Temporal trajectories can represent the complex mappings between story time and clock time that are to be found in shared interactive narratives such as computer games and interactive performances. There are three kinds. Canonical trajectories express an author's intended mapping of story time onto clock time as part of the plot and schedule of an experience. Participant trajectories reflect a participant's actual journey through story time and clock time as they interact with the experience. Historic trajectories represent the subsequent selection and reuse of segments of recorded participant trajectories to create histories of past events. We show how temporal trajectories help us analyse the nature of time in existing experiences and can also generate new approaches to dealing with temporal issues such as: disengagement and reengagement, adapting to different paces of interaction, synchronising different participants, and enabling encounters and travel across time. Author...