The Universe: Finite or Infinite?

[mattex]

OK, please let me begin by declaring that, YES, I have read around this topic, but I am still stumped.

It continually plagues me. I even had a friend blurt out of the blue the other day, "What's with the universe? Does it just keep on going forever? Or does it stop? If so, what's beyond it?"

I could sense he was troubled by the whole cosmic concept (as we ALL should be!)... and so am I.

All I have read is convoluted ambiguous stuff about definitions of "universe" and "nothingness" etc = word games, no less.

I read a recent thread here about "metrics"... which still doesn't do it for me. I'm not interested in an artificial concept, I'm only interested in the Reality of the whole situation.

Is the universe finite? (= implies a "Beyond")
Is the universe infinite? (= seems nonsensical, and counter-intuitive to "Big Bang" theory)

PLEASE help!

This is a very important & fundamental thing, for ALL of us (even if we aren't aware of it). Thanks!

 

[marcus]

Is the universe finite? (= implies a "Beyond")
Is the universe infinite? (= seems nonsensical, and counter-intuitive to "Big Bang" theory)

Both your parenthetical additions involve a mistake.

Finite does NOT imply a beyond. A ring, for example, is a finite one-D universe with no beyond.

a sphere surface is a finite 2-D universe with no beyond.

Imagine that there was no space besides that spherical 2D surface. a traveler in that surface would never meet a boundary----no wall would mark the edge of his world

the analogous 3D thing is called "ess-three" and written S³
it is finite, and has no boundary.

if the universe space is finite, it is possible that it is a boundaryless space like S³

It could also be infinite and why do you say that would be counterintuitive?
Bigbang theory does not say that the universe began as a point. Popular books that say that are misleading the public.
Bigbang theory actually does not specify whether the initial singularity was finite or infinite.

The space-finite versus space-infinite issue is undecided among cosmologists at present and there is some controversy about this heating up. Many cosmologists prefer to assume space-infinite because it simplifies the math or for various other reasons. Indeed to make it even simpler to calculate, they assume it is spatially FLAT as well as infinite---just your vanilla flat 3D graphpaper space!
Others say, since we don't KNOW for sure that it is infinite or flat, you shouldn't assume it because it introduces errors in the analysis of data. They say you should analyze data in a way that leaves open both possibilities.

Two guys in particular have been arguing forcefully for this viewpoint. Edward Wright and Bruce Bassett. they each have written papers recently about it.

According to Ned Wright, the best-fit finite-space picture would have space be S³ with a radius of curvature about 130 billion light years.Then the bigbang singularity could be described in a finite localized region. Space is very very big now (but still not infinite) and it could have been a smallish compact space when it started expanding.

the other version, with infinite-space, would assume that the initial bigbang singularity was already also spatially infinite---extending straight out to infinity in all directions.

Ned Wright and Bruce Bassett do not favor one over the other. They don't say that the infinite space picture is WRONG. They just warn that you can misinterpret observational data and get trapped in circular reasoning if you ASSUME the infinite case when we don't actually know which is right.

So far, allowing for observational uncertainty, the data is consistent with either case.

 

[mattex]

Thank you for the detailed response!

I think my problem boils down to a basic inability to visualise/conceptualise, say, a 1D "ring" without the 2D paper it is drawn on. Likewise, a 2D spherical "surface" without any 3D "inside" or "outside".

But let me play some more, maybe I'll ask more qu's down the track.

Thanks again!

 

[marcus]

I think my problem boils down to a basic inability to visualise/conceptualise, say, a 1D "ring" without the 2D paper it is drawn on. Likewise, a 2D spherical "surface" without any 3D "inside" or "outside".

I'm glad it was helpful. As far as being able or not able to imagine a finite volume boundaryless space which is NOT embedded in an abstract space of higher dimension...I have some advice.

My advice is relax and not to worry. Personally I think it is perfectly fine to think of a 2D sphere embedded in an abstract surrounding space.

but if you live in one along with other 2D creatures you have to remember not to BUG the 2D astronomers by asking about the abstract centerpoint and talking as if it has some location or even some physical existence.

If we lived in a 2D expanding balloon then the CENTER of the expansion would not be a point in the balloon. It would not be a real physical location for us, it would only exist in some higher (3) dimensional space that we can't navigate or triangulate or peer at with a telescope. So it is better not to talk about it.
=======================

So by analogy imagine we live in an ESS-THREE (symbol S³)
which is the 3D analog of the balloon.
Quite possibly we do. the cosmologist Ned Wright posted a paper earlier this year where he gives a best-fit which allows one to estimate the radius of average curvature of the ess-three as 130 billion lightyears.

BUT YOU CAN'T POINT AT THE abstract CENTER, BECAUSE ALL THE DIRECTIONS YOU CAN POINT ARE IN OUR 3D SPACE.

there could be this abstract higher dimension space that our ess-three is engulfed in and it might have a center but that is all non-science fantasy because you can't do an experiment about it. you can't point at it.
it has no practical existence.

So you have to remember not to bug astronomers and such by asking about it.

suppose they come next year or in 10 years and they way "well! we have measured more accurately and now we are pretty sure the universe is finite and has a certain intrinsic curvature which you can measure by summing the angles inside big triangles and our best guess is that the universe is spatially an ess-three with a radius of curvature of 130 billion LY."

Then what you must absolutely not do, this is an absolute no-no, is ask they "Where is the center?"

the center would only be an abstract idea, you could not point at it because all directions are in your world, there would be no scientific evidence that it exists.

Some people cannot imagine a 3-sphere with no inside and no outside and some people CAN imagine a 3-sphere with no inside or outside (by imagining the experience of inhabitants who go exploring and get back to the same place and stuff like that). whether one can or cannot imagine does not cut the ice----what counts is whether it can be defined mathematically, and it can.

So the advice is to imagine it anyway that works for you but don't ask the astronomers where the center is

 

[Wallace]

hmm I must admit I havn't followed your reasoning fully here Marcus, but I think there is a confusion of ideas. The question of whether the Universe is flat or curved and the question of whether it is finite or infinite are unrelated. You seem to be implying that a positively curved ('closed') Universe is necessarily finite which it not true. The 'ess-three' analogy you make with the surface of a balloon and 2D observers can trick you into thinking that the finite volume that someone crawling on the balloons surface can visit implies that the total volume of the Universe is also finite. This is not true, all it tells you is something about a given observers future light cone, i.e. that it converges. There can be infinitely more observers whose allowed region of travel does not overlap yours.

