Understanding the Causes of Photon Redshift

[mysearch]

Hi,
Basically, I am trying to understand whether there is an accepted and consistent description of the cause of http://en.wikipedia.org/wiki/Redshift" when discussed in terms of photons propagating through the vacuum of expanding space. An initial search on the subject of redshift seems to list 3 potential causes, as detailed in the various links highlighted:

1 http://en.wikipedia.org/wiki/Relativistic_Doppler_effect"
2 http://en.wikipedia.org/wiki/Gravitational_redshift"
3 http://en.wikipedia.org/wiki/Redshift#Expansion_of_space"

By virtue of its name, the idea of relativistic Doppler initially seems to be an extension of the basic http://en.wikipedia.org/wiki/Doppler_effect" . However, in terms of the physical mechanism at work, this seems to be somewhat misleading; for the basic Doppler effect only seems applicable to a continuous wave propagating though some physical medium. The outline of gravitational redshift cited above also seems a bit vague on the actual cause of the redshift, i.e. exactly when and where it occurs. Equally, the explanation of cosmological redshift appears to default to a description in terms of an expanding universe and the ‘stretching’ of the wavelength of light in transit. How these explanations are actually applied to a photon is unclear, although this is possibly understandable given the general vagueness surrounding the structure of a photon in transit. This said it would seem that the basic physics of both relativistic and gravitational redshift might both be explained in terms of time dilation.

In the diagram attached to this 1st post, a source (S) can either be thought of as a very small mass (m) with a relativistic velocity (v) or a very large stationary mass (M) that is emitting photons into the vacuum at a fixed frequency [f] with an energy [E=hf]. How any subsequent measure of frequency and energy of the photons is determined would seem to depend on the description of the destination in terms of its relative mass and/or its velocity. Therefore, the 1st diagram shows 2 permutations, where (X) and (Y) either represent another equal mass (M) or another small mass (m) traveling with a corresponding velocity (+/-v). For the purposes of this description individual photons are emitted from the same source (S) and arrive at (X) and (Y) at the same point in space after the same relative time with respect to (S).

So what redshift is measure and why?

Speculating on the ‘why’ first. If the redshift is explained in terms of either velocity or gravitational time dilation, the measure of redshift would depend of the relative tick of the clock in the source and destination.

In the case of (X), if its velocity (v) is in the same direction as (S), it would seem to have no relative velocity with respect to (S).

If so, would the tick of the clock in (S) and (X) be the same, such that there would be no redshift?

In the case of (Y), its velocity is in the opposite direction as (S), therefore the issue of time dilation needs to be resolved. While, at face value, (S) and (Y) are both inertial constant velocity systems with a relative velocity based on the relativistic sum of [u=v+v], either might declare the other to be the frame in motion. Therefore, (Y) declares the clock in (S) must be ticking slower and the frequency [f] should be redshifted. However, let (S) and (Y) be occupied by twins and note that it was actually (Y) that earlier accelerated away from (S), plus we now understand (S) to be stationary with respect the CMB frame.

If so, might it be argued that time in (Y) is ticking slower, so would the frequency (f) be blueshifted at (Y)?

At this point, we might switch the description of the relative perspective of (S), (X) and (Y) in terms of 3 large stationary masses with no relative velocity. This set of permutations would seem to suggest that all 3 sit in an identical gravitational field and therefore are all subject to the same time dilation.

If so, would there be no redshift in these cases?

I will raise a second example regarding the issue of cosmological redshift in my 2nd post.

 

[mysearch]

As an extension of post #1, in the diagram attached to this post, the source (S) and destination (Z) might be described as having no effective mass or apparent velocity, as both (S) and (Z) are both stationary with respect to the CMB frame and initially separated by some relatively small distance (x).

As such, might we assume that the tick of the clock is the same in (S) and (Z) and therefore no redshift would be observed associated with photons emitted from (S) and arriving at (Z)?

However, over a huge time scale, the distance (x) is subject to ‘space expansion’ such that (S) and (Z) might be said to end up receding away from each other with a perceived and relative velocity , even though they remain stationary with respect to the CMB frame.

