More on infinity

[Pjpic]

Why does the balloon analogy not accurately describe the universe?

Common sense would say that an expanding isomorphic homogenous space would have to be curved in a higher, infinite, spatial dimension.

Astronomers seem unsure if the universe is finite or infinite.
Physicists seem to, according to wiki, wish to avoid the concept of infinity.
Mathematicians are a little opaque, for me, on most issues; so, I don't know if they are saying infinity can expand.


Can anyone tell me what the "official" teaching on the balloon analogy is?

[epkid08]

Why does the balloon analogy not accurately describe the universe?

Common sense would say that an expanding isomorphic homogenous space would have to be curved in a higher, infinite, spatial dimension.

Astronomers seem unsure if the universe is finite or infinite.
Physicists seem to, according to wiki, wish to avoid the concept of infinity.
Mathematicians are a little opaque, for me, on most issues; so, I don't know if they are saying infinity can expand.


Can anyone tell me what the "official" teaching on the balloon analogy is?

I would say that the notion of infinity expanding goes against the definition of infinity. I think it's quite obvious that the three spatial dimensions we are bound to are finite. Although, higher dimensions, like the one the balloon model suggests, may or may not be finite; who knows, maybe they even have the predisposition of being infinite.

[Pjpic]

I would say that the notion of infinity expanding goes against the definition of infinity. I think it's quite obvious that the three spatial dimensions we are bound to are finite. Although, higher dimensions, like the one the balloon model suggests, may or may not be finite; who knows, maybe they even have the predisposition of being infinite.
I suppose something would either be infinite or have a boundry beyond which there is nothing.

[Hurkyl]

Common sense would say that an expanding isomorphic homogenous space would have to be curved in a higher, infinite, spatial dimension.
How could it, or anything else on this topic, possibly be common sense?

[Chronos]

The universe is not constrained by the limits of human comprehension.

[HallsofIvy]

I suppose something would either be infinite or have a boundry beyond which there is nothing.
No, that's not true. To use, again, the "balloon" analogy, the surface area of sphere is finite but has no boundary.

If the universe has positive overall curvature, then it could be finite without having a boundary.

[marcus]

Why does the balloon analogy not accurately describe the universe?

Common sense would say that an expanding isomorphic homogenous space would have to be curved in a higher, infinite, spatial dimension.

Astronomers seem unsure if the universe is finite or infinite.
Physicists seem to, according to wiki, wish to avoid the concept of infinity.
Mathematicians are a little opaque, for me, on most issues; so, I don't know if they are saying infinity can expand.
...

You sound as if you've already made a pretty good start towards understanding this business.

You probably understand the point that HallsofIvy just made----a balloon surface is finite area.

You may be going to get tripped up by the idea of intrinsic curvature. Ever since around 1850 it has been possible to understand how a surface can be curved without living in higher dimensional surroundings. You can test curvature by measuring the angles of a triangle, or testing the pythagoras right triangle rule, or various other ways.

We could be living in the 3D analog of a balloon surface and measure the curvature and yet there might not be a surrounding space. Our 3D space could be the only space there is and yet it could be curved. This (in my experience at PF cosmology forum) is probably what newcomers find hardest to grasp.

The thing to remember is that we have no right to expect that the angles of a triangle add up to 180 degrees. Maybe with very large triangles they add up to more! It is the case with Euclidian geometry that they add up to 180 degrees. But we have no guarantee that the geometry of our world is Euclidian.
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About what you said about physicists not liking infinity----you have to be careful what you mean here. There are two ideas of infinity: infinite spatial extent and infinite volume is a harmless commonplace type of infinity. It is one possibility in cosmology and in my experience physicists and everybody else are comfortable with it.
The other kinds of infinities are where a mathematical model breaks down or blows up and stops computing reasonable numbers. then it is just broken and it is time to fix it. Say some model starts giving answers like in some bounded region there is infinite energy or infinite density or infinite radiant power or electric charge. That would be a singularity (a mathematical breakdown of the theory).

If you are still bothered by the idea that physicists don't like infinities, that you found in Wikipedia, you could bring a link to the Wikipedia article and we could look at it. They probably are not talking about infinities like infinite spatial extent or volume---it's probably the other kind.
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The most recent WMAP report (the 5 year CMB data, implications for cosmology) gave a lowerbound estimate for the radius of curvature of space.

They said it was at least 100 billion lightyears, if I remember correctly---some estimate of that magnitude. At least means it could be infinite too, which would be the flat Euclidian case. Anyway a finite but very large RoC fits in with the balloon picture you mentioned. If you want a link to that WMAP report let us know. I think it's neat that they gave an estimate.

[Pjpic]

No, that's not true. To use, again, the "balloon" analogy, the surface area of sphere is finite but has no boundary.

If the universe has positive overall curvature, then it could be finite without having a boundary.

Wouldn't there be a boundry between the surface and what is "above" the surface?

[Pjpic]

The universe is not constrained by the limits of human comprehension.

And the limit of human comprehension is what?

[Pjpic]

How could it, or anything else on this topic, possibly be common sense?

Because the balloon analogy is common sensical.

[Pjpic]

We could be living in the 3D analog of a balloon surface and measure the curvature and yet there might not be a surrounding space. Our 3D space could be the only space there is and yet it could be curved. This (in my experience at PF cosmology forum) is probably what newcomers find hardest to grasp.

This is what I'm not understanding. I can see how there may be nothing beyond our space but wouldn't that mean there is a boundry between our space and nothing (or what might not be nothing)?

[marcus]

Indeed there COULD be some surrounding higher dim'l space---though we have no evidence of it so far.

And there also might not be. To repeat: Our 3D space could be the only space there is.
In that case there is obviously no boundary.
I can't say it any clearer Pj, no boundary because no other space---you either get it or you don't. :smile:

[Pjpic]

Indeed there COULD be some surrounding higher dim'l space---though we have no evidence of it so far.