All FRW solutions are valid only for infinite universes, including flat, closed and open ones. We don't really know how to write the GR solutions for finite Universes, which in itself is no reason not to consider the possibility, but it is important to realize that 'finite universe' effects that may at some point be observable are unrelated to issues of spatial curvature.

 

[marcus]

hmm I must admit I havn't followed your reasoning fully here Marcus, but I think there is a confusion of ideas. The question of whether the Universe is flat or curved and the question of whether it is finite or infinite are unrelated. You seem to be implying that a positively curved ('closed') Universe is necessarily finite which it not true. The 'ess-three' analogy you make with the surface of a balloon and 2D observers can trick you into thinking that the finite volume that someone crawling on the balloons surface can visit implies that the total volume of the Universe is also finite. This is not true, all it tells you is something about a given observers future light cone, i.e. that it converges. There can be infinitely more observers whose allowed region of travel does not overlap yours.

All FRW solutions are valid only for infinite universes, including flat, closed and open ones. We don't really know how to write the GR solutions for finite Universes, which in itself is no reason not to consider the possibility, but it is important to realize that 'finite universe' effects that may at some point be observable are unrelated to issues of spatial curvature.

Hi Wallace, are you talking about infinite in a 4D sense?

I was only talking about spatial finiteness. I think that is what the questioner was asking about.

 

[Wallace]

I'm not quite sure what 'infinite in a 4D sense' means?

In a positively curved FRW universe there is an infinite amount of space, however there is only a finite amount of space that a given observer can visit, due to the convergence of future light cones. In most (see http://arxiv.org/abs/astro-ph/0609271" for some pedantic details) flat universes, given enough time, an observer can visit an infinite amount of space, by which I mean that they can reach any arbitrary point in space a given distance from their starting point (the pedantic issues arise because 'distance' is tricky as we know!).

Now in our curved space, even given infinite time there is a finite distance from the origin that an observer can go to before, despite their best efforts, they find themselves coming closer to the origin once more (by the balloon analogy, they are on the opposite of the balloon to the origin). However, what you must not do is assume therefore that this maximal distance the observer can travel to defines the limit of the spatial volume of the Universe. It only defines the finite volume that is accessible to the given observer.

There is nothing in this that prevents an infinite amount of space to exist, just that an observer can only get to a finite amount of space. So just because there is a maximal distance that you can go from the origin does not mean that there is no space at greater than that distance.

As I say, all FRW solutions describe universes with an infinite amount of space, this includes curved ones.

 

[marcus]

I can see all that Wallace,
as soon as you allow time into the picture it changes things.

I was talking about a single spatial slice.

I think that was what the questioner was wondering about

 

[marcus]

I think it is simply untrue that you can't have FRW solutions for a universe that is topologically equivalent to R x S³

that is a 3-sphere cross a time axis.
there are plenty of metrics that are solutions and live on that.
So we should try not to say anything that appears to contradict that.

I was talking very informally about how one might imagine the experience of living in a SMALL ess-three from the inside. Then one can explore all around, perhaps in a few minutes or hours or days.

I want to make the point that one can imagine these spaces from the inside without picturing a surrounding higherdimensional space.

I was not talking about exploring the fullsize universe
there one is limited by the speed one can travel. it isn't practical
=================

maybe we can figure out some way to operationally check if our universe is spatially finite by having helpers in a chain of galaxies that go all the way around the equator. never happen but as a Gedanken experiment.

 

[Wallace]

If you don't want to talk about time then you should also avoid talking about motion (in this case the wandering on the Balloon). I don't see that the OP asked anything about constant time slices, I'm pretty sure you introduced that idea ;)

The question was pretty simple and fair. Is the universe finite or infinite. It is an interesting question but one that is not related in anyway to spatial curvature.

 

[marcus]

I think we can put the question clearly

something like "does the universe have a compact spatial slice?"

maybe you or one of the others would like to help rephrase it.

here is a link to something I posted earlier about Bruce Bassett's paper
https://www.physicsforums.com/showthread.php?p=1326040#post1326040

==============

my guess is that we get a lot of questioners here who have the same question in mind

if you could take an instantaneous snapshot of space-----as Wallace said, a "constant time slice"----or as I said a "spatial slice"-----
and that is how many people think of space----then would that be finite or infinite?

It could be that mattex, who started this thread, had this kind of question in mind. It is sometimes hard to tell until you talk what the question is.

==============
People also wonder about whether, if you could take an instantaneous snapshot of space would it have a BOUNDARY, a kind of wall, or skin?

A lot of people's questions are fundamentally TOPOLOGICAL in nature. they ask how can space be finite (i.e. topologically compact) and not have a boundary? So we need to be prepared to answer. How do you suggest to someone to imagine a compact boundaryless space? (at that point the finite speed of light does not enter, it can be something you explore in a few days or years, like the surface of the Earth which is finite yet boundaryless)

 

[Wallace]

But that's not the question that was asked, and it is not what lay people generally mean when they ask 'is the Universe finite or infinite'. We can change the question to make it easier to answer, but then we are answering a different question!

 

[marcus]

But that's not the question that was asked, and it is not what lay people generally mean when they ask 'is the Universe finite or infinite'. We can change the question to make it easier to answer, but then we are answering a different question!

How would you paraphrase mattex' question? I am interested.
And what do you think lay people generally mean when they ask "is the Universe finite or infinite?"

 

[Wallace]

I would paraphrase it like this, is there an infinite number of stars/galaxies/atoms etc in the Universe? The answer is the same regardless of the overall geometry of the Universe.

 

[marcus]

I would paraphrase it like this, is there an infinite number of stars/galaxies/atoms etc in the Universe? The answer is the same regardless of the overall geometry of the Universe.

Great! I might not have thought of that.

I think to make that question meaningful you may need to say something like is there a finite number NOW AT THIS MOMENT

if particles can change from one kind to another, and time goes on forever, then the history of the universe might have an infinite number of different particles even though there were allowed to be only, say, TEN particles at anyone time.

