# Q & A: twins in a finite universe

Q:
What happens to the twin paradox (http://en.wikipedia.org/wiki/Twin_paradox) if the universe has periodic boundary conditions? i.e. say there are two twins, one on Earth and one in a ship going near the speed of light. The ship is traveling in a direction that will, due to the periodic boundary conditions of the universe, return it to the exact same location without any acceleration. At instant A the twins high five. Then, after a while, the ship returns to the same spot and the twins high five again. Who's older / what happens?
- John (age 24)
South Bend, IN, USA
A:
Wow, that's a tough question. I started to work through a rough answer, found it to be inconsistent, and turned to local expert Brian Fields. He referred us to a couple of papers:

.

Here's a key passage:
The twin paradox can be resolved in compact space and we will show that the twin in the rocket is in fact younger than her sibling after a complete transit around the compact space. The resolution hinges on the existence of a preferred frame introduced by the topology, one consequence of which is the inability of the twin in the rocket to synchronize her clocks. (Barrow and Levin)

This is total news to me too.

Mike W.

(published on 08/30/2012)

## Follow-Up #1: twins in a finite universe

Q:
If one twin is moving in a spaceship near the speed of light, then in his reference frame he is stationary and the other on the earth is moving near the speed of light. Then why does the one on the earth becomes older and the one on the spaceship is younger?
- Razin Shaikh (age 13)
Navsari, Gujarat, India
A:
The point is, and this is something I just learned, that in a finite universe one of the twins would know there was something wrong with his spaceship. Let's say that it's a simple uniformly curved finite universe. Julian's  flashbulb goes off sending light rays in all directions, just as Joaquin passes by, say heading east. After waiting a very long time, Julian sees the light returning from all the directions simultaneously. That tells him he has nice simple laws of physics in his frame. In a uniform universe, light travels the same speed in all directions.

Now what does Joaquin see? He's also traveling without acceleration, at less than the speed of light according to Julian. So he hasn't gotten back to Julian when all the light gets there. Joaquin sees the light which had been going east, and now is wrapping around from the west, after he sees the light that had been heading west and now is wrapping around from the east. If he tries to say that the universe is uniform (as it looks) and that light travels the same speed in all directions, he can't explain why he sees one direction before the other. His reference frame just doesn't allow the same simple laws of physics.

So we can't use those simple laws to figure out how things look to Joaquin. We know how things look to Julian, so that's how we figure out that Joaquin is the younger of the two when they get back together.

Mike W.

(published on 09/05/2012)