[geordief (OP)]

I think the question deserves inverting - often a good starting point for an investigation.

If the universe is finite, either it has a boundary, or we can define a vector r with its origin here and its endpoint outside the universe. So what is outside that boundary?  Why can't we define a vector with magnitude 2r?

Reminds me of the ending to The Truman Show where the intrepid hero comes to the end of the world and discovers it is made of  billboard paper.

Also reminds me of the crock of gold at the end of the rainbow

I feel  I can live with an infite  universe , but I wouldn't bet the house on it :-)

[Halc]

If the universe is finite, either it has a boundary, or we can define a vector r with its origin here and its endpoint outside the universe.

Those sound like the same option. The boundary is when the vector changes to being outside.
No, the 2nd option is that a vector r with its origin here has its endpoint also here.
This is true of the surface of Earth (positive curvature, finite area, no boundary). It is also true of a torrid surface (like the Asteroids video game, no curvature, finite area, no boundary). In such cases, any vector comes back to someplace it's been before.

So what is outside that boundary?  Why can't we define a vector with magnitude 2r?

The Milne universe is sort of like that. Everywhere isotropic, and yet finite/bounded with 'nothing' beyond. The vector can be defined (you can give coordinates to locations outside), but you can't go there because no event outside the universe is in the future light cone of any event inside it.

[alancalverd]

The Milne universe is sort of like that. Everywhere isotropic, and yet finite/bounded with 'nothing' beyond.

This surely defines the observable universe, not the universe, which must include everything (or all the nothing) "beyond".

[alancalverd]

Those sound like the same option. The boundary is when the vector changes to being outside.

Not so mathematically. An unbounded set (cats) does not include objects that are not members of that set (dogs), but we can define a vector (quadrupeds) in terms of the parameters of that set, which can be extended beyond all possible members of the set (other quadrupeds, all dead cats....).

[Harri]

Does the big bang theory cause a problem for the infinitely expanding universe theory? Our universe is currently expanding and my understanding is that a reduction of that expansion would bring us to the big bang. But wouldn't that mean that the reduction would also have to be infinite?

[geordief (OP)]

Does the big bang theory cause a problem for the infinitely expanding universe theory? Our universe is currently expanding and my understanding is that a reduction of that expansion would bring us to the big bang. But wouldn't that mean that the reduction would also have to be infinite?

(think my head just expanded   )

Well could you have it so that some of the universe did fall back on itself but some was just too far distant and "out of reach" so that it  continued its expansion "to infinity and beyond"   ?

[Halc]

Does the big bang theory cause a problem for the infinitely expanding universe theory?

The big bang theory is the infinitely expanding universe theory

Our universe is currently expanding

Careful. The space in our universe is expanding over time. 'The universe' is typically defined as all of (or sometimes the visible portion of) spacetime, and spacetime doesn't expand or otherwise change, so while wording it that way is common in pop articles, it is technically wrong.

my understanding is that a reduction of that expansion would bring us to the big bang.

That would be a big crunch, a sort of different thing that the big bang in reverse since the entropy would be so much higher. Our expansion doesn't look like it will ever slow let along reverse, so no crunch is anticipated.

But wouldn't that mean that the reduction would also have to be infinite?

The expansion isn't infinite, so neither need be the reduction. The expansion is currently at a non-infinite rate of 70 km/sec/mpc and might eventually settle on an exponential rate of around 57.  The size of space is posited as infinite, but you can expand that or reduce it by any finite figure and it's still infinite. Expansion/reduction works just the same (same finite measured rate) regardless of whether the size of space is finite or not.

[Halc]

Well could you have it so that some of the universe did fall back on itself

That's one way to describe a black hole. All very crunchy.

[geordief (OP)]

Well could you have it so that some of the universe did fall back on itself

That's one way to describe a black hole. All very crunchy.

Wasn't expecting that. Do the models of the BH and any possible Big Crunch differ in other respects?

[Halc]

Do the models of the BH and any possible Big Crunch differ in other respects?

In both cases, time ends abruptly for a given worldline, just as it starts abruptly at the big bang.

