Recognitions:
Gold Member

## Could there be an edge to the Universe?

 Quote by KingOrdo 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

 Quote by Garth 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.

 Quote by Garth 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'.

Recognitions:
Gold Member
Staff Emeritus
 Quote by KingOrdo 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.

 Quote by SpaceTiger There's a whole community of trained scientists who disagree with your view.
I have never found appeals to consensus very persuasive. If there is empirical evidence, I would like to hear it.

 Quote by SpaceTiger 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.
Well, there's no plausible physical origin for an infinite Universe, either. Those aren't physical questions. And indeed, the cosmological principle is not an empirical one--it's a faith-based leap that in my view is on very shaky ground (compare it to the well-founded Copernican principle). The clever Bedouin who believes that all human beings are surrounded by desert because he is is wrong. What I've been asking is: Is there any empirical evidence against a bounded Universe? N.B. even if not, that doesn't mean the Universe is bounded. But since there is no empirical evidence that the Universe is unbounded, we have to decide the matter on non-empirical grounds: Occam's razor, for example. And my intution seem to differ from others'.

Recognitions:
Gold Member
Staff Emeritus
 Quote by KingOrdo I have never found appeals to consensus very persuasive. If there is empirical evidence, I would like to hear it.
I do not find appeals to popular opinion very convincing, but when faced with the opinion of an untrained layman and a community of scientists, I am more convinced. The trouble is that your intuition is not developed for the problem you're attempting to tackle, while a cosmologist's is. I've already cited some empirical evidence for inflation (the truth of which would also suggest the applicability of the cosmological principle) yet you haven't responded.

 Well, there's no plausible physical origin for an infinite Universe, either.
The arguments that we're making do not necessarily suggest an infinite universe. You are aware that a finite universe can exist that does not have a boundary?

 Those aren't physical questions. And indeed, the cosmological principle is not an empirical one--it's a faith-based leap that in my view is on very shaky ground (compare it to the well-founded Copernican principle).
The Copernican principle is more abstract than the cosmological principle and the two aren't really comparable. The cosmological principle is very straightforward -- it posits large-scale homogeneity and isotropy. In contrast, the Copernican principle states rather vaguely that we are not "special" and that theories which suggest that we are should be treated with suspicion. I certainly agree with this statement, but think it's much less clearly defined.

Furthermore, the cosmological principle can be tested empirically within our observable universe. Beyond this, we can't test any theory -- for all we know gravity and electromagnetism are completely different outside of our observable universe. Does this mean that the law of gravity cannot be tested empirically?

 But since there is no empirical evidence that the Universe is unbounded, that means we have to decide the matter on non-empirical grounds: Occam's razor, for example. And my intution seem to differ from others'.
Occam's Razor can be formulated more rigorously as the statistical maximization of entropy. When we introduce a boundary, we need to specify its location and extent, free parameters that act to decrease the entropy of the theory. A universe that obeys the cosmological principle is simpler in this regard. Any other use of the word "simple" would be irrelevant to the discussion.

It's not clear to me that you understand the problem fully enough to be reaching such sweeping conclusions. If you're confused about something, please ask. This forum is primarily designed to have experts answer the questions of non-experts, not for the formulation of personal theories. Please be careful that this does not turn into one.

Recognitions:
Gold Member
 Quote by KingOrdo 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. ...
thanks for your reply, KingOrdo. my thoughts on this are similar. it's an important issue what the current best Omega errorbar is, so I try to stay posted.
Personally the most authoritative and recent source I know is March 2006
http://arxiv.org/abs/astro-ph/0603449

Everybody cites it----it's the official implications for cosmology part of a multipaper series reporting the 3rd year data from the WMAP satellite.
If you look on page 50, caption to figure 17, you see a 68 percent errorbar for Omega which is [1.010, 1.041]
The errorbar is based on combined data from four major projects: WMAP CMB, supernova, the Sloan digital sky survey, and the 2-degree-field galaxy redshift survey.
As of 2006 that was about as good as it gets, and I haven't seen anything since then that is more highly cited.

To me that 1.01 is not SURPRISINGLY close to one. Reasons have been offered why, if the universe is spatially S^3, one would nevertheless expect it to be very expanded and so have a small curvature----to be near flat in other words.
The errorbar being close to one is not especially remarkable. What is remarkable IMO is that it does not contain one---it is all on the upside.

