Could there be an edge to the Universe?

[FX89]

And what exactly do you mean by "when the universe comes apart" ?

I've heared in many places that according to the expansion theory all matter has a tendency to move away from other matter. They extrapolated that sooner or later, even atoms will disintegrate. This is known as the big rip.

Check out this article: http://en.wikipedia.org/wiki/Big_Rip

 

[docbill]

You guys are forgetting, the edge of the universe, does not need to be the edge of space, it could just be an edge to interesting space. Perhaps, there is only a finite region of space were matter can form... Maybe the initial "egg" of matter that formed the universe was of finite size. It could be that the mass distribution in the universe is not constant, but indeed there is an edge. Beyond that, there is no matter. Of course, because matter would continue to expand out at the speed of light, we could never physically reach that edge. However, eventually we would be able to see it.

Of course, I am not saying this is the case. But given our current level of understanding, we could neither prove or disprove this conjecture at this point in time.

 

[docbill]

Another thing to consider is in our current models, the universe is finite.

Consider, when we look out into space, we can only see a finite amount. Eventually, if we look far enough, we see the very beginning of the universe. This is known as the observable universe, which consists of a finite number of particles, with a finite number of possible states. Now, consider every point in the real universe is the center of a finite universe. Since every observable universe has a finite size, and there are only a finite number of possible states for a finite system, there are a finite number of unique observable universes.

A basic premise of physics is when two objects are indistinguishable, they are the same object. Ergo, there are only a finite number of observable universes. Since the universe is the sum of all observable universes, the universe is finite. If you could travel far enough you would end-up back where you started... But then since you are the center of your observable universe, you would also find you had never left where you started from.

Of course, this argument is assuming the number of possible states is finite...

 

[Valjean]

The edge of what?

It seems to me that...Isn't considering the edge of the universe, not just that occupied by matter but the entire home for everything occupied or not, about the same as considering the end of time, the edge of it, or even the beginning of it? As far as everything being the center of the universe...everything moves. If one thing is considered the center, at rest, then everything else is moving as one unit in relation to it. That would require the entire universe to move as a unit but since the entire universe takes up the entire space there is no way it can move. There's no room for it to move.

 

[SpaceTiger]

I have no scientific explanations for this, but that's what i feel it is.

Let's keep in mind that this is a science subforum and that idle speculation and philosophizing should be kept to a minimum. These discussions sometimes have a tendency to get philosophical, but cosmology is still a scientific discipline that is not conducted by feelings, opinions, or popular vote.

The discussion so far is mostly reasonable, but this reminder should be noted by everyone contributing.

 

[pyrojelli]

I second the motion

 

[CERDES]

Is it not possible to postulate that there is an endless "area" in which the known universe (ours) as well as many other separate universal constructs exist, endlessly, multiplicatively?
This would imply an infinity worth of separate spatial sectors (universes) each with the same or perhaps totally dissimilar sets of physical laws. Making up an Omniverse based on the aggregate of all said systems. Wondering.
CERDES

The answer, I am told, is 'No'. But I do not understand why. Assume:

(1) The Universe is spatially flat. It will one day stop expanding.

(2) There is no weird dark energy.

These are, I think, plausible assumptions.

Then: What evidence is there to weigh against the conclusion that there is an edge to the Universe (and therefore a unique center)?

It is certainly compatible with the observed expansion, no? To use a rubber sheet example: Imagine the Universe is a standard 2D sheet of computer paper, but made of rubber. Stick coins to it to represent galaxies. Then stretch it apart to represent the expansion--fast at first, but slowing asymptotically to zero. Then we have (1) all galaxies receding from each other, (2) a unique center, but not one that would be easily (or perhaps even possibly) evident to the galaxies' inhabitants.

Thanks in advance.

 

[Valjean]

could there be an edge to the universe

Space Tiger...Keep in mind, also, that many advances in cosmology and other scientific areas, especially those considered breakthrough, were originally little more than gut feelings that let to an opinion that led to submitting for consideration and eventual acceptance. Even Einstein's views were initially disregarded until he proved right on a couple things, like light waves bending around a large mass, and then popular vote led his views to prominence and accceptance.

