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

[abbott287]

That turns out not to be the case. One can describe a notional rubber band without requiring that it be embedded in a higher dimensional space, infinite or not.

Which is just imagined. Not real.

 

[jbriggs444]

Which is just imagined. Not real.

How do you know it's not real?

That is, if there is no contradiction in the imagination of a hypothetical rubber band, how do you conjure up a contradiction in the possibility of an analogous real construct.

 

[russ_watters]

Which is just imagined. Not real.

Says who? I think it may be your imagination that is lacking; the math has no trouble describing it, despite your suggestion that it can't.

 

[PeroK]

Define infinite.

The simplest definition of "infinite" is "not finite".

 

[Arman777]

You seem to be contradicting yourself. You said do not think of it as a point, which is how I think of it.

Yes, it didnt started with a point. Big bang started with a singularity.

Then you told me the distance beteeen points was zero, which makes everything a point!

You can read the previous discussions for the answer, which I was also confused at that time.

Then if the big bang happened everywhere, there was a lot of something there pre big bang!

There was nothing before the big bang.

 

[gary350]

If the universe is not infinite that means is stops somewhere. If the universe stops then what is on the other side of the universe? It is beyond comprehension that the universe stops or is infinite.

 

[jbriggs444]

If the universe is not infinite that means is stops somewhere. If the universe stops then what is on the other side of that? It is beyond comprehension that the universe stops or is infinite.

You have to stop as thinking about the universe as being embedded in some containing [three dimensional?] space. It does not need to be embedded in anything.

 

[PeroK]

If the universe is not infinite that means is stops somewhere. If the universe stops then what is on the other side of the universe? It is beyond comprehension that the universe stops or is infinite.

One problem with saying that something is beyond comprehension is that it is an excuse to stop thinking or learning.

These questions in contrast could be an excuse to start thinking and learning.

There is a wealth of ideas in topology and geometry - not to mention General Relativity - that brings at least a measure of comprehension to such questions.

 

[Ibix]

These questions in contrast could be an excuse to start thinking and learning.

I had started to write almost exactly this, citing Einstein's famous dislike of quantum mechanics as an example.

 

[dreens]

If the universe is not infinite that means...

I like you’re thinking here. There are ways that a universe obeying general relativity could exist and be finite. I don’t think a universe with a sharp edge is viable mathematically... the curvature tensor would become undefined at the edge. But one of the simplest possibilities would be S^3, the surface of a 4D sphere. 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.

Another interesting possible universe is the white hole... this is what you get mathematically by running a black hole in reverse. This one is also infinite, obeys general relativity, but in a key distinction with the FRW flat universe, it has a center. The reason we don’t think this is our universe is two-fold: again it has curvature we ought to detect, and it also has a center and our observations are inconsistent with that.

Of course there’s no reason our universe couldn’t actually be either a giant white hole or a giant S^3, as long as “giant” means so giant that on the length scale of the observable universe it still looks flat and not curved.

So if you really disbelieve in infinity on philosophical grounds, you could always assume that our universe is actually S^3 on some suitably large enough scale so as to remain consistent with known and observed physics, but nonetheless still finite.

 

[Sue Rich]

The theory is that our universe started with the Big Bang. You're now saying it's possible the entire universe could have started infinite. If so. then how was the infinite universe started?

 

[jbriggs444]

The theory is that our universe started with the Big Bang. You're now saying it's possible the entire universe could have started infinite. If so. then how was the infinite universe started?

Why does it need to have had a first state? What is the smallest strictly positive real number?

 

[PeroK]

The theory is that our universe started with the Big Bang. You're now saying it's possible the entire universe could have started infinite. If so. then how was the infinite universe started?

The Big Bang theory can't rewind things all the way back to $t=0$. The maths breaks down. In particular there is no consistent way to get from a point to our universe, infinite or otherwise. No one knows how it started.

 

[mfb]

The theory is that our universe started with the Big Bang. You're now saying it's possible the entire universe could have started infinite. If so. then how was the infinite universe started?

