<p>The redshift is indeed not caused by the movement of the objects, but by the expansion itself. This is a theoretical result from considering the <a href="https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric" rel="nofollow noreferrer">FLRW metric</a> for a light ray traveling on a null geodesic.</p>
<p>A derivation can be found <a href="https://ned.ipac.caltech.edu/level5/Watson/Watson2_2_3.html" rel="nofollow noreferrer">here</a>.</p>
<p>The cosmological redshift <span class="math-container">$z$</span> is given by <span class="math-container">$z+1 = 1/a$</span>, where <span class="math-container">$a$</span> is the scale factor (the size of the Universe) at the time the light was emitted. Notice that this result doesn't care <em>how</em> the Universe expanded. In principle, you could imagine a universe which was static when the light was emitted, and static when the light is observed, but expanded by the factor <span class="math-container">$a$</span> at some point in between, and you'd observe the same redshift as if that universe had expanded gradually in the meantime. This is in sharp contrast to a normal Doppler shift, where in such a hypothetical case, the result would be &quot;no observed redshift&quot;.</p>
<p>Note also that galaxies receding faster than the speed of light <span class="math-container">$c$</span> is no hindrance for us to see them; all galaxies with a observed redshift larger than <span class="math-container">$z\simeq1.4$</span> recede faster than <span class="math-container">$c$</span>. The most distant observed galaxy GN-z11 has a redshift of <span class="math-container">$z=11.09$</span>, and recedes at <span class="math-container">$v\simeq2.2c$</span>. When it emitted the light we see, it receded even faster, namely at <span class="math-container">$v \simeq 4.3 c$</span>. See the <a href="https://en.wikipedia.org/wiki/Ant_on_a_rubber_rope" rel="nofollow noreferrer">ant on a rubber rope &quot;paradox&quot;</a> for an intuitive explanation.</p>

CC BY-SA 4.0
2023-07-14T06:00:03.153Z
In the "static space" interpretation of the "loitering universe" (static when the light was emitted and received but expanding in between), it is not true that there is no redshift! The redshift in that interpretation arises from the gravitational forces that start and stop the expansion. In general, there is no phenomenon that requires expanding space to explain, because expanding space is only a coordinate choice.
Sten
CC BY-SA 4.0
2023-07-14T11:32:50.973Z
@Sten I knew I had some old answers on expansion where I was a bit more confident than I am now, but had missed this. But can you expand (sorry) a bit on how the gravitational force would cause the same redshift? My scenario is not exactly a "typical" loitering universe, which I think usually is thought of as [expanding-loitering-expanding], whereas my example is [loitering-expanding-loitering].
pela
CC BY-SA 4.0
2023-07-14T11:54:12.613Z
I haven't calculated it explicitly but can give a qualitative picture. Say the photon is going from left to right and we're in the center between the photon's source and its destination. When expansion begins, objects on the left are kicked leftward and objects on the right are kicked rightward. The photon is still on the left, but moving right, so it is kicked opposite to its motion and hence redshifted. Later, to stop expansion, objects on the right are kicked leftward and vice versa. Now the photon is on the right and moving right, so it's kicked opposite to its motion and redshifted again.
Sten
CC BY-SA 4.0
2023-07-14T11:59:54.613Z
[Bunn & Hogg](https://arxiv.org/abs/0808.1081) also addressed this scenario, although they explain it in different times. They consider parallel transporting the velocity vector along the light ray. If you do this, the relative velocity always corresponds exactly to the value needed for the Doppler shift formula to give the correct cosmological redshift, regardless of what the expansion history is. (The relationship to my explanation is, I guess, that the spacetime curvature responsible for the expansion-starting and -stopping kicks shifts the velocity vectors during the parallel transport.)
Sten
CC BY-SA 4.0
2023-07-14T12:59:53.747Z
@Sten I suppose the scenario doesn't make physical sense in a static universe, because how should galaxies stop and start receding. But would you say that Tamara Davis is simply wrong, or am I misunderstanding, when in [her 2004 paper ](https://ui.adsabs.harvard.edu/abs/2004PASA...21...97D) she says that the SR interpretation of the redshift-magnitude relation is 23 σ off?
pela
CC BY-SA 4.0
2023-07-14T15:13:16.690Z
It's unclear to me what the supposed SR interpretation in that paper is, conceptually. The $v=HD$ Hubble flow velocity is not the correct velocity to put into special relativistic formulae, since it's computed without regard for relativistic velocity addition. But more generally, the only truly self-consistent SR interpretation is to set $\Omega_\mathrm{curvature}=1$ (flat spacetime), and I don't doubt that this is ruled out at some comparable level of confidence.
Sten
CC BY-SA 4.0
2023-07-14T15:21:48.710Z
I guess if "SR interpretation" really just means "uses the relativistic Doppler formula", then the only issue is what velocity to plug in. According to Bunn & Hogg, you get the correct answer by plugging in the relative velocity evaluated by parallel transport along the light path. According to Davis & Lineweaver, you get the wrong answer by plugging in $HD$ (if my reading is correct).
Sten
CC BY-SA 4.0
2023-07-14T22:33:35.843Z
@Sten Okay, I'll take a closer look on the Bunn & Hogg paper. Geraint Lewis had a similar paper a while back that didn't convince me, but maybe this will :)
pela
CC BY-SA 4.0
2019-04-08T12:02:46.517Z
2023-07-14T01:24:50.370Z
2023-07-14T01:24:50.370Z
pela
<blockquote>
  <p>If objects don't move when the universe expands, how can the expansion result in redshift?</p>
</blockquote>

