<blockquote>
  <p>What is the difference between the way light travels in a gravitational field and the way it travels through an expanding universe?</p>
</blockquote>

<p>In the former situation spacetime is curved across space, in the latter situation spacetime is curved over time. </p>

<blockquote>
  <p>A photon is travelling through space. As it travels, the space through which it travels is expanding. Does this describe: 
  A - a photon travelling from a distant galaxy to earth<br>
  B - a photon travelling from a point of higher to a point of lower gravity
  C - either</p>
</blockquote>

<p>It describes A. It can also be likened to a photon travelling from a point of low gravitational potential to a point of high gravitational potential. Hence we talk of gravitational redshift, and cosmological redshift. </p>

<blockquote>
  <p>If like me you think the answer is C, can you explain why light should travel differently through a gravitational field to how it travels through an expanding universe? In other words, why in one case does the speed of the photon vary, while in the other case it doesn't? </p>
</blockquote>

<p>Who says it doesn't? We can find Einstein saying the speed of light varies with gravitational potential year after year:</p>

<p><em><a href="https://einsteinpapers.press.princeton.edu/vol4-trans/144" rel="nofollow noreferrer">1912</a>: “On the other hand I am of the view that the principle of the constancy of the velocity of light can be maintained only insofar as one restricts oneself to spatio-temporal regions of constant gravitational potential”.</em></p>

<p><em><a href="https://einsteinpapers.press.princeton.edu/vol4-trans/325?highlightText=%22incompatible%" rel="nofollow noreferrer">1913</a>: “I arrived at the result that the velocity of light is not to be regarded as independent of the gravitational potential. Thus the principle of the constancy of the velocity of light is incompatible with the equivalence hypothesis”.</em> </p>

<p><em><a href="https://einsteinpapers.press.princeton.edu/vol4-trans/295?highlightText=%22postulate%22" rel="nofollow noreferrer">1914</a>: “In the case where we drop the postulate of the constancy of the velocity of light, there exists, a priori, no privileged coordinate systems”.</em></p>

<p><em><a href="https://einsteinpapers.press.princeton.edu/vol4-trans/271?highlightText=%22abandoned%22" rel="nofollow noreferrer">1915</a>: “the writer of these lines is of the opinion that the theory of relativity is still in need of generalization, in the sense that the principle of the constancy of the velocity of light is to be abandoned”.</em> </p>

<p><em><a href="https://einsteinpapers.press.princeton.edu/vol6-trans/340?highlightText=%22cannot%20claim%20any%20unlimited%20validity%22" rel="nofollow noreferrer">1916</a>: “In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity”.</em></p>

<p><em><a href="https://einsteinpapers.press.princeton.edu/vol7-trans/156?highlightText=%22spatially%20variable%22" rel="nofollow noreferrer">1920</a>: “Second, this consequence shows that the law of the constancy of the speed of light no longer holds, according to the general theory of relativity, in spaces that have gravitational fields. As a simple geometric consideration shows, the curvature of light rays occurs only in spaces where the speed of light is spatially variable”.</em></p>

<p>We can also find Irwin Shapiro saying the same thing in 1964. See line 7 of his paper in the fair-use excerpt <a href="https://i.sstatic.net/IlSrh.jpg" rel="nofollow noreferrer">here</a>. It's even on <a href="https://en.wikipedia.org/w/index.php?title=Shapiro_time_delay&amp;oldid=875091556" rel="nofollow noreferrer">Wikipedia</a>: <em>“the speed of a light wave depends on the strength of the gravitational potential along its path”</em>. For something more recent see <a href="http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html" rel="nofollow noreferrer">Is The Speed of Light Everywhere the Same?</a> by  PhysicsFAQ editor Don Koks. He says <em>“Einstein talked about the speed of light changing in his new theory”</em> and <em>"a "global" observer can say that ceiling light does travel faster than floor light"</em>. Also see Ned Wright’s <a href="http://www.astro.ucla.edu/~wright/deflection-delay.html" rel="nofollow noreferrer">Deflection and Delay of Light</a>, where you can read this: <em>“In a very real sense, the delay experienced by light passing a massive object is responsible for the deflection of the light"</em>. </p>