With the Big Bang.
Note that a possible singularity, no matter if we had one or not, is not part of the Big Bang.

f the universe is not infinite that means is stops somewhere.

Counterexample: The surface (!) of Earth is not infinite, but it doesn't stop somewhere.

 

[Grinkle]

The theory is that our universe started with the Big Bang. You're now saying it's possible the entire universe could have started infinite. If so. then how was the infinite universe started?

According to the below link, there is evidence to support theories that go as far back as 1e-43s after time zero. Earlier than that, we don't have theory to describe. I would re-state your comment to be - The theory of the early universe is that when it was very very young, it underwent a period of very rapid expansion that we call the Big Bang.

Your statement implies there are claims that the Big Bang is about creation; it is not. It is about evolution of the early universe and it says that the early universe was much hotter / denser than it is today. Its natural for a person to jump to the implication that therefore the early universe was smaller than it is today - but that is not any part of the Big Bang theory or family of theories.

Of course any finite piece of the entire universe (eg our observable universe) was smaller in extent earlier than it was today.

https://en.wikipedia.org/wiki/Chronology_of_the_universe

 

[Khashishi]

The theory is that our universe started with the Big Bang. You're now saying it's possible the entire universe could have started infinite. If so. then how was the infinite universe started?

You probably are imagining the Big Bang as starting with a single point at t=0. The truth is, the point at t=0 is not a valid point in the theory. It is an extrapolation to a region where the math no longer makes any sense.

Consider Charles's Law of volumes for gases. This law states that the volume of a gas is proportional to the absolute temperature (at constant pressure). It predicts that the volume will go to zero at absolute zero temperature. But this is incorrect. In reality, the gas will change phase and no longer behave as an ideal gas as the temperature approaches 0, so Charles's law is no longer valid. Nevertheless, it remains a useful law at higher temperatures. We now have some more accurate theories which we can use at low temperatures.

We shouldn't expect the Big Bang theory to be correct at times earlier than a Planck time (t ~ 10^(-43) s), but it might be wrong much later too. We have some hints from CMB observations that inflation had occurred around 13.7 billion years ago, but we really can't say anything about what happened before that.

 

[Drakkith]

The theory is that our universe started with the Big Bang. You're now saying it's possible the entire universe could have started infinite. If so. then how was the infinite universe started?

Note that the big bang as an event is different than the big bang as a theory. The big bang theory (BBT) is our description of how the universe evolved over time from a hot, compact state in the distant past to the cool and sparse state that we are in now. Since we occupy the present and have to look outwards into the universe in order to observe what the universe was like in the past, the BBT was first formulated, and is continuously being updated, using observations of the present and steadily working backwards in time as our telescopes and other instruments become larger and more advanced. I say this because I feel it is important to understand how the BBT was developed and to realize that predictions about the origin of the universe are problematic, as we cannot observe the origin. Instead, we take our observations and fit them together into a theory, extrapolating into the distant past by using our observations of the not-so-distant past and our knowledge of fundamental physics.

The big bang, as an event, is a result of taking the fact that the universe is expanding and extrapolating backwards to the point where the density of every point in the universe is so high that the math for our gravitational calculations can't be done anymore. It's like trying to divide by zero in all of our calculations. The answers are undefined. We call this result a singularity, and it occurs everywhere in the universe at the same time. It is believed that this singularity is not real and that it is the result of our incomplete knowledge of physics at the temperatures and densities of the very early universe.

One thing to remember is that when we run our model of the universe backwards we get the result that the density of the universe increases the further back we go. But this doesn't say that the size of the universe decreases, only that the matter within the universe gets closer together. A square volume of space one-light-year across on each side simply accrues more and more matter. The cube doesn't shrink*. How it is possible that all of this matter can be compressed without the size of the universe decreasing is a direct result of the universe being infinite in size. An infinite universe does not have a size. By that I mean that there is no number you can plop down on a diagram and say, "That's how big the universe is." Whatever number you choose, there will always be another number larger than it. Because of this, it isn't possible for us to say that the universe gets smaller or larger over time. That would imply that the universe has a set size, which would mean it isn't infinite**.

