# Cmb 13.7 billion light years away

1. Oct 25, 2009

### xMonty

Cosmic Microwave Background radiation is coming to us from about 13.7 billion light years away... is that correct?

The reason its coming from 13.7 billion ly away is because the universe is 13.7 billion years old... is that correct?

so when the universe was only 12 billion years old the CMB coming to us was slightly hotter and coming to us from 12 billion ly away?
And using the same logic when the universe is 15 billion years old CMB will come to us from 15 billion ly.. is that correct?

2. Oct 25, 2009

### Amanheis

Re: Cmb

Unfortunately, you got it all wrong. The universe is expanding, so the source of the CMB that we observe today is further away.
Measuring distances in the universe is not a trivial thing to do, you can read up on it here:
http://arxiv.org/pdf/astro-ph/9905116

3. Oct 25, 2009

### xMonty

Re: Cmb

Great

i understand that the source was close to us when it emitted the radiation and now its far far away but we see the CMB as coming from around 13 billion ly, what is the reason its coming from 13b?

4. Oct 25, 2009

### ideasrule

Re: Cmb

It's NOT coming from 13 billion ly. Keep reading; it's coming from roughly the edge of the observable universe, which is roughly 13.7*3 billion ly away.

5. Oct 25, 2009

### marcus

Re: Cmb

It often causes confusion when people use light travel time as a measure of distance.
There's a website aimed at teen-agers where they use that as a measure of distance. But astronomers are more apt to use the presentday actual distance----gauged by how long it would take light to travel if you could freeze expansion.

That is less ambiguous. The expansion rate has varied greatly over time, so the actual distance to the source NOW doesn't have any simple fixed relation to the time the light has been en route to us. It is better to talk in terms of actual distance (with frozen expansion) than to talk about light travel time.

Although I can't be sure what you are saying, it sounds like you might have the right physical picture in mind but are simply using dorky distance terminology. The other people could simply be confused by the way you express distance. What I would advise is that you start talking in actual distance, and also in redshift terms. And get familiar with the online calculator that calculates the NOW distance when you give it an incoming redshift. The usual symbol for redshift is z.

Google "wright calculator". (Ned Wright is a top cosmologist and has the most popular cosmo website). It will immediately tell you the distance corresponding to a redshift of z = 3.

Now you can plug in different z. The redshift of the CMB happens to be about 1090. If you plug that in for z, and press calculate, it will tell you the presentday distance from us to the matter that (way back when) emitted the light that is now arriving to us as microwave background.

Last edited: Oct 25, 2009
6. Oct 26, 2009

### marcus

Re: Cmb

When you first google "wright calculator" and go to
http://www.astro.ucla.edu/~wright/CosmoCalc.html
it will tell you that, as an example, redshift z = 3 means that
the light started out when the emitter was 5.3 billion ly from here

(actually it says 5.2678 but I round off to 5.3)

and the light took 11.5 billion years to get here (do you see where it says that?)

and it says that today the distance to the emitter is 21.1 billion light years.

=======================
The distance then, the distance to the emitter when the light started on its journey, is technically called "angular size distance". Do you see where the calculator gives it?

The actual distance now (what would be measured by a powerful radar if you could freeze expansion) is technically called "comoving". It is the distance which fits in with the Hubble Law and a bunch of other cosmology basics.
=======================

Redshift is the fractional extra that the wavelengths are longer by. z = 0.1 means longer by 10 percent. So the length now is 1.1 times what it was at the time of emission.

z = 0.66 means longer by 66 percent. Length now is 1.66 times longer than at emission.

z = 3 means that the waves are 4 times longer than when they were emitted.

the factor you multiply by, to convert length then into length now, or to convert distance then into distance now, is always 1+z.

z is a really handy number. So what do you get for the distances then and now, to the material which emitted the CMB?

You have to plug 1090 into the calculator to get those distances.