<p>Of course, some people will claim that c=1 and the speed of light is truly constant, but they're contradicting Einstein and not understanding the tautology. John Moffat and João Magueijo explained that in their <a href="https://arxiv.org/abs/0705.4507" rel="nofollow noreferrer">Comments on “Note on varying speed of light theories”</a>. Contemporary physicists use the local motion of light to define the second and the metre, then use them to measure the local speed of light. Hence they'll say the local speed of light is 299,792,458 m/s, at both the floor and the ceiling. Moffat and Magueijo (and others) were the authors of variable speed of light theories as an alternative to inflation. See <a href="https://en.wikipedia.org/w/index.php?title=Variable_speed_of_light&amp;oldid=836079117#Einstein&#39;s_updated_proposals_(1905%E2%80%931915)" rel="nofollow noreferrer">Wikipedia</a>. They said the speed of light was much faster in the early universe. Sadly I think they got that back to front, but never mind.   </p>

<blockquote>
  <p>Alternatively can you explain why you don't think it's C?</p>
</blockquote>

<p>It isn't C because space isn't expanding in a gravitational field. Instead it's <a href="https://einsteinpapers.press.princeton.edu/vol7-trans/192?highlightText=%22neither%20homogeneous%22" rel="nofollow noreferrer">"neither homogeneous nor isotropic"</a>. That's what Einstein said in 1920. Note though that when space is expanding, it's inhomogeneous over time. Note this paper: <a href="https://iopscience.iop.org/article/10.1088/0256-307X/25/5/014/meta" rel="nofollow noreferrer">Inhomogeneous Vacuum: An Alternative Interpretation of Curved Spacetime</a>. Einstein referred to inhomogeneous vacuum whilst most modern authors refer to curved spacetime, but they're talking about the same thing.  </p>

CC BY-SA 4.0
2019-02-11T23:02:57.047Z
Thanks for that, a lot of interesting points there. Sorry I got the low and high gravity the wrong way round accidentally. You also misinterpreted my meaning about speed of light being variable. I believe far more strongly than most that the speed of light varies due to gravity, it was the fact that we treat it as constant through expansion that concerned me.
Alan Gee
CC BY-SA 4.0
2019-02-12T07:44:24.487Z
@Alan Gee : my pleasure. Note what Einstein was saying - the speed of light doesn't vary _due_ to gravity, gravity is due to the speed of light being variable. With that in mind, yes, it does seem rather odd to treat the speed of light as constant regardless of the energy density of the early universe. I guess too many people were taught that c=1 before the Einstein digital papers were online. Do make sure you read the Wikipedia [VSL](https://en.wikipedia.org/wiki/Variable_speed_of_light#Einstein's_updated_proposals_(1905–1915)) article.
John Duffield
CC BY-SA 4.0
2019-02-12T07:56:53.980Z
Sounds like you may agree with my answer to this question here https://physics.stackexchange.com/questions/133482/speed-of-light-in-general-relativity . If you can spare the time to read through it, I am sure you'll find it interesting.
Alan Gee
CC BY-SA 4.0
2019-02-12T13:11:49.190Z
@Alan Gee : I read it. There are a few things that aren't quite right I'm afraid. The "deflection" of light is twice the deflection of matter, and gravitational potential energy is converted into kinetic energy leaving you with a mass deficit. But I think you're thinking along the right lines, and it's good to see somebody thinking for themself.
John Duffield
CC BY-SA 4.0
2019-02-13T20:54:30.983Z
Thank you - your constructive comments are again very useful. I have deleted that answer until such time as I have had a chance to work out what you mean and review the credibility of my answer. I should not have posted it really, but I do like to push the boundaries a bit.
Alan Gee
CC BY-SA 4.0
2019-02-14T08:15:35.810Z
@Alan Gee : my pleasure Alan. You might want to take a look at [this](http://physicsdetective.com/the-speed-of-light/). I wrote it.
John Duffield
CC BY-SA 4.0
2019-02-14T16:59:23.100Z
I read through your article briefly and couldn't see anything I disagreed with. In your earlier comment, can you tell me what you meant by "there is a mass deficit"?
Alan Gee
CC BY-SA 4.0
2019-02-14T18:20:29.803Z
@Alan Gee : see the Wikipedia [binding energy article](https://en.wikipedia.org/wiki/Binding_energy#Mass-energy_relation). When you drop a brick, gravity converts potential energy in the brick into kinetic energy. When the brick hits the ground this gets dissipated, and you're left with a mass deficit. A brick on the ground has less mass than a brick at 10,000 feet. Conversely when you lift a brick up off the ground you do work on it, you add energy to it, and since E=mc², you increase its mass.
John Duffield
CC BY-SA 4.0
2019-02-14T20:59:30.040Z
Yes, those who believe that the speed of light is constant would say that when they raise a glass they are increasing its energy by increasing its mass very slightly. I say that when I raise my glass I am increasing its energy by taking it to a place where the speed of light is higher. I thought you were in my camp.
Alan Gee
CC BY-SA 4.0
2019-02-14T23:40:34.927Z
@Alan Gee : either way you add energy to that brick, and since _the mass of a body is a measure of its energy-content_, the mass increases.
John Duffield
CC BY-SA 4.0
2019-02-15T08:43:31.510Z
So you are now treating c as constant?
Alan Gee
CC BY-SA 4.0
2019-02-16T10:59:03.900Z
@Alan Gee : no. When you lift the brick E increases and m increases. Because you lift it to a place where c increases.
John Duffield
CC BY-SA 4.0
2019-02-11T21:50:20.637Z
2019-02-11T21:50:20.637Z
John Duffield
<blockquote>
  <p>If like me you think the answer is C, can you explain why light should travel differently through a gravitational field to how it travels through an expanding universe? In other words, why in one case does the speed of the photon vary, while in the other case it doesn't?</p>
</blockquote>