 

[SpaceTiger]

Space Tiger...Keep in mind, also, that many advances in cosmology and other scientific areas, especially those considered breakthrough, were originally little more than gut feelings that let to an opinion that led to submitting for consideration and eventual acceptance. Even Einstein's views were initially disregarded until he proved right on a couple things, like light waves bending around a large mass, and then popular vote led his views to prominence and accceptance.

This is not a place to be presenting personal theories. Even if it were, I still would not accept a "gut feeling" alone as justification for an argument. Einstein's ideas were a response to specific experiments that couldn't be explained in the classical framework and were presented quite rigorously. He didn't just go up to his colleagues and say, "I have a feeling that Mercury's orbit is responding to the curvature of spacetime". If an idea starts as a gut feeling, then you must hash it out logically before you can meaningfully converse with other people.

I am a scientist by trade, so I know how the process works. Discussion here is much more pedagogical, but the basic mode of discourse is the same. If what you have to say is supported by scientific research and/or general knowledge, then say it and present your support. If not, then you can either ask about it or keep it to yourself.

 

[Dr_Zinj]

There is an 'edge'

Given: This universe came into existence with the big bang.
Given: This universe expanded from a point source (actually this is a couple of givens; one, that the universe came from a point source, and two, that the universe expanded).
Given: That this universe only exists where matter and energy from the big bang exist.

Therefore: The point source could be considered the "center" of the universe.
Therefore: The edge of the universe can be considered to be the wave front of light, or matter, expanding from the big bang.

The mapping of galaxies and galactic clusters, along with their movements, is done in part, for the goal of establishing where the center of the universe is, and for finding where the 'edge' is.

Of course the universe may be expanding from all space within it as virtual particle pairs come into existence and then fail to annihilate each other.

 

[rogerperkins]

How can there be an edge if it is 4 deminisional (at least), the universe is expanding 4 deminsionally, if time is the 4th deminision then we must already be on the edge. i.e. Since the universe was smaller in the past and will be larger in the future, that means that currently we must be on the edge.

 

[Dr_Zinj]

Part of the problem is an imprecise definition of what an "edge" is. Edges are traditionally the termination of a two dimensional surface; a discontinuity between something and something (or nothing) else. The edges of a piece of paper are generally the top, bottom and sides of a paper as you view it from a point normal to the largest surface area; if you treat the paper as a two-dimensional object only. But the edge could also be the front or the back of the paper as viewed from the side, being an extreme case of viewing it three-dimensionally. This would be the same as saying the edge of the top of a box; the top being treated as a two-dimensional surface.

If we were to set it up as a calculus, as the number of sides of a fixed volume container approaches infinity, the length of the edges of each surface approach zero. So for a perfect sphere, the surface would have no edge. The edge only comes back into being as a concept if we take a 2-dimensional plane through the sphere, in which case the edge is the circle that represents the intersection of the plane with the sphere. Assuming the universe is a sphere of some sort (not necessarily true, but let's work with it); any plane through it would intersect the outer surface and the circle representing that intersection can then be referred to as an edge. If the intersection of any plane with the surface of a sphere generates an edge two-dimensionally, then we could be safe in saying that the surface of any sphere represents the edge of that sphere.

Somehow this almost sounds like a quantum theory definition. When the edges of all the sides disappear, the whole surface becomes the edge.

 

[SpaceTiger]

Given: This universe expanded from a point source

The universe did not expand from a point in three-dimensional space; rather, space itself expanded. As such, when we go back to t=0, the physical size of the universe (space included) approaches zero, but matter and energy fill space just as completely as at earlier times. The universe need not have an edge.

 

[Contrapositive]

I have a quick question: does an edgeless universe necessarily imply that the universe loops back on itself, for lack of a better word. For example, if the universe wasn't expanding and I moved forward, would I eventually circle back around to were I started? Like circumnavigating the Earth.