 

[marcus]

here is the original question that we are paraphrasing

"What's with the universe? Does it just keep on going forever? Or does it stop? If so, what's beyond it?"
..
..
Is the universe finite? (= implies a "Beyond")
Is the universe infinite? (= seems nonsensical, and counter-intuitive to "Big Bang" theory)
..

I would say that this refers to an instantaneous snapshot of space. Does it keep going on forever or does it stop (i.e. have a boundary, and something beyond)at the present moment?

If you include time in the discussion then it quickly boils down to asking about does time go on forever or will everything end say in 50 billion years from now? That is an an interesting question too, but I don't think he was asking about a possible end of time.

I think the question was analogous to someone who asks about the surface of the earth.

"Does the surface of the Earth go on forever? Or does it stop, at some kind of boundary, and have something beyond it?"

People used to ask this question. they imagined the surface of the Earth ending at a cliff. with some danger of falling off.
I think we are hearing a similar sort of curiosity concerning the extent of space.

Maybe we should start a thread and ask people!

 

[Wallace]

Right, so as you pointed out well in your reply there are so fundamental misconceptions about what either option (finite or infinite) would imply. Having sorted them out I don't see how the remaining question pertains to spatial curvature?

Whether or not the universe 'goes for ever' is not a question who's answer depends on the overall geometry. Whether we could travel in one direction forever and not end up where we started is such a question, but it is a different one.

Edit: Okay so since posting this the previous post from Marcus has grown! I can't see how the issue of time comes into this at all? Regardless of whether the universe is curved (positively or negatively) or is flat the question of spatial finiteness has the same answer whether or not you 'consider time'. That answer is independent of the geometry! In a constant time slice of a curved FRW universe there is an infinite amount of space. When you throw time into the mix you find that there is a finite volume of space that can be visited by an observer.

If you want to talk about truly spatially finite universes you need to come up with a different solution than FRW, one that does not obey the cosmological principle.

 

[mattex]

This is a terrific discussion!

You people have certainly forced me to re-evaluate my fundamental assumptions. Yes, I suppose I was talking about a "spatial slice" of the universe - not taking into account time, or light-cones, or speed-of-light limitations, etc.

I suppose what I'm really after is a "God's eye view" of the universe, HERE and NOW - which, in hindsight, is simply wishful thinking.

I sincerely hope this discussion can continue!

 

[marcus]

In a constant time slice of a curved FRW universe there is an infinite amount of space...

Wow! we may have to leave it at that, at least for the time being.
by positive curved I understand Omega = 1.01, for instance, say.
by "amount of space" I understand you to mean volume.

the slice I am thinking of is a spatial slice. I translate finite to mean compact, so for instance the whole spacetime could be topologically R x S³

What I gather is that you (whom I regard as expert) consider that impossible.

 

[George Jones]

I, too, am somewhat confused here.

If constant instants of cosmological time are used to foliate a Freidmann-Robertson-Walker spacetime into spacelike sections, then (as marcus has posted) \mathbb{R} \times S^3 results when the spacelike sections have constant positive spatial curvature with respect to the spatial metric induced on the the spacelike sections by the spacetime metric. In this case, each spatial section is compact and has finite volume 2\pi^2a^3. See Box 27.2 of Misner, Thorne, and Wheeler.

 

[marcus]

I, too, am somewhat confused here.

If constant instants of cosmological time are used to foliate a Freidmann-Robertson-Walker spacetime into spacelike sections, then (as marcus has posted) \mathbb{R} \times S^3 results when the spacelike sections have constant positive spatial curvature with respect to the spatial metric induced on the the spacelike sections by the spacetime metric. In this case, each spatial section is compact and has finite volume 2\pi^2a^3. See Box 27.2 of Misner, Thorne, and Wheeler.

thanks for the reference!

Back in January when Ned Wright's "best fit" paper came out, I calculated the volume using George Smoot's lecture notes for a UC Berkeley course he taught called physics 139. I think they can be found online.

This is the Ned Wright BEST FIT volume
In his recent article (January 2007) Wright gives a version of the universe that he calls best fit (to 4 or 5 different datasets) and Omega = 1.011

According to Smoot's notes the radius of curvature R is equal to the current Hubble radius divided by the square root of (Omega - 1) and the square root of 0.011 is around 0.105

so you divide the Hubble radius 13.8 billion LY by 0.105 and you get R = 130 billion LY.

2 \pi^2 R^3, which you quote from Misner Thorne Wheeler is the 3 volume of the 3-sphere of radius R, just as one would expect.

It is easy to calculate because 2 \pi^2 is 20 and R³ is 2.2 E33 cubic LY which if you multiply by 20 you get 4.4 E34 cubic LY.
I remember when Ned Wright's "best fit" paper came out I was very enthused and immediately calculated this volume and converted the volume to metric and went ahead and calculated the matter content including dark matter but not dark energy. It was some ridiculously large number.
I think the total energy equivalent of all the matter (excluding dark energy) came to E73 joules.

=======
that 2 \pi^2 R^3
is the surface of a 4-ball of 4-volume equal to

\frac{\pi^2}{2} R^4

sometimes the ball volumes of various dimensions are easier to remember or to find than the sphere volumes (and then you just take derivative)

=======
and of course the actual volume could be some other number or even INFINITE we don't know!
this 4.4 E34 cubiclightyears is just the BEST FIT volume
http://arxiv.org/abs/astro-ph/0701584

 

[Wallace]

Hmm I'm having a good think about this guys, didn't want you to think I'd justed walked away from this discussion though! I'll get back to you...

 

[Chronos]

All I see are finite operators, so I've missed the point.

 

[marcus]

Ned Wright's january paper has been accepted for publication by the Astrophysical Journal, he posted the revised version at the end of April, just a few days ago

http://arxiv.org/abs/astro-ph/0701584

this compares the flat LCDM with curved LCDM and with several other cases where you don't have a strict cosmo constant (i.e. w not equal -1)

ON BALANCE I would say that the evidence he presents, combined from several sets of data, could be construed to favor FLAT LCDM. At least it is consistent with flat LCDM---it doesn't rule it out.

On the other hand, the "best fit" LCDM is closed with Omega = 1.011
(slight positive curvature, radius of curvature 130 billion LY)
but Wright points out that the improvement of fit is NOT STATISTICALLY SIGNIFICANT.

