B Does an infinite universe contradict a Big Bang origin?

[DaveC426913]

Compact has a specific meaning in maths, which isn't relevant to this case. It was just hot and dense.

OK (sorry if I'm going around in circles) I still don't see how a (whole) universe that is infinite in extent can undergo "a period of extremely rapid growth (aka inflation)".

 

[Ibix]

I still don't see how a (whole) universe that is infinite in extent can undergo "a period of extremely rapid growth (aka inflation)".

And I'm having trouble understanding what you want to know here if it isn't some variant on "what's it expanding into". Universes filled with matter (or other stuff in the case of inflation) expand or collapse - it's just what they do.

 

[DaveC426913]

Universes filled with matter (or other stuff in the case of inflation) expand or collapse - it's just what they do.

But not if they're infinite in extent. They can't expand or collapse.

Or is it some variant on finite but unbounded?

I understand how a universe can start off in a compact, hot dense state (smaller than an atom) and expand to be finite (say, 140Gly in diameter, or whatever the OU is now) but unbounded - without it having to have something to expand into.

The easiest way I can envision that is if it wraps around, so if you were in a (magical) spaceship a few million years after the BB, you could cross the universe and arrive back where you started. (It may not be the correct way, but it's a way.)

Still, finite but unbounded is not infinite.

 

[Ibix]

But not if they're infinite in extent. They can't expand or collapse.

Yes they can. Imagine a line of stakes in the ground each 1m from the next. Come back a while later and you find the stakes are now 1.1m apart. That's expansion, whether there's a finite number of stakes or an infinite number of them.

 

[DaveC426913]

Yes they can. Imagine a line of stakes in the ground each 1m from the next. Come back a while later and you find the stakes are now 1.1m apart. That's expansion, whether there's a finite number of stakes or an infinite number of them.

Ah. A Hilbert's hotel thing.

I think that strikes at the crux of my confusion.

 

[Orodruin]

Ah. A Hilbert's hotel thing.

I think that strikes at the crux of my confusion.

Indeed, and the point is it is space itself that is expanding and becoming larger (in the usual cosmological coordinates). It doesn’t need anywhere to expand, it is just growing. So all of the matter in the universe becomes less dense - thereby also cooling down. Volume per mass grew and so density went down.

 

[javisot20]

Ah. A Hilbert's hotel thing.

I think that strikes at the crux of my confusion.

An infinite universe can expand, no edge of the universe is necessary for that to happen, expansion is an intrinsic property of space-time.

1- Choose a point in the universe to carry out observations with your best telescope.

2- You will observe very young galaxies in the distance, and CMB will be further away. On a large scale you determine that the universe has a certain content of matter and energy, and certain properties

3- Imagine at that moment you move instantly in any direction, for example to Andromeda, to mount your telescope again and observe the distance

4-You will see the same thing, young galaxies in the distance and the CMB further away, in addition, the content and properties of the large-scale universe will be the same as what you determined in the other point.

5- If the cosmological principle is correct, and it seems to be, you can move in any direction as much as you want and conclude the same thing

 

[DaveC426913]

Thanks all. I grok it now.

Not sure I'm in a position to explain it to someone with even less of a grasp of cosmology than i, but still...

 

[PeroK]

But not if they're infinite in extent. They can't expand or collapse.

I gave you an example of the number line expanding over time.

In any case, the mathematical basis of cosmology is precisely this. That we have an infinite universe with galaxies dotted around approximately uniformly at a large enough scale. But, as time goes on the galaxies become further apart. There is no mathematical contradiction.

That said, it's not really possible to visualise an infinite universe. You have to rely on the mathematics. And not to rely on intuition for the finite objects we are familiar with.

PS I nearly mentioned the Hilbert Hotel.

 

[jfmcghee]

That said, it's not really possible to visualise an infinite universe. You have to rely on the mathematics. And not to rely on intuition for the finite objects we are familiar with.

This is the part that gets me every time, even though I know better. I know that this is not possible, but it's almost impossible not to start doing it. And it makes it that much harder to try to explain to someone else, especially if they are not exposed to subjects where this kind of thinking is "normal."

 

[Orodruin]

That said, it's not really possible to visualise an infinite universe. You have to rely on the mathematics. And not to rely on intuition for the finite objects we are familiar with.

