# Is Universe Infinite?

Hi everyone! My question is: is the universe infinite? If so, can you prove it? Web Sites with information might be useful.
Thanks
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Commented:
Something that needs to be clarified as far as dimensions goes too.  It is often explained that gravity is a curvature in 3D space, just as a line can be curved in 2D space and a rubber sheet can be curved in 3D space.

Not so.

Most attempts you see on the web and in popular books to explain it like that a a load of codswallop.

The above are examples of "extrinsic" curvature, whereas Einstein proposed an "intrinsic" curvature, and that is quite a different thing.

This geometry (actually Einstein borrowed it from math Bernhard Riemann (1826-1866)), leads to a positively curved, finite, but unbounded space.

What may you ask does this mean?

Well it nicely avoids both the problems of finite space and infinite space as they were traditionally conceived, and this is an IMPORTANT point that is always misunderstood.

With extrinsic curvature, curving something straight pushes it up to one more higher dimension.  So extrinsic curvature of 3D space would cause 4D space to be occupied, and this is not what Einstein proposed at all.

Einstein proposed to use a geometry where a line could be curved whilst remaining one dimensional, where a plane could be curved whilst remaining 2 dimensional, and a volume could be curved whilst remaining 3 dimensional.  Intrinsic curvature has nothing to do with any kind of higher dimension.

We can discuss the 2D case to make the explanation easier.

A two-dimensional positively curved surface with intrinsic curvature looks like a two dimensional flat surface.  But because of its intrinsic curvature, the geometry of objects drawn on this flatland is a little different than a zero curvature surface.  For example it is possible to draw a triangle with three rightangles in it, (just like you can on the surface of a ball).  Just remember that it is not the surface of a ball, even though in many ways it behaves like one.  Straight lines on this surface are just that, straight lines on this surface.

And even more interestingly, this kind of plane surface can be a finite size, in the same sense that an extrinsic surface like a ball has a finite size, and it does not have to have a center either.  So as you go for a walk over this flat surface, your perspective might be like being on a ball in some ways, even though you are not.

Then the real questions are just what do we need to believe about this surface?  Do we need to believe that it has finite size just as the surface of a ball has a finite size?  Do we need to believe that it has no center just as the surface of a ball has no center?

We could let our imaginations run wild at this point.  Who says that the universe has to obey our narrow ideas of geometry?  What if we had the kind of surface that we could reason that it had a circular boundary x distance away from where we were, but like the red queen episode in alice in wonderland, no amount of travel would get you any closer, in other words all of the points we stand at cause us to come to the same conclusion, we are no closer to the edge. In other words we give up the property of "closeness" between any two points, or to put it another way, all points can be proven to be equally close to eachother?  These are perfectly reasonable suppositions.

Back to the flat magic paper again, what would it mean to draw non overlapping circles on this magic paper?  Perhaps these are parallel lines ?  Should we understand that when you go up to three dimensions the orbits of planets must be parallel lines in Einstein's intrinsically curved 3D space?

Intrinsic curvature can be more exotic that positive only.  What if each point of 3D space had intrinsic  "saddle" curvature?  and as you moved about, the saddle property remained the same.  Then there would be the possibility of the opposite saddle too.  These saddle universes would be infinite.

Given that we have an intrinsically curved surface,
we are in fact quite free to extrinsically embed it into  quite a different geometry.

I am reminded that the axions of arithmetic are being shown to be fairly arbitrary.  Maybe geometry is the same.

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Commented:
From the point of view of an engineer THIS GALAXY is infinite!  The reason is that
engineers work with dimensions that can be reproduced in physical, mechanical designs.
Physicists and astronomers would disagree, but they can deal only in approximations of
stellar distances and times.  Now Quantum Mechanics gets into the act and things get
even more confusing.  Here is a current thread that goes into considerable detail, with

http://www.experts-exchange.com/jsp/qManageQuestion.jsp?ta=philos_relig&qid=20309872

Personally, I don't plan to hold my breath until Hawking, Penrose and others come up
with a "Theory of Everything".  My reasoning is based on the impossibility of developing
any mathematics that can start at a fixed location and map any remote location that is
far distant in space and time. In my view, the best that could be developed would be a system
of moving frames of reference. Even that could not really cope with the massive space
curvature produced by gravity.
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Commented:
This is the most credible link that I could find:

http://www.astro.ucla.edu/~wright/infpoint.html

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Commented:
I can't remember which seventeenth centuary personage it was, but he simply asked why it is dark at night?