<p>Because the objects <em>are</em> moving in relation to one another. Neither is moving through space, but space is expanding. So two galaxies that used to be 1 billion light years apart are now 2 billion light years apart. </p>

<blockquote>
  <p>According to the wiki page on the expanding universe, the universe is expanding (which is how we see redshifted light from distant galaxies), however this expansion does not result in the movement of objects across space away from each other. Instead, this expansion is the formation of new space such that all of the objects in space maintain a static relationship with space. </p>
</blockquote>

<p>Yes, they maintain a static relationship with their local space, but not with each other. See the <a href="https://www.google.co.uk/search?q=raisin+cake+analogy&amp;source=lnms&amp;tbm=isch&amp;sa=X&amp;ved=0ahUKEwikw_m6yMDhAhUEQxUIHbhYDGMQ_AUIDigB&amp;biw=1280&amp;bih=894" rel="nofollow noreferrer">raisin cake analogy</a>. The galaxies are moving apart because they're embedded in space which is expanding. </p>

<blockquote>
  <p>This should mean, that as light produced by a distant light source that is expanding away from us, it is not moving away from the photon. The photon then travels across space, and this trip takes longer as a result of the expansion, but once the photon is in space near to Earth, the earth is not moving away from the light. By the time the light is at the same distance from the telescope as a flashlight held in front of the telescope, the telescope is not moving away from the photon any more than it is moving away from the photon produced by the flashlight. So, IF the expansion is not the result of motion across space, HOW do we show redshift?</p>
</blockquote>

<p>Because space expands, so two galaxies are moving apart, so they have a relative speed, so the photon looks redshifted. It hasn't actually been redshifted. It hasn't lost any energy. When you move away from a source of light it looks redshifted, but the light didn't change, instead you changed. Cosmologist Tamara Davis says the same thing in the 2010 Scientific American article <a href="https://kaiserscience.files.wordpress.com/2015/08/is-the-universe-leaking-energy-law-conservation.pdf" rel="nofollow noreferrer">Is the Universe leaking energy?</a>: </p>

<p><a href="https://i.sstatic.net/To4tX.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/To4tX.jpg" alt="enter image description here"></a> </p>

