Red shift and blue shift as relating to time dilation

[Vesc>C]

I was listening to a lecture about the expansion of the universe and found myself confused about the light we see from very distant galaxies. These galaxies are red shifted because they are moving away from us and the photons are being stretched. Does this mean that the galaxy will appear to be rotating slower than it actually is to us? If yes, is this what is meant by time dilation? Also, if the distant galaxy were to be moving towards us instead, would it appear to be rotating faster?

 

[jfy4]

Time dilation is a separate effect from relativistic Doppler-shift. They are fairly easy subjects to find reading material for. For instance Wikipedia has some good articles on both of those topics, where their origins and observable consequences can be read about. Also a google search on both of those topics will provide various university resources that can be downloaded. Special relativity is not particularly controversial anymore and so the material you find will most likely be reliable. Good luck.

 

[Naty1]

Vesc...your questions are good ones, I think, since those interpretations have been the subject of arguments [differences] here among expert people I respect. For the time being retain your uncertainty about exacty what is going on. I do not know how to accurately answer you in a brief statement. I've been reading part time about such stuff for several years and am just beginning to get a bit of an understanding.

The simple and inaccurate [not so good] answer to your questions could be 'yes'. If that program was your first exposure to cosmology, ok, go with that for now but be aware that's a ridicuously simplistic answer if you are really interested in what is happening. Time dilation, relativistic Doppler shift and cosmological redshift are actually three DIFFERENT phenomena.

Even the statement 'photons are being stretched' is NOT so simple. How can a free falling, photon change characteristics?? Where would such energy come from or go to? Does light change color over vast cosmological distances? Well, it turns out measuring the redshift [color] of photons is unambiguous [it's whatever the measuring device says it is] but interpreting what the color change [redshift] MEANS is arbitrary. So within one set of conventions, arbitrary but useful to facilitate discussion, redshift can be attributed a change in frequency or wavelength as your program discussed.

Are you aware that in cosmology for two galaxies whose relative 'recession velocities' are greater than the speed of light, within each galaxy light still passes an observer at 'c' and clocks still tick at the same fixed rate? This means we have some handy references.
On the other hand, cosmological distances are NOT fixed...'space expands' is one way to say it, 'distances increase over time' is a better way. And our observations [measures] are out of date and limited: about all we can observe is light and that may have taken billions of years to reach us. So everything we see is 'old', the way it used to be. Such characteristics are not so 'convenient'.

And cosmological 'velocities' are different than velocities in special relativity where the relativistic Doppler effect [of relative speeds] is utilized. The so-called cosmological recession "velocity" is actually a rapidity which includes speeds greater than 'c'. So "superluminal" [faster than light] recession 'velocities' are common. Also, the speeds and distances and other effects you calculate in cosmology are model dependent; that is, as you describe cosmological effects via different models, you get different answers because, for example, the 'metric' [distance measure] is different in different models. No one cosmological model answers all questions and provides all the best insights.

Some recommended Cosmology reading:

An introductory discussion of some of these effects [by Lineweaver and Davis, a standard reference in these forums, from Scientific American] go here:

http://space.mit.edu/~kcooksey/teaching/AY5/MisconceptionsabouttheBigBang_ScientificAmerican.pdf I found a wonderful discussion from 2007 here on redshift issues here:

https://www.physicsforums.com/showthr...nt+flow&page=4

Try reading posts from the 40's thru 50's and see the pros and cons about redshift interpretations.

When you think you understand those, try here to read Lineweaver and Davis' professional level article and you'll find [like me] there is a LOT more beneath the surface:

http://arxiv.org/abs/astro-ph/0310808

This article takes some real concentration!

 

[yuiop]

I was listening to a lecture about the expansion of the universe and found myself confused about the light we see from very distant galaxies. These galaxies are red shifted because they are moving away from us and the photons are being stretched. Does this mean that the galaxy will appear to be rotating slower than it actually is to us? If yes, is this what is meant by time dilation? Also, if the distant galaxy were to be moving towards us instead, would it appear to be rotating faster?

This is a very good question and I hope you get some thoughtful answers. Here are some thoughts to get you started. Consider a set of ideal galaxies that are all at rest with the "Hubble flow" such that the further away from us the faster they appear to be receding. If we measure the redshift from these galaxies we can interpret the results in a number of ways (some of which are naive.) Perhaps the most naive interpretation is that over vast distances, space is essentially flat and static the observes red shift is pure relativistic redshift, ie it has contributions from classical Doppler red shift and from relativistic time dilation. In this interpretation there is no stretching of photons in transit and the distant galaxies would be rotating slower to us due to time dilation relative to what is measured locally.

In another (perhaps more mainstream) interpretation, the galaxies in the Hubble flow are (near enough on the grand scale of things) at rest with their local "space" just as we are (near as dammit, relative to the local CMBR) and so there is no relative time dilation in the strictly SR sense. The observed redshift is accounted for by the "stretched" wavelength explanation. In this interpretation there is a sense in which distant galaxies can be moving away from us at greater than the speed of light. Some support for this interpretation is the fact that the observers at rest with the Hubble flow locally observe the local CMBR to be isotropic however far away from us they are. It is only when they move relative to there local "space" so that they are not at rest with the Hubble flow, that the CMBR becomes anisotropic.

Interestingly, when Saul Perlmutter's Supernova Cosmology Project team made observations of a type 1A supernovae explosion that helped them deduce that the expansion of the universe was accelerating, they noticed that the time for the flash of the explosion to decay from peak brightness was delayed by a factor that corresponded exactly with that predicted by relativity. (We have to question what interpretation of universe expansion he was using here). This suggests that the rotation of galaxies would appear to similarly time dilated.

One difficulty is that very distant galaxies with high redshift are so distant that they appear as point sources like single stars and rotation velocities of the galaxies are very difficult if not impossible to measure.

My guess is that if we calculate the velocity of galaxies and calculate there nominal relative velocity using the relativistic Doppler equation, then their rotation rate will slow down in accordance with the time dilation expected for that nominal velocity, independent of whatever interpretation we use.

 

[Naty1]

Here is synopsis of Doppler shift and redshift that I adapted from two experts here here Marcus, PAllen:

Redshift is a measured shift in received frequency versus emitted frequency. Doppler [shift] refers to one of two formulas (pre-relativistic; relativistic) for relating redshift to velocity. Doppler shift is a particular explanation of redshift,relating velocity between source and receiver, with a particular formula. It is not a measure of redshift.

[Doppler is like a radar speed trap: The radar signal goes out and returns and keeps the same 'color', but we record the difference in wavelength as a speed measure.]

Where the speeds of source and the receiver relative to the medium are lower than the velocity of waves in the medium, we use the classical Doppler shift formula; in cosmology, where we deal with lightspeed 'c' and recessional 'velocities' greater than 'c' we need the relativistic version of the formula.

Cosmological redshift is typically considered distinct from Doppler redshift because it is a relation between distance and redshift rather than [Doppler] speed and redshift, under the assumption that both source and target are motionless relative to center of mass of the local matter (here, local is quite large - galaxy or galaxy cluster). [These are also Yuiop's assumptions]

Don’t think of the redshift as a Doppler [relative velocity] effect. It is not the result of some particular speed. The [Redshift] formula involves the entire [varying] factor by which cosmological distances have expanded during the whole time the light has been traveling.