Eroica

2003-Dec-04, 08:25 AM

Peter and Paul are twins. Peter is on the Earth, to which our stationary frame of reference is attached. Paul is sitting at the controls of his spaceship out in space, far away from any gravitational fields. Paul is also at rest in the stationary frame. Peter’s clock and Paul’s clock are synchronized.

Paul now switches on the rockets on his spaceship and accelerates away into deep space at an acceleration of 1g (≈ 9.8 m/s^2). After 1 year he is travelling close to the speed of light and is benefiting from relativity’s time dilation effects.

5 years after the start of his journey (as measured by his own clock) Paul turns his ship around, but keeps his rockets firing. He is now slowing down at 1g relative to the Earth.

After another 5 years Paul’s ship comes to rest relative to the Earth. However, he keeps his rockets firing and now starts to accelerate back towards the Earth.

After another 5 years Paul’s ship is halfway back to Earth. Paul turns the ship around again, but once again he keeps his rockets firing. He is now slowing down at 1g.

After another 5 years Paul’s ship comes to rest relative to the Earth and Paul now switches off his rockets. He is now back where he began. But when he compares his clock with Peter’s he discovers that while he has aged only 20 years, Peter has aged 3348 years!

But this age difference must be due entirely to the effects of SR, because during the entire experiment Peter and Paul have been subject to exactly the same GR effects. Peter has been on the Earth, whose gravity has been accelerating him at 1g, while Paul has been subject to an identical acceleration of 1g in his ship. By GR’s Principle of Equivalence, these two accelerations are indistinguishable and produce identical effects. Ergo, the age difference at the end of the experiment must be caused entirely by the SR effects of Paul's travelling at high velocities.

QED …? :-k

Paul now switches on the rockets on his spaceship and accelerates away into deep space at an acceleration of 1g (≈ 9.8 m/s^2). After 1 year he is travelling close to the speed of light and is benefiting from relativity’s time dilation effects.

5 years after the start of his journey (as measured by his own clock) Paul turns his ship around, but keeps his rockets firing. He is now slowing down at 1g relative to the Earth.

After another 5 years Paul’s ship comes to rest relative to the Earth. However, he keeps his rockets firing and now starts to accelerate back towards the Earth.

After another 5 years Paul’s ship is halfway back to Earth. Paul turns the ship around again, but once again he keeps his rockets firing. He is now slowing down at 1g.

After another 5 years Paul’s ship comes to rest relative to the Earth and Paul now switches off his rockets. He is now back where he began. But when he compares his clock with Peter’s he discovers that while he has aged only 20 years, Peter has aged 3348 years!

But this age difference must be due entirely to the effects of SR, because during the entire experiment Peter and Paul have been subject to exactly the same GR effects. Peter has been on the Earth, whose gravity has been accelerating him at 1g, while Paul has been subject to an identical acceleration of 1g in his ship. By GR’s Principle of Equivalence, these two accelerations are indistinguishable and produce identical effects. Ergo, the age difference at the end of the experiment must be caused entirely by the SR effects of Paul's travelling at high velocities.

QED …? :-k