[yor_on]

PB, reading you I get a distinct impression of Neil Cornish et al defining a universe from what I define as a 'container perspective' ?
If that is so? Then it's a outdated perspective in my view.
The thing is, there is a complementary principle involved, but stretch it too long and it will break.

[yor_on]

And John "No, it isn't settled, and it definitely isn't dogma to point out that a universe that was small 13.8 billion years ago cannot be infinite now."

You really need to look up the logic used there. what it will tell you is that there is no 'origin', or that everywhere is the 'origin'.

Both of those statements should tell you the same. There is no origin, the universe is indeed infinite, no expansion needed. and what that should tell you is that there are different types of logic, some fitting this universe, others won't, that doesn't discuss the mathematics 'reality', just where we exist.

[PhysBang]

PB, reading you I get a distinct impression of Neil Cornish et al defining a universe from what I define as a 'container perspective' ?
If that is so? Then it's a outdated perspective in my view.
The thing is, there is a complementary principle involved, but stretch it too long and it will break.

I'm not sure what you mean. There are a number of ways of defining regions within the universe. One is to identify the region at a given time that can possibly send light to Earth. One is to identify a region that has once sent light to Earth. In both cases, these are not the entirety of the universe unless the universe is finite and, in one sense, small.

The CNN article was reporting on the failure of some observations to detect a signal that the universe was so small that the entire universe is within the visible universe in the second sense above.

[JohnDuffield (OP)]

My understanding is that, by tracing back all that makes up our current observable universe, it can be concluded that very near the time of the big bang it all must have been in a very small space (high density), but that this argument does not necessarily mean that the *entire universe* was that small.

That's what people used to say. Google on big bang singularity. Somehow we've gone from the universe used to be small to the observable universe used to be small and that non-sequitur that a flat universe must be an infinite universe. Like I was saying, Neil Cornish was talking about the universe, not just the visible universe.

One could imagine an infinite universe with an initially high density that expanded into the density that we observe today while remaining infinite in scope from inception onward.

I can't. Because from what I know of relativity, an infinite universe can't expand. IMHO the very expansion of the universe is hard scientific evidence that the universe is not infinite.

If, in fact, the zero-energy universe theory is correct

It isn't. That's a myth that arises on the mistaken idea that gravitational field energy is negative. It isn't, it's positive. See The Foundation of the General Theory of Relativity where Einstein said the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy. The people who propose the zero-energy universe cannot have read this.

I think it would be just as possible to for an infinite amount of matter to "come into being" as it would for any finite amount.

I don't know how or why the big bang occurred, but I know of no infinities in nature, and I'm not comfortable with some infinite amount of space and matter and energy just popping into existence.

On the other hand, I am not convinced that the universe "must be" infinite, merely because it is the simplest solution that fits with our observations.

That's the thing - I don't think it is the simplest solution.

However, this is mostly a philosophic point (for now), as we can model the universe as infinite or just arbitrarily large and reach most of the same conclusions. Certainly we cannot perform any experiment that proves that the universe is finite.

Neil Cornish et al had a go, WMAP looked at flatness as did Planck which also looked for the toroidal topology. So never say never.

We could show that the universe is flat here, there, and everywhere we we can observe, but that doesn't ultimately prove that there isn't either a point beyond which the universe does curve, or a point beyond which there is some kind of "edge."

Agreed.

At this point, I am satisfied knowing that we don't know the answer, and hypothesizing that it is possible that we cannot know the answer. But that's just me.

Me too. Only I reject "the universe is infinite" as a non-answer that runs counter to big bang cosmology.   

[JohnDuffield (OP)]

You really need to look up the logic used there. what it will tell you is that there is no 'origin', or that everywhere is the 'origin'.

I take no issue with that. Space itself is expanding.

Both of those statements should tell you the same. There is no origin, the universe is indeed infinite, no expansion needed.

Sorry yor-on, but expanding space doesn't mean infinite space. And we have good evidence that space is expanding. Not only that, but look at Einstein's stress-energy-momentum tensor. See that energy-pressure diagonal? Einstein should have predicted that space had an innate "pressure" and just had to expand. He didn't, and it was his greatest blunder.

