Is there a problem in assuming the universe has a boundary?

[id10tothe9]

I hear about the balloon analogy, and that there is no need to say that the universe has a boundary, but is that the only reason or would it be problematic to assume that space-time has a volume and a boundary?

 

[Drakkith]

When we get down to it the theory and models don't care whether there is a boundary or not for the most part. (If there is it MUST be significantly further away than we can see, otherwise it would be noticeable)

IF the universe is finite in size, then it is very likely that it is "boundless", which just means that you can keep going forever in a direction, but you will keep passing by the same places, like going off the screen on an old arcade game only to come back in from the other side.

 

[id10tothe9]

thanks for the quick reply :)

 

[HallsofIvy]

An interesting question would be- what would the boundary be made of?

 

[phinds]

I hear about the balloon analogy, and that there is no need to say that the universe has a boundary, but is that the only reason or would it be problematic to assume that space-time has a volume and a boundary?

What would happen to physics as we know it at the boundary? How could our physics possibly deal with an "edge" to the universe? That of course does not PROVE the lack of a boundary, but you asked if it would be problematic. How about a total breakdown of all of our known cosmology? You lose isomorphism, you lose isotropy ... basically you pretty much lose your mind trying to figure out how do model a boundary.

 

[bcrowell]

Since we don't see any evidence for a boundary, we have no evidence on which to base any theory of how physics would work at a boundary.

 

[twofish-quant]

I hear about the balloon analogy, and that there is no need to say that the universe has a boundary, but is that the only reason or would it be problematic to assume that space-time has a volume and a boundary?

It would be problematic because we don't see anything observationally that looks like a boundary. If there were a boundary then it would be so far away that we wouldn't see any evidence for it, and do for the purpose of doing calculations, it's assumed that the boundary is irrelevant.

 

[twofish-quant]

What would happen to physics as we know it at the boundary? How could our physics possibly deal with an "edge" to the universe?

As a theorist, I don't think it would be that difficult to come up with something. If we actually did come up with something that looked like a boundary to the universe, you'd just look at it and see what happens there.

 

[turbo]

There could be some kind of a boundary, but we can't see it. Once we have an orbiting telescope that pushes farther into the IR, I expect that we will see further "back" in terms of BB cosmology, but I don't expect to see an edge. Any boundary at this point would probably be an artifact of our inability to detect fainter and fainter objects. I could be wrong about this, but I doubt it.

 

[id10tothe9]

But wouldn't having a boundary be in conflict with the isotropy, ie. the assumption/measurement (which is it?), that the relative velocity of matter would look the same any where in the universe and that there is no center of the universe?

 

[Drakkith]

But wouldn't having a boundary be in conflict with the isotropy, ie. the assumption/measurement (which is it?), that the relative velocity of matter would look the same any where in the universe and that there is no center of the universe?

If it does, and we find a boundary, then we'd have to re-examine our ideas about the universe.

 

[genericusrnme]

basically you pretty much lose your mind trying to figure out how do model a boundary.

we may lose our minds but it'll sure be exciting!

 

[QuantumHop]

The expansion of space causes a natural boundary.

Any objects separated in space by a distance that the expansion between them exceeds speed c then they become causally disconnected. In short our visible universe is surrounded by a collapsing event horizon beyond which the known laws of nature cannot communicate.

 

[phinds]

The expansion of space causes a natural boundary.

Any objects separated in space by a distance that the expansion between them exceeds speed c then they become causally disconnected. In short our visible universe is surrounded by a collapsing event horizon beyond which the known laws of nature cannot communicate.

I don't think that's what the OP was asking about at all. I'm not arguing w/ your statement, just saying that it is irrelevant to this discussion.

 

[bcrowell]

I don't think that's what the OP was asking about at all. I'm not arguing w/ your statement, just saying that it is irrelevant to this discussion.

Yes, "boundary" has a technical definition here http://en.wikipedia.org/wiki/Manifold_with_boundary#Manifold_with_boundary , and whether the OP knew it or not, #1 was using the term in a way that was consistent with that definition.

 

[phinds]

Yes, "boundary" has a technical definition here http://en.wikipedia.org/wiki/Manifold_with_boundary#Manifold_with_boundary , and whether the OP knew it or not, #1 was using the term in a way that was consistent with that definition.

Yes, that definition is consistent w/ how I thought about the term, but I don't see how the event horizon of our observable universe can be what the OP had in mind, as QuantumHop seems to think.

Again, I was not arguing at all w/ what QuantumHop was saying, just about the relevance to the OPs question, which I took to be a question about the "whole" universe, not the observable universe.

 

[rbj]

An interesting question would be- what would the boundary be made of?

stretchy latex.

 

[audioloop]

I hear about the analogy, and that there is no need to say that the universe has a boundary, but is that the only reason or would it be problematic to assume that space-time has a volume and a boundary?

