The Universe: Finite or Infinite?

[Vincent So]

The energy states of a system are quantized if and only if the system is bounded. Light energy is quantized. Hence I believe our universal is bounded, i.e. finite.

 

[jreelawg]

The question is entirely meaningless unless everyone agrees on a definition of "universe".
What we all see is a big sea of quantum vacuum. There could be other bodies of substance out there that are each contained. So our bubble could be finite in an infinite universe. People like to call their bubble the universe which is kind of a roadblock in answering the question.

Magical human inventions modeling the universe as the surface of sphere make no sense to me. For one, the universe has three spatial dimensional. The "surface" of a sphere model would require that there is a thickness to the "surface" defeating the whole meaning of the word surface, therefore that model is nothing less than a sphere with a magically missing chore and nothing outside it. What is the point of that, why not just call it a sphere with nothing around it?

Besides, how thin can a surface be before it doesn't exist. There must be some thickness in order for a surface to exist, and therefore, there must be an up, and a down. The surface of a sphere thing just adds an interior boundary as well as an external boundary, the paradox remains exactly the same.

 

[hartgravesmik]

infinate. it could be no other way. if there was and end then there would be something beyond it. i don't care how many bubbles there are, or bubbles of bubbles ect and so on. the definition of a universe includes everything and therefore it does not stop.

 

[marcus]

The energy states of a system are quantized if and only if the system is bounded. Light energy is quantized. Hence I believe our universal is bounded, i.e. finite.

I agree that the universe could be spatially finite in a volume sense----but I don't imagine it having any boundary or edge. It might simply have a finite spatial volume with no boundary. However I don't follow your argument that it has to be that way. It seems to me that we don't know yet whether space is finite volume or infinite volume. There is a curvature measurment to decide this. Some progress has been made but it isn't conclusive yet. So I think the prevailing opinion is it could go either way

The question is entirely meaningless unless everyone agrees on a definition of "universe"...

We should never expect everyone to agree on a definition of anything, and yet if we define our terms as we go, we can have meaningful discussions. One simple way to go is just adopt the prevailing notion of universe among observational cosmologists, like the WMAP group. Their job is to study the universe, measure it various ways, reconstruct its past history---so they have a pretty good practical working definition. You have the right to define it for yourself however you want (just be explicit about it). But it would be awfully convenient if we could all share a common basic terminology.

infinate. it could be no other way. if there was and end then there would be something beyond it.

Space could have a finite volume, and yet have no end. With a little effort one can imagine a finite 3D volume with no boundary or edge of any sort. So I don't see the logical force of your argument.

 

[Earnest Stuar]

I agree that the universe could be spatially finite in a volume sense----but I don't imagine it having any boundary or edge. It might simply have a finite spatial volume with no boundary. However I don't follow your argument that it has to be that way. It seems to me that we don't know yet whether space is finite volume or infinite volume. There is a curvature measurment to decide this. Some progress has been made but it isn't conclusive yet. So I think the prevailing opinion is it could go either way

Hi Marcus – If the universe had a finite volume extending somewhere beyond what could be observed by zooming around the outer observable bodies, I could imagine the core element between constructs – space – ending with another, as-yet-unidentified element beginning and extending to infinity. As we are imagining, with no proof either way, that would be as plausible as the same element of “our” space extending to infinity without any apparent constructs beyond what we can presently observe with our best glasses.

Space could have a finite volume, and yet have no end. With a little effort one can imagine a finite 3D volume with no boundary or edge of any sort. So I don't see the logical force of your argument.

As we have no way to know the nature of the “edge” of the Universe, or even the initial, presumed undifferentiated source driving its expansion that leads to Planck’s thoughts on how matter came about, and begs the question "is the Big Bang pushing out like they say?", then there is zero evidence on whether the stuff we can measure in space goes on to infinity or stops like the edge of a bubble in water. A bubble forming in water behind a submarine at 500 meters depth, if one were born inside it at that moment, but one was the smartest being on the planet and had more degrees than a thermometer, would have a hard time figuring out what was the edge of that bubble or if there was an edge to that bubble..even with that extremely short burst of light around them in the bubble, which would occur, to see with. Everything would be dark out there, but there would be an edge to the bubble. And the ocean is big and other bubbles and things unseen exist beyond that which wouldn't be seen from the universe of that tiny bubble.

Seems all thoughts on the edge or beginning of the Universe have no real basis in science (yet), and are imaginings..one being as good as another.

