# I Infinity vs expansion

1. Aug 17, 2016

### thetexan

I had a question after watching a Discovery Channel show on the universe.

They talked about how some speculate the infinitude of the universe as opposed to a finite sized universe and I have also heard the same on this forum...and it got me to thinking...

Isn't an infinite universe incompatible with the theory of expansion? How can a singularity expand to an infinite size? And it would have to because if it had not have done so (ie it expanded to some less than infinite size early on and if the universe then further expanded to the infinite) then at some point the expansion would have had to continue to complete the process to expand to infinity. At that point the expansion would have had to be infinitely fast to fill an infinite universe, and that doesn't seem doesn't seem possible since when is the expansion into an infinite universe complete? Whether that The mechanics of expansion of space/time would require a beginning event and an ending event. ie, if it starts it must have either ended or has not ended yet and therefore not infinite.

So mustn't the logic demand that if there were a beginning event such as the big bang, and there was expansion, then there must not be infinitude?

Another way of stating it is this...any process such as expansion that takes time can not result in an infinite result because the infinite result would have required an infinite time.

tex

2. Aug 17, 2016

### phinds

Not in the least

You clearly do not understand what "singularity" means. Likely you have been misled by pop-sci garbage stating the the singularity is a point in space. It is not. It is just the place where our math model breaks down and we don't know what was happening.

No, it would not have had to. The universe might have started out infinite.

no. see above

3. Aug 17, 2016

### Bandersnatch

If it is infinite now, then it was always infinite.

Think of an infinite universe, and how every distance in it shrinks as you go back in time. You still reach a point (in time!) of infinite density, when everything is basically on top of each other, but you never lose the infinite extent. I.e., if you've got an infinite number of arbitrarily selected distances, and you shrink them all towards zero, then you still get infinite density at the limit of this shrinkage.

4. Aug 17, 2016

### Staff: Mentor

I think you may be misunderstanding what the OP was saying. Singularity or not, if the universe started at a very small volume and then expanded, that would imply finite sizes when people think in 3 dimensional analogues. The reality is that scientists don't really know if that is true or not.

Either way, you should tone down the harshness of your posts.

5. Aug 17, 2016

### phinds

Fair enough. Thanks.

6. Aug 17, 2016

### ebos

There are some times when the answer, at the moment, is, "We don't know." Even though we have a need to explain things to others, we have to start realizing that it's OK to give that as an answer.

7. Aug 17, 2016

### phinds

But we DO know that the answer to "Isn't an infinite universe incompatible with the theory of expansion?" is no, as explained above.

8. Aug 17, 2016

### phinds

By the way, @thetexan , one of the things people often have trouble with is that if the universe IS infinite, how can it keep expanding? It can of course and for some help on understanding this if you do find it confusing, as most of us do at first, Google "Hilbert Hotel"

9. Aug 17, 2016

### ebos

Sorry, I should have been more specific. Parts of the question were answerable; parts were not. For example, the nature of the singularity is unknown and you answered that correctly.

10. Aug 17, 2016

### phinds

Fair enough.

11. Aug 17, 2016

### ebos

Hey Phinds, I personally miss your 'snappy' answers. However, rules are rules I guess. What I wanted to convey to you is my gratitude in making me look at the 'Balloon Analogy' and the 'Hilbert Hotel' analogy again. This time with a better understanding and a whole new perspective. I also find it helpful to include the ' Flatland Analogy' with the 'Balloon Analogy'. It has given me a much clearer understanding of the "shape" of the universe and some of its mechanics. I'm even taking a look at trying to understand multiple dimensions. So thanks for that and keep on keeping us on our toes - once in awhile anyways. It's a very pragmatic approach but it works for me. It's like when you're stuck and someone says, "Go back to the basics." Always gives me a fresh new look and gets me out of my head which can be a pretty confusing place sometimes. Thanks again, ebos (and my dog).

12. Aug 17, 2016

### phinds

Happy to help, even if I do get a bit peckish sometimes

Flatland is a great book. I somehow almost never think to point it out to people but I agree w/ you that it adds to our understanding of dimensions.

EDIT: and by the way, I appreciate that you like my posts, but actually I think Russ is right. Direct and to the point is one thing but I DO get unnecessarily harsh sometimes and it's worth working on since it is more off-putting than educational.

Last edited: Aug 17, 2016
13. Aug 17, 2016

### ebos

When I first came here I was also upset by your answers (sometimes) until I realized that I was the seeker and you guys were the oracles. And if you've ever read any stories about the ancient oracles and how they treated their seekers well you're a bit of a pussy : )
Besides, it's not the messenger or the nature of the messenger but the message that counts. If someone has emotion behind their messages then they're probably important too them and so should also be important to me. But you better listen to the mentors, I guess. You've helped me a lot and the nature of your message and how I perceived it has always been my problem. As soon as I realized that, I was well on my way.

