If the universe is truly infinite in size....

[abbott287]

If you are imagining the big bang as a some kind of bomb explosion, that's a really wrong description.
You are still thinking as a point explosion.

Okay let's think like this. You have a plane with an "infinite" size. This will be the description of the universe. It's inifite, so you can't think of any edge or something else.

You are a creature that living on that surface. Now try to think like this; infinite plane divided be equal size squares. Each square has an area of $a^2$.

1-How many squares are they ?
The answer is infinite. Why ? Because universe is infinite
2-What's the total area of the universe ?
Well it's simple each square has an area of $a^2$ and there are infinite sqaures so the answer can be found by,
$a^2.∞$ which its equal to $∞$.

Now, let's think what happens in an expanding universe. The area of each square increases. Let's suppose it increased by twice respect to the current size.

3-Whats the area of the each square ?
Well simply $2a^2$.
4-Whats the total area of the universe?
Again, each square has $2a^2$ area and there are infinite squares so the answer would be,
$2a^2.∞=∞$
Well the universe expanded twice but since there are infinite squares the universe is still infinite.

Now let's come to the case where that, we are all interested. "What happens when each size of these squares gets smaller and smaller ?""

Lets suppose the squares are shrinked to a size where its area is now $(\frac {a} {4})^2=\frac {a^2} {16}$
5-What is the total area of the universe ?
Well each square has a size of $\frac {a^2} {16}$ and there are infinite squares, so the answer is still infinite.

The important thing is that we can do this process until a point where the area of the square reaches nearly zero. For example, area of the each square can be $0.000000000000001a^2$ but since there are "infinite" squares the total area of the universe will be again, infinite.

The cruical point is, the universe is still infinite at this "after big bang" stage. Universe is still infinite and you can't think this, like a growing thing explosion.

Now the important question is "What happens when the size of the each square becomes zero"

Let's try to calculate it. The area of each square is "0" but there are infinite squares, hence we get $0.∞$ which its "undefined".

This is the main problem that we are dealing with. Also this is the singularity that we can call.

You and every point on this "plane" universe can shrink to a state where the size gets till zero but at zero it becomes a singularity and our equations don't work.

Why we say "it happened everywhere" ?
As I said before each square on this infinite plane shrinks to an event that we call singularity.

Hope this helps

Thank you! That does help that view of infinity. But what if you say each square TRIED to doubled its size, but could not, as every square met another to infinity. There was ni way anything could expand, because it all went to infinity all ready. Same problem, the opposite way. It seems either way could be correct depending on how one defines infinity. Impossible right now, because we do not understand infinity. My mind would be the universe is expanding, so chances are the universe is not infinite. I can clearly see your point on arguing it the other way. Its the same argument I presented with a birthday. Both answers could be correct or incorrect. Its how you view infinity, which seems beyond our comprehension at this point in time.

 

[PeterDonis]

what if you say each square TRIED to doubled its size, but could not, as every square met another to infinity

Then your theory would not match observations, which is why, even though such a model is logically possible, it's not the one we use in cosmology.

It seems either way could be correct depending on how one defines infinity.

Mathematically, yes, either possibility is consistent. But physically, only one possibility matches observations.

Impossible right now, because we do not understand infinity.

Sure we do, at least as regards both of the possible models. We understand what their observational consequences are, and that only one of them matches observations.

 

[PeterDonis]

Thread closed for moderation.

 

[PeterDonis]

The OP question has been answered. Thread will remain closed.