Imagine the following scenario: There is a train, that crosses the entire planet, and has the lenght of the earth diameter (has no start or no end, it's like a "ring"). This train has in the floor a treadmill that runs in the opposite direction of the train. Also, the treadmill has the lenght of the train. The train travels at near speed of light. The treadmill runs at exact same speed of the train. Now imagine three observers, each one with a personal clock. The first (A) is outside the train, the second (B) is inside the train, but not over the treadmill, and the third (C) is standing over the treadmill. The observer A sees observer B running at near speed of light. The observer B sees observer C running at near speed of light. The observers A and C can see each other all the time, from their point of view they are not moving. If observer A looks at observer B running at near speed of light, then time runs more slow for observer B, when comparing to A. (B < A) If observer B looks at observer C running at near speed of light, then time runs more slow for observer C, when comparing to B. (C < B) If B < A and C < B, then we could assume that C < A, in other words, time for observer C will pass much more slow when comparing to observer A. But the thing is that observers A and C see each other not moving at all, so it seems the time for both should have no dilation. Somebody can explain what am I missing? Time dilation by speed doesn't care about direction, but in this example it seems that direction is relevant.