Theoretically (of course), if I set out through the universe in a straight line (an I am not sure how space curvature complicates this), will I end up right back where I started?
Good question. I’ve wondered this myself. I do recall reading some science writer (Isaac Asimov?) who answered the question in the negative (but it was a long time ago). He said that even if you set out at very nearly the speed of light, you will never get back where you started because the universe is expading too fast. I’m not sure what the current thinking is.
Ignoring expansion, the question is really whether the universe finite or infinite. If the universe is finite, then yes you would eventually reach your stating point. If the universe is positively curved, then it is finite. If it is flat it could be finite or infinite. I think Chronos said that negatively curved space could be finite or infinite. However, as bibliophage pointed out, since the universe is expanding, there are regions that receed faster than light, so in our expanding universe, you could never traverse the universe. Although, I wonder about, if the universe is closed, it will eventually contract. I don’t know about the answer in that phase, but something tells the answer is still no, because it would collapse before your round trip.
Since space is “flat” your straight line would remain straight except when altered by gravity (like passing by a star, etc.). This seems obvious, but in an “open” or “closed” universe, your straight line would also be altered by the topology of space itself. (In a flat universe, 2 parallel light beams would remain parallel forever whereas they would converge or diverge in a closed or open universe, respectively.)
With the expansion of space, you’ll never reach the “edge” of our “visible universe” (and even if you did, there still more universe beyond what we can currently see).
My impression is that our flat universe is infinite and you would not reach your starting point. But you would reach your starting point if the universe was closed (space would curve back on itself). But Chronos’ past posts make me uncertain on this matter.
Let me just add…
I have no friggin’ clue where I got the word “Transversing” from in the Subject header. I of course meant “Traversing”.
Well, it’s possible that the Universe is flat or open but finite, with a topology similar to an Asteroids screen (can someone please think of some other common video game with that topology? I’m sick of talking about Asteroids), where something that leaves one side of the screen comes back on on the opposite side. Hence, even though the screen is flat, it’s finite, and there’s effectively no “edges” (or at least, if there are, they’re indistinguishable from the rest of the Universe). It’s rather more complicated with negatively curved space, and I’m not going to even try to describe the shapes used, but it’s still possible. As to whether this is, in fact, the case, if the Universe is small enough and not simply connected, then data from the MAP sattellite will show this (with the interesting side effect that one of my professors will become instantly famous). It’s considered a bit unlikely, though.
Another point: If the Universe does, indeed, behave like this, then you likely won’t come back to exactly where you started if you travel in a straight line, but you’ll pass arbitrarily close to your starting point.
Hey, a while back I heard that it’s also theoretically conceivable that in making this transUniversal journey, you’d mirror-image yourself, meaning you’d write backward, and be left-handed, and all that weird stuff. Of course, to you, you’d be normal, and everyone else would be backward. Interesting if fanciful; is this still a tossed-around theory?
Chronos: “can someone please think of some other common video game with that topology?”
So glad you asked. 
Pac-Man and Joust have the same idea on a left-right basis, and Galaga has the same idea on a top-bottom basis. Perhaps you could combine these. All three of the Star Control games use a combat screen much like Asteroids’s. Populous: The Beginning is also set on a map of this topology, as are the Chaos Emerald stages in Sonic the Hedgehog 3.
Achernar:
Because I’m left-handed! I never realized there were cosmic implications to that. Seems like I’d be older than 34, and have some memories of the voyage.
Isn’t PacMan more of an example of a wormhole?
(hijack!)
Well, a 3-dimensional Klein bottle topology (sort of like a Mobius strip with a vengeance) will produce the flipping effect that Achernar is talking about, and it can’t be ruled out, but it’s considered unlikely. There’s many things at a subatomic level which have a definite parity. Neutrinos, for instance, appear to all be left-handed (so to speak), meaning that their angular momentum vector is in the opposite direction to their velocity vector. If a neutrino ever made the round-trip in such a Universe (and if anything can, it’s neutrinos… They move at the next-best thing to the speed of light, and aren’t slowed down by much of anything), then when it got back, it’d have the opposite parity. Since no right-handed neutrino has ever been observed, it’s safe to say, at a minimum, that if the Universe is connected in that manner, it’s on a scale larger than our lookback radius.
Actually, I did know of a few other toroidal video games, but I was just afraid that nobody else would be familiar with the original King’s Quest, or Final Fantasy I, or Space Tag. Pac-man could be wormholes; it’s hard to say, since the edges only connect at specific points.
If you travelled in a direction away from the earth and happened to be in a locally shaped part of the universe you might come back to where you started but it might be on the other side of the earth unless the earth had rotated in such a way as to make that unnecessary. Meanwhile it is revolving around the sun and so even if you could keep a straight line, which would mean following the curves of the spae at the moment, it would be very unlikely in any case.