 

[KingOrdo]

There's been a lot of very interesting commentary on this thread, and I thank everyone for that. However, my fundamental question has not been addressed; let me put it another way that might be clearer:

Assuming Omega=1 and the Universe is spatially R^3--therefore one day reaching a maximum volume (or asymptotically approaching a maximum volume), what empirical evidence is there that the Universe is not bounded?

I certainly understand that this scenario (R^3) is compatible with an infinite universe--but it also seems compatible with a universe that has a boundary. Imagine, again, a sheet of rubber, with pennies stuck to it representing (e.g) galaxies: You stretch the paper out, fast at first, but slowing asymptotically to some maximum area. Little spaceships leaving the galaxies and going in one direction would, eventually, run into a 'brick wall' which they could not penetrate.

As far as I know, all our observations are totally compatible with this picture: But am I wrong about this? That's really what I want to know.

I understand that the assumption of isotropy means that there is no boundary. But isotropy is not empirical evidence--it is an assumption.

 

[Futobingoro]

such, when we go back to t=0, the physical size of the universe (space included) approaches zero...

Why must it?

A balloon has the same amount of rubber whether it is inflated or fully deflated.

Why must there have been less space in the initial universe than there is today?

All we hypothesize is that matter/energy was more densely distributed within space, not how much space there was.

 

[SpaceTiger]

I understand that the assumption of isotropy means that there is no boundary. But isotropy is not empirical evidence--it is an assumption.

The CMB is pretty strong evidence for isotropy, at least within the observable universe. However, the cosmological principle could break down well outside the observable universe and there would be no way for us to know.

 

[Contrapositive]

A balloon has the same amount of rubber whether it is inflated or fully deflated.

You're taking an analogy too literally. The surface area of the balloon is simply analogous to the volume of universe.

 

[SpaceTiger]

Why must it?

A balloon has the same amount of rubber whether it is inflated or fully deflated.

Why must there have been less space in the initial universe than there is today?

All we hypothesize is that matter/energy was more densely distributed within space, not how much space there was.

You're right in the sense that an infinite universe could still be infinite in extent as t -> 0 (my statement only holds true for a finite universe). I don't think this is what you mean, however. The balloon analogy is only a crude analogy and we shouldn't consider the "amount of rubber" as equivalent to the "amount of space" or the physical size of the universe. In a finite universe obeying the cosmological principle, the universe does approach zero size as t -> 0. In the analogy, the size of the universe that we measure is analogous to the distance around the surface of the balloon.

 

[KingOrdo]

The CMB is pretty strong evidence for isotropy, at least within the observable universe. However, the cosmological principle could break down well outside the observable universe and there would be no way for us to know.

Actually, the CMB is just empirical evidence in support of isotropy in the Solar System. It does not weigh in in favor of isotropy elsewhere in the observable universe. It's like a Bedouin concluding that since he sees sand in all directions, all human beings see sand in all directions. That's both (1) false, and (2) a corruption of the Copernican principle.

In the case I'm curious about (R^3), the universe is almost everywhere isotropic (everywhere but near the boundary). Therefore, it is no surprise that appears isotropic to us, and moreover the Copernican principle is upheld because we inhabit the 99.999 . . .% of the 'normal' universe.

 

[Garth]

There's been a lot of very interesting commentary on this thread, and I thank everyone for that. However, my fundamental question has not been addressed; let me put it another way that might be clearer:

Assuming Omega=1 and the Universe is spatially R^3--therefore one day reaching a maximum volume (or asymptotically approaching a maximum volume), what empirical evidence is there that the Universe is not bounded?

Point 1 - In a plain GR expanding universe, where the scale factor in the Robertson-Walker metric is determined by the GR field equation (Friedmann equation), without a Cosmological Constant or Dark Energy (DE) (with negative pressure), and if "$\Omega=1$ and the Universe is spatially R^3" then the universe will expand forever and not reach a maximum volume.

