# Is the Universe infinite?

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2 hours ago, Tub said:

I'd be happier believing that the Universe is infinite, that's a comforting thought, but i can't help feeling that it's finite, simply because what we can see of it is still expanding in space/time. If the Universe was already infinite,( and eternal ),wouldn't that prevent any further expansion of space/time?  I hope i can be shown to be completely wrong.

The Big Bang model works with both a finite (but unbounded) and an infinite universe. If it didn't then the question would be considered closed.

Thinking that only a finite universe can expand seems to imply that it is expanding "into" something, which isn't the case.

If you take the integer number line as an analogy, you can represent expansion by multiplying every number by 2, hence doubling the distance between them. You can do this with a finite list of numbers (where the last number will end up twice as far away as it was) or the infinite series (in which case the list is still infinite after each doubling).

20 minutes ago, Handy andy said:

The question is philosophical

Also scientific as it might be answerable by a future model or further evidence.

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36 minutes ago, Tub said:

Thanks, Carrock. Can i assume, then, that an infinite Universe would have to be a steady-state Universe, or have i misunderstood your post? ( I'm not a mathematician. )

Depends what you mean by steady state. Non cosmologists use a definition like this:

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In electronics, steady state is an equilibrium condition of a circuit or network that occurs as the effects of transients are no longer important.

The steady state theory of Bondi and Gold was disproved mathematically and the steady state theory of Hoyle was disproved observationally. These are the only theories that most cosmologists would describe as steady state.

Basic lambda-cdm (and some theories modified for dark energy) predict that startup transients such as the cmbr and stars and cosmologists will eventually become unimportant as the universe continues expanding, becoming colder and emptier and approaching an unchanging state. No cosmologist will ever describe that as steady state for historical reasons.

An implication of my previous post is that that unchanging state must end after limited or unlimited time.

An infinite universe whose volume does not eternally increase or decrease exponentially is the only one which can exist for infinite time and be topologically consistent with current physics. A non cosmologist might describe that as 'steady state.'

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Regarding "Dark Flow":

"A more recent statistical work done by Ryan Keisler[11] claims to rule out the possibility that the dark flow is a physical phenomenon because Kashlinsky et al. do not consider the primary anisotropies of the cosmic microwave background (CMB) to be as important as they are.

NASA's Goddard Space Center considered that this could be the effect of a sibling universe or a region of space-time fundamentally different from the observable universe. Data on more than 1,000 galaxy clusters have been measured, including some as distant as 3 billion light-years. Alexander Kashlinsky claims these measurements show the universe's steady flow is clearly not a statistical fluke. Kashlinsky said: "At this point we don't have enough information to see what it is, or to constrain it. We can only say with certainty that somewhere very far away the world is very different than what we see locally. Whether it's 'another universe' or a different fabric of space-time we don't know."[12]Laura Mersini-Houghton and Rich Holman observe that some anisotropy is predicted both by theories involving interaction with another universe, or when the frame of reference of the CMB does not coincide with that of the universe's expansion.[13]

In 2013, data from the European Space Agency's Planck satellite was claimed to show no statistically significant evidence of existence of dark flow.[5][14] However, another analysis by a member of the Planck collaboration, Fernando Atrio-Barandela, suggested the data were consistent with the earlier findings from WMAP.[15] Popular media continued to be interested in the idea, with Mersini-Houghton claiming the Planck results support existence of a  multiverse.[16][17][18]

Maybe there is a multiverse of an infinite number of universes stacked on each other like pancakes of infinite length and width, but finite height.

Edited by Airbrush
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32 minutes ago, Airbrush said:

Regarding "Dark Flow":

Kashlinsky said: "At this point we don't have enough information to see what it is, or to constrain it. We can only say with certainty that somewhere very far away the world is very different than what we see locally. Whether it's 'another universe' or a different fabric of space-time we don't know."[12]

Interesting quote from Kashlinsky, but the link to the original is dead, so I'll reserve judgement...

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6 hours ago, Strange said:

The Big Bang model works with both a finite (but unbounded) and an infinite universe. If it didn't then the question would be considered closed.

Thinking that only a finite universe can expand seems to imply that it is expanding "into" something, which isn't the case.

Thank you, Strange, that's what i was thinking -  that an infinite Universe would leave no " room " for expansion.

6 hours ago, Carrock said:

Depends what you mean by steady state. Non cosmologists use a definition like this:

The steady state theory of Bondi and Gold was disproved mathematically and the steady state theory of Hoyle was disproved observationally. These are the only theories that most cosmologists would describe as steady state.