And there also might not be. To repeat: Our 3D space could be the only space there is.
In that case there is obviously no boundary.
I can't say it any clearer Pj, no boundary because no other space---you either get it or you don't. :smile:


I wonder what book or article would explain this. It sounds like a contradiction in terms if the "offical" teaching is that something is finite but has no end point (infinite).

[MeJennifer]

In general relativity the question is a simple one, spacetime is either open or closed and that implies that the universe is finite if spacetime is closed and infinite if spacetime is open.

[Pjpic]

In general relativity the question is a simple one, spacetime is either open or closed and that implies that the universe is finite if spacetime is closed and infinite if spacetime is open.

Is the spacetime concept of a closed universe mean that there is a boundry in time (the big crunch)? But I'm still confused as to where the boundry in space would be.

[robertm]

Is the spacetime concept of a closed universe mean that there is a boundry in time (the big crunch)? But I'm still confused as to where the boundry in space would be.

Boundaries have no meaning in a boundless system. Weather infinite or not, curved, closed, or flat, the picture seems to be one of no "boundaries in space".

"The analogue of the two-dimensional sphere is called a three-sphere. In the rather unlikely event of four-dimensional creatures existing, they would be able to visualize the curvature of three-dimensional space in just the same way we can visualize that of two-dimensional space. However, like the two-dimensional sphere, the possible curvature of three-space is an intrinsic property and there is no actual need of a higher-dimensional space for it to live in. Obtaining a correct mental picture of this is one of the big challenges in understanding our Universe!
A Universe with a spherical geometry, like the surface of the Earth, has a finite size but no boundary. All points are equivalent. If we live in a spherical geometry, and travel in a straight line, we would not go on for ever and ever. Rather, eventually we would come back to where we had started from, from the opposite direction, exactly in the manner that someone travelling outward from the North Pole on the Earth eventually returns there from the opposite direction." An introduction to Modern Cosmology 2nd ed, Liddle

So even if the geometry of the universe turned out to be one of finite scope (the 'closed' positive curvature case), the concept of boundaries, on a cosmologic scale, seems to be omitted from reality.

[Pjpic]

the possible curvature of three-space is an intrinsic property and there is no actual need of a higher-dimensional space for it to live in


This is the part I don't understand. Is there an accessible, to a lay person, literature on the subject?

I can see how space could be curved like the iso-bars on a weather map without recourse to a fourth dimension. But I don't see how a finte object can be without boundry without recourse to a higher dimesion.

[Chronos]

Unbounded, but, finite - in the words of Stephen Hawking. It is well known the universe is observationally finite [surface of last scattering]. No experiment capable of discerning whether it is 'spatially' finite has been proposed and executed.

[robertm]

This is the part I don't understand. Is there an accessible, to a lay person, literature on the subject?

It is an intrinsic mathematical consequence, that being the maths of the theory of General Relativity. Not too much tough stuff, but does rely on differential calculus.

I suppose this would be your best bet for a good cursory introduction. He also gives some links to other materials for further study:

http://www.astro.ucla.edu/~wright/relatvty.htm

[Pjpic]

However, like the two-dimensional sphere, the possible curvature of three-space is an intrinsic property and there is no actual need of a higher-dimensional space for it to live in. Obtaining a correct mental picture of this is one of the big challenges in understanding our Universe!

This is the understanding I'm trying to grasp. I understand 'intrinsic' to mean that the (for example) sadle shape of universe can be discovered by people within the universe without referencing a higher dimension (because, for example, angles in a triangle don't add up to 180).

What I don't understand is how there can be a curved space without being embedding in a higher dimension (like the balloon analogy).

[PhanthomJay]

What I don't understand is how there can be a curved space without being embedding in a higher dimension (like the balloon analogy).
I am in full agreement with you. The 2D curved surface of a balloon, although finite and without edge, is bounded , both within and without, by the third (and higher order)dimension. That is not common sense; it is fact. It's curvature could not exist without a third dimension; it's curvature is into the third dimension. Now whether that analogy holds for our multidimensioned universe, is I guess open to question. However, the curvature of light in 3-space, in the presence of mass, has been measured at least once during the famous experiment carried out during a solar eclipse, where such curvature from light of a star was observed and measured. My question is: was that curvature into the 4th spatial dimension? Or just an ordinary ho-hum curve in the boring 3rd dimension? I think not.

[kev]

What I don't understand is how there can be a curved space without being embedding in a higher dimension (like the balloon analogy).
I am in full agreement with you. The 2D curved surface of a balloon, although finite and without edge, is bounded , both within and without, by the third (and higher order)dimension. That is not common sense; it is fact. It's curvature could not exist without a third dimension; it's curvature is into the third dimension. Now whether that analogy holds for our multidimensioned universe, is I guess open to question. However, the curvature of light in 3-space, in the presence of mass, has been measured at least once during the famous experiment carried out during a solar eclipse, where such curvature from light of a star was observed and measured. My question is: was that curvature into the 4th spatial dimension? Or just an ordinary ho-hum curve in the boring 3rd dimension? I think not.

There is a way that the time dimension acts as the "4th spatial dimension". Differences in the way time advances in different regions of space brings about a curvature that appears like an extra spatial dimension. The role of time as a 4th spatial dimension can be seen in the mathematical equations of relativity. It is easier to visualise this in the analogy of 2D creatures living on a 2D surface. With a bit of imagination, you could place the 2D creatures on a circular piece of paper that is perfectly flat (in 3D), and by placing suitable time dilation on the concentric circles you could convince the 2D creatures by every measurement that they can make in 2 dimensions, that they are living on a 3D sphere. In the same way, it is a matter of personal taste whether you choose to see the universe as 3 spatial dimensions + 1 time dimension or as 3 visible spatial dimensions + 1 invisible spatial dimension. Mathematically they are the same thing. Everything that can be explained by an additional invisible spatial dimension can be explained by time dilation and length contraction.