So does the description of cosmological redshift require photons arriving at (Z) from (S), at some later time, to always be redshifted?

Post #1 outlined a number of permutations regarding time dilation caused by relativistic velocity and gravity, but it is not clear what actually causes this redshift in this case.

Space stretches and in so doing it stretched the wavelength of the photon?

It seems very difficult to align this description to any known physics. First, the structure of a photon in transit appears to be unknown; plus most descriptions of the expansion of space seem to then suggest that this will still leave most structures unaffected, e.g. atoms, solar systems and even galaxies. Therefore, the only advantage of the ‘stretching’ idea seems to be that you don’t have to address the issues thrown up by time dilation.

So if we abandon the idea of stretched space, what about time dilation?

Well, initially, it was suggested that the tick of the clock in (S) and (Z) was the same, as no gravity or relative velocity appeared to be involved. However, after many billions of years, (S) and (Z) now appear to be receding with an effective velocity (u) due to what is described as the ‘expansion of space’. This velocity can exceed the speed of light [c], but is said not to violate special relativity because this velocity cannot be measured in any local frame.

So, is this relative velocity ‘real’ in the sense that it causes time dilation?

However, in order to determine the nature of red/blue shift, we would need to resolve the level of time dilation in each frame of reference. Unlike the resolution of the twin paradox, it seems difficult to attach any acceleration force to either of these frames in order to resolve the relative tick of time. However, the stretched space analogy seems to suggest that redshift would be observed in all frames in an expanding universe.

So what description of cosmological redshift is generally accepted and what physics is used to explain it?

Would really appreciate any informative insights on the issues raised. Thanks

 

[harrylin]

Hi,
Basically, I am trying to understand whether there is an accepted and consistent description of the cause of http://en.wikipedia.org/wiki/Redshift" when discussed in terms of photons propagating through the vacuum of expanding space. An initial search on the subject of redshift seems to list 3 potential causes, as detailed in the various links highlighted:

1 http://en.wikipedia.org/wiki/Relativistic_Doppler_effect"
2 http://en.wikipedia.org/wiki/Gravitational_redshift"
3 http://en.wikipedia.org/wiki/Redshift#Expansion_of_space"

[..]

A first quick response, as a primer:

- Einstein clearly explained that according to GRT, gravitational redshift is due to the reduction of clock rates (and thus also: reduction of emission frequencies) in the neighbourhood of massive bodies.

- Okun explained this also in the AJP, some years ago.
And I now see that this was already brought up in this forum, together with useful links:

https://www.physicsforums.com/archive/index.php/t-86716.html

Of course this doesn't address "expanding space", but in view of the existing confusions regarding non-expanding space (or, as you put it, "a bit vague on the actual cause of the redshift, i.e. exactly when and where it occurs"), those explanations may serve as a basis for that discussion.

Harald

 

[mysearch]

Thanks for the comments. I guess what I was trying to do was to separate out the various causes of potential redshift in respect to relativity, i.e. velocity and gravity. Your comments, and the thread referenced, seem to be primarily focused on the effects of gravitational mass. As far as I am aware, time dilation appears to provide a reasonable and consistent description of any resulting redshift observed when the source and destination are located in mass-gravity wells. This is an assumption not an assertion.

The issue of time dilation with respect to a relativistic velocity seemed to be more problematic because without resolving the ‘inertial history’ of the source and destination, it seemed unclear as to which clock was actually ticking slower. See post #1 for the various examples I cited. Again, I am trying to clarify how accepted science explains these cases rather than attempting to forward yet more speculation.

However, the various descriptions of cosmological redshift did seem ‘vague’ to me; especially when using the photon particle model rather the EM wave description. For this reason, I introduced the 2nd example, which also attempt to see whether cosmological redshift could be clarified in terms of time dilation, but this then returns to some of the ‘seemingly paradoxical’ issues raised in post #2.