[yor_on]

Ok PB, I see how you define it. It doesn't answer the definitions I'm wondering about though. That means that I need a link, to see for myself I suspect
A 'containetr' in my view is a try for something that will 'hold it all'. And I don't expect that, what I expect are rules, and 'properties' scaling.
=

Actually PhysBang, what I really expect is a symmetry.

[yor_on]

Ouch, I told you that a expansion isn't needed, if you use the logic, or premises, defining a Big Bang. You don't really need it, as long as you understand that our 'spherical observer' find the origin of light coming to him wherever he goes, and at a exact same 'time scale'. If that logic is correct then there is no defined origin in the usual sense, as with some force expressing itself normally (Explosion). And I better point out that I don't see your arguments as being 'less' in any way. You and me both want to discuss, And we both want to use our imagination Not such a bad thing in my view. Too few that dare.
=

I told you John, I'm on a single malt diet today, have nothing to do with logic, just life.

[JohnDuffield (OP)]

I'm sorry yor_on, I don't know what you mean. We have what looks like good evidence that the universe is expanding, and from what I know of the nature of space, it just has to expand. See the stress-energy-momentum tensor above? It "describes the density and flux of energy and momentum in spacetime". See the energy-pressure diagonal? See the sheer stress? It's like space is this gin-clear ghostly elastic that can curve and wave. I kid ye not, google it. And Einstein's greatest blunder is that he talked about gravitational fields being everywhere, but he didn't think of space has having a pressure everywhere. For some reason he didn't follow his theory to its logical conclusion, and instead was convinced that the universe was static. So he didn't predict the expanding universe.

[yor_on]

Ok John. different definitions
I don't like 'shear stress' when applied on a vacuum.  Doesn't state that it must be wrong. Same as the idea of a vacuum, a vacuum according to old views is complementary. Yin and Yang.  That's a very naive interpretation naturally, doesn't mean it hasn't a logic though. I'm questioning a vacuum, as I do most everything.

[PhysBang]

Like I was saying, Neil Cornish was talking about the universe, not just the visible universe.

This really is all that needs to be pointed out about Mr. Duffield: he cherry-picks statements, he then uses this selective quotation to mislead his readers, then he ignores all the evidence that shows that he is misleading his reader, finally, he returns to the cherry-picked quotation.

Did Cornish discuss the universe as a whole? Yes. Did Cornish claim that the universe as a whole was a sphere of a certain size? No, he explicitly said something about the visible universe (given a certain definition).

This is essentially the only technique that Mr. Duffield has to attempt to harness scientific results.

[PhysBang]

The idea that the shear-stress component of the field equation play a role in cosmology at the largest scales is a relic of the electric universe or plasma universe theories. These theories do not currently have serious and sane proponents.

The standard cosmological model sets these components to 0, because the ideal particles of the model (galaxy clusters) do not interact except for with gravity.

[yor_on]

PhysBang, you're one of the clearest minds here,  as far as I know it at least. And John, the difference is the one between expecting 'measurable force' and mathematics. Using mathematics is one thing, it's 'ideal', defining a relation. Expecting the universe to be a 'force' is another.

[yor_on]

The point is that you don't need 'elastics' to define reality. You do need logics though. When those take you into paths not seen you have you to ask yourself what is most correct, the mathematics, or my preconceptions of how 'it is'? I will go for the mathematics, as long as they make sense That means that they need to fit what we already know. It doesn't guarantee that you can translate them into 'measurable forces' though, as with the Einstein stress energy tensor. That's actually a challenge I think you're trying to answer John. But you're still stuck with 'forces', as far as I can see?

[Bill S]

This is reminiscent of that song by The Fortunes:  “Here it Comes Again”.  I suppose discussions about infinity will always be with us, and frequently they will be about the question as to whether or not the universe is infinite.

Why will they never go away, or reach any reasonable conclusion?

The answer, I believe, is that different people mean different things by “infinite” and “universe”.  It seems that, in general scientists avoid trouble by treating “infinite” as though it were synonymous with “unbounded”; and if that works so well and good.  If your ladder reaches the roof, why grumble that it is not 6ft longer?

