#expansion" class="postlink">Here's a reasonable writeup:
Quote:
According to the big bang theory all stars move outwards on the perimeter of a sphere from the center. The moving speed of this matter is much less than the speed of light. If that is correct how can telescopes pointed to the center today pick up any light emitted from stars that were formed billions of years ago when this light should have passed us long time ago? How does the red shift in the light frequency determine a distance?
Your questions stems from a slight misunderstanding about how we picture the expansion of the universe. As you write, one way to think about this, is to picture stars (actually galaxies, which are just bound conglomerations of stars) attached to the perimeter of a sphere, which itself is expanding, carrying the galaxies with it. Personally I like the balloon analogy, where one pictures an inflating balloon with little ants crawling around on the surface, representing the galaxies.
The key point in either analogy is that our three-dimensional space is represented by the (2D) SURFACE of the sphere/balloon. In this analogy it doesn't make sense to look at the center, since the center of the balloon isn't part of space. It lies somewhere in hyperspace, but our observations have nothing to say about this point. As the universe expands, the fabric of space itself is actually growing, the universe is getting larger, just like the surface area of the balloon. On average every ant on the surface is moving away from every other ant. I say "on average", because one must allow for the possibility of an ant (or a galaxy) moving relative to the underlying space, at a rate greater than the expansion itself. A real life example is M31 (Andromeda galaxy). It happens to have a large peculiar velocity, in a direction towards us, and is actually blueshifted. On average, however, all galaxies are moving away from all others.
It's also not true that this recession velocity must be less than the speed of light. Einstein's special relativity does state that nothing may travel faster than the speed of light, but this holds for objects moving with respect to an underlying reference frame. Einstein's theory says nothing about how fast space itself can expand. Two galaxies that are receding from each other at twice the speed of light due to the expansion of the underlying space, are not able to exchange any kind of information, since this information is confined to travel through the expanding space itself, at a speed no greater than the speed of light. Thus Einstein's theory is not violated in any way.
If you think through this expanding balloon analogy in more depth, you will discover that the rate of recession between two ants must be proportional to the distance between the two. Again, this distance would not be calculated by drawing a straight line from one ant to the other, piercing the surface of the balloon, but instead by measuring the distance from one to the other along the surface of the balloon. Think the distance between Sydney and London (10562 miles / 16997 km) - what's meant is the path along the surface of the earth, not the length of a hypothetical tunnel through the center of the earth.
So, the fact that we can pick up light emitted by galaxies billions of years ago is explained by the fact that the universe (the surface of the balloon) has expanded to an incredible size, and the photons we receive from these galaxies cannot travel outside of our three-dimensional world.
I think the above should have also clarified why redshift is proportional to distance. As you correctly state, the redshift depends on the relative speed between the objects. By the sphere/balloon analogy you now understand that in our expanding universe the average recession rate is proportional to distance and hence the direct relation between distance and redshift - Hubble's Law.
Edit -- applause to Lave for surely being the first person in the history of physics to describe a streak of piss as blueshifted.