More on Infinity: Why Does Balloon Analogy Not Describe Universe?

[Pjpic]

However, the size of the universe at any fixed time is always finite.


That entire answer will help me, thanks. The part where you say the universe is finite is still tricky for me. Because, in my lexicon, finite means there is an end point. I suppose set of ten marbles could be finite and yet not have an end point. Is this the concept?

 

[MeJennifer]

However, the size of the universe at any fixed time is always finite.

That is simply untrue.

If a spacetime is closed it is finite and if it is flat or open it is infinite. The same with a 3D space inside such a spacetime, in a flat of open spacetime the volume of any past or future light cone is infinite at any point in time.

 

[marcus]

I'm sorry if my misunderstanding has somehow offended your sense of ethics.

Try quoting exactly, rather than attributing your own paraphrase to someone else.
You need to apologize for misrepresenting (not for misunderstanding).

 

[Arch2008]

MeJennifer, a light cone is a projection into the future or past:
http://en.wikipedia.org/wiki/Light_cone
That is why it can be infinite. As I pointed out, a finite universe that starts smaller than an atom and that expands at a finite rate cannot be infinite in size until an infinite time has passed. I don’t see how this can be untrue.

 

[MeJennifer]

Arch2008, the universe that we observe at each instance is contained in our past light cone. In each instance there could be an infinite number of galaxies inside such a light cone unless it is a closed spacetime.

 

[marcus]

...Astronomers have been trying to determine a value for omega, the density of the universe, which describes the ultimate fate of the universe. If the universe is open, (omega less than one) then it expands forever. If it is closed (omega greater than one) then the universe “crunches” back into a singularity at some point. Otherwise, the universe is flat (omega equals one) and expands forever while slowing gradually but never stopping. Within this description, an open universe is described as infinite and a closed universe as finite. However, the size of the universe at any fixed time is always finite. The universe expanded from a finite volume smaller than an atom at a finite rate, and therefore, to its current finite size. It has never expanded at an infinite rate, nor has it yet to expand for an infinite amount of time, therefore it simply cannot currently be infinite in size. The term “infinite universe” describes an open universe whose fate is to expand forever, nothing more. Thus the balloon analogy does apply, in that a finite space expands unbounded forever.
http://en.wikipedia.org/wiki/Ultimat...f_the_universe

...

Arch you have it basically right, but your link to WikiP doesn't work and if one fixes it
http://en.wikipedia.org/wiki/Ultimate_fate_of_the_universe
then we get them saying that a closed universe does NOT necessarily crunch

==quote your Wiki article==
Closed universe

If Ω > 1, then the geometry of space is closed like the surface of a sphere. The sum of the angles of a triangle exceeds 180 degrees and there are no parallel lines; all lines eventually meet. The geometry of the universe is, at least on a very large scale, elliptic.

In a closed universe lacking the repulsive effect of dark energy, gravity eventually stops the expansion of the universe, after which it starts to contract until all matter in the universe collapses to a point, a final singularity termed the "Big Crunch," by analogy with Big Bang. However, if the universe has a large amount of dark energy (as suggested by recent findings), then the expansion of the universe can continue forever – even if Ω > 1.
==endquote==

since 1998, with dark energy estimated at 70-75 percent, Crunch is not talked about much as a possibility. So closed does not mean crunch.
When people say closed they usually mean spatial closed. That is, finite volume space. At anyone moment the volume is finite, although it is increasing with time. Like the surface area of the balloon (the 2D analogy for 3D space)

===============================
Jennifer let's make sure we are using the same definitions. What do you call a spacetime that is spatially flat, with Omega = 1, with positive cosmological constant?
I assume you call it flat, even though the spacetime is not geometrically flat, it is only spatially flat.

What do you call a spacetime that is spatially closed, with Omega > 1 and with positive cosmological constant---say sufficient dark energy to cause indefinite expansion?

I know your posts are usually very well-informed and helpful. But I don't understand this one. In many cases I am used to thinking of past lightcones as finite volume---the usual teardrop shape.