 

[danda22]

But that's not the question that was asked, and it is not what lay people generally mean when they ask 'is the Universe finite or infinite'. We can change the question to make it easier to answer, but then we are answering a different question!

alright. hey i don't know if anyone still reads this but i thought id post a comment anyways on my beliefs. It is true and has been stated many times that nothing can be destroyed? true? well.. if this is stated to be true. then we must also assume that nothing can be created (assuming there is no "god" matter) in which case. if nothing can be created and nothing can be destroyed (in a 3D sence) then the spatial expance of our "uni"verse is finite. that is to say any mass inside our universe is finite...

also my theorum on the big bang/s. and the big crunch/s... ok. so i just thought of this one now. but.. we all know how atoms react with each other.. see atom bomb hydrogen bombetc.. what i believe has been happening since the beggining of time..( or maybe there's nosuch thing as a begining...lets just say since universes have been around) is that .. god this is hard to explain lol... uhm./ ok let's just say there were finite trillions of atoms swirling around etc... they are elements yet..hmm... i dunno. the basisof what I am trying to say as hard as I am making it sound is that. the big bang is a chemical reaction.all the atoms at verry high temperatures reacting and exploding forcing all atoms and particles away at superfast speeds. which explains why the universe is forever expanding. if there's such a thing as "the big crunch" then when all of the atoms, starts, planets and galaxies are squashed back in the middle vaporised into there key elements, another big bang will occur and this will be the start of another universe. also. i see the universe as not flat.. not "balloon" but more like a cone shape.. or a circle with a slight dent in the middle... stick with me here..

lets imagine the galaxies as balls on a giant playgroundwhich justsohappens to be slopingtowards the middle.. the balls have been kicked (lol..) outwartds from the middle and will keep going until the force behind them stops.at which time they will slowly roll back towards the middle.

this is how i see the universe. although i realize there are a few flaws in my theory.. Also. the problem with my balltheory is that.. if the force behind each ball just so happens to be that of an entire universe... would they ever stop?

uhm yeah. so please tell me of any flaws and if u agree/not and why please

 

[Pjpic]

PLEASE help!


I think I understand the logic of your question, but I haven't been able to find a source that specializes in dealing with it. Steven Hawking talks about it some at the end of 'Universe in a Nutshell 'but only very broadly. It almost seems like trying to find someone that wants to talk about traffic congenstion but the only people you find are mechanics (who specialize in the internal combustion).

 

[marcus]

...
It continually plagues me. I even had a friend blurt out of the blue the other day, "What's with the universe? Does it just keep on going forever? Or does it stop? If so, what's beyond it?"...
Is the universe finite? (= implies a "Beyond")
Is the universe infinite? (= seems nonsensical, and counter-intuitive to "Big Bang" theory)
...

PLEASE help!

I think I understand the logic of your question, but I haven't been able to find a source that specializes in dealing with it. ... It almost seems like trying to find someone that wants to talk about traffic congenstion but the only people you find are mechanics (who specialize in the internal combustion).

...If constant instants of cosmological time are used to foliate a Freidmann-Robertson-Walker spacetime into spacelike sections, then (as marcus has posted) \mathbb{R} \times S^3 results when the spacelike sections have constant positive spatial curvature with respect to the spatial metric induced on the the spacelike sections by the spacetime metric. In this case, each spatial section is compact and has finite volume 2\pi^2a^3. See Box 27.2 of Misner, Thorne, and Wheeler.

Dear Pjpic,
George Jones who is both a PF mentor and someone with academic specialization in cosmology effectively answered the question. But you couild reasonably ask for more elaboration and say that what you've been able to find in your other readingon it is either:
1. not spelled out in simple language, or
2. too contaminated with noise and disagreement about the meaning of words.
So I'll make a stab at clarifying for you.

I think what Mattex is asking is if you could freeze expansion at the present instant of cosmological time and then were able to wander freely around and explore all of space,then would it turn out to have infinite volume or would it have finite volume?

And if it turned out to have finite volume then Mattex is worried that might imply there was a boundary and some more space beyond or outside. He probably can't picture being inside a finite-volume boundaryless space which is not contained in a surrounding infinite volume.

The reason to imagine that you freeze expansion and look at space at the present instant (which is what George was talking about---he said how to calculate the volume in a particular case) is that if you allow space to get bigger while you are exploring it you get into confusions about how much of it you can visit depending on how fast your travel and how fast distances are increasing. So it gets too complicated. The simple thing is, freeze it and then take your time and have a look around.

