# Round trip to earth in a straight line?

## Main Question or Discussion Point

I talked to an astronomy student recently, and he told me that if I travel out from earth in a straight line, I will finally return to earth. Is this true?

## Answers and Replies

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That would only be true if the universe had curvature, current studies show that the universe is completely flat.

Well, he told me that it is bent in higher dimensions. Much in the same way as a imagined 2D-creature wouldnt understand why he comes back to the samt point after walking round earth.

HallsofIvy
Homework Helper
It is, in fact, not known whether the total curvature of the universe is positive, which is what would give that result (The earth does, in fact, have positive curvature). If this person told you that would result because the universe is "bent in higher dimensions" he didn't know what he was talking about! There are some string theories that require higher dimensions and it is thought that we don't "notice" them because they are "curled" up- imagine a 2 dimensional paper rolled up into a very, very, tight cylinder: it now looks like it is one-dimensional.

However, that has nothing to do with what would happen if we were walking (or flying in a space ship) in a "regular" dimension that we do notice!

But if the universe has a curvature, it will be practically impossible to travel in a straight line and return to earth, no?

But if the universe has a curvature, it will be practically impossible to travel in a straight line and return to earth, no?
The contrary is true, if the universe has NO curvature, it's impossible to travel in a straight line and return to Earth.

We'll use a 2D analogue: A basketball. The surface of the basketball is a 2D space with positive curvature. Traveling in a straight line from a point along the surface of the ball will eventually lead back to that same point. Now take that same basketball and flatten it. Now there's no way to return to the origin by traveling in a straight line.

But if the universe has a curvature, it will be practically impossible to travel in a straight line and return to earth, no?
That is correct, there are no straight lines in a curved space-time.
The thing that comes closest is a so-called geodesic.

But even then it is not automatically true that if you travel away from A along a geodesic you will meet A again, even if space-time has a positive curvature.

If this person told you that would result because the universe is "bent in higher dimensions" he didn't know what he was talking about!
I would not go that far in saying that.
While it is custom to describe curved space-time as intrinsic curvature, it would not be impossible to embed it in a higher dimension.

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Chronos
Gold Member
The universe is expanding too rapidly for any traveller to return to their point of 'origin', irrespective of curvature.

The universe is expanding too rapidly for any traveller to return to their point of 'origin', irrespective of curvature.
Yes, indeed.

By the way, do the researchers know more about whether the universe is flat or if it will start to contract or just continue to expand? I remember from high school that my physics book said we would probably never know.

HallsofIvy
Homework Helper
That is correct, there are no straight lines in a curved space-time.
The thing that comes closest is a so-called geodesic.

But even then it is not automatically true that if you travel away from A along a geodesic you will meet A again, even if space-time has a positive curvature.

I would not go that far in saying that.
While it is custom to describe curved space-time as intrinsic curvature, it would not be impossible to embed it in a higher dimension.
You are right. I had interpreted "bent in higher dimensions" as meaning "curled up in some dimensions". I think your interpretation as "embedded in higher dimensions" it better.

I talked to an astronomy student recently, and he told me that if I travel out from earth in a straight line, I will finally return to earth. Is this true?
This can quite definately be ruled out, because of the expansion of space.

Even when sending out a light signal, it can never catch up with the drift of space at large, because of the space expansion.

So, ultimately, this has the effect of that in all respects, the universe can best be seen as infinitely large.

This can quite definately be ruled out, because of the expansion of space.

Even when sending out a light signal, it can never catch up with the drift of space at large, because of the space expansion.

So, ultimately, this has the effect of that in all respects, the universe can best be seen as infinitely large.

But if light had infinite speed, would it then "return" to earth after beeing sent out?

Chronos