Anyway, I would appreciate any other insights.
Thanks

 

[Naty1]

Good insights here, but really, really long and involved :
https://www.physicsforums.com/showthread.php?t=368958

 

[mysearch]

Hi,
Many thanks, this looks like an excellent thread. It is a bit late in my time zone to start reading into the details, but I will start tomorrow and raise any issues afterwards. I noticed that this thread was in cosmology, is it possible that this topic is of more interest in that sub-forum?
Thanks

 

[Naty1]

I think the following summarizes the thread I posted just above...I hope some of the principles will see this and confirm or deny my perception: (Note: these are comments from a variety of participants in that prior discussion. I think that not all agreed, but am not even psoitive about that.)

Issue:
"How to separate out the various causes of potential redshift in respect to relativity, i.e. velocity and gravity."

"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.

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

"...time dilation is a natural consequence of expansion. Photons do not realize space is stretching as they travel through it. The same number of wave crests reach us as were emitted - without regard for expansion [conservation of energy thing]. The finite speed of light means it takes longer for all of them to get here.


"It is the difference in gravitational potential between source and observer that matters. (See my comment below,) Dropping a little bit into and then out of the gravitational well along the way may alter the direction of light, but that's all.

"Redshift is purely doppler, there are no gravitational effects.

My comment: I can accept the last two quotes from the perspective that the universe is isotropic and homogeneus on large scales...but I don't know if that's what those people really meant.

So it seems to me "doppler", "cosmological" and "time dilation" are different aspects of the same phenomenon. Gravity is a separate effect. It was also mentioned that negative dark energy potential may intdouce a gravitational effect.

 

[mysearch]

Naty1,
Thanks for your summary in post #7, it was helpful to have those comments in mind before working through the thread discussing “https://www.physicsforums.com/showthread.php?t=368958" Just to be clear on one point before making any comments of my own, I am primarily looking to better understand the accepted position on a number of issues, e.g. known fact, basic assumption or pure speculation.

The thread cited above opens with a statement and question:

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?

My first impression was that the thread almost immediately takes off in another direction, which does not really address the OP. As I understand it, the local distribution of red and blue shift relates to the somewhat random distribution of galaxy motion with respect to the CMB. The further away you get, the average recessional velocity v=Hd will overwhelm any random blueshift and the net average would become increasingly redshifted. The next few posts seem to be exchanging ideas relate to a range of models and assumptions without necessarily clarifying the status of these models. Based on my comments above, it is my understanding that cosmological redshift is linked to the expansion of the universe and not the random distribution in the gravitational potential between source and observer.

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

While a 'few' photons arriving here on Earth may have been subject to extreme gravitational effects, it is my assumption that the time dilation caused by the difference in gravitational potential between source and destination does not account for Hubble’s law. As such, we appear to be left to explain the nature of recessional velocity and its effects on photon frequency, as observed here on Earth.

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

I apologise if I have taken this comment out of context to highlight an issue of my own. What is actually meant by ‘doppler redshift’ seems important to me, because it was my understanding that the classical description of the Doppler effect was essentially restricted to continuous waves in a physical media. One of the questions I raised in this thread was the applicability of this mechanism to discrete photons? As a side issue, we also see in the comment above, the assumption about dark energy, which cannot really be explained by the current particle model and was essentially introduced in order to underpin certain features of the current cosmological model. As cited in post #1, many references list relativistic Doppler, gravitational and cosmological as the primary causes of observed redshift. However, from my perspective they all seem to be relativistic effects due to either velocity or gravity. However, based on comments above and assuming a generalised homogeneous model of a spatially flat universe, I cannot see how gravity plays a major role in what is described as a cosmological redshift. As such, we appear to be left with only 2 mechanisms that might account for the observed redshift, i.e. the expansion of space and the recessional velocity linked to Hubble’s law.

….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 they 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.