John Gribbin’s suggested usage of “Universe”, “universe” and “cosmos”, to avoid confusion, has not caught on in the almost 20 years since he published it.  Could this be because scientists always specify exactly what they mean when they talk of the universe?  I’m not hazarding any guesses about that.

[Bill S]

John, I have spent a lot of time on forums trying to come to grips with what seemed logical and inevitable to me, and comparing it with what seemed logical and inevitable to others.  Most often, these viewpoints were very different when infinity was involved.  What was the outcome? 

On the basic issues, I would say: no real change.  However, what was really important to me was not so much trying to establish who was right, and who wrong, as trying to understand why those other people thought as they did.  I like to think I have made some progress on that front.

Have you tried looking at answers to a few questions while varying your terminology?

Consider, for example:

Can something finite become infinite?  No.
Can something small and expanding always have been infinite?  No.

Can something finite become boundless?  Yes.
Can something small and expanding always have been boundless?  Yes.

If you regard “infinite” and “unbounded as synonymous, do the answers to those questions remain the same?  No:  all the answers can become “Yes”.

[JohnDuffield (OP)]

Did Cornish discuss the universe as a whole? Yes. Did Cornish claim that the universe as a whole was a sphere of a certain size? No, he explicitly said something about the visible universe (given a certain definition).

No, he didn't explicitly say something about the visible universe. Here's the article again:

http://www.cnn.com/2004/TECH/space/05/24/universe.wide/

He was talking about the universe, not the visible universe. I'm not cherry-picking, I'm giving the reference, and you're trying to claim the cosmologist said something he didn't.

The point is that you don't need 'elastics' to define reality...

No, but when we're talking about space, it's good to look at things like the stress-energy-momentum tensor. 

...It seems that, in general scientists avoid trouble by treating “infinite” as though it were synonymous with “unbounded”; and if that works so well and good.

It isn't true Bill. The Planck mission found no evidence of the toroidal universe that is finite but unbounded. That's like the old asteroids game, where you go thataway and end up coming back thisaway. In that scenario there's no edge to the universe, it is unbounded, but it has a finite size. The infinite universe is very different. Again there's no edge and it is unbounded, but it goes on and on. From your latest post:

Can something finite become infinite?  No.
Can something small and expanding always have been infinite?  No.

That's my point.

Can something finite become boundless?  Yes.
Can something small and expanding always have been boundless?  Yes.

Agreed. Again this is the toroidal universe akin to the asteroids game. But there's no evidence for it, or for any kind of intrinsic curvature in wherein you go thataway and end up coming thisaway.

If you regard “infinite” and “unbounded as synonymous, do the answers to those questions remain the same?  No:  all the answers can become “Yes”.

But they aren't synonymous. The surface of a sphere is boundless but not infinite. And if the universe started small 13.8 billion years ago, it can't be infinite. It could be boundless, but we have no evidence for it. So we surely have to consider that it might be bounded. 

[Ethos_]

This is reminiscent of that song by The Fortunes:  “Here it Comes Again”.  I suppose discussions about infinity will always be with us, and frequently they will be about the question as to whether or not the universe is infinite.

Why will they never go away, or reach any reasonable conclusion?

I might suggest that they don't go away because; like the universe, opinions have an infinite character.

[Bill S]

John, you missed the point I was trying to make.

When I said: 

It seems that, in general scientists avoid trouble by treating “infinite” as though it were synonymous with “unbounded”

I was not referring to the toroidal universe or the asteroids game.  I was simply saying that by treating the two (incorrectly, in my view) as though they were synonymous, one could make claims about infinity that you and I might take issue with.

Similarly, when I said:

If you regard “infinite” and “unbounded as synonymous, do the answers to those questions remain the same?  No:  all the answers can become “Yes”.

I was not advocating considering them as synonymous; just pointing out that holding that view could be considered to “justify” answering any of those questions: “Yes”.

[yor_on]

Ethos, you're one of the most emphatic minds I've meet. Go for it.

[yor_on]

As well as I would hate TNS to be a place where we color people to our purpose, I want it to be a place where we have room to breath, all of us.