If the universe was infinite there would be enough stars to light up the sky at night like at daytime. So he concluded that the universe was not infinite.
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Author Commented:
BigRat: If the universe is not infinite, then is it contained inside something? Do the universe boundaries exist? If so, Where are them?

hmmmmmm, interesting. But then, are there any experiments that verify or at least make scientists believe, that the universe is infinite? I find it hard to believe that we are part of something which... is infinite. How can this be possible? Do boundaries exist? or they ar just a product of our mind? Do we have to realize that there is nothing imposible?
And I have another topic. If the universe is infinite, how can it be in expansion!!?? HELP!
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Commented:
I provided a link to a site created by an astronomer at UCLA in Los Angeles.  If you
look through his web pages you will see that he answers your question.
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Author Commented:
pleasenospam: i looked at the web pages. They are quite good, but they have a lot of info. I'm watching them. Meanwhile, i still continue looking up for info.
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Commented:
I know a mouse who has spent the last years running around a Moebus Strip. (It has "77" written on it and she's a fan of Cookie). The Stip IS finite, yet the mouse hasn't stopped running.
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Commented:
a) infinite
b) proof1 is that otherwise it would be boring, suffering inevitable repetition, however long that may take to achieve
c) proof2 is that choices may be made, introducing a variety that can keep any repetition from ever occuring
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Commented:
BigRat,
I first bought that, why is sky dark. Later.. I dunno

Counter argument is that the amount of light reaching us is less and less and less as each circumferential measurement is accumulated from further distances.

Simlilar perhaps to fractional concepts that grow, continually, but by so little it never achieves being overwhelming.

.3
.33
.333
.3333
.33333

keep adding an additional decimal value, the number keeps growing, but never makes it to = 1.  Or 100, or anything else one could guess from an infinite growth pattern. So the lumens do dot achieve the overriding brilliance at night. Just enough to barely see well enough to walk a beaten path, and still a lot more than the default provided spelunkers. So they say.
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Commented:
From the link I provided above:

Why is the sky dark at night?

If the Universe were infinitely old, and infinite in extent, and stars could
shine forever, then every direction you looked would eventually end on the surface
of a star, and the whole sky would be as bright as the surface of the Sun. This is
known as Olbers' Paradox after Heinrich Wilhelm Olbers [1757-1840] who wrote about
it in 1823-1826 but it was also discussed earlier. Absorption by interstellar
it absorbs within a few minutes, which is much less than the age of the Universe.
However, the Universe is not infinitely old, and the expansion of the Universe
reduces the accumulated energy radiated by distant stars. Either one of these effects
acting alone would solve Olbers' Paradox, but they both act at once.
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Commented:
>>BigRat: If the universe is not infinite, then is it >>contained inside something? Do the universe boundaries >>exist? If so, Where are them?

Just because it is finite, does not mean it has to be inside something. Similarly, being finite does not imply a boundary. The usual way to put it is that spacetime only exists inside the finite universe, there is no outside.

The universe does not work in an intuitive way, why should it.

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Commented:
SunBow: The "why dark at night" is a simple question suggesting a relatively simple answer. Whether such an answer exists I don't know. I have seen several web sites trying desparately to explain the expansion and the "finiteness" (or even infinite but enumerable) and I must say they all sound very convincing if not complicated. The mouse analogy is simpler.

The "appending 3s behind the dot" is analogulous to "the critical density" (you can choose a value according to your argument).

gbentley: I don't quite see what you are trying to quote from me? I think that the universe is far more banal than one thinks.

