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

[Vanadium 50]

Just playing with code tags:

do
   abbott287 posts a misconception
   PF corrects it
while universe <> heat death

Abbott, if you want to make progress, you're going to have to give up some of the things you think you know but are not the case.

 

[timmdeeg]

This is a space that is finite, three dimensional, and a valid manifold. If you travel far enough in any direction you return to your start point.

My understanding is that if our universe were like this, there ought to be measurable curvature. This would manifest somehow in cosmological observations, but currently the measured curvature of the universe is consistent with zero. Zero curvature is consistent with the FRW metric, an infinite and flat manifold expanding over time as discussed at length above.

Not only. Zero spatial curvature is also consistent with a 3-torus which is finite in size.

 

[Khashishi]

Abbott, you are making assumptions which may be intuitively obvious, but the real world is actually not intuitive. We don't know that the universe is infinite, but we don't know that the universe is not infinite either. You can't just discount an infinite universe on pure philosophical grounds.
There could be an infinite future and an infinite past, or an infinite future and finite past, or even a finite future and finite past. These are questions we can only answer by making models and testing them with experiments.

Ex: There were an infinite amount of days before I was born, so I could never have been born. Ex:2. Yes there were an infinite amount of days, but you were born on one of them... Both examples can be right or wrong, depending on how you look at it.

It's not a matter of how you look at it. You are trying to use logic to answer a question that can't be answered by logic. Logical deduction requires you to start from certain assumptions or axioms. It doesn't help if we don't know all the laws of the universe. Probability fails when you have an infinite event space. That doesn't mean that it's impossible to have an infinite event space.

 

[dreens]

Not only. Zero spatial curvature is also consistent with a 3-torus which is finite in size.

Agreed. That’s a more obvious way to get a finite, uncurved, 3D space. Especially if you think of a 3-torus as a cube with opposite sides identified, so that if you go through the right you appear on the left, etc.

Does anyone know how well this possibility is excluded by astrophysical observations?

If we were a 3-torus, everything would repeat itself on a 3D lattice with three potentially different length scales. We know of very distant objects, like quasars, which are clearly not repeating on a scale much smaller than our distance to them. Maybe this sets the limit?

 

[mfb]

A torus is not isotropic - the directions aligned with the sides look different from the other directions. It is not ruled out by experiment, but it would be odd.

Whatever the shape is, even if it is finite the universe has to be notably larger than the observable universe, otherwise we would see a structure in the cosmic microwave background.

 

[timmdeeg]

Agreed. That’s a more obvious way to get a finite, uncurved, 3D space. Especially if you think of a 3-torus as a cube with opposite sides identified, so that if you go through the right you appear on the left, etc.

Does anyone know how well this possibility is excluded by astrophysical observations?

Interestingly Steiner has claimed that a torus "gave the best match" to the WMAP data.

https://www.nature.com/news/2008/080523/full/news.2008.854.html
Steiner’s team used three separate techniques to compare predictions of how the temperature fluctuations in different areas of the sky should match up in both an infinite Universe and a doughnut one. In each case, the doughnut gave the best match to the Wilkinson Microwave Anisotropy Probe data. The team has even been able to pin point the probable size of the Universe, which would take around 56 billion light years to cross.

But this wasn't confirmed by the Planck data. And I think cosmologists anyway don't believe a non-trivial topology to be likely.

 

[mfb]

“Gives the best match” is not a good argument if you compare an easy model to one with 6 (?) free parameters more.

 

[dreens]

Interestingly Steiner has claimed that a torus "gave the best match" to the WMAP data.

https://www.nature.com/news/2008/080523/full/news.2008.854.html

Thanks for the WMAP link, great stuff!

“Gives the best match” is not a good argument if you compare an easy model to one with 6 (?) free parameters more.

Touché. I agree with your “(?)” though- I think it’s only 1 or 2 paramaters. The donut doesn’t care where you think of the edge as being, so that knocks out 3. The dataset is probably only 2D so that knocks out another. Then they could have fixed the sides to have the same length to remove another.

 

[mfb]

Ah right, your position doesn't matter. You still have the overall size and three degrees of freedom for the orientation of the axes, for a total of four that should all be observable.
If you want a more general torus, you can give it three different lengths, or even angles different from 90 degrees between the axes. You can add many degrees of freedom if you want.

 

[dreens]

Ah of course the orientation. Hopefully we’ve finally ironed out each other’s mistakes ;-)

The lack of isopotry in direction is so odd in the 3-torus. Would definitely be a real surprise if that was our universe.

Although not as big a surprise as if we were a 3D version of a Klein bottle- square with opposite sides identified but one reversed. Can that one even be flat? Trippy. I guess it’s the same dilemma as for the curled up dimensions. So many possibilities and how to decide which one is somehow more elegant than other.

 

[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.