# Thread: Straight line through curved space

1. Newbie
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## Straight line through curved space

I'm sure this has come up before.

If, due to the curvature of space as some theorize, any straight line in the universe will end up where it started. Or as Dr. Pamela put it, 'you shoot a laser beam into the universe it will eventually hit you in the back of the head.'

And since the big bang everything is essentially moving in a straight line (more or less) outward.

Will not all the stuff of the universe eventually re-converge on the same spot on the 'other side' of the universe?

2. Originally Posted by themank
Will not all the stuff of the universe eventually re-converge on the same spot on the 'other side' of the universe?
Only if the gravity is strong enough to make the universe "closed", i.e., to make it all fall back together in the "Big Crunch". Note that current observations do not favor this scenario-- the laser will most likely never hit you in the back.

3. Also, I feel it is worth pointing out that everything is not essentially moving in a straight line outward since the big bang, in the way (I think) you mean.

There is no specific location within this universe where the big bang can be said to have occurred, more than any other location. It is not as if there was an explosion in space and everything expanded outwards from that point. It is probably better to think of it as an expansion of space, with everything being dragged along by that expansion, although that is a very simplified model.

Imagine a volume of space with a three dimensional grid of points in it. Each point is 1 metre away from its neighbouring points. It doesn't matter where you put yourself in that volume of space, whatever point you choose to sit on you see points at 1, 2, 3, 4, 5... metres away in each direction, whether you look up, down, backwards, forwards, left or right. You cannot see the edge of this volume of space, you just see points receding off in all directions.

Now, taking one second to do so, expand that volume of space to twice its original size. If you choose a point to sit on now, your nearest neighbouring points are 2 metres away and now you see points at 2, 4, 6, 8, 10.... metres away in all directions. The nearest point has moved from 1 to 2 metres away while in the same length of time the 5th point moved from 5 to 10 metres away.

So whatever point you choose to sit on, your nearest point has receded in a straight line from you at 1 metre per second while the 5th point receded from you at 5 metres per second. The further you look, the faster a point seems to be receding from you, and this is entirely due to a simple expansion of the volume or grid to double its original size in 1 second.

This model is more like how our universe expands, with the points representing clusters of galaxies, all receding from each other at the same rate, but whatever galaxy you choose to sit in you would see distant galaxies receding faster, the further you look. We actually think the rate of expansion has changed over the history of the universe, starting incredibly fast and slowing down but more recently speeding up again. So our "grid" is not as linear as in my example above, but the principle should help you understand how the theory behind the big bang works.

Wherever you are, it looks like everything outside your local supercluster of galaxies is expanding in a straight line away from you whatever direction you look in, and the further you look the faster an object is apparently receding from you. Anywhere in the universe might consider itself to be at the centre of the expansion, as everything is expanding away from everything else at the large scales.

4. Originally Posted by themank
Will not all the stuff of the universe eventually re-converge on the same spot on the 'other side' of the universe?
The Universe doesn't have sides. Its expansion involves making space itself "bigger", for lack of a better term. It's like asking "If you blow a balloon up big enough, won't its sides eventually meet?"

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Regardless of the universe having sides or if it is an expansion of space, if I can fire 2 hypothetical lasers in the theoretical universe Pamela mentioned, and they stay parallel and hit me in the back of the head. What if instead of firing a laser, I fire a couple galaxies. Gravity aside, wouldn't these galaxies eventually come back to hit me in the head too? If that is possible, then what about firing 300 billion of them from a singularity in all directions. It seems like what is good for the laser beam should be good for a few hundred billion galaxies too. They should all return to their starting point.

6. Originally Posted by themank
Regardless of the universe having sides or if it is an expansion of space, if I can fire 2 hypothetical lasers in the theoretical universe Pamela mentioned, and they stay parallel and hit me in the back of the head. What if instead of firing a laser, I fire a couple galaxies. Gravity aside, wouldn't these galaxies eventually come back to hit me in the head too? If that is possible, then what about firing 300 billion of them from a singularity in all directions. It seems like what is good for the laser beam should be good for a few hundred billion galaxies too. They should all return to their starting point.
If you can find a universe like that, feel free to try the experiment. Make sure to tell us how it turns out.

