?  Even if the galaxy is receding solely due to the expansion of space, I'd still expect to observe a Doppler shift, because its distance from us is increasing.  Am I missing something?  If the universe continues to expand while the light is on its way to us, of course there would be an additional cosmological redshift.
Matt
CC BY-SA 4.0
2022-02-16T12:34:39.510Z
@Matt In my answer I'm distinguishing between a Doppler redshift arising from a difference in velocity between emitter and observer, and a cosmological redshift arising from the photon traveling through expanding space. The former _only_ occurs if there's a difference in velocity between [the emitter at the time of emission] and [the observer at the time of observation]. The latter _only_ occurs if space expands at any of the positions that the photon passes, _and_ — and this is important — at the time the photon passes that location [cont'd below].
pela
CC BY-SA 4.0
2022-02-16T12:35:52.237Z
That means that, in principle, you could have a wacky universe where space expands in some place between the galaxy and us, but for some reason not exactly where the photon is. In that case, the distance between the galaxies would increase, but the photon would not experience any redshift. _Our_ universe isn't so wacky, we believe, but seems to be expanding roughly the same everywhere [cont'd below].
pela
CC BY-SA 4.0
2022-02-16T12:36:15.237Z
On the other hand, you could in principle also have a static Universe — the observed redshift would then _only_ be a result of 1) the velocity of the distant galaxy _at the moment it emitted the photon_, and 2) the velocity of us _at the moment we receive it_.
pela
CC BY-SA 4.0
2022-02-26T20:54:13.590Z
Let's look at your wacky universe where space is expanding only in a small region between the distant galaxy and us (and assume that neither that galaxy nor us is moving through space).  Because of that expansion, the distance between that galaxy and us is increasing.  So, because of that increasing distance, when the photon is emitted,  I'd expect a Doppler shift -- just from the fact that the distance between the two galaxies is increasing (even though that distance increase is coming from an expansion where the photon is not present).  Am I missing something?
Matt
CC BY-SA 4.0
2022-02-27T08:23:22.223Z
@Matt No, there wouldn't be a Doppler shift: Let's say the Milky Way is at $x=0$, and the galaxy is at $x=10$ (in some units). A photon is emitted with λ = 1216 Å from $x=10$ in the negative $x$ direction. Space is static, so when the photon passes $x=9$, its wavelength is still λ = 1216 Å in the local reference frame. Same when it passes $x=9$. When it passes $x=8$, the space between $x=5$ and $x=6$ expands rapidly by a factor of 10, such the total distance from MW to the galaxy is now 19 [cont'd below]
pela
CC BY-SA 4.0
2022-02-27T08:23:33.400Z
But λ is still 1216 Å at the location of the photon. Nothing happened there that would change its wavelength. Only now that location — formerly called $x=8$ — now lies 17 distance units from MW, i.e. at $x=17$. The distance from the other galaxy to the photon is still $\Delta x=2$ though. The photon continues with its 1216 Å to $x=16$, $x=15$, etc., and the wacky space now stays static. The photon travels through the region _did_ expand, but is now just "regular" space, and hence it simply stays at 1216 Å, also when it arrives at MW.
pela
CC BY-SA 4.0
2022-02-14T15:53:20.957Z
2022-02-14T15:53:20.957Z
pela
<p>There are several existing threads on the difference between cosmological and Doppler redshifts.  However, I don't see that any of them answered the  question below.</p>
<p>@pela gave the following example:
&quot;In principle you could have a universe ... that were static when a distant galaxy emitted a photon, then at some point expanded quickly by a factor of 2, and then again is static. In this hypothetical case, the observer would still measure the photon to have been redshifted by a factor of 2 (i.e. =1).&quot;</p>
<p>That very nicely made a clear distinction between cosmological and Doppler redshifts.  However, suppose we modify this scenario so that the universe is already expanding when the light is emitted from some distant galaxy.  Then the distance between that galaxy and ours is increasing when the light is emitted, and therefore we should expect a Doppler shift.  Then, while the light is on its way to us, the universe is still expanding, and the light is  getting further redshifted due to the expansion.  So then it seems like the redshift we observe should be a combination of both a Doppler shift AND a cosmological redshift.  Is that correct?  And, if so, how does one disentangle the two and determine the contribution from each redshift mechanism?</p>

<cosmology><redshift>
Doppler Redshift vs. Cosmological Redshift ... or Both?
Matt
# Doppler Redshift vs. Cosmological Redshift ... or Both?

(Asked by: username_0 on 2022-02-14)

There are several existing threads on the difference between cosmological and Doppler redshifts. However, I don't see that any of them answered the question below.

@pela gave the following example:
"In principle you could have a universe ... that were static when a distant galaxy emitted a photon, then at some point expanded quickly by a factor of 2, and then again is static. In this hypothetical case, the observer would still measure the photon to have been redshifted by a factor of 2 (i.e. =1)."