7. Oct 26, 2009

### mikeph

Re: Cmb

It has been travelling for 13.7 billion years, but the expansion of the universe over that period means that the actual distance from emission to observation points is now a lot longer. If we had a static universe then you would be correct.

You're right about the temperature though, but I am not sure about your reasoning. The universe expands due to whatever density contributions you have, and that expansion means the energy density of the CMB photons decreases, since you have the same number of photons in a larger volume, and also the wavelength of the photons is "streched" due to expansion. So the CMB was once a lot hotter than it currently is, and as time goes on, so long as expansion continues, it will be cooler.

8. Oct 26, 2009

### xMonty

Re: Cmb

Thank you for such detailed explanation, i got what you mean
i plugged in z = 1090 and i got these values

It is now 13.666 Gyr since the Big Bang.
The age at redshift z was 0.377 Myr.
The light travel time was 13.665 Gyr.
The comoving radial distance, which goes into Hubble's law, is 13995.7 Mpc or 45.648 Gly.

ok here is what i make of the above numbers

Light was emitted towards us from a source which was 0.041834 Gly away
Universe was expanding so light had more and more distance to cover and finally it got to us after traveling for 13.665 Gyr.
but because of expansion of universe the source was also receding so when the light finally got to us (after 13.665 Gyr) the source is actually 45.648 Gly away.

(Can this be compared to the Sun scenario, light from sun takes 8 mins to get here so when i look up at sun its not really at the place where it seems its a bit further to the right)

This brings me to another question.
We are seeing the light (CMB) that was emitted from something which was 0.041834 Gly away so what happened to stuff that was closer than 0.041834 Gly and stuff that was further than 0.041834 Gly?

i am guessing that the closer stuff's photons have passed us and the further stuff's photons havent gotten to us yet, is this correct?

9. Oct 26, 2009

### Chronos

Re: Cmb

10. Oct 26, 2009

### xMonty

Re: Cmb

Damn why didnt i think of that

11. Oct 26, 2009

### marcus

Re: Cmb

Absolutely right.
========================

There is another conceptual tool which I anticipate you might eventually find a need for. That is the idea of an observer being at rest with respect to the CMB.

An observer is at rest wrt Background if the temperature of the microwave sky is almost exactly the same in all directions.
No doppler "dipole" in the temperature map.

An observer moving at a significant speed wrt Background will see a doppler hotspot ahead and a corresponding coldspot to the rear. The forward temperature increase will be the same fraction of the average sky temperature as the speed of motion expressed as a fraction of the speed of light.

The solar system is moving (as a result of combined motions of the galaxy and the sun's orbit within the galaxy) in the direction of constellation Leo at a speed which amounts to 1/8 of one percent of the speed of light.
So the microwave background is 1/8 of one percent hotter in the Leo direction. And actually the galaxies in that direction appear to be receding from us at rates which are 380 km/s less than Hubble Law would have us expect. This has to be allowed for when data is interpreted.

"Morally speaking" to be at rest wrt Background is to be at rest with respect to the ancient matter of the universe, or at least the light that emanated from it. Or equivalently to be at rest relative to the expansion process itself (which has been called the "Hubble flow"). Before the CMB was observed they had this same idea of being at rest, but the accepted term for it was "comoving with the Hubble flow". The Hubble law only works, is the same proportion in all directions, for an observer at universe-rest. So even before CMB was observed, and its dipole measured, astronomers could detect the motion of the solar system wrt the expansion process, and adjust the data to eliminate it.
This idea of an observer at rest wrt Background is useful in several contexts. Kind of basic.

I appreciated the lucidity of your questions and your response. Thanks for trying out Ned Wright's calculator. He has a fun computer animation to watch which shows photons struggling to get from one galaxy to another while the distances between galaxies are increasing. If you want, google "wright balloon model".
In the balloon model, points which stay at the same latitude/longitude are at rest wrt the expansion process, equivalently at rest relative to Background. In the animation, the galaxies (being approximately at rest) stay at the same location on the balloon surface, while the photons move at some fixed speed like 1 millimeter per second. Of course it is merely a 2D analogy, a 3D hypersphere is hard to imagine, so one resorts to the 2D toy version.