<p>I think the reason is, we can take the Cosmological redshift as a Doppler redshift, where the speed of the photon does not change but only the wavelength changes due to the expansion of the universe.</p>

<p>Meanwhile, in Gravitational redshift, its the "redshift" is purely caused by GR and it's possible that the light loses its speed due to this effect.</p>

<p>Here is the link why I think cosmological redshift can be thought as Doppler redshift. </p>

<p><a href="https://www.physicsforums.com/insights/coordinate-dependent-statements-expanding-universe/" rel="nofollow noreferrer">Here</a></p>

CC BY-SA 4.0
2019-01-24T18:18:18.110Z
I agree with most of what you said, but the speed of light does change due to gravity. This is normally, however, referred to as gravitational time dilation.
Alan Gee
CC BY-SA 4.0
2019-01-24T18:20:27.077Z
Well I am sorry then, I did not know that.
seVenVo1d
CC BY-SA 4.0
2019-01-24T18:22:15.983Z
When you say the speed of light changes, you are using a particular coordinate system, and all that is changing is the coordinate speed of light.  In other words, you have some coordinates x,t and the path of the light is x(t), and then dx/dt is changing.  Coordinates are useful devices, but that's pretty much true of anything in any coordinates, you can make coordinate speed be anything you want.  All local observers will always get c when they measure the speed of light, even in a gravity field, so it is more empirically grounded to say the speed is not changed.
Ken G
CC BY-SA 4.0
2019-01-24T18:25:17.200Z
@Reign No problem. Thanks for taking the trouble to answer.
Alan Gee
CC BY-SA 4.0
2019-01-24T18:27:39.413Z
@AlanGee Can you show a source that it says speed of photon varies ?
seVenVo1d
CC BY-SA 4.0
2019-01-24T18:33:26.480Z
@Reign not at hand, but it can be easily shown that time dilation and a reduction in the speed of light are different ways of describing the same phenomenon.
Alan Gee
CC BY-SA 4.0
2019-01-24T18:34:44.217Z
That being that the wavelength has decreased for a given frequency of light.
Alan Gee
CC BY-SA 4.0
2019-01-24T18:48:42.860Z
But cant we also take it as a constant and do calculations like that ?
seVenVo1d
CC BY-SA 4.0
2019-01-24T19:23:37.573Z
@AlanGee If we more think about the why the light lose irs speed then maybe we can suggest that cosmological redshidt can be also thought as a doppler redshift meanwhile the gravitational constant is pure GR effect.
seVenVo1d
CC BY-SA 4.0
2019-01-24T20:29:00.173Z
@ken g I wouldn't disagree at all that we can't directly measure changes in the speed of light. I also know why. That doesn't mean it doesn't t change though.
Alan Gee
CC BY-SA 4.0
2019-01-24T20:29:53.547Z
@Reign See https://en.wikipedia.org/wiki/Shapiro_time_delay Note that when measured locally, the speed of light in a vacuum is *always* $c$. Also see http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html
PM 2Ring
CC BY-SA 4.0
2019-01-24T20:41:49.893Z
@Reign I think the key word is 'measured'. It is well known that we always measure the same speed of light, but you have to remember that time is based on the speed of light and speed is based on time. What can you expect.
Alan Gee
CC BY-SA 4.0
2019-01-24T20:42:03.497Z
@PM2Ring thanks for the links.
seVenVo1d
