If the universe is finite then there must be an outer edge to it, and if so, what is beyond that outer edge? Everything cannot eventually “end” without there being at least empty space beyond it, so this must mean there is infinite space.
If the age of the universe is finite, then there must be a specific point at which the universe was “born”, and if so, what was before that? Surely you can’t believe that time didn’t exist before that. So time must span infinity.
My question is, how can you *not[/] believe in infinity? Infinity, IMHO, is a great argument for the non-existence of god: Given infinite time and infinite space, the right conditions are eventually going to occur and life is just going to “happen”, that’s all there is to it.
True.
False
True.
False
Of course, you could also easily argue that given infinite time and space, a god like power will also eventually occur.
Oh, and have you ever read Vonnegut’s wonderful ideas about chronosynclastic infidibulum? That’s when the whole infinity thing starts to get perplexing.
So is the circumference of a circle infinitely long then?
Is the surface of a sphere infinite?
pan
I was under the impression that we shouldn’t regard it as a sphere with a central point… But that’s what I get for reading the Science section of the newspaper.
no lenin, you’re right. But that’s not relevent to the analogy I was making. After all, we shouldn’t regard the universe as a circle either.
The point is that things can be finite and yet not have a start and end point.
By the time you get to the 4-dimensional topology of the universe, things get very tricky to imagine indeed. But the principle is the same.
pan
Gary Kumquat
Don’t mean to nit-pick, but for the record, it’s infundibulum. For those who might not know, the idea is one of an experience (or reference-frame) cone.
kabbes
My understanding from what I have heard Stephen Hawking say is that the boundaries of the universe are its black holes. Is that incorrect?
Cisco
I can’t tell you how precious that is, particularly since it is intended to counter a remark from Jab. I’m sure that, had he known his comment might be construed as evidence of God’s existence, he would have clarified to a fare-thee-well.
At any rate, you’re messing with some nebulous metaphysics. There are many arguments that might be drawn from pondering infinity, including the one cited by Gary. Mathematically, infinity has cardinality only, and not ordinality. Philosophically, infinity is an attribute often attributed to God.
Lib it’s been a few years since I studied astrophysics, and I wasn’t much good at it then either.
But as far as I remember, using the word “boundaries” when we’re talking about space is very dangerous.
Black holes are simply where our knowledge of physics breaks down. Since light cannot escape from them, there can be no information transition from them. Another way of looking at it is that light takes an infinitely long time to escape from a black hole, so when it gets to black holes, if I may paraphrase Henry Ford, “Time is bunk”.
As such, I don’t really think that one can think of black holes as a universe’s “boundaries” in the usual sense of the word “boundary”. They don’t exist on the “edge” of the universe. I suppose they are boundaries to the extent that once anything has entered them, it cannot return to the non-black hole universe however. I think that Hawking was just evoking a bit of imagary, to be honest with you.
I don’t know if you know this - if so consider it for those who don’t:
The common way the shape of the universe is explained is to imagine that it is the surface of a balloon. If we blow up the balloon, the surface gets bigger. Two points marked on the balloon will get further apart and yet the surface itself hasn’t expanded into anything (that is to say, it is the same surface as it was before - no “extra” bits of surface have been added). Of course, the universe is not a two dimensional surface, but a whole lot more complicated than that. But the same effect is going on - expansion but not expanding into anything, just expanding the space between all points. As such, there are no boundaries.
If you could see far enough, you’d see the back of your own head.
pan
For a wonderful treatment of black holes, I would strongly suggest Kip Thorne’s “Black Holes and Time Warps” or John Gribbon’s “In Search of the Big Bang” which covers much of the so-called “boundries” (but as the title implies, deals more with the events immediately following the big bang and how we have the universe we have today). Hawking’s “Black Holes and Baby Universes” is pretty good, too.
At any rate, we can use the balloon analogy provided the universe is closed (that is, spatially finite and you can see the back of your own head). If it is open then the analogy can only be used to show how space exapnds, but not to describe the “edge” of the universe.
