OK, here's one for those learned in GR. I have heard three separate interpretations of cosmological redshifts in mainstream astronomy:
1) Doppler shifts due to motions caused by the expansion
2) wavelength stretching due to expansion
3) gravitational redshifts due to, yes, expansion

So it's clear that it is caused by the increasing distances between galaxies. But my question is, is it true that all three of these interpretations are perfectly correct in the appropriate coordinate system, or are there clear advantages for one? Are some of them actually wrong? Specifically, what does each say about what we would observe if the expansion turned around and a Big Crunch started. Would they all correctly describe how the turnaround would appear? Personally, I tend to prefer (3), and (1) seems wrong, but I've heard that in the right coordinate system (1) works fine. Can anyone set me straight on this?

well, I'm limited but will try.


first, all galaxies are moving even without the expansion. As you already know, the Doppler reddening or blueing occurs for 2 objects moving radially. You can hear it with a train. So, the Doppler shift is independent of expansion.

2) yes, light waves redshift due to space expansion.

3) no, gravitional redshifts are not due to expansion. All matter affects all other matter. It even affects light traveling near it. You've heard of gravitational lensing. well, as the light leaves a galaxy to come here, the mass of the galaxy pulls on the light lensing it. But instead of bending the light, the mass reddens it.


I hope this helps, and I hope my take is right

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My understanding is that about one percent, or perhaps slightly
less than one percent of the cosmological redshift is due to the
gravitational potential difference between earlier times and now.
The rest is due directly to Doppler and/or expansion of space.

-- Jeff, in Minneapolis

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I'm not sure where the one percent comes from, that must be some particular type of gravitational redshift. Actually, it is perfectly acceptable to consider all of the cosmological redshift as a gravitational redshift, since one can view the entire universe as "climbing out of a potential well". It sounds like cross is talking about the Sachs-Wolfe effect, which deals with how structure formation imprints a (very!) tiny redshift onto the light. I'm talking within the cosmological principle of a homogeneous universe, yet the galaxies are getting farther apart so there is an evolution of the gravitational potential and there is gravitational redshifting. My problem is, if all 3 of the above pictures are valid, why would they not all be going on at once? It has to be related to the way you choose your coordinates or your reference frame or some such thing. What are the corresponding frames? This might be too tough an issue, but it would sure be nice to make some sense out of these seemingly disjoint concepts.

I may be wrong, but my understanding is that only about one
percent of the observed cosmological redshift is due to the
entire Universe climbing out of its own potential well.

The way I've heard it is that they are all going on at once.

-- Jeff, in Minneapolis

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Not sure what you mean there JeffR. The Doppler shift I refer to is due to the expansion, not peculiar galaxy motions. Thus the stretching of the wavelength, which is also viewed as due to the expansion, is the same effect. You can't have both, you'd get too much redshift. As for the 1% figure, do you know where that comes from? It was my understanding that the cosmological gravitational redshift is also the entire effect.

I think I may get what you mean, JR, about the 1% gravitational redshift. That must the galactic redshifts due to the galaxy's own gravity, is that correct? But I'm talking about the universe's gravity, not that of individual galaxies. The redshfit I mean would appear in the CMB even if it had never gone anywhere near a galaxy. Maybe that's an argument for choice (2), because it doesn't lead to confusion involving peculiar motions or local gravities.

Ken,
In determining the total redshift of a galaxy, you have to take into account the doppler (the peculiar motion of the galaxy), the gravitational (determined by the galaxy) and the cosmological (the expansion of the universe). The problem is, you can't determine from the spectrum (which is where we get the observed redshift) the individual components of the total redshift (there are ways to estimate each component, depending on the galaxy). Except for our local group, almost all of the redshift is due to expansion (the closer the galaxy, the less the cosmological redshift). The cosmological redshift is determined by something called the "scale factor". It is basically a comparison of the total curvature of the universe at the time the light was emitted to the time it was received. This site has a discussion of the different types of redshift.

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thanks for the link.