Friedmann–Lemaître–Robertson–Walker cosmology requieres a connected universe hence a non-trivial topology.

 

[PeterJ]

Would I be right in thinking that a boundary to the universe is an absolute, and that physics does not deal with absolutes.

 

[LastTimelord]

When people refer to the balloon analogy, they are actually making a dimensional analogy. The surface of the balloon is a two dimensional plane expanding in a three dimensional way, which is meant to represent the three dimensional space expanding in a four dimensional way, if that makes any sense.

 

[Drakkith]

Would I be right in thinking that a boundary to the universe is an absolute, and that physics does not deal with absolutes.

Any boundary, if it were observable, would be dealt with by science. *Breaks out the shotgun* I'm going to deal with it right now actually.

 

[Flatland]

So what would this boundary be like? The only thing I can think of is that it would be like some kind of cosmic event horizon. Once you cross over you'd cease to exist. It would be like falling into a black hole.

 

[PeterJ]

Any boundary, if it were observable, would be dealt with by science. *Breaks out the shotgun* I'm going to deal with it right now actually.

Okay. But I'm assuming it wouldn't be observable for reasons already given.

 

[id10tothe9]

well, yes, my question is about the whole universe or put in a better way all that came out of the big bang in this universe. When we say the universe has no boundary, I think it means we talk about a n-1 submanifold of a n dimensional manifold, so if we say we live in a 3D universe and it has no boundary then we live on the surface of a 4D universe. Or is there another concept behind "no boundary"?

 

[id10tothe9]

Friedmann–Lemaître–Robertson–Walker cosmology requieres a connected universe hence a non-trivial topology.

thnx didn't see there is already a second site for the answers, got to look into that..

 

[PeterJ]

Would there not have to be a difference of definition between 'the whole universe' and 'all that came out of the Big Bang' in order to make sense of the latter?

Here's my problem with this. Some physicists seem to have concluded that spatial extension is some sort of illusion. One calls it a 'mystical' illusion. Presumably this would include temporal extension also. This seems to considerably alter the boundary problem, and perhaps even make possible a solution.

I'm shooting the breeze, by the way, not proposing anything. But I have read clear statements from a few physicists about this, and unless I am misreading them, which is perfectly possible, then we cannot simply take it for granted that extension is real for an fundamental ontology, and would have to bear this in mind when considering the size of the universe and its boundaries.

I've been warned about my off-beat posts so here's a couple of quotes to lend this point some credibility.

"What is mystical is the picture of the world as existing in an eternal three-dimesional space, extending in all directions as far as the mind can imagine. The idea of space going on for ever and ever has nothing to do with what we see. … When we imagine we are seeing into an infinite three-dimensional space, we are falling for a fallacy in which we substitute what we actually see for an intellectual construct. This is not only a mystical vision, it is wrong."

Lee Smolin
Three Roads to Quantum Gravity
Weidenfeld & Nicolson, 2000 (64)

(It is , of course, the very opposite of a mystical vision, but the point seems to stand anyway. )

"In Leibnitz’s view, the ultimately real, something that depends on nothing else for its existence, cannot have parts. If it had parts, its existence would depend on them. But whatever has spatial extension has parts. It follows that what is ultimately real cannot have spatial extension, …"

Penguin Dictionary of Philosophy
Ed. Thomas Mautner (2002)

 

[audioloop]

thnx didn't see there is already a second site for , got to look into that..

a topology of T2x R1 (a torus) a flat finite universe with
two dimensions compactified, and one infinite.The Topology of the Universe
http://www.maths.lse.ac.uk/personal/mark/topos.pdfThe Topology and Size of the Universe from the Cosmic Microwave Background
http://arxiv.org/pdf/1104.0015.pdf

...the most probable topology is a T2x R1 (a torus)...Creation of a Compact Topologically Nontrivial Inflationary Universe
http://arxiv.org/pdf/hep-th/0408164v2.pdf

...that compact flat or open universes with nontrivial topology should be considered a rule rather than an exception...
http://www.uni-ulm.de/nawi/nawi-theophys/frank-steiners-group.html

...A non-trivial topology of the Universe can lead to a finite volume which in turn implies a suppression of anisotropies on the largest scales. Such a suppression is indeed observed in the CMB radiation...
...In the case of a spatially flat Universe the simplest non-trivial example is that of a 3-torus...

 

[Tim13]

A balloon expands against the atmosphere. If the atmospheric pressure were to increase the balloon would shrink.

So what is the universe expanding against? And if there is nothing to expand against wouldn't that mean a rapidly accelerating rate of expansion?

 

[cepheid]

A balloon expands against the atmosphere. If the atmospheric pressure were to increase the balloon would shrink.

So what is the universe expanding against? And if there is nothing to expand against wouldn't that mean a rapidly accelerating rate of expansion?

