# Why are the distant stars so far apart?

1. Aug 13, 2009

### beeresearch

This may be a totally silly question, it's nagging at me and I figure you guys can give me peace.

We observe that the Universe is expanding, and draw the conclusion that matter started of in a dense state.......,

.. so why is it, that when we look back in time, to the furthest observable part of the universe, the stars are so far apart?

How did they get that far apart so long ago?

Steven

2. Aug 13, 2009

### tiny-tim

Hi Steven!

I think it's because we can only see to the edge of our observable universe, which is where light can't keep up with the expansion of space, and that's nowhere near the beginning.

3. Aug 13, 2009

### beeresearch

Tim,

So what if we hypothetically counted all galaxies in a spherical shell at some distance r from here, then counted all galaxies at some distance 2r from here,....

Would it follow from dividing the number of galaxies counted by 4(pi)r^2, that the density increases with distance?

Steven

4. Aug 13, 2009

### ideasrule

By definition, the edge of our observable universe is the beginning. That is, the photons we see from the very edge of the observable universe are from the Big Bang itself. However, we can't in actuality see all of the observable universe; the oldest detectable light is the cosmic microwave background, and that light was emitted when the universe was only 400 000 years old.

To the OP: I don't know what you mean by "far apart"; if you do the math and calculate how far apart the distant galaxies really were, you'll see that they were actually very close at the time the light we're now receiving was emitted. If you mean that the distant galaxies are spread evenly across the sky, that's just because the universe is roughly uniform and the galaxy density should be similar in all directions. There's no paradox here.

5. Aug 13, 2009

### beeresearch

...yes excactly, the stars/galaxies appear to be uniformly distributed, how can this not be a contradiction, when the light from the most distant stars is supposed to be from shortly after the big bang?

We look back in time and still see a mass distribution wich is the same as it is now????

Obviously if this were not the case, we would see the whole sky as white, or alternatively see all the stars in one direction, which we don't.

My guess is that someone over there at the horizon is looking back at us and pondering the same question ;)

Steven

6. Aug 13, 2009

### PRDan4th

If the big bang was a point in time/space 13.7 billion years ago and we can only see the light emitted when it was 400,000 years old, then if we could see back further 400,000 years we would see a point in all directions that we look. Therefore everything we see at the visible edge of the universe is quite close together rather than far apart.

7. Aug 13, 2009

### ideasrule

Alright, a detailed explanation. Let's consider all galaxies that are 11 billion light years away (measured by the travel time of light).

Let's time-travel to the moment when these galaxies were only 2 billion light years away. They all emit light, and some of this light heads towards the Milky Way. Imagine a ball, representing the Milky Way, surrounded by a number of equidistant balls representing the other galaxies. The galaxies all shoot an arrow (representing light) towards the central ball. The Universe expands; the distance from the Milky Way to these galaxies grows; eventually, the red-shifted light catches up with Earth. The light rays, or the arrows, arrive at Earth from all directions. That's why distant galaxies are found distributed evenly across the sky.

8. Aug 13, 2009

### beeresearch

Amazing then how distorted space must be....

Imagine observing one of those Galaxies 11 bn light years in the past, then rotating your telescope 180˚ and observing another Galaxy in the opposite direction 11 bn light years away, and drawing the conclusion that these two Galaxies are actually very close to each other, even though we intuitively would calculate that they are (pi)r or at least 2r apart, or 35 bn light years apart.

The paradox here is that if they were 22-35 bn light years apart 11 bn years ago, then the Universe would have had to be that old 11 bn years ago.

Unless space itself is shorter in the past, in such a way that euclidean geometry does not hold. If time at the observers distant event horizon is at a standstill, then we can can justify the paradox, by saying that the surface area of the ball that forms the observable Universe is constant.

Area = (4(pi)(r-r=∞)^2)X = K

We know that 4(pi)r^2 holds for small radii, but it appears to me at least, that for large radii the surface area to radius ratio does not hold, and that it flattens out to a level xr=xA for large radii.

Steven

9. Aug 13, 2009

### marcus

If you want to give clear explanations of the kind of thing OP asked about, I would advise you to use proper distance which is what you'd measure if you could freeze expansion.

What beeres, the OP, asked about was essentially the angular size and angular separation of stuff that we see from early times---that is, high redshifts.

What that depends on, a lot, is how far the matter was from our matter then.
As a real distance. (the relation between light travel time and real distance is very irregular due to different rates of expansion during travel, it depends on when the trip was made, better not to use traveltime as measure of distance in this situations)

Ned Wright's calculator gives you angular size conversion numbers for the various redshifts.

But a good way to understand is with a simple example. Back around 380,000 some matter (call it "A") radiated some light which we are now receiving as microwave. The actual distance to A then, if you could have frozen expansion, was only 41 million LY! That's fairly close.
Matter A and our matter (which became our galaxy and us) were only 41 million LY apart.
Now we are 45 billion LY apart. The conventional figure for the microwave background redshift is z = 1090. That's how much the distances have expanded and also the wavelengths, while the light was traveling.

So when we look back in time----to high redshifts like z = 1090----we really are examining a very dense universe where the material which eventually became millions of galaxies was arrayed around us on a sphere with radius only a measely 41 million LY.
So dense in fact that sound waves could travel through it and did so, contributing overdense and underdense regions that became part of the cobwebby structure of vast strands and clusters of galaxies which we can observe. We observe the (effects of the) soundwaves in that denser gaseous universe.

You can do the same with smaller redshifts like z = 7, where we can already see protogalaxies, quasars. Ned Wright's calculator will tell you the angular-size distance, which was the distance then (real distance measured by light travel if you could have frozen expansion then).

Thanks for explaining the angular separation of the stars to beer-research. I'm just suggesting how to improve/sharpen the concepts, not any basic change.
The physical meaning of angular separation in the sky depends on the distance that you attribute, which should be the distance then. You should always be prepared to grab the wright calculator and find out what distance then corresponds to a given redshift.

For people who aren't familiar with the wright calculator---just google "wright calculator" and you will get
http://www.astro.ucla.edu/~wright/CosmoCalc.html
and if you put in z=7 you will get that the distance then was 3.6 billion LY, and of course the distance now is 7 times farther. It also tells the travel time. (but not the travel time "distance", which is a concept for kiddies.)

Last edited: Aug 13, 2009
10. Aug 13, 2009

Marcus,