# Thread: Size and infinity concerning the Universe

1. ## Size and infinity concerning the Universe

A couple of questions concerning the size of the universe…

What is the definition of infinity in this sense?

I am left with two options here…

1) It is a universe where there is no ending.
2) It is a universe that loops round on itself so that you arrive back at the beginning

If option two is this case, how can this be classed as infinity? It suggests that the universe is of a finite size but allows infinite travel. Just as the Earth is of finite size but you could travel forever around the equator.

Now we take a bit of a jump and come on to boundaries! Assuming that option two is the correct answer

No boundary! Yep, read that. But is this set or just current dogma?

Firstly, could the speed of the expansion of the universe deny a boundary being seen or reached?

Or,

Secondly, is it possible that because of the way the universe is, it creates its own sort of physical illusion that allows for option two and denies any measurement or perception of a boundary? Being that the universe automatically affects the observer as well as the observed.

In other words, is there a possibility that the universe may have a boundary, and by its own devious nature not allow the boundary to be observed or approached?
Also, if we talk of a multi-verse, and by just allowing for a multi-verse, are we not automatically defining a boundary that separates one universe from another?

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In other words, is there a possibility that the universe may have a boundary, and by its own devious nature not allow the boundary to be observed or approached?
Also, if we talk of a multi-verse, and by just allowing for a multi-verse, are we not automatically defining a boundary that separates one universe from another?
I think "yes."

ETA: Short answer? LOL I'm multi-tasking heavily and feeling a bit like THIS...

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Firstly, could the speed of the expansion of the universe deny a boundary being seen or reached?
Yes, and it already has, which is why we appear to be in the center of the universe. What we can see we call the observable universe, and due to expansion, it's outermost edge is receeding from us at the speed of light (which is why we can't observe anything beyond this boundary).

We don't really know the size of the actual universe, what's beyond the observable boundary.

Secondly, is it possible that because of the way the universe is, it creates its own sort of physical illusion that allows for option two and denies any measurement or perception of a boundary? Being that the universe automatically affects the observer as well as the observed.

In other words, is there a possibility that the universe may have a boundary, and by its own devious nature not allow the boundary to be observed or approached?
Also, if we talk of a multi-verse, and by just allowing for a multi-verse, are we not automatically defining a boundary that separates one universe from another?
I don't believe it loops back in on itself, if that's what you're suggesting. However, I do believe the actual edge of the universe is forever beyond our capability of getting there.

I know it is something that will - probably - never be proven, but I felt that after reading a few threads in Q&A...
We can discount the boundary as having an effect or playing any part in the observable universe, but can speculate with reasonable probability that one may exist.... andyoucouldtherforespeculateithasanoutside!

Okay, strictly ATM I know, I just wanted to be sure that the notion of 'a boundary' was not open to some severe thigh slapping and head shaking

O, and nevermind Neverfly... snarf!

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I know it is something that will - probably - never be proven, but I felt that after reading a few threads in Q&A...
We can discount the boundary as having an effect or playing any part in the observable universe, but can speculate with reasonable probability that one may exist.... andyoucouldtherforespeculateithasanoutside!

Okay, strictly ATM I know, I just wanted to be sure that the notion of 'a boundary' was not open to some severe thigh slapping and head shaking

O, and nevermind Neverfly... snarf!
As I understand it, many see it as a closed system that turns back on itself (Think of a banking curve- only so heavy you end up back inside while traveling in a straight line as an analogy.)

If it's ATM to speculate on it, I spend a lot of time in ATM land

6. Originally Posted by Neverfly
As I understand it, many see it as a closed system that turns back on itself (Think of a banking curve- only so heavy you end up back inside while traveling in a straight line as an analogy.)

If it's ATM to speculate on it, I spend a lot of time in ATM land

That's been my general view of it, but then I hear no boundary which suggests infinite size rather than infinite travel in a straight line.
I like boundaries - you know where you stand with boundaries

Which then led to what is on the other side of the boundary... but that's speculation.

