Cosmological redshift explanation?

[iantresman]

Can anyone explain how the expansion of space time "couples" to photons and hence lengthens and redshifts the photons?

Presumably if the photon looses energy, then spacetime gains the energy? In what form?

If Nereid is reading this, presumably there are some sums that would be helpful? :-)

Regards,
Ian Tresman

[Thanatos]

Photons do not lose energy when redshifted. They are time dilated. While intensity per second, in the local oberver frame, is reduced, they persist long enough to make up for the deficit.

[Nereid]

As it seems this is a straight-forward question (no ATM ideas anywhere in sight), I'm moving the thread to the Q&A section.

[iantresman]

Photons do not lose energy when redshifted. They are time dilated. While intensity per second, in the local oberver frame, is reduced, they persist long enough to make up for the deficit.

Isn't a red photon at less energy than a blue photon? So if a blue photon is redshifted into a red photon, surely energy is lost? Or are you saying that a blue photon has a higher energy "density" (because it is shorter)?

And how does space-time couple to the photon?

Regards,
Ian Tresman

[Tensor]

Can anyone explain how the expansion of space time "couples" to photons and hence lengthens and redshifts the photons?

What do you mean by "couple"? I'm assuming that you mean "how exactly does spacetime cause the photon to lose energy"? If this is what you mean, it doesn't couple, the change in energy is due to a change in a frame of reference.

Presumably if the photon looses energy, then spacetime gains the energy? In what form?

No, it doesn't. The photon doesn't really "lose" energy. In GR, the concept of energy is frame dependent.

If Nereid is reading this, presumably there are some sums that would be helpful? :-)

We don't need Nereid for sums. You can have fun with this paper, which give a mathematical backround for a FLWR cosmology. Note section 4.5.1. It describes the cosmological redshift as a time dilation effect (which is a frame dependent effect). Also note equation 118 in that section. It give the scale factor (for computing the cosmolgical redshift) for a FLWR metric. If a different metric from the FLWR metric is used, the scale factor would be different.

[Ken G]

Photons do not lose energy when redshifted. They are time dilated. While intensity per second, in the local oberver frame, is reduced, they persist long enough to make up for the deficit.

This was also said on another thread by someone else, but this is not correct. Where does this idea come from? A redshifted photon certainly has less energy, no matter how long you wait. Shifting reference frames does not conserve energy from one frame to another, period. The same is true for a car, as for a photon.

[iantresman]

This was also said on another thread by someone else, but this is not correct. Where does this idea come from? A redshifted photon certainly has less energy, no matter how long you wait. Shifting reference frames does not conserve energy from one frame to another, period. The same is true for a car, as for a photon.

So, there does not appear to be an agreement whether a cosmologically redshifted photon has the less energy than an unshifted one.

Nor does there seem to be any explanation of whether Space-time can "couple" to photons, except perhaps to suggests that it's all down to changes in frames of references. So is cosmological expansion merely a change in frames of reference, or is it a genuine expansion?

Regards,
Ian Tresman

[alainprice]

Space expands, and light travels at a fixed speed through it, so therefore we experience an evolving reference frame. The expansion of space would be the root cause of cosmological redshift, yet the true reason is like everyone has said, essentially a doppler shift of light.

So light does have energy, depending on where you measure it from. From the frame of a photon, wouldn't time be null and hence energy meaningless?

[Ken G]

There is no frame of a photon, which removes this problem. But as you go faster and faster in the direction of photon propagation, the energy does get smaller without bound, and time slows down without limit relative to the original frame, so in a sense that is correct, but only as an unrealizable limit.

[Tensor]

So, there does not appear to be an agreement whether a cosmologically redshifted photon has the less energy than an unshifted one.

Ian, what you are seeing, most of the time, is a disagreement between two people's (who often don't understand the math) interpretation/understanding of someone else's description, in words, of what the math means. There is a lot of potential for disagreement there. Instead of picking on that, why don't you just go right to the math see what the math says? I did provide you with the mathematical backround of a FLWR universe.

Nor does there seem to be any explanation of whether Space-time can "couple" to photons,

I asked before, what exactly do you mean by a photon coupling with spacetime?

except perhaps to suggests that it's all down to changes in frames of references.

It's what the math says. And the problem with this is what, exactly?