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This is a nice link, but my original question still stands. I am only talking about the cosmological redshift, the third term in the equation in the link. The other two are much more straightforward. The link claims that the
cosmo redshift is inherently the mechanism (2) I started with. But that is exactly my question. Is it really necessary to consider this solely as mechanism (2), or can (1) or (3) be extended correctly to the cosmo redshift in the appropriate coordinate system or reference frame? In other words, are we being glib when we purport that photon wavelengths "really" expand with space, or is this, as is so often true, contingent on a particular choice of reference frame? I suspect the latter, as I can see (3) working just fine for cosmological redshifts if you define a gravitational potential for the homogeneous universe. I have heard that (1) works fine too, and I was wondering how it would look in the case of an expansion that turns around.
I think the key for making (1) work is you have to look not only at what the galaxy was doing that emitted the light, but also what you are doing when you observe it, and that's how the light finds out what has happened to space since it got emitted.

One thing to include in favor of (2) is that expanding space will decrease the intensity of light with distance faster than the inverse-square Euclidean case, by a factor (1+z)^2. Observationally, this is in addition to the time-dilation factor in photon arrival rate, narrowing of the observed filter width due to redshift, and the redshifting of photon energy, and is part of the "Tolman dimming" used as a test of the expansion. Without this effect, magnitudes of high-redshift supernovae (for example) would make even less sense than they do in an accelerating model - this effect is much larger than the measured departure from constant or decelerating expansion.

That's a pretty good point, it does make the dimming seem more natural. So it's an advantage for (2), as ngc3314 points out. But note this by itself does not make (2) correct and the others incorrect. I would imagine that light leaving from near a black hole must suffer the same type of dimming, yes? That case is normally explained in terms of a gravitational redshift. So it means the gravitational approach requires more work than just the redshifting, no pun intended.
I've often wondered why you hear statements that sound like "reality", such as, the gravity of a black hole will slow down time, and the Big Bang expands space. These both strike me as reference-frame dependent statements that are purported as being objectively true. The core of objective reality is not the words chosen to describe it, it is the knowledge of appropriate words in one frame, coupled with the ability to anticipate how the words would change by knowing the transformations to other frames. I think we too often forget that, and it is part of the problem we run into when we try to communicate in simplified terms to nonscientists. Indeed, that is a "transformation" that we probably know way too little about!

I think R is independent of the coordinate sytsem, so it would change with respect to time in any set of coordinates. So you can't make 2) disappear by any changing the coordinates.

I may be wrong, but I suspect that the difference between 1) and 2) is intrinsic - not an artifact of the choice of coordinates.

The use of a scale factor *is* a choice of coordinatization. Distance does not have to be characterized that way. I apologize for posting a question and then challenging the answers offered, and I do appreciate the opinions given, but it really isn't this simple. But note the point here-- we ourselves don't really know the full range of possibilities for a correct description of the Big Bang, and we wonder why pseudoscientific types massacre the jargon so much! We only get what wisdom "trickles down" to us, we need real answers from those who actually work with these theories. Maybe it's our fault for not researching it enough, but heck, we don't have time to make ourselves experts, and we don't want to be handed a "party line" that only encompasses a small fraction of the truth. The issue of "what is reality" within this theory is very germane to what constraints it imposes on our conception of the universe. Much of the time spent debating the flaws of nonstandard models would be better invested in helping us get a better understanding of the standard model!

To have any description, you have to chose some coordinates. As Fortunate pointed out, the scale factor is independent of the choice of coordinates. 1) does depend on the choice of coordinates.

For the same reason some non-pseudoscientific types don't know the full range of possiblitiies, it's not something they've bothered to study.

Most of the time, the experts give us as much of the real answers as can be understood, without learning more.

This is exactly the problem.

If you're not going to take the time to understand math and jargon used by the experts, you really can't complain about not being able to understand the "Full Truth".

Sorry, a small fraction of the "truth" is all your going to understand, without learning the math and jargon. You don't even have to become an expert, but you do have to take the time to learn it. The experts do quite well putting quite abstract ideas into plain words. But most of those abstract concepts, cannot be fully understood without having bothered to learn the math and jargon. That is not the expert's fault.