Speculation: No proof required at this time

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That's been my general view of it, but then I hear no boundary which suggests infinite size rather than infinite travel in a straight line.
I like boundaries - you know where you stand with boundaries

Which then led to what is on the other side of the boundary... but that's speculation.

Speculation: No proof required at this time
Ok, let me try again.

From what I understand:

The universe is not infinite.

The speculation:
There isn't another side to the boundary.
We are so accustomed to thinking there is always something outside, it is a bit irrational to think that something could exist- take up space- and have nothing outside of it.
But that's the point isn't it?
Because the only reason things take up space here- is because space is part of our universe.
The only reason things take time- is it's part of the Universe.
Anything outside that- there would be no space- or time.

8. Originally Posted by Neverfly
Ok, let me try again.

From what I understand:

The universe is not infinite.

The speculation:
There isn't another side to the boundary.
We are so accustomed to thinking there is always something outside, it is a bit irrational to think that something could exist- take up space- and have nothing outside of it.
But that's the point isn't it?
Because the only reason things take up space here- is because space is part of our universe.
The only reason things take time- is it's part of the Universe.
Anything outside that- there would be no space- or time.

Thanks for that. I know it's been said before. I was just wondering if this was applied to a finite size.

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just wondering if this was applied to a finite size.
Hmm?

10. Originally Posted by Neverfly
Hmm?
lol... I think the main point was the definition of infinity.

The universe is either infinite in size - in which case boundaries do not apply.

Or it is an enclosed system that requires boundaries to be an enclosed system - but allows for infinite travel in a straight line without reaching a boundary. Though the universe as a whole is of finite size.

The fact that nothing can exist outside the universe would still be applicable to either premise.

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The Universe could be infinite, or it could be finite but unbounded, as
you described in your second option, or it could be finite and bounded.

There is essentially no direct evidence to favor any of those three.
What we know for sure is that the Universe we can see is absurdly
enormous, and the whole Universe is bigger than the part we see.

This will be the first time I have ever made reference to Ockham's
razor: By that principle, it seems reasonable to say that the "finite
but unbounded" option is the least-supportable idea of the three.
It is consistent with what is seen, but in no way does it help to
explain what is seen. The part of the Universe that we see appears
to be geometrically "flat" overall. A finite but unbounded geometry
is curved overall. So the simplest choice is to say that it probably
is not finite but unbounded.

If the Universe is finite and bounded, there would seem to be four
sub-possibilities: That there is empty space beyond the boundary;
that there is/are other universe(s) beyond the boundary; that the
boundary is some kind of impassible barrier; or that there is just
nothing beyond the boundary, not even empty space.

Again by the principle of Ockham's razor, I'd rule out an impassible
barrier as an interesting but unneeded idea. The idea that there is
nothing, not even empty space beyond some boundary, is a notion
I can fantasize but not understand. It has no meaning for me.

So I think that if the Universe is finite, it is most likely surrounded
either by empty space or by other universes. Both of those have our
Universe in an infinite space. If we call all of that space "the Universe",
then I seem to be dismissing the likelyhood of a finite Universe, whether
I intended to or not.

-- Jeff, in Minneapolis

12. In reply to you Jeff, I cannot favour a universe of infinite size. I give two reasons for this:-

The first and weaker point is that we know the universe had a beginning about 13.7 billion years ago, and this would require the universe to be of infinite size in a finite amount of time.

The second and stronger point which is related to the first point, is the fact the universe is expanding. By the very definition of expansion we are saying that from one moment to the next the universe is getting larger. It cannot be infinite in size and be getting larger at the the same time. One must denounce the other.

Bounded or unbounded.

I felt this was more grey, but if we take the universe as bounded, than does that not leave the possibility open of crossing the boundary?
I appreciate that such a thing may well be impossible due to the speed of expansion and the size of the universe, but I wonder if by defining the universe as bounded we open the door for such a thing to be taking into consideration.