Basic lambda-cdm (and some theories modified for dark energy) predict that startup transients such as the cmbr and stars and cosmologists will eventually become unimportant as the universe continues expanding, becoming colder and emptier and approaching an unchanging state. No cosmologist will ever describe that as steady state for historical reasons.

An implication of my previous post is that that unchanging state must end after limited or unlimited time.

An infinite universe whose volume does not eternally increase or decrease exponentially is the only one which can exist for infinite time and be topologically consistent with current physics. A non cosmologist might describe that as 'steady state.'

Thank you too, Carrock. I must admit that i didn't have Bondi/Gold/|Hoyle in mind when thinking of a " steady state " Universe. I didn't see an infinite Universe as being " in stasis ", only thinking that, if it was infinite, it couldn't  possibly expand " outwards " anymore, as it would have nowhere left to expand  " into ", whereas, if it was finite, it would be able to keep expanding  "into " empty space, which Strange has said is not what is  actually happening. I hadn't considered eternal exponential volume increase/decrease either, only a simple scenario  that would allow the Universe to continue to expand only if it had that " room " for expansion. As a non-cosmologist, then, i was  simply using " steady state "  to mean a Universe that couldn't expand any more. Sorry for the confusion.

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1 hour ago, Tub said:

I hadn't considered eternal exponential volume increase/decrease either, only a simple scenario  that would allow the Universe to continue to expand only if it had that " room " for expansion. As a non-cosmologist, then, i was  simply using " steady state "  to mean a Universe that couldn't expand any more. Sorry for the confusion.

Cosmologists agree and the BB tells us that the observable universe has no center to speak of,(as all of spacetime was packed within the singularity from whence the BB arose) and also no edge or barrier.....Our spacetime is all their is according to the BB, there is no outside.   And while accepting the universe is expanding, I agree that the next intuitive question would be what is it expanding into? But I've also been taught that sometimes the universe does not adhere to what our intuition tells us.....perhaps the question is irrelevant, or invalid as much as the apparent intuitive question re the boundary or edge...I actually believe the problem is more with trying to get our head around what "infinity" means. These seem to me at this time, questions we just do not have a validated scientific answer to at this time.

I'm more relaxed with accepting that the universe is finite in extent and content but very very big, and that our spacetime is all there is.

Edited by beecee
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On 15/08/2017 at 6:28 PM, Airbrush said:

Very interesting explanation and I plan to spend more time studying "A Brief Intro to Infinity".

Can we agree for my example to exclude other dimensions from this discussion of universes?

So you can chop an infinite universe in half on any plane you choose.  On each side of your "chop plane" there are 2 infinite universes that are butt up against each other at the "chop plane".  Each of these half universes are half as infinite as the two were together, right?  How do you select your next chop plane?  Do you chop your 2 universes into 4 on an intersecting perpendicular plane?  Ok, you now have 4 quadrants to the universe.  But that is not a natural configuration for big bangs.  Big bangs do not neatly butt up against each other in 4 quadrants.  Big bangs should be an amorphous blob or even roughly spherical shaped.  Right, don't we see animation CGI of big bangs, and they are roughly spherical in shape?  Also how does something infinite in size pop out of a point smaller than a proton?

You can chop up infinity as many times as you like and each piece will always be infinite. How one visualises that is irrelevant.

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Also how does something infinite in size pop out of a point smaller than a proton?

You should know by now that only pertains to the observable universe portion.

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9 hours ago, Carrock said:

.

9 hours ago, Carrock said:

An infinite universe whose volume does not eternally increase or decrease exponentially is the only one which can exist for infinite time and be topologically consistent with current physics. A non cosmologist might describe that as 'steady state.'

That does not compute with me I'm afraid. If we cut an infinite universe in half, each half is still infinite, correct? So why then cannot an infinite universe not expand or stretch if you will? According to the BB, the universe is all there is...it is expanding into nothing, just as it has no borders or edges. Again I see the fact that the concept of infinity itself is the problem. An infinite universe still expanding/stretching, may seem to be against our intuition, but the universe does not really give a damn about our limited intuition.

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33 minutes ago, beecee said:

That does not compute with me I'm afraid. If we cut an infinite universe in half, each half is still infinite, correct? So why then cannot an infinite universe not expand or stretch if you will? According to the BB, the universe is all there is...it is expanding into nothing, just as it has no borders or edges. Again I see the fact that the concept of infinity itself is the problem. An infinite universe still expanding/stretching, may seem to be against our intuition, but the universe does not really give a damn about our limited intuition.

Opinions aside, you have written little inconsistent with what I've said.

"Again I see the fact that the concept of infinity itself is the problem." - Cantor developed a very rigorous mathematics of transfinite numbers; what is the problem?