As stated, I also have problems in trying to understand how the ‘expansion of space’ stretches the photon wavelength in transit. I am not saying it is not possible, I simply don’t understand how you can describe an effect on the structure of a photon, when science does not yet seem able to define this structure. As anybody ever even detected a photon in transit? Yes, I agree, it is probably a meaningless question! However, the general idea also seems at odds with the basic concepts of relativity in as much that it appears to indirectly suggest that the fabric of space has some structure that is capable of expanding. Of course, if we put photon stretching debate on the back-burner, we seem to be left with only velocity, which as cited in post #1, requires some explanation.

I think we will get along just fine as long as you're not telling newbies that galaxies aren't moving.

As far as I know distant galaxies are not moving (except trivially) relative to CMB.

However, in order to explain cosmological redshift, it would seem that the relativistic velocity of recession, as defined by Hubble’s law, has to be ‘real’ in the sense that it leads to a tangible time dilation between source and destination. In part, this was the point raised in post #2, which I shall simply quote:

So if we abandon the idea of stretched space, what about time dilation?

Well, initially, it was suggested that the tick of the clock in (S) and (Z) was the same, as no gravity or relative velocity appeared to be involved. However, after many billions of years, (S) and (Z) now appear to be receding with an effective velocity (u) due to what is described as the ‘expansion of space’. This velocity can exceed the speed of light [c], but is said not to violate special relativity because this velocity cannot be measured in any local frame.

So, is this relative velocity ‘real’ in the sense that it causes time dilation?

However, in order to determine the nature of red/blue shift, we would need to resolve the level of time dilation in each frame of reference. Unlike the resolution of the twin paradox, it seems difficult to attach any acceleration force to either of these frames in order to resolve the relative tick of time. However, the stretched space analogy seems to suggest that redshift would be observed in all frames in an expanding universe.

So what description of cosmological redshift is generally accepted and what physics is used to explain it?

From my perspective, one of the problems associated with many of the ideas forwarded in the thread reviewed was simply trying to understand the general validity and acceptance of the many variant models introduced. In this respect, the simple examples outlined in post #1 and #2 were an attempt to focus any discussion on the actual mechanisms of redshift based on the underlying premise of a photon propagating through a vacuum.

Again, would appreciate any other insights. Thanks

 

[harrylin]

Thanks for the comments. I guess what I was trying to do was to separate out the various causes of potential redshift in respect to relativity, i.e. velocity and gravity. Your comments, and the thread referenced, seem to be primarily focused on the effects of gravitational mass. As far as I am aware, time dilation appears to provide a reasonable and consistent description of any resulting redshift observed when the source and destination are located in mass-gravity wells. This is an assumption not an assertion.

As I cited, it's an assertion of the theory that predicted it. Time dilation is a cause of redshift.
Edit: Note that there is no gravitational red shift between two equal gravitation wells.

According to GRT light doesn't really "fall" in a gravitation well in the sense that it is modeled as a wave: a ray bends due to a decrease in speed and it cannot change its frequency or energy in free space, because the number of cycles is conserved. Only locally the same frequency is measured differently at different locations, when it is compared with differently running clocks.

The issue of time dilation with respect to a relativistic velocity seemed to be more problematic because without resolving the ‘inertial history’ of the source and destination, it seemed unclear as to which clock was actually ticking slower. See post #1 for the various examples I cited. Again, I am trying to clarify how accepted science explains these cases rather than attempting to forward yet more speculation.

I think that there was never any confusion or disagreement about effects from velocity; this is straightforward special relativity and so I didn't mention it. The total Doppler effect from speed is simply that of classical Doppler for a frame in rest, plus the time dilation effects from the source and/or receiver.
Of course, this is still only laying the basis of your discussion, for it still assumes a static space. But you will do well to make sure of understanding this basis before porting your discussion to Cosmology.

However, the various descriptions of cosmological redshift did seem ‘vague’ to me; especially when using the photon particle model rather the EM wave description. For this reason, I introduced the 2nd example, which also attempt to see whether cosmological redshift could be clarified in terms of time dilation, but this then returns to some of the ‘seemingly paradoxical’ issues raised in post #2.

As Arnold Neumaier mentioned in a parallel thread, there seem to be several (and incompatible?!) photon models.

