- #1

zytsang

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**The problem statement**

Suppose the universe is a 2-torus, thus there exists a spatial path that you will go back to where you start eventually. Let Observer A and Observer B travel on this closed path. Observer B is travelling at a constant speed of 0.9c relative to Observer A, where c is the speed of light.

At time t0, Observer A and Observer B are in the same spatial location and they synchronize their clocks. Then they travel apart. At time t1>t0, Observer B meets Observer A and compares their clock.

Paradox: from the view point of Observer A, Observer B is travelling at 0.9c, thus B's clock should run slower than A's clock; from the view point of Observer B, Observer A is travelling at 0.9c, thus A's clock should run slower than B's clock. Therefore when A and B compare their clock at t1, there seems to be a contradiction.

Question: resolve this "paradox", draw the space-time diagrams for both Observer A and Observer B.

**My attempt**

The lecturer has talked about the Twin Paradox, and I know that the acceleration and deceleration leads to the clock discrepancy. However here I think both Observer A and B are in inertial reference frames, so the clock should not be affected by acceleration. But I just can't find any loopholes in the problem. My experience told me that, the paradoxes in special relativity are always caused by clock synchronization (correct me if I am wrong). Is the answer to this paradox due to the fact that, it is impossible for A and B to synchronize their clocks at t0? Why? Or my attempt is wrong and the solution lies on other aspects?

Thank you for your help!!