"So why then cannot an infinite universe not expand or stretch if you will?" - it can.

"According to the BB, the universe is all there is...it is expanding into nothing, just as it has no borders or edges." - ambiguous.

"An infinite universe still expanding/stretching, may seem to be against our intuition, but the universe does not really give a damn about our limited intuition." - my limited intuition is that the universe, infinite or not, is expanding locally, perhaps everywhere, but that is not in itself proof that the universe is not expanding.

You're describing a universe which only expands exponentially for finite time, where I was describing one which expands for infinite time.

If you want a full response from me, claim something inconsistent with my earlier posts, rather than repeating some of it and saying what I wrote 'does not compute.'

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15 hours ago, StringJunky said:

You can chop up infinity as many times as you like and each piece will always be infinite. How one visualises that is irrelevant.

You should know by now that only pertains to the observable universe portion.

If the actual universe is only a thousand times as big as the observable universe, then does that mean that such a big bang would have popped out of a region only a thousand times as large as a proton?

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11 hours ago, Carrock said:

You're describing a universe which only expands exponentially for finite time, where I was describing one which expands for infinite time.

No, I'm describing a universe as evidenced, that is expanding over large scales and will continue to expand...at least at this time we have no reason to believe anything contrary, ánd I don't believe the universe being infinite in anyway affects that....as per my reasoning.

Quote

If you want a full response from me, claim something inconsistent with my earlier posts, rather than repeating some of it and saying what I wrote 'does not compute.'

What I said was it does not compute with me...And any disagreement or debate on the issue is probably a result of our less then positive understanding of infinite and why that would curtail infinite expansion. You imo, seem to be saying that an infinite universe, will not undergo expansion for an infinite time

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An infinite universe whose volume does not eternally increase or decrease exponentially is the only one which can exist for infinite time and be topologically consistent with current physics

I don't see it that way.

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5 hours ago, beecee said:

any disagreement or debate on the issue is probably a result of our less then positive understanding of infinite and why that would curtail infinite expansion. You imo, seem to be saying that an infinite universe, will not undergo expansion for an infinite time

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An infinite universe whose volume does not eternally increase or decrease exponentially is the only one which can exist for infinite time and be topologically consistent with current physics

I don't see it that way.

Consider a volume of space (finite or countably infinite i.e. at most aleph-null finite spatial elements) which expands exponentially for aleph-null years i.e. for infinite time.

During that time it will double in size aleph-null times i.e. its volume will be 2^(aleph-null) finite spatial elements.

2^(aleph-null) finite spatial elements is equal to aleph-one finite spatial elements, whose number is equal to the number of irrational numbers, or the number of points in aleph-null units of space.

So space must contain aleph-one finite units of space.

There cannot be a one to one correspondence between the non-denumerable set of points (aleph-one) in space and the set of all finite non overlapping spatial elements.

This is an argument by contradiction, showing that there cannot be aleph-one finite units of space.

Informally, you cannot store a finite volume of space in a point.

I don't think it's necessarily impossible to have eternal expansion, but I don't think it's acceptable to say 'but the universe does not really give a damn about our limited intuition' so infinite expansion must be possible.

There's a lot more to this of course but I'll just refer you to

and

International Journal of Theoretical Physics, Vol. 12, No. 3 (1975), pp. 217-223

Cosmological Models and Non-Denumerable Singularities
RICHARD SCHLEGEL

My link to this has died.

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Your terminology (aleph-one)  did have me scratching my head....I am a strictly amateur and lay person as far as cosmology and the sciences are concerned. All I will add is that according to the BB the universe is not expanding into anything...it is everything. Again I don't believe we are or can be totally familiar with the term "infinite"  and that also applies to our definition of "nothing"  from whence the BB arose.

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4 hours ago, beecee said:

I really recommend reading up on Cantor's work on infinity (if you haven't already). It is fascinating (and eye opening) stuff.

Edited by Strange
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The universe, as a whole, is not expanding.
And I clarify that by saying you cannot go to the edge and watch it 'grow' into another volume.
It makes no sense to discuss an 'edge' because anything beyond that 'edge' is still part of the universe.

Rather, the universe is all there is. And the separation between things ( galactic clusters ) is increasing.

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18 minutes ago, MigL said:

The universe, as a whole, is not expanding.
And I clarify that by saying you cannot go to the edge and watch it 'grow' into another volume.
It makes no sense to discuss an 'edge' because anything beyond that 'edge' is still part of the universe.

Rather, the universe is all there is. And the separation between things ( galactic clusters ) is increasing.