This is the thing though. People misunderstand what ”intuition” actually is. Intuition is built through familiarity with something. Everyone has intuition about mundane processes occurring all around us. But for things not occurring around us all the time - intuition needs to be trained before it can be effective. For dealing with infinite universes and advanced physics topics, intuition comes from exposing oneself to them, solving problems and going through arguments. Having done so, one can have intuition for such things - not so much without.

 

[timmdeeg]

Assuming that we will never be able to decide if we life in a very large sphere or if the universe is flat in the euclidean sense my intuition is just switched off. So, ad acta.

 

[256bits]

Indeed, and the point is it is space itself that is expanding and becoming larger (in the usual cosmological coordinates). It doesn’t need anywhere to expand, it is just growing. So all of the matter in the universe becomes less dense - thereby also cooling down. Volume per mass grew and so density went down.

I gave you an example of the number line expanding over time.

Much like the 2D representation of the expanding balloon surface, but that is a finite universe representation, is it not?

The left side/right side of the observable universe had no time to communicate during expansion, but are surprisingly similar. Inflation is theorized to explain the similarity.

So is there a horizon problem hidden within the infinite universe, or within the large universe models.
If our observable universe was hot and dense, as well as the infinite universe being the same, how did all the parts of the infinite universe, or large universe, communicate to all start to expand and become less dense, less hot .

 

[PeroK]

Much like the 2D representation of the expanding balloon surface, but that is a finite universe representation, is it not?

That represents a finite universe. The key concept there, which again can be hard to grasp, is that the universe is only the balloon's surface. And that surface can be defined mathematically as a 2D manifold in its own right, without being embedded in a space of higher dimension (i.e. 3D).

 

[WWGD]

That represents a finite universe. The key concept there, which again can be hard to grasp, is that the universe is only the balloon's surface. And that surface can be defined mathematically as a 2D manifold in its own right, without being embedded in a space of higher dimension (i.e. 3D).

Doesn't it have to live, be embedded within some version of spacetime?

 

[PeroK]

Doesn't it have to live, be embedded within some version of spacetime?

You can't always do it with only one additional dimension. See, for example:

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

 

[Hornbein]

I like the infinite raisin bread dough model. The yeast expands the dough which causes all the raisins to move away from one another. There is no center.

 

[PeterDonis]

You can't always do it with only one additional dimension. See, for example:

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

In the case of models of our universe, however, the analogue of the "balloon" is a 3D spacelike hypersurface that is embedded in a 4D spacetime. This is true whether the universe is spatially finite or spatially infinite.

It is also true that the analogue of the "balloon" can be analyzed as a 3D manifold in its own right, independent of its embedding in spacetime. But it still is so embedded, for this particular case.

 

[WWGD]

In the case of models of our universe, however, the analogue of the "balloon" is a 3D spacelike hypersurface that is embedded in a 4D spacetime. This is true whether the universe is spatially finite or spatially infinite.

It is also true that the analogue of the "balloon" can be analyzed as a 3D manifold in its own right, independent of its embedding in spacetime. But it still is so embedded, for this particular case.

Well, I guess we have to define terms carefully, clearly. I thought " The Universe" is the totality of all there is. How then can it be embedded in something containing it. Maybe we're not using the right language to talk about it, or at least I'm not understanding the current usage of it. Edit: Pretty sure this topic has been brought up way before this post of mine.

 

[PeterDonis]

I thought " The Universe" is the totality of all there is.

That's a common definition, yes. But the term is ambiguous. See below.

How then can it be embedded in something containing it.

The universe at one instant of time, which is a spacelike 3-surface, is embedded in the 4D spacetime that describes the entire history of the universe.

 

[WWGD]

.

That's a common definition, yes. But the term is ambiguous. See below.


The universe at one instant of time, which is a spacelike 3-surface, is embedded in the 4D spacetime that describes the entire history of the universe.

Does that description aply to all models, metrics and in general, special cases?

 

[PeterDonis]

Does that description aply to all models, metrics and in general, special cases?

It applies to all models that are used to describe our universe. In more technical language, it applies to all FRW spacetimes.

 

[WWGD]

It applies to all models that are used to describe our universe. In more technical language, it applies to all FRW spacetimes.

Thanks for answering my basic questions. My rigorous courses at ChatGpt U didn't make any mention of any of this :).

