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There has always been something that has bothered me about the twin paradox. We always discuss the twin B as accelerating to near the speed of light and not accelerating to a velocity of near or actually 0. Ignoring the universes expansion and the solar system orbiting in the galaxy consider the sun with a velocity of 0 with the earth still orbiting the sun and twin B decides to jump of the planet and almost instantly accelerate to a velocity of 0 and twin A continues to travel around the sun. Eventually a year goes by and A meets B at the same location B left the planet. In this case relative to each other they would see the same thing as in the normal paradox that the other is moving away rapidly. The question is would B actually be older then A after they meet up even though B is the one that has accelerated but according to his velocity relative to the speed of light he would age faster? And if you could get to a an actual velocity of 0 would your time move infinitely fast so all of this would just be void because nothing could of happened in-between instances of time relative to twin B? If that is true just replace velocity of 0 with a near 0 velocity. I have other thoughts on this but I figured I better stop here and wait to see if this clears up any of them.
- Scott (age 24)
You've put your finger on a very important point. In a gravitational field, the twin problem involves complications not included in the usual version.
The precise story you've told, however, is not possible. The twin who tries to be at rest with respect to the Sun would not stay that way without continually firing a rocket. Without that, he would fall into the Sun. At any rate, with that addition the two twins stay at the same distance from the Sun, but have very different experiences. The one 'at rest' actually feels the force from the rocket. The other one is in free fall and feels no corresponding force. Because they're at the same height from the Sun the net gravitational time shift between the two is zero. The one being pushed away from the Sun sees the same time effects as if there were no gravity and he was accelerating away. That means he sees the other twin aging slower. The one who makes the orbital trip ends up younger than the stay at home in this version too.
On another question, actual velocities of 0 can always be obtained just by choosing the right reference frame. That doesn't make anything dramatic happen.
(published on 07/02/09)
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