Let's agree to base volume on proper distance---observers at rest with respect to Hubble flow, or CMB if you wish.

...
If a spacetime is closed it is finite and if it is flat or open it is infinite. The same with a 3D space inside such a spacetime, in a flat of open spacetime the volume of any past or future light cone is infinite at any point in time.

I'm not sure what some of this means.
Couldn't we have a spatial flat universe, with Omega = 1, where the past lightcone has finite volume and the future lightcone has infinite volume?

 

[marcus]

Arch2008, the universe that we observe at each instance is contained in our past light cone. In each instance there could be an infinite number of galaxies inside such a light cone unless it is a closed spacetime.

Again I'm not sure I understand your terminology, Jennifer. What if I have Omega = 1 so things look approximately like our universe? Just as an example.
Say the particle horizon is 45 billiion LY, about like ours.
It seems to me that within that horizon there is only a finite volume of space, a finite amount of matter, a finite number of galaxies.

But from what you say it sounds as if we can't expect to have a finite number UNLESS the universe is closed, though in my example we do have a finite number and the universe is not spatially closed.

Maybe there is a verbal problem, or something I'm not getting: could you clarify what you mean by "there could be an infinite number of galaxies inside such a light cone unless it is a closed spacetime"?

 

[Arch2008]

MeJennifer, I’m still not getting the simple truth where a finite universe expands at a finite rate for a finite time and then somehow becomes infinitely large at any point in time less than infinity.

Thanks for clarifying that Marcus. In this article of “my Wiki” it says:
http://en.wikipedia.org/wiki/Dark_energy
“In the Friedmann-Lemaître-Robertson-Walker metric, it can be shown that a strong constant negative pressure in all the universe causes an acceleration in universe expansion if the universe is already expanding, or a deceleration in universe contraction if the universe is already contracting. More exactly, the second derivative of the universe scale factor, is positive if the equation of state of the universe is such that w < − 1 / 3.”

Which I though meant that a “crunching” universe would just do so more slowly, but not stop, under the effects of DE.

 

[marcus]

Which I though meant that a “crunching” universe would just do so more slowly, but not stop, under the effects of DE.

that's right. The important thing to realize is simply that Omega > 1 does not imply crunch.
In your Wiki article, the term CLOSED has been taken over to mean Omega > 1
which means spatial closure.
In the Wiki article's terminology (which is pretty common) a closed universe does not necessarily crunch.

In our universe, with 70-75 percent dark energy, crunch is typically not taken as a serious possibility, but spatial closure----meaning Omega > 1-----certainly is! In fact the current estimates for Omega are lopsided on the positive side of 1----more around 1.01.

I'm just an onlooker---retired math person interested in cosmology. I follow the research literature and occasionally talk to astrophysicists at the university where I live. By studying major articles by leading people I get an impression of where the field is going. All I can do is report as accurately as I can. More and more often, I see the top cosmologists considering the case of closed universe, i.e. finite spatial volume, as well as---in addition to--the simpler and dominant case of Omega = 1. So when they analyze new data they may very well analyze it for both cases. In other words squeeze an extra column in the table, or another data-oval diagram, an extra curve plotted or an extra table of numbers. It is more work, more calcluation, but apparently the possibility is real enough to warrant it.

In neither case would crunch be involved---I'm talking typical big mainstream papers (not marginal stuff on the fringe that nobody much reads.)

It's a mathematical possibility of course, but so out of touch with observational data that it's not worth people's time thinking about.

 

[marcus]

MeJennifer, I’m still not getting the simple truth where a finite universe expands at a finite rate for a finite time and then somehow becomes infinitely large at any point in time less than infinity.
...

Arch, it could always be possible that Jennifer uses words in her own way. She may talk in a way that confuses you because she doesn't mean the same thing that Wikipedia does. I don't think Jennifer would ever say that the universe can abruptly switch from being spatial finite to spatial infinite!

