Submitted by **PoufPoal** t3_1118du3
in **askscience**

Hi, all.

First of all, apologies if my question is kind of naïve, or even dumb. I'm not that smart of a person, and I just know the basics in most science fields. Just think of me as a 5 year old trying to understand the world around him.

I'm trying to understand the twin paradox, and I've stumbled upon this video (in french, but automatic English translation is quite good), where he explains that the paradox is resolved by the fact that the situations of the two twins are not really symmetrical, despite of what we think, because the traveling twin has to U-turn at some point, and doing so subjects him to an acceleration (at 16:11). So, in short, it's because he has to accelerate at some point (to U-turn) that their situations are not symmetrical, and that he is indeed the one that age less.

After that, in relativity, there is no more any notion of simultaneity, which is why the traveling twin is not getting younger (or the Earth-one older) suddenly at the exact moment of the U-turn. This part I'm having a lot of trouble grasping, but that's not the point of my question.

So, I have two question about all this:

- Is his explanation "correct", or at least does it give the right insight about the whole thing? If not, how does this really work?
- If he's right, and the acceleration is the root of the age difference at the end, what would happen in this hypothesis:

> We are in an infinite universe without borders, where if you travel long enough straight forward, you come back to your starting point from the other side. The traveling twin hops in his rocket, take off and travel straight forward until he comes back to Earth (which has magically stayed in the same place and still exists, don't question it too far) from the other side. He has not made any U-turn, so in theory, I guess their situations are still symmetrical.

Which one would have age more, and why?

Aseyhet1_j8eashy wroteIt might help to realize that

the elapsed time for each object is just the length of its path in spacetime. This should make it clear that there is never any ambiguity about whose elapsed time is longer. Just compare path lengths.In the traditional twin paradox, the question is whether a straight line (twin who stays behind) or a bent line (twin who travels) is longer. The straight line is longer, due to the particular form of the spacetime metric.

In your last paragraph you are asking, what happens if we bend spacetime into a cylinder-like shape, so that time goes along the cylinder and space goes around the cylinder? There is still no ambiguity: you are now simply comparing the length of a path drawn along the cylinder with a path that circles around the cylinder like a helix.

In particular, the two twins' situations are not symmetrical because when you bend the spacetime into a cylinder, you have to choose a special reference frame. That's the frame in which spatial surfaces exactly loop back on themselves and time points exactly along the cylinder. Try physically bending a sheet of paper into a cylinder so that the edges just meet. You will probably choose to make the corners meet as well, but that is just one option. You could also offset the corners as much as you want. These different possibilities correspond to different preferred frames.

So the two twins' elapsed times will depend on how fast they are moving with respect to this preferred frame.