[Chronos]

A concise explanation of unbounded surfaces is not trivial. It requires very complex geometrical concepts to convey with mathematical precision. The common sense, logical explanation you are seeking, Pjpic, does not exist. Analogies are good, but, logically imprecise - as you have deduced. That defect does not exist in the more rigorous mathematics behind them.

[PhanthomJay]

In the same way, it is a matter of personal taste whether you choose to see the universe as 3 spatial dimensions + 1 time dimension or as 3 visible spatial dimensions + 1 invisible spatial dimension. Mathematically they are the same thing. Everything that can be explained by an additional invisible spatial dimension can be explained by time dilation and length contraction.Kev, that is a very helpful explanation, thanks. But, what about M-Theories 5th and 6th etc. extra dimensions? Are they postulated to be time-like or space-like? Or both? Could not our 4D spacetime universe be curved into these dimensions?

[ThomasT]

Because the balloon analogy is common sensical.
I don't see how the balloon analogy is common sensical. If one assumes some form of a Big Bang conjecture wrt the origin of our universe, then common sense would seem to dictate that our universe is some sort of expanding wave structure, and that the contents (the flotsam and jetsam created in the wake of the expanding universal wave front) of that expanding wave structure is bounded by an expanding universal wave front.

We, and all other material phenomena that we collectively refer to as our universe, are the inside of the isotropically expanding universal wave structure. The surface (and beyond) of this universal wave structure would seem to be necessarily off limits to us or anything else that originated inside it because the rate of expansion would circumscribe an absolute limit wrt the rate of propagation of any disturbance. This is my grossly oversimplified, common sensically speculative view of what our universe is (it's not meant as an analogy).

I realize that the balloon analogy is offered as one way to reify (or at least visualize) the idea of curved space or spacetime which arises via a geometric interpretation of general relativity.

But one doesn't have to take this interpretation literally. More likely, in my common sensical view, GM is itself a gross simplification of the deep reality of gravitational behavior -- which might eventually be modeled in terms of complex wave interactions.

[marcus]

I don't see how the balloon analogy is common sensical. .

that could be because you haven't understood the balloon analogy. In the analogy there is no existence where air is----either inside or outside surrounding the balloon.
the only thing that exists is the balloon. That is why it is an analog for the universe.

All that exists is the balloon surface---an idealized 2D world----and the objects and inhabitants are 2D beings in this 2D surface space. That is the analogy.

In your discussion you seem to be imagining a 3D world with an expanding spherical wavefront, and stuff inside of that----a solid ball. That is not the balloon analogy. As far as I can see what you picture does indeed makes no sense, common or otherwise, as an analogy for the universe. Take another try at understanding the balloon analogy. It is actually a pretty good one, and a lot of people find it understandable on a commonsense basis. :smile:

the real universe is the 3D analog of the 2D surface of the balloon---with a little work almost anyone can get it, Thomas.

[robertm]

with a little work almost anyone can get it

And if you are searching for more than what has already been said, that work will by necessity involve the mathematics of the general theory of relativity.

[ThomasT]

that could be because you haven't understood the balloon analogy. In the analogy there is no existence where air is----either inside or outside surrounding the balloon.
the only thing that exists is the balloon. That is why it is an analog for the universe.
I think I understand the balloon analogy. I don't think it's a common sense (or a very good) analogy for our universe. I prefer the raisin bread analogy. :smile:

All that exists is the balloon surface---an idealized 2D world----and the objects and inhabitants are 2D beings in this 2D surface space. That is the analogy.
Yes, I understand. But if space isn't actually curved (a la a particular geometric understanding of the deep nature of gravitational behavior), then the balloon analogy is obviated, isn't it?

The reason that cosmologists speak of curved space at all comes from GR, doesn't it?
Can't GR be used without reifying its curved space geometric representation? That is, current (working) gravitational theories don't really say anything about what the fabric of space is -- just that there is one, and, vis GR, at large cosmological scales it's curved. Is this correct?

I don't think that GR is a realistic theory. It's geometry is a (necessary for calculation?) simplification of the deep nature of gravitational behavior, which, my common sense tells me, isn't curved space but complex wave interactions.


In your discussion you seem to be imagining a 3D world with an expanding spherical wavefront, and stuff inside of that----a solid ball. That is not the balloon analogy.
Right, it's the raisin bread analogy -- which I think is much more common sensical, based on what I know of astronomical observations, than the balloon analogy.


As far as I can see what you picture does indeed makes no sense, common or otherwise, as an analogy for the universe.
What I visualize, as I mentioned, was not meant as an analogy per se (at least not in the way that the expanding 2D surface of a balloon is an analogy for an expanding 3D, curved space volume).

Based on observations, some time in the very distant past there was a Big Bang, an incomprehensibly huge disturbance of some sort, a humongous explosion ... right? This was the beginning of our universe.

While this explosion, and resulting disturbance(s), happened (and continue to evolve) in a homogenous, fundamental medium of unknown and unknowable structure, there's no reason to believe that the wave physics that might be used to represent behavior on cosmological (and submicroscopic, for that matter) scales is essentially different than the wave mechanics that is useful on the macroscopic scale that circumscribes our sensory experience.

One can (ideally) picture our universe as an isotropically expanding sphere whose leading edge (boundary) is the shock wave front created during the Big Bang.

We, and the rest of the accessible universe, are inside the boundary of the expanding sphere. We can never breach this boundary -- not because space is curved, but because the universe is expanding. The rate of expansion might vary, but whatever it is during any particular epoch sets the speed limit for the propagation of disturbances within our universe.

Everything is wave behavior. Particles arise from wave interactions. Produce enough particles and you have a particulate medium. The physical universe, the universe that is amenable to our sensory apprehension, including gravitational behavior, is the interfacing and interaction of waves of the various particulate media. Of course, the deep nature of the physical universe isn't amenable to our sensory apprehension, so we have notions like instantaneous-action-at-a-distance and curved space to contend with.