Obviously, a photon model is perfectly consistent with GRT if it is modeled as a wave packet - it may remain localized like a particle, but any stretching etc. must be in accordance with wave theory. Essentially this means that the frequency cannot change according to non-local observations, only the speed and the wave length.

Anyway, I would appreciate any other insights.
Thanks

You're welcome! As soon as the basics of SRT and GRT are clear to you, you will be ready to discuss this with cosmologists.

 

[Naty1]

My own interpretation, perhaps too simple minded, is that because space is isotropic and homogeneous, gravity (potential wells as, say, along the route light travels or between source and observer) does not play a role.,,or if it does it seems inconsequential...

On the other hand, if the real inquiry here is for explanation involving a single photon, that might better be discussed in quantum mechanics rather than GR...but that's a speculation on my part as well...

In any case, there can't seem to be huge gravitational effects...because the CMS IS rather uniform. On the other hand, surely ONE photon must arrive here every so often that has passed by a black hole and just barely escaped being swallowed. But whether we'd be able to detect such a photon is another issue.

 

[Drakkith]

On the other hand, surely ONE photon must arrive here every so often that has passed by a black hole and just barely escaped being swallowed. But whether we'd be able to detect such a photon is another issue.

Wouldn't that photon be accelerated and blueshifted on the way in, then redshifted and decelerated on the way out, with an equal frequency to before it was sucked towards the black hole? Or not?

 

[Dale]

Redshift is the ratio of the proper time between two successive peaks in a wave at the emitter and the proper time between the same two peaks at the receiver. The worldlines of the peaks form a pair of null geodesics. Even if those geodesics remain parallel the ratio can be different from 1 if the worldlines of the emitter and receiver cross the null geodesics at different angles. And in a curved spacetime those worldlines may converge or diverge.

 

[Drakkith]

Redshift is the ratio of the proper time between two successive peaks in a wave at the emitter and the proper time between the same two peaks at the receiver. The worldlines of the peaks form a pair of null geodesics. Even if those geodesics remain parallel the ratio can be different from 1 if the worldlines of the emitter and receiver cross the null geodesics at different angles. And in a curved spacetime those worldlines may converge or diverge.

Umm, what are you saying with this Dalespam?

 

[Dale]

Just giving a unified framework where all the different kinds of redshift can be understood in the same way.

 

[Drakkith]

Just giving a unified framework where all the different kinds of redshift can be understood in the same way.

Ah, ok.

 

[mysearch]

On the other hand, if the real inquiry here is for explanation involving a single photon, that might better be discussed in quantum mechanics rather than GR...but that's a speculation on my part as well...

Fair enough comment as the wave-particle duality issue does appear to lead to contradictions, which may only be resolved in quantum mechanics. However, the reason for ‘trying’ to impose the photon restriction on this discussion was to limit the ‘degrees of freedom’ in describing the relativistic effects. At a basic level, it would seem that a photon can be described in fairly simple terms E=hf, where (E) is energy, and (f) is frequency, which is then dependent on the ‘proper time’ in the local frame. I believe this is the key point being made here:

Redshift is the ratio of the proper time between two successive peaks in a wave at the emitter and the proper time between the same two peaks at the receiver.

So, on the assumption that E=hf holds true in all frames of reference, then any differences in the rate of time between the emitter and receiver due to time dilation would result in a change of frequency and a change in energy, i.e. redshift. By virtue of the relationship $$c=f \lambda$$ and the postulate of [c] also being invariant in all frames, it would seem to suggest that both the wavelength and frequency will differ in the emitter and receiver. As such, I am not sure that I understand the following statements in the context of photons propagating through a vacuum:

…a ray bends due to a decrease in speed and it cannot change its frequency or energy in free space, because the number of cycles is conserved. ……

…..Obviously, a photon model is perfectly consistent with GRT if it is modeled as a wave packet - it may remain localized like a particle, but any stretching etc. must be in accordance with wave theory. Essentially this means that the frequency cannot change according to non-local observations, only the speed and the wave length.

