# Is space Infinite? **URL:** \ **Category:** Factual Questions\ **Created:** [December 1, 2011, 2:57am UTC](https://boards.straightdope.com/t/is-space-infinite/604657 "2011-12-01T02:57:13Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![Candyman74](https://avatars.discourse-cdn.com/v4/letter/c/ad7895/32.png) [@Candyman74](https://boards.straightdope.com/u/Candyman74)\ **Post date:** [December 2, 2011, 10:54pm UTC](https://boards.straightdope.com/t/is-space-infinite/604657/21 "2011-12-02T22:54:30Z")
> [@Hari\_Seldon](#): > > Space can be flat and still be finite, without boundary. > > To see how this is possible, I will start with a two-dimensional flat space without boundary. You normally think of a torus as curved, but it can be given a flat geometry. One way of thinking about this is as a square with the top and bottom edges identified (thought of as identical) and the right and left edges identified. Now do the same to a three dimensional cube with the front and back face identified, the left and right face identified, and the top and bottom face identified. (I hesitated whether to say face or faces in this description. The English language is not quite up to describing this situation.) > > If you have ever played go on a toroidal board you will understand what I am saying. There is an instance of the smallest safe group that consists of 10 stones arrayed in the proper configuration using all four corners. There is no safe group with fewer than 10 stones, since the board actually has no edges or corners. Finite but without boundary. A hyperbolic geometry necessarily has finite volume, but it could have infinite extent. A spherical geometry has finite extent but no boundary. I know exactly what it is you’re trying to say; but even knowing that, your description confused me! You somehow managed to make it sound even\* more\* complex! I don’t think it’s gonna help most people understand the point (though I should acknowledge the possibility that it’s just me, and that I’m far dumber than average!) It’s hard to describe stuff. 🙂 ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [December 3, 2011, 12:11am UTC](https://boards.straightdope.com/t/is-space-infinite/604657/22 "2011-12-03T00:11:37Z")
> [@](#): > > A hyperbolic geometry necessarily has finite volume, but it could have infinite extent. There’s no reason a hyperbolic geometry couldn’t have infinite volume, and in fact the simplest topology on a hyperbolic space is infinite in volume. ---
**Author:** ![JWT\_Kottekoe](https://avatars.discourse-cdn.com/v4/letter/j/3ec8ea/32.png) [@JWT\_Kottekoe](https://boards.straightdope.com/u/JWT_Kottekoe)\ **Post date:** [December 3, 2011, 3:04am UTC](https://boards.straightdope.com/t/is-space-infinite/604657/23 "2011-12-03T03:04:14Z")
> [@Hari\_Seldon](#): > > If you have ever played go on a toroidal board you will understand what I am saying. Or if you are old enough to have played one of the original space war games, which took place in a toroidal, 2D universe. ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [December 3, 2011, 3:24am UTC](https://boards.straightdope.com/t/is-space-infinite/604657/24 "2011-12-03T03:24:44Z")
> [@coremelt](#): > > for practical purposes yes, because the latest estimate is that the size of the universe is expanding many times faster than the speed of light. Huh? ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [December 3, 2011, 3:36am UTC](https://boards.straightdope.com/t/is-space-infinite/604657/25 "2011-12-03T03:36:15Z")
> [@hibernicus](#): > > I never heard this until it was mentioned several times recently on the SDMB by knowledgeable people. > > I had always understood that the Big Bang Theory posited a very small universe at the very start. Not just very dense, as you are saying now, but tiny. > > Can I ask you, is this a new way of thinking? Or has it always been part of the Big Bang Theory that I have consistently misunderstood? > > I am a bit mystified because I have read numerous popular science books on this subject over the years and somehow missed this very important point. Seconded. Mind was blown by the other thread. I’ve never heard of this idea before. And apparently, it’s not just some idea–it’s _the_ idea. Popularizations, AFAIK, never explain this correctly! ---
**Author:** ![Mosier](https://avatars.discourse-cdn.com/v4/letter/m/7ea924/32.png) [@Mosier](https://boards.straightdope.com/u/Mosier)\ **Post date:** [December 3, 2011, 3:41am UTC](https://boards.straightdope.com/t/is-space-infinite/604657/26 "2011-12-03T03:41:43Z")
> [@BigT](#): > > No they can’t. The edge of the balloon is wherever the outside happens to be located. All objects with volume have an edge. Okay mister smartypants, the two dimensional surface of a balloon can expand without having an edge. ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [December 3, 2011, 3:42am UTC](https://boards.straightdope.com/t/is-space-infinite/604657/27 "2011-12-03T03:42:38Z")