<p><sup><em>Image by Tamara Davis and Scientific American, see <a href="https://kaiserscience.files.wordpress.com/2015/08/is-the-universe-leaking-energy-law-conservation.pdf" rel="nofollow noreferrer">Is the Universe leaking energy?</a></em></sup></p>

<blockquote>
  <p>The whole reason it can make sense that objects far enough away can expand away from us FASTER than the speed of light (which is the reason why telescopes can't see further) is that these objects are not moving across space to achieve this expansion. </p>
</blockquote>

<p>We can see galaxies that have always been receding from us faster than light. See <a href="https://arxiv.org/abs/astro-ph/0310808" rel="nofollow noreferrer">Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe</a> by Tamara Davis and Charles Lineweaver. Also see <a href="https://en.wikipedia.org/wiki/Ant_on_a_rubber_rope" rel="nofollow noreferrer">the ant on the rubber rope</a></p>

CC BY-SA 4.0
2019-04-09T02:37:32.863Z
Well, all Ive done yet is go to work and read these relpies, but i do plan to look up some of the recommended reading. ,,,
tsmspace
CC BY-SA 4.0
2019-04-09T02:41:31.960Z
however,,, i still want to rebutle, that still in my perspective, I see it this way. If the galaxies are now further apart, it has no bearing on the speed of the photon relative to the telescope on impact. As the photon nears the telescope, space is expanding less between them, until just before the photon hits the telescope, there will be virtually no expansion between them, therefore the photon should still impact as if it were travelling the speed of light and the earth is not moving away from it significantly.
tsmspace
CC BY-SA 4.0
2019-04-09T22:19:40.410Z
@tsmspace : don't overthink it. Tamara Davis was describing galactic redshift as something that can be likened to Doppler shift, and I think that's the correct approach. Do read the article. I think the wrong approach is to think that the CMB photon somehow loses energy via some mysterious mechanism. I say that because I know of no situation wherein energy is not conserved.
John Duffield
CC BY-SA 4.0
2023-07-14T06:07:20.633Z
In an interview with Chodorowski, Davis specified that spatial expansion is "not a force or drag" carrying objects with it: The galaxies may remain stationary amid the expanding space, although there may be other factors affecting their locations, as mentioned in the 3rd paragraph of the other answer and projected in our impending collision (to be completed in a remote future) with Andromeda.
Edouard
CC BY-SA 4.0
2019-04-08T13:28:02.350Z
2019-04-08T13:28:02.350Z
John Duffield
<p>I am approaching this topic from a layman's perspective and view this as a logic puzzle, but when someone tries to get me to accept the logic, I'm never convinced by their arguments. </p>

<p>According to the <a href="https://en.wikipedia.org/wiki/Expansion_of_the_universe" rel="nofollow noreferrer">wiki page on the expanding universe</a>, the universe is expanding (which is how we see redshifted light from distant galaxies), however this expansion does not result in the movement of objects across space away from each other. Instead, this expansion is the formation of new space such that all of the objects in space maintain a static relationship with space. </p>

<p>This should mean, that as light produced by a distant light source that is expanding away from us, it is not moving away from the photon. The photon then travels across space, and this trip takes longer as a result of the expansion, but once the photon is in space near to Earth, the earth is not moving away from the light. By the time the light is at the same distance from the telescope as a flashlight held in front of the telescope, the telescope is not moving away from the photon any more than it is moving away from the photon produced by the flashlight. </p>

<p>So, IF the expansion is not the result of motion across space, HOW do we show redshift?????? </p>

<p>Another comment, laymans perspective<br>
The whole reason it can make sense that objects far enough away can expand away from us FASTER than the speed of light (which is the reason why telescopes can't see further) is that these objects are not moving across space to achieve this expansion. </p>