I am not sure that I agree with the following statement either.

I think that there was never any confusion or disagreement about effects from velocity; this is straightforward special relativity and so I didn't mention it.

While the observed redshift described as cosmological redshift does appear to align to the recessional velocity defined by Hubble’s law, the scope of this velocity was questioned, because velocity in isolation does not explain redshift, i.e. the cause appears to be the time dilation resulting from velocity, e.g.

So, is this relative velocity ‘real’ in the sense that it causes time dilation?

However, in order to determine the nature of red/blue shift, we would need to resolve the level of time dilation in each frame of reference. Unlike the resolution of the twin paradox, it seems difficult to attach any acceleration force to either of these frames in order to resolve the relative tick of time. However, the stretched space analogy seems to suggest that redshift would be observed in all frames in an expanding universe.

While I understand the premise of the next statement, it does not appear address the issue raised in previous threads, i.e. classical Doppler only appears to be applicable to a continuous wave in a physical medium. As such, I was questioning the suitability of this description in the context of discrete photons propagating through a vacuum.

The total Doppler effect from speed is simply that of classical Doppler for a frame in rest, plus the time dilation effects from the source and/or receiver.

Finally, was the following comment meant to be funny or condescending?

You're welcome! As soon as the basics of SRT and GRT are clear to you, you will be ready to discuss this with cosmologists.

 

[Dale]

So, on the assumption that E=hf holds true in all frames of reference, then any differences in the rate of time between the emitter and receiver due to time dilation would result in a change of frequency and a change in energy, i.e. redshift. By virtue of the relationship $$c=f \lambda$$ and the postulate of [c] also being invariant in all frames, it would seem to suggest that both the wavelength and frequency will differ in the emitter and receiver.

Yes, with the caviat that the postulate of c being invariant refers specifically to inertial frames, so it is not always true in arbitrary coordinate systems or in curved spacetime. Also, note that energy is conserved, but not invariant. So the fact that the energy is different in the emitter's frame and the receiver's frame is not a contradiction.

As such, I am not sure that I understand the following statements in the context of photons propagating through a vacuum:

You will have to take those up with harrylin. They both seem incorrect to me. The experimentally measured frequency certainly can and does change, that is the whole point of redshift. So I don't know in what sort of sense he claims that the frequency cannot change.

 

[mysearch]

Yes, with the caviat that the postulate of c being invariant refers specifically to inertial frames, so it is not always true in arbitrary coordinate systems or in curved spacetime.

I understand that Einstein himself raised some concerns about the constancy of [c] in all frames of reference after developing his ideas on general relativity. Therefore, your caveat concerning inertial frames is noted. However, would it be true to say that within the scope of this general discussion concerning the redshift of photons from the universe, as a whole, we might continue in the general assumption of [c] being constant?

Also, note that energy is conserved, but not invariant. So the fact that the energy is different in the emitter's frame and the receiver's frame is not a contradiction.

I am assuming that energy invariance is caused by the frequency change linked to time dilation within the present discussion. While I understand the axiom of energy conservation, I have never really got to the bottom of the caveats concerning energy conservation within general relativity. Therefore, I would appreciate it if anybody knows of a good on-line paper that might outline some of the key issues in this area. Thanks

You will have to take those up with harrylin. They both seem incorrect to me. The experimentally measured frequency certainly can and does change, that is the whole point of redshift. So I don't know in what sort of sense he claims that the frequency cannot change.

Given your knowledge of this subject I am reassured that any context in which the statements made might be true was not immediately obvious to you either. Thanks

 

[harrylin]

[..] At a basic level, it would seem that a photon can be described in fairly simple terms E=hf, where (E) is energy, and (f) is frequency, which is then dependent on the ‘proper time’ in the local frame. So, on the assumption that E=hf holds true in all frames of reference, then any differences in the rate of time between the emitter and receiver due to time dilation would result in a change of frequency and a change in energy, i.e. redshift.