The present standard $\Lambda$CDM mainstream model has $\Omega=1$, or thereabouts and added 73% DE so it accelerates in its expansion and so it will also not reach a maximum volume.

Point 2 - By the nature of the question there can be no empirical evidence to prove that the universe is not bounded, except that as far as we can see no boundary in encountered, which is indeed the case.

I certainly understand that this scenario (R^3) is compatible with an infinite universe--but it also seems compatible with a universe that has a boundary. Imagine, again, a sheet of rubber, with pennies stuck to it representing (e.g) galaxies: You stretch the paper out, fast at first, but slowing asymptotically to some maximum area. Little spaceships leaving the galaxies and going in one direction would, eventually, run into a 'brick wall' which they could not penetrate.

Why would they "run into a 'brick wall' which they could not penetrate"? They might just go on forever...

As far as I know, all our observations are totally compatible with this picture: But am I wrong about this? That's really what I want to know.

Observations are also totally compatible with the hypothesis that there are timid fairies at the bottom of my garden that are so scared they always hide when somebody comes near, because I never see them. But that does not mean they are actually there, the simpler hypothesis is that my garden is uninhabited by fairies.

I understand that the assumption of isotropy means that there is no boundary. But isotropy is not empirical evidence--it is an assumption.

No, isotropy on the largest scales is more than an assumption, it is an observation - at these scales the sky in one part of the sky looks like the sky in any other part, as far as the CMB is concerned it is isotropic to about one part in 10⁵.

Garth

 

[SpaceTiger]

Actually, the CMB is just empirical evidence in support of isotropy in the Solar System. It does not weigh in in favor of isotropy elsewhere in the observable universe. It's like a Bedouin concluding that since he sees sand in all directions, all human beings see sand in all directions. That's both (1) false, and (2) a corruption of the Copernican principle

Note the caveat "within the observable universe". An observer a great distance away would have a different observable universe, seeing things that we could not see, even if they were within our observable universe. All we can say is that the parts of our observable universe that they can see will be isotropic.

So yes, the CMB is only evidence for homogeneity/isotropy within our observable universe, but it is near the limits of the evidence we can ever expect to have. Asking for further empirical evidence is unrealistic with what we currently know about the universe.

 

[KingOrdo]

Point 1 - In a plain GR expanding universe, where the scale factor in the Robertson-Walker metric is determined by the GR field equation (Friedmann equation), without a Cosmological Constant or Dark Energy (DE) (with negative pressure), and if "$\Omega=1$ and the Universe is spatially R^3" then the universe will expand forever and not reach a maximum volume.

So this is false: "If the universe were flat, it would also expand forever, but the expansion rate would slow to zero after an infinite amount of time."? (http://skyserver.sdss.org/dr1/en/astro/universe/universe.asp)

Why would they "run into a 'brick wall' which they could not penetrate"? They might just go on forever...

No, ex hypothesi the ants cannot go on forever (it is a truly 2D piece of paper--not a normal piece of paper).

Observations are also totally compatible with the hypothesis that there are timid fairies at the bottom of my garden that are so scared they always hide when somebody comes near, because I never see them. But that does not mean they are actually there, the simpler hypothesis is that my garden is uninhabited by fairies.

No. You are the one making the extraordinary claim here. You are positing something that we have no empirical evidence of. We have only your intuition--an intuition not shared by everyone (viz. me). That's precisely why my central question is, 'What is the empirical evidence in support of a boundaryless Universe?' The burden of proof is on you to prove such a thing. That's the entire problem with this issue: You're taking a physical issue on faith because, I suspect, it satisfies some other prejudicial notions. But these are physical decisions that should be made on empirical evidence. Einstein made a similar mistake when he added Lambda to the equations of GR. He said: 'Whoa! My equations imply the Universe had a beginning. That's too much like what those nutty religious folks say. How can I get it to be steady-state?' Einstein, unwittingly, let his physics be perverted by religion (albeit in an somewhat inverted way). And I cannot help but get the sense that all this opposition to a boundary is due to similar reasons. Remember, good physics is about ignoring religion/faith/etc. totally and looking objectively at the evidence.