> [@JWT\_Kottekoe](#): > > The latter. For a universe that is flat or hyperbolic, the model has always been that the size was infinite, with a density that diminshes with time. For a closed universe, the story is different. In that case, at any given point in time, the universe has a finite size. If you extrapolate back to zero (the singularity), the size is zero. Of course we can’t extrapolate all the way back, because the current laws of physics can’t explain the singularity itself. Serious yet horrifically flaky sounding question: If the universe is closed, is it necessarily true that its size is increasing, or could the physics be interpreted instead as involving everything in the universe shrinking? (If you’re floating next to me in empty space, and we’re both shrinking, then we will appear to each other to be receding from each other in the sense that you will be a greater and greater number of armslengths away from me.) ---
**Author:** ![Mosier](https://avatars.discourse-cdn.com/v4/letter/m/7ea924/32.png) [@Mosier](https://boards.straightdope.com/u/Mosier)\ **Post date:** [December 3, 2011, 3:46am UTC](https://boards.straightdope.com/t/is-space-infinite/604657/28 "2011-12-03T03:46:45Z")
Follow up related question: Is it understood that there are, or must be, two particles in the universe which are further apart from each other than any other combination of particles? If there is a finite amount of matter in the universe (which seems likely), it MUST be true that there are two particles which are further away from each other than other combation of particles. If that is the case, why couldn’t the two furthest-apart particles be thought of as the “edges” of space? ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [December 3, 2011, 3:51am UTC](https://boards.straightdope.com/t/is-space-infinite/604657/29 "2011-12-03T03:51:45Z")
Here’s what I think JWT Kottekoe is saying. Nothing can become infinite. Things either are infinite or not. Therefore, if the universe today is infinite, then it was always infinite. Even if the universe started in a singularity, it went immediately, without any transition, to infinite. (Similar to how photons go from creation to moving at the speed of light without transition.) If the universe is finite, OTOH, then it was always finite, and always will be. No matter how long it expands, it can only become a larger finite size. Which is it? It all depends on the curvature of the universe. A flat universe, which as I said is what current understanding is, corresponds to an infinite universe. Therefore the universe always was infinite and never small, even though the parts of it we can see today - the observable universe - must have been smaller earlier. This is completely contrary to common sense, because all infinities are contrary to common sense. Another reason to abandon common sense, all ye who enter physics. Mosier, the answer to your question is that no such particles can exist. Every particle can be thought of as the center of the universe and thus is equally far away from the end of the observable part from its reference frame. ---
**Author:** ![Naxos](https://avatars.discourse-cdn.com/v4/letter/n/50afbb/32.png) [@Naxos](https://boards.straightdope.com/u/Naxos)\ **Post date:** [December 3, 2011, 4:03am UTC](https://boards.straightdope.com/t/is-space-infinite/604657/30 "2011-12-03T04:03:51Z")
> [@'/v\\@l](#): > > [!3/V+!+;14517015’]Is space Infinite? “Space” is has not been precisely defined yet by our physics knowledge. We don’t know what “space” is. You’ll have to rephrase your question. ---
**Author:** ![Mosier](https://avatars.discourse-cdn.com/v4/letter/m/7ea924/32.png) [@Mosier](https://boards.straightdope.com/u/Mosier)\ **Post date:** [December 3, 2011, 4:44am UTC](https://boards.straightdope.com/t/is-space-infinite/604657/31 "2011-12-03T04:44:31Z")
> [@Exapno\_Mapcase](#): > > Mosier, the answer to your question is that no such particles can exist. Every particle can be thought of as the center of the universe and thus is equally far away from the end of the observable part from its reference frame. I am not limiting my question to the observable universe or a particular reference frame, unless “universal” counts as a reference frame. Are there two particles in existence that are further away from each other than any other combination of two particles? ---
**Author:** ![DHMO](https://avatars.discourse-cdn.com/v4/letter/d/ecc23a/32.png) [@DHMO](https://boards.straightdope.com/u/DHMO)\ **Post date:** [December 3, 2011, 8:22am UTC](https://boards.straightdope.com/t/is-space-infinite/604657/32 "2011-12-03T08:22:39Z")
> [@Mosier](#): > > I am not limiting my question to the observable universe or a particular reference frame, unless “universal” counts as a reference frame. Are there two particles in existence that are further away from each other than any other combination of two particles? As currently understood, and very well explained above, _any particle_ in existence will find, from its point of view (its “frame of reference”) that it is at the center of an infinite number of other particles, which go off in every direction to infinity. This applies to _any particle_ which you can identify, so it is not possible to locate two particles which are farther apart than any other combination of particles. This is precisely related