As for finite universes and edges, I like to think of infinite sums that converge on a limit. True, there are an infinite number of parts, but the series never exceeds, say, 2. It doesn’t “stop” at two. There isn’t “something else” after two, except by our convention.
If we model the universe and come up with, for the sake of argument, a nice sphere that can only grow so large many will invariably ask, “But what’s outside of the sphere?” I would point to the model and say, “A room with inquisitive minds.” :shrug: It isn’t included in the model so you’ll just have to make something up. But we can say with increasing certainty that, even if something exists outside our universe (like in the many worlds theory, for instance) they are forever locked away from us and we may not interact. So, there you have it. Anything outside the universe? Do you take cream with your coffee?
False. True. True.
Perhaps Jab1 meant to say that we have no material models that are infinite in scope. This might be true if we accept that both time and space are fully quantiized. Of course, since the mathematics which allows us to develop quantum dynamics is inherently infinite, one could then argue that the Universe is a material model of infinite scope, regardless of whether the combinatorial possibilities for every quanta can be finitely expressed.
**Lib[/]
I beleive that Hawking speaks of black holes as the boundaries of our Universe in 2 senses: the preceptual boundary represented by the event horizon and the temporal boundary they represent in several cosmological boundaries. I don’t think that he arues they form a spatial boundary to the inflationary model.
Then there’s people like me who imagine infinity to be the flipside of zero, that is, like the positive and negative sides of the magnet. They are opposites in action, but absolutely the same in relation. I tend to think of infinity as the complete absence of zero, and zero as the absence of infintity. Of course, it’s all semantic, you could word your definitions of the two to be the same if you wanted to.
I saw a model on NIST.gov one time, but I can’t find the page, where they showed a 4-d cube that you could spin, rotate, invert, etc. This cube, in my mind, only backed up my theory.
The only realistic difference between infinity and zero is that we start zero at where we are, and infinity is the point farthest from that, which would be, in an infinite universe, right where we are. When I say “we start zero” I mean our definition of zero in relation to anything is that we start at what we have, and then work forward. Zero is always our starting point regardless of the reality of the starting point. Infinity is always the furthest from zero.
Of course, then there’s my theory of derivatives and fours, but that’s neither here nor there.
–Tim
Thusly:
While I was never exactly clear on how Hobbes gets from our inability to conceive of infinity to knowledge of its non-existence, I would agree that when we say that the universe (e.g.) is infinite, we are merely saying (from a philosophical point of view) that we ae unable to “conceive the ends and bounds of the thing named.”
As usual, I find “I don’t know” to be a satisfactory answer to the question at hand.
Please explain, especially the first two points. I realize that I am usually in over my head when I step into GD and I very well could be wrong but the word “False” just doesn’t seem to satisfy. What was before time? What is beyond the beyond? How can infinity not exist?
Sure thing, mister.
Right, a tricky one to conceptualize, as we inherently think in 3 spatial dimensions. You seem to be considering the universe in these terms, and as such believe that if it is finite it must be contained by something. The answer is a question - why must it be contained by anything? Why can it not exist of itself, yet still be limited in size. As I’m at work, and lazy anyway, let me repost Kabbes analogy:
This is a fairly nice one to visualize, but it’s a bit limited as it requires a closed model. There are open models for a non contained finite space, but it takes a better man than me to explain them.
Now, for your next point:
Now this is a lot easier to answer. There are all manner of theories for a start date for the universe, for example most big bang theories date the universe at somewhere between 10 billion and 20 billion years old. That means time must span 10 to 20 billion years, which is obviously not an infinity.
Of course, the answers to both of your points could be true as well - the universe could be infinite in size, and it could have existed forever. Varlosz gives the only accurate answer - we don’t know anything for certain, but we can have lots of fun hypothesizing.
