[JohnDuffield]

I understand this argument John, but to that argument I will ask you this question:

If our universe occurred within this nothingness, producing waves and fields restrained within our present physical "water droplet", it's logical to assume that this same process can repeat itself again somewhere else in your defined nothingness.

No it isn't. This nothingness is not space. It isn't some void. There is no place for light to go beyond the edge of space.

Or is our present location the only place where a universe can form? And why would we assume to limit this event to a single location?

Maybe now's a good time to remind you that the word universe comes from "uni" as in one and "verse" as in vice versa. It means turned into one. It means everything. What you're asking about, is more than one everything. Does the universe, this everything, go on forever? If the answer is no, it doesn't make sense to say there's an infinity of other everythings beyond it.

As you may have already figured out, I tend to believe in either flat space or the Multiverse concept.

WMAP found that space looks flat, so we have evidence to support the idea that space is flat. But we have no evidence to support the idea of a  multiverse. None whatsoever.

In either case, space would be infinite.

Not so. It's a non-sequitur to say space is flat and therefore infinite. It's like the old flat-Earth belief, only back to front. In ancient times people (allegedly) believed the world was flat, and therefore had an edge. In modern times people believe the universe is flat, but they cannot believe it has an edge.   

Given that this may be an accurate view of physical reality, can you see where this view of things would involve an infinite arena or place where present reality exists? If not, why only one finite universe?

If can't see how the universe can be infinite, because an infinite universe can't expand. And I can't see how you can have more than one everything.

Murphy's Law; If it can happen it will. And if it happened once, it will happen again, and again, and again..........

It's no substitute for scientific evidence. And we have scientific evidence that the universe is flat, and is expanding. I think that's also scientific evidence for a finite universe.

[Ethos_]

It's no substitute for scientific evidence. And we have scientific evidence that the universe is flat, and is expanding. I think that's also scientific evidence for a finite universe.

No..............better minds than anyone of us conclude that flat space defines an infinite universe. Either way, you seem to have missed my points JD. I think I'll have to agree with Pete about things here. When ever I hear someone use the term: "it seems to me", that usually means they are not bright enough to understand or they simply refuse to consider the facts. Which ever case is true concerning this debate is something we will all have to decide at the personal level.

Whether material space is infinite or whether nothingness is infinite, the fact is, that infinity is inescapable. I suggest that if our material universe is finite, then your supposed nothingness beyond our present bubble is infinite.

If you can't "seem to get this" we have nothing left to discuss.

[Bill S]

Hi Dlorde, you are right, we have been here before.  We have seen these questions, and these answers, before.  The trouble is, as I said to Pete earlier in this thread, answers tend to take the form: “this is the answer, whatever the question was”. 
 

By that logic, anywhere on the road is the middle, which makes 'middle' meaningless in this context.

Great! 

It is unclear if you are saying that you consider “middle” to be meaningless, or just that the logic I applied would make it meaningless.  However, I would contend that middle, beginning or end; or indeed any position, in infinity is meaningless, but that’s probably a step further than we would be ready to go until we can progress beyond constantly returning to mathematical “infinities”.

Half of infinity is still infinity. You have two infinite roads.

You have two unbounded roads, but I argue that unbounded and infinite are not necessarily synonymous.     

“Unbounded” can be quite different from “infinite”, because, although infinity can rightly be said to be boundless, all that is boundless is not necessarily infinite.  For example, in an infinity of nothingness there could, in theory, exist a universe.  The surrounding nothingness would place no limit on the amount of matter or energy that could be added to that universe, nor would there be any limit to the extent to which the universe could expand.  Nevertheless, however much was added to the universe, or however great was its expansion, it would always be finite. 

Its potential might be said to be infinite, as it has an infinity of nothingness into which it can expand, but even this is not strictly correct.  It can never reach infinity; therefore it does not have the potential to become infinite.  Nothing finite can become infinite.

Yes. An infinite extent can have a beginning.

Beginning and end are directional concepts.  Turn round and your beginning becomes an end which, by definition, infinity cannot have.

You may say that the start is a specific point on the road, and the PIF, infinitely far away, are also at a specific point on the road, but these two points cannot be related by measurement;

Does it seem strange that something that constantly returns to mathematical definitions cannot be related by measurement?  I am not disagreeing with you here; I too believe that points in infinity cannot be related by measurement; but take that logic a step further and it becomes: Two points in infinity cannot be distinguished from each other.