No, isotropy on the largest scales is more than an assumption, it is an observation - at these scales the sky in one part of the sky looks like the sky in any other part, as far as the CMB is concerned it is isotropic to about one part in 10⁵.

No. The Universe is isotropic from the Solar System. But it is an assumption to say that measurements taken elsewhere (say, outside the Virgo Supercluster) would be the same.

 

[marcus]

...
(1) I'm talking about a standard FRW model in which Omega=1. To answer Contrapositive's question, it's vital that the Universe be flat because if, say, the geometry were S^3, then there's obviously no edge...

KingOrdo, I'm curious to know if you reject picturing space as S^3 for some reason.

You are the one who first mentioned it, in this thread and you mention the fact that it has no boundary. Since you know that shape, and it is consistent with the data, do you ever consider that as a possibility.

In case other people who don't know the background on this are following, S^3 would be favored if we got a high-confidence errorbar for Omega like [1.005, 1.015]
That is, if we could EXCLUDE the case that Omega is exactly 1.00 with high confidence.
If we could say confidently that Omega is something > 1 somewhere around 1.01, then we'd say the universe is spatially nearly flat and might look like a slightly banged-up S^3.

roughly spherical but locally dented and bumpy by local above and below average concentrations of matter-----spherical on average.

with such a large radius of curvature that it looks almost flat (the way the surface of the Earth does, only moreso)

I see errorbars approximately like that with 65 percent confidence, from time to time, but that is not enough. We would need them to be 95 percent or better, in order to start talking. But I think it MIGHT be and it looks like an interesting possibility.

So do you take account of that, KingOrdo? Or do you exclude that one for some reason?

 

[SpaceTiger]

No. You are the one making the extraordinary claim here. You are positing something that we have no empirical evidence of. We have only your intuition--an intuition not shared by everyone (viz. me). That's precisely why my central question is, 'What is the empirical evidence in support of a boundaryless Universe?'

This is why many observational cosmologists prefer to just use "universe" to describe the observable universe. We can't know for sure what lies beyond it. One of the main reasons that there is a prejudice towards the applicability of the cosmological principle on the largest scales (aside from Occam's Razor) is inflationary theory. This "early universe" theory posits that an early exponential expansion of space causally disconnected our observable universe from other regions of space and that the "real" universe is actually much, much larger than what we can see. If this theory is correct, then the exponential expansion would have naturally "smoothed" things out and the larger universe would obey the cosmological principle as well. Although this theory naturally solves the flatness, horizon, and monopole problems, subsequent evidence for it has been hard to come by. So far, the best evidence is in the spectrum of cosmological perturbations, which appears to be well described by a gaussian random field and has a power law slope consistent with the expectations of inflation.

 

[Garth]

So this is false: "If the universe were flat, it would also expand forever, but the expansion rate would slow to zero after an infinite amount of time."? (http://skyserver.sdss.org/dr1/en/astro/universe/universe.asp)

That statement is completely true, what is false is your statement "one day reaching a maximum volume (or asymptotically approaching a maximum volume)".

If the universe's expansion rate slows to zero after an infinite amount of time its maximum volume is infinite.

No, ex hypothesi the ants cannot go on forever (it is a truly 2D piece of paper--not a normal piece of paper).

But the sheet of paper, as a 2D representation of the 3D space, is infinite in your example - see my last comment.

No. You are the one making the extraordinary claim here. You are positing something that we have no empirical evidence of. We have only your intuition--an intuition not shared by everyone (viz. me). That's precisely why my central question is, 'What is the empirical evidence in support of a boundaryless Universe?' The burden of proof is on you to prove such a thing. That's the entire problem with this issue: You're taking a physical issue on faith because, I suspect, it satisfies some other prejudicial notions. But these are physical decisions that should be made on empirical evidence.

What evidence do you look for, a 'brick wall at the end of the universe? It is that that I find extraordinary - that is why I used a ridiculous example - to make a point.