It also helps if you think of time logarithmically. At the beginning of the universe, the situation was equivalent to a black hole. All the matter in the universe as now, but compressed to a single point. Therefore, time was “slower”. Light took an infinitely long time to go anywhere. We essentially measure time by light’s movement, so there was no time.
This may seem incomprehensible, but works if you think of time as a log function. Log of zero is negative infinity. We were at time zero.
Another way of looking at it - the coldenst temperature you can get is absolute zero. As you try to take more and more heat away from an object, you’ll asymptotically approach absolute zero, but you’ll never get there. Well, we can get asymptotically close to time zero but we can never get to actual time zero.
Not sure if this helps really. Just remember that as you try to travel back in time, it’s harder and harder to go back one second, one millisecond, one nanosecond. Eventually you reach the point where you can try as hard as you want and you won’t go back any further.
pan
False. Even with a finite universe, there would be no edge. In this case, space would curve back upon itself. Kind of like how the surface of a sphere does not have an edge (like kabbes said).
http://itss.raytheon.com/cafe/qadir/q2527.html
http://itss.raytheon.com/cafe/qadir/q1741.html
http://itss.raytheon.com/cafe/qadir/q37.html
True re: age but false re: size. Current evidence is that the topology of the universe is “flat” which implies that the universe will expand forever and is infinite in extent. Of course, our “visible” universe is finite due to the finite speed of light.
http://itss.raytheon.com/cafe/qadir/q2439.html
http://itss.raytheon.com/cafe/qadir/q2325.html
Other relevant links…
http://itss.raytheon.com/cafe/qadir/q836.html
http://itss.raytheon.com/cafe/qadir/q26.html
http://itss.raytheon.com/cafe/qadir/q1514.html
http://itss.raytheon.com/cafe/qadir/q1513.html
[nitpick]
Not exactly. A black hole is only defined within the context of spacetime (i.e., a black hole is an object WITHIN the universe). The Big Bang “seed” (whatever that was) was not sitting within any spacetime that we know of (i.e., the “seed” WAS the universe).
[/nitpick]
Oops. I’d actually meant to say false to that one, as per the balloon’s surface image. Sorry.
I heard a nice analogy, possibly better than the ‘surface of a balloon’ one. Suppose you have a mix for raisin muffins. That is, you have a very small amount of muffin mix, and the raisins are distributed fairly evenly throughout the mix.
Put said mix into an oven. These are unusual muffins, because someone’s added way too much raising agent. Also, the muffin mix is pretty transparent, so you can see what’s going on inside.
Place mix into oven. Watch what happens to the raisins. They all move away from each other (in 3d) as the thing expands. Raisins (of course) = galaxies.
I have not read all of Hawking, but from what I’ve read, he seems to favor a no-boundary principle.
Ordinality and cardinality are both mathematical concepts. There are perfectly valid mathematical systems that use infinities as ordinal numbers.
Mmmm. . . I don’t know. It could be argued that god (or gods) created an infinite universe so that the right conditions would eventually occur and allow life to happen.
About the balloon analogy vs. the raisin bread analogy: The balloon analogy supposes a higher dimension to imbed your space. The raisin bread analogy has an outer boundary. They are both good analogies as long as you realize their limitations.
Well, your links are down so I can’t check exactly which evidence you are citing. As far as I know, the topology of the Universe has yet to be determined. While several pieces of evidence argue against a closed Universe and we have long known that it is “close to flat”, the final question is unresolved. The COBE experiments have argued that no toroidal topologies are likely, but they did not eliminate the possibility of saddles. I seem to recall some observations of distant galaxies which argued for an open topology. You might be referring to the BOOMERANG project, which did indeed find evidence for a Euclidean topology. I think it is a mistake, though, to present the issue as closed.
More to the point, I was not responding to the statement that the Universe might expand infinitely. I was responding to the statement that the UNiverse in finite in size. That statement is true and will be true at any point in time that someone makes it.