Whereas an unbounded universe allows for a finite universe where boundaries do not have to be taken into consideration.
Is it possible that we view the universe as flat from our perspective by the sheer fact it is so huge?
I was thinking that if we could see beyond the observable universe then perhaps we would begin to see the curve in space-time. But again the universe may well deny us this by the illusion of infinity it creates through being unbounded.

The other side.

I understand what Neverfly said and appreciate where he is coming from, but that doesn't stop the niggles! It is hard to get to grips with an inside that has no outside.
Then I was wandering about a multi-verse which seems to be current thinking in QM theory at the moment. By allowing for more than one universe we must have a boundary between them.
I suppose you could say they are linked together like a chain of soap bubbles and, hypothetically, if you crossed the boundary of this universe you would automatically be in another universe - there is no gap between.
But then I'm left wondering how you would allow for expansion! Which then gets really strange with alternating contracting and expanding universes.
It would be novel to think that our universe may be forced into contraction by adjacent universes going through a Big Bang phase.

But to the crux of the thing, I'm more inclined to agree with a finite but unbounded universe even though this, as you pointed out, goes against Ockham's Razor.

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FadingStar, I gave myself a migraine once by thinking for about three hours straight about folding a tessaract into a hypercube. I was sure I could do it if I just tried hard enough!

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In reply to you Jeff, I cannot favour a universe of infinite size.
I give two reasons for this:-

The first and weaker point is that we know the universe had a beginning
about 13.7 billion years ago, and this would require the universe to be of
infinite size in a finite amount of time.
has been infinite from the beginning. That is, immediately after the Big
Bang (or immediately after the Big Bang began), the Universe was already
infinite in extent. I don't understand it, but there you go.

There is another, simpler objection to your first objection, but it applies
to your second objection too, so let's go on to that...

The second and stronger point which is related to the first point, is the
fact the universe is expanding. By the very definition of expansion we are
saying that from one moment to the next the universe is getting larger.
It cannot be infinite in size and be getting larger at the the same time.
Why not?

That is a completely serious question. I've discussed this with several
other people who had a problem with something infinite expanding. My
recollection is that I first read an explanation of it when I read 'One,
Two, Three... Infinity
' by George Gamow when I was in junior high
school in 1967 or 1968.

There are infinitely many ways one could explain it -- here's one:

You are the night manager at the Infinite Hotel. The hotel has an
infinite number of rooms, numbered 1, 2, 3, and so on forever, so
there is no limit to the number of guests you can put up. But you
have a problem. You've just been told that an infinite number of
new guests will be arriving shortly, and you can't seem to find any
free rooms! Whatever will you do??

You decide to bite the bullet and ask all the guests to move from the
room they are in to the room number that is twice their current room
number. So the guest in room #1 will move to room #2, the guest in
room #2 will move to room #4, the guest in room #3 will move to
room #6, and so on. Everyone will end up in even-numbered rooms,
leaving all the odd-numbered rooms open for the infinitely-many new
guests who are about to arrive.

Imagine that the dots in this animation are just a tiny part of an
endless line of dots -- imagine that it extends infinitely to the left
and right from the very first frame:
Uniform expansion

The fact that the line of dots is infinite in length doesn't prevent the
dots from moving farther apart.

I said above that there is a second objection to your first objection,
which also applies to your second objection. :-)

There are two possible meanings when someone asserts that the
Universe is, or may be, infinite: One is that space and the matter
in it, which began expanding at the moment of the Big Bang, are
endless in extent. The other is that space is infinite, but the matter
which was involved in the Big Bang is not infinite. The Big Bang might
have involved only a finite portion of infinite space. In that case the
Universe we know could have started out infinitesmally tiny, taking
care of your first objection, and it would have been a finite amount
of stuff spreading out into an infinite space, taking care of your
second objection.

