Does space ever end?

Our 7 year old daughter asked this question today and both my husband and I could not give her a great answer. Could anyone help us to answer this in a meaningful way for a 7 year old?

Thanks!

This may be a question best left unanswered.

Vitali Zholobov:
"When I saw that star and realised that space is a bottomless abyss, the first thought that occurred to me was that it would take thousands of years to get to that star - and that's not the end of our world. One can travel further and further and there is no limit to that journey. I was so shocked by this thought that I felt something crawling up my spine."

I don't know if this is on a 7 year old level or not, but compare space to the surface of the Earth. There is no edge to the Earth but it has a finite surface area. This is because the 2 dimensional surface of the Earth is curved in 3 dimensions. In an analogous way, 3 dimensional space, even though it has no edge, is curved in a higher dimension and has a finite volume. At least that is the theory. You might try reading the book "Flatland, A Romance of Many Dimensions".

http://www.ibiblio.org/eldritch/eaa/FL.HTM

Of course this begs the question, does that higher dimensional space have any end? You could say it is curved in yet a higher dimension, but that begs the question, are there an infinite number of dimensions? If so, then even though our 3 dimensional universe has a finite volume, the larger, infinite dimensional universe does not. At this point it starts to sound like the question, "who created God?" and I have to agree with nihiladrem, some questions are best left unanswered; or even unasked! Try telling THAT to a 7 year old!

I have a 4-year old whom understands that infinity never ends, that it is the same as counting forever... still she asked me, "what is the last number?"

I explained to her about googol and googolplex and that googolplex was considered to be the "last number before infinity," and that it would take thousands of millions of years to count that high. I explained that if she spent her whole life counting that she would reach a few million; and by giving her that kind of personal scale I was able to provide some perspective.

So, rather than engaging the n-dimensional geometry, perhaps you should explain that space does have an end, but it is so far away that the fastest spaceship in the world could never reach it in a billion trillion years.

Or, if your daughter prefers the geekspeak: "Space is finite, but is arbitrarily large; so large that it is practiceably infinite for all applications of human technology"

I wouldn't have been placated with explanations like that, even when I was 7. Space may be larger than our technological reach but not larger than our imagination's reach. Even though we can't really travel far enough to make the answer important, we can imagine traveling that far and wonder what it would be like.

I remember finally, really, understanding infinity in high school when my chemistry teacher and another student tried to convince me that 0.999...=1 exactly, if there are an infinite number of nines. I objected strongly, arguing that there is a small difference, no matter how many nines you write. Late that night I woke suddenly and had an epiphany. If there are an arbitrarily large, but not infinite, number of nines, then it does not equal 1. When there ARE enough nines to equal 1, then there are an infinite number of nines.

Well, then Froggy can break out the Mobius Strip (or, better yet, the Klien Bottle) and see where that gets her...

Shucks -- all this fuss over a kid. If we can't break things down to their level, folks, then the game's already lost for us: we need to get each successive generation involved in this.

*thinks for a minute on the question at hand*

The absolute best answer: nobody knows. If space has an end, it's so far away that we can't see it with our best telescopes (and this is a fantastic point for you to introduce her to the wonders of amateur astronomy). For that matter, we're not even sure what it'd look like. Either way, we can see far enough to know that it's really, REALLY big, and I can assure you that astronomers won't quit looking until they've seen it with their own eyes.

-- Stephen Deisher
Aerospace Engineering Sophomore
Georgia Tech

May not be the proper answer to a seven years old child but meant only to mention it: There was an article last year or 2004 saying that the lack of wavelengths above a certain level is considered to indicate that the diameter of the universe is 70 billion light year.

So the diameter and the volume is finite. If wanted I will look for that article - may be it was german only.



Dipl.-Volkswirt (bdvb) Augustin (Political Economist)

Well statements like "If space has an end, it's so far away that we can't see it" and "the diameter of the universe is 70 billion light years" imply that there is an edge and our curious 7 year old is wondering what the edge would be like if we could see it, just like I did many years ago. Probably the best answer is that we don't really know for sure and maybe you can be the one to find out when you grow up, so study hard in school!

But if the theories are correct, it is both disappointingly ordinary and mind-bendingly strange, all at once. Remember now, everything that follows is theory, not "THE TRUTH".

If we assume that the 3-D universe does not have infinite volume, then where is the edge and what is the diameter? It doesn't have any, just as the Earth's 2-D surface does not have a diameter or an edge in the 2nd dimension. The Earth's 2-D surface has a circumference, but no edge. You can walk anywhere on the Earth and it all looks pretty much the same, and you never come to any edge that could be called "the end of the Earth". If you could magically and instantly go (not physically travel which brings up all sorts of relativity problems) anywhere in the 3-D universe it would all look pretty much the same and you would never come to any kind of edge or end. In this way it is disappointingly ordinary.

However, you might say, the Earth DOES have a diameter, so the universe must too. Yes, it does, but only in a higher dimension. The problem here is that we cannot perceive it! We are 3-D creatures stuck in the 3-D universe and cannot look out into the 4th dimension and measure the diameter of the universe, or even have any way to imagine what it would really be like. But we are not really 2-D creatures stuck on the Earth's 2-D surface, so we CAN look out in the 3rd dimension and intuitively know what is going on, and measure the diameter in the 3rd dimension. When you ask, "where is the edge of the Earth?", the answer is, right here, everywhere. It is the surface you are standing on. You are right at the edge all the time but never even think about it. Jumping and flying are trips into another dimension, the 3rd dimension! So by analogy the edge of space is everywhere, right here and wherever you are. We are, all of us, always at the edge of the universe. It is not far away, it is RIGHT HERE. The only problem is that we really are 3-D beings and cannot look out into the 4th dimension. We cannot "jump" or "fly" off our 3-D "surface" or ever take any kind of trip into the 4th dimension. Here I put the words "jump", "fly" and "surface" in quotes because I am using them in a way not in the dictionary, but in an analogous way for the 4th dimension. There are no words to describe what I am trying to say, so I must rely on analogy. In this way it is mind-bendingly strange.

Reading Flatland will really help with understanding all this.

http://www.ibiblio.org/eldritch/eaa/FL.HTM

Looks about the same to me.....

We also could bring parrallel Universes into the discussion, which makes things even more complicated -

Thanks to all who took the time to reply. I haven't had the chance to dicusss all this with my daughter, but I was intrigued by it all as I am sure she will be. I guess we will have to explain what light years are - don't think she has learned that one in school yet. I am sure it will lead to more questions, and we may have to resort to campbelps reply

But not nearly as much fun as

Good point.... But then again, we're supposed to be inspiring this kid, not scaring her off with technobabble. Either way, we're both saying the same thing in different ways: "Damn'f I know...."

Read http://www.ibiblio.org/eldritch/eaa/FL.HTM and then . There is no technobabble, just all that wordy 19th century language!