CC BY-SA 4.0
2019-01-24T20:55:06.057Z
@AlanGee I edited my post what do you think now ?
seVenVo1d
CC BY-SA 4.0
2019-01-24T21:07:37.297Z
@Alan Gee--  this is science, what we cannot measure we cannot make claims about.  This is the first rule that separates science from belief systems.  You can have any personal belief you wish, but it is belief, not knowledge.
Ken G
CC BY-SA 4.0
2019-01-24T21:11:05.087Z
@ken g There is such a thing in science as deduction. We can deduce from practical measurement of gravitational time dilation that the speed of light is changing. See my earlier comment.
Alan Gee
CC BY-SA 4.0
2019-01-24T21:18:23.540Z
No such deducton is required, it all depends on chosen coordinates.  You are talking about a coordinate speed, dx/dt.  State how you arrive at your deduction, and I will tell you the arbitrary coordinates you are using.
Ken G
CC BY-SA 4.0
2019-02-12T13:22:11.453Z
@Ken G : I'm afraid the "knowledge" says the speed of light varies in the room you're in. That's why [NIST](http://www.learner.org/courses/physics/scientist/transcripts/wineland.html) optical clocks go slower when they're lower. The "belief" is that this is due to some magical mysterious thing called time going slower. Do note that Einstein called it the speed of light, not the coordinate speed of light, and do try to understand the tautology: when you define your second and your metre using the local motion of light, you will always declare the local speed of light to be the same.
John Duffield
CC BY-SA 4.0
2019-02-12T17:44:51.040Z
"Why" questions in physics are quite often answered via a choice of coordinates (since we use coordinates to inform language), and the answer generally depends on those chosen coordinates.  The claim that the speed of light varies in a gravitational field is an absolutely classic example of what I'm talking about.  And when someone says we can't measure something but it's true anyway, I think that speaks for itself.
Ken G
CC BY-SA 4.0
2019-01-24T17:15:51.657Z
2019-01-24T20:54:47.017Z
2019-01-24T20:54:47.017Z
seVenVo1d
<p>A photon is travelling through space. As it travels, the space through which it travels is expanding</p>

<p>Does this describe</p>

<ul>
<li><p>A - a photon travelling from a distant galaxy to earth</p></li>
<li><p>B - a photon travelling from a point of higher to a point of lower
gravity</p></li>
<li><p>C - either</p></li>
</ul>

<p>If like me you think the answer is C, can you explain why light should travel differently through a gravitational field to how it travels through an expanding universe? In other words, why in one case does the speed of the photon vary, while in the other case it doesn't? </p>

<p>Alternatively can you explain why you don't think it's C?</p>

<p>I have asked a similar question on the Physics Stack, but I probably worded it badly, so I just got a load of down votes and no answers. I hope I haven't offended anyone here with this wording.</p>

<light><space-time><cosmological-inflation>
What is the difference between the way light travels in a gravitational field and the way it travels through an expanding universe?
Alan Gee
# What is the difference between the way light travels in a gravitational field and the way it travels through an expanding universe?

