Andromeda and the cosmological redshift

[nmsurobert]

I understand that andromeda is blue shifted because it is moving towards us, but do we see any kind of redshift because of the expansion of the universe.
Is andromeda less blue shifted than it should be because of cosmological redshift?

 

[Orodruin]

No. The local group is gravitationally bound.

Also, it is not possible to assign part of the frequency shift to motion and part to expansion in the way you suggest.

 

[Ken G]

The way I would put it is, all we can really measure and therefore determine unambiguously is the frequency shift. How we describe the reasons for that shift is generally not unique, and depends on how we connect the local reference frame we are into the global coordinates we are using to describe the entire process. So to me your question is like asking, when you put a basketball on your driveway and it starts to roll, is that rolling motion due in some small part to the fact that the Earth is a sphere, or isn't it? The answer depends on how you choose to describe your driveway-- do you start with a spherical Earth and then look at however that shape got perturbed by some small hill before your house was built, in which case you say the spherical shape does in some tiny way affect the rolling, or do you simply look at the bulldozer that graded your property and say that it would have ended up the same regardless of whether the Earth was a sphere or a pancake? How you choose to build up your coordinates affects the answer.

 

[russ_watters]

Also, it is not possible to assign part of the frequency shift to motion and part to expansion in the way you suggest.

Why not? Expansion has a specific rate that can be calculated if the distance can be measured by another means.

 

[Orodruin]

Why not? Expansion has a specific rate that can be calculated if the distance can be measured by another means.

This is related to a particular coordinate system and therefore a coordinate dependent construction. See https://www.physicsforums.com/insights/coordinate-dependent-statements-expanding-universe/

 

[nmsurobert]

No. The local group is gravitationally bound.

Does the strength of gravity between the galaxies "cancel" out the effects of cosmological redshift?

Also, it is not possible to assign part of the frequency shift to motion and part to expansion in the way you suggest.

So we treat coordinate system that Doppler shift is on as a completely separate coordinate system than the expansion of the universe?

 

[Orodruin]

Does the strength of gravity between the galaxies "cancel" out the effects of cosmological redshift?So we treat coordinate system that Doppler shift is on as a completely separate coordinate system than the expansion of the universe?

I am sorry, but I cannot decipher what you mean by either of those questions.

 

[nmsurobert]

What does being gravitational bound have to do with my initial question?

Why is it is not possible to assign part of the frequency shift to motion and part to expansion in the way I suggest.

 

[Orodruin]

What does being gravitational bound have to do with my initial question?

Bound objects do not expand.

Why is it is not possible to assign part of the frequency shift to motion and part to expansion in the way I suggest.

This is described in the PF Insight I linked to earlier. However, note that it is written at A-level. Also, it is possible to do it in a particular coordinate system, but the split is coordinate dependent and therefore unphysical.

 

[nmsurobert]

Bound objects do not expand.

ah ok. Simple enough. And now that I think about it, that makes total sense.

This is described in the PF Insight I linked to earlier. However, note that it is written at A-level. Also, it is possible to do it in a particular coordinate system, but the split is coordinate dependent and therefore unphysical.

I'll started reading the Insight. I think it's answering the the question I asked.

 

[russ_watters]

This is related to a particular coordinate system and therefore a coordinate dependent construction. See https://www.physicsforums.com/insights/coordinate-dependent-statements-expanding-universe/

That does not appear to me to answer my/the previous question; I live on Earth and I suspect you and the OP do as well.

I'll put a finer point on it:
-Andromeda's motion WRT us is about 200,000 km/s
-Andromeda's distance can be measured by means other than redshift.
-Based on Andromeda's distance the expected recession velocity due to the expansion of the universe is about 55 km/s.

So doesn't that make the motion due to our gravitational attraction roughly 200,055 km/s to overcome the universe's expansion of 55 km/s (caveat about significant figures)?

So I would think @nmsurobert would be interested to know the proper motion swamps the expected expansion of the universe at Andromeda's distance. What's more, I'm also seeing that "expansion of the universe" is itself not a uniform proposition in that gravity apparently tugs on the "fabric" of the universe to limit expansion near massive objects. Perhaps this is what "gravitationally bound" means, but it isn't a way of describing the phenomena I'd seen before.
https://astronomy.stackexchange.com...re-being-drawn-together-if-there-was-big-bang

 

[Orodruin]

That does not appear to me to answer my/the previous question; I live on Earth and I suspect you and the OP do as well.

This does not mean you have identified a coordinate system or a simultaneity convention. You are certainly not at rest in standard comoving coordinates.

Andromeda's distance can be measured by means other than redshift.

Andromea is close enough to be quite local. Enough to ignore large scale curvature effects. Still, you generally have a problem with identifying what ”distance” means in SR. The issue of simultaneity does not go away, I even used Minkowski space with different coordinates as an example. Sure you could say let me use standard Minkowski coordinates, but this does not make your result any less coordinate dependent. The point is that I have seen many cases of people claiming ”cosmological redshift is not the same as Doppler shift” and that is simply untrue.