No, both infinities in this thought experiment are the same size. If you want to know about different 'sizes' or orders of infinity, check out Georg Cantor's Transfinite Numbers.

This is a recurring problem when trying to discuss infinity.  Cantor’s infinities are valuable as mathematical tools, but let’s not forget that even Cantor had problems dealing with “absolute infinity”. 

I don't know what you mean by it, but there are different orders of infinity. For example, there are an infinite number of natural numbers, but a larger infinity of real numbers.

This is another of those things that always comes up, but is never resolved.  This, I think, is a shame, because Cantor’s work on infinities is a masterpiece, but it should not be expected to apply beyond the sphere of maths.   

[Bill S]

Maybe now's a good time to remind you that the word universe comes from "uni" as in one and "verse" as in vice versa. It means turned into one. It means everything. What you're asking about, is more than one everything. Does the universe, this everything, go on forever? If the answer is no, it doesn't make sense to say there's an infinity of other everythings beyond it.

  ......better minds than anyone of us conclude that flat space defines an infinite universe.

I think we are running into semantic troubles here.  John, correct as your etymology of “universe” is; you have to allow language to evolve.  I hesitate to keep on about John Gribbin’s usage, but it does tend to militate against confusion. Possibly you and Ethos are understanding different things when using the word “universe”.

As far as what “better minds than anyone of us conclude”, let’s not forget that most of the best minds in geology thought that Wegener was wrong.

I think I'll have to agree with Pete about things here. When ever I hear someone use the term: "it seems to me", that usually means they are not bright enough to understand or they simply refuse to consider the facts.

That has to be one of Pete’s more elitist comments.   

[Bill S]

It seems I may not be “the voice of one crying in the wilderness”.  Unbounded does not necessarily equal infinite!  Even Stephen Hawking agrees with that.

http://www.hawking.org.uk/the-beginning-of-time.html

The conclusion of this lecture is that the universe has not existed forever. Rather, the universe, and time itself, had a beginning in the Big Bang, about 15 billion years ago. The beginning of real time, would have been a singularity, at which the laws of physics would have broken down. Nevertheless, the way the universe began would have been determined by the laws of physics, if the universe satisfied the no boundary condition. This says that in the imaginary time direction, space-time is finite in extent, but doesn't have any boundary or edge. The predictions of the no boundary proposal seem to agree with observation.

[Ethos_]

Possibly you and Ethos are understanding different things when using the word “universe”.

I agree Bill,......That's the reason I said; "you seem to have missed my points JD". In any event, discussing a concept like infinity is a big challenge. I think it all boils down to whether the individual has the intuition to wrap their minds around this mental abstraction. Those that do will side with infinity and those that don't will contend against it.

So, who's right? It could be that neither one of us is depending on how we define the word. Until we get on the same page with our definitions, this discussion will fail to render any positive results.

[dlorde]

It is unclear if you are saying that you consider “middle” to be meaningless, or just that the logic I applied would make it meaningless.  However, I would contend that middle, beginning or end; or indeed any position, in infinity is meaningless, but that’s probably a step further than we would be ready to go until we can progress beyond constantly returning to mathematical “infinities”.

The 'middle' means equidistant from specified extremes. Infinite extremes are not measurable so equal distance can't be known. On the other hand, if you decide the infinities either side are effectively equal in size, then any point qualifies, which means all points are the middle; which, I submit, makes it meaningless.

You have two unbounded roads, but I argue that unbounded and infinite are not necessarily synonymous.

I agree - where 'unbounded' means 'having no boundaries' -  a sphere is finite but unbounded. 

Beginning and end are directional concepts.  Turn round and your beginning becomes an end which, by definition, infinity cannot have.

That's just semantics. I can equally say that depending which way you turn, you either have an infinite extent ahead of you or behind you.

I too believe that points in infinity cannot be related by measurement; but take that logic a step further and it becomes: Two points in infinity cannot be distinguished from each other.

Only two points infinitely distant from each other will be problematic. It's an interesting point (they're interesting points![] ) - can you detail the logical step that takes them from not being related by measurement to them being indistinguishable?

Cantor’s infinities are valuable as mathematical tools, but let’s not forget that even Cantor had problems dealing with “absolute infinity”.

I don't see how Cantor's ideas of 'absolute infinity' (God) are relevant.

... Cantor’s work on infinities is a masterpiece, but it should not be expected to apply beyond the sphere of maths.

