I was reading this page:
http://www.guardian.co.uk/science/2011/oct/23/brian-cox-jeff-forshaw-answers
and I found this sentence by Brian Cox:
That seems to imply that everything is flying away from us and we're therefore somehow in a privileged position; that isn't true. The way it's often described is if you imagine some bread with raisins in it that you're baking in the oven and as you heat it, it expands. On any particular raisin, if you look, you can see all the other raisins receding from it. So it's space that stretching, it's not that everything's flying away.
I already heard this raisins analogy, but it never persuaded me:
I understand that the "big bang" is more like a "big stretch", and I see how every 2 observers in the universe are being distanced farther and farther away (regardless of their position)
Yet one of the Big Bang ideas is that the universe isn't anymore considered infinite and completely homogeneous
But the fact that the universe is finite, while inflating to me implicates that it should have some kind of bounds (not that we can reach these "bounds", since our distance to them is getting bigger, but they should still exist)
(And the fact that it's spreading inhomogeneous mass and energy over big distances, is thus making it more homogeneous, but this doesn't probably matter)
So: the very idea of a big bang seems to me in contradiction to the assertion that there's no such thing as a "center of the universe":
If it has a finite mass and some kind of bounds, then it should also have a barycenter.
And if we consider the bread with raisins analogy: the bread has a center from which it's expanding
Surely, the universe isn't homogeneous (like the distribution of the raisins), and so, in its hypothetical center, there may not be actually anything... but I think (even if it's really unlikely) it should still be theoretically possible to have a raisin in the exact centre of the bread
Answer
The question of the center of the universe is a question of whether the universe is the same at all points. The easiest way to see that the universe now does not have a center is to use the Newtonian big bang. In such a description, everything is flying away from everything else with a velocity vector proportional to the position vector, where we are at the origin:
$$ v= a r $$
Suppose you are on one of the objects at position r. Then, from your point of view, everything is shifted in $r$, because of your new center $r\rightarrow r-r_0$, but everything is also shifted in $v$, because your velocity is not zero relative to us, but you will describe yourself as stationary. So $v\rightarrow v-ar_0$. The result is that you describe the objects as flying away from you with a speed proportional to their position vector.
The Newtonian big-bang is homogenous--- everyone feels that they are at the center. It is exactly analogous to the relativistic big-bang, which is also homogenous. But the Newtonian big-bang is infinite, while the relativistic big-bang is finite, in that there is no horizon in Newton.
The horizon in relativity occurs where the objects fly away at the speed of light, or equivalently, where the light-rays that reach you emerge straight from the big-bang (since looking further out is looking back in time). The horizon makes the space bounded, but it does not pick out a center, because every point has a horizon symmetric around itself.
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