Based on Andromeda's distance the expected recession velocity due to the expansion of the universe is about 55 km/s.

Again. The local group is gravitationally bound. I believe we have had several threads discussing why bound objects don’t expand.

 

[Ken G]

It seems to me we have two quite different issues going on here, one which we agree on (and Orodruin's insight article describes in some rigor), and the other which is the source of disagreement but is not of great significance. What we agree on is that we can treat Andromeda as moving toward us through a static spacetime (Orodruin's local MInkowski space) thereby accounting for the blueshift purely as a Doppler shift, or we can treat both our galaxies as stationary in a dynamical spacetime (that is not locally a Hubble law), thereby accounting for the blueshift purely as something happening to the spacetime (dominated by the local gravity). We can also choose a kind of combination of the two, where we (arbitrarily) decide to coordinatize the spacetime as a Hubble law, and treat all local deviations as Doppler shifts. These are all arbitrary choices, but we can do them, and it's not unusual for us to use language that describes "contributions" to what we see based on our arbitrary choice of coordinatization. Hence Orodruin's central point that one cannot say the blueshift is definitely a Doppler shift and not a dynamical spacetime that is different from the Hubble law-- I believe he is essentially stating that the Hubble Law is not the only dynamical treatment of spacetime that is possible, we can get the local curvature right and coordinatize the manifold any way we like.

Where the disagreement comes in is in the ramifications of these facts. It almost sounds like Orodruin is saying that no coordinate-dependent language is allowed, but that doesn't necessarily follow. Instead, we must not use coordinate dependent language as if it was a statement of absolute truth. So if the OP is simply reworded like "can we choose coordinates where we treat Andromeda as having a large proper motion sitting on top of a very weak average Hubble law", then the answer is "yes, but we have to take pains to get the local gravity right." If we replace the "can" by a "must", then the answer is "no." If the question is should we want to coordinatize it that way, then the answer is "that's really up to you."

 

[Orodruin]

It almost sounds like Orodruin is saying that no coordinate-dependent language is allowed, but that doesn't necessarily follow.

I am sorry if it sounds that way. It is certainly allowed as long as one remembers that one's language is coordinate dependent and that the imposition "this is Doppler shift and this is cosmological redshift" is an ambiguous truth that does not necessarily hold for any description of the phenomenon. The same goes for statements such as "gravitational waves stretch and compress the path traveled by the light signals". Sure, you can choose coordinates where this would be a valid description, but you can also choose coordinates where the description is different and I believe one should remember this also when teaching in order not to give the impression that that description is the only valid one.

 

[Ken G]

"Don't reify the coordinates" is good advice. And thanks for that insight article, it's advanced but I know a mathematician cannot bring themself to say it any less than the correct way!

 

[Orodruin]

"Don't reify the coordinates" is good advice. And thanks for that insight article, it's advanced but I know a mathematician cannot bring themself to say it any less than the correct way!

Well, I am still a physicist. I wrote it at advanced level because my target audience was people who should know better than to categorically say that Doppler shift and cosmological redshift are separate phenomena (ie, teachers), but still made such claims. I have seen many university professors get relativity wrong and think that needs correction - one of the most blatant errors being claims such as ”the muons move 1 km in their rest frame before decaying”.

 

[Ken G]

Yes, covering a distance in a rest frame is quite a trick! And I agree about the language we often see, I've never been a fan of "the BIg Bang model asserts that space itself is expanding," I prefer "a favorite picture that works really well is that space itself is expanding, though we have no theory of space and no way to establish what it is actually doing." Sometimes I even say "the expansion of the universe really means there is an increasing contrast between distances across wide unbound systems versus smaller-scale bound systems," which I prefer to "bound systems don't expand with space." On that issue, some questions are actually easier to answer by picturing the bound systems as shrinking, questions like "how does the wavelength stretch" or "what is space expanding into." But above all, the coolest lesson of relativity is how much of what we think is a language about what is happening is actually a language about how we are choosing to think about what is happening. We never appreciated that distinction before.

 

[nmsurobert]

Thanks for all the replies! I guess my question was not as simple as I thought it was.

I teach high school astronomy and I could hear a couple of students asking me this question. Maybe I'll just link them to this thread lol. While I don't expect to give them the most in depth answer, I would like to be able to give them some kind of coherent response.

 

[Ken G]

It's very hard to communicate Big Bang ideas at the high school level without basically telling "lies to children." It's a difficult choice, when you know what you are saying isn't really true, but you judge it close enough to be all they can really understand! I'd say if a student asks you a question as nuanced as the one you asked, you shouldn't worry about answering it, just praise them for drawing the connections between Doppler shifts and cosmological shifts and say that these are all issues of current research and the answer might be different in the next theory that comes along! That might encourage them to be curious and realize that not all questions can be answered as easily as they can be asked. Just make sure that they understand if everything expanded equally, it would be like no expansion at all, so bound systems cannot expand with the rest of the universe or we wouldn't call it expansion.

