Why is the Cosmological Redshift z Confusing?

[AlephClo]

I am confused about the physical meaning of the redshift. Let say the non-relativistic one z=v/c.

When I read Barbara Ryden, Intro to cosmology, she demonstrate the z is not related to the space expansion between the source and the receiver, but 'it does tell us what the scale factor was at the time the light from the galaxy was emitted'.
When I read J.E. Lidsey, ASTM108/PHY7010U Cosmology, he syas that 'the time taken to be emitted is t=Lamda-emitted/c' and during that time for a stationary observer the source will move a distance vt, which adds to the wave lenght. From that we can obtain (I understand co-move) Lamda-observed=Lamda-emitted+vt, and derive Lamda-Obs/Lamda-Em = 1 + v/c.

My questions are:
1) is the extension of the wavelenght a local action only during the time of emission caused by the co-movement, and therefore independently from the distance of far away observers?
2) if it is independent of the far away observers, i.e., receivers, and independent of the space expansion in between the source and the receiver, all observers should measure the same emitted wavelength because once the photon is emitted it is not transformed anymore.

Thank you.

 

[phinds]

My questions are:
1) is the extension of the wavelenght a local action only during the time of emission caused by the co-movement, and therefore independently from the distance of far away observers?

Yes, if you are talking about the relative proper motion of one thing vs another, that's independent of distance (although the strength of the signal will depend on distance)

2) if it is independent of the far away observers, i.e., receivers, and independent of the space expansion in between the source and the receiver, all observers should measure the same emitted wavelength because once the photon is emitted it is not transformed anymore.

No, that's not correct. The emitted signal is affected by TWO things, the distance-independent effect due to relative proper motion AND the effect (MUCH bigger) due to the expansion, so the farther away you are the more the overall red-shift will be. You can (theoretically at least) compensate for the expansion (assuming you know the distance) and calculate the effect of proper motion.

 

[Chalnoth]

When I read Barbara Ryden, Intro to cosmology, she demonstrate the z is not related to the space expansion between the source and the receiver, but 'it does tell us what the scale factor was at the time the light from the galaxy was emitted'.

This is confusing to me. The redshift is given exactly by the amount that space has expanded between the source and receiver.

That is, if $a_s$ is the scale factor at the time the source emitted the photon, and $a_r$ is the scale factor at the time the receiver absorbed the photon, then $z + 1 = a_r / a_s$. So if objects in the universe have, on average, become twice as far from one another, then the photon's wavelength will have doubled.

 

[UVCatastrophe]

The scale factor comes from the RFWL metric, and is only dependent on when you are in the universe, not where. You can think of it as a meter-stick that changes size as a function of time -- what you mean by "the wavelength is X meters" changes as time progress. Suppose a photon of wavelength $\lambda$ is emitted from a distance star at $a(t_0)$ (*note: this is a different convention than used in cosmology, where $t_0 = \text{now}$ and $a(t_0) = 1$ ). It travels for a long time $T$ and then enters a spectroscope on Earth when the scale factor is $a(t_0 + T)$. You should find that the observed $\lambda'$ wavelength depends on how much time elapses until it is observed.

Of course, the time $T$ is a function of how far away the photon had to travel to get to Earth. If the galaxy was nearby, then it had to travel less time, and so the scale factor will not have changed significantly by the time it arrives at Earth. In contrast, if the galaxy is far away from Earth, then the scale factor will have changed a lot, leading to more redshift. Thus, if we know the wavelength of the emitted light when it was emitted (i.e., from atomic/nuclear spectroscopy), we can calculate how far away the galaxy is.

I think one thing that is important to keep in mind is that we're only ever observing from Earth (or nearby Earth). It might help to imagine an entire locus of hypothetical observers. Pick your favorite distant galaxy -- for every emitter, there are successive loci of equal redshifts, since the light requires a finite amount of time to travel, and in that time the scale factor will have changed by a fixed amount.

I would also recommend checking out an article in Scientific American March 2005, pp 36-45, "Misconceptions about the Big Bang". That really helped me when I had to teach these concepts.

 

[marcus]

I would also recommend checking out an article in Scientific American March 2005, pp 36-45, "Misconceptions about the Big Bang". That really helped me when I had to teach these concepts.

Last time I checked, Charley Lineweaver had an online copy of that SciAm article at his website. I put the link in my small print signature. If that link doesn't work, to get a free online copy, could someone else post a better link, and save folks a trip to the library?

It still works.
http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf
When it comes up you see a blank screen because the first page is blank, so just scroll down a page and you will see the article.

Bravo, UVcat, for using it as supplemental course reading material. I'll bet it was a fun course both to teach and to learn.

 

[AlephClo]

My orginal understanding was correct, i.e., the wavelength expands as the space expands between the source and the emission as very well discribed by UVCatastrophe. I have read the Scientific American March article and it sheds more light :-) on the topic. To have an open mind sometimes let some confusion in, but with this great community it all clears out. Thank you all.