It is possible that the galaxies etc. could just peter out at a certain distance from us, but there is no evidence of such a thing.

Now absence of evidence is not evidence of absence - but it does mean the thing proposed has no evidence (yet) on which to build our hypothesis.

Einstein made a similar mistake when he added Lambda to the equations of GR. He said: 'Whoa! My equations imply the Universe had a beginning. That's too much like what those nutty religious folks say. How can I get it to be steady-state?' Einstein, unwittingly, let his physics be perverted by religion (albeit in an somewhat inverted way). And I cannot help but get the sense that all this opposition to a boundary is due to similar reasons. Remember, good physics is about ignoring religion/faith/etc. totally and looking objectively at the evidence.

Agreed - religion has nothing to do with it, good science is about sticking to testable and falsifiable theory and evidence - what evidence do you have for the hypothesis of a boundary?

No. The Universe is isotropic from the Solar System. But it is an assumption to say that measurements taken elsewhere (say, outside the Virgo Supercluster) would be the same.

I never said anything about measurements/observations made elsewhere - all we have to build our theory on are the observations we make from our own little solar system.

We can make all kinds of speculations about what we might see if we were at the far side of the universe, but until we can go there that is all they would be - speculations.

Garth

 

[KingOrdo]

KingOrdo, I'm curious to know if you reject picturing space as S^3 for some reason.

You are the one who first mentioned it, in this thread and you mention the fact that it has no boundary. Since you know that shape, and it is consistent with the data, do you ever consider that as a possibility.

In case other people who don't know the background on this are following, S^3 would be favored if we got a high-confidence errorbar for Omega like [1.005, 1.015]
That is, if we could EXCLUDE the case that Omega is exactly 1.00 with high confidence.
If we could say confidently that Omega is something > 1 somewhere around 1.01, then we'd say the universe is spatially nearly flat and might look like a slightly banged-up S^3.

roughly spherical but locally dented and bumpy by local above and below average concentrations of matter-----spherical on average.

with such a large radius of curvature that it looks almost flat (the way the surface of the Earth does, only moreso)

I see errorbars approximately like that with 65 percent confidence, from time to time, but that is not enough. We would need them to be 95 percent or better, in order to start talking. But I think it MIGHT be and it looks like an interesting possibility.

So do you take account of that, KingOrdo? Or do you exclude that one for some reason?

Oh, I certainly accept that as a possibility. Like you said, if the evidence comes in for Omega > 1, then that's it: the Universe is S^3, no boundary, it makes perfect sense to me why, etc. Nice, elegant, and all tied up.

I will say that I think the fact that Omega appears to be so darned close to 1 might give some extra support to Omega=1. I mean, of all the possible values of Omega, it's right near the critical value? There might be some anthropic reasoning there, though, that I haven't taken account of; I haven't thought too much about that.

But again: If we got an errorbar like the one you mentioned, S^3 and no boundary it is.

-----

That statement is completely true, what is false is your statement "one day reaching a maximum volume (or asymptotically approaching a maximum volume)".

If the universe's expansion rate slows to zero after an infinite amount of time its maximum volume is infinite.

Okey, something’s not making sense to me. Why does (1) the Universe’s expansion rate slowing to zero after an infinite amount of time not imply (2) the Universe will asymptotically approach a maximum volume?

But the sheet of paper, as a 2D representation of the 3D space, is infinite in your example - see my last comment.

Again, no: in my example, it really is a 2D world. It is not an embedding. A 2D ant will reach a boundary which it cannot cross.

Agreed - religion has nothing to do with it, good science is about sticking to testable and falsifiable theory and evidence - what evidence do you have for the hypothesis of a boundary?

The principle of parsimony--Occam's razor. Since apparently there is no empirical evidence against the existence of a boundary, and no empirical evidence in favor of infinite space (instead, only talk of 'best fit', conceptual clarity, etc.), I will judge a theory based on its simplicity. I have never encountered the infinite except in the abstract (in mathematics). Everything I have ever encountered is finite. Everything else in physics is finite—masses, velocities, stars, galaxies, clusters, superclusters, black holes, supernovae, etc. Why should the Universe be any different? Unless there’s evidence to say it is, you’ve still got work to do--or so it seems to me.