So is cosmological expansion merely a change in frames of reference, or is it a genuine expansion?

As Alain has pointed out, it is an expansion. Due to that expansion, different points in time will be in different frames, mostly due to a different radius of curvature for each time. Different frames will see different amounts of energy. The exact amount will depend on the scale factor(which, basically, compares the radius of curvature for each time), which depends on the specific metric used.

[Ken G]

As Alain has pointed out, it is an expansion.

I feel I must speak up when I see absolute statements of this kind. The observations do not require that the universe be expanding, this is a choice of pedagogy that is standard in the normal interpretation of general relativity as applied to cosmology. It is a good and valid description, and if you use it, then people will know what you are talking about. That is all it is, it is by no means an absolute statement about the reality of the universe, and is not required by the observations. (Other interpretations are possible, but must be, at the end of the day, the same theory in different clothes or they won't agree with the observations.) Of course, we can't always preface every remark with this caveat, so let it be implicit most of the time, but sometimes the words sound so absolute that the caveat may be in danger of being forgotten.

[Tensor]

I feel I must speak up when I see absolute statements of this kind. The observations do not require that the universe be expanding, this is a

snip....

but sometimes the words sound so absolute that the caveat may be in danger of being forgotten.

And most of the time I would preface such a remark. But since Ian was specifically asking about the expansion, causes and such, I didn't see the need to either nitpick or pontificate on the statement. In addition, since this is the question and answer forum, those answers are from the mainstream point of view, which views the universe as expanding.

[Fr. Wayne]

According to above referenced math, the author(s) claim that the degree to which matter moves under forces other than gravity plus inertia MUST split the electromagnetic field into electric and magnetic parts. Called the Maxwell Field Strength Tensor, I question this step. Present day physicists have correctly demonstrated that the photon (or whatever) is acted on by a third variable within the electro-magnetic field. But to split the field into three parts is even worse. So my opinion is that we are stuck until this third part can gain acceptance among the Maxwell paradigmers who will probably take another 10 years to reopen this issue. Maxwell's original data must be revisited. http://openseti.org/Docs/Hall_Photon...ce_Paper_B.pdf

[Ken G]

And most of the time I would preface such a remark.

Granted, it need not be said every time. I almost said something when alainprice said "Space expands, and light travels at a fixed speed through it, so therefore we experience an evolving reference frame." This sounded like a statement of reality, even in the Q&A section, but I let it go for just the reasons you point out. Then you referred to the statement again in equally absolute terms (in answer to a question of "genuine" expansion, no less) and I thought I'd pipe in. You are right that this should perhaps be left out of the Q&A section, I've tried similar remarks in other sections and what typically happens is I end up being the one accused of being ATM. But what I am saying is entirely M. But since you agree, that's all I wanted to say. I see why you feel it is "pontificating", but in fact, I do see it as a point that is often missed here, and people who post to Q&A need to know this more than anyone.

[iantresman]

Referring to the maths is one thing, understanding what is going on is another. I just don't understand space-time. Space I know. Time I have a feel for.

I'm pretty sure that if space expanded, then it would have no effect on photons or anything for that matter. Space is nothing, and nothing can not causes any effect on photons because there is nothing to do so. In that sense, space does not couple to photons. But expanding space-time apparently does effect (ie couples to) photons.

But then again, the expansion of space is really just an expansion of the frame of references, and it doesn't really expand (in its own frame), it just looks like it in our rest frame?

So that leaves the time aspect of space-time. Presumably the expansion of space-time implies the lengthing of time. If "time" expands around the photon, but its velocity is constant, then the "back" of the photon takes longer to reach where the "front" was, and the wavelength is increased ?

Regards,
Ian Tresman

[alainprice]

One cannot understand time yet not understand space. They are one and the same, spacetime. They are woven together like a fine piece of silk. You either see the fabric, or unravel it into threads.

A reference frame is chosen by the person who wishes to do measurements. Nothing can affect a reference frame, that is why is it a REFERENCE.

I cannot help you as you dance in circles.

The expansion of space is that, expansion of the coordinates themselves, not the matter. So if Alpha Centauri is 4 light years away and has no relative motion, it will be 8 light years away when the universe has 'doubled' in 'size'. Kind of a lame example, but in theory it is true.