This approach was taken in one of the standard textbooks, as an exercise. George gave a page references.

Then it is all pretty simple. The answer will probably not satisfy you though.

The answer is cosmologists don't know. Given the present data it could be either finite volume or infinite volume. It is mathematically possible to be in a boundaryless finite volume space that is not contained in any larger volume. Infinite volume is also a mathematical possibility.

Technically there is a curvature number that satellite instruments help measure which will help decide the issue. A new satellite instrument was just launched this year. If the curvature number turns out to be one or less then infinite volume is very likely. If it turns out to greater than one then finite volume is favored.

In 2008 a NASA report (from the WMAP mission) gave some numbers for that particular finite volume case that let you calculate a lower bound on the volume using the formula in George's post. Basically they said that with 95% confidence R > 100 billion lightyears and to get a lower bound on the volume, in cubic lightyears, you should plug that into the formula V = 2 pi² R³.

Presumably you don't want to know that, you want only nontechnical interpretation, but the upshot is that they don't know yet, and the boundaryless finite volume case is one case that they have a handle on and are considering. The infinite volume case is also a very good possibility. (This would mean also an infinite volume at the start of expansion which doesn't conform to many people's picture of the big bang, but it is a mathematical possibility that cannot be ruled out.)

 

[TalonD]

hey Marcus, just curious, how would you do the calculations. (I'm not much of a mathemetician) Assume finite volume and radius is 100 bly, what would the radius and volume be at plank density? or I think I read in a post that bounce theory says it would be about 40% plank density is that right?

one other question. I don't have a problem with finite volume and no boundary, but why so insistant on having no boundary? Is it just because it is mathmatically possible? I realize we 'don't know for sure one way or the other, but is there a reason for saying it has no boundary other than just some intelectual bias? Or is there a reason why it absolutely can not have a boundary, some theoretical concrete reason?

 

[marcus]

one other question. I don't have a problem with finite volume and no boundary,..

That's good! In that case I would have no reason to stress this in talking with you. I am fighting against other people's mental bias where they seem to think if something is finite it "has to be bounded". So they automatically, almost involuntarily, put an "edge" into the picture. And then *duh!* they start wondering what is beyond the "edge".

That shows you the trouble with boundaries and edges thinking. It is an unnecessary complication that Occam's razor alone would rule out. I have no bias against it---I can, if I choose, picture a region of space with a boundary, and something beyond it---as in one of the more extravagant multiverse inflation conjectures. But it isn't necessary. I have enough on my plate already with a simple boundaryless universe. (This is what you automatically get when you make the usual Cosmological Principle assumption of uniformity: you know the homog and isotropic assumption---automatically no boundary there.)

Or is there a reason why it absolutely can not have a boundary, some theoretical concrete reason?

Look, cosmo is a mathematical science which means getting the best fit to the data with the simplest mathematical model. And you keep refining that model until whoopee! you find a discrepancy that forces you to change the model. At no point do you assume anything is "true". In fact you are always hoping that new observations will show your current model is false. But after some features of the model have survived testing for many decades one gets skeptical as to how much you can reasonably expect them to change. Some features are probably robust and will probably carry over to the next version. Like the expansion feature Friedman described in 1922.

So ask yourself: would putting a boundary into the Friedman model make it fit the data better? If not, then in the context of a mathematical science it is simply not interesting. If some jerk wants to fantasize about a boundary, that's fine! Why not? And I think the answer to the question is no. Adding a boundary onto the standard mainstream Friedman model would not (as far as I know) make it fit the data better.

If I ever did hear that it would improve the fit, I would immediately be all excited about boundaries of course, that would be a major revolution. But I'm skeptical that it ever would turn out that way. So far the mainstream model is homogeneous and isotropic and not even the faintest hint of an edge.

hey Marcus, just curious, how would you do the calculations. (I'm not much of a mathemetician) Assume finite volume and radius is 100 bly, what would the radius and volume be at plank density? or I think I read in a post that bounce theory says it would be about 40% plank density is that right?

Talon, I didn't say that R = 100 billion lightyears was the estimated RADIUS. Be careful. It is a lowerbound on a length called the "radius of curvature", which is different from a real radius.