 

[Futobingoro]

You're taking an analogy too literally. The surface area of the balloon is simply analogous to the volume of universe.

The thing I have a problem with is that the surface area expands only from the perspective of somebody watching the balloon inflate. One would need to leave our universe to gain that same perspective (which brings its own challenges and uncertainties assuming it is even possible or meaningful).

You must realize that the balloon is an analogy to the very fabric of our universe. Stretching, squeezing or deforming the balloon neither adds to nor subtracts from the amount of fabric in the balloon. This is important because an expanding universe needs an addition of fabric. The balloon model is therefore insufficient in visualizing a mechanism by which expansion takes place.

 

[andrewj]

The answer, I am told, is 'No'. But I do not understand why. Assume:

(1) The Universe is spatially flat. It will one day stop expanding.

(2) There is no weird dark energy.

These are, I think, plausible assumptions.

Then: What evidence is there to weigh against the conclusion that there is an edge to the Universe (and therefore a unique center)?

It is certainly compatible with the observed expansion, no? To use a rubber sheet example: Imagine the Universe is a standard 2D sheet of computer paper, but made of rubber. Stick coins to it to represent galaxies. Then stretch it apart to represent the expansion--fast at first, but slowing asymptotically to zero. Then we have (1) all galaxies receding from each other, (2) a unique center, but not one that would be easily (or perhaps even possibly) evident to the galaxies' inhabitants.

Thanks in advance.

do you assume that you could pass the edge of space as the universe is not only expanding but being created

 

[Contrapositive]

do you assume that you could pass the edge of space as the universe is not only expanding but being created

What do mean by 'being created'? The universe? Space?

 

[SpaceTiger]

The thing I have a problem with is that the surface area expands only from the perspective of somebody watching the balloon inflate. One would need to leave our universe to gain that same perspective (which brings its own challenges and uncertainties assuming it is even possible or meaningful).

As the balloon inflates, wouldn't an ant on its surface find that it took longer to get from point to the next as time went on? Similarly, would an immortal observer in our universe not find that it takes longer for light to reach them from a distant galaxy as the universe expands?

The "amount of rubber" between two objects on the balloon's surface is somewhat analogous to a comoving distance, but not to a physical one. As was already explained to you, we have "rulers" that allow us to place a scale on the expansion of the universe without having to leave the universe.

 

[Contrapositive]

The thing I have a problem with is that the surface area expands only from the perspective of somebody watching the balloon inflate. One would need to leave our universe to gain that same perspective (which brings its own challenges and uncertainties assuming it is even possible or meaningful).

Imagine two ants on the surface of a balloon. As it expands, the two ants see each other move away from each other. So you can be on the balloon (i.e. inside the universe) and see it expand.

You must realize that the balloon is an analogy to the very fabric of our universe. Stretching, squeezing or deforming the balloon neither adds to nor subtracts from the amount of fabric in the balloon. This is important because an expanding universe needs an addition of fabric. The balloon model is therefore insufficient in visualizing a mechanism by which expansion takes place.

Who said the rubber in the balloon exactly represents the fabric of space-time? You're taking an analogy too literally.

 

[Garth]

Okey, something’s not making sense to me. Why does (1) the Universe’s expansion rate slowing to zero after an infinite amount of time not imply (2) the Universe will asymptotically approach a maximum volume?

The expansion of the universe, without the influence of DE that makes the expansion accelerate, can be compared to a projectile leaving Earth at near escape velocity.

If it is launched at just below escape velocity it will eventually fall back to Earth and there will be a maximum altitude that it will reach.

If launched at above escape velocity it will carry on into 'outer space' to infinity always at some positive velocity.

If launched at exactly escape velocity it will be "slowing to zero after an infinite amount of time", yet it will still reach an infinite altitude but asymptotically approaching zero velocity as it does so.