I don't know for sure, because Jennifer has not defined how she is using words like closed, flat, open, finite, infinite. Until she does, I wouldn't worry about any apparent contradiction, since it could simply be verbal.

If we stick to the Wikipedia terminology (pretty common in my experience) a CLOSED universe is simply one with Omega > 1. That means spatial closure, it doesn't mean that there is going to be a crunch (which would be a kind of time-axis closure, a finiteness of the whole spacetime, but that usage of words is confusing to most people, I think).

It is possible that when Jennifer says closed universe or closed spacetime she means something different from what your Wikipedia article does! Same with when she says finite. I don't know. That could be the basis for her contradicting you several times. I asked for clarification earlier, and hopefully she will tell us. Maybe Cosmology forum needs a Sticky thread with basic definitions.

 

[Arch2008]

Well. you know her better then I. I think she probably just confused the infinite universe explanation from the search for omega with a universe that is actually infinite at present. I read a lot of posts where someone has done this and even some magazines. No big deal really.:)

P.S. I also found this:
Is the Universe really infinite or just really big?
We have observations that say that the radius of curvature of the Universe is bigger than 70 billion light years. But the observations allow for either a positive or negative curvature, and this range includes the flat Universe with infinite radius of curvature. The negatively curved space is also infinite in volume even though it is curved. So we know empirically that the volume of the Universe is more than 20 times bigger than volume of the observable Universe. Since we can only look at small piece of an object that has a large radius of curvature, it looks flat. The simplest mathematical model for computing the observed properties of the Universe is then flat Euclidean space. This model is infinite, but what we know about the Universe is that it is really big.
http://www.astro.ucla.edu/~wright/cosmology_faq.html#RB

 

[ThomasT]

You're not helping your case ...

I'm not making a case per se. Just threw a few more or less commonsense ideas out there. The original poster seemed to like at least one of them. Of course, I'm still at the "exposion good, balloon bad" stage in exploring this. But, isn't the path to eventual mathematical models sometimes paved with the spitballs of mechanical intuition, analogies from our recollections of sensory experience, and the logic of ordinary language?

... you've just spouted a big pile of incorrect ideas that one could get by pushing the explosion too far.

Only if our universe didn't begin with an explosion. However, what we can see of it looks to me like the remnant of some sort of explosion. Are there no professional cosmologists who think of it this way?

Does this notion challenge the current standard LCDM cosmological model? Not by itself. But there are some things which seem to follow logically from the explosion assumption. Hence, my big pile of incorrect ideas.

1. GR does not involve any extradimensional physics -- all the dynamics of GR are purely intrinsic. Even if we take a viewpoint where we embed the observable universe in a higher-dimensional space-time, whatever happens in those extra dimensions is completely irrelevant to the goings-on in the observable universe.

OK.

2. In GR, the big crunch is not a thermodynamic impossibility -- if the bulk composition of the universe is right (e.g. overall matter density, cosmological constant), it is something certain to happen. (Although I don't know if it's merely thermodynamically certain, or absolutely certain)

Calculational systems (mathematical models of physical systems) sometimes produce symbolic behavior which doesn't correspond to anything in the physical world. Is this the case with GR? Is it the case with electrodynamics?

Statistical thermodynamics allows some things which would be precluded by a deeper mechanical understanding of the systems involved.

Given the assumption that the kinetic energy of the expansion is the dominant energy in our universe, then a big crunch is an absolute impossibility.

 

[Hurkyl]

Just threw a few more or less commonsense ideas out there.

Commonsense is irrelevant here; we're dealing with things well outside of the realm of 'common' experience. (And even in the realm of common experience, commonsense is often wrong)

But, isn't the path to eventual mathematical models sometimes paved with the spitballs of mechanical intuition, analogies from our recollections of sensory experience, and the logic of ordinary language?

Intuition does not supercede fact.

Calculational systems (mathematical models of physical systems) sometimes produce symbolic behavior which doesn't correspond to anything in the physical world.

