2 ships, A and C are travelling on a parallel course, separated by some distance x. As their velocity is constant, I could say that they share an inertial frame of reference, or in other words are at rest wrt to each other. Their clocks have also been synchronised and I will assume for this thought experiment no gravitational influences so their clocks tick at the same rate wrt to each other. There is a third ship B, which passes right by A as it intersects A’s trajectory at an angle of 60°, travelling towards C’s trajectory. As it passes ship A, it sends a signal that contains its clock time. Ship A passes that information onto ship C along with Ship A’s clock time. It just so happens that due to B’s speed, angle of trajectory of 60°, and the distance x, that B will pass right by C as it intersects C’s trajectory. (So if you imagine a right angle triangle, ship B is travelling along the hypotenuse.) The distance covered in this time by ship B is twice the distance ship C will travel, which is ok as ship B is travelling at twice the speed of ship C. http://img97.imageshack.us/img97/3895/image2el.jpg [Broken] When ship B passes right by ship C, it sends its clock time to ship C. Ship C makes a note of B’s clock time. Then it subtracts A’s clock time form its own clock time in order to work out how long it took ship B to pass between ships A and C from A and C’s frame. It compares that result to the difference in time from Ship B’s clock times and finds that due to time dilation, ship B’s clock had registered less time. So far so good I hope! So here are my conundrums. 1) At no point did ships A, B or C undergo any acceleration. However time dilation still occurred. So does that mean that acceleration is not required in order for time dilation to occur between two frames? (I was thinking of the twin paradox.) 2) As A and C are at rest wrt to each other, A nor C can say that they are ‘in motion’. So from A’s frame of reference, if ship B did not intersect ifs trajectory at 90°, then it would never meet up with ship C. (Ship A would use the tip of the ship to the stern in order to work out angle of trajectory.) Yet ship B does meet up with ship C. So are angles relative? Does ship A have to measure ship B’s trajectory at 90°? 3) If A did see ship B pass its trajectory at 60° and then later finds out that ships B and C passed each other, does that mean that ships A and C can say that they are in absolute motion? Because if they weren’t there is no way ship B could have passed by ship C.