That is it will reach 'inifinity' and take an 'infinite' amount of time to do so!

The really significant point is that its velocity will only approach zero at 'infinity', i.e. it will never actually do so, it will go on and on to infinity at slower and slower velocity but never reach zero velocity wrt the Earth.

The principle of parsimony--Occam's razor. Since apparently there is no empirical evidence against the existence of a boundary, and no empirical evidence in favor of infinite space (instead, only talk of 'best fit', conceptual clarity, etc.), I will judge a theory based on its simplicity. I have never encountered the infinite except in the abstract (in mathematics). Everything I have ever encountered is finite. Everything else in physics is finite—masses, velocities, stars, galaxies, clusters, superclusters, black holes, supernovae, etc. Why should the Universe be any different? Unless there’s evidence to say it is, you’ve still got work to do--or so it seems to me.

I also hold Occam's Razor in high regard, read my signature (the first one), and see my avatar.

I repeat my question, "What (observational) evidence do you have for the hypothesis of the existence of a boundary?"

Garth

 

[KingOrdo]

The expansion of the universe, without the influence of DE that makes the expansion accelerate, can be compared to a projectile leaving Earth at near escape velocity.

If it is launched at just below escape velocity it will eventually fall back to Earth and there will be a maximum altitude that it will reach.

If launched at above escape velocity it will carry on into 'outer space' to infinity always at some positive velocity.

If launched at exactly escape velocity it will be "slowing to zero after an infinite amount of time", yet it will still reach an infinite altitude but asymptotically approaching zero velocity as it does so.

That is it will reach 'inifinity' and take an 'infinite' amount of time to do so!

The really significant point is that its velocity will only approach zero at 'infinity', i.e. it will never actually do so, it will go on and on to infinity at slower and slower velocity but never reach zero velocity wrt the Earth.I also hold Occam's Razor in high regard, read my signature (the first one), and see my avatar.

I'm sorry; I'm still not getting it. I don't dispute that what you're saying is right; it's just not clicking for me. It seems to me that if something is getting slower and slower, and we know the numbers involved, we can calculate a maximum distance. Could you perhaps give a more mathematically rigorous example of this sort of motion?

Also, a related question: Even if in cases when Omega=1 the Universe has no maximum volume, is there any value for Omega for which the Universe will (1) stop expanding (like in Omega=1), and (2) have a finite maximum volume? Thanks.

I repeat my question, "What (observational) evidence do you have for the hypothesis of the existence of a boundary?"

And I repeat my answer: The impetus is on you, not me, to prove your theory. We encounter bounded physical things all the time: stars, black holes, masses, velocities, etc. We never encounter physically boundless things. Matter can only be divided so far. Things can only go so fast. And so on. Yet you claim that the Universe goes on forever. Fine: you might be right. But you need to adduce empirical evidence for such a view.

At worst, we might say that since both the bounded case and unbounded case have no empirical evidence weighing one way or the other (which apparently is true in practice, and what I've been wondering throughout the thread), we need to choose one model on other grounds (e.g. Occam's razor). My intuition, as discussed here and elsewhere, is that the bounded model is simpler, more common sensical, and less 'faith based'.

 

[SpaceTiger]

At worst, we might say that since both the bounded case and unbounded case have no empirical evidence weighing one way or the other (which apparently is true in practice, and what I've been wondering throughout the thread), we need to choose one model on other grounds (e.g. Occam's razor). My intuition, as discussed here and elsewhere, is that the bounded model is simpler, more common sensical, and less 'faith based'.

There's a whole community of trained scientists who disagree with your view. Adding a boundary adds at least one free parameter to our model of the universe. Furthermore, there is no plausible physical origin for such a boundary, while a universe obeying the cosmological principle arises naturally in many early universe theories.

You don't have to accept that the universe obeys the cosmological principle on scales beyond what we can see to accept the mainstream cosmological model, but I think the issue of which is "simpler" boils down to the number of free parameters needed in the model. In this regard, we are always drawn to the cosmological principle.