So what [1.010, 1.041] says to me personally is that they already HAVE an errorbar that says S^3, they just don't have enough confidence on it. 68 percent is not enough to disfavor the infinite R^3 case. So I could conclude something if I saw a similar errorbar like [1.010, 1.041] and it had 95 percent confidence.

There are technical issues about how you interpret. Like this particular figure assumes dark energy had constant pressure/volume ratio, but they let the constant ratio take on various values. And people can argue should they have allowed time-varying dark energy, or maybe should they have forced the ratio to always be exactly one etc etc. But the technical details don't change the overall sense I get that nowadays the Omega errorbar tends to be mostly over to the > 1 side-----saying "nearly but not exactly" flat. And that the confidence is not high enough to reject the flat case, so one says it is still "consistent with the data" (i.e. flat is not ruled out.)

Recognitions:
 Quote by KingOrdo But since there is no empirical evidence that the Universe is unbounded, we have to decide the matter on non-empirical grounds: Occam's razor, for example. And my intution seem to differ from others'.
Occam's Razor is an often misused concept. As Space Tiger (and others I think) have pointed out several times, adding an edge when one is not observed is adding more parameters and hence complexity to the model. Hence it's an open and shut case that assuming, via the mathematical model for the Universe, that it is infinite is the simpler option clearly favoured by Occam's razor. Less parameters = simpler model, and that is a purely objective way of evaluating model simplicity, without having to get a straw poll of people's intuition.

The point is that if our model describes an infinite Universe, whereas in fact we are in a Universe that is very very big (much bigger than the observable Universe) then the model works perfectly well. If in the future we discovered the Universe was in fact finite, but much much bigger than the observable Universe we would for most cases simply use the infinite model, since the difference between the two is vanishingly small and the calculations are easier in the infinite model. We do things like this all the time, for instance we think General Relativity is the true theory or gravity, however we usually use Newtonian gravity for most things since the Newtonian model is simpler and easier to work with and the two models give the same answer for most questions we have.

This is how science works, we seek to find models that match what we observe, described in the simplest way possible, rather than making metaphysical statements about the extent of reality. If the infinite model works we'll use it, it doesn't matter if whether or not the Universe is truly infinite, that's not the point of the assumption or the model.

Recognitions:
Gold Member
 Quote by KingOrdo 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?
If $\Omega = 1$ and with no Dark Energy (DE) or other forms of pressure or cosmological constant then we have the Einstein de Sitter model in which the scale factor

$$a(t) = a(t_0)(\frac{t}{t_0})^{\frac{2}{3}}$$

and so as $t \rightarrow \infty$ so $a(t) \rightarrow \infty$.
 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.
Yes, In the absence of DE or the cosmological constant the universe will have a maximum volume if
$\Omega$ > 1.

However, with the present understanding of DE the universe will continue to expand, and accelerate in its expansion, even if $\Omega$ > 1.
 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.
I do not claim the universe goes on forever, it could be finite yet unbounded, the standard theory describes a homogeneous and isotropic universe, in this case if $\Omega \leq 1$ the universe will be infinite and unbounded.

What type of boundary are you thinking of anyway?

Garth

 Quote by SpaceTiger I do not find appeals to popular opinion very convincing, but when faced with the opinion of an untrained layman and a community of scientists, I am more convinced. The trouble is that your intuition is not developed for the problem you're attempting to tackle, while a cosmologist's is.
I think you've got things backwards. Sometimes that "untrained layman"--whom, do not forget, may be far smarter than you--has a more veridical intuition because he is approaching things fresh. A good example would be Einstein in 1905. How did that "untrained layman" catch something so obvious, beautiful, and simple (viz. Special Relativity) that the initiated missed? Do not mistake dogmatism for erudition.

 Quote by SpaceTiger I've already cited some empirical evidence for inflation (the truth of which would also suggest the applicability of the cosmological principle) yet you haven't responded.
Assume inflation is true. Then the observable Universe is causally disconnected from other parts of the Universe. That does not weigh in on whether the Universe does or does not have a boundary.

 Quote by SpaceTiger The arguments that we're making do not necessarily suggest an infinite universe. You are aware that a finite universe can exist that does not have a boundary?
You have obviously not read my posts. How many have I devoted to S^3 geometries?