Can you expand on that please? Your statement seems to be at odds with what a Google search finds in just about every article I find when I ask "is the universe expanding".

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Sure Zap.

Don't think of the universe as an inflating balloon expanding into an 'outside' volume.
Why wouldn't that outside volume be part of the universe ? the universe is, by definition, everything there is.
And if there was an edge, what would keep everything from 'spilling out ? If you stuck your hand through that edge, could you retrieve it ( in which case the 'outside' is no different ) ? Or is there some physical separation ( ?? ) ?
An 'edge'  complicates things with no purpose.

Think of it instead as a number line, whether infinite in length or circular ( loops back on itself , and curvature is intrinsic ) doesn't matter. It just cannot have an end ( for the reasons outlined above ). Now take two units on that number line and double the separation between them. You have increased the separation, but, in the case of an infinite universe, you have not changes the class of infinity, because there is still a one to one correspondence between the original units and the doubled units.

Edited by MigL
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Few questions:

1. Why do we assume now that the Universe could be infinite?

2. Why an infinite Universe has no impact on the BBT?

3. How could it be that an infinite Universe had been set in only 13.8 BY?

Edited by Dan B.
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2 hours ago, MigL said:

Sure Zap.

Don't think of the universe as an inflating balloon expanding into an 'outside' volume.
Why wouldn't that outside volume be part of the universe ? the universe is, by definition, everything there is.
And if there was an edge, what would keep everything from 'spilling out ? If you stuck your hand through that edge, could you retrieve it ( in which case the 'outside' is no different ) ? Or is there some physical separation ( ?? ) ?
An 'edge'  complicates things with no purpose.

Think of it instead as a number line, whether infinite in length or circular ( loops back on itself , and curvature is intrinsic ) doesn't matter. It just cannot have an end ( for the reasons outlined above ). Now take two units on that number line and double the separation between them. You have increased the separation, but, in the case of an infinite universe, you have not changes the class of infinity, because there is still a one to one correspondence between the original units and the doubled units.

This is only semi-accurate. If the universe in total is infinite, then I think saying that the universe is not expanding but the distances between things are merely getting larger, I think this is a valid interpretation, although you could quibble a bit over whether or not that counts as overall expansion.

If the universe is finite but unbounded (or finite and bounded, although that seems like the strangest option) then the total volume of the universe would be increasing and the universe would very much need to be considered expanding.

And, of course, the Observable Universe is finite and bounded by the Hubble Horizon, so it is very much expanding.

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56 minutes ago, Dan B. said:

1. Why do we assume now that the Universe could be infinite?

Because there is no evidence either way.

56 minutes ago, Dan B. said:

2. Why an infinite Universe has no impact on the BBT?

Because a universe that is evolving from an early hot dense state. Being finite or infinite doesn't affect this.

56 minutes ago, Dan B. said:

3. How could it be that an infinite Universe had been set in only 13.8 BY?

Not sure what I this means. But if the universe is infinite then it has always been infinite.

Edited by Strange
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21 minutes ago, Strange said:

.....But if the universe is infinite then it has always been infinite.

You mean that if the universe is infinite in size, then it popped out of a region of infinite size?

Edited by Airbrush
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4 minutes ago, Airbrush said:

You mean that if the universe is infinite in size, then it popped out of a region of infinite size?

I'm not sure what "popped out of" means. But if the universe is now infinite then it was also infinite when it was hotter and denser.

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32 minutes ago, Strange said:

I'm not sure what "popped out of" means. But if the universe is now infinite then it was also infinite when it was hotter and denser.

So do you mean that:

1. The Universe had been created 13.8 B years ago from an infinite hot denser.

Therefore, the idea (based on the BBT) that the size of the hot denser was compact and finite at the first second is just incorrect.

or

2. The Universe had been created Infinite time ago and therefore it is infinite now

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Just now, Dan B. said:

So do you mean that:

1. The Universe had been created 13.8 B years ago from an infinite hot denser.

Therefore, the idea (based on the BBT) that the size of the hot denser was compact and finite at the first second is just incorrect.

or

2. The Universe had been created Infinite time ago and therefore it is infinite now

There is no evidence that the universe was "created". It may be infinitely old. We don't (currently) know.

The early hot dense universe was finite if the universe is finite. It was infinite if the universe is infinite.

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8 minutes ago, Dan B. said:

2. The Universe had been created Infinite time ago and therefore it is infinite now

If the universe is infinite it has always been in existence. It could, as one or more theories propose, be going through recurring cycles of evolution that allows change to keep occurring ad ininfitum. I think it's better to think of the BB period as just a step in an ongoing evolution.

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