to the inadequacy of analogies to make reality more “user-friendly.” Reality is what it is, which, unfortunately, is very counter-intuitive. We create “Models” of parts of reality, which necessarily leave out some aspects, and severely limit others, to describe some portion of reality in terms we can comprehend. The problems arise when we try to think of the _Model_ as if it _ **was** _ the reality. Most workers in technical fields run into this dilemma: to describe their field to a non-specialist, they must make compromises. Do they use words which the average well-educated person would know, even though those words may be freighted with connotations and ancillary meanings which will, inevitably, confuse the audience? Or do they use the “jargon” specialists in the field use to describe their work—words which precisely, and unambiguously, define the ideas which they wish to convey—but nobody outside their field will understand without lengthy footnotes? Neither option is fully satisfactory. Most popularizations of technical material, cosmology in this case, have opted for the former solution—using commonly-understood words. This inexorably leads to confusion when the audience extrapolates the words beyond the purview of the model. In the “language” appropriate to the subject, _mathematics_, all this talk of infinities resolves neatly into well-understood concepts. There are areas which are not completely known (which is why research continues at a frenetic pace, even today) but we have a pretty good handle on the constraints within which we believe “reality” will eventually be described. ---
**Author:** ![kanicbird](https://avatars.discourse-cdn.com/v4/letter/k/5f8ce5/32.png) [@kanicbird](https://boards.straightdope.com/u/kanicbird)\ **Post date:** [December 3, 2011, 1:58pm UTC](https://boards.straightdope.com/t/is-space-infinite/604657/33 "2011-12-03T13:58:20Z")
From how I understand it space is ‘infinite’ if you can’t travel faster the the speed of light, as space is being created inbetween itself at a rate that there are places you will never be able to get to because you can’t travel faster then the rate that the universe is expanding. Space may have a similar characteristic to a black hole, with a finite ‘size’ if observed from the outside and a infinite size if observed from the inside, along with points you can never reach without exceeding the SoL. The universe as we know it may be the inside of a very large black hole. ---
**Author:** ![Mosier](https://avatars.discourse-cdn.com/v4/letter/m/7ea924/32.png) [@Mosier](https://boards.straightdope.com/u/Mosier)\ **Post date:** [December 3, 2011, 3:59pm UTC](https://boards.straightdope.com/t/is-space-infinite/604657/34 "2011-12-03T15:59:24Z")
> [@DHMO](#): > > As currently understood, and very well explained above, _any particle_ in existence will find, from its point of view (its “frame of reference”) that it is at the center of an infinite number of other particles, which go off in every direction to infinity. This applies to _any particle_ which you can identify, so it is not possible to locate two particles which are farther apart than any other combination of particles. In order for that to be true, there must be an infinite number of particles in the universe. It was my understanding that our best guess at the moment is that there is NOT an infinite number of particles in the universe. Am I wrong? ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [December 3, 2011, 4:33pm UTC](https://boards.straightdope.com/t/is-space-infinite/604657/35 "2011-12-03T16:33:52Z")
> [@kanicbird](#): > > From how I understand it space is ‘infinite’ if you can’t travel faster the the speed of light, as space is being created inbetween itself at a rate that there are places you will never be able to get to because you can’t travel faster then the rate that the universe is expanding. > > Space may have a similar characteristic to a black hole, with a finite ‘size’ if observed from the outside and a infinite size if observed from the inside, along with points you can never reach without exceeding the SoL. The universe as we know it may be the inside of a very large black hole. You are confusing two different issues. It is completely possible for a finite space to have regions that are not in communication with one another. The observable universe has a radius (or better, [comoving distance](http://en.wikipedia.org/wiki/Comoving_distance)) of 13.7 billion light years. 13.7 billion is also considered to be the age in years since the big bang. Yet because of the expansion the size of the universe is 46 billion light years. Both numbers are finite, but we will never, even theoretically, be in communication with anything 46 billion light years away. Infinite is a basic property of space if it exists. It is not being created by expansion. Our universe could be one of many independent universes in infinity. That’s my limit of understanding, though, and I don’t want to say anything more that is likely to be incorrect or misleading. ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [December 3, 2011, 4:40pm UTC](https://boards.straightdope.com/t/is-space-infinite/604657/36 "2011-12-03T16:40:44Z")