Sorry, this takes a lot of time and effort on the part of the person who wants to understand, there is no other way. There are plenty of assets on the web, there are college classes available, libraries, etc, to learn what is needed to understand the experts. It's not their job to fully educate the people here. It's up to the the people who are here, and want to understand more than the simple explainations , to take the time and effort to learn what is needed, if they want.

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OK, I asked for this, by starting a thread and then ending up blaming the "experts" for not getting a satisfactory resolution. My bad. But note I'm not blaming forum members, I think we should all have been given the tools to answer this query, even without the "math and jargon". Don't get me wrong Tensor, I respect your physics acumen. I think you've been sold a bill of goods, so the fact that you have a great deal of physics knowledge is kind of exactly my point.

All three do! This is my point. You will find a million places that say choice (2) is "correct", no "math and jargon" necessary. But where will you find the correct answer, which I'm suspecting more and more is that *all three* are perfectly valid descriptions of reality. If you don't believe me, and you care to find out, you may be surprised. But I don't think you should have to-- this should already be common knowledge! After all, it is of no passing importance to understand how many perspectives are appropriate for describing the history of our universe.

That sounds like a copout to me. Feynman is my physics hero expressly because he never hid behind math and jargon, he found ways to get to the core of the physics in the most intuitive terms.



Well, I agree to some extent with this, and also your point that pseudoscientists rarely understand much science. But philosophically, I feel that the physics ends when the math begins. Physics is what you do to *set up* the math, it should not be necessary to understand how to solve the equations to understand what they mean. GR is a perfect example, we could never solve those equations ourselves, and we shouldn't have to.

It's not an issue of fault. The experts need to publish results, and they don't need to care if more than 10 people in the world really understand what they did. I'm talking about what is good for science, and if the experts care about that issue, then we need Feynman-like individuals to arm the knowledgable public (physics-major types, I mean here) with the tools to really understand what these theories mean, at the deepest level possible.

But in truth, I really just wanted to know if there were insights into my original thread, since the level around here is pretty high. It was probably too difficult a question, but again, I think that is the fault of the experts, and it's up to them to care or not.

Well, they're valid descriptions of reality within their own range of application, but gravitational and doppler redshifts would NOT be valid explanations for the very large redshifts measured from very distant objects. THAT redshift is due to the cosmological effect of expanding space. At least, that's what most of today's best minds agree on.

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Really? I was not at all aware there was any such agreement. Do you have a reference? I'm serious, my guess would have been that the "best minds" would have agreed that all three are perfectly valid, and I do mean for the CMB redshift. My question was more around the relative pedagogical advantages of each, and initially I was skeptical about (1), but I think I just didn't like that it sounded so pedestrian.

1) Doppler shifts due to motions caused by the expansion



IMO, this has nothing to do with CMB

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The idea behind (1) is that the gas emitting the CMB, which is recombining hydrogen, was moving at a velocity determined by the Hubble law. Indeed, this was the initial interpretation of the Hubble law. It was only with the invention of "co-moving coordinates", which give us the expansion of the scale factor, that we have the picture that the CMB-emitting gas was not actually moving. It's a bit tricky to use the velocity picture, because velocity is dx/dt and you have to define what you mean by x and by t. I think the x is the distance measured by a chain of comoving observers, and the t is the proper age of the universe. I think approach (1) requires more care than the picture of a growing scale factor, which is why (2) is often preferred. I kind of like (3) however, because it allows you to think physically instead of geometrically. It is the approach often used when discussing "normal" gravitational redshifts, but note that approach (1) or (2) could *also* be used there, I claim, although I think (1) would be pretty funky and I'm not sure how it would work. I think (2) would be straightforward, space is indeed expanding for a chain of comoving observers along a path leaving from near a massive body. (I believe that is part of what is meant by "curvature"). What I'm trying to say is, we should not make the mistake of thinking that a particular description is in any sense "the real one".
The choices made are pedagogical, as long as the right redshift emerges. This thread is being interpreted as an issue of right and wrong physics, whereas I claim it is actually just pedagogy because the predictions are correct. But pedagogy can be fascinating, since you and I don't follow this stuff to make predictions, we do it to get a picture of what happened to the CMB etc.

