Does (it make sense to say that ) the universe has a center?

Question

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 1

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.

Answer 2

The answer to your question depends on knowing what the true configuration of the universe is, and we do not have that knowledge at this time. It is conceivable that the space we see is somehow naturally embedded in a larger space for which the notion of center is well-defined. It is also quite possible that we live in a space where the notion of center is not meaningful.

We tend to build up an intuition that everything has a center, because that is true of everyday objects around us, such as loaves of raisin bread. These objects can be bounded inside a finite size box, and the space around us is flat enough that we can use Euclidean methods to determine centers (e.g., by integrating a characteristic function multiplied by a Cartesian coordinate). If our universe is in fact of this form, then it is meaningful to have a distinguished place that we can point to and call the center. So far, there doesn't seem to be any experimental evidence in favor of the idea that our universe has such a shape.

Most abstract manifolds that are potential spacetimes have no distinguished point that can be viewed as a center. These spacetimes are presented as an infinite set of points, together with a notion of nearness, and there is usually a group of diffeomorphisms that moves points around but doesn't really change the physics. This symmetry is what usually destroys any hope of having a point for which we have a good reason to describe as "the center" - we expect the physics to be the same at such a point and at nearby points, so that point is not distinguished for any physical reason.

Answer 3

General Relativity is about describing (the dynamics of) a curved spacetime. So you need a collection of events, and a metric that tells you the interval between nearby events.

That's it.

You can a stress energy source term too. But anything else is either unphysical or a straight up bias brought into a theory for no reason. There are some easily visualized examples that show a homogeneous finite space without boundary, let's start with the simplest.

Start with radial coordinates $r \in[0,\infty)$ and $\phi \in [0,2\pi)$ for the polar plane then consider the metrics like

$ds^2=c^2dr^2-\left( a(r)\right)^2\left( d\phi^2 \right)$

Where $r$ is a time coordinate and different $\phi$ correspond to different locations. So the big bang is the origin and all the rays emanating from the origin are the distinct locations, all the concentric rings are the different moments of cosmological time. And every location is perfectly equal to every other.

Similarly you can have a 3d spacetime with a 2d space. Start with spherical coordinates $r \in [0,\infty),$ $\phi \in [0,2\pi)$ and $\theta \in [0,\pi]$ then consider the metrics like

$ds^2=c^2dr^2-\left( a(r)\right)^2\left( d\theta^2+\sin^2\theta d\phi^2 \right)$

Where $r$ is a time coordinate and different $\theta$ and $\phi$ correspond to different locations. So the big bang is the origin and all the rays emanating from the origin are the distinct locations, all the concentric spherical thin shells are the different moments of cosmological time. And every location is perfectly equal to every other.

Similarly you can have a 4d spacetime, the concentric hyperspheres are the different moments, and the locations again are the rays from the origin.

So questions can be answered, such as expanding space, it expands into the future because surfaces farther from the origin are farther in the future. Why every point looks the same, every point on a circle looks the same, every point on a sphere looks the same and every point of a hypersphere looks the same.

There are no edges, just like a circle or a sphere has no edge. And all the General Relativity happens by finding out the dynamics of $a(r).$ And doing that is standard cosmology.

Answer 4

Yes! The center of the universe is the one place where time is "correct". That is, not influenced by extraneous gravitational fields. So by 'correct' I mean where time is running faster (or no slower) than anywhere else.

It is left as an exercise to the reader how this location might be found.

Answer 5

It does makes sense to say where is the center of Universe. But unfortunately it is always explained in ambiguous way.One easy way to explain is this video

The explanation basically depends from what reference point you are looking at the Universe. For example if I am standing on Earth, I can say the Earth is stationary but if I am on another planet, I can see that the Earth moving not only in its orbit but also around its own axis.

Basically there no explosion in Big Bang. It was only an Expansion. Simply matter expanded in sort of a blast and started moving away from each other. It is much like a gas in a container. Lets suddenly expand the container, all the molecules will move away from each other. There will be no center because the expansion is uniform. Important point here inside that gas, not outside . So to you it will look as if you are the center of Universe because everything is moving away from you.

Now if you change the reference point, lets say you are looking at the universe from outside, you will see thee is a center, from which everything is expanding. Since we are inside that gas/matter, we assume there is no center because to use everything seems expanding from every single object. So I guess it really depends from which angle you are looking at the universe.