Theory of relativity

[Max Pain]

During a lecture about special relativity at my university a question occurs to me that my Prof couldn t answer. Maybe one of the clever people here can give me an answer.
There is this thing called twin paradox. One of the twins travels with a high velocity rocket into space and the other stay down at earth. When he comes back from space, he aged less due to the effects of time dilation.
Because every intertial frame is äquivalent, you could also assume that the rocket is not in motion, but the earth is (after the acceleration phase). So when you pass the earth in the rocket, you see the clocks going more slowly on the earth, than in you rocket. The other way round, people on earth see the clocks on the rocket ship going more slowly.
So how it is determined who from the two twins aged less? The one in the rocket or the one on earth.
I think it must has to do something with the acceleration and deceleration phase of the rocket because that is the only difference between the two frames. So maybe there is more than special relativity required to understand this problem.

 

[Urwumpe]

Yes, you need to take acceleration into account. I think, the twin paradox exists only in special relativity, but is no paradox anymore in the general theory of relativity.

http://en.wikipedia.org/wiki/Twin_paradox#Resolution_of_the_paradox_in_special_relativity

 

[agentgonzo]

There are a few explanations for this. The one that I know is uses the fact that acceleration and gravitation are indistinguishable. Since one twin is accelerating to travel away from the other one you can say that he is experiencing 'gravity'. From this you can use gravitational time dilation to get to a result.

Further reading:
http://en.wikipedia.org/wiki/Twin_paradox

 

[Max Pain]

Ok thanks, I read through the articles. It seems that it is not that gravitation and acceleration are distinguishable but that the twin in the rocket has to turn around. I think I will have to go through the maths of general relativity to fully understand this, because the special relativity doesn t take acceleration into account.

 

[Fizyk]

The paradox doesn't need general relativity to be solved. It's just that the travelling twin has to turn around, so his world line is no longer a straight line, thus it is shorter than the world line of the twin that stayed on Earth (in spacetime, the straight line is the longest of the lines connecting two points).

EDIT: Oh, yeah, I realised that there is a bit of general relativity involved, if we want to calculate the lengths respective to the moving twin - we then have to take the acceleration into account, and that will make his line still shorter than the non-moving twin's (from his point of view, the non-moving twin's line is curved, but it is in the curved spacetime, so everything is more complicated).

 

[Lunar Pilot]

Twin Paradox

From what I remember, the twin in space ages less because he has experienced less time than the twin on Earth, simply because he was traveling faster than the other twin.