Imagine a ring. All existence is concentrated on that ring. There is nowhere else and there is nothing else besides what lives in that 1 dimensional ring. That ring has no radius because it has no surrounding space. The only space that exists is the ring. However the 1D people living in the ring manage to measure the circumference and find that it is 6.28 inches (they use some unit of length they call an inch.) One of their greatest mathematicians invents a concept "radius of curvature" which is the radius the ring would have if it were surrounded by a higher dimensional space, a 2D space which they have great difficulty imagining. He then calculates the "radius of curvature" of their universe and determines that it is approximately 1 inch.

Imagine the surface of a sphere, perhaps the surface of a balloon. All existence is in that surface---not the balloon, but the purely 2D surface itself. There is nowhere else and nothing exists except in that 2D surface. The surface has no radius.

However it has a radius of curvature which the 2D creatures sliding around in the surface would be able to discover by measuring angles (because the angles wouldn't add up to 180 degrees) and circumnavigating and measuring great circles, and stuff. So even though their world has no physical center and no physical radius (not being engulfed in some surround space of higher dimensionality) it nevertheless has a radius of curvature which the creatures can determine.

I'm sure you get the picture, Talon

 

[Ike47]

My thanks to Danda22 and others who revived this thread. I asked a question in the stickied Cosmological thread and have been waiting (hoping) for an answer from Marcus. Now I find he's already given the answer here! And I never would have found this thread if it had not been revived.

Of course, Marcus's answer leads to futher questions on my part, so I shall plow on. My questions will involve only the first page or so of this thread, since that was where my question was answered, and I don't particularly have a problem with the topics which have come up since then.

Anyway, Marcus, you have said, if I understand you correctly (please correct me if not): if the universe is finite, which we don't know at this point, it would be curved and without a boundary. I have no problem comprehending this (or at least I hope I don't; it seems 'visualizable' to me).

Further, even if the universe is finite, we can never "map" all of it, because of the restrictions of our light cone. In other words, because of the finite speed of all energy (c) and the ongoing expansion of the universe, we can never 'see' all the universe even though (under our assumption) it is finite. In theory at least, however, this limitation could be overcome by communicating with 'people' in other galaxies, each adjacent to each other, so that finally 'everyone' could share a 'map' of the entire universe. I'm not saying this is feasible, just theoretically possible.

Finally, you have said in this thread that the assumed finite universe could have a 'center' in a higher dimension, but a) that doesn't mean that higher dimension (and so that center) actually 'exists', and b) never ever ask a scientist about that 'center' because it is not amenable to scientific analysis.

My original questions was that if the universe should be finite, shouldn't it have a theoretical center, even if we couldn't determine where it was and even if mathematically it would have to be in a dimension that may well not actually exist. (I'm not sure exactly what 'a dimension not existing' means, but I am comfortable understanding that we can mathematically model dimensions that don't exist, as well as being unable to gather any data from (higher) dimensions that may exist.)

So it seems that you have answered my original question in the positive, which helps restore my sanity in regard to feeling that I can understand, in some small degree, the possible physical (geometric/topological) nature of our universe.

I hope I don't upset you with this, but I'd now like to ask a question that is in apparent contradiction to your strongly worded command not to ask questions of a scientist about the hypothetical "center" of our universe. I think my question is valid, that is, that it does not ask a scientist (you) to do something you cannot, but if I'm wrong, I will accept that and apologize.

If the universe is finite, curved, and without boundary, and if (as a thought experiment) we could "map" the entire S³ universe by conversing over billions (or more) years with many peoples in galaxies each adjacent to the next, could we not determine mathematically the theoretical "center" of the universe, even though, because it would be in a higher dimension (which may well not even exist), we might not be able measure any distances to it nor even point toward it (give it a direction from any specific location within our universe)?

Now perhaps it is mathematically impossible to calculate the center of a shape from the data available only within the dimensions of that shape, when the center would be in another dimension. I don't know enough topology or geometry to have a clue on that. But if it is theoretically possible, then would the answer to my question of the previous paragraph not be 'yes'?

Second question: if the answer to the previous question is indeed yes, so we had a mathematical definition of the center of our universe, might we not be able to determine whether our universe is 'symmetric' around that center? In other words, has the expansion of the universe always been 'even', or, like the slight lumpiness of matter in the very early universe that presumably made possible galaxies--and us--, are some points in the universe that were once equidistant from the universe's center now not equidistant?