[iantresman]

The expansion of space is that, expansion of the coordinates themselves, not the matter. So if Alpha Centauri is 4 light years away and has no relative motion, it will be 8 light years away when the universe has 'doubled' in 'size'. Kind of a lame example, but in theory it is true.

So how do I differentiate between expanding space, and the space between two objects which is just increasing because the objects are moving apart?

In other words, how do we differentiate the between the Universe expanding due to Hubble, rather than due to movement (and Doppler). It seems that the only indicator is redshift, and Doppler redshift looks the same as Cosmological redshift.

Regards,
Ian Tresman

[Blob]

Hum,
Generally you don't have to bother for very distant objects.
For local objects in our galaxy or near by you can use other techniques to calibrate the distance.

[Ken G]

. If "time" expands around the photon, but its velocity is constant, then the "back" of the photon takes longer to reach where the "front" was, and the wavelength is increased ?

Yes, I think that is quite a reasonable way to think about it.

So if Alpha Centauri is 4 light years away and has no relative motion, it will be 8 light years away when the universe has 'doubled' in 'size'. Kind of a lame example, but in theory it is true.

Actually, this isn't even true in principle, it's not that simple. The space between us and alpha Cen does not expand with the cosmological expansion. This is because we are all in a bound system, our galaxy, which resists the Hubble expansion. Apparently, the local gravity holds the space together, in some sense, such that the expansion of the universe does not affect it. Also, photons propagating across our galaxy don't redshift with the Hubble flow, for the same reason, though they would experience gravitational redshifts in our galaxy. For this reason, I like to think of the cosmological redshift as just another type of gravitational redshift.

[Bad jcsd]

Let's say we stick to FRW cooridinates, we're not changing our coordinate system and general relativity works in the same in all coordiante systems, but the energy still appears to just be disappearing.

At the end of the day it simply comes down to how you define energy as to whethr the energy is simply lost or whether it's conserved. John Baez has written an article about it here:http://math.ucr.edu/home/baez/physic...energy_gr.html

[Ken G]

Good point. Remember that energy is often defined in such a way that will make it be conserved (witness potential energy), it is not a fundamental idea that people then came along and said "hey, this thing is conserved, what do ya know?" The Baez article points out that even in GR, you can monkey with energy to get it to be conserved, but in any case general enough to handle the expansion of the universe you end up with an awkward version that does not conform to the normal things you want in relativity, so many don't even use that approach and are happy to just let energy go unconserved.

[Ari Jokimaki]

So how do I differentiate between expanding space, and the space between two objects which is just increasing because the objects are moving apart?

In other words, how do we differentiate the between the Universe expanding due to Hubble, rather than due to movement (and Doppler). It seems that the only indicator is redshift, and Doppler redshift looks the same as Cosmological redshift.

Apparently, there is a difference, see Grey's first post in page 3 of this old thread. It has to do with angular size of objects vs. redshift. (You also might find some kind of answer to your original question there.)

[Ken G]

I couldn't find the post you refer to, but I'm skeptical that there is that much of a difference. As I just found out from Grant Hutchison, even the normal Doppler shift monkeys with angular size in a way that is very reminiscent of what cosmological redshifts do. I think the formulations are equivalent, the point is that we are so used to using the "comoving frame" coordinates to describe cosmology (it is the most convenient way) that we lose track of the fact it is not necessarily "the reality".

[iantresman]

I keep reading about a subject, and assume I understand certain things, and then I read something, and I realise that perhaps it is not what I thought at all.

So, during cosmological expansion, does space-time between two objects (ie. two galaxies) "force" the two galaxies further apart, or does the space-time expand around the objects?

• If the two galaxies are "forced" further apart, are they pushed further apart, or does the "reference frame" change and they just appear further apart
• If space-time expands around the galaxies, why are they uneffected, but photons are not; in which case, what other particles are effected; neutrinos?

Regards,
Ian Tresman

[Ken G]

So, during cosmological expansion, does space-time between two objects (ie. two galaxies) "force" the two galaxies further apart, or does the space-time expand around the objects?

