# Redshift calculation problem

1. May 26, 2012

### eggman100

I have my answer of the doppler shifting as 2.5 meaning redshift,
but what does this mean, 2.5 what? if its 2.5 'units' then how can I work out the speed of the object going from my Stationary position?

it's all nice knowing for example my object could be going at 0.1m under the speed of light but i want to know if it's possible to work out the speed of the object using observable red shift?

anyone know?

Thanks =)

2. May 26, 2012

### JDoolin

http://en.wikipedia.org/wiki/Redshift

z = emitted frequency / observed frequency - 1

So unless I've made a careless error, the observed frequency is slower by a factor of 3.5.

If you want to find the velocity see attached.

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3. May 29, 2012

### Naty1

I did not read all of #2, but starting with that relativistic Doppler version is the way to go.

Last edited: May 29, 2012
4. May 29, 2012

### Naty1

I just noticed under the Wikipedia link provided above that the actual relativistic Doppler shift {see the "Redshift Summary table} apparently applies to flat Minkowski space, not our universe...via the FLRW model ......so what's different between the two redshift calculations???

5. May 29, 2012

### JDoolin

There are two different hypotheses regarding the nature of the universe, and the Big Bang. One is that redshift is caused predominantly by recession velocity. The other is that redshift is caused by a difference in the "scale factor" of space.

The second hypothesis more-or-less derives from the (probably reasonable) assumption that we occupy no special place in the universe (i.e. the cosmological principle) and from the seemingly reasonable premise that "if the universe is everywhere isotropic, it must be everywhere homogeneous." For the universe to be homogeneous and growing over time, the concept of recession doesn't quite work right.

So in the late 20's or early 30's Eddington introduced an idea of stretching space, and we've been stuck with it, ever since.

6. May 29, 2012

### Naty1

yes, I agree with your explanation.....
but how does one calculate the velocity as in the above example in the FRW model?? It never occurred to me previosuly that the Doppler calculation was for flat spacetime.....I never thought about it....

As I understand it, the scale factor is unique to the FRW model, and found some aspects of it here:
http://en.wikipedia.org/wiki/Friedmann-Lemaître-Robertson-Walker_metric

All I understand so far is that the scale factor is a non uniform one wrsp to time....
Thanks.

7. May 30, 2012

### JDoolin

Here, I'll summarize a little bit about what I know about it. I recently got a writing pad and heard about this Jing software. It's kind of nice, for a change, since I can't read my own notes most of the time, I could watch these videos and actually remember what in the world I was doing.

http://screencast.com/t/PTSKqy01uNVI
Looking up the FLRW metric on Wikipedia, I "imagine" that dSIGMA is sort of a volume element, then scroll down to the definition of dSIGMA, and find it's sort of a modified form of a volume element. I'm not entirely confident in the concept of "Reduced circumference." An aside about the tangent function.

http://screencast.com/t/gnazhwpw5hFU
Trying to convert dSIGMA from spherical into cartesian Coordinates. (I'm not well-practiced at differential equations, by the way, so I'm not entirely sure this approach will get you very far). derivatives of arc-cosine and arc-tangents found at: http://www.themathpage.com/acalc/inverse-trig.htm. This video starts the problem but doesn't finish it.

http://screencast.com/t/ui4UQ63mhvn
I remembered that when I've tried this problem before, I was converting from cartesian-to-spherical, which may be easier to do, but still quite time-consuming. Again, this video only starts the problem. It would take much longer than five minutes to do the whole thing.

http://screencast.com/t/apU5PpGn
Here are Einstein Field Equations, and two solutions to it; the FLRW metric, and the Schwarzschild metric, Coefficients in front of dr^2 and dt^2. Effect of setting k=0 and a(t)=1 in the FLRW metric. This video asks a couple of questions that I really never have figured out. (1) how can you plug these metrics into the EFE's and actually see that they are "solutions" and (2) How can you have a function of r as a coefficient of the dr^2 term, and still be a homogeneous metric?

8. May 31, 2012

### ibysaiyan

Redshift is dimensionless since redshift by definition is : Observed velocity of an object / speed of light = ms^-1 / ms^-1 = 'n' integer , redshift tells us of the validity of Hubble's law. One can even define scale factor (cosmology) in terms of the redshift.

There are many variations of redshift formula :
Z = v/c is the simplest of all , for speeds << 1 .
On the other hand when you have redshift >>1, such as quark jets then we use the relativistic version (i think though I could be wrong since their apparent speed formula is different) :
Z = $\sqrt{[1+v/c ]/[ 1-v/c]}$

EDIT: Thanks Jdoolin for your informative post.

Last edited: May 31, 2012
9. Jun 1, 2012

### Naty1

I have more work to do on this myself, but that Jing software is cool.....