The "best fit" LCDM, which is a finite spatial volume universe, is only one chi-square point better fit than the flat. So if you *like* flat, you are not going to feel pressured to give it up!

This is summarized in the table he has at the end, in the conclusions section. Especially the caption to that table.

However what i like about this is that he doesn't simply ASSUME flat, like so many of his colleagues. He recognizes the pitfall of doing that and so he is careful to do his analysis allowing for the nearly flat, slightly curved, spatial finite case.
the paradigm natural philosopher. bravo.

================
anyway, one is equally justified to say the data is consistent with (spatial) closed LCDM
in fact a statistically insignificant hair MORE consistent
and so it is consistent with the "best fit" LCDM which has a current spatial volume of 4.4 x 10³⁴ cubic lightyears.
Aint science wonderful

 

[Wallace]

However what i like about this is that he doesn't simply ASSUME flat, like so many of his colleagues. H recognizes the pitfall of doing that and so he is careful to do his analysis allowing for the nearly flat, slightly curved, spatial finite case.
the paradigm natural philosopher. bravo.

I don't know that this is fair. The only reason people restrict analysis to flat space-times only is due to the exact kind of analysis the Ned Wright presents. It is common to see some statement like 'Since the current evidence from (wherever) suggest that the Universe appears to be flat, i.e. see Smart Folk (200X) we will restrict our analysis to such models'. The alternative would be for every paper to start with 10 pages of statistics justifying the use of flat models only, which would waste every bodies time!

If cosmologists didn't bother to read the papers they are citing and never convince themselves that the data really supports this position then maybe this criticism is justified. In my experience however I don't think this the case.

There are a number of papers that look at the data the way Ned Wright has done (including both WMAP cosmology papers) and they have all come to the same conclusions, so the question is hardly controversial.

 

[marcus]

The issue of whether one should assume flat is controversial. The reason I paraphrase and quote cosmologists criticising other cosmologists for engaging in this practice is because I want to get at the controversy and see what the extent of it is.

Here is a high visibility instance of it that I didnt mention yet. In November 2005 there was a highvisibility conference in Munich
"Relativistic Astrophysics and Cosmology - Einstein's Legacy"

Ned Wright gave a talk. (WMAP3 results were embargoed until 3 months later, but he doubtless knew them since he was a central member of the WMAP team). The talk was called
http://arxiv.org/abs/astro-ph/0603750
A Century of Cosmology
The proceedings are to be published by Springer.

On page 8 you see this cartoon making fun of people who assume spatial flatness. The caption under the cartoon is:

Fig. 1. The circular argument popular among current searches for w and w'. Models fits should always allow Omega_tot to be a free parameter.[/color]

The Figure 1 cartoon of the "circular argument" is a big circle made of the words
If w = -1, then flat LambdaCDM is a good fit to all the data.
If Omega = 1, then w = -1 is a good fit to all the data.[/size]



This joke was one of the main messages of his Einstein Year talk.

My point is that assuming flat is controversial and I think your post illustrates that. You present a certain kind of thinking about a controversial issue.
It is certainly a legitimate viewpoint, namely that it would be too much trouble to do what Wright urges his colleagues to do, namely when fitting data always allow Omega to be a free parameter

 

[marcus]

Wallace I think the main issue is what is considered good professional practice and what is viewed as sloppy.

We have to let the professional community decide that. No one person's word is final. I am interested in the controversy so I paraphrase and quote what I hear of one cosmologist criticising others about this practice.

Here are some exerpts from:
Bruce Basset et al
http://arxiv.org/abs/astro-ph/0702670
Dynamical Dark Energy or Simply Cosmic Curvature?
5 pages, 1 figure
"We show that the assumption of a flat universe induces critically large errors in reconstructing the dark energy equation of state at z>~0.9 even if the true cosmic curvature is very small, O(1%) or less. The spuriously reconstructed w(z) shows a range of unusual behaviour, including crossing of the phantom divide and mimicking of standard tracking quintessence models. For 1% curvature and LCDM, the error in w grows rapidly above z~0.9 reaching (50%,100%) by redshifts of (2.5,2.9) respectively, due to the long cosmological lever arm... These results show that including curvature as a free parameter is imperative in any future analyses attempting to pin down the dynamics of dark energy, especially at moderate or high redshifts."

That was from the abstract. Note the date on the paper. It's quite recent. Here are some excerpts from the main body of the paper:

===quote Basset et al===
However, we will show that ignoring Omega_k induces errors in the reconstructed dark energy equation of state, w(z), that grow very rapidly with redshift and dominate the w(z) error budget at redshifts (z > 0.9) even if Omega_k is very small. The aim of this paper is to argue that future studies of dark energy, and in particular, of observational data, should include Omega_k as a parameter to be fitted alongside the w(z) parameters.

Looking back, this conclusion should not be unexpected. Firstly the case for flatness at the sub-percent level is not yet compelling: a general CDM analysis [Dunkley et al], allowing for general correlated adiabatic and isocurvature perturbations, found that WMAP, together with largescale structure and HST Hubble constant constraints, yields
Omega_k = −0.06 ± 0.02. We will show that significantly smaller values of Omega_k lead to large effects at redshifts z ~ 0.9 well within reach of the next generation of surveys.

Secondly, Wright (e.g.[14]) has petitioned hard against the circular logic...

Given that the constraints on Omega_k evaporate precisely when w deviates most strongly from a cosmological constant,
it is clearly inconsistent to assume Omega_k = 0 when deriving constraints on dynamical dark energy...
===endquote===

 

[Teresa]

ok, this may be a really dumb question, but i really should b doing an assignment atm and i don't have time 2 read the long responces ppl have posted... so if this has already been mentioned, feel free 2 ignore me haha

has ne1 tried 2 answer the question from the point of view of what the universe would b like (theoretically, of course) if it was infinite, or if it was finite?