As far as I know, the only framework for dealing with the concept of infinity is mathematical. It's a mathematical abstraction. What else can we use when considering thought experiments about physical infinities?

[PmbPhy]

That has to be one of Pete’s more elitist comments.   

You're wrongly accusing me of having made elitist comments. Please show me these elitist comments that I've made to people they didn't actually and accurately apply to.

I may have said that someone wasn't that bright but only in extreme cases and even then only with nutcases like JD but never simply because someone used the phrase "it seems to me".

[JohnDuffield]

No..............better minds than anyone of us conclude that flat space defines an infinite universe.

I reject that. Who concludes that flat space means the universe is infinite? And do they also conclude that the universe was always infinite. 

Either way, you seem to have missed my points JD. I think I'll have to agree with Pete about things here. When ever I hear someone use the term: "it seems to me", that usually means they are not bright enough to understand or they simply refuse to consider the facts. Which ever case is true concerning this debate is something we will all have to decide at the personal level.

Ask around about how the universe got to be infinite in a finite time, or was always infinite. You won't get a satisfactory answer.   

Whether material space is infinite or whether nothingness is infinite, the fact is, that infinity is inescapable. I suggest that if our material universe is finite, then your supposed nothingness beyond our present bubble is infinite.

You're still not getting the "no space" concept. Space isn't nothing, it's something. See the shear stress in the stress-energy tensor? Note the energy-pressure diagonal? Space is kind of like some ghostly gin-clear elastic that can be deformed or pressurized or curved. If you reached the edge of space, there is no beyond it. Nothing isn't space.   

If you can't "seem to get this" we have nothing left to discuss.

Noted.

[JohnDuffield]

I think we are running into semantic troubles here. John, correct as your etymology of “universe” is; you have to allow language to evolve.

I don't there's much of an issue with the word universe. If we do find there's some confusion, we could soon clear it up.

I hesitate to keep on about John Gribbin’s usage, but it does tend to militate against confusion. Possibly you and Ethos are understanding different things when using the word “universe”.

I don't think so. We seem to have an irreconcileable difference regarding a universe that's infinite. 

As far as what “better minds than anyone of us conclude”, let’s not forget that most of the best minds in geology thought that Wegener was wrong.

Well said. I refuse to be told to just accept something because "better minds than us" say it's right. 

That has to be one of Pete’s more elitist comments.

He thinks of himself as the expert, and reacts badly to any challenge or correction.

It seems I may not be “the voice of one crying in the wilderness”.  Unbounded does not necessarily equal infinite!  Even Stephen Hawking agrees with that.

http://www.hawking.org.uk/the-beginning-of-time.html

The conclusion of this lecture is that the universe has not existed forever. Rather, the universe, and time itself, had a beginning in the Big Bang, about 15 billion years ago. The beginning of real time, would have been a singularity, at which the laws of physics would have broken down. Nevertheless, the way the universe began would have been determined by the laws of physics, if the universe satisfied the no boundary condition. This says that in the imaginary time direction, space-time is finite in extent, but doesn't have any boundary or edge. The predictions of the no boundary proposal seem to agree with observation.

There's no actual evidence to support Hawking's no-boundary hypotheses. Or his imaginary time. Or an infinite universe. But there is evidence to support the idea that space is flat, that it doesn't curve back round on itself, and that it's expanding. IMHO people say the universe is infinite because they just can't conceive of some kind of boundary to it. And then they forget that it can't be infinite unless it was always infinite, which I think is most unsatisfactory.

[Ethos_]

While we are trying to get our minds wrapped around the meaning of infinity, something occurred to me that might be of interest for some of our members.

Let's ask ourselves; "What existed before the big bang?"

While proving any particular theory about this question is impossible, most of us will reason that what existed before the big bang was simply nothing. And even now, as we exist in a universe which many assume is finite, this present universe sprang up within this nothingness.

We've reasoned in prior posts that maybe it would be time to define what we mean when we say "Universe". But it would also be a step forward to define what we mean when we say "Nothingness"

My point with these thoughts are this:

Before the big bang, nothingness was truly infinite. If nothing else existed in this historical epic, then nothing anywhere but nothing is logically an infinity of nothingness.

So to clarify my position on what I mean when I say: "Universe"

"All that is." This would include our present material existence and all that nothingness which our present material universe sprang up within during the big bang.

[JohnDuffield]

Let's ask ourselves; "What existed before the big bang?" While proving any particular theory about this question is impossible, most of us will reason that what existed before the big bang was simply nothing.