(Asked by: username_0 on 2019-01-24)

A photon is travelling through space. As it travels, the space through which it travels is expanding

Does this describe

* A - a photon travelling from a distant galaxy to earth
* B - a photon travelling from a point of higher to a point of lower
  gravity
* C - either

If like me you think the answer is C, can you explain why light should travel differently through a gravitational field to how it travels through an expanding universe? In other words, why in one case does the speed of the photon vary, while in the other case it doesn't?

Alternatively can you explain why you don't think it's C?

I have asked a similar question on the Physics Stack, but I probably worded it badly, so I just got a load of down votes and no answers. I hope I haven't offended anyone here with this wording.

**Tags:** light, space-time, cosmological-inflation


---

## 2 answers

### Answer by username_1 on 2019-02-11. Score: 0 | Accepted answer

> What is the difference between the way light travels in a gravitational field and the way it travels through an expanding universe?

In the former situation spacetime is curved across space, in the latter situation spacetime is curved over time.

> A photon is travelling through space. As it travels, the space through which it travels is expanding. Does this describe:
> A - a photon travelling from a distant galaxy to earth  
> B - a photon travelling from a point of higher to a point of lower gravity
> C - either

It describes A. It can also be likened to a photon travelling from a point of low gravitational potential to a point of high gravitational potential. Hence we talk of gravitational redshift, and cosmological redshift.

> If like me you think the answer is C, can you explain why light should travel differently through a gravitational field to how it travels through an expanding universe? In other words, why in one case does the speed of the photon vary, while in the other case it doesn't?

Who says it doesn't? We can find Einstein saying the speed of light varies with gravitational potential year after year:

*[1912](https://einsteinpapers.press.princeton.edu/vol4-trans/144): “On the other hand I am of the view that the principle of the constancy of the velocity of light can be maintained only insofar as one restricts oneself to spatio-temporal regions of constant gravitational potential”.*

*[1913](https://einsteinpapers.press.princeton.edu/vol4-trans/325?highlightText=%22incompatible%): “I arrived at the result that the velocity of light is not to be regarded as independent of the gravitational potential. Thus the principle of the constancy of the velocity of light is incompatible with the equivalence hypothesis”.*

*[1914](https://einsteinpapers.press.princeton.edu/vol4-trans/295?highlightText=%22postulate%22): “In the case where we drop the postulate of the constancy of the velocity of light, there exists, a priori, no privileged coordinate systems”.*

*[1915](https://einsteinpapers.press.princeton.edu/vol4-trans/271?highlightText=%22abandoned%22): “the writer of these lines is of the opinion that the theory of relativity is still in need of generalization, in the sense that the principle of the constancy of the velocity of light is to be abandoned”.*

*[1916](https://einsteinpapers.press.princeton.edu/vol6-trans/340?highlightText=%22cannot%20claim%20any%20unlimited%20validity%22): “In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity”.*

*[1920](https://einsteinpapers.press.princeton.edu/vol7-trans/156?highlightText=%22spatially%20variable%22): “Second, this consequence shows that the law of the constancy of the speed of light no longer holds, according to the general theory of relativity, in spaces that have gravitational fields. As a simple geometric consideration shows, the curvature of light rays occurs only in spaces where the speed of light is spatially variable”.*

We can also find Irwin Shapiro saying the same thing in 1964. See line 7 of his paper in the fair-use excerpt [here](https://i.sstatic.net/IlSrh.jpg). It's even on [Wikipedia](https://en.wikipedia.org/w/index.php?title=Shapiro_time_delay&oldid=875091556): *“the speed of a light wave depends on the strength of the gravitational potential along its path”*. For something more recent see [Is The Speed of Light Everywhere the Same?](http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html) by PhysicsFAQ editor Don Koks. He says *“Einstein talked about the speed of light changing in his new theory”* and *"a "global" observer can say that ceiling light does travel faster than floor light"*. Also see Ned Wright’s [Deflection and Delay of Light](http://www.astro.ucla.edu/~wright/deflection-delay.html), where you can read this: *“In a very real sense, the delay experienced by light passing a massive object is responsible for the deflection of the light"*.

