Oldness/Flatness Problem

[otseng]

This has been mentioned a couple of times in different threads: Anthropic Principle and Intelligent Creation (God) as opposed to Evolution. But, I'd like to put this in its own thread.

So for debate. Why is the universe flat? That is, why does it have Euclidean geometry?

[otseng]

That's fine. It's a very common difficulty when met for the first time, so much so that there is a paper specifically aimed at overcoming this difficulty for students.

I know I might be asking for too much, but is there any possibility of a more accessible explanation for someone who is not pursuing a PhD in Cosmology? If not, then I think it's very understandable why few people can grasp the concept.

I don't see the problem unless you somehow imagine things being woven into that "fabric"- which, by General Relativity, they are not.

Would not matter have to be part of the fabric rather than just "sitting on top of it"? When we say "fabric", it is in 3 dimensions. There is no fourth dimension that matter can be a part of to allow it to sit on a 3 dimensional fabric.

I've thought of a test to determine if the fabric is indeed expanding. Position 3 small balls in outer space with a large distance between them. Determine the initial distance between them. Then after some time, measure it again and factor out any known forces acting on them (gravity, etc). If the fabric is expanding, the distance between them should be larger.

Are there any other tests (or even evidence) that the space-time fabric is expanding?

Another thing, I still am not convinced the universe is non-Euclidean. The observable universe is measured to be flat. Yet, scientists still claim that the unobservable universe is curved. How can this be reconciled with the evidence that it is flat?

[QED]

It's not so easy getting from A to B in Astrophysics without the mathematics. After a bit of searching I wondered if this webpage might help answer some of your questions about the expansion. The author uses a "raisins in cookie dough" analogy for the stretching of space, which I agree is better than the balloon. But it doesn't help with the Horizon problem, so I'll keep looking.

[otseng]

The author uses a "raisins in cookie dough" analogy for the stretching of space, which I agree is better than the balloon. But it doesn't help with the Horizon problem, so I'll keep looking.

Unfortunately, the cookie dough analogy makes things just as confusing.

What is the distance between two galaxies? In the old picture, this is an easy question to answer theoretically (though not necessarily in practice!). Just get yourself a giant tape measure and clip it to a faraway galaxy, then come back to our galaxy and hold on tight. As the galaxy moves away, it will pull on the tape measure, and you will easily be able to read off the distance as the tape measure unwinds... one billion light-years, one and half billion light-years, two billion light-years, etc.

In our new picture of the universe, however, with the raisins and the dough, the tape measure will not unwind at all as the universe expands, because the galaxies are not actually moving with respect to each other! Instead, it will read one billion light-years the whole time. You could be perfectly justified in saying that the distance between the galaxies has not changed as time goes on. When you bring the tape measure back in, however, you will notice something unusual; due to the stretching of space, your tape measure will have stretched as well, and if you compare it to an identical tape measure which you had sitting in your pocket the entire time, you will see that all the tick marks on it are twice as far apart as they used to be. Using the tape measure from your pocket as a reference, you would now say that the galaxy is two billion light-years away, even though the first tape measure said it was one billion light-years away. As you can see, the concept of "distance" in this new picture of the universe is somewhat more complicated than in the old picture! It is unclear whether the universe as a whole is really "expanding" - all that we really measure is a stretching of the space between each pair of galaxies. (Note that we might have to have an "imaginary" tape measure whose atoms aren't actually being held together by intermolecular forces in order for the scenario described above to actually take place as described.)

He says that the raisins in the cookie dough do not stretch. Yet, he says that the tape measure would stretch. Why the difference?

In fact, we can go a step further and imagine that the center isn't even there at all! How? Well, what if instead of just being really really big, the dough were infinitely big - that is, you could walk forever in a straight line and never reach a place where the dough ends. In that case, there really would be no center of the universe - the only way you can define the center is to mark out the edges and find the point that's equally in between all of them. So if the universe is infinitely big and has no edges, then it also has no center, not even on a theoretical level.

How can he say that the cookie dough is "infinitely big"?

If he means that the cookie dough is curved, then "infinitely big" is not the best way to describe it. It would just mean there is no edge.

If, however, he means an infinite volume, then can can an infinite volume start from a finite volume?

That's because on these relatively small scales, the effect of the universe's stretching is completely overwhelmed by other forces (i.e. the galaxy's gravity, the sun's gravity, the Earth's gravity, and the atomic forces which hold people's bodies together).

Here, he does say that some force is holding things together during the stretching.

And if forces are holding the raisins together, why wouldn't it also hold the measuring tape together?