Assume that a rocket ship leaves the earth in the year 2100. One of a set of twins born in 2080 remains on the earth (inertial frame); the other rides in the rocket. The rocket ship is so constructed that is has an acceleration g in its own rest frame (this makes the occupants feel at home). It accelerates in a straight-line path for 5 years (by its own clocks), decelerates at the same rate for 5 more years, turns around, accelerates for 5 years, decelerates for 5 years, and lands on earth. The twin in the rocket is 40 years old.(adsbygoogle = window.adsbygoogle || []).push({});

(a) What year is it on earth?

(b) How far away from the earth did the rocket ship travel?

I managed to find solutions for this problem...but they seemed paradoxical, not for the reason that the moving observer appears to time travel - that is perfectly legitimate. While in the frame of the earth, the quotient of the outward distance and time was less than c - no problems there. However, I then asked myself "what if the observer during the accelerating portion of the journey decides to stop accelerating and continue in an intertial reference frame?". Both observers are now intertial, and thus must agree on the distance between them: my results say otherwise. In fact they show that the distance between them, divided by the time on the moving observors clock can be greater than c.

I think the paradox may arise at my assumption that we can see the outward journey as a series of interial rest frames of the rocket. Or perhaps my calulations are correct, up until the point where the rocket stops accelerating: it could be that the deceleration must occur in finite time...

Anyway, I will not post my solutions (yet), so that anyone who wants to can have a go at the problem themselves. If you want to, you are very welcome to find how the earth appears to the observer in the rocket.

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# Accelerating twin.

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