Could there be an edge to the Universe?

[KingOrdo]

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.

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'.

 

[SpaceTiger]

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.

 

[marcus]

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.)

 

[Wallace]

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.

 

[Garth]

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

 

[KingOrdo]

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.

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.

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?

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).

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.

 

[KingOrdo]

Thanks, Garth--this is really helpful.

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?

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)!

 

[SpaceTiger]

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.

 

[KingOrdo]

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.

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.

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

I do. Read the thread.

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.

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.)

 

[cristo]

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!

 

[Dozent100]

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!

 

[SpaceTiger]

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:

http://xxx.lanl.gov/abs/astro-ph/0002156"

 

[Dozent100]

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?

 

[KingOrdo]

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.

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?

 

[SpaceTiger]

I responded to that remark. You have failed to explain yourself--you essentially said, 'No, you're wrong'. And that is not an argument.

Please see my posts for cited evidence for inflation:

https://www.physicsforums.com/showpost.php?p=1536453&postcount=61"

If you need me to expand or clarify anything, please say so rather than pretending it was never posted. It took several nearly identical explanations of Occam's Razor before you stopped trying to use it in your arguments.

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.

I'm glad you found their posts useful, they are among the more helpful and knowledgeable members here and there is much to be learned from them. Certainly many of my posts were addressing the tone of the discussion, as it is my responsibility to moderate these forums as well as to contribute to them. If you're not finding my posts helpful, then perhaps I'm not communicating myself well, and If you have more questions, I can assure you that I will address them as directly as I can.

 

[Dozent100]

I already gave you some empirical evidence for inflation. If you need clarification, please ask, don't ignore it.
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.

Certainly, here's a review by Guth himself:

http://xxx.lanl.gov/abs/astro-ph/0002156"

--------------------------------------------------------------------------------------
I got to go with Space Tiger on this one. I think your questions have been adequately answered several times over. Some very smart people, myself not included, have looked at your problem from several different angles. Cosmology is a not a hard science. There are not a lot of hard facts around to base assumptions on. And we can talk till the cows come home, but if you reject all explanations offered, what are we accomplishing?

My experience is more on the nuclear Engineering side, but I try to keep up with what is going on. I will caution you that There is a lot of Pseudo Science running around and I wonder if this where you are coming from. Psudo-Science attempts to make the science fit the desired outcome, rather than the other way around. And where the facts don't support the theory, the facts are ignored.
There has been a lot of that going around since the Clinton Years.



s

 

[KingOrdo]

Please see my posts for cited evidence for inflation:

https://www.physicsforums.com/showpost.php?p=1536453&postcount=61"

If you need me to expand or clarify anything, please say so rather than pretending it was never posted. It took several nearly identical explanations of Occam's Razor before you stopped trying to use it in your arguments.

I can't make things any clearer to you on this matter. Regarding Occam's Razor: You apparently still don't understand it. It's not: The simplest theory is the best. It is: Do not multiply entities without need. There is a subtle, but important, difference there. You are the one making a positive claim; the burden of proof is on you, not me. You believe that X? Great: adduce some evidence in support.

I got to go with Space Tiger on this one. I think your questions have been adequately answered several times over. Some very smart people, myself not included, have looked at your problem from several different angles. Cosmology is a not a hard science. There are not a lot of hard facts around to base assumptions on. And we can talk till the cows come home, but if you reject all explanations offered, what are we accomplishing?

I'm not interested in your pet theories, conjecture, poetic impressions, etc. I'm interested in evidence. I'm interested in someone saying: 'Hi, KingOrdo: We know that the Universe is infinite because satellite A measured b. We already know because of law Y that b if and only if c. But if c then d. Therefore d.'

My experience is more on the nuclear Engineering side, but I try to keep up with what is going on. I will caution you that There is a lot of Pseudo Science running around and I wonder if this where you are coming from. Psudo-Science attempts to make the science fit the desired outcome, rather than the other way around. And where the facts don't support the theory, the facts are ignored.