 

[nmsurobert]

It's very hard to communicate Big Bang ideas at the high school level without basically telling "lies to children." It's a difficult choice, when you know what you are saying isn't really true, but you judge it close enough to be all they can really understand! I'd say if a student asks you a question as nuanced as the one you asked, you shouldn't worry about answering it, just praise them for drawing the connections between Doppler shifts and cosmological shifts and say that these are all issues of current research and the answer might be different in the next theory that comes along! That might encourage them to be curious and realize that not all questions can be answered as easily as they can be asked. Just make sure that they understand if everything expanded equally, it would be like no expansion at all, so bound systems cannot expand with the rest of the universe or we wouldn't call it expansion.

That makes sense. And that's something that I've said before. They really wanted to talk about black holes. Before we dove into it I made sure to tell them a lot of what I was about to talk about is current research and may change tomorrow... just like you said. Also, I would still like to be able to answer questions like these even if I shouldn't worry about answering them. I know it's not a university but I should still know my shizzz, you know.

 

[Ken G]

I understand, you don't want to feel like you are telling them everything you know, you want to feel like you are measuring what you say and deciding what is worth saying and what will only confuse. Should you explain what a coordinate is, and teach them that language only has meaning when you couple it to the referents that give it meaning, or do you let them continue to think that "words just mean stuff" without the referents? What are they ready to know?

 

[JMz]

-Andromeda's motion WRT us is about 200,000 km/s

FYI, its speed relative to the center of the MW is about 200 km/s, not 200,000, according to NASA. (More like 100, actually.)

 

[PAllen]

One way to try to make this question independent of coordinates is consider a given scenario in different possible universes. For example:

1) We have two observers whose round trip light signal times are comparable to Milkyway to Andromeda, and the initially have no mutual red or blue shift (in terms of an FLRW cosmology, this means that one of them would have a small so called peculiar velocity).

2) One of the observers triggers an explosion of locally known characteristics.

3) We can ask about the peak blueshift from said explosion observed by the other observer for the following cases:

a) Flat spacetime (i.e.Minkowski spacetime)
b) an expanding universe with neither accelerating nor decelerating expansion
c) a universe with accelerating expansion
d) a universe with deceleration expansion.

Then, I believe, the following are true:

(a) and (b) will show the exact same maximal blueshift

(c) will show slightly less maximal blueshift than (a) or (b)

(d) will show slightly more maximal blueshift that (a) or (b).

One way to understand the possibly surprising equivalence of (a) and (b) for this case is that the maximal non-accelerating expansion case (without cosmological constant) of FLRW metrics is the so called Milne cosmology which is actually just (a) in funny coordinates.

 

[Orodruin]

One way to try to make this question independent of coordinates is consider a given scenario in different possible universes.

I am sorry, but I am not sure what you want to say by these examples. You have different universes and in each one you have the same sort of ambiguity. It is unclear to me how you would "match" the universes to each other, they are different universes.

 

[alantheastronomer]

Taking the local Hubble constant to be approximately 70 km/sec/Mpc and the distance between the Milky Way and Andromeda to be approximately 80 kpc, we get a recessional velocity due to the expansion of the universe of 5.6 km/sec. The velocity of approach as measured by blueshift is about 130 km/sec. So without the expansion of the universe we should have been seeing an approach velocity of 135.6 km/sec.

 

[JMz]

Distance to M31 is 800 kpc, right? So we would get the earlier 55 km/s estimate.

 

[alantheastronomer]

Distance to M31 is 800 kpc, right? So we would get the earlier 55 km/s estimate.

OMG you're absolutely right, I misplaced a decimal point! Sorry!

 

[JMz]

OMG you're absolutely right, I misplaced a decimal point! Sorry!

'S OK. I have never in my life misplaced a decimal point. Or a minus sign. Hah! ;-)

 

[nikkkom]

Taking the local Hubble constant to be approximately 70 km/sec/Mpc and the distance between the Milky Way and Andromeda to be approximately 80 kpc, we get a recessional velocity due to the expansion of the universe of 5.6 km/sec. The velocity of approach as measured by blueshift is about 130 km/sec. So without the expansion of the universe we should have been seeing an approach velocity of 135.6 km/sec.

This is logically flawed: "without the expansion of the universe" there would be no Milky Way, no Andromeda. No galaxies at all.

Now, you can look at the current situation of where these two galaxies are and how they move, disregarding their deep past. In this case, "expansion of space" or lack thereof is simply a choice of coordinates. You can choose one where "space expands" or one where it does not. Both are equally valid. Physical observables, such as relative velocity of these two galaxies, are independent from coordinate choice. Ergo, "we should have been seeing" the same approach velocity.

Physically observable changes are only seen for the case where expansion of space is not constant - in particular, when it is increasing, as appears to be the case. But this (1) has very little effect on the distance scale of Andromeda;
and (2) the effect is very small anyway - if you want to directly measure (as opposed to inferring it by comparing observed data to cosmological models w/o dark energy) that expansion of space is increasing, by showing that distant galaxies' redshifts are increasing [actually, that "they decrease slower than they should"] - this would require very precise and very long-baseline measurements. IIUC such measurements are not within our capabilities yet.