Detailed wave models of reality aren't possible yet, but it is possible to recognize that the idea of a curved space and the use of a balloon analogy to help visualize it are only necessary if one takes the current models of nature (eg., GR) as literal descriptions of it. They aren't.

Take another try at understanding the balloon analogy. It is actually a pretty good one, and a lot of people find it understandable on a commonsense basis. :smile:
I do understand it. I just don't think it's a good one -- whether we want to call it common sensical or not. :smile:

the real universe is the 3D analog of the 2D surface of the balloon ...
I don't think so. What's being attributed to curved space now will eventually be explained in terms of wave interactions.

Thanks for your response -- I do read most all of the stuff you post. On this thing, I must stubbornly refuse to accept curved space as real until a more compelling argument than the geometry of GR is put forth.

[MeJennifer]

Hi Thomas you say repeatedly you understand but reading your posting I believe you do not understand some things.

Can't GR be used without reifying its curved space geometric representation?

It can, but you still have to deal with things like closed spacetimes.

Based on observations, some time in the very distant past there was a Big Bang, an incomprehensibly huge disturbance of some sort, a humongous explosion ... right? This was the beginning of our universe.

I think you would do good in checking some literature as to what the big bang actually is, you are clearly misinformed.

One can (ideally) picture our universe as an isotropically expanding sphere whose leading edge (boundary) is the shock wave front created during the Big Bang.

There is no such thing as a shock wave front, you are misinformed.

We, and the rest of the accessible universe, are inside the boundary of the expanding sphere. We can never breach this boundary -- not because space is curved, but because the universe is expanding.

Even if there is no expansion and spacetime is not closed this is true. Since each observer, that has mass, is within the confines of the expanding future light cone.

[ThomasT]

It can, but you still have to deal with things like closed spacetimes.
I choose not to deal with things like that, but if it works for you ... :smile:


I think you would do good in checking some literature as to what the big bang actually is, you are clearly misinformed.The Big Bang was an explosion. You can say that a singularity or some finite volume of space spontaneously started expanding during some time in the distant past, but that's just another way of saying that our universe began with an explosion.

And, explosions produce shock waves.

There is no such thing as a shock wave front, you are misinformed.And, of course there are such things as shock wave fronts.

[dx]

The Big Bang was an explosion. And, explosions produce shock waves.

The Big Bang was not an explosion in the sense of a dynamite explosion, located at some point in space, if that's what you're thinking. Understanding the Big Bang requires an understanding of General Relativity.

[ThomasT]

The Big Bang was not an explosion in the sense of a dynamite explosion, located at some point in space, if that's what you're thinking. Understanding the Big Bang requires an understanding of General Relativity.
A number of different things might cause an explosion. Detonating some dynamite is one of them. Nobody knows what caused the Big Bang. I'm with you in thinking that it probably wasn't dynamite. :smile:

Nevertheless, vis the Big Bang, we're living in the evolving aftermath of a cataclysmic explosion.

I agree that GR might give one some sort of understanding of the Big Bang, just as it provides some sort of understanding of gravitational behavior. Unfortunately, even though it has provided a means of making fairly accurate calculations, there's no way to know how closely the qualitative geometric model corresponds to reality.

[robertm]

Nevertheless, vis the Big Bang, we're living in the evolving aftermath of a cataclysmic explosion.

...there's no way to know how closely the qualitative geometric model corresponds to reality.

If you must parafrase, try, "We are living in the aftermath of a cataclysmic expansion."

Saying over and over that the BB event was some sort of explosion with out backing the claim with any evidence is not conducive to yours, or anyone else's attempt to understand the nature of what modern cosmology currently (and well foundedly) theorizes.

Intellectual honesty is integral to any meaningful conversation.

[ThomasT]

If you must parafrase, try, "We are living in the aftermath of a cataclysmic expansion."A sudden, "cataclysmic expansion", accompanied by a "release of energy in an extreme manner", and the "generation of high temperatures" is the definition of the word, explosion.

What's the problem? Why do some people seem averse to calling the Big Bang event an explosion?

I don't care how you refer to it. Really. But if your understanding of the Big Bang fits the criteria mentioned above, then it's ok to call it an explosion.

Saying over and over that the BB event was some sort of explosion with out backing the claim with any evidence is not conducive to yours, or anyone else's attempt to understand the nature of what modern cosmology currently (and well foundedly) theorizes.What do you want to call it? How about a spontaneous apocalyptic expansion coinciding with the release of a virtually incalculable amount of energy? Does that seem more in line with what modern cosmology currently theorizes? Add in temperatures of a few billion degrees Kelvin and guess what -- we can call it an explosion. :smile:

I'd be willing to bet that you can find some astrophysicists and cosmologists that refer to the Big Bang event as an explosion.


Intellectual honesty is integral to any meaningful conversation.
I agree. So please tell me what you think the Big Bang event actually was if it wasn't an explosion of some sort -- keeping in mind the definition of the word, explosion. :smile:

I'm fascinated by this stuff, as I presume you must be -- so lighten up and have some fun exploring different ways of thinking about current theories, the observational data, etc.

I've made a few conjectures. If we can get over what seems to be a small semantic hump I'd enjoy hearing some criticism. marcus has already replied that what I've said makes absolutely no sense to him -- and of course I can't really argue with that. :smile:

[Hurkyl]

A sudden, "cataclysmic expansion", accompanied by a "release of energy in an extreme manner", and the "generation of high temperatures" is the definition of the word, explosion."
The big bang started with high temperatures, and I'm not sure in what sense one could say that energy has been released....

What's the problem? Why do some people seem averse to calling the Big Bang event an explosion?
You describe an event where some buildup of potential energy was converted into thermal energy, which subsequently propagated through space. Neither of these features resemble the big bang theory.