That is certainly correct for local measurements.
However, it can be misleading to call a difference in the measurement of a photon's frequency a "change of frequency": according to GR, a light ray's frequency in free space (no dispersion) is in fact constant in any inertial reference frame that uses synchronized clocks (such as the GPS uses, in approximation).

Of course, that is explained in the thread that I linked to, which also links to Okuns' paper that clarifies these things.
Here are the links again:

https://www.physicsforums.com/archive/index.php/t-86716.html
http://xxx.lanl.gov/abs/physics/9907017

By virtue of the relationship $$c=f \lambda$$ and the postulate of [c] also being invariant in all frames, it would seem to suggest that both the wavelength and frequency will differ in the emitter and receiver. [..]

That postulate belongs to SR, for inertial frames; in GR it does not have unlimited validity, as Einstein put it (http://www.bartleby.com/173/22.html).
Light speed invariance is only locally valid in GR. Non-locally this is not so. The variation of the speed of light as function of position and direction (as non-locally determined) leads to such effects as gravitational time dilation, gravitational lensing (bending), Shapiro time delay etc.

Note that locally measured, all clocks also have zero time dilation ("proper" time); but I don't think that "zero" is very useful for this kind of discussions.

While the observed redshift described as cosmological redshift does appear to align to the recessional velocity defined by Hubble’s law, the scope of this velocity was questioned, because velocity in isolation does not explain redshift, i.e. the cause appears to be the time dilation resulting from velocity, e.g.
'So, is this relative velocity ‘real’ in the sense that it causes time dilation?
However, in order to determine the nature of red/blue shift, we would need to resolve the level of time dilation in each frame of reference. Unlike the resolution of the twin paradox, it seems difficult to attach any acceleration force to either of these frames in order to resolve the relative tick of time. However, the stretched space analogy seems to suggest that redshift would be observed in all frames in an expanding universe.

.

Acceleration force does not play an essential role in the twin example; what matters for the redshift there is the relative velocities. Similar for redshift from gravitation, what matters is the difference in gravitational potentials.

While I understand the premise of the next statement, it does not appear address the issue raised in previous threads, i.e. classical Doppler only appears to be applicable to a continuous wave in a physical medium. As such, I was questioning the suitability of this description in the context of discrete photons propagating through a vacuum.

The "wave packet" approach (which models discrete photons without abandoning GR) must be suitable, except if you contemplate a theory according to which GR is wrong.

Finally, was the following comment meant to be funny or condescending?

It was meant to be funny but in fact it was serious: when you are sure to understand redshift in static space, then you will have the basis for a lucid discussion of the possible effects expanding space - which is a topic that really goes beyond my understanding. I will perhaps follow that discussion, it will be very interesting!

 

[Dale]

However, would it be true to say that within the scope of this general discussion concerning the redshift of photons from the universe, as a whole, we might continue in the general assumption of [c] being constant?

I would not make that assumption, no. Over cosmological distances curvature is significant so your coordinates are necessarily non-inertial.

I am assuming that energy invariance is caused by the frequency change linked to time dilation within the present discussion.

You mean frame-variance of energy, not invariance. But yes, it is linked to time dilation.

While I understand the axiom of energy conservation, I have never really got to the bottom of the caveats concerning energy conservation within general relativity. Therefore, I would appreciate it if anybody knows of a good on-line paper that might outline some of the key issues in this area. Thanks

I would start here:

http://www.phys.ncku.edu.tw/mirrors/physicsfaq/Relativity/GR/energy_gr.html

It is very "digestible" and gives a good overview of the challenges.

 

[Dale]

a light ray's frequency in free space (no dispersion) is in fact constant in any reference frame that uses synchronized clocks (such as the GPS uses).

That is fine. It refers to a specific class of coordinate systems which is constructed such that it is true. In those coordinate systems the frequency does not change.

 

[mysearch]

I would start here:
http://www.phys.ncku.edu.tw/mirrors/physicsfaq/Relativity/GR/energy_gr.html . It is very "digestible" and gives a good overview of the challenges.