If you ask me I suspect that the universe is finite yet extremely large. I also suspect that thermodynamic rather than quantum effects regulate its workings. The expansion is there simply to make it work.
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Commented:
Try to look far in universe with most powerful telescope you can find follow the link:http://oposite.stsci.edu/pubinfo/pictures.html

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Commented:
What I was talking about was the sequence of "is not infinite" followed by "must be contined inside something". It doesn't neccesarily follow. Something can be finite, but not be contained in anything.

Gordon
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Commented:
BigRat + pleasenospam, "why dark at night"..

The same (or similar) counter argument can be applied to (and has been, pardon my poor memory on names for quoting) the "every direction you looked would eventually end on the surface" as for the lumens. That being, that there is so much space, distance, between the lit objects, there would ever remain gaps as the objects further and further out get smaller and smaller (in appearance on the ever distant earth). So the sky would never be painted in entirety, and the gaps permit the darkness

> "If the Universe were infinitely old,"
> "However, the Universe is not infinitely old,"

hmm, I lose something there. First the age is a question, then it is an assumed given. I missed the connecting up there from the source.

gbentley,
> "universe does not work in an intuitive way, why should it."

yeah, why should it?
but it likely is working intuitively, to one who discovered everything about it. while we admit to having some further discoveries to make, then we must accept that the intuitiveness may elude our capacity and our capability.

BigRat,
> analogulous to "the critical density"
not sure, Ive lost that train of thought, the meaning, but
> (you can choose a value according to your argument).
For sure, I tried to own up in the thread, but as suppl. info, I considered .6666667, for example, but contrived that it would be an unnecessary distraction, and given continued rounding, be too close to possible value 1. How the scientific argument, papers were phrased, I've forgotten.
> "The mouse analogy is simpler"
Well, the Moebus Strip, anyway, for sure. (the remainder eludes me). I'd forgotten name (Moebus) but the strip remains a good visual for me on an infinity concept self-contained, w/o borders.

schachmann,
ans = Finite
> "is far more banal than one thinks"
yeah, I 2nd BigRat there, with what we have found to date, there is simply too-oo much consistency for any closed or open system to accomodate a completely unbounded randomness of infinite possibilities. I'd be tempted to say it is too boring, despite the excitement of discoveries and interesting conjectures. But the term 'banal' seems a better fit.
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Commented:
What is possible, or even probable, is that the rules of the game might be changing
while we observe.  The change might not be readily apparent, but we have no way
of proving that such is not the case.  Intuitively, it doesn't seem plausible, but
most of what we observe in the sky isn't plausible by any
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Commented:
"the only constant around here is change"
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Commented:
It has been expanding for about 4 billion years.  The dating of rocks supports that as does a ton of other evidence.  That means it is 4 billion light years across.  Assuming it doesn't have one of those geometries like a mobius strip that turns back on itself, then it that is the radius.
The geometry question is interesting - there is a serious attempt to look at opposite parts of the sky to see if we can see the SAME constellations, actualy in two places at once.  Like if you go far enough in one direction you will come back the other way.  This would make the case for infinite a lot weaker.  Sorry no web ref but I will try find it.
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Commented:
>gbentley,
> "universe does not work in an intuitive way, why should it."

>>yeah, why should it?
>>but it likely is working intuitively, to one who >>discovered everything about it. while we admit to having >>some further discoveries to make, then we must accept >>that the intuitiveness may elude our capacity and our >>capability.

My use of "intuitive" means in a way that makes sense to people. If it eludes our ability to understand it isn't intuitive.

Look at the stranger behaviours one finds at sub-atomic scales. That isn't the way the world appears to work "intuitively". One expects "intuitively" that an object can have only a single location, and it's either there or not. At the sub-atomic level, things don't work that way.

Regards
Gordon
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Author Commented:
What can be finite and not be contained inside something? And, If it is finite, wouldn't you be able to reach the end of that something?
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Commented:
http://www.m-w.com/

One entry found for Möbius strip.

Main Entry: Mö·bi·us strip
Pronunciation: 'm[OE]-bE-&s-, 'm&(r)-, 'mO-
Function: noun
Etymology: August F. Möbius died 1868 German mathematician
Date: 1904
: a one-sided surface that is constructed from a rectangle by holding one end fixed,
rotating the opposite end through 180 degrees, and joining it to the first end

Illustration:

http://www.m-w.com/mw/art/mobius.htm

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Commented:
http://www.m-w.com/

One entry found for Klein bottle.

