martillo
Registered Senior Member
I suggest to introduce another little variant yet to have a really interesting problem.apologies if this has been posted before.
There are two twins, Dick and Mick. Then there's their idiot younger brother Tom.
Dick and Mick get into identical rocketships. In Tom's "rest" frame, they both jet off at the same time, travel the same distance in opposite directions, then return at the same time. the paths taken are linear.
So to tom, both would have experienced equal time dilation.
However, wouldnt Dick and Mick see their other two siblings as having experienced time dilation instead? How do we answer this paradox?
Let consider that at the end they meet again at a crossing point but they do not reunite. Let assume they would not stop and they would continue travelling at some constant relativistic velocity but at the croosing point the observations in the three reference frames are compared. Each one can take a photograph of himself at the crossing instant and send it to the otherones to see how each one has aged. For example how long is the beard of each one at that time (assuming they didn't cut it, of course).
The point is not to choose which frame of observation would be choosed to get the best result. The point is to get the observations in the three frames and compare them. The observations cannot be contradictory. Afterall the same phenomenon is observed just by different frames of observation.
To simplify the problem I think it can be considered that when the two twins travels away and stop to turn back is an instant when all the clocks are re-synchronized since at that instant all are at rest in relation to the others. Then just the travel back to the crossing point matters.
It must be assumed that both twins acquire a relativistic velocity in a small time compared with the trip and always have perfectly symmetrical velocities.
In each frame of observation the relativistic predictions of the state of the three guys must be made and compared. There should be no contradictory results between them.
I think all them contradict the others:
_ Each twin would see the other twin aged less (they would see themselves with a long beard and the other without it) what is contradictory.
_The guy "at rest" would see both twins aging the same (let say with a half beard) what contradicts the observations above.
As a comment on the accelerations needed to acquire relativistic velocities I think they don't play a fundamental role in the problem since the Lorentz Transforms just depend on the velocities. Einstein postulated his famous problem of the train at a relativistic velocity without any mention on the needed acceleration to reach it.
I must say at this point that this problem is presented in detail as a consideration against Relativity Theory at http://www.geocities.ws/anewlightinphysics although is not available online for now.
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