Is the universe finite?

January 12, 2005 12:27 PM

Can anyone recommend any good recent articles or papers on whether the universe is infinite or finite? I've heard that scientists suspect that the universe is flat, which lends credence to the infinite-universe hypothesis. I've decided I don't know enough about this. Nothing too technical, please, though I'd prefer something more complex than an article from a newspaper science section.
posted by painquale to science & nature (20 comments total)

Awhile back I had an email exchange with the fellow who did logarithmic maps of the known universe. Essentially, if we would see the astrological equivalent of the "backs of our heads" with telescopes (think of the tunnels in Ms. Pac Man), the universe would appear to be a finite space. But the current imaging is inconclusive (if I understood him correctly).
posted by AlexReynolds at 12:41 PM on January 12, 2005

Oops: That would be "cosmological", not "astrological".
posted by AlexReynolds at 12:43 PM on January 12, 2005

A good resource for this is PhysicsWeb. I've found the articles there are often the right mix of non-technical and yet still explanatory with a supplement of Journal links should you wish to go deeper.

Here's a recent one on the CMB, which is essentially what you're looking for.
posted by vacapinta at 12:50 PM on January 12, 2005

I don't have any academic mumbo-jumbo to support it, but a physics professor in college put it to me this way (in '92, don't know if thinking has radically changed since then)- the universe is finite, but without boundaries.

In other words- there is a limit to how far the physical laws that govern our universe extend, as a result of the Big Bang. Beyond that is... we don't know. If you started at the center of the universe and moved outward in a straight line, the outermost reaches of the Universe cause your "straight" line to actually curve hyperbolically, so that you will never reach the "border".
posted by mkultra at 12:53 PM on January 12, 2005

Some of these links are pretty good, but none are really addressing the question I'm most curious about:

Is it possible that the universe is both flat and finite without being hyperconnected (a torus, like a Pac-man screen)? Do any cosmologists hold this position?
posted by painquale at 1:36 PM on January 12, 2005

Nothing too technical, please, though I'd prefer something more complex than an article from a newspaper science section.

I thought this is the reason that Stephen Hawking is so popular. You might try "brief history of time" (it's available as audio too, so that might be an option if you don't like reading physics)
posted by milovoo at 1:37 PM on January 12, 2005

You could try contacting Preposterous Universe (Sean Carroll) or other cosmologist/physicist blogs and suggesting a topic. Not that I've ever tried emailing them, but when the mood strikes they seem quite happy to explain things in a manner comprehensible to those without graduate level physics education.
posted by blender at 2:13 PM on January 12, 2005

I don't have a direct link for you, but I'd recommend a subscription to Scientific American. Amongst other totally awesome things, they take up this issue from a variety of viewpoints a few times every year.
posted by kavasa at 2:22 PM on January 12, 2005

Indeed -- Scientific American sent out a special supplement to subscribers titled "Parallel Universes" not long ago that covered a lot of this ground.
posted by gimonca at 4:17 PM on January 12, 2005

You need to redefine "flat" for yourself. Definitely look into Physicsweb and Hawking's books.

The short version is that there is a boundary, but it is unobservable and evanescent. While being flat (as I think you understand it) means that the universe never wraps back on itself a-la pac-man, that doesn't mean that space doesn't take on all sorts of strange shapes when you are dealing with wacky things like gravity, or the edge of the universe.
posted by plexiwatt at 4:17 PM on January 12, 2005

To Painquake: the answer is no. (And yes, IAAMathematician.) The basic assumption is that any straight line segment in our space M -- where "straight" means "geodesic", i.e. it's the shortest distance between any two sufficiently close points on the segment -- can be continued indefinitely. Otherwise we could just take a finite region in R^n (usual n-dimensional space) and physics would be very weird as things fell off the ends in finite time. (BTW, plexiwatt, find me a physicist who talks about the boundary of the universe; I've never seen this written about.)

Now fix a point p and think about all the straight lines coming out of that point. Given a vector v in R^n, we can set off along the geodesic that starts at p and goes in the direction of v, and go for a distance equal to the length of v. This gives a corresponding point in M. This function from R^n to M is called the "exponential map" for reasons unimportant here.

The exponential map wraps R^3 around M. It's easy to picture in the case M the surface of the Earth. Let p be the South Pole, and try to wrap up the Earth as a present. Even if you use some clingy rubber material so that it clings tight, you find a whole circle's worth ending up at the North Pole.

Flatness lets you avoid this sort of bad behavior, where very nearby points in R^n map to exactly the same point in M. The flatness assumption guarantees you that the exponential map gives you good coordinates, locally, anywhere on M, nothing like the failure of latitude/longitude nearby the North Pole. (Negative curvature, like a Pringles potato chip, works too -- this isn't special to flatness.)

Now there are two cases: either you can wrap back around by following geodesics, or not. If not, then we have a nice 1:1 correspondence between R^n and M, so M isn't finite. Or we can, in which case M isn't simply connected. (I would substitute the standard mathematical term "not simply connected" for your "hyperconnected".)
It might be neither, like an infinite cylinder.

Hope this gives some idea.
posted by Aknaton at 6:06 PM on January 12, 2005

This might touch on some of the things you're looking for. Its about the origins of the universe, but I think it also describes different cosmological models, including ones the posit it as finite/infinite.
posted by googly at 6:13 PM on January 12, 2005

Aknaton, that was fantastic, and exactly what I was looking for. Thanks.