I felt this was more grey, but if we take the universe as bounded, than
does that not leave the possibility open of crossing the boundary?
That possibility was implied in the first two of the four sub-possibilities
under bounded cases.

Is it possible that we view the universe as flat from our perspective by
the sheer fact it is so huge? I was thinking that if we could see beyond
the observable universe then perhaps we would begin to see the curve
in space-time.
That is a possibility that I tried to imply.

-- Jeff, in Minneapolis

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## An Essential Book

Originally Posted by Jeff Root

The part of the Universe that we see appears to be geometrically "flat" overall.
To within 2% to 3%. Lke, if it's curved, it's down in the noise.

Originally Posted by Jeff Root

A finite but unbounded geometry is curved overall. So the simplest choice is to say that it probably is not finite but unbounded.
Therefore, probably infinite and flat.

I would highly recommend George Gamow's "1,2,3 . . . Infinity" if you can find a copy.

16. Jeff

has been infinite from the beginning. That is, immediately after the Big
Bang (or immediately after the Big Bang began), the Universe was already
infinite in extent. I don't understand it, but there you go.
Neither do I.

You are the night manager at the Infinite Hotel.
I see where you're coming from with Hilbert's Hotel, and can go with that, but I must confess to getting seasick in an ocean of Cantorian infinities sometimes.

Otherwise, thanks for the clarifications.

17. Quick Query if anyone can.

Is Cantor's absolute infinity an absolute?

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Quick Query if anyone can.

Is Cantor's absolute infinity an absolute?
Interpretation?
I'm wondering how you mean the question...

As I understand it- Yes, as Cantor described.

19. Olbers' paradox is a related issue.

For the record:
*- Einstein has at least one published lecture where he describes the universe finite but unbounded.
*- Carl Sagan described the universe as finite but unbounded in the Cosmos TV series.

Or so I recall.

20. Originally Posted by Neverfly
Interpretation?
I'm wondering how you mean the question...

As I understand it- Yes, as Cantor described.
I wanted to know if it was an absolute or a variable, after wading my way through Cantor's infinites. If it encompasses everything, does that make it an absolute because it can't encompass anything else?

Also, while we're here

If aleph-null is smaller than aleph-one, then at some point aleph-null becomes aleph-one as you get bigger. Is this an absolute point, a variable, or breaking the rules?

My thought was on whether infinity is an absolute or a variable, and intially you could say variable because you can always add one, but you can't add one to Cantor's absolute infinity.

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My thought was on whether infinity is an absolute or a variable, and intially you could say variable because you can always add one, but you can't add one to Cantor's absolute infinity.
See? You just said it here. Cantors is absolute because you cannot add one.

ETA: I need to look this up dangit. If I recall correctly, that is what Cantor had said about it. That you cannot add one.

22. So could you say the universe is an example of Cantor's absolute infinity?

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So could you say the universe is an example of Cantor's absolute infinity?
No, that is not how I see the Universe. I see the Universe as Finite.
I've heard all the arguments for an infinite Universe, but they all fall short.

I find Sagans "Finite, unbounded" to be (In my uneducated position) the best match for observation.

I haven't yet googled Cantor, so I'm going off my aging (At 29 ) Memory- Cantor described the absolute infinity as a concept- not necessarily a physical construct.
But if you apply that concept to the Universe, it would mean that no matter what direction you went in, you would go on forever and ever and ever in that direction and never find an edge (Not the same as finite but unbound- as you could travel forever but would actually be making a loop). You would just keep passing stars. Since, observationally, we are not seeing this effect from Earth (Infinite space would seem to require infinite time- thus a star in every direction you look) it appears the Universe is finite.

24. But if you apply that concept to the Universe, it would mean that no matter what direction you went in, you would go on forever and ever and ever in that direction and never find an edge
An infinite universe

Not the same as finite but unbound- as you could travel forever but would actually be making a loop
Confused with infinite as unbounded! Wouldn't absolute infinity be applied to an infinite universe whether unbounded or bounded?