Last edited: Oct 26, 2009
12. Oct 26, 2009

### xMonty

Re: Cmb

One more question what will happen to the CMB as time goes by, i am guessing it will get more and more red shifted and the light travel time will increase as time passes.

Can you suggest some book or online material where i can read up more on this stuff?

Thanks a lot for your time

13. Oct 26, 2009

### marcus

Re: Cmb

A vision of the CMB future is contained in an article by Larry Krauss and somebody else.
It is on arxiv. You could learn to use arxiv.org.

That gets you to http://arxiv.org/
Click on "search" at the top of the page.
Type "L Krauss" into the author box. The year is around 2007 as I recall but you don't need that, just the author.

Yes, I did the search, here it is:
http://arxiv.org/abs/0704.0221

Heh heh. Gloomy picture. The CMB redshifts so much as to become undetectable. Cosmologists become clueless. The universe no longer offers enough clues for them to deduce that it is expanding. (Unless of course they have reliable records from earlier observation.) The poor dolts think the universe is static, consisting just of the Milkyway galaxy plus whatever has accreted to it. The moral is we should get busy and do our cosmology now, while it is still possible. Things won't always be so easy

The CMB will always consist of light that was emitted around year 380,000, because that was when the gas filling space became cool enough to be effectively transparent. It was no longer so ionized that it kept scattering the photons. So the photons were free to fly in all directions from that moment onwards.

So since the CMB will always be light emitted in or around year 380,000 the light travel time will always be the expansion age of the universe minus 0.38 (or say 0.4) million. As you say, the light travel time will increase as time passes.

As for books or online resources. Ned Wright's website is pretty good. He's a worldclass cosmologist who likes to teach as well. Wayne Hu also has a website. I haven't used it much but he is another top cosmologist. Charles Lineweaver is another prominent person. I have a link in my signature (at bottom of post) to a SciAm article by him.
About books, you can waste money on hardcopy books unless you browse them first. A good way to browse is to visit a college or university library. Sometimes they have a small departmental reading room at the Astro department. Are you near a campus? The important thing is to get something that is at the right level. Popular books for mass audience oversimplify so much that they can give the wrong impression. So the idea would be to find something that is not too hard for you but which is above the common denom mass audience level.
If you are at a university library you might also want to look at the current authoritative maximum difficulty book on cosmology, to see what a graduate student would be reading. I think that would be Steven Weinberg's book titled simply "Cosmology". He's a Nobel particle physicist who got more interested in cosmology and moved over. So after writing the book on Quantum Field Theory he changed fields and now has written the book on Cosmology. Just flip thru and see what the chapter headings are. So what if it is over-the-head hard? Why not? Take a squint at the whole mountain but don't spend your money on the book.

Last edited: Oct 26, 2009
14. Oct 26, 2009

### mikeph

Re: Cmb

My text was by Andrew Wiley from the University of Sussex, very approachable book on cosmology which avoids the general relativity which usually makes it so inaccessible.

15. Oct 26, 2009

### xMonty

Re: Cmb

Great there's a happy thought :uhh:

Yo easy bro... didnt get that... need to think about that for a while... so we will never ever see past CMB but why wont the photons ever get past us (.... thinking... when they get past us new ones will take their place..)

16. Oct 27, 2009

### Chronos

Re: Cmb

CMB photons were not an instantanous emission, so we see them over an extended interval. Time dilation stretches that interval out for a virtual eternity.

17. Oct 27, 2009

### xMonty

Re: Cmb

That was really enlightening (actually it explained a lot of things i was confused about... kind if an aahhhhaaa moment ) , where can i read more on this?

18. Oct 28, 2009