<p>Another comment in reference to the Raisin Cake. 
understanding the expanding universe as a raisin cake swelling, therefore the actual cake that is in contact with any raisin stays in contact with that raisin,, the raisins do not move through the cake,,, <em>APART</em>. BUT, in space, the raisins actually ARE moving through the cake. Also, the PHOTON that travels across space from the distant light source to the telescope, travels across space. additionally, it's NOT useful to think of this transaction of energy in a raisin cake, because the raisins DO travel across space away from each-other as the cake swells, but this is NOT how we can possibly understand objects in space expanding away from us on Earth faster than the speed of light. </p>

CC BY-SA 4.0
2019-04-08T08:28:06.167Z
Because saying that space between two objects expands can be formulated also as new space forms, and it is equivalent with respect to doppler to saying that one object moves with respect to the other one. The rest is of relevance in a full cosmological point of view. Space expansion is different than a system expanding in space. But the point is irrilevant in your discussion. Also a simple Doppler formula does not apply as for the history between emission and observation must be taken in account. Both both can be regarded as kind of doppler shift.
Alchimista
CC BY-SA 4.0
2023-07-14T06:04:50.000Z
That Wikipedia article is a giant ball of misconceptions.
Sten
<universe><redshift><dark-energy>
If objects don't move when the universe expands, how can the expansion result in redshift?
tsmspace
# If objects don't move when the universe expands, how can the expansion result in redshift?

(Asked by: username_0 on 2019-04-08)

I am approaching this topic from a layman's perspective and view this as a logic puzzle, but when someone tries to get me to accept the logic, I'm never convinced by their arguments.

According to the [wiki page on the expanding universe](https://en.wikipedia.org/wiki/Expansion_of_the_universe), the universe is expanding (which is how we see redshifted light from distant galaxies), however this expansion does not result in the movement of objects across space away from each other. Instead, this expansion is the formation of new space such that all of the objects in space maintain a static relationship with space.

This should mean, that as light produced by a distant light source that is expanding away from us, it is not moving away from the photon. The photon then travels across space, and this trip takes longer as a result of the expansion, but once the photon is in space near to Earth, the earth is not moving away from the light. By the time the light is at the same distance from the telescope as a flashlight held in front of the telescope, the telescope is not moving away from the photon any more than it is moving away from the photon produced by the flashlight.

So, IF the expansion is not the result of motion across space, HOW do we show redshift??????

Another comment, laymans perspective  
The whole reason it can make sense that objects far enough away can expand away from us FASTER than the speed of light (which is the reason why telescopes can't see further) is that these objects are not moving across space to achieve this expansion.

Another comment in reference to the Raisin Cake.
understanding the expanding universe as a raisin cake swelling, therefore the actual cake that is in contact with any raisin stays in contact with that raisin,, the raisins do not move through the cake,,, *APART*. BUT, in space, the raisins actually ARE moving through the cake. Also, the PHOTON that travels across space from the distant light source to the telescope, travels across space. additionally, it's NOT useful to think of this transaction of energy in a raisin cake, because the raisins DO travel across space away from each-other as the cake swells, but this is NOT how we can possibly understand objects in space expanding away from us on Earth faster than the speed of light.

**Tags:** universe, redshift, dark-energy

> **Comments:**
> **username_1**: Because saying that space between two objects expands can be formulated also as new space forms, and it is equivalent with respect to doppler to saying that one object moves with respect to the other one. The rest is of relevance in a full cosmological point of view. Space expansion is different than a system expanding in space. But the point is irrilevant in your discussion. Also a simple Doppler formula does not apply as for the history between emission and observation must be taken in account. Both both can be regarded as kind of doppler shift.  
> **username_2**: That Wikipedia article is a giant ball of misconceptions.  

---

## 2 answers

### Answer by username_3 on 2019-04-08. Score: 6

The redshift is indeed not caused by the movement of the objects, but by the expansion itself. This is a theoretical result from considering the [FLRW metric](https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric) for a light ray traveling on a null geodesic.

A derivation can be found [here](https://ned.ipac.caltech.edu/level5/Watson/Watson2_2_3.html).