What do you want to call it?
How about... 'the big bang'?

[ThomasT]

The big bang started with high temperatures ...You can only extrapolate back to a certain interval in time. During that time, our universe was denser, hotter, and its radius was increasing. So far, that fits the criteria for the word, explosion.


... and I'm not sure in what sense one could say that energy has been released.... The Big Bang defines a certain interval in time. There was, as far as anyone can know, a beginning to our universe. So, as far as we can be concerned, at some time in the past there was a humongous release of energy manifested as an expanding, superdense primordial fireball. Notice I put fireball in italics. :smile:

NASA release 98-75, May 6, 1998:
" A recently detected cosmic gamma ray burst released a
hundred times more energy than previously theorized, making it the
most powerful explosion since the creation of the universe in the
Big Bang."

You describe an event where some buildup of potential energy was converted into thermal energy, which subsequently propagated through space. Neither of these features resemble the big bang theory. I'm not exactly saying that. We can't say what the universe is propagating through, or what precipitated it, or what medium or media existed before it -- just that it's behavior resembles the aftermath of an explosion. That there was a great deal of thermal energy involved is a feature of every account of the various Big Bang scenerios that I've read. And insofar as there are quantities of kinetic and thermal energy involved it follows that there was an energy potential which preceded them.

Here's a quote from the first Big Bang guy:
"The evolution of the world can be compared to a display of fireworks that has just ended; some few red wisps, ashes and smoke. Standing on a cooled cinder, we see the slow fading of the suns, and we try to recall the vanishing brilliance of the origin of the worlds." Lemaitre

How about... 'the big bang'?The Big Bang satisfies the criteria for the term, explosion. One reason for calling it an explosion is that explosions have certain salient features that might prove to be heuristically rich in developing models of the origin and evolution of our universe. Not to mention that you can study explosions in laboratories.

[Hurkyl]

The Big Bang satisfies the criteria for the term, explosion. One reason for calling it an explosion is that explosions have certain salient features that might prove to be heuristically rich in developing models of the origin and evolution of our universe. Not to mention that you can study explosions in laboratories.
(emphasis mine) This is exactly what you cannot do. The fallacious line of reasoning is common enough that it even has a name: false analogy (http://www.fallacyfiles.org/wanalogy.html). Yes, the big bang has some superficial similarities to the things we usually describe as 'explosions' -- but you cannot push the analogy too far. And I'm pretty sure that asserting we can learn about the big bang by studying terrestrial explosions counts as pushing the analogy too far.

superdense primordial fireball
For example, the BBT was most certainly not a fireball. One reason (among several, I believe) is that the BBT was too hot to be a fireball!

So, as far as we can be concerned, at some time in the past there was a humongous release of energy manifested as an expanding,
Again, I don't see in what sense energy was released. The energy was already there, and already thermal during the big bang -- the BBT does not speculate about the 'origin' of that energy. And since there's nowhere else for it to go, all of that energy is still here. (at least, to whatever degree conservation of energy makes sense in GR)

[Integral]

Explosions happen IN Space/Time.

The BB happened TO Space Time. Before the BB there was no space time, after the BB there is expanding space time. It is only after the BB that there is any space for an explosion to occur in. Surely you can see that the expansion of space/time itself is not the same as and explosion in space time.

[MeJennifer]

Before the BB there was no space time....
How do you conclude that? I think that nothing in GR indicates that statement to be definitely true.

[Pjpic]

It seems we either have an expanding 'actual' infinite space or an unbounded finite space. Both of these seem like oxymorons to the lay customer.
An expanding shockwave within a larger infinite space or an expansion through a higher spatial dimension would make an easier sale. Because, with either; the greater universe becomes unbounded and non-expanding and this is easier to grasp.

[Cryptonic]

Chapter 1 of Lee Smolin's book "Three Roads To Quantum Gravity" - ("There Is Nothing Outside The Universe") - helped me a lot towards a layman's understanding of this thing we call our "universe".

It seems we are constantly trying to paint a picture in our heads, but this picture is an imagined "God's eye" POV and assumes a spatial universe populated by "things". What Lee Smolin suggests is that there simply is no "God's eye" perspective, it is an illogical/impossible concept. And the universe consists not of things, but processes. So it is impossible to picture a "snapshot" of the universe, because no such thing exists, it is rather a dynamic and relativistic thing and we are enmeshed within it in a deep fundamental sense.

Sometimes I think our quibbling over "finite vs infinite universe" belies a fundamental misunderstanding of relativity and spacetime reality. We think too much in "spatial" terms only.

Just my layman's 2cents!

[Chronos]

That 'nothing outside the universe' thing really confuses people. Mathematicians easily grasp this notion. It is set theory 101. A set is a self contained grouping of numbers with relational properties [they interact]. There is no claim other numbers do not exist, merely that they are meaningless [do not interact]. It's hard to wrap your head around this unless you are well versed in mathematics. It's also difficult to explain to those who are not.

[MeJennifer]

That 'nothing outside the universe' thing really confuses people. Mathematicians easily grasp this notion. It is set theory 101. A set is a self contained grouping of numbers with relational properties [they interact]. There is no claim other numbers do not exist, merely that they are meaningless [do not interact]. It's hard to wrap your head around this unless you are well versed in mathematics. It's also difficult to explain to those who are not.
I disagree with the notion that this is some kind of a fact and that anyone who does not see that is not math savvy enough.

We simply do not know if there is only one possible universe in existence. Please tell me what laws or what theory excludes the existence of more than one universe? In GR there is absolutely nothing that excludes that, on the contrary; for instance the extended Schwarzschild solution is a simple example where two different universes could be connected. Obviously we can argue whether such solutions are physical, but it is going to far IMHO to state as a fact that there is only one possible universe in existence.

