Here is some interesting material from Østby et al. on the brain basis of the quality of our remembering the past or imagining the future:
A core brain network is engaged in remembering the past and envisioning the future. This network overlaps with the so-called default-mode network, the activity of which increases when demands for focused attention are low. Because of their shared brain substrates, an intriguing hypothesis is that default-mode activity, measured at rest, is related to performance in separate attention-focused recall and imagination tasks. However, we do not know how functional connectivity of the default-mode network is related to individual differences in reconstruction of the past and imagination of the future. Here, we show that functional connectivity of the default-mode network in children and adolescents is related to the quality of past remembering and marginally to future imagination. These results corroborate previous findings of a common neuronal substrate for memory and imagination and provide evidence suggesting that mental time travel is modulated by the task-independent functional architecture of the default-mode network in the developing brain. A further analysis showed that local cortical arealization also contributed to explain recall of the past and imagination of the future, underscoring the benefits of studying both functional and structural properties to understand the brain basis for complex human cognition.