Are you talking about pseudo-science in the Popperian sense? It's not clear to me what you're saying here. I am asking questions about the structure of the Universe.

There has been a lot of that going around since the Clinton Years.

I don't know what you're saying here. I don't see what politics, or my liberalism, has to do with anything.

 

[Wallace]

I'm not interested in your pet theories, conjecture, poetic impressions, etc. I'm interested in evidence. I'm interested in someone saying: 'Hi, KingOrdo: We know that the Universe is infinite because satellite A measured b. We already know because of law Y that b if and only if c. But if c then d. Therefore d.'

I think we are getting somewhat off track in this discussion! No one is suggesting that we can conclusively prove the Universe is infinite but I'm curious to know why you think 'the burden of proof' rests on the 'case for infinite' side of the argument? It could equally be argued that if one was to suggest the Universe is finite, then evidence for this must be presented.

However, neither of the above arguments I just made are reasonable. Clearly we do not have conclusive evidence either way. What we do know is that we have not reason to doubt that the cosmological principle applies for the extent of our observable universe, for this we do have hard evidence such as the isotropy of the CMB (the anisotropies are of course of great interest, but are very small in agreement with the cosmological principle), and the general isotropy of galaxies and QSO's seen in large redshift surveys.

Given this data then, we can see that if the Universe is finite, it is clearly at least much bigger than the observable Universe, and for all intents and purposes is infinite. Assuming the Universe is infinite makes the equations easier to deal with, since there are less parameters.

I'm not sure how to discussion got to the point of demanding conclusive evidence for the infinite nature of the Universe? Surely this is impossible! We can only ever say that was haven't observed something, we can never have proof that is doesn't exist. To make a whimsical example, it is not reasonable to demand that someone who says that talking monkeys with tea-pots for hands do not exist provide evidence for their non-existence. All you can do is point to the evidence that we have not observed such things, and it makes evolution a simpler model if it does not have to explain why monkeys should have evolved tea-pots in place of their hands. To further the silly analogy, we could make theoretical predictions about the problems monkeys would face with tea-pot hands, just as we can make predictions about the problems an edge to the Universe would introduce. In both cases our theories may suggest the non-existence of something but to prove with evidence the non-existence is clearly impossible.

Theories are constructed based upon what is observed, and are made to be as simple as possible given those observations. This is why we assume the Universe is infinite, in full knowledge that this is not absolutely neccessarily the case.

 

[pervect]

Regardless of whether or not there is an edge to the universe, there is a definite edge to this thread. A rather unpleasant one.

So, let's all try to be nice to one another, and get the thread back on track (as Wallace ha noted, it's started to drift).

Otherwise, I'm going to get grumpy and start doing grumpy things...

One thing that pushes my buttons is Ordo's idea that SpaceTiger should have unlimited amounts of time to answer his (Ordo's) questions. In an ideal world, this would be nice, but people have to be able to live with the fact that moderators and mentors may actually have other things in their life other than PF, hard as it may be to believe...

 

[cristo]

Certainly, here's a review by Guth himself:

http://xxx.lanl.gov/abs/astro-ph/0002156"

Thanks

 

[KingOrdo]

I think we are getting somewhat off track in this discussion! No one is suggesting that we can conclusively prove the Universe is infinite but I'm curious to know why you think 'the burden of proof' rests on the 'case for infinite' side of the argument?

Because that's a positive claim: 'The Universe is infinite.' Okey, fine: Maybe you're right. Why is that so? What empirical evidence do you have in support?

It could equally be argued that if one was to suggest the Universe is finite, then evidence for this must be presented.

Indeed. And in a previous post I made precisely this point. If I were prepared to make a rigorous claim that the Universe were finite, the onus would be on me to defend it.

However, neither of the above arguments I just made are reasonable. Clearly we do not have conclusive evidence either way. What we do know is that we have not reason to doubt that the cosmological principle applies for the extent of our observable universe, for this we do have hard evidence such as the isotropy of the CMB (the anisotropies are of course of great interest, but are very small in agreement with the cosmological principle), and the general isotropy of galaxies and QSO's seen in large redshift surveys.