Wallace said "is there an infinite number of stars/galaxies/atoms etc in the Universe?", but that question is very difficult 2 answer... so going backwards, what would it b like if there was "an infinite number of stars/galaxies/atoms etc in the Universe?" and what would it b like if they were finite? and which is more like the universe we live in?

surely that would b the only way we could come up with an answer to the question? tho i am tempted to put in the number 42 here, as i am suggesting that we find the question from the answer... haha... 42 =P

 

[marcus]

... what would it b like if there was "an infinite number of stars/galaxies/atoms etc in the Universe?" and what would it b like if they were finite?

either way it could be just like it is now
(to answer your previous question, yes, people HAVE thought about this and tried to see if there would be some noticeable difference)

and which is more like the universe we live in?

with a very tiny exception, both cases would be equally like the universe as we experience it
========================
the tiny exception goes like this:
By plugging in different numbers, the standard cosmology model called LCDM can be made to fit the observed data in EITHER case (finite or infinite).

there is a number called Omega which can be measured by making massive amounts of astronomical observations and it looks like this number is either exactly 1, or just slightly bigger than 1 (by maybe around a percent)----in other words something like 1.01.
If the true value of Omega were 1.01 it would mean spatially finite universe
If the true value were exactly 1 or much much closer to one like 1.0001 then it would strongly suggest infinite.
But we don't know the true value, we only have "plus-or-minus" uncertain estimates. More data will narrow it down.

the difference between the two cases of finite and infinite is in the finite case you expect that by doing more and more observations (to get the measurement more and more accurate) it would narrow down to something like 1.01

and if it is truly infinite then when you do more and more measurments it would narrow down closer to exactly one.

So far the range of uncertainty on this number is still enough uncertainty that one cannot say which case.

The last time I saw a "confidence interval" for Omega (in a major-league astronomy article) it said something like the "65 percent confidence interval" was [1.003, 1.03]
I don't remember the exact numbers but something like 65% probability that Omega was somewhere between 1.003 and 1.03
(assuming other things etc etc...)

But that still leaves plenty of probability that the true value is outside that interval and that it could, among other things, be exactly equal ONE.
So the issue of finite versus infinite is far from settled!

 

[Voltage]

I read a book about infinity once. I think it was The Infinite Book by John D. Barrow, and I think his conclusion was there are no actual infinities in nature and it's just a concept. But I'm not too sure, so don't take my word as gospel. I'll check when I get home.

 

[Vincent So]

The energy states of a system are quantized if and only if the system is bounded. Light energy is quantized. Hence I believe our universal is bounded, i.e. finite.

 

[jreelawg]

The question is entirely meaningless unless everyone agrees on a definition of "universe".
What we all see is a big sea of quantum vacuum. There could be other bodies of substance out there that are each contained. So our bubble could be finite in an infinite universe. People like to call their bubble the universe which is kind of a roadblock in answering the question.

Magical human inventions modeling the universe as the surface of sphere make no sense to me. For one, the universe has three spatial dimensional. The "surface" of a sphere model would require that there is a thickness to the "surface" defeating the whole meaning of the word surface, therefore that model is nothing less than a sphere with a magically missing chore and nothing outside it. What is the point of that, why not just call it a sphere with nothing around it?

Besides, how thin can a surface be before it doesn't exist. There must be some thickness in order for a surface to exist, and therefore, there must be an up, and a down. The surface of a sphere thing just adds an interior boundary as well as an external boundary, the paradox remains exactly the same.

 

[hartgravesmik]

infinate. it could be no other way. if there was and end then there would be something beyond it. i don't care how many bubbles there are, or bubbles of bubbles ect and so on. the definition of a universe includes everything and therefore it does not stop.

 

[marcus]

The energy states of a system are quantized if and only if the system is bounded. Light energy is quantized. Hence I believe our universal is bounded, i.e. finite.

I agree that the universe could be spatially finite in a volume sense----but I don't imagine it having any boundary or edge. It might simply have a finite spatial volume with no boundary. However I don't follow your argument that it has to be that way. It seems to me that we don't know yet whether space is finite volume or infinite volume. There is a curvature measurment to decide this. Some progress has been made but it isn't conclusive yet. So I think the prevailing opinion is it could go either way

The question is entirely meaningless unless everyone agrees on a definition of "universe"...

We should never expect everyone to agree on a definition of anything, and yet if we define our terms as we go, we can have meaningful discussions. One simple way to go is just adopt the prevailing notion of universe among observational cosmologists, like the WMAP group. Their job is to study the universe, measure it various ways, reconstruct its past history---so they have a pretty good practical working definition. You have the right to define it for yourself however you want (just be explicit about it). But it would be awfully convenient if we could all share a common basic terminology.

infinate. it could be no other way. if there was and end then there would be something beyond it.

Space could have a finite volume, and yet have no end. With a little effort one can imagine a finite 3D volume with no boundary or edge of any sort. So I don't see the logical force of your argument.

 

[Earnest Stuar]

I agree that the universe could be spatially finite in a volume sense----but I don't imagine it having any boundary or edge. It might simply have a finite spatial volume with no boundary. However I don't follow your argument that it has to be that way. It seems to me that we don't know yet whether space is finite volume or infinite volume. There is a curvature measurment to decide this. Some progress has been made but it isn't conclusive yet. So I think the prevailing opinion is it could go either way

Hi Marcus – If the universe had a finite volume extending somewhere beyond what could be observed by zooming around the outer observable bodies, I could imagine the core element between constructs – space – ending with another, as-yet-unidentified element beginning and extending to infinity. As we are imagining, with no proof either way, that would be as plausible as the same element of “our” space extending to infinity without any apparent constructs beyond what we can presently observe with our best glasses.

Space could have a finite volume, and yet have no end. With a little effort one can imagine a finite 3D volume with no boundary or edge of any sort. So I don't see the logical force of your argument.

As we have no way to know the nature of the “edge” of the Universe, or even the initial, presumed undifferentiated source driving its expansion that leads to Planck’s thoughts on how matter came about, and begs the question "is the Big Bang pushing out like they say?", then there is zero evidence on whether the stuff we can measure in space goes on to infinity or stops like the edge of a bubble in water. A bubble forming in water behind a submarine at 500 meters depth, if one were born inside it at that moment, but one was the smartest being on the planet and had more degrees than a thermometer, would have a hard time figuring out what was the edge of that bubble or if there was an edge to that bubble..even with that extremely short burst of light around them in the bubble, which would occur, to see with. Everything would be dark out there, but there would be an edge to the bubble. And the ocean is big and other bubbles and things unseen exist beyond that which wouldn't be seen from the universe of that tiny bubble.

Seems all thoughts on the edge or beginning of the Universe have no real basis in science (yet), and are imaginings..one being as good as another.