You might try "brief history of time" (it's available as audio too, so that might be an option if you don't like reading physics)

Hey Milovoo, if you hate Stephen Hawkings that much, why don't you explain space curvature to me yourself? But please send it to me on mp3. I hate reading this stuff.
posted by painquale at 8:44 PM on January 12, 2005

wow. i have a degree in physics and a phd in astronomy and it's taken me 10 minutes to work out (vaguely) what aknaton is saying and as far as i can see either it doesn't answer your question or i am misunderstanding one of you. maybe it's the phrase "Nothing too technical, please".

as far as i can tell, aknaton was saying that if space is smooth then it's either open or closed, but not which of those cases we believe is the best description of the universe.

the standard model in astronomy has changed a fair amount recently, with the introduction of "dark energy", which is why you may be seeing conflicting reports on this. unfortunately, while i know enough to make snide comments about mathematicians (while being vaguely self-deprecating) i'm no longer in astronomy. from what i recall of a rather drunk conversation with a cosmologist a few months ago, i believe it's flat, but...

[stops, walks down hall, chats with someone who did some of the fundamental work on distance scales that made us revise our models of the universe]

ok, the answer is (and this is slipping away from me as i type - it seems so clear when you talk to someone, then doubts creep in...) that it is flat, to within a few percent.

that means that, locally (which i'll get to in a minute) our universe appears to be "normal" 3d space. if you head off in one direction you keep going that way. parallel lines stay the same distance apart, euclid is happy etc etc.

however it seems that we got like this by a period of rapid expansion. rapid is the key here - faster than the speed of light (you really don't want to go there). in other words all our universe - all that we can ever be aware of, or that can ever affect us, or be affected by us - may be flat, but that doesn't mean that you can't imagine a "meta-verse" in which our universe is one embedded fragment, in which the curvature may be different.

that may seem like it's irrelevant, but it answers a "philosophical" problem i had which was that i couldn't see how the curvature could change sign (or become exactly zero if it was initially positive) without some qualitative change in "how things are" - how can you "evolve" (which implies a gradual process) from a closed universe (pre-inflation) to an open one (now).

as i said, i don't fully understand this. others might be able to clarify some points. but i hope that gives you a more physical understanding.

also, this is all broad-brush stuff. space is not uniformly curved/flat at local and small scales (gravity, quamtum mechanics, etc).
posted by andrew cooke at 5:14 AM on January 13, 2005

actually, after thinking a bit more, i think i do understand what aknaton was trying to explain and maybe it's worth adding that when astronomers/cosmologists talk about models of the universe they (nearly) awlays assume a homogenous and isotropic universe. this leads to the famous einstein / de sitter solutions (the description here looks to do the maths right, although they don't seem to cover recent developments in astronomy).

that's why you could imagine a universe something like swiss cheese, which would be consistent with aknaton's explanation, with local variations in curvature, but don't find such things discussed much in the literature (swiss cheese not being homogenous (though it may be homogenized ha ha ha sigh)).
posted by andrew cooke at 6:04 AM on January 13, 2005

duh. maybe i've really misunderstood things. are you referring to the recent microwave background loopy stuff? if so, sorry! imho that's still pretty far out (but, coincidentally, there's a seminar on it here later today - if it has anything to add i'll report back). also, what aknaton said makes even more sense (how embarassing) in that context. sorry again...
posted by andrew cooke at 6:46 AM on January 13, 2005

Thanks for the posts, Andrew! I'm definitely swimming in deeper waters than I should be, so any confusion on your part is probably due to me, not you. Let me see if I can synthesize some of the stuff in this thread.

I was prompted to ask this question because I heard that recent investigations have shown that the universe is flat, which implies that it's infinite. I wanted to know if this decisively settled the open/closed universe question: is it possible for a universe to be finite without being globally curved (or not simply connected)? I'm not sure what I was thinking, really: I don't exactly know what it would look like if there were a borderless flat finite space, but I thought I read somewhere that such a thing is possible. I wanted some real mathematics and astrophysics to set me straight.

aknaton (I take it) said no: if it's flat it's either not simply connected or it's infinite. You provided a little more context: the knowable universe might seem flat and infinite (we'll never hit anything if we keep going in one direction), but this could just be a local feature of a universe that is globally curved and closed... which might explain how a pre-inflation closed universe could have evolved into something that looks like it is open.

Anyway, I got a bunch of good links in the process too. The Einstein link you provided looks excellent (perfect level of technicality) and will be something for me to pour over later. Thanks! I got exactly what I wanted out of this thread.
posted by painquale at 1:01 PM on January 13, 2005

You might try "brief history of time" (it's available as audio too, so that might be an option if you don't like reading physics)

Hey Milovoo, if you hate Stephen Hawkings that much, why don't you explain space curvature to me yourself? But please send it to me on mp3. I hate reading this stuff.

Huh? I do have his books on audio, and he does a good job of explaining them at an above layman level.
I didn't mean anything bad by that.
posted by milovoo at 1:22 PM on January 13, 2005

Sorry about that then, milovoo. I thought I detected snark in your response, but I guess I was wrong. Apologies!
posted by painquale at 3:33 PM on January 13, 2005

I was trying to convey surprise that no one had yet mentioned Hawking,
as he describes exactly that scenario in BHoT, but I seem to have some
disease lately that everything I say sounds snarky or bitter.
It's like that Kids in the Hall skit where the guy is permanently sarcastic.
I'm working on it.
posted by milovoo at 4:06 PM on January 14, 2005