[ThomasT]

This is exactly what you cannot do.
What, you're saying that you can't study explosions in laboratories? Sure you can. Or, are you saying that there's nothing about the Big Bang that lends itself to laboratory study?

http://www.usatoday.com/tech/science/discoveries/2005-04-19-big-bang-mystery_x.htm

Yes, the big bang has some superficial similarities to the things we usually describe as 'explosions' -- but you cannot push the analogy too far.
All I'm saying is that it deserves some consideration in that nobody really knows yet just how far the analogy might be extended. It might be possible to improve on the current, standard Big Bang representation.

And I'm pretty sure that asserting we can learn about the big bang by studying terrestrial explosions counts as pushing the analogy too far.
I'm not so sure.

For example, the BBT was most certainly not a fireball. One reason (among several, I believe) is that the BBT was too hot to be a fireball!Yes, that's why I put fireball in italics. It was more like some sort of plasma at the point of departure of the Big Bang theory. A photon plasma? Did the universe ever go through anything resembling a fireball epoch?

Again, I don't see in what sense energy was released. The energy was already there, and already thermal during the big bang ... Ok, it isn't necessary to speak in terms of energy release in order to keep the explosion analogy. After all, the Big Bang account starts some time after the initial event.
... -- the BBT does not speculate about the 'origin' of that energy.Ok.

And since there's nowhere else for it to go, all of that energy is still here. (at least, to whatever degree conservation of energy makes sense in GR)
Here is where looking at our universe as evolving from an explosion in some medium of unknown and unknowable structure might be helpful. Assume that a finite (if incomprehensibly huge) amount of kinetic energy was imparted via the initial explosive event. This leads to a high rate of expansion of the resultant universal scale wavefront, and extremely high temperature of the volume circumscribed by that boundary.

As the expansion proceeds, it, in general, slows down, and the temperature of the universe, in general, decreases -- a finite amount of kinetic energy was imparted (taking many different forms within our universe) and that energy is dispersing and dissipating.

Viewed as an explosion, it's readily apparent that our universe is bounded wrt both space and time. The dominant energy is the kinetic energy of the expansion. All other forms of energy, all behavior (including gravitational) is a byproduct of this energy. But the allotted universal energy is being used up by the expansion and internal events.

There won't be any Big Crunch (the mechanics of the universe slowing down, coming to a stop, more or less, and then reversing and becoming, in effect, an advanced rather than a retarded wave would be very interesting if they weren't impossible) because the mechanics of our universe preclude it (just like the mechanics of our universe preclude broken teacups spontaneously reassembling themselves, etc.).

Rather our universe will simply reach equilibrium with whatever medium it's a disturbance in, and will then quietly cease to exist.

[marcus]

Chapter 1 of Lee Smolin's book "Three Roads To Quantum Gravity" - ("There Is Nothing Outside The Universe") - helped me a lot towards a layman's understanding of this thing we call our "universe".

It seems we are constantly trying to paint a picture in our heads, but this picture is an imagined "God's eye" POV and assumes a spatial universe populated by "things". What Lee Smolin suggests is that there simply is no "God's eye" perspective, it is an illogical/impossible concept. And the universe consists not of things, but processes. So it is impossible to picture a "snapshot" of the universe, because no such thing exists, it is rather a dynamic and relativistic thing and we are enmeshed within it in a deep fundamental sense.

Sometimes I think our quibbling over "finite vs infinite universe" belies a fundamental misunderstanding of relativity and spacetime reality. We think too much in "spatial" terms only.

Just my layman's 2cents!

Cryptonic, thanks for bringing the discussion back to traditional meanings! There is a lot of sense to what you say, and to the quote from Smolin that comes through.
Traditionally the universe has always meant all that exists or considered as process it is all physical process, all that happens.

there cannot be more than one, simply by definition.

what interferes with this is a temporary fad (lasting a century or so I expect) of equating the universe with a certain mathematical idea of limited validity, namely a connected region of spacetime which is a solution to certain equations, namely vintage 1915 General Relativity!

If someone is aggressively promoting that vintage 1915 view, then when GR encounters a singularity (a theory breakdown) they will call that a boundary, and whatever might be on the other side they will consider to be a different universe!!!

But that is obviously an artifact of the GR theory which has broken down. GR is currently being replaced by quantized versions of GR which do not experience a singularity at the big bang or at the pit of a black hole. therefore our universe does not end there in the new theoretical context.

if there is a contracting region prior to our big bang, it is part of our universe (and we call it a big bounce :smile:). if there is an expanding region continuing from the pit of a black hole then it too is part of our universe.

so we can go back to the traditional centuries-old meaning of the word---all process, all existence.

logically there can only be one, by definition. it's in the etymology (uni-) as everyone can see.

we still need could use a convenient term for our part, a bit like the Romans' name for the Mediterranean Sea---I believe they called it "Mare Nostrum".
Our Part would be everything coming after the onset of expansion, everything after the bang/bounce, and excluding everything that might be wildly sprouting from the pits of black holes. A nice trim FILLET of universe, that we can call our own proper turf.

Maybe someday the sematic kinks will get worked out and the current tug-of-war over the world-word will be forgotten.

Anyway, thanks for the post. Glad to be reminded of Smolin's Three Roads!

[cristo]

What, you're saying that you can't study explosions in laboratories? Sure you can. Or, are you saying that there's nothing about the Big Bang that lends itself to laboratory study?

http://www.usatoday.com/tech/science/discoveries/2005-04-19-big-bang-mystery_x.htm

What Hurkyl means (or at least, what I think he means) is that, if you decide to draw analogies and compare the "big bang" to an explosion, then it is certainly not the kind of "explosion" that can be recreated in the lab. Regardless of any popular science articles or news stories you try and use, this is a fact. In fact, the 'standard model' of cosmology does not say anything about the "birth" of the universe; it merely states that the universe was once in a state that was a lot hotter and denser than it is today. Now people try and extrapolate back to "t=0" and find that their theory has a singularity, but really all this means is that the theory they are using breaks down. There have been models that have tried to "bounce through" the singularity, but these have not been proven as of yet.