 

[danda22]

But that's not the question that was asked, and it is not what lay people generally mean when they ask 'is the Universe finite or infinite'. We can change the question to make it easier to answer, but then we are answering a different question!

alright. hey i don't know if anyone still reads this but i thought id post a comment anyways on my beliefs. It is true and has been stated many times that nothing can be destroyed? true? well.. if this is stated to be true. then we must also assume that nothing can be created (assuming there is no "god" matter) in which case. if nothing can be created and nothing can be destroyed (in a 3D sence) then the spatial expance of our "uni"verse is finite. that is to say any mass inside our universe is finite...

also my theorum on the big bang/s. and the big crunch/s... ok. so i just thought of this one now. but.. we all know how atoms react with each other.. see atom bomb hydrogen bombetc.. what i believe has been happening since the beggining of time..( or maybe there's nosuch thing as a begining...lets just say since universes have been around) is that .. god this is hard to explain lol... uhm./ ok let's just say there were finite trillions of atoms swirling around etc... they are elements yet..hmm... i dunno. the basisof what I am trying to say as hard as I am making it sound is that. the big bang is a chemical reaction.all the atoms at verry high temperatures reacting and exploding forcing all atoms and particles away at superfast speeds. which explains why the universe is forever expanding. if there's such a thing as "the big crunch" then when all of the atoms, starts, planets and galaxies are squashed back in the middle vaporised into there key elements, another big bang will occur and this will be the start of another universe. also. i see the universe as not flat.. not "balloon" but more like a cone shape.. or a circle with a slight dent in the middle... stick with me here..

lets imagine the galaxies as balls on a giant playgroundwhich justsohappens to be slopingtowards the middle.. the balls have been kicked (lol..) outwartds from the middle and will keep going until the force behind them stops.at which time they will slowly roll back towards the middle.

this is how i see the universe. although i realize there are a few flaws in my theory.. Also. the problem with my balltheory is that.. if the force behind each ball just so happens to be that of an entire universe... would they ever stop?

uhm yeah. so please tell me of any flaws and if u agree/not and why please

 

[Pjpic]

PLEASE help!


I think I understand the logic of your question, but I haven't been able to find a source that specializes in dealing with it. Steven Hawking talks about it some at the end of 'Universe in a Nutshell 'but only very broadly. It almost seems like trying to find someone that wants to talk about traffic congenstion but the only people you find are mechanics (who specialize in the internal combustion).

 

[marcus]

...
It continually plagues me. I even had a friend blurt out of the blue the other day, "What's with the universe? Does it just keep on going forever? Or does it stop? If so, what's beyond it?"...
Is the universe finite? (= implies a "Beyond")
Is the universe infinite? (= seems nonsensical, and counter-intuitive to "Big Bang" theory)
...

PLEASE help!

I think I understand the logic of your question, but I haven't been able to find a source that specializes in dealing with it. ... It almost seems like trying to find someone that wants to talk about traffic congenstion but the only people you find are mechanics (who specialize in the internal combustion).

...If constant instants of cosmological time are used to foliate a Freidmann-Robertson-Walker spacetime into spacelike sections, then (as marcus has posted) \mathbb{R} \times S^3 results when the spacelike sections have constant positive spatial curvature with respect to the spatial metric induced on the the spacelike sections by the spacetime metric. In this case, each spatial section is compact and has finite volume 2\pi^2a^3. See Box 27.2 of Misner, Thorne, and Wheeler.

Dear Pjpic,
George Jones who is both a PF mentor and someone with academic specialization in cosmology effectively answered the question. But you couild reasonably ask for more elaboration and say that what you've been able to find in your other readingon it is either:
1. not spelled out in simple language, or
2. too contaminated with noise and disagreement about the meaning of words.
So I'll make a stab at clarifying for you.

I think what Mattex is asking is if you could freeze expansion at the present instant of cosmological time and then were able to wander freely around and explore all of space,then would it turn out to have infinite volume or would it have finite volume?

And if it turned out to have finite volume then Mattex is worried that might imply there was a boundary and some more space beyond or outside. He probably can't picture being inside a finite-volume boundaryless space which is not contained in a surrounding infinite volume.

The reason to imagine that you freeze expansion and look at space at the present instant (which is what George was talking about---he said how to calculate the volume in a particular case) is that if you allow space to get bigger while you are exploring it you get into confusions about how much of it you can visit depending on how fast your travel and how fast distances are increasing. So it gets too complicated. The simple thing is, freeze it and then take your time and have a look around.

This approach was taken in one of the standard textbooks, as an exercise. George gave a page references.

Then it is all pretty simple. The answer will probably not satisfy you though.

The answer is cosmologists don't know. Given the present data it could be either finite volume or infinite volume. It is mathematically possible to be in a boundaryless finite volume space that is not contained in any larger volume. Infinite volume is also a mathematical possibility.

Technically there is a curvature number that satellite instruments help measure which will help decide the issue. A new satellite instrument was just launched this year. If the curvature number turns out to be one or less then infinite volume is very likely. If it turns out to greater than one then finite volume is favored.

In 2008 a NASA report (from the WMAP mission) gave some numbers for that particular finite volume case that let you calculate a lower bound on the volume using the formula in George's post. Basically they said that with 95% confidence R > 100 billion lightyears and to get a lower bound on the volume, in cubic lightyears, you should plug that into the formula V = 2 pi² R³.

Presumably you don't want to know that, you want only nontechnical interpretation, but the upshot is that they don't know yet, and the boundaryless finite volume case is one case that they have a handle on and are considering. The infinite volume case is also a very good possibility. (This would mean also an infinite volume at the start of expansion which doesn't conform to many people's picture of the big bang, but it is a mathematical possibility that cannot be ruled out.)

 

[TalonD]

hey Marcus, just curious, how would you do the calculations. (I'm not much of a mathemetician) Assume finite volume and radius is 100 bly, what would the radius and volume be at plank density? or I think I read in a post that bounce theory says it would be about 40% plank density is that right?

one other question. I don't have a problem with finite volume and no boundary, but why so insistant on having no boundary? Is it just because it is mathmatically possible? I realize we 'don't know for sure one way or the other, but is there a reason for saying it has no boundary other than just some intelectual bias? Or is there a reason why it absolutely can not have a boundary, some theoretical concrete reason?

