Why does time seem to fly by when we are absorbed? The case of listening to music is of particular interest, given that listening to music itself requires experiencing time. In this paper, I argue that neither the prevailing psychological model nor some initially appealing alternative explanations can account for the experience of time flying by in cases where, like listening to music, the activity we are absorbed in itself requires experiencing time. I then put forward a novel view on (...) which the fragmentation of felt time is what best explains these cases. More specifically, I develop a view on which attentive engagement fragments felt time such that we experience the activity we are engaged in as if it is located in a temporally isolated branch or fragment of the main timeline. Time then seems to pass only in this branch, creating the sensation — upon integration — that less time has passed in the main timeline. In support of this proposal, I draw upon ideas in the empirical literature, and I suggest some underlying neuropsychological mechanisms that might serve to implement the model. I then extend the fragmentation model to cases where thinking about time makes it feel as though more of it passes. I end the paper by examining the possibility that an analogous model holds for the case of space. (shrink)