And sometimes, they produce symbolic behavior which does correspond to something in the physical world. But you're still firmly planted in the realm of the hypothetical -- GR is the best we've got, and the evidence says that GR doesn't make mistakes in this domain.

Given the assumption that the kinetic energy of the expansion is the dominant energy in our universe, then a big crunch is an absolute impossibility.

Given the assumption that the universe is a big rubber band, then a big crunch is a (nearly) absolute certainty. We can invent all sorts of crazy assumptions to support whatever worldview we like -- but none of that changes the fact that the science says that a big crunch is a possibility, and would be the expected outcome if the bulk statistics of the universe were slightly different.

 

[Pjpic]

The open, closed, and flat universes still seem to have boundries at(before?) zero and actual infinity. So, assuming we don't reside in a special area of space, I'm still not sure why the balloon analogy breaks down.

 

[ThomasT]

Commonsense is irrelevant here; we're dealing with things well outside of the realm of 'common' experience.

Ok, poor choice of words on my part. Making and dealing with the conjectures or assumptions I presented for consideration requires a bit more than an ordinary commonsense knowledge of cosmological observations and theories. I have an uncommon, but still only superficial, knowledge of both.

But please treat my statements as questions -- even if I present them as arrogant assertions. Ultimately I'm here to learn, and I do appreciate your (and others') replies.

Intuition does not supercede fact.

I think a more appropriate answer to my question would have been yes or no accompanied by examples (if yes).

And sometimes, they produce symbolic behavior which does correspond to something in the physical world.

I'd say they quite often produce symbolic behavior which corresponds to something in the physical world -- following suitable interpretation. Otherwise they'd be mostly meaningless.

But you're still firmly planted in the realm of the hypothetical ...

Isn't this where cosmology is planted?

... GR is the best we've got ...

Agreed.

... and the evidence says that GR doesn't make mistakes in this domain.

What domain? Cosmology? Are you absolutely sure about that?

Given the assumption that the universe is a big rubber band, then a big crunch is a (nearly) absolute certainty.

Do you really think that my statement (Given the assumption that the kinetic energy of the expansion is the dominant energy in our universe, then a big crunch is an absolute impossibility.) is that silly? If so, why? Is it that you don't think that the energy of the expansion could possibly be the dominant energy, or is it that you don't see how this precludes a big crunch, or what? The kinetic energy of the expansion is manifested in every different sort of energy and behavior.

From the kinematics of the universe, we're used to thinking in terms of attraction and repulsion. We think of gravity as an attractive force and dark energy as a repulsive force. But if you think of it in terms of the isotropic expansion of the universe, then there's only one direction -- the direction of the expansion, which is any and every possible direction.

The thermodynamics of the universe is what it is precisely because the universe is expanding. There's a radiative arrow of time because the universe is expanding. Advanced waves are impossible because the universe is expanding. Travelling backward in time is impossible because the universe is expanding. Solar, galactic, and intergalactic structures are what they are because the universe is expanding.

There's not going to be a big crunch because the universe is expanding. As it expands, its condensed structures become more widely dispersed (reducing the probability of interaction), and the energy required for the expansion (and everything else that's happening) is dissipating the finite amount of energy imparted via the origin event.

We can invent all sorts of crazy assumptions to support whatever worldview we like ...

Does anything I've written seem crazy to you? If so, what and why?

... but none of that changes the fact that the science says that a big crunch is a possibility, and would be the expected outcome if the bulk statistics of the universe were slightly different.

Theories aren't, by themselves, science. Science doesn't say that a big crunch is possible. A combination of certain mathematical-geometrical models says that it's possible. The interpretive view of gravitational behavior via this approach says that it's due to the bending in of spacetime around and toward massive objects. And thus, the deep nature of gravitational attraction is explained.

I think this is possibly a wrongheaded approach to understanding gravitational behavior (notwithstanding the usefulness of GR as a calculational tool) and has lead to some silly predictions (like a possible big crunch).