 Quote by SpaceTiger Furthermore, the cosmological principle can be tested empirically within our observable universe. Beyond this, we can't test any theory -- for all we know gravity and electromagnetism are completely different outside of our observable universe. Does this mean that the law of gravity cannot be tested empirically?
You're missing the point. You can test gravity all the time. That's why it's a valid scientific theory. But it would be wrong to drop a ball at one point on the Earth and then claim that, due to that single measurement, gravity holds everywhere on the Earth. You have to test it and test it and test it--under different conditions, in different places, and so on. In addition, gravity fits in a relation of coherence with our other scientific theories (e.g. the Standard Model).

 Quote by SpaceTiger It's not clear to me that you understand the problem fully enough to be reaching such sweeping conclusions. If you're confused about something, please ask. This forum is primarily designed to have experts answer the questions of non-experts, not for the formulation of personal theories. Please be careful that this does not turn into one.
You should take due care not to insult. I have been polite and honest throughout the thread; I expect the same from you. I have asked questions, and solicited answers. Remember that some of us are smarter than you, and some of us are more important than you. Perhaps not me; but some of us. Be nice.

 Quote by Garth Yes, In the absence of DE or the cosmological constant the universe will have a maximum volume if $\Omega$ > 1.
I should have been more specific: Are there any cases where the Universe will have a maximum volume and not recollapse? That is, reach a maximum size and just stop? If so, what would Omega have to be?

 Quote by Garth What type of boundary are you thinking of anyway?
No bloody idea. When I think about it I just imagine stopping. You're in the vacuum, everything is black, and you can't go any farther. Put as much energy into it as you like and you can't penetrate. But maybe I'm wrong and it's the Pearly Gates (I'm an atheist)!

Recognitions:
Gold Member
Staff Emeritus
 Quote by KingOrdo I think you've got things backwards. Sometimes that "untrained layman"--whom, do not forget, may be far smarter than you--has a more veridical intuition because he is approaching things fresh. A good example would be Einstein in 1905. How did that "untrained layman" catch something so obvious, beautiful, and simple (viz. Special Relativity) that the initiated missed? Do not mistake dogmatism for erudition.
Ugh, not this again. Einstein was a trained physicist, not a layman. It does not matter how intelligent you are or think you are, if you don't know enough about the problem you're trying to solve, you won't solve it.

 Assume inflation is true. Then the observable Universe is causally disconnected from other parts of the Universe. That does not weigh in on whether the Universe does or does not have a boundary.
It does, in fact. I suggest you do some reading on eternal inflation, the most favored form of it right now.

 You have obviously not read my posts. How many have I devoted to S^3 geometries?
And yet you don't understand how they're distinct from a flat, matter-dominated universe that is infinite in extent?

 You're missing the point. You can test gravity all the time. That's why it's a valid scientific theory. But it would be wrong to drop a ball at one point on the Earth and then claim that, due to that single measurement, gravity holds everywhere on the Earth. You have to test it and test it and test it--under different conditions, in different places, and so on. In addition, gravity fits in a relation of coherence with our other scientific theories (e.g. the Standard Model).
Every independent patch of space that we observe is a test of the cosmological principle -- it is not wrapped up in "one point" as you put it. Observing the universe from the Virgo cluster would only increase the data a very small fraction, since only a small portion of the "outside" universe would be revealed.

 You should take due care not to insult. I have been polite and honest throughout the thread; I expect the same from you. I have asked questions, and solicited answers. Remember that some of us are smarter than you, and some of us are more important than you. Perhaps not me; but some of us. Be nice.
I'm surprised that you think that you have been polite to the people responding to you, but the last paragraph in my post was not meant as an insult, but as a warning. Unless you are claiming that you actually are an expert on cosmology, you should not be selling you ideas or "intuition" as fact. The debate over Occam's Razor is a good example of what I'm talking about.

 Quote by SpaceTiger Ugh, not this again. Einstein was a trained physicist, not a layman. It does not matter how intelligent you are or think you are, if you don't know enough about the problem you're trying to solve, you won't solve it.
I'm not trying to solve a problem. I'm asking questions. When someone tells me 'B', I ask why and they say, 'Because either A or B', I'm going to wonder what's up.