*Talking about distances in an expanding/contracting universe governed by General Relativity is complicated and prone to misunderstandings, but I hope I got my point across well enough.

**I think so at least. I'm not that knowledgeable about how infinities work in math (which is actually quite complicated and non-intuitive), so I could be mistaken. But once again, I hope I'm getting the general idea across well enough. The universe can expand or contract without its size going from infinite to finite or vice versa.

 

[abbott287]

You have to stop as thinking about the universe as being embedded in some containing [three dimensional?] space. It does not need to be embedded in anything.

There has to be something if its expanding. It can't expand into something that's not there.

 

[abbott287]

With the Big Bang.
Note that a possible singularity, no matter if we had one or not, is not part of the Big Bang.

Counterexample: The surface (!) of Earth is not infinite, but it doesn't stop somewhere.

 

[abbott287]

Then define singularity. You cant. Its a word meaning we don't know.

The Earth is round. So you have a start point and an end point. Then you just start over again. If the universe is looped, why don't we see things coming back at us from the past, just like we would see someone walking back around to the starting point on the round earth. Infinities don't work, and they do work, depending on how you view them. 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. Thats the paradox of infinite. Black holes are not crushed out of existence, or we would see no signs of them hanging around. If they exist, the crushing seems to have stopped at some point.

 

[PeroK]

Then define singularity. You cant. Its a word meaning we don't know.

The Earth is round. So you have a start point and an end point. Then you just start over again. If the universe is looped, why don't we see things coming back at us from the past, just like we would see someone walking back around to the starting point on the round earth. Infinities don't work, and they do work, depending on how you view them. 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. Thats the paradox of infinite. Black holes are not crushed out of existence, or we would see no signs of them hanging around. If they exist, the crushing seems to have stopped at some point.

Have you no interest in learning cosmology then? Are you happy with your own intuitive misconceptions?

 

[PeroK]

There has to be something if its expanding. It can't expand into something that's not there.

It doesn't have to expand into anything. Expansion refers to metric expansion, which relates to the changing distances between points in space.

 

[Arman777]

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

You seem to be contradicting yourself. You said do not think of it as a point, which is how I think of it.

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

 

[Drakkith]

There has to be something if its expanding. It can't expand into something that's not there.

If the universe is infinite in size, then there is no boundary between "in the universe" and "outside the universe". There cannot be, because if the universe is infinite in size then you can travel any distance in any direction and you will ALWAYS be inside the universe still. So there isn't even an "outside the universe" for the universe to expand into.

Then define singularity. You cant. Its a word meaning we don't know.

That is incorrect. We have precise definitions for the word "singularity" that describe it just fine. There's little ambiguity or disagreement about it. It's just very difficult to explain it to laymen because it's a defining something that happens in math, and then this has to be brought into the context of General Relativity and the Big Bang Theory, which means you need to explain both of those as well. This is very difficult, and the meaning of "singularity" gets lost and misunderstood along the way.

That's not to say that we know what happens in the real world where our models have singularities. That's the unknown part. What is actually happening in the middle of a black hole? Or at t=0 for the BBT? We don't know.

 

[Grinkle]

Then define singularity. You cant. Its a word meaning we don't know.

Because one does not know or have an explanation for real world behavior when a model breaks down does not invalidate other aspects of the model. What invalidates a model or theory is experiment (or observation) that contradicts a prediction that model or theory makes. No predictions are made where models have singularities.

There has to be something if its expanding. It can't expand into something that's not there.

Science is a process of developing theories that make testable predictions and then testing the theories. A human difficulty in picturing an infinite space and/or picturing any space that is finite but not embedded in anything does not count as an experiment testing a prediction of a theory. Both of those things I cannot make a mental image of - there is no logic to saying that means they are impossible.

 

[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.