> [@Mosier](#): > > In order for that to be true, there must be an infinite number of particles in the universe. It was my understanding that our best guess at the moment is that there is NOT an infinite number of particles in the universe. Am I wrong? What you’re trying to argue is equivalent to saying that the universe has a center, a preferred reference frame from which everything is expanding from. That’s not true. (You might want to check for the many threads in which this is explained better than I can.) The universe expands equally everywhere. That’s because all reference frames are equal, and therefore every particle can look at itself as the center. That’s true no matter how many particles are in the universe, even if that number is finite. If there is no fixed center, then there can be no fixed edge. You’re trying to define a diameter. The universe doesn’t have a diameter; it has only radii. Yes, that’s not common sense. ---
**Author:** ![JWT\_Kottekoe](https://avatars.discourse-cdn.com/v4/letter/j/3ec8ea/32.png) [@JWT\_Kottekoe](https://boards.straightdope.com/u/JWT_Kottekoe)\ **Post date:** [December 3, 2011, 6:14pm UTC](https://boards.straightdope.com/t/is-space-infinite/604657/37 "2011-12-03T18:14:28Z")
> [@Mosier](#): > > Follow up related question: > > Is it understood that there are, or must be, two particles in the universe which are further apart from each other than any other combination of particles? If there is a finite amount of matter in the universe (which seems likely), it MUST be true that there are two particles which are further away from each other than other combation of particles. If that is the case, why couldn’t the two furthest-apart particles be thought of as the “edges” of space? Let me answer this for the case of a finite universe. The simplest finite but unbounded (no edges) universe is analogous to the surface of a hypersphere. In the expanding balloon analogy, every point on the balloon has an anitpode, a point that is maximally distant, all the way on the other side of the balloon. The same is true in a closed, positively curved universe. Thus, while you are correct that with a finite number of particles, barring exact coincidences, there would be two of these that are the furthest apart of any pair, these two particles will not in any sense constitute an edge. ---
**Author:** ![kanicbird](https://avatars.discourse-cdn.com/v4/letter/k/5f8ce5/32.png) [@kanicbird](https://boards.straightdope.com/u/kanicbird)\ **Post date:** [December 4, 2011, 1:22pm UTC](https://boards.straightdope.com/t/is-space-infinite/604657/38 "2011-12-04T13:22:37Z")
> [@Exapno\_Mapcase](#): > > You are confusing two different issues. > > It is completely possible for a finite space to have regions that are not in communication with one another. The observable universe has a radius (or better, [comoving distance](http://en.wikipedia.org/wiki/Comoving_distance)) of 13.7 billion light years. 13.7 billion is also considered to be the age in years since the big bang. Yet because of the expansion the size of the universe is 46 billion light years. Both numbers are finite, but we will never, even theoretically, be in communication with anything 46 billion light years away. > > Infinite is a basic property of space if it exists. It is not being created by expansion. Our universe could be one of many independent universes in infinity. That’s my limit of understanding, though, and I don’t want to say anything more that is likely to be incorrect or misleading. Wouldn’t’ time as a dimension and a hard upper limit of the SoL make it infinite? ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [December 4, 2011, 3:47pm UTC](https://boards.straightdope.com/t/is-space-infinite/604657/39 "2011-12-04T15:47:17Z")
> [@kanicbird](#): > > Wouldn’t’ time as a dimension and a hard upper limit of the SoL make it infinite? Try the balloon analogy once again. It’s a two-dimensional finite surface. You can add a third, time, dimension to it. It can have a fixed speed of light of any number. Yet it is obviously not infinite. A three-dimensional curved space would work the same way. ---
**Author:** ![kanicbird](https://avatars.discourse-cdn.com/v4/letter/k/5f8ce5/32.png) [@kanicbird](https://boards.straightdope.com/u/kanicbird)\ **Post date:** [December 4, 2011, 4:11pm UTC](https://boards.straightdope.com/t/is-space-infinite/604657/40 "2011-12-04T16:11:50Z")
> [@Exapno\_Mapcase](#): > > Try the balloon analogy once again. It’s a two-dimensional finite surface. You can add a third, time, dimension to it. It can have a fixed speed of light of any number. Yet it is obviously not infinite. A three-dimensional curved space would work the same way. Again from the outside it has a fixed dimension, though inside could it be infinite as some postulate is inside a black hole? From some models of a black hole spacetime gets ‘stretched’ to infinity, which creates infinite space inside a finite space. [Previous page](https://boards.straightdope.com/t/is-space-infinite/604657.md?page=1) [Next page](https://boards.straightdope.com/t/is-space-infinite/604657.md?page=3)