 

[jackjack2025]

Yes they can. Imagine a line of stakes in the ground each 1m from the next. Come back a while later and you find the stakes are now 1.1m apart. That's expansion, whether there's a finite number of stakes or an infinite number of them.

I can see it can be considered expansion for a finite number of stakes, because it is measurable, but for infinite, not really. Hilbert Hotel does not expand

 

[Ibix]

I can see it can be considered expansion for a finite number of stakes, because it is measurable, but for infinite, not really. Hilbert Hotel does not expand

Well, when you have a row of stakes and the distance between them is growing over time, cosmologists call that metric expansion whether the row is finite or not. You can call it something else if you like, but remember every time you use your private language you'll have to translate for everyone else who uses standard terminology.

 

[jackjack2025]

Well, when you have a row of stakes and the distance between them is growing over time, cosmologists call that metric expansion whether the row is finite or not. You can call it something else if you like, but remember every time you use your private language you'll have to translate for everyone else who uses standard terminology.

That's fair point.

But I do think the original poster has a point about what expansion means in an infinite universe.

So in your analogy, in the finite case, you can measure the first to last stake and say it expanded. In the infinite case of stakes... we can't have a metric and see it has expanded. From the first stake to the last is the same length. From the first stake to the second stake has grown from 1 to 1.1m, but that's very different, maybe some stakes went missing and the stakes are actually contracting, it was the 2m stake that is now at 1.1m. I know that sounds mad, but it isn't something clearcut or easily provable.

 

[Ibix]

That's fair point.

But I do think the original poster has a point about what expansion means in an infinite universe.

It means everything is further apart today than it was yesterday, and by the same multiplicative factor everywhere.

 

[jackjack2025]

It means everything is further apart today than it was yesterday, and by the same multiplicative factor everywhere.

If I take the integers and measure between 1 and 2 and 3 and so on and say the distance is one. These are your stakes, that's my universe in this example.

Now... something occurs that all even numbers have been removed. So the stake looks to me as 1, 3, 5. Has the universe expanded? It doesn't work in infinity.

 

[Ibix]

If I take the integers and measure between 1 and 2 and 3 and so on and say the distance is one. These are your stakes

Now... something occurs that all even numbers have been removed. So the stake looks to me as 1, 3, 5. Did they numbers expand? It doesn't work in infinity.

Removing stakes isn't the same as smoothly increasing the distance between them, but if the stakes aren't labelled and I'm not paying attention it might look like expansion, because the distance between adjacent stakes has doubled.

There's no problem increasing the distance between the stakes even if there are infinitely many of them (ironically, there's a plausibility argument for this based on Hilbert's hotel). Again, if you don't want to call that expansion that's up to you. Everyone else does.

 

[jackjack2025]

Removing stakes isn't the same as smoothly increasing the distance between them, but if the stakes aren't labelled and I'm not paying attention it might look like expansion, because the distance between adjacent stakes has doubled.

There's no problem increasing the distance between the stakes even if there are infinitely many of them (ironically, there's a plausibility argument for this based on Hilbert's hotel). Again, if you don't want to call that expansion that's up to you. Everyone else does.

"Hilbert Hotel Expansion​

Hilbert's hotel, a thought experiment introduced by mathematician David Hilbert, demonstrates the counterintuitive properties of infinity. The paradox shows that even a fully occupied hotel with an infinite number of rooms can accommodate more guests. When a new guest arrives, the manager can move each current guest to the next room, freeing up the first room for the new guest.23

In the case of an infinite number of new guests, the manager can double the room numbers of all current guests, thus freeing up all the odd-numbered rooms for the new guests.3 This shows that the hotel can expand to accommodate more guests, even when it is initially fully occupied, due to the nature of infinity.23

However, the paradox does not imply that the hotel's capacity expands in the traditional sense. The hotel's capacity remains infinite, but the concept of infinity allows for the accommodation of additional guests without reaching a limit.23

The idea that the hotel can accommodate more guests without expanding its physical structure challenges our understanding of infinity and highlights the unique properties of infinite sets."


"Everyone else does"? You sure?

The premise of what you said was that stakes are planted into the ground and then you return and see some stakes and see, actually 1.1m apart. This works in a finite way. This does not work in an infinite way. You are just observing the stakes, you aren't controlling them, right?