Alice and Bob are moving in opposite directions around a circular ring of radius R, which is at rest in an inertial reference frame. Both move with constant speed u as measured in that frame. Each carries a clock, which they synchronize to zero time at a moment when they are at the same position on the ring. Bob predicts that when next they meet, Alice's clock will read less than his due to time dilation because she has been moving with respect to him. Alice predicts that Bob's clock will read less than hers for the same reason. (a) Briefly explain what's wrong with their arguments. (b) What times will the clocks read when they meet again?

Alice and Bob are moving in opposite directions around a circular ring of radius R, which is at rest in an inertial reference frame. Both move with constant speed u as measured in that frame. Each carries a clock, which they synchronize to zero time at a moment when they are at the same position on the ring. Bob predicts that when next they meet, Alice's clock will read less than his due to time dilation because she has been moving with respect to him. Alice predicts that Bob's clock will read less than hers for the same reason. (a) Briefly explain what's wrong with their arguments. (b) What times will the clocks read when they meet again?