Thank you for your patience reading through this (if you indeed have that much patience). I hope I have made my questions clear enough to be understandable, but I can't be sure that I have. If not, please point out where I am not making sense and/or note any unreasonable or illogical assumptions I may be making that I'm not even aware of. Thank you!

 

[TalonD]

on boundarys, ok, that's a good enough explanation to satisfy me. I could understand why the average person, would insist on a boundary and now I can understand why you often say that one isn't neccesary. That it's not just your personal bias vs. someone elses. You have good reasoning.

radius of curvature... Yep, I get it now! The radius a circle 'would' have 'if' it had one, based on it's curvature. That makes sense.

There's still the question though. If the universe has a curvature then it must have a finite volume right? Just as your curved sphere would have finite surface area? and the circle would have a finite circumference? even though none of them have a higher dimensional surounding space. As I recall we calculated that volume in another post and I had my decimal point in the wrong place :P, I'll have to go look for it or recalculate it. Then I'm curious what that volume would be if you shrink it all the way back to the beginning.

But then... is it possible for a curved universe to still have an infinite volume? after all, a circle or a sphere could be infinite in size just as a flat plane could be, right?


and then just reading the previous post from IKE47, it got me thinking about the center. Since the radius of curvature is sort of a virtual radius rather than a real one, then there would be r+r = the virtual diameter of curvature, then half way in between would be the virtual center. That's kind of meaningless of course but I like the way it sounded.

 

[danda22]

hmmm... ok.. "if it is rounded it can still be infinite?" no. if it is all curving inwards it must be finite... but... it all depends i suppose.. the way i see it now. is that. the space of the universe may be infinite. ever growing/expanding. but the mass of the universe if finite :) which is pretty simple to understand :)

Also. i think we are going about this the wrong way. "finite or infinite?" how bout. what changes if it is "finite or infinite"
how does this change our day to day lives?"
how does this change how we are to view the universE?"

If this universe is infinite. then where do all the other universes fit in?? [ quoting "stephen hawkings theory on everything ] it is possible for there to be thousands, millions of universes all stacked together in a donut shape.. i don't know if anyones seen it. but.. if there are other universes... will our universe meet them one day? if so what happens?

uhm ok that was kind of off track. just a random thought.. also. measuring the universe would be impossible. because by the time u have measured it. it is about a million years infront of us...

 

[TalonD]

if a flat or open surface can be infinite, I don't see why a curved surface can't be infinite. In that case the radius of curvature mentioned earlier would be infinite.
And of course we still don't know.

 

[danda22]

if a flat or open surface can be infinite, I don't see why a curved surface can't be infinite. In that case the radius of curvature mentioned earlier would be infinite.
And of course we still don't know.

hmm. well. an open flat surface can be infinite because it will never touch itself.. uhmm.. i don't know if u mean curved as in a sphere or curved as in a cylindeR?

 

[danda22]

oh actually u r right.. sorry. lol. i was just looking at the shape as in the outer layer.. i think maybe for it to be inifinite it would look more like a dandelion

 

[Pjpic]

The definition of finite, seems to be from "finire - to stop". So, it would appear that something finite would have to stop.

Maybe the difficulty in understanding (which I share with you) stems from the definition of terms. I have found these instances that might give a clue.

-- George Cantor seems to have added some sublties to the definition of infinite.

-- There is math construct called Gabriel's Horn (infinte surface surrounding a finite volume)

-- "Intrinsic curvature" seems to talk about how you don't have to deal with what a curve is embedded in.

-- I read that questions of this type are not helpful so they are not worked on.

-- There's the difference between an actual and a potential infinitity

-- I seem to find similar problems at the infitessimal scale too. Questions that deal with where does a particle end and empty space begin.

-- There could be some sort of 'math trick' involved. (a variation on Gabriel's horn)

-- The problem of finere doesn't seem as difficult if you're thinking how many dimensions there are if the "highest' one isn't curved. But it always seems difficult when thinking about time.

-- There is something(?) in relativity where the closer you get to infinity along one axis you get further from along another.

So, sorry about taking the space (and/or time); but if you find a amature level book on the subject - that'd be great.

