# Am I understanding Cosmological Redshift rightly ?

Discussion in 'Astronomy, Exobiology, & Cosmology' started by sweetpea, Sep 1, 2017.

1. ### sweetpeaRegistered Senior Member

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Am I understanding Cosmological Redshift rightly now?

My first way of understanding was...

The space expands between two galaxies A and B. light leaves A and travels to B.

Notice that whilst the light is being emitted from A it will be red shifted (that is, the light is going in the opposite direction to which A is moving). So, that's one red shift.

Now, when the light nears B the light will be red shifted again as it has to catch up with a receding B. That's another red shift.

Notice it is the expansion of space which is making A and B receded from each other, but it is not space ''stretching'' the wavelength. It's the emitting and catching up parts that ''stretches'' the wavelength. My error here is interpreting the Doppler effect as a velocity of the galaxy itself in the same way as Hubble.
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Now, after reading this Sean Carroll recommended pdf...
https://arxiv.org/abs/astro-ph/0310808
Notice they say special relativistic velocity Doppler shift formula should not be used with anything to do with space expansion. The equation to use is a General Relativity equation... the pdf gives this equation..
Another help was the wiki redshift article and a couple of PMs to a member here, won't mention name incase I wrong in my understanding.
So, if the pdf tells us we cannot use any SR velocity equations and only use GR, are we left with the following way of understanding cosmological redshift...

Back to galaxies A and B.

In the rest frame of galaxy A, there is just a light emitted into space at such and such a frequency, ie. no red shift in A's frame of rest.

In B's frame of rest, a light is received at such and such a frequency, the observer at B then allows for the expansion of space by using the General Relativity equation. Can only use GR because of the metric expansion of space between A and B. Can't use SR because galaxies are not moving through space with a velocity. Is this right?

The thing is, I have known for along time space expansion was responsible for recession of distant galaxies, but 'now' know how to interpret that expansion in the case of the local rest frames of A and B.

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3. ### exchemistValued Senior Member

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Thanks for posting this. Until a year or so ago I had always interpreted the cosmological red shift as a straight forward Doppler effect. Then I read that it should be seen as due to something more fundamental, viz. and expansion of space itself - which is of course what is responsible for the recession of sources from each other anyway. But I had sort of assumed that the two explanations would be mathematically equivalent. However from what you have posted here, it seems that is not so and that a Doppler effect explanation leads to a wrong result. Thanks for clarifying this point.

Regarding your splitting of recession velocity into two parts, namely a rd shift due to recession of A and a second component due to recession of B, I think that is unnecessary as it implicitly introduces an arbitrary intermediate observation position (and frame of reference), relative to which both A and B are receding. I don't see the point of that, myself. I'd have thought you should simply measure the rate of recession of A as seen from B or vice versa and work it out from that.

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5. ### sweetpeaRegistered Senior Member

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Yes, I can see that may be the way. That is, forget the 'third frame' and just use GR for observations made at the galaxy receiving the light.

As for the rest frame of the light emitting galaxy, there won't be any reason to assume a Doppler effect as the light is emitted away from it. Except of course Gravitational Redshift, but that's another story.

Last edited: Sep 2, 2017

7. ### StrangerInAStrangeLandSubQuantum MechanicValued Senior Member

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^^^
Galaxies A & B would need to be in different groups. It is not that galaxies on their own are moving away from each other but that galaxy groups & clusters are moving away from each other.
Some galaxies move toward each other such as Andromeda & the Milky Way.

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9. ### timojinValued Senior Member

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If we all start from the so called B.B. so the B. B. is the center of the explosion so every fragment is a vector moving away. So how ca Andromeda & Milky Way move to each other ? I could see that one Galaxy is slow mover and Milky way is catching up the Andromeda.

10. ### StrangerInAStrangeLandSubQuantum MechanicValued Senior Member

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^^^
Andromeda & the Milky Way are in the same Local Group.

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^^^
???

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12. ### sweetpeaRegistered Senior Member

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Replace the word galaxies in the above quote with the words galaxy clusters.

If you would have done that, then there would have been no need for your post:
Notice, Exchemist understood it without any help.

13. ### James RJust this guy, you know?Staff Member

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30,252
timojin:

Just to be clear...
Basically, the gravitational effect of objects that are near enough to one another overcomes the effect of the expansion of space, so that locally objects can still attract one another. Andromeda and the Milky Way are close enough to each other that they attract each other, even though the universe as a whole is expanding. On a smaller scale, the Earth isn't going to fly apart any time soon due to the expansion of space, even though it is happening right here, same as everywhere else. All the matter in the Earth causes a local gravity that easily holds the planet together against the tendency for space to expand.