Main Entry: Klein bottle
Pronunciation: 'klIn-
Function: noun
Etymology: Felix Klein died 1925 German mathematician
Date: 1941
: a one-sided surface that is formed by passing the narrow end of a tapered tube
through the side of the tube and flaring this end out to join the other end
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Commented:
Nice picture thanks.  The mobius strip is a real physical object with has one face and one edge only.  Try this - make one with adding tape and glue.  Then draw a line along the centre of the strip with a marker.  Eventually you will get back where you started, because it only has one face.
Now it gets interesting.
Take some scissors and CUT the strip completely in half by following the line you made with the marker.

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Commented:
Assume you live in a two dimensional universe. If that universe is actually structured like a sphere, then there is only so much of it(it is finite) but no matter how far you travel (in your two dimensional world) you will never reach a boundary. Similarly, it doesn't have to be contained in anything.
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Commented:
kaller2>It has been expanding for about 4 billion years.

One year it is 4 billion. Then another it is finve.
Now objects are flying away fast (or were) at about 20 billion ago.
Some have it at thirty bills by now.

In the last century, for every few years of humankind, the universe ages by a billion or two.

Could it be,
we are such bratty children
that it is our fault?

Finite vs Infinite => must be infinite. Age increases faster than a sub-set member = human
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Commented:
Let's back up a minute.  You can't say that anything is "infinite" without asking
what is being measured and what is the measuring "stick". For example: If what is being
measured is the TIME it takes to get from "here" to the "edge" and if the measuring
"stick" is something less than the speed of light (or even the speed of light) then we can
NEVER get to the "edge".  That makes it "infinite", by definition!
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Commented:
Think about the spherical surface, you never reach the edge, but it is not infinite.
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Commented:
"then we can NEVER get to the "edge".  That makes it "infinite", by definition!"

Strictly speaking not. This is the difference between open and closed sets. The set of real numbers -1<x<1 is an openset since it does not include its boundaries. The set -1<=x<=1 is closed since it does. Both are sets of un-enumerable elements, ie: (loosely) infinite in size.
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Commented:
Yes, thanks BB, when I posted the 4 bill I realised I made a mistake but we can't edit these posts :(
I never was that found of inflation, pay-rises I can relate to.  4 bill is just our solar system perhaps, your figure sounds closer.
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Commented:
I made another clunker when I said radius, maybe diameter was a beetr word, but then that kind of assumes a topology maybe.
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Commented:

the universe is finite for the human brain,

where are its boundries?
the boundry is at the limits of your imagination.

people think about the universe as a physical place which can be measured in human terms. no.

the universe is infinite in infinite ways.

its really sad to see scientist applying their earthly laws of science in an attempt to understand the universe.

read the bhagavat gita for more on life and the universe.

those science guys are just stuck at studying one (the physical) dimension when there are infinite other dimensions.
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Commented:
Um, sorry, but physics has given mythology a beating.
For example the shape of the universe as discovered by Einstein doesn't allow for any kind of universal fluid - period.  Anything "cosmic" like cosmic energy, magic fluid, etc, spiritual rays that enter the top of your head, pyramid power, all of these things presume some kind of fluid and as such are totally outlawed concepts under relativity.  Unfortunately most forms of mysticism rely on beliefs in various kinds of invisible life giving fluids.

And your use of the word "dimension" is so wonderfully vague as to be practically meaningless.  As the nature of physical reality is clarified thare are fewer and fewer places to retreat these concepts to, unfortunately.
Every inch of science has had to be bitterly fought with the clerics and religious beliefs of mankind who stubbornly claimed ownership of every abstraction, and one by one they have had to let them go as the intellectual bankruptcy of theology was exposed.
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Author Commented:
Kaller2:
I liked your comment very much, though i will have to read it again to understand what you are saying. At last i found a good explanation for the problem. And the open ending was good also.