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An infinite universe

Confused with infinite as unbounded! Wouldn't absolute infinity be applied to an infinite universe whether unbounded or bounded?
Finite but unbounded.

And no, because in an infinite universe you would literally never reach an end traveling in a straight line. You would not be in a loop that closes you back to point of origin along the way.
In a finite but unbound universe there are boundaries- unbound only means that your loop returns you to origin even while traveling in a straight line.

Also, if I'm wrong on any of this- someone please correct me so that I'm not leading anyone astray...

26. Originally Posted by Neverfly
Finite but unbounded.

And no, because in an infinite universe you would literally never reach an end traveling in a straight line. You would not be in a loop that closes you back to point of origin along the way.
In a finite but unbound universe there are boundaries- unbound only means that your loop returns you to origin even while traveling in a straight line.

Also, if I'm wrong on any of this- someone please correct me so that I'm not leading anyone astray...
Yep. I see that. The change was you can't have an infinte and unbounded universe.

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Infinite but unbounded...

That hurts my brain just thinking about it...

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Originally Posted by Neverfly
No, that is not how I see the Universe. I see the Universe as Finite.
I've heard all the arguments for an infinite Universe, but they all fall short.

I find Sagans "Finite, unbounded" to be (In my uneducated position) the
best match for observation.
That sounds like a "closed" universe.

Current observation shows the Universe to be very nearly "flat"
overall, on the largest scales we can see. That means the Universe
either is "flat" overall, or has significant overall curvature only on a
scale considerably larger than what we can see. There are reasons
to think that the geometry should be "flat" overall. If I understand
correctly, overall flatness implies that the Universe is not closed.

However, my personal favored geometry could be described as
"finite but unbounded", even though it is open, not closed. That
is an overall flat geometry in which a finite quantity of mass-energy
took part in the Big Bang, within an infinte spacetime. Matter and
energy are finite and bounded; spacetime is infinite and unbounded.
This seems like the simplest possibility. Maybe too simple.

Originally Posted by Neverfly
But if you apply that concept to the Universe, it would mean that no
matter what direction you went in, you would go on forever and ever
and ever in that direction and never find an edge (Not the same as
finite but unbound- as you could travel forever but would actually be
making a loop). You would just keep passing stars. Since, observationally,
we are not seeing this effect from Earth (Infinite space would seem to
require infinite time- thus a star in every direction you look) it appears
the Universe is finite.
The standard explanation, which makes no sense to me, is that if the
Universe is infinite, it was infinite from the beginning, and thus did not
need any time to become infinite. If I understand your point of view
correctly, I agree with you -- it seems totally unreasonable that the
matter we see, expanding equally everywhere, could have got into
that condition throughout an infinite universe. So it seems impossible
that the matter of the Universe could be infinite in extent.

However, given that the age of the matter is finite, it hasn't been
around long enough for light from very distant stars to reach us.
And because the Universe is expanding, light from very distant stars
is redshifted so much that we will never be able to see it. So your
argument about seeing a star in every direction you look is definitely

-- Jeff, in Minneapolis

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Hi...I am new to this site. I just wanted to ask if the concept that the farther out into space we are looking means that we are looking at things that are as far back in the past? If that is true then how can we be positive that those objects still exist? How can we be sure that there IS a physical universe out there still, and that we are not simply looking at earlier stages of our own past?
Finite/Infinite...neither makes sense to the logical side of your brain....it cannot have an end because there cannot just be nothing there...the nothing we know is just a blank between objects...our brains can only conceive of a next object. It cannot go on forever...we cannot conceive of something that has no end,,,I try and always see at least empty space beyond...space is not an end...it is still space with atoms...molecules...w/e....it is still something.

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My apologies.

I deleted my original message as it was in very poor taste and incorporated an attitude I inadverantly carried over from another issue.

I have a copy of it on my hard drive in case the mods insist I restore it. For more information, please see the Reason for Editing immediately below.