 Quote by SpaceTiger It does, in fact. I suggest you do some reading on eternal inflation, the most favored form of it right now.
If I could find the answer to this question, I wouldn't be asking it in this forum. Again: If there is empirical evidence (i.e. not magic), please tell me what it is.

 Quote by SpaceTiger And yet you don't understand how they're distinct from a flat, matter-dominated universe that is infinite in extent?

 Quote by SpaceTiger Every independent patch of space that we observe is a test of the cosmological principle -- it is not wrapped up in "one point" as you put it. Observing the universe from the Virgo cluster would only increase the data a very small fraction, since only a small portion of the "outside" universe would be revealed.
Right. This is induction.

 Quote by SpaceTiger I'm surprised that you think that you have been polite to the people responding to you, but the last paragraph in my post was not meant as an insult, but as a warning. Unless you are claiming that you actually are an expert on cosmology, you should not be selling you ideas or "intuition" as fact. The debate over Occam's Razor is a good example of what I'm talking about.
I don't understand what your problem is, but I've certainly been polite to everyone--even you. And I'm not "selling" anything. I'm asking questions. You obviously don't want to answer them. Fine--go somewhere else. (Cf. Garth's posts if you need an example of how to be helpful.)

Mentor
 Quote by SpaceTiger I suggest you do some reading on eternal inflation, the most favored form of it right now.
What exactly is eternal inflation, SpaceTiger? (or anyone else who's reading!) My gut instinct says it must have to do with a scenario in which inflation continues forever in some regions. Is this something to do with the way in which the inflaton decays at the end of inflation; i.e. the way in which the inflaton decays into radiation is a quantum mechanical process, and so all regions will not have inflation ending at the same time. I guess this implies that in some regions inflation will never end? This latter point is getting towards how structure formation is explained, isn't it?

Any review papers you can suggest will be appreciated!
 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.[/QUOTE] AMEN to that!

Recognitions:
Gold Member
Staff Emeritus
 Quote by KingOrdo If I could find the answer to this question, I wouldn't be asking it in this forum. Again: If there is empirical evidence (i.e. not magic), please tell me what it is.
I already gave you some empirical evidence for inflation. If you need clarification, please ask, don't ignore it.

 I don't understand what your problem is, but I've certainly been polite to everyone--even you. And I'm not "selling" anything. I'm asking questions.
You certainly have asked questions, but after having them answered, you've quickly formed a position against the person responding to your question. If your intentions really are to learn, then I have no quarrel with you, but your responses suggest to me that you consider your ideas to be not only contrary to mainstream science, but more reliable than the mainstream because you're thinking outside the box. Perhaps you can see why this might ring warning bells for a moderator of an internet forum.

 What exactly is eternal inflation, SpaceTiger? ... Any review papers you can suggest will be appreciated!
Certainly, here's a review by Guth himself:

Inflation and Eternal Inflation
 But The universe has at least 4 dimensions by the most conservative estimate and 11 or 12 dimensions as the normally accepted Number. S or R =3?

 Quote by SpaceTiger I already gave you some empirical evidence for inflation. If you need clarification, please ask, don't ignore it.
I responded to that remark. You have failed to explain yourself--you essentially said, 'No, you're wrong'. And that is not an argument.

 Quote by SpaceTiger You certainly have asked questions, but after having them answered, you've quickly formed a position against the person responding to your question. If your intentions really are to learn, then I have no quarrel with you, but your responses suggest to me that you consider your ideas to be not only contrary to mainstream science, but more reliable than the mainstream because you're thinking outside the box. Perhaps you can see why this might ring warning bells for a moderator of an internet forum.
I've had lots of questions answered; none by you. I must say, I don't understand why you've involved yourself in this discussion in the first place, and why you persist in causing trouble. The rest of us are having a nice conversation. If you need examples of how to rigorously respond to inquiries, I recommend looking at the posts of (e.g.) Garth, Wallace, and marcus.

Also, I am not presenting a theory here. This you must understand. I am asking about the justificatory basis of your theory (viz. the infinite Universe). If you have a sound argument, you should be able to present it without difficulty. I'm simply asking for clarification and pointing out lacunae if I see them.

It is sometimes good to have a logician looking over your back, don't you think?