 

[marcus]

one other question. I don't have a problem with finite volume and no boundary,..

That's good! In that case I would have no reason to stress this in talking with you. I am fighting against other people's mental bias where they seem to think if something is finite it "has to be bounded". So they automatically, almost involuntarily, put an "edge" into the picture. And then *duh!* they start wondering what is beyond the "edge".

That shows you the trouble with boundaries and edges thinking. It is an unnecessary complication that Occam's razor alone would rule out. I have no bias against it---I can, if I choose, picture a region of space with a boundary, and something beyond it---as in one of the more extravagant multiverse inflation conjectures. But it isn't necessary. I have enough on my plate already with a simple boundaryless universe. (This is what you automatically get when you make the usual Cosmological Principle assumption of uniformity: you know the homog and isotropic assumption---automatically no boundary there.)

Or is there a reason why it absolutely can not have a boundary, some theoretical concrete reason?

Look, cosmo is a mathematical science which means getting the best fit to the data with the simplest mathematical model. And you keep refining that model until whoopee! you find a discrepancy that forces you to change the model. At no point do you assume anything is "true". In fact you are always hoping that new observations will show your current model is false. But after some features of the model have survived testing for many decades one gets skeptical as to how much you can reasonably expect them to change. Some features are probably robust and will probably carry over to the next version. Like the expansion feature Friedman described in 1922.

So ask yourself: would putting a boundary into the Friedman model make it fit the data better? If not, then in the context of a mathematical science it is simply not interesting. If some jerk wants to fantasize about a boundary, that's fine! Why not? And I think the answer to the question is no. Adding a boundary onto the standard mainstream Friedman model would not (as far as I know) make it fit the data better.

If I ever did hear that it would improve the fit, I would immediately be all excited about boundaries of course, that would be a major revolution. But I'm skeptical that it ever would turn out that way. So far the mainstream model is homogeneous and isotropic and not even the faintest hint of an edge.

hey Marcus, just curious, how would you do the calculations. (I'm not much of a mathemetician) Assume finite volume and radius is 100 bly, what would the radius and volume be at plank density? or I think I read in a post that bounce theory says it would be about 40% plank density is that right?

Talon, I didn't say that R = 100 billion lightyears was the estimated RADIUS. Be careful. It is a lowerbound on a length called the "radius of curvature", which is different from a real radius.

Imagine a ring. All existence is concentrated on that ring. There is nowhere else and there is nothing else besides what lives in that 1 dimensional ring. That ring has no radius because it has no surrounding space. The only space that exists is the ring. However the 1D people living in the ring manage to measure the circumference and find that it is 6.28 inches (they use some unit of length they call an inch.) One of their greatest mathematicians invents a concept "radius of curvature" which is the radius the ring would have if it were surrounded by a higher dimensional space, a 2D space which they have great difficulty imagining. He then calculates the "radius of curvature" of their universe and determines that it is approximately 1 inch.

Imagine the surface of a sphere, perhaps the surface of a balloon. All existence is in that surface---not the balloon, but the purely 2D surface itself. There is nowhere else and nothing exists except in that 2D surface. The surface has no radius.

However it has a radius of curvature which the 2D creatures sliding around in the surface would be able to discover by measuring angles (because the angles wouldn't add up to 180 degrees) and circumnavigating and measuring great circles, and stuff. So even though their world has no physical center and no physical radius (not being engulfed in some surround space of higher dimensionality) it nevertheless has a radius of curvature which the creatures can determine.

I'm sure you get the picture, Talon

 

[Ike47]

My thanks to Danda22 and others who revived this thread. I asked a question in the stickied Cosmological thread and have been waiting (hoping) for an answer from Marcus. Now I find he's already given the answer here! And I never would have found this thread if it had not been revived.

Of course, Marcus's answer leads to futher questions on my part, so I shall plow on. My questions will involve only the first page or so of this thread, since that was where my question was answered, and I don't particularly have a problem with the topics which have come up since then.

Anyway, Marcus, you have said, if I understand you correctly (please correct me if not): if the universe is finite, which we don't know at this point, it would be curved and without a boundary. I have no problem comprehending this (or at least I hope I don't; it seems 'visualizable' to me).

Further, even if the universe is finite, we can never "map" all of it, because of the restrictions of our light cone. In other words, because of the finite speed of all energy (c) and the ongoing expansion of the universe, we can never 'see' all the universe even though (under our assumption) it is finite. In theory at least, however, this limitation could be overcome by communicating with 'people' in other galaxies, each adjacent to each other, so that finally 'everyone' could share a 'map' of the entire universe. I'm not saying this is feasible, just theoretically possible.

Finally, you have said in this thread that the assumed finite universe could have a 'center' in a higher dimension, but a) that doesn't mean that higher dimension (and so that center) actually 'exists', and b) never ever ask a scientist about that 'center' because it is not amenable to scientific analysis.

My original questions was that if the universe should be finite, shouldn't it have a theoretical center, even if we couldn't determine where it was and even if mathematically it would have to be in a dimension that may well not actually exist. (I'm not sure exactly what 'a dimension not existing' means, but I am comfortable understanding that we can mathematically model dimensions that don't exist, as well as being unable to gather any data from (higher) dimensions that may exist.)

So it seems that you have answered my original question in the positive, which helps restore my sanity in regard to feeling that I can understand, in some small degree, the possible physical (geometric/topological) nature of our universe.

I hope I don't upset you with this, but I'd now like to ask a question that is in apparent contradiction to your strongly worded command not to ask questions of a scientist about the hypothetical "center" of our universe. I think my question is valid, that is, that it does not ask a scientist (you) to do something you cannot, but if I'm wrong, I will accept that and apologize.

If the universe is finite, curved, and without boundary, and if (as a thought experiment) we could "map" the entire S³ universe by conversing over billions (or more) years with many peoples in galaxies each adjacent to the next, could we not determine mathematically the theoretical "center" of the universe, even though, because it would be in a higher dimension (which may well not even exist), we might not be able measure any distances to it nor even point toward it (give it a direction from any specific location within our universe)?

Now perhaps it is mathematically impossible to calculate the center of a shape from the data available only within the dimensions of that shape, when the center would be in another dimension. I don't know enough topology or geometry to have a clue on that. But if it is theoretically possible, then would the answer to my question of the previous paragraph not be 'yes'?