That very nicely made a clear distinction between cosmological and Doppler redshifts. However, suppose we modify this scenario so that the universe is already expanding when the light is emitted from some distant galaxy. Then the distance between that galaxy and ours is increasing when the light is emitted, and therefore we should expect a Doppler shift. Then, while the light is on its way to us, the universe is still expanding, and the light is getting further redshifted due to the expansion. So then it seems like the redshift we observe should be a combination of both a Doppler shift AND a cosmological redshift. Is that correct? And, if so, how does one disentangle the two and determine the contribution from each redshift mechanism?

**Tags:** cosmology, redshift

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## 1 answers

### Answer by username_1 on 2022-02-14. Score: 3

Firstly, I think it's important to note that in general relativity there is only *one* redshift, and that a cosmological redshift can be interpreted as the result of infinitely many infinitesimal redshifts between infinitesimally small inertial frames receding from one another. But I still think it makes sense to distinguish between "regular" Doppler shifts and redshifts due to expanding space, for the reason you quote me for.

If we make that distinction, then it seems to me that your scenario is mixing two things: If space is expanding when a photon leaves a distant galaxy, then that photon experiences a cosmological redshift from the beginning. But the galaxy is not moving *through* space away from us, so it does not experience a Doppler shift.

In reality, the Universe *is* in fact expanding from the beginning (although it doesn't expand as fast close to the galaxy, because the mass density is above average).

#### Peculiar velocities

Also in reality, the galaxy does in factmove through space, so there *is* actually a Doppler shift, albeit not because of the effect you mention. This motion is called the *peculiar velocity* of the galaxy, and in principle there is no way to distinguish, although various methods exist to estimate it. For instance, you can deduce the peculiar motion by measuring the redshifts of the galaxies in a group or a cluster, all assumed to be at the same cosmological distance and hence have the same cosmological redshift.

> **Comments:**
> **username_0**: I understand what you've written.  Isn't it true that as long as the distance between us and a distant galaxy is increasing, we will observe a Doppler shift?  Even if the galaxy is receding solely due to the expansion of space, I'd still expect to observe a Doppler shift, because its distance from us is increasing.  Am I missing something?  If the universe continues to expand while the light is on its way to us, of course there would be an additional cosmological redshift.  
> **username_1**: @Matt In my answer I'm distinguishing between a Doppler redshift arising from a difference in velocity between emitter and observer, and a cosmological redshift arising from the photon traveling through expanding space. The former _only_ occurs if there's a difference in velocity between [the emitter at the time of emission] and [the observer at the time of observation]. The latter _only_ occurs if space expands at any of the positions that the photon passes, _and_ — and this is important — at the time the photon passes that location [cont'd below].  
> **username_1**: That means that, in principle, you could have a wacky universe where space expands in some place between the galaxy and us, but for some reason not exactly where the photon is. In that case, the distance between the galaxies would increase, but the photon would not experience any redshift. _Our_ universe isn't so wacky, we believe, but seems to be expanding roughly the same everywhere [cont'd below].  
> **username_1**: On the other hand, you could in principle also have a static Universe — the observed redshift would then _only_ be a result of 1) the velocity of the distant galaxy _at the moment it emitted the photon_, and 2) the velocity of us _at the moment we receive it_.  
> **username_0**: Let's look at your wacky universe where space is expanding only in a small region between the distant galaxy and us (and assume that neither that galaxy nor us is moving through space).  Because of that expansion, the distance between that galaxy and us is increasing.  So, because of that increasing distance, when the photon is emitted,  I'd expect a Doppler shift -- just from the fact that the distance between the two galaxies is increasing (even though that distance increase is coming from an expansion where the photon is not present).  Am I missing something?  
> **username_1**: @Matt No, there wouldn't be a Doppler shift: Let's say the Milky Way is at $x=0$, and the galaxy is at $x=10$ (in some units). A photon is emitted with λ = 1216 Å from $x=10$ in the negative $x$ direction. Space is static, so when the photon passes $x=9$, its wavelength is still λ = 1216 Å in the local reference frame. Same when it passes $x=9$. When it passes $x=8$, the space between $x=5$ and $x=6$ expands rapidly by a factor of 10, such the total distance from MW to the galaxy is now 19 [cont'd below]  
> **username_1**: But λ is still 1216 Å at the location of the photon. Nothing happened there that would change its wavelength. Only now that location — formerly called $x=8$ — now lies 17 distance units from MW, i.e. at $x=17$. The distance from the other galaxy to the photon is still $\Delta x=2$ though. The photon continues with its 1216 Å to $x=16$, $x=15$, etc., and the wacky space now stays static. The photon travels through the region _did_ expand, but is now just "regular" space, and hence it simply stays at 1216 Å, also when it arrives at MW.  

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