The big crunch is not a black hole in that matter is still evenly distributed everywhere over infinite space.
I'm not sure if light is still prevent from reaching null-infinity in the crunch scenario. It seems to depend if there's something like anti-inflation at the end. I'd be guessing if I posted an opinion on that.

[yor_on]

I think I will agree with you Kryptid, although also presuming a 'infinite time' for it. Depending on permutations, assuming that there are only so many ways to arrange them. Atoms, electrons whatever.


syntax
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Thinking some more of it, I don't need that infinite time, do I? It should be enough with a combination of restricted permutations in a infinite universe for it to be possible. Thermodynamics assume a heat death so with that everything has a end of sorts. But in between, in a universe without end everything (inside those permutations) should be possible. Locally defined at least :) If we add observer dependencies it becomes really tricky.

Although, quantum physically not even a heat death stops those random processes as I understand.
And damn, if that is correct 'time' must exist, even in a heat death of a universe.

I should have realized this sooner. Both Relativity and quantum mechanics agree on this. And it's a shot across the bow for the idea of equalizing thermodynamics to the arrow of time, isn't it?

[yor_on]

And yes, the universe is weird but no weirder than the assumption of it being some sort of ball containing everything. Once you made that presumption the next question becomes

What's outside it?

[alancalverd]

The implications of an infinite universe are pretty startling, actually. When you have an infinite amount of matter and energy.......

But a finite amount of stuff expanding into an infinite void is not at all difficult to visualise. Just think of any explosion in a space movie, on a really big scale.

[yor_on]

What physics refers to as 'densities', isn't it Alan? :)
Funny word that.

[Zer0]

Perhaps Fancy Science Magazines are responsible for this logical contradiction.

The Universe, They say...was once packed into a small impeccable point...then grew from a mustard seed to a football in a flash...then inflation from football to earth size...n then kept expanding Forever!

Ps - So then...it's quite possible to pack an Infinity of mangoes into a Finite picnic basket.
🍊
(I cannot see the Earth as a whole one planet until i go into space, and the Earth has no edges...hence the Earth must be Infinite.)

[yor_on]

Did you know that you have neurons in your stomach Zero? Communicating with your brain :)

There is nothing stating that a 'brain' must be centralized, it may be easier that way but it depends on evolution I think. And I seem to remember that sea stars have neurons too?

https://www.ted.com/talks/heribert_watzke_the_brain_in_your_gut
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so talking about having a 'gut feeling' may not be that much off the mark.

[Zer0]

Did you know that you have neurons in your stomach Zero? Communicating with your brain

There is nothing stating that a 'brain' must be centralized, it may be easier that way but it depends on evolution I think. And I seem to remember that sea stars have neurons too?

https://www.ted.com/talks/heribert_watzke_the_brain_in_your_gut
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so talking about having a 'gut feeling' may not be that much off the mark.

What are you even on about?
🤔
I am unable to make a sensible connection with what i said, & what your responded with.
🙏
I'm not asking you to elaborate, maybe im simply Not at your level hence even if you explained, i still might not get it.

[yor_on]

Sorry zero, looking at it again I don't see what I reacted on here? Probably me placing it in the wrong thread? It was a comment by you about brains, as far as I remember?

[Zer0]

Sorry zero, looking at it again I don't see what I reacted on here? Probably me placing it in the wrong thread? It was a comment by you about brains, as far as I remember?

Section - Physics, Astronomy & Cosmology.

https://www.thenakedscientists.com/forum/index.php?topic=83391.msg658496#msg658496

You are Spot On Buddy!
👍
I dug it up n found it.
(Reply #15)

Very Nicely Done!
& Yes l, what you say resonates & makes sense to me.

Ps - i Apologize i could not relate to it before.
🙏
Now i truly understand what it means when people say, " i have a gut feeling about this "...thinking/guessing/memory is not just in the domain of the brain alone.
(No wonder heart transplant patients report a change of taste or pick up a new habit)
💓

[JohnPi]

IMHO, universe is just a circle. It may seem that every time you reach its edge it is the universe's end, but it's actually not. Of course many common space facts won't let u believe it, but how we can be sure about fact that universe is not infinite if we have never reached its end, and would we?