The cosmological redshift $z$ is given by $z+1 = 1/a$, where $a$ is the scale factor (the size of the Universe) at the time the light was emitted. Notice that this result doesn't care *how* the Universe expanded. In principle, you could imagine a universe which was static when the light was emitted, and static when the light is observed, but expanded by the factor $a$ at some point in between, and you'd observe the same redshift as if that universe had expanded gradually in the meantime. This is in sharp contrast to a normal Doppler shift, where in such a hypothetical case, the result would be "no observed redshift".

Note also that galaxies receding faster than the speed of light $c$ is no hindrance for us to see them; all galaxies with a observed redshift larger than $z\simeq1.4$ recede faster than $c$. The most distant observed galaxy GN-z11 has a redshift of $z=11.09$, and recedes at $v\simeq2.2c$. When it emitted the light we see, it receded even faster, namely at $v \simeq 4.3 c$. See the [ant on a rubber rope "paradox"](https://en.wikipedia.org/wiki/Ant_on_a_rubber_rope) for an intuitive explanation.

> **Comments:**
> **username_2**: In the "static space" interpretation of the "loitering universe" (static when the light was emitted and received but expanding in between), it is not true that there is no redshift! The redshift in that interpretation arises from the gravitational forces that start and stop the expansion. In general, there is no phenomenon that requires expanding space to explain, because expanding space is only a coordinate choice.  
> **username_3**: @username_2 I knew I had some old answers on expansion where I was a bit more confident than I am now, but had missed this. But can you expand (sorry) a bit on how the gravitational force would cause the same redshift? My scenario is not exactly a "typical" loitering universe, which I think usually is thought of as [expanding-loitering-expanding], whereas my example is [loitering-expanding-loitering].  
> **username_2**: I haven't calculated it explicitly but can give a qualitative picture. Say the photon is going from left to right and we're in the center between the photon's source and its destination. When expansion begins, objects on the left are kicked leftward and objects on the right are kicked rightward. The photon is still on the left, but moving right, so it is kicked opposite to its motion and hence redshifted. Later, to stop expansion, objects on the right are kicked leftward and vice versa. Now the photon is on the right and moving right, so it's kicked opposite to its motion and redshifted again.  
> **username_2**: [Bunn & Hogg](https://arxiv.org/abs/0808.1081) also addressed this scenario, although they explain it in different times. They consider parallel transporting the velocity vector along the light ray. If you do this, the relative velocity always corresponds exactly to the value needed for the Doppler shift formula to give the correct cosmological redshift, regardless of what the expansion history is. (The relationship to my explanation is, I guess, that the spacetime curvature responsible for the expansion-starting and -stopping kicks shifts the velocity vectors during the parallel transport.)  
> **username_3**: @username_2 I suppose the scenario doesn't make physical sense in a static universe, because how should galaxies stop and start receding. But would you say that Tamara Davis is simply wrong, or am I misunderstanding, when in [her 2004 paper ](https://ui.adsabs.harvard.edu/abs/2004PASA...21...97D) she says that the SR interpretation of the redshift-magnitude relation is 23 σ off?  
> **username_2**: It's unclear to me what the supposed SR interpretation in that paper is, conceptually. The $v=HD$ Hubble flow velocity is not the correct velocity to put into special relativistic formulae, since it's computed without regard for relativistic velocity addition. But more generally, the only truly self-consistent SR interpretation is to set $\Omega_\mathrm{curvature}=1$ (flat spacetime), and I don't doubt that this is ruled out at some comparable level of confidence.  
> **username_2**: I guess if "SR interpretation" really just means "uses the relativistic Doppler formula", then the only issue is what velocity to plug in. According to Bunn & Hogg, you get the correct answer by plugging in the relative velocity evaluated by parallel transport along the light path. According to Davis & Lineweaver, you get the wrong answer by plugging in $HD$ (if my reading is correct).  
> **username_3**: @username_2 Okay, I'll take a closer look on the Bunn & Hogg paper. Geraint Lewis had a similar paper a while back that didn't convince me, but maybe this will :)  

---

### Answer by username_4 on 2019-04-08. Score: 1

> If objects don't move when the universe expands, how can the expansion result in redshift?