This is just carrying the balloon analogy too far. The physics driving the expansion of a balloon has nothing to do with the physics driving the expansion of the universe. Trying to understand the latter in terms of the former is therefore misguided.

I would say that the balloon analogy is helpful in understanding the effects or properties of the expansion, but not its cause.

 

[Tim13]

I agree that the balloon analogy is too simplistic. Like you say it doesn't explain the physics driving the expansion of the universe. And it is potentially misleading because a balloon has a latex "boundary" while the universe may not have a measurable boundary.

 

[phinds]

I agree that the balloon analogy is too simplistic. Like you say it doesn't explain the physics driving the expansion of the universe. And it is potentially misleading because a balloon has a latex "boundary" while the universe may not have a measurable boundary.

You might find this exposition on the balloon analogy helpful:

www.phinds.com/balloonanalogy

if you read it all the way through, particularly the "FORTH: NO STRETCHING" part.

 

[twofish-quant]

But wouldn't having a boundary be in conflict with the isotropy, ie. the assumption/measurement (which is it?), that the relative velocity of matter would look the same any where in the universe and that there is no center of the universe?

Yes it would, which is why you can infer limits on what a boundary would be like by measuring the isotropy of the universe.

One thing about the universe is that it would be really, really weird if there were a boundary in the universe and we happened to be dead center. A universe which had a spherical boundary in which we were *exactly* in the middle of sphere would be indeed be hard to see.

However, either there would be something "special" about our location or else we would be slightly off center, and if we were slightly off center from the boundary of the universe or our location in space was slightly weird, we'd eventually spot something weird. Likewise if the boundary wasn't spherical, we'd spot something weird. And the papers that audioloop posted show the sort of "weird stuff" we would see (and argue that we might be seeing it).

It's also possible that the boundary is so far away that we can't see it, but you can turn that around and ask how close a boundary has to do before we would notice something, and people have come up with some numbers.

 

[twofish-quant]

I'm shooting the breeze, by the way, not proposing anything. But I have read clear statements from a few physicists about this, and unless I am misreading them, which is perfectly possible, then we cannot simply take it for granted that extension is real for an fundamental ontology, and would have to bear this in mind when considering the size of the universe and its boundaries.

Lots of things are possible. That's why you have to do observation. You will get nowhere if you just sit in a room and try to speculate about what the universe is like. What you need to do is to ask yourself "if the universe was a doughnut, what would I see?" and then point your telescope to see if you actually see it.

The papers that audioloop posted do that. Basically if the universe is a doughnut then only certain wavelengths in the gas that form the universe would be not possible, and you would see weird stuff as you look at the texture of the early universe. The papers that he/she mentioned go a bit further and say that they think we might be seeing signs of the universe being a doughnut. Looking at their interpretation, I'm not sure, but it's something that will get resolved with more data.

When we imagine we are seeing into an infinite three-dimensional space, we are falling for a fallacy in which we substitute what we actually see for an intellectual construct. This is not only a mystical vision, it is wrong.

I'm interested to understand why he thinks it's wrong.

In Leibnitz’s view, the ultimately real, something that depends on nothing else for its existence, cannot have parts. If it had parts, its existence would depend on them. But whatever has spatial extension has parts. It follows that what is ultimately real cannot have spatial extension, …

This is the type of "useless word games" that I don't think are useful. The problem is that words are tools that describe things, and the words and concepts we use are those that describe our daily life. The universe can play by very different rules, which makes trying to "figure things out" by "word games" not useful. When you study cosmology, ultimately you have to use the language of math which turns out to be able to describe things that we can't describe in our daily life.

 

[cepheid]

I agree that the balloon analogy is too simplistic. Like you say it doesn't explain the physics driving the expansion of the universe. And it is potentially misleading because a balloon has a latex "boundary" while the universe may not have a measurable boundary.

You misunderstand the balloon analogy completely if you think that it has a boundary. The balloon analogy is a 2D analogy for the universe. In other words, the 2D surface of the balloon represents the expanding universe in this model. The 2D surface, of course, has no boundaries, and no centre.

 

[Tim13]

You misunderstand the balloon analogy completely if you think that it has a boundary. The balloon analogy is a 2D analogy for the universe. In other words, the 2D surface of the balloon represents the expanding universe in this model. The 2D surface, of course, has no boundaries, and no centre.

Hmm. I apologize. I am not sure I understand your point. However I think your point may only add to mine in that the balloon analogy is potentially misleading. Obviously a real balloon is a 3D object and so if it was intended to be a 2D analogy for the universe then I did misunderstand "completely". But please tell me if I understand you correctly - do you posit that a 2D surface could never have any "boundaries"?

Plus, isn't the real universe still 3D even if it is a little flat? Hence the potential confusion when the original topic was about the real 3D universe and whether there is a problem with assuming it has a boundary?