Not me. I just don't believe in creation ex nihilo.   

But it would also be a step forward to define what we mean when we say "Nothingness". My point with these thoughts are this:

Before the big bang, nothingness was truly infinite. If nothing else existed in this historical epic, then nothing anywhere but nothing is logically an infinity of nothingness.

So to clarify my position on what I mean when I say: "Universe"

"All that is." This would include our present material existence and all that nothingness which our present material universe sprang up within during the big bang.

I think the pre-big-bang universe was something like a "frozen star" black hole myself. Interestingly, when you look at the gravastar, which is somewhat similar to the frozen star black hole, you can read this: "This region is called a 'gravitational vacuum', because it is a void in the fabric of space and time." It's like a black hole really is a hole in space. Sounds unfamiliar I know, but note the shear stress in the stress-energy-momentum tensor, and think of space as something like gin-clear ghostly elastic. Then think of a party balloon, then look at this picture:


CCASA image by Alain r, see http://en.wikipedia.org/wiki/Black_hole

See it? The depiction looks like a balloon with a hole in it. Like a black hole really is a hole. A hole in space. I have a hunch the early universe was something similar. Only there wasn't any space around it. Maybe this deserves a thread all of its own.   

[Ethos_]

Let's ask ourselves; "What existed before the big bang?" While proving any particular theory about this question is impossible, most of us will reason that what existed before the big bang was simply nothing.

Not me. I just don't believe in creation ex nihilo.   

I was under the impression that you believe our universe is a finite region of material existence lying within a region of absolute nothingness. If that is so, why didn't that nothingness also exist before the big bang?

[dlorde]

Let's ask ourselves; "What existed before the big bang?"

... most of us will reason that what existed before the big bang was simply nothing. And even now, as we exist in a universe which many assume is finite, this present universe sprang up within this nothingness.

I'd like to see your data supporting 'most of us'; I, for one, don't reason that. 

... it would also be a step forward to define what we mean when we say "Nothingness"

Please do, your usage makes no sense at all to me.

Before the big bang, nothingness was truly infinite. If nothing else existed in this historical epic, then nothing anywhere but nothing is logically an infinity of nothingness.

Nothing has no properties - it is a negation, the absence of anything, even empty space. It doesn't exist - it has no extent of any kind, so it can't be infinite. What 'nothingness' means, apart from a poetic appeal to a sense of nothing, I'm curious to know; please enlighten me.

[dlorde]

... you believe our universe is a finite region of material existence lying within a region of absolute nothingness. If that is so, why didn't that nothingness also exist before the big bang?

A finite region of nothingness? how does that work? You seem to be using 'nothingness' in the sense of being something that can exist and can occupy a region... I don't understand.

Are you sure you don't mean some kind of empty space?

[Ethos_]

See it? The depiction looks like a balloon with a hole in it. Like a black hole really is a hole. A hole in space. I have a hunch the early universe was something similar. Only there wasn't any space around it. Maybe this deserves a thread all of its own.

"A hole in space." "Only there wasn't any space around it."

Now you've really sent my train off the tracks.......................

[Ethos_]

... you believe our universe is a finite region of material existence lying within a region of absolute nothingness. If that is so, why didn't that nothingness also exist before the big bang?

A finite region of nothingness? how does that work?

I didn't say "a finite region of nothingness." I was referring to what I understood JD's vision of reality was. A finite region of material existence lying within a region of nothingness.

[Ethos_]

Let's ask ourselves; "What existed before the big bang?"

... most of us will reason that what existed before the big bang was simply nothing. And even now, as we exist in a universe which many assume is finite, this present universe sprang up within this nothingness.

I'd like to see your data supporting 'most of us'; I, for one, don't reason that. 

I stand corrected dlorde.................That was very presumptuous of me.

[Ethos_]

This discussion would benefit from:

The Man Who Knew Infinity, a book about the life of Srinivasa Ramanujan

While I agree that infinity is not a number, it is worthy of being called; A mathematical abstraction. And Ramanujan was, by all accounts, one of the greatest mathematical genius's, if not the greatest, to ever live.

 

[dlorde]

I didn't say "a finite region of nothingness." I was referring to what I understood JD's vision of reality was. A finite region of material existence lying within a region of nothingness.

Sorry, my mistake. So you reject the idea of a 'region of nothingness'?

I'm still curious to hear your definition of nothingness and how it could be infinite (e.g. infinite in what respect?).