Observers that pass each other with a relative speed close to the speed of light will observe length contraction and time dilation at the other observer. In a spacetime diagram, this would be represented by two worldlines making an angle, right? Some textbooks suggest that some of the length is traded for time due to the different spacetime perspectives of the observers. Is there a way to visualize the length contraction and time dilation in such a spacetime diagram? However, I would think the mere difference in spacetime perspective cannot be the whole story, because e.g. in the twin paradox, there will be a real change in relative time passage. How does this work, does one of the observers skip time coordinates, or is the spacetime structure different for him? In this respect, I also read (e.g. Brian Greene) that all objects have a spacetime trajectory which equals c. Light is special, because the whole trajectory is in space and does not extend in time. In a spacetime diagram, I would think that this implies a vertical worldline for light, which would mean it could in fact not arrive at observers in the future. How come it actually does arrive at obervers in the future?