14. Aug 17, 2016

### thetexan

My question is this...expansion implies a change of condition from this to that, whatever this or that is. How does a universe that is expanding expand if it is already at infinity? I've studied enough to know that the theories say expansion began in the first few fractions of a second after the bang. Ok...that means that at that beginning point of expansion the universe could not be infinite YET...so how does one expand from a beginning to infinitely big over a period of finite time?

An analogy would be if I started out driving a car slowly at first then within a few gillionths of a second I accelerate fast enough to get infinitely far down the road within 13.7 billion years. When discussing infinity 13.7 billion is a blink an eye. So how do I get infinitely far down the road in a blink of an eye.

Back to the universe and expansion...if expansion continues it implies it hasn't achieved infinitude yet...if it has achieved infinitude then why expand any more?

I believe it could be infinite from the start as was stated but then there is no need for expansion as a explanation to the condition of infinitude.

So I restate my point. Aren't infinitude and expansion mutually exclusive and unnecessary for one to explain the other? Expansion implies moving toward some future condition greater that the current condition and infinitude implies we are there and it can exist without expansion ( that last term is based on my albeit poor grasp of all of this so it may be wrong).

I don't want an argument or insults. I'm just a novice looking for some guidance.

Tex

15. Aug 17, 2016

### phinds

Expansion certainly means that things got farther apart which is one kind of change of condition but, and I may be misinterpreting you, I think you are implying a state change, yes? That's not the case. That very likely WAS the case during the creation event but not quite right for the early inflation (which is what I assume you are talking about here)

Did you do as I suggest and read about the Hilbert Hotel?

Yes. TINY fractions.
no it does not. What is your reasoning?

You cannot. But if you start at infinity there is no problem.

I'm not aware of anyone every making any such claim and in fact it would be nonsensical to do so since you can't get from finite to infinite in a finite amount of time (I'm not sure you can do it in an infinite amount of time ... infinite math makes my head hurt).

They are not related. The expansion might have started from a finite state, in which case it is still finite, or it might have started from an infinite state in which case it is still infinite

Not sure what you mean with this.

16. Aug 17, 2016

### thetexan

Well I have no defense other than maybe my flawed assumption. I clearly don't understand how, in a Big Bang/inflation system you can begin with an infinite universe.

Every time I have this explained I'm told that the size of the universe, if it has a finite size, is due to the effects of inflation. To me that makes sense. Space/time is growing...why...because of expansion. The term growing, to me, implies something short of infinite. And if the universe is infinite and began that way then why inflation?

tex

17. Aug 17, 2016

### phinds

Nor does anyone I know or am aware of. There are conceptual problems with an infinite beginning BUT there are also conceptual problems with a finite beginning (what, for example, is the shape of the universe if it is finite but unbounded?)

IF it has a finite size then the particular size that it is now is a function of both the starting size and the rate of expansion. That is HAS a size is not due to expansion. If it started as finite, then of course it is finite now and has a particular size. That is not particularly significant, especially compared to the question of whether or not it IS finite.

Well, I can only repeat. Read about the Hilbert Hotel as a beginning of understanding that.

I'm not aware that there is any known reason for inflation, we just observer that it happened, just as we observe that the universe is currently expanding at an accelerating rate.

You might also find it informative to read the link in my signature.

Good

18. Aug 18, 2016

### Ken G

Another way to frame an answer to this question is to make a subtle but important distinction between the attributes of a model, and the attributes of a universe. No one can answer anything about the attributes of a universe that have never been observed-- and the size of the universe has never been observed, all we have is a lower limit on the order of 100 billion light years in size at the current time. So that is all that can be said about size that has been measured. However, you can ask about the attributes of the Big Bang model of the universe, and that model includes a feature called the "cosmological principle." That principle says that the universe is the same everywhere at large enough scales, so it only changes with time, not location. Here's the crucial point: no one has any idea if the universe itself actually obeys that principle, all we know is that the Big Bang model uses that principle at its core, and it is a useful unifying principle that is not contradicted by observation. So it is that principle, and nothing else, that says that the only way the universe could be finite is if it has a small but nonzero positive spatial curvature. We don't know if the actual universe (assuming such a concept even has a scientific meaning, which is far from obvious but let's not get into that here) has a small but positive curvature, since all we measure is that the curvature is consistent with zero, and we don't know if the actual universe obeys the cosmological principle anyway, but we can certainly say that the simplest model of the universe that we have at our disposal is one that does obey the cosmological principle and is flat-- which is an infinite model of an unknown universe.

In science, we ask about the attributes of models, and we look for ways to test those models, and that's all we get-- all else is philosophy. There are certainly many who have philosophical objections to an infinite universe, but there were also many who had philosophical objections to a universe with a finite age. Science is something a bit different from that.