Second question: if the answer to the previous question is indeed yes, so we had a mathematical definition of the center of our universe, might we not be able to determine whether our universe is 'symmetric' around that center? In other words, has the expansion of the universe always been 'even', or, like the slight lumpiness of matter in the very early universe that presumably made possible galaxies--and us--, are some points in the universe that were once equidistant from the universe's center now not equidistant?

Thank you for your patience reading through this (if you indeed have that much patience). I hope I have made my questions clear enough to be understandable, but I can't be sure that I have. If not, please point out where I am not making sense and/or note any unreasonable or illogical assumptions I may be making that I'm not even aware of. Thank you!

 

[TalonD]

on boundarys, ok, that's a good enough explanation to satisfy me. I could understand why the average person, would insist on a boundary and now I can understand why you often say that one isn't neccesary. That it's not just your personal bias vs. someone elses. You have good reasoning.

radius of curvature... Yep, I get it now! The radius a circle 'would' have 'if' it had one, based on it's curvature. That makes sense.

There's still the question though. If the universe has a curvature then it must have a finite volume right? Just as your curved sphere would have finite surface area? and the circle would have a finite circumference? even though none of them have a higher dimensional surounding space. As I recall we calculated that volume in another post and I had my decimal point in the wrong place :P, I'll have to go look for it or recalculate it. Then I'm curious what that volume would be if you shrink it all the way back to the beginning.

But then... is it possible for a curved universe to still have an infinite volume? after all, a circle or a sphere could be infinite in size just as a flat plane could be, right?


and then just reading the previous post from IKE47, it got me thinking about the center. Since the radius of curvature is sort of a virtual radius rather than a real one, then there would be r+r = the virtual diameter of curvature, then half way in between would be the virtual center. That's kind of meaningless of course but I like the way it sounded.

 

[danda22]

hmmm... ok.. "if it is rounded it can still be infinite?" no. if it is all curving inwards it must be finite... but... it all depends i suppose.. the way i see it now. is that. the space of the universe may be infinite. ever growing/expanding. but the mass of the universe if finite :) which is pretty simple to understand :)

Also. i think we are going about this the wrong way. "finite or infinite?" how bout. what changes if it is "finite or infinite"
how does this change our day to day lives?"
how does this change how we are to view the universE?"

If this universe is infinite. then where do all the other universes fit in?? [ quoting "stephen hawkings theory on everything ] it is possible for there to be thousands, millions of universes all stacked together in a donut shape.. i don't know if anyones seen it. but.. if there are other universes... will our universe meet them one day? if so what happens?

uhm ok that was kind of off track. just a random thought.. also. measuring the universe would be impossible. because by the time u have measured it. it is about a million years infront of us...

 

[TalonD]

if a flat or open surface can be infinite, I don't see why a curved surface can't be infinite. In that case the radius of curvature mentioned earlier would be infinite.
And of course we still don't know.

 

[danda22]

if a flat or open surface can be infinite, I don't see why a curved surface can't be infinite. In that case the radius of curvature mentioned earlier would be infinite.
And of course we still don't know.

hmm. well. an open flat surface can be infinite because it will never touch itself.. uhmm.. i don't know if u mean curved as in a sphere or curved as in a cylindeR?

 

[danda22]

oh actually u r right.. sorry. lol. i was just looking at the shape as in the outer layer.. i think maybe for it to be inifinite it would look more like a dandelion

 

[Pjpic]

The definition of finite, seems to be from "finire - to stop". So, it would appear that something finite would have to stop.

Maybe the difficulty in understanding (which I share with you) stems from the definition of terms. I have found these instances that might give a clue.

-- George Cantor seems to have added some sublties to the definition of infinite.

-- There is math construct called Gabriel's Horn (infinte surface surrounding a finite volume)

-- "Intrinsic curvature" seems to talk about how you don't have to deal with what a curve is embedded in.

-- I read that questions of this type are not helpful so they are not worked on.

-- There's the difference between an actual and a potential infinitity

-- I seem to find similar problems at the infitessimal scale too. Questions that deal with where does a particle end and empty space begin.

-- There could be some sort of 'math trick' involved. (a variation on Gabriel's horn)

-- The problem of finere doesn't seem as difficult if you're thinking how many dimensions there are if the "highest' one isn't curved. But it always seems difficult when thinking about time.

-- There is something(?) in relativity where the closer you get to infinity along one axis you get further from along another.

So, sorry about taking the space (and/or time); but if you find a amature level book on the subject - that'd be great.

 

[TalonD]

There are more than one kind of infinity and some infinities are bigger than others. for example the infinity of all integer numbers is smaller than the infinity of all fractions because there is not a one to one correlation between the two. There is the infinity of all points on a line segment also, and others. Those are abstractions, so one question I would have is, is it possible for something physical like the universe to be infinite? If it is possible to concieve of something physical being infinite then there should be no problem with having a sphere who's radius and diameter are infinite, then multiply by pi and you find an infinite circumference. Now in the case of our universe. If it were a sphere surface with infinite size, it would be identical from our point of view to an infinite flat plane because the radius of curvature would be infinately long. So the only way we can know if our universe is flat, open or closed is to measure the critical density. which is currently pretty close to 1 but still undetermined. So if we are able to narrow that down and say for certain that the universe is curved then it 'has' to be finite because if it is infinite then the radius of curvature would be so great that it would be indistinguishable from flat.

at least that's the way I see it, of course I could be wrong!

so... critical density is either less than 1, greater than 1 or exacltly 1. In which case, if we can narrow it down to one of those 3 possibilities, then we will know if it is open, flat, or close. And that depends on future measurements so we still don't know

Right?

 

[Pjpic]

If it is possible to concieve of something physical being infinite then there should be no problem with having a sphere who's radius and diameter are infinite,

This is over my head but if both the diameter and radius are infinite wouldn't the diameter have to equal the radius. And if the only the diameter was infinite wouldn't the circumference have to be greater than infinity?

 

[Ike47]

I don't see why curvature requires a finite space. Hyperboloids and paraboloids are infinite curved shapes, so why couldn't a curved universe be infinite as well? That doesn't mean that the universe can't be curved and finite of course, but just that the one doesn't force the other. Of course, I may be wrong. :)