Thanks, but while this article is ‘digestible’ it seems to sway the argument of energy conservation in GR backwards and forwards, so that it not so easy to reconcile any clear picture, e.g.
“Those who harbor no qualms about pseudo-tensors will say that radiant energy becomes gravitational energy. Others will say that the energy is simply lost.”

There is also a lot of cross-referencing to different perspectives, e.g.
“It's time to look at mathematical fine points. There are many to choose from! The definition of asymptotically flat, for example, calls for some care (see Stewart); one worries about "boundary conditions at infinity". (In fact, both spatial infinity and "null infinity" clamor for attention -- leading to different kinds of total energy.) The static case has close connections with Noether's theorem (see Goldstein or Arnold). If the catch-phrase "time translation symmetry implies conservation of energy" rings a bell (perhaps from quantum mechanics), then you're on the right track. (Check out "Killing vector" in the index of MTW, Wald, or Sachs and Wu.)”

However, it would seem that the definition, and need, for potential energy in Newtonian physics versus GR is at the root of the discrepancy?
“GR relates curvature to gravity. Now, even in Newtonian physics, you must include gravitational potential energy to get energy conservation. And GR introduces the new phenomenon of gravitational waves; perhaps these carry energy as well? Perhaps we need to include gravitational energy in some fashion, to arrive at a law of energy conservation for finite pieces of spacetime?”

Anyway, I will try to delve a little deeper into this issue. However, I would also like to clarify an issue you commented on below as it raised a few additional issues in my mind:

I would not make that assumption, no. Over cosmological distances curvature is significant so your coordinates are necessarily non-inertial.

First, I am assuming that you are referring to spacetime curvature in the context of some large-scale cosmological model, where spatial curvature k=0. If so, can I assume this curvature is simply caused by the expansion of space along which a photon travels?

There are various ‘cosmic calculators’ that allow you to input various values of redshift from which they determine various parameters. A photon with a value of z=1089 is said to correspond to the decoupling era in the cosmological model ~380,000 years after the Big Bang. The point this photon originated is now calculated to be ~46GLYs away, but originally started off only ~42MLYs away. The difference in the distance calculated is attributed to the expansion of space. However, in our frame of reference, this photon has been in transit for ~13.7 billion years.

So how far did the photon actually travel ‘through’ expanding space? If [c] was constant at every point along this path, I would have assumed that this photon had traversed a distance of ~13.7 billion LYs? Do you disagree?

There are some time dilation implications associated this example, but I wanted to see whether there were any fundamental issues with the premise of the example before I run out of time tonight. Thanks

 

[Naty1]

So how far did the photon actually travel ‘through’ expanding space? If [c] was constant at every point along this path, I would have assumed that this photon had traversed a distance of ~13.7 billion LYs? Do you disagree?

Time to reread Dalespam's post...EVERYTHING is relative...no one local inertial frame is preferred over any other..."actually" has no real meaning...
You answered you own question in our frame...we observe 13.7. so what??

 

[pervect]

A quick comment. When one thinks of things in a manner which depends on the choice of coordinate systems and/or choice of local 'frame' of reference, the answer to some questions depends on the coordinates or frames one chooses.

This is not a result of the underlying physics itself being dependent on the coordinate choice used - though it does imply that the formulation of physics being used is not "explicitly covariant". The covariance, or independence of the results of measurement on the coordinate choice, is 'hidden' in such formulations.

Tensor formulations are explicitly covariant, unfortunately they tend to be hard to follow unless one has the required background.

It's important to realize that in the end, what can actually be measured must not depend on the choice of coordinates. The actual red-shift itself is an example of such a measurement.

 

[Dale]

So how far did the photon actually travel ‘through’ expanding space? If [c] was constant at every point along this path, I would have assumed that this photon had traversed a distance of ~13.7 billion LYs? Do you disagree?

I don't disagree. I am sure that you could come up with a perfectly reasonable coordinate system where that is true. It would not be true in all coordinate systems, so I wouldn't particularly spend much effort arguing for it either.