Of course, some people will claim that c=1 and the speed of light is truly constant, but they're contradicting Einstein and not understanding the tautology. John Moffat and João Magueijo explained that in their [Comments on “Note on varying speed of light theories”](https://arxiv.org/abs/0705.4507). Contemporary physicists use the local motion of light to define the second and the metre, then use them to measure the local speed of light. Hence they'll say the local speed of light is 299,792,458 m/s, at both the floor and the ceiling. Moffat and Magueijo (and others) were the authors of variable speed of light theories as an alternative to inflation. See [Wikipedia](https://en.wikipedia.org/w/index.php?title=Variable_speed_of_light&oldid=836079117#Einstein's_updated_proposals_(1905%E2%80%931915)). They said the speed of light was much faster in the early universe. Sadly I think they got that back to front, but never mind.

> Alternatively can you explain why you don't think it's C?

It isn't C because space isn't expanding in a gravitational field. Instead it's ["neither homogeneous nor isotropic"](https://einsteinpapers.press.princeton.edu/vol7-trans/192?highlightText=%22neither%20homogeneous%22). That's what Einstein said in 1920. Note though that when space is expanding, it's inhomogeneous over time. Note this paper: [Inhomogeneous Vacuum: An Alternative Interpretation of Curved Spacetime](https://iopscience.iop.org/article/10.1088/0256-307X/25/5/014/meta). Einstein referred to inhomogeneous vacuum whilst most modern authors refer to curved spacetime, but they're talking about the same thing.

> **Comments:**
> **username_0**: Thanks for that, a lot of interesting points there. Sorry I got the low and high gravity the wrong way round accidentally. You also misinterpreted my meaning about speed of light being variable. I believe far more strongly than most that the speed of light varies due to gravity, it was the fact that we treat it as constant through expansion that concerned me.  
> **username_1**: @username_0 : my pleasure. Note what Einstein was saying - the speed of light doesn't vary _due_ to gravity, gravity is due to the speed of light being variable. With that in mind, yes, it does seem rather odd to treat the speed of light as constant regardless of the energy density of the early universe. I guess too many people were taught that c=1 before the Einstein digital papers were online. Do make sure you read the Wikipedia [VSL](https://en.wikipedia.org/wiki/Variable_speed_of_light#Einstein's_updated_proposals_(1905–1915)) article.  
> **username_0**: Sounds like you may agree with my answer to this question here https://physics.stackexchange.com/questions/133482/speed-of-light-in-general-relativity . If you can spare the time to read through it, I am sure you'll find it interesting.  
> **username_1**: @username_0 : I read it. There are a few things that aren't quite right I'm afraid. The "deflection" of light is twice the deflection of matter, and gravitational potential energy is converted into kinetic energy leaving you with a mass deficit. But I think you're thinking along the right lines, and it's good to see somebody thinking for themself.  
> **username_0**: Thank you - your constructive comments are again very useful. I have deleted that answer until such time as I have had a chance to work out what you mean and review the credibility of my answer. I should not have posted it really, but I do like to push the boundaries a bit.  
> **username_1**: @username_0 : my pleasure Alan. You might want to take a look at [this](http://physicsdetective.com/the-speed-of-light/). I wrote it.  
> **username_0**: I read through your article briefly and couldn't see anything I disagreed with. In your earlier comment, can you tell me what you meant by "there is a mass deficit"?  
> **username_1**: @username_0 : see the Wikipedia [binding energy article](https://en.wikipedia.org/wiki/Binding_energy#Mass-energy_relation). When you drop a brick, gravity converts potential energy in the brick into kinetic energy. When the brick hits the ground this gets dissipated, and you're left with a mass deficit. A brick on the ground has less mass than a brick at 10,000 feet. Conversely when you lift a brick up off the ground you do work on it, you add energy to it, and since E=mc², you increase its mass.  
> **username_0**: Yes, those who believe that the speed of light is constant would say that when they raise a glass they are increasing its energy by increasing its mass very slightly. I say that when I raise my glass I am increasing its energy by taking it to a place where the speed of light is higher. I thought you were in my camp.  
> **username_1**: @username_0 : either way you add energy to that brick, and since _the mass of a body is a measure of its energy-content_, the mass increases.  
> **username_0**: So you are now treating c as constant?  
> **username_1**: @username_0 : no. When you lift the brick E increases and m increases. Because you lift it to a place where c increases.  