 

[TalonD]

There are more than one kind of infinity and some infinities are bigger than others. for example the infinity of all integer numbers is smaller than the infinity of all fractions because there is not a one to one correlation between the two. There is the infinity of all points on a line segment also, and others. Those are abstractions, so one question I would have is, is it possible for something physical like the universe to be infinite? If it is possible to concieve of something physical being infinite then there should be no problem with having a sphere who's radius and diameter are infinite, then multiply by pi and you find an infinite circumference. Now in the case of our universe. If it were a sphere surface with infinite size, it would be identical from our point of view to an infinite flat plane because the radius of curvature would be infinately long. So the only way we can know if our universe is flat, open or closed is to measure the critical density. which is currently pretty close to 1 but still undetermined. So if we are able to narrow that down and say for certain that the universe is curved then it 'has' to be finite because if it is infinite then the radius of curvature would be so great that it would be indistinguishable from flat.

at least that's the way I see it, of course I could be wrong!

so... critical density is either less than 1, greater than 1 or exacltly 1. In which case, if we can narrow it down to one of those 3 possibilities, then we will know if it is open, flat, or close. And that depends on future measurements so we still don't know

Right?

 

[Pjpic]

If it is possible to concieve of something physical being infinite then there should be no problem with having a sphere who's radius and diameter are infinite,

This is over my head but if both the diameter and radius are infinite wouldn't the diameter have to equal the radius. And if the only the diameter was infinite wouldn't the circumference have to be greater than infinity?

 

[Ike47]

I don't see why curvature requires a finite space. Hyperboloids and paraboloids are infinite curved shapes, so why couldn't a curved universe be infinite as well? That doesn't mean that the universe can't be curved and finite of course, but just that the one doesn't force the other. Of course, I may be wrong. :)

 

[TalonD]

If it is possible to concieve of something physical being infinite then there should be no problem with having a sphere who's radius and diameter are infinite,

This is over my head but if both the diameter and radius are infinite wouldn't the diameter have to equal the radius. And if the only the diameter was infinite wouldn't the circumference have to be greater than infinity?

I don't think it's meaningful to draw a distinction between radius and diameter like that. if you draw a circle there is one length acros it, that is diameter. Radius is just a subset of that disance. it can be used mathematically to determine circumference. I think if any of it is infinite then all of it is equally infinite. But as I said earlier, there is a such thing a some infinities being larger or smaller than other infinities.

Comparing infinite radius to infinite diameter seems almost like the old paradox of an arrow shot from a bow can never reach it's target because first it must travel half the distance, then half the remaining distance etc. etc. etc... ad infinitum.


but again, wheather our universe is curved, flat, finite or infinite has to do with the critical density... I think..

 

[Ike47]

...

but again, wheather our universe is curved, flat, finite or infinite has to do with the critical density... I think..

Sounds just like me, lol. I should put a disclaimer into a sig saying all my posts may be incorrect.

 

[phmovies101]

I have thought about this question all the time. I'm not PhD. Physicist, but I like to think about things like this. I'm sure if there is fact, or at least not yet, but I believe that this question brings about a belief in people. You have to decide what you think is the most reasonable.

My idea on this is not scientifically based, but maybe it could work. I believe in the big bang theory, and I believe in the finite universe. However, I do not like to believe in the fact that the universe is flat-ish. I think the objects in space are pulled around a center where the big bang was suppose to happen. Maybe there is an intense field of gravity and was produced by the massive explosion of the condenced particles. The area of space surrounding the site of explosion has no matter or particles. The force acting on the celestial objects is to far away to pull it toward the center. The universe is definitely expanding. If you can imagine on of those glass balls that has the tesla coil on the inside and shoots off beams of electricity. The Objects in space are dependant on the center. Thier rotation creates a sphere. Objects move infinitely until they are acted on by other forces. Matter is pushed outwards, but at the same time, rotating due to the intense amount of energy.

P.S. I don't expect you to believe this, but I did the best I could.

 

[Quisquis]

If it is possible to concieve of something physical being infinite then there should be no problem with having a sphere who's radius and diameter are infinite,

This is over my head but if both the diameter and radius are infinite wouldn't the diameter have to equal the radius. And if the only the diameter was infinite wouldn't the circumference have to be greater than infinity?

I have an experiment for you to try that might help you understand how if the radius of a sphere extending to infinity means that you have created a flat surface:

Take a piece of paper and roll it up into a cylinder. This cylinder has a defined radius. Now take the edges of the paper that you just rolled together and pull them apart. As you pull them apart, imagine that there's more paper filling in the gap so that you are creating a larger and larger cylinder. The radius is getting larger in your cylinder... now as you get closer and closer to having a flat piece of paper, your radius is expanding more and more... once you have a flat piece of paper again instead of a cylinder, you've reached the point where your radius has approached infinity.