There seem to be a lot of misconceptions, or at best misunderstandings of each others' words floating around in this thread. Anyway, I should mention that personal theories are not permitted here at PF, unless in the Independent Research forum. I urge all participants in this thread to adhere to that rule.

[ThomasT]

What Hurkyl means (or at least, what I think he means) is that, if you decide to draw analogies and compare the "big bang" to an explosion, then it is certainly not the kind of "explosion" that can be recreated in the lab.Various sorts of explosions in various media have certain things in common. And there is credible research being done wrt Big Bang, or initial cosmological explosion event (not necessarily synonymous with Big Bang) if you prefer, analogous, laboratory produced explosions.


Regardless of any popular science articles or news stories you try and use, this is a fact.It's a fact that hundreds of experiments aimed at simulating cosmological explosions and primordial cosmological conditions have been done. With the large hadron collider there will be even more of these sorts of experiments. So, I'm not sure what you're saying.

In fact, the 'standard model' of cosmology does not say anything about the "birth" of the universe; it merely states that the universe was once in a state that was a lot hotter and denser than it is today.Yes, but the limitation on backward extrapolation wrt the standard cosmological model doesn't prohibit thinking of the beginning of the universe as an explosion, does it?


Now people try and extrapolate back to "t=0" and find that their theory has a singularity, but really all this means is that the theory they are using breaks down. There have been models that have tried to "bounce through" the singularity, but these have not been proven as of yet.OK


There seem to be a lot of misconceptions, or at best misunderstandings of each others' words floating around in this thread. Anyway, I should mention that personal theories are not permitted here at PF, unless in the Independent Research forum. I urge all participants in this thread to adhere to that rule.Thanks for your (and others) input. I'm not looking to advance any sort of personal theory. My motive in first posting in this thread was that the balloon analogy didn't seem at all commonsensical to me. It still doesn't. So, I posted what did seem to me to be a commonsensical overview of the universe, and this met with some resistance.

Here are some links to papers that pertain to aspects of what's being discussed here:

"Cosmological" quasiparticle production in harmonically trapped superfluid gases
Authors: Petr O. Fedichev, Uwe R. Fischer
http://arxiv.org/abs/cond-mat/0303063

Analogue models for FRW cosmologies
Authors: Carlos Barcelo (University of Portsmouth), Stefano Liberati (University of Mayland), Matt Visser (Victoria University of Wellington)
http://arxiv.org/abs/gr-qc/0305061

Cosmology with a shock wave
Authors: Joel Smoller, Blake Temple
http://arxiv.org/abs/astro-ph/9812063


Cosmology, Black Holes and Shock Waves Beyond the Hubble Length
Authors: Joel Smoller, Blake Temple
http://arxiv.org/abs/math-ph/0302036

The Big Bang quantum cosmology: The matter-energy production epoch
Authors: V. E. Kuzmichev, V. V. Kuzmichev (Bogolyubov Institute for Theoretical Physics)
http://arxiv.org/abs/0712.0464

The Fluid Mechanics of Gravitational Structure Formation
Authors: Carl H. Gibson (Univ. Calif. San Diego)
http://arxiv.org/abs/astro-ph/0610628


Analogue models for FRW cosmologies
Authors: Carlos Barcelo (University of Portsmouth), Stefano Liberati (University of Mayland), Matt Visser (Victoria University of Wellington)
http://arxiv.org/abs/gr-qc/0305061

The evolution of the Universe
Authors: Juan Garcia-Bellido
http://arxiv.org/abs/hep-ph/0303153

Big bang simulation in superfluid 3He-B -- Vortex nucleation in neutron-irradiated superflow
Authors: V.M.H. Ruutu, V.B. Eltsov, A.J. Gill, T.W.B. Kibble, M. Krusius, Yu.G. Makhlin, B. Placais, G.E. Volovik, Wen Xu
http://arxiv.org/abs/cond-mat/9512117

Resolution of Cosmological Singularity and a Plausible Mechanism of the Big Bang
Authors: D.C. Choudhury
http://arxiv.org/abs/astro-ph/0111425

Testing cosmological defect formation in the laboratory
Authors: T.W.B. Kibble
http://arxiv.org/abs/cond-mat/0111082

[marcus]

...
There seem to be a lot of misconceptions, or at best misunderstandings of each others' words floating around in this thread. Anyway, I should mention that personal theories are not permitted here at PF, unless in the Independent Research forum. I urge all participants in this thread to adhere to that rule.

To amplify, an additional point could be made. Cosmology is a mathematical science, which means the emphasis is on fitting data to mathematical models of the universe----

not to verbal descriptions, and not to mechanical analogs. So if someone wants to offer an alternative to the conventional LCDM model, they are expected to provide a specific mathematical model (not some purely verbal scenario, or generalities about labwork from condensed matter to engineering.)

By coincidence I happen to have looked at few of the papers that ThomasT just listed, not recently but must have glanced at some in the past as an occasional title rings a bell. My impression is that what I saw did not actually challenge the LCDM model in the sense of offering a substitute. In what I saw, the experiments with material serve primarily as ways to illustrate aspects of the conventional model and explore its limits. In the end, the results always get interpreted in the context of conventional cosmology with its FRW metric. I can't say for sure but that's my impression: someone else may have more definite things to say.

The thing to remember is that a material model does not replace the mathematical one, though it may show things about it. It is important not to push material analogy too far---a lab demonstration may nicely illustrate some behavior but still have limited applicability as something you can fit real astronomical data to.

ThomasT,
unless you can show us a mathematical model that is different from the standard LCDM, then you appear to be arguing on a purely verbal level-----the message being some vague generality like "explosion good! balloon bad!". But neither explosions nor balloons actually model anything.