 

[Number Nine]

do you posit that a 2D surface could never have any "boundaries"?

No, he stated that the surface of the balloon which is two dimensional surface, has no boundary, which is true. The expansion of the surface of the balloon provides the analogy for the expansion of space. The surface of the balloon happens to be embedded in three dimensional space, but it doesn't have to be. Space is not embedded in anything.

 

[Tim13]

No, he stated that the surface of the balloon which is two dimensional surface, has no boundary, which is true. The expansion of the surface of the balloon provides the analogy for the expansion of space. The surface of the balloon happens to be embedded in three dimensional space, but it doesn't have to be. Space is not embedded in anything.

That is probably what he meant. Yet if he believes that space is relatively flat but not strictly 2D (perhaps Euclidian and 3D) then it only adds more evidence that the balloon analogy is potentially misleading for numerous reasons.

Plus, my question was a little more nuanced. I was asking if he posits that a 2D surface could never have any boudaries. I wasn't limiting my question to only 2D surfaces which happen to be balloons because it is possible that he was making a general statement about 2D surfaces. And the last time I looked out my window the obsevable universe isn't shaped like a balloon.

 

[phinds]

That is probably what he meant. Yet if he believes that space is relatively flat but not strictly 2D (perhaps Euclidian and 3D) then it only adds more evidence that the balloon analogy is potentially misleading for numerous reasons.

Plus, my question was a little more nuanced. I was asking if he posits that a 2D surface could never have any boudaries. I wasn't limiting my question to only 2D surfaces which happen to be balloons because it is possible that he was making a general statement about 2D surfaces. And the last time I looked out my window the obsevable universe isn't shaped like a balloon.

I take it you did not read the exposition at the link I gave you.

 

[Tim13]

I take it you did not read the exposition at the link I gave you.

I confess that I only skimmed it and didn't fully understand the exposition at the link you gave. I just now went back and reread it. It does a much better job of explaining the potential confusion created by the analogy than what I was attempting to convey. I initially misunderstand the analogy too for some of the reasons stated in the article. Thanks.

 

[phinds]

I confess that I only skimmed it and didn't fully understand the exposition at the link you gave. I just now went back and reread it. It does a much better job of explaining the potential confusion created by the analogy than what I was attempting to convey. I initially misunderstand the analogy too for some of the reasons stated in the article. Thanks.

Glad it was helpful. Several of the members here helped me put it together for exactly this purpose.

 

[Tim13]

Glad it was helpful. Several of the members here helped me put it together for exactly this purpose.

I apologize that I didn't read it more thoroughly earlier. I would have saved myself and others from unnecessary key strokes. Is there a collection of such expositions for different topics on this website?

 

[Mark M]

I apologize that I didn't read it more thoroughly earlier. I would have saved myself and others from unnecessary key strokes. Is there a collection of such expositions for different topics on this website?

This article is frequently recommended, it was written in Scientific American:

http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf

Note that the first page is blank, scroll down.

And two very good FAQs that you may find helpful are these:

http://www.astro.ucla.edu/~wright/cosmology_faq.html
http://preposterousuniverse.com/writings/cosmologyprimer/faq.html

 

[PeterJ]

Lots of things are possible. That's why you have to do observation. You will get nowhere if you just sit in a room and try to speculate about what the universe is like. What you need to do is to ask yourself "if the universe was a doughnut, what would I see?" and then point your telescope to see if you actually see it.

Then you have to sit in a room and and speculate on the meaning of what the telescope has revealed. I really cannot get this idea that thinking is useless compared with experiment.

I'm interested to understand why he thinks it's wrong.

I'm afraid I can't remember the discussion. I could not comment much on it anyway. I just took his proposal to mean that physics allows for the possibility that he is right. It intrigued me that for Smolin extension is a mystical illusion while for mystcism it is a scientific one.

This is the type of "useless word games" that I don't think are useful. The problem is that words are tools that describe things, and the words and concepts we use are those that describe our daily life. The universe can play by very different rules, which makes trying to "figure things out" by "word games" not useful. When you study cosmology, ultimately you have to use the language of math which turns out to be able to describe things that we can't describe in our daily life.

This seems unfair on Leibnitz. He wasn't bad at mathematics. But the language of maths has as much trouble with fundamentals as any other language. His point was simply that if there is a fundamental, non-dependent or original phenomenon, then our reason concludes it cannot be extended. If it is extended, then the universe breaks the laws of thought and is paradoxical. He does not claim to know which it is. There is a connection with Russell's paradox so it is not an entirely non-mathematical point. As I see it, he is saying that the original phenomenon cannot be manifest for the same reason that the set-of-all-sets cannot be manifest in naive set-theory. Logic and reality would be in total accord.

I don't thing we need any experiments to form a view about this. It seems to be significant that the idea of a boundary to the universe gives rise to contradictions and does not compute.