B Does an infinite universe contradict a Big Bang origin?

[WWGD]

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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?

 

[phinds]

"Everyone else does"? You sure?

yes

 

[phinds]

This does not work in an infinite way.

yes, it does. You clearly haven't gotten your head around the concept of infinity and you apparently think it acts the same as a finite number. It doesn't.

 

[jbriggs444]

"Hilbert Hotel Expansion

@Ibix and the rest of us are quite comfortable with Cantor and transfinite cardinalities.

However, cardinality has nothing to do with metric expansion. No one is trying to say that the the cardinality of the set of stars now is less than the cardinality of the set of stars a moment from now.

We are not talking about counting rooms at all. We are talking about measuring the length of the carpet between rooms. The guests go to the beach for the day with 10 meters of carpet between adjacent rooms (for instance) and arrive back at the hotel to find 11 meters of carpet between adjacent rooms.

The guests do not have to run a measuring tape from one end of the hall to the other to observe such a change. They only have to measure one pair of rooms. Or enough to get a statistically significant sample.

In practice, the measurements that are made are not done with measuring tapes, of course. We use spectra, luminosity, time delays and various other hints to put together a coherent model for the shape of the universe and the distribution of stars, galaxies and clusters within it. The shape has a feature that is commonly referred to as metric expansion.

If this "metric expansion" does not fit with the meaning that you intuitively expect for "expanding universe" then that is not a problem with the idea of "metric expansion". The problem is with your non-standard interpretation of the meaning of the phrase.

 

[phinds]

If this "metric expansion" does not fit with the meaning that you intuitively expect for "expanding universe" then that is NOT a problem with the idea of "metric expansion". The problem is with your non-standard interpretation of the meaning of the phrase.

I think the word I added in red is what you had in mind.

EDIT: I see you beat me to it.

 

[PeterDonis]

From the first stake to the last is the same length

No, it isn't, because in a spatially infinite universe there is no "last stake". You simply can't apply this intuitive picture to the case under discussion.

 

[PeterDonis]

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