I guess I misread.

it now seems to me that 1) and 2) are the same.

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and 3) doesn't seem right at all.


gravitational redshift has nothing to do with expansion. IMO

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Of course, all three are the same! In the sense that they can be transformed into each other in the appropriate reference frame or coordinate system. The issue is which choice to make when one wants to use a pedagogical explanation. I would argue we should all be versed in all three, as we make many pedagogical explanations and should understand the transformations.
The way you use (3) to get the CMB redshift is you look at the gravitational potential of the homogeneous universe. Voila.

that sounds complicated.


Our universe is not homogeneous??

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My understanding is that redshift, by definition, causes a shift in all wavelengths towards the red end of the electrmagnetic spectrum. Certain mechanisms also cause a shift in SOME wavelengths, creating a spectral signature that will identify the mechanism.

It seems to me that all mechanisms that cause a full-spectrum frequency-independent redshift, are INDISTINGUISHABLE, and these include (a) Expansion (b) Doppler (movement) (c) Gravitational.

Interestingly, the Wolf Effect may produce EITHER a redshift with a characteristic spectrum, or a full-spectrum redshift which would also make it INDISTINGUISHABLE from cosmological redshift.

However, the Wolf Effect is considered controversial, and its full-spectrum frequency-independent redshift is generally "not accepted", even though it has been verified in the laboratory, despite my having it confirmed by the discovered, Emil Wolf, and a number of other researches.

It is interesting reading the Wikipedia redshift discussion page where full-spectrum frequency-independent Wolf Effect is flatly denied with no supporting evidence.

Regards,
Ian Tresman

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I completely agree with iantresman about the redshifts, although I don't know anything about the Wolf effect (sounds interesting, but difficult...)

The Wikipedia redshift discussion page is an interesting link, thank you. While many of the statements there fail to recognize the frame-ocentrism of any pedagogical redshift explanation, I did find this quote which I feel is right on:
"Things in the universe are generally receding from each other. It's just that experts are a bit leary of words like that becase they want to avoid words implying normal motion and make a very important point. They want to convey the extreme coolness of the fact that space itself, the empty fabric of reality, is malleable, shapeable, stretchable."
This explains a pedagogical advantage of approach (2). Note that going any further and saying that it is correct while the others are incorrect is simple a failure to recognize that the fundamental message of relativity is that no statement of reality is accurate without also specifying the appropriate reference frame. Have we not learned this lesson yet? The true fabric of reality emerges from the *transformations* between frames.

For a particular object, is there a way to differentiate between the proportion of (a) Cosmological redshift (b) Doppler redshift (c) Gravitational redshift (d) Alternative redshift?

Regards,
Ian Tresman

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As far as I know, no. Until you identify your reference frame, that is. Conventionally, the chosen frame is the "comoving frame" which moves with the average motion of the galaxies the photons are passing at any given age. In this frame, the differentiation is fairly straightforward, as described on Wikipedia and many other websites that discuss cosmology from this frame without identifying it as such.

It depends, to a large extent, on which 'particular object'!

For example, an object which has a well determined trig parallax of (say) 0.01" (10 mas), is an unresolved point source to (say) 0.001" (1 mas), and the spectrum of a main sequence star ... within the error limits of any redshift determination today, you could rule out a, c, and d (caveat: you may know of an 'alternative redshift' which is part of complete overthrow of 20th century physics).

More generally, one knows considerably more about 'an object' than just its 'redshift'. Specifically, that redshift is calculated from a spectrum, which contains strong hints about the state of the object, in terms of an awful lot of the physics that must be relevant to that object. That physics will often allow you to constrain the contribution of each of your four sources to the observed redshift.

In cases where the redshift exceeds what would normally be classified as cosmological redshift, I agree with Nereid's points. If the question is instead aimed at redshifts that are in line with cosmological redshifts and one wants to know how to meaningfully partition the sources of redshift, that's where the coordinate system becomes so important. Perhaps the first type should be "expansion redshift" rather than "cosmological redshift", as the latter is more of an over-arching term.