So, in conclusion, if you have ANY curvature at all to your sphere, you have a finite radius.

Hopefully that clears things up for ya.

EDIT: I hadn't thought about this like that until now. That's sort of an interesting concept to think about actually. Thanks for giving me the chance to fire off some neurons. :-D

 

[eha]

space is endless in 3D, our universe has boundaries, there might be other universes, maybe there are so many different universes and they all occupy a certain volume within endless space. this is my opinion, frankly.

 

[Pjpic]

space is endless in 3D, our universe has boundaries,


That seems reasonable. Because, if It is not endless how could we ever be sure there wasn't something else past the boundary where nothingness started or past where a particular discipline was focused.

 

[x→∞]

Is the universe finite? (= implies a "Beyond")
Is the universe infinite? (= seems nonsensical, and counter-intuitive to "Big Bang" theory)

Finite does not imply boundary. Infinity and unbounded are two different concepts.

For example consider a spherical object. If you are a two dimensional creature embedded in the surface of a sphere, and you start moving in the same direction (you can only travel forward or backward and up and down since you are 2D), you would not find the end of the sphere, and since you are a two dimensional creature you would not have a brain to see a 3D object (because you don't need to), you would feel that you are traveling in a straight line. See that the area of the sphere is finite.

Now you are a 3D creature embedded in a 3D world. We would not see the boundaries of the universe just like the creature on the sphere. Only a higher creature outside our 3D universe, in a higher dimension, would be able to see the "finiteness" of our universe.

Therefore, we have no way of telling, we can only guess.

Even if traveling infinitely fast, you may or may not be able to reach a boundary where time and space would cease to exist. You could not go past this boundary because on the other side there is no time, and there is no space.

 

[Pjpic]

Finite does not imply boundary. Infinity and unbounded are two different concepts.

---- I don't quite understand why infinity and unbounded are different concepts. Because, in my understanding, infinity means 'without end' and unbounded means "without an ending".

See that the area of the sphere is finite.

--- In the example of a two dimensional creature living on a 3 dimensional sphere, the boundary is that which prevents the creature from moving off the surface of the sphere (that which prevents movement within the space which it is embedded). Even if the creature is not aware of it, it is still a boundary.


Even if traveling infinitely fast, you may or may not be able to reach a boundary where time and space would cease to exist. You could not go past this boundary because on the other side there is no time, and there is no space.

--- If there is a boundary that forms the end of the universe, it deals raises questions of nothingness (I think I read that constructive geometry considers 'nothing 'to be the inverse of 'infinte'). For example on the micro scale "nothingness" is often thought to separate two particles. Could that also be the case when thinking about a potenial nothingness beyond our universe (that the nothingness just separates us from other universes)?

 

[Chiclayo guy]

To a layman like me with absolutely no science background or training it seems incredibly simple. Space is a void. It is eternal and infinite. I’m content with that description. I don’t need to struggle with questions of where it came from or how it came about or what existed before. It simply is and always was. The universe is the physical matter occupying space. As I understand it, that physical matter all resided at one small central point some 14 billion years ago and has since expanded. I don’t have to deal with defining “small” or where that central point is/was located or how the physical matter got there. I have an image of both “small” and “central point” and am content with that. It’s a little harder for me to conceptualize matter as being eternal. As I see it space is ‘nothing’ and nothing doesn’t require a beginning or an end, but matter is ‘something’ and all the matter I’m familiar with has a beginning and an end, or at least changes form dramatically. Anyway to me it seems that whatever path is taken will ultimately lead to infinity and eternity because questions like “what was/is before or beyond ?” can be asked for…well…eternity.

 

[x→∞]

--- If there is a boundary that forms the end of the universe, it deals raises questions of nothingness (I think I read that constructive geometry considers 'nothing 'to be the inverse of 'infinte'). For example on the micro scale "nothingness" is often thought to separate two particles. Could that also be the case when thinking about a potenial nothingness beyond our universe (that the nothingness just separates us from other universes)?

By micro scale do you mean the Planck length? I understand what you are saying, you're right. All together, an infinite amount of seeming-to-us as being nothing (in reality being extremely tiny amounts of something) may add up to be quite a large amount of something? Or would the quantity/mass of that something be infinite as well, since it is found in an infinite amount of space, and there is an infinite amount of its particles?