Because the objects *are* moving in relation to one another. Neither is moving through space, but space is expanding. So two galaxies that used to be 1 billion light years apart are now 2 billion light years apart.

> According to the wiki page on the expanding universe, the universe is expanding (which is how we see redshifted light from distant galaxies), however this expansion does not result in the movement of objects across space away from each other. Instead, this expansion is the formation of new space such that all of the objects in space maintain a static relationship with space.

Yes, they maintain a static relationship with their local space, but not with each other. See the [raisin cake analogy](https://www.google.co.uk/search?q=raisin+cake+analogy&source=lnms&tbm=isch&sa=X&ved=0ahUKEwikw_m6yMDhAhUEQxUIHbhYDGMQ_AUIDigB&biw=1280&bih=894). The galaxies are moving apart because they're embedded in space which is expanding.

> This should mean, that as light produced by a distant light source that is expanding away from us, it is not moving away from the photon. The photon then travels across space, and this trip takes longer as a result of the expansion, but once the photon is in space near to Earth, the earth is not moving away from the light. By the time the light is at the same distance from the telescope as a flashlight held in front of the telescope, the telescope is not moving away from the photon any more than it is moving away from the photon produced by the flashlight. So, IF the expansion is not the result of motion across space, HOW do we show redshift?

Because space expands, so two galaxies are moving apart, so they have a relative speed, so the photon looks redshifted. It hasn't actually been redshifted. It hasn't lost any energy. When you move away from a source of light it looks redshifted, but the light didn't change, instead you changed. Cosmologist Tamara Davis says the same thing in the 2010 Scientific American article [Is the Universe leaking energy?](https://kaiserscience.files.wordpress.com/2015/08/is-the-universe-leaking-energy-law-conservation.pdf):

[![enter image description here](https://i.sstatic.net/To4tX.jpg)](https://i.sstatic.net/To4tX.jpg)

*Image by Tamara Davis and Scientific American, see [Is the Universe leaking energy?](https://kaiserscience.files.wordpress.com/2015/08/is-the-universe-leaking-energy-law-conservation.pdf)*

> The whole reason it can make sense that objects far enough away can expand away from us FASTER than the speed of light (which is the reason why telescopes can't see further) is that these objects are not moving across space to achieve this expansion.

We can see galaxies that have always been receding from us faster than light. See [Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe](https://arxiv.org/abs/astro-ph/0310808) by Tamara Davis and Charles Lineweaver. Also see [the ant on the rubber rope](https://en.wikipedia.org/wiki/Ant_on_a_rubber_rope)

> **Comments:**
> **username_0**: Well, all Ive done yet is go to work and read these relpies, but i do plan to look up some of the recommended reading. ,,,  
> **username_0**: however,,, i still want to rebutle, that still in my perspective, I see it this way. If the galaxies are now further apart, it has no bearing on the speed of the photon relative to the telescope on impact. As the photon nears the telescope, space is expanding less between them, until just before the photon hits the telescope, there will be virtually no expansion between them, therefore the photon should still impact as if it were travelling the speed of light and the earth is not moving away from it significantly.  
> **username_4**: @username_0 : don't overthink it. Tamara Davis was describing galactic redshift as something that can be likened to Doppler shift, and I think that's the correct approach. Do read the article. I think the wrong approach is to think that the CMB photon somehow loses energy via some mysterious mechanism. I say that because I know of no situation wherein energy is not conserved.  
> **username_5**: In an interview with Chodorowski, Davis specified that spatial expansion is "not a force or drag" carrying objects with it: The galaxies may remain stationary amid the expanding space, although there may be other factors affecting their locations, as mentioned in the 3rd paragraph of the other answer and projected in our impending collision (to be completed in a remote future) with Andromeda.  

---