"Intrinsic curvature can be more exotic that positive only.  What if each point of 3D space had intrinsic  "saddle" curvature?  and as you moved about, the saddle property remained the same.  Then there would be the possibility of the opposite saddle too.  These saddle universes would be infinite."

I don't think i quite get this part. Cuold you explain the concept of saddle curvature?
Thanks

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Commented:
>  Cuold you explain the concept of saddle curvature?

Hyperbolic?
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Commented:
Yes.  You can extrinsically bend a sheet into two directions like a saddle.  Then there is one point of the saddle that has the unique property of being bent in two directions.
What if we forget about the rest of the saddle and construct a line or a surface or a space just using lots of points just like the saddle point.  We could also make an oppposite space using the inverse saddles.
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Commented:
There are other clues that you might be living in a wierd geometry.  For example when the relationship between points on a plane is distorted.  I already mentioned that you can have a flat surface with the properties of the surface of a sphere.  Then you could make a triangle with three right angles.  And you have to be very careful when trying to define what you want to mean by the concept of parallel lines.  Another give-away might be when you compare the length of the circumference of a circle to its diameter.  What if you found that the circumference divided by the diameter was not pi (3.14259...) but it had a value of exactly 2?  That is the distance from the equator to the pole on a ball, so you would begin to suspect your magic plane surface had some more "ball-like" properties, or you would look for a class of objects that had that property that you knew about, and learn about them some more.  You might even get interested in dougnuts, mobius strips, and and Klein bottles.
Topologists are mathematicians who try to classify these kinds of things and see what minimum sets of assumptions they need to assume to derive different geometries.
one of my favorite theorems (although I cannot claim credit for it) is to imagine a surcface is hairy, and then consider its "comb-ability" and looking at what partings result.  For example you can comb a hairy doughnut but you cannot comb a hairy ball.
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Commented:
Imagine that the flat-earth society was actually right all along.

Imagine that the flat earth retained the geometric surface properties of a sphere.

Imagine that the flat-earth horizon was unreachable.

Imagine that the parallel lines of longtitude became more curved, the further away from you they were.

Imagine that the parallel line at the horizon had infinite curvature as it circled a hypothetical pole.

Imagine that all lines of equal intrinsic curvature at a given point, (think of the globe) were therefore actually moving in some sense at that point.

Then you begin to get the picture.
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Commented:
Oops sorry missed out a word:-

Imagine that all lines of equal intrinsic curvature at a given point, (think of the globe) were therefore actually moving *together* in some sense at that point.

(This kind of thinking led Einstein to conceive of gravity and accelerative effects in metrical terms, except that his "flat earth" starting point was already the 4D spacetime of special relativity))
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Author Commented:
YOu have the points kaller
Excellent explanation, though i will have to work with it for a while
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Commented:
Yeah, but in the end can't you reduce that to brief:
yin/yan?                   (coin/symbol)
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Commented:
For the PAQ, note that there are MANY interactive applets on the Net which
allow you to track various geometries that behave as kaller2 has suggested.
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Commented:
>  two-dimensional positively curved surface with intrinsic curvature looks like a two dimensional flat surface

"The universe is flat"
(as below, so above)
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Commented:
<< If the Universe were infinitely old, and infinite in extent, and stars could
shine forever, then every direction you looked would eventually end on the surface
of a star, and the whole sky would be as bright as the surface of the Sun. >>

Stars don't shine forever but even if they did, there is a limited # of them that are close to us. I'm am pretty certain that there is a star in every direction you can look at. You just don't see them all just yet. Most of them are just too far away that no telescope are light sensitive enough to pick them up. Just look at the Hubble telescope deep space pictures and just start counting the galaxies. We will eventually see a lot more of them as technology improves.
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Commented:
ditto the problem of distance, producing additional lumens at diminishing returns.

This is like taking a number like:

.12

and appending digits "12" repetetively, beginning:

.12
.1212
.121212
.12121212
...

While number result keeps getting larger, it never really gets that big, even if you perform same additive process infinitely.
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Commented:
Assuming the law of isotropy.
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