Thanks for this response. But why isn't the onus on you to justify your claim: 'The universe is isotropic from Earth. Therefore, the universe is isotropic from every point in the observable universe.' That's a leap that does not seem to be entailed by the empirical evidence. The Bedouin would be wrong to say, 'The world looks desert-y in all directions to me. Therefore, the world looks desert-y from all spots on the Earth.' How does going from local isotropy (observationally true) to the cosmological principle not make the same mistake?

Given this data then, we can see that if the Universe is finite, it is clearly at least much bigger than the observable Universe, and for all intents and purposes is infinite. Assuming the Universe is infinite makes the equations easier to deal with, since there are less parameters.

But here's a technical question I asked earlier that has not been answered: Is there any amount of matter that would halt the expansion of the Universe (that is, such that the Universe asymtotically approaches a maximum volume)? If so, the Universe is identical to the observable universe (right?) and if there's a boundary, we could eventually find it (our progeny, that is). Other than the cosmological principle and (your) intuitions about simplicity, is there anything that weighs against a finite universe?

Theories are constructed based upon what is observed, and are made to be as simple as possible given those observations. This is why we assume the Universe is infinite, in full knowledge that this is not absolutely neccessarily the case.

Okey. Our inuitions just differ on this point. Thanks again for your very clear and informative reponse.

-----

One thing that pushes my buttons is Ordo's idea that SpaceTiger should have unlimited amounts of time to answer his (Ordo's) questions. In an ideal world, this would be nice, but people have to be able to live with the fact that moderators and mentors may actually have other things in their life other than PF, hard as it may be to believe...

Are you talking about someone else here? I never claimed any such thing; in fact, I've asked SpaceTiger to stay out of the discussion. Part of being a good scientist--indeed, a good human being--is honesty in argument, pervect.

 

[Valjean]

It may be that condidering the edge of the universe is like considering the edge of time. Many advances in knowledge have come at the expense of contradicting current accepted conclusions. Maybe a different look at the basis would help answer some of the questions...most likely not but maybe. Consider, from the same starting place as the bang, formation of strings and such...nothing. Then a contraction of space into bits of compressed space each surrounded by expanded space, both created by the same action, like a teeter, totter. Just as a compressable spring with equal alternate sections compressed it will expand the other sections and they will pull beteen the compressed sections but not move them if that pull is equal in both directions. Equate that to space, multi-dimensional, spherical. The likeness stops there but it could help understand how the expanded space is necessary to produce attraction between the compressed bits of space. Under this scenario the area we consider an empty vacuum of nothingness is not. It is near infinitely flexible expanded space. It would be the conduit that transfers energy fluctuations from bit to bit and the ever larger units they combine to form. Compressed space (energy) surrounded by expanded space (energy) Some combine to form units around which other individual or smaller units of bits orbit in regular frequencies and amplitudes, increasing and decreasing the level of attraction strength between them and others comensurate with the changing distance. Those we can detect with our instruments. The ones who do not move in regular patterns we can detect would still retain their attraction component (dark matter). And if units combine into large accumulations their attraction increases accordingly and could be the source of what is considered "warped space". This would violate and contradict many currently held notions. But one of the frequenct comments shared by most scientific disciplines is something akin to "Because of this we're going to have to reconsider our conclusions about...". It's those rethinkings that produce progress.

 

[SpaceTiger]

I can't make things any clearer to you on this matter. Regarding Occam's Razor: You apparently still don't understand it. It's not: The simplest theory is the best. It is: Do not multiply entities without need. There is a subtle, but important, difference there. You are the one making a positive claim; the burden of proof is on you, not me. You believe that X? Great: adduce some evidence in support.

Okay, I think it's time to lock this thread. It's clear that the OP isn't going to accept the answers given to them, so for the sake of everyone's time, the discussion should probably stop. Other folks with lingering questions (about eternal inflation, or whatever) should feel free to start another thread. Thanks to everyone who took the time to respond.