---

### Answer by username_2 on 2019-01-24. Score: 2

> If like me you think the answer is C, can you explain why light should travel differently through a gravitational field to how it travels through an expanding universe? In other words, why in one case does the speed of the photon vary, while in the other case it doesn't?

I think the reason is, we can take the Cosmological redshift as a Doppler redshift, where the speed of the photon does not change but only the wavelength changes due to the expansion of the universe.

Meanwhile, in Gravitational redshift, its the "redshift" is purely caused by GR and it's possible that the light loses its speed due to this effect.

Here is the link why I think cosmological redshift can be thought as Doppler redshift.

[Here](https://www.physicsforums.com/insights/coordinate-dependent-statements-expanding-universe/)

> **Comments:**
> **username_0**: I agree with most of what you said, but the speed of light does change due to gravity. This is normally, however, referred to as gravitational time dilation.  
> **username_2**: Well I am sorry then, I did not know that.  
> **username_3**: When you say the speed of light changes, you are using a particular coordinate system, and all that is changing is the coordinate speed of light.  In other words, you have some coordinates x,t and the path of the light is x(t), and then dx/dt is changing.  Coordinates are useful devices, but that's pretty much true of anything in any coordinates, you can make coordinate speed be anything you want.  All local observers will always get c when they measure the speed of light, even in a gravity field, so it is more empirically grounded to say the speed is not changed.  
> **username_0**: @Reign No problem. Thanks for taking the trouble to answer.  
> **username_2**: @AlanGee Can you show a source that it says speed of photon varies ?  
> **username_0**: @Reign not at hand, but it can be easily shown that time dilation and a reduction in the speed of light are different ways of describing the same phenomenon.  
> **username_0**: That being that the wavelength has decreased for a given frequency of light.  
> **username_2**: But cant we also take it as a constant and do calculations like that ?  
> **username_2**: @AlanGee If we more think about the why the light lose irs speed then maybe we can suggest that cosmological redshidt can be also thought as a doppler redshift meanwhile the gravitational constant is pure GR effect.  
> **username_0**: @ken g I wouldn't disagree at all that we can't directly measure changes in the speed of light. I also know why. That doesn't mean it doesn't t change though.  
> **username_4**: @Reign See https://en.wikipedia.org/wiki/Shapiro_time_delay Note that when measured locally, the speed of light in a vacuum is *always* $c$. Also see http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html  
> **username_0**: @Reign I think the key word is 'measured'. It is well known that we always measure the same speed of light, but you have to remember that time is based on the speed of light and speed is based on time. What can you expect.  
> **username_2**: @PM2Ring thanks for the links.  
> **username_2**: @AlanGee I edited my post what do you think now ?  
> **username_3**: @username_0--  this is science, what we cannot measure we cannot make claims about.  This is the first rule that separates science from belief systems.  You can have any personal belief you wish, but it is belief, not knowledge.  
> **username_0**: @ken g There is such a thing in science as deduction. We can deduce from practical measurement of gravitational time dilation that the speed of light is changing. See my earlier comment.  
> **username_3**: No such deducton is required, it all depends on chosen coordinates.  You are talking about a coordinate speed, dx/dt.  State how you arrive at your deduction, and I will tell you the arbitrary coordinates you are using.  
> **username_1**: @username_3 : I'm afraid the "knowledge" says the speed of light varies in the room you're in. That's why [NIST](http://www.learner.org/courses/physics/scientist/transcripts/wineland.html) optical clocks go slower when they're lower. The "belief" is that this is due to some magical mysterious thing called time going slower. Do note that Einstein called it the speed of light, not the coordinate speed of light, and do try to understand the tautology: when you define your second and your metre using the local motion of light, you will always declare the local speed of light to be the same.  
> **username_3**: "Why" questions in physics are quite often answered via a choice of coordinates (since we use coordinates to inform language), and the answer generally depends on those chosen coordinates.  The claim that the speed of light varies in a gravitational field is an absolutely classic example of what I'm talking about.  And when someone says we can't measure something but it's true anyway, I think that speaks for itself.  

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