It may depend on what you are asking. In one interpretation of what you might be saying, there wouldn't appear to be any difference between those choices. But if you mean does the space expand on past the objects, then it depends on whether or not the objects are bound together by some force (other than gravity). If not, then the objects are embedded in the space and move apart when space expands, which certainly seems more relevant for cosmological distances. Note that if they are gravitationally bound, like in a galaxy cluster, then the space itself lags the cosmological expansion, the local gravity overrules it.

[*]If the two galaxies are "forced" further apart, are they pushed further apart, or does the "reference frame" change and they just appear further apart

How are you going to distinguish those possibilities?

[*]If space-time expands around the galaxies, why are they uneffected, but photons are not; in which case, what other particles are effected; neutrinos?

Two things are happening-- there's the cosmological expansion, and there's the local gravitational attraction in and between galaxies. Which dominates depends on the scale, but whichever it is, the photons are also dominated by that same thing. I suspect that you can think of it as photons are tracers of spacetime itself, so there can never be any difference between the two behaviors.

[Ari Jokimaki]

I couldn't find the post you refer to, but I'm skeptical that there is that much of a difference.

Sorry, I should have been more specific, it's post #64 in the linked thread.

[Ken G]

OK, I looked back at the thread and the points Grey raised. My conclusion is that one must be very careful what models are being compared. There is a kind of strawman model here which doesn't work, this is the model that says our galaxy is in an inertial frame with other galaxies streaming away from us through static space. Note this model doesn't even conform to the Cosmological Principle, because the other galaxies will feel gravity and slow down (or speed up), but if we are taken to be in an inertial frame, then we are not participating in that noninertial behavior. So yes, that model can be ruled out by the observations. However, note that a normal Doppler shift gets tricky when you have noninertial frames. It depends on which object does the accelerating, because there may be a difference between the relative velocity at the time the light was emitted and the relative velocity at the time the light is detected. Which velocity should one use in the Doppler formula? If you couple the Doppler formula to the Cosmological Principle, it seems to me that you will end up doing precisely the same calculation that is now conventionally done in co-moving coordinates (i.e., expanding space). So yes, one does need to generalize the concept of a "normal" Doppler shift to be consistent with the Cosmological Principle in noninertial reference frames, but still it is a purely kinematical concept, and does not specifically require that anything be happening to space itself. The expanding space model is a particular pedagogy, not an absolute statement of reality, I maintain and have so far not been refuted in a clear and intuitive way (though I could be wrong, because I haven't worked through the detailed mathematics, it is my intuition that is speaking).

[Bad jcsd]

comoving coordinates are the natural choice of coordinate system and when we're tlaking about redshift, apparent energy loss, recession, etc we're talking about what happens in comoving cooridnates (though that's not to say that these thigns don't happen in other coordiante systems, it's just that we always work in this coordinate system) so we're not changing coordinate systems. Of course we could say that these are comparing what happens locally at one point with what happens locally at another.

Comoving cooridnates is the system in which the cosmological principle is 'truest' as it's the only one in which the universe is complelty homogeneous and isotropic (ignoring the fact that this is slightly idealized). For spacetimes like the one we're tryign to describe, no global coordinate system can truly be called inertial so we shouldn't expect energy to be conserved as a matter of course.

[Grey]

Before I reply here, can you link me to the conversation with Grant discussing angular size changes from a straight Doppler shift?

[Ken G]

I can't find it Grey, but I'll give you the gist of it. We were talking about how a blueshifted star that approaches us would appear to have a higher blackbody temperature. I figured that if the star kept it's angular size, it would brighten at all wavelengths due to the blueshift. But Grant said that it would only brighten at some wavelengths, and darken at others. Turns out he was right, because the approaching star appears smaller, and at some wavelengths, that supercedes the higher brightness temperature. Unfortunately I don't have the article he cited, but it sounded an awful lot like the cosmological calculations of what happens to angular size (though for redshifting it would presumably mean the star would look larger, and I recall that the redshift factor raised to the fourth power appeared somewere, reminiscent of the cosmological effect, but unfortunately I can't recall exactly how it worked out. Still, my intuition is blinking-- and it says that special relativistic effects can be made to mimic the cosmological effects in the right reference frame.) It would be interesting to see this in better mathematical detail-- how can the Hubble expansion be recasted as a special relativistic effect applied to noninertial frames that exhibit the Cosmological Principle? I think it can be done.