[Hurkyl]

Here is where looking at our universe as evolving from an explosion in some medium of unknown and unknowable structure might be helpful. ...
You're not helping your case -- you've just spouted a big pile of incorrect ideas that one could get by pushing the explosion too far. For example:

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.

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)

[Pjpic]

.

Sometimes I think our quibbling over "finite vs infinite universe" belies a fundamental misunderstanding of relativity and spacetime reality. We think too much in "spatial" terms only.

I appreciate the citation; I'll check it out - other cites would also be appreciated. But, I don't know if it is psychologically possible to stop about thinking it until something infinitely large is finally found.

It almost seems like there are axioms that state 'we don't need infintiy in our discipline therefore it need not exist.' This does not seem how scientists would usually approach a subject that still has great mystries to resolve.

[marcus]

.

It almost seems like there are axioms that state 'we don't need infintiy in our discipline therefore it need not exist.' This does not seem how scientists would usually approach a subject that still has great mystries to resolve.

Einstein said "Make everything as simple as possible, but not simpler." The first part of that is a traditional scientific principle called Occam's Razor.

This principle goes back hundreds of years. Applied to a mathematical science like cosmology, it says don't put stuff in your model that isn't needed.

So far this applies to extra dimensions. You can put extra dimensions in your model, if you want. But so far I find that the simpler models with 4D spacetime are working just as well. I keep an open mind, so whenever I see a 5D model that works noticeably better, then I will eagerly consider it.

I don't know any professionals who are close-minded about this, or who treat 4D as an axiom.
=================

About infinity, you are misinformed. The great majority of professional cosmologists use a infinite spatial volume model for most of their work. The main reason is because it is simpler to calculate with.

the standard cosmology model, LambdaCDM, comes in two versions: either space is infinite volume or it is finite volume, depending on how you set the numbers up in the model. They typically use the infinite version. Both fit the data OK but the infinite version is easier to calculate with.
But there is no rigid doctrine about this. The professional community is open-minded. I see plenty of evidence that the finite space version is being considered.

You depict cosmologists as being close-minded and doctrinaire in preferring the finite version. This is a very unflattering picture applied to a large group of people as a kind of stereotype. I would say this picture is totally wrong---you have things turned around backwards. I'm curious how you got the idea.

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

About which way the universe actually IS in reality, there is no use discussing since at this point we simply don't know!
the practical question is which mathematical model works better and fits the data better---for the time being cosmologists will use the model that works best: that fits the data and makes the calculations easy.

[Pjpic]

I'm curious how you got the idea.

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

Far be it from me to promote a negative stareotype. Thats why I used the phrases "it almost seems" and "this does not seem like".

I have read things like: we don't need an extra dimension, it is meaningless to discuss what is "outside" the balloon, there is nothing beyond our finite unbounded space. These lead me to think the 5d universe is not really part of current thought. But if you say it is, then I suppose it is.

[marcus]

These lead me to think the 5d universe is not really part of current thought. But if you say it is, then I suppose it is.

What did I say?

[Pjpic]

I keep an open mind, so whenever I see a 5D model that works noticeably better, then I will eagerly consider it.

I don't know any professionals who are close-minded about this, or who treat 4D as an axiom.
=================

I took this to mean that the 5d model is still considered a possibility. Which leads me to think, doubtless incorrectly, that the balloon analogy doesn't necessarily break down.

[marcus]

...
I have read things like: we don't need an extra dimension, it is meaningless to discuss what is "outside" the balloon, there is nothing beyond our finite unbounded space...

Where have you read such statements?

Let's have some actual quotes with links to source. Not merely fragments taken out of context because whoever you are quoting might have qualified by saying things like "in thus and thus version of the model" or "in the case where space is finite"...

Quoting out of context is generally considered unethical or dishonest. I'm sure you wouldn't want to do that.

[Pjpic]

Where have you read such statements?

Let's have some actual quotes with links to source. Not merely fragments taken out of context because whoever you are quoting might have qualified by saying things like "in thus and thus version of the model" or "in the case where space is finite"...

Quoting out of context is generally considered unethical or dishonest. I'm sure you wouldn't want to do that.

Let me run some of those down. There must have been many qualifiers. Though I don't want to pretend that I understand them or to let my inadaquate attempts at pecision needlessly obfustate the materiality of the question (of if the balloon analogy is an officially accepted possibility for a model of the universe).

[marcus]

... These lead me to think the 5d universe is not really part of current thought. But if you say it is, then I suppose it is.

What did I say?

I keep an open mind, so whenever I see a 5D model that works noticeably better, then I will eagerly consider it.
I took this to mean that the 5d model is still considered a possibility...

So you misrepresented what I said. You pretended that I said that a 5D universe is part of current thought.
I did not say that, nor would I ever say such a thing.

Would you consider apologizing for misquoting me? I think the important issue here is not cosmology or 4D versus 5D. It has rather more to do with the ethics of honest discussion. Would you agree?

[Chronos]

That's the trouble with infinities - any discrete number may emerge at random.

[Arch2008]

Pjpic, I think that you are confused about the search for the value of omega. 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

None of this requires a higher dimensional space, however some scientists are proposing that events before the Big Bang may be determined by using data from the WMAP. This may provide scientific evidence for an extradimensional “hyperspace” description that is currently only conjecture. Dr. Lisa Randall also presents an argument for an extradimensional space where gravity leaks into our universe.
http://discovermagazine.com/2006/jul/interview-randall/

Remember though, the existence of a hyperspace that cannot be proven will never be scientific.

[Pjpic]

So you misrepresented what I said. You pretended that I said that a 5D universe is part of current thought.
I did not say that, nor would I ever say such a thing.

Would you consider apologizing for misquoting me? I think the important issue here is not cosmology or 4D versus 5D. It has rather more to do with the ethics of honest discussion. Would you agree?

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

[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 unverse 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 any one 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. :smile: 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. :smile:


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).