7. Order of Kilopi
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Ken and speedfreek gave the first- and second-most important aspects
of the answer to your original question. The third is that, in a closed
universe, light would only have time to go halfway around the universe
before the universe ended in a Big Crunch, even if the light was emitted
at the Big Bang. The bigger the universe is, the more time the light has
to go around, but the farther it has to go. Halfway is the the best it
can do.

-- Jeff, in Minneapolis

8. Originally Posted by themank
Regardless of the universe having sides or if it is an expansion of space, if I can fire 2 hypothetical lasers in the theoretical universe Pamela mentioned, and they stay parallel and hit me in the back of the head.
As Jeff said above, in a closed universe the light would not have the time to circumnavigate the universe before it collapsed, but I am getting the feeling that in your original post you were confusing the curvature of space, to which Jeff is referring, with the possible topology of the universe, which is a different kettle of fish. If the topology of the universe were such that "when you exit on one side you enter from the other", as with pacman, then yes, that is one of the possible models for the topology of our universe. If the universe were static and small enough, and light had the time to propagate, we might find that the universe has a non-trivial topology and end up looking at the same region of distant space when looking in different directions. A laser would eventually "loop back" and return from the opposite direction.

What if instead of firing a laser, I fire a couple galaxies. Gravity aside, wouldn't these galaxies eventually come back to hit me in the head too? If that is possible, then what about firing 300 billion of them from a singularity in all directions. It seems like what is good for the laser beam should be good for a few hundred billion galaxies too. They should all return to their starting point.
In a theoretical small universe that has that kind of non-trivial topology, was either static or had such a slow expansion rate that light could circumnavigate it, if you could somehow get a galaxy moving near the speed of light that galaxy would indeed also circumnavigate that theoretical universe.

Unfortunately, even if our universe had such a topology, the rate of expansion precludes light from circumnavigating it.

We have looked for areas in the WMAP data that match in different directions, searching for evidence of topologies such as the Poincare dodecahedral space.

Extending the WMAP Bound on the Size of the Universe is a paper that gives a very good insight into these issues but claims to rule out the Poincare dodecahedral space.

But an article from last month, The Poincare Dodecahedral Space model gains support to explain the shape of space is claiming the opposite!
Last edited by speedfreek; 2008-Mar-05 at 09:51 PM. Reason: typo

9. Member
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I'm a little confused with the whole "hit you in the back of the head" aspect of a closed universe. Chances are pretty high I have it wrong so please DO correct me if I'm wrong, but that concept seems to take the idea of a spacetime diagram depicting a closed universe to literally.

Assuming there is no intervening gravity well of some description to deviate its path, if I send a light beam out from my position, and the universe reaches the point where it begins it's collapse, that beam of light will still be moving away from me through its own local space during collapse, it's just that our coordinates will be contracting in a reverse way to our currently expanding universe.

Help ???????

Andrew.
Last edited by Garvs; 2008-Mar-05 at 09:59 AM.

10. Have a look at this link: The Shape of Space - it covers the basic concepts involved here.

It is easy to get confused here, as we are actually talking about two separate but intrinsically linked properties of the universe - the topology and the curvature. You can, for instance, have a flat, open universe where an imaginary straight line heading away in front of you actually comes back at you from behind! See section 6 of that link above.

11. Originally Posted by themank
If that is possible, then what about firing 300 billion of them from a singularity in all directions. It seems like what is good for the laser beam should be good for a few hundred billion galaxies too. They should all return to their starting point.
That does not describe what occured in the big bang.

It was not an explosion at a single point in space from which all matter fired out "in all directions".

Originally Posted by speedfreek
Also, I feel it is worth pointing out that everything is not essentially moving in a straight line outward since the big bang, in the way (I think) you mean.

There is no specific location within this universe where the big bang can be said to have occurred, more than any other location. It is not as if there was an explosion in space and everything expanded outwards from that point. It is probably better to think of it as an expansion of space, with everything being dragged along by that expansion, although that is a very simplified model.

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## thanks for all the good answers

Yippee, that's settled. Now, I'll go brush up quick on the Poincare Dodecahedral Space model!!

13. Banned
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Originally Posted by Ken G
Only if the gravity is strong enough to make the universe "closed", i.e., to make it all fall back together in the "Big Crunch". Note that current observations do not